# Retrieval-Accuracy Returns to Instrument Investment in Earth-Science Radiometers: a Hedonic Regression of Validated Science Accuracy on Cost Drivers

**Doctoral Dissertation**

**Candidate:** JPL_ASTRO_EARTH_10  
**Program:** COLLEGIUM 1st Battalion  
**Category:** NORTH STAR / JPL Earth Science Missions  
**Hall-of-Shoulders anchors:** Sherwin Rosen (inverted hedonic surface); the NICM and Stahl parametric-cost lineage (cost as a hedonic index); Alberto Abadie (selection-on-observables identification and covariate balancing); Herbert Simon (bounded rationality, satisficing, and near-decomposability, supplying the concavity prior)  
**Date:** 2026-06-15


## Abstract

NASA and the Jet Propulsion Laboratory hold a stewardship over public funds that commits large fractions of every Earth-observing mission budget to instrument development, yet no one has characterized the relationship between the dollars spent on a radiometer and the validated geophysical accuracy the instrument ultimately delivers as a quantitative function. Cost-estimating relationships such as the NASA Instrument Cost Model (NICM) predict what an instrument will cost from its design attributes, and calibration-and-validation programs report how accurate the retrieved products are. The two literatures have never been joined to ask whether accuracy returns to cost are linear or concave. This dissertation specifies a hedonic regression of validated Level-2 and Level-3 retrieval-error metrics on instrument development cost and on the design attributes that drive both cost and accuracy: spectral-channel count, swath, spatial resolution, and calibration approach. The single falsifiable claim (H1) is that validated retrieval accuracy is a concave function of instrument cost, so that the marginal accuracy gained per additional dollar declines and collapses beyond an estimable spectral-channel count, identifying an over-specification region; the null (H0) is that accuracy is linear in cost with no diminishing returns. The method inverts Rosen's hedonic price framework so that accuracy, rather than market price, becomes the hedonic outcome, and it uses a partially linear semiparametric specification in which cost enters through a shape-constrained smooth function while design controls enter linearly. Identification follows the Abadie program-evaluation discipline of selection-on-observables within common support, with covariate balancing across instrument classes, and the concavity prior comes from Simon's account of bounded rationality and near-decomposable design. The data are validated accuracy metrics published by Earthdata Distributed Active Archive Centers and the peer-reviewed cal/val literature, NICM-class instrument cost records, and NASA Technical Reports Server design specifications, assembled at the instrument-product level.

This is a design-stage dissertation. It fixes the estimator, the identification strategy, the threats to validity, and a pre-registered analysis plan with a decision rule committed before any data are run, and it labels every numerical expectation as illustrative and not yet executed on the full assembled dataset. The contribution, if confirmed, is a defensible estimate of the accuracy-per-dollar frontier and of the spectral-channel count beyond which additional specification stops paying for itself in validated science, giving cost-capped Earth-science mission formulation a stopping rule for spectral specification; if the null holds, the result removes diminishing returns as an unexamined assumption from instrument budgeting. Either outcome advances the JPL Earth Science portfolio's ability to convert dollars into validated science by evidence rather than by instinct.


## Table of Contents

**Front Matter**

- Abstract
- Table of Contents
- List of Tables

**Chapter 1: Introduction**

- 1.1 Executive thesis: the answer this dissertation pursues
- 1.2 The problem: cost and accuracy are never placed on the same axes
- 1.3 The gap and why it persists
- 1.4 The falsifiable contribution: H1 against H0
- 1.5 Why it matters for NASA, JPL, and the named stakeholders
- 1.6 Scope and what this dissertation does not claim
- 1.7 Definitions of key terms
- 1.8 Design-stage statement
- 1.9 Roadmap of the dissertation

**Chapter 2: Theoretical Framework**

- 2.0 Chapter thesis and problem frame
- 2.1 The hedonic framework and its deliberate inversion
- 2.2 Identification of hedonic functions and their hazards
- 2.3 Bounded rationality and satisficing
- 2.4 The architecture of complexity and near-decomposability
- 2.5 The behavioral prior: decision under risk as a complement to satisficing
- 2.6 Value-driven design and tradespace exploration: the aerospace operationalization
- 2.7 Synthesis: why concavity is the expected result, not an arbitrary guess

**Chapter 3: Literature Review**

- 3.0 The chapter's answer, stated first
- 3.1 The first literature: instrument cost-estimating relationships
- 3.2 The second literature: parametric telescope and payload cost models
- 3.3 The third theme: cost growth, optimism bias, and the reliability of the cost regressor
- 3.4 The fourth theme: modern and machine-learning cost-estimation practice
- 3.5 The fifth theme: the calibration and validation literature as a body
- 3.6 The anchor literatures as they bear on the gap
- 3.7 The unfilled join, stated precisely, and the propositions that follow
- 3.8 Synthesis tables
- 3.9 Conclusion of the chapter

**Chapter 4: Data and Measurement**

- 4.1 The chapter's answer: a defensible, three-source instrument-product table
- 4.2 Named data source one: validated accuracy from Earthdata DAACs and the peer-reviewed cal/val literature
- 4.3 Named data sources two and three: NICM cost records and NTRS design specifications
- 4.4 The dependent variable: requirement-normalized, sign-oriented validated accuracy
- 4.5 The cost variable: development cost in constant-year dollars
- 4.6 Design and difficulty controls: the X vector
- 4.7 Coverage of the assembled table
- 4.8 Data quality, validation against known values, and the named biases
- 4.9 Ethics, access, and provenance transparency
- 4.10 Measurement table

**Chapter 5: Research Design and Identification**

- 5.1 The answer this chapter delivers
- 5.2 The estimand
- 5.3 The estimator
- 5.4 Identification
- 5.5 The over-specification test
- 5.6 Threats to validity
- 5.7 Power and minimum detectable effect
- 5.8 Robustness battery
- 5.9 Pre-registration commitment
- 5.10 Computational and software plan
- 5.11 How this chapter advances the argument

**Chapter 6: Analysis Plan and Expected Results**

- 6.1 The chapter's answer, stated first
- 6.2 Problem frame for the analysis plan
- 6.3 Pre-registration statement
- 6.4 Step 1: Assembly
- 6.5 Step 2: Balance and common support
- 6.6 Step 3: Baseline linear (H0) model
- 6.7 Step 4: Semiparametric concave model, and Step 5: the over-specification test
- 6.8 The decision rule
- 6.9 Illustrative, not-yet-executed expectations
- 6.10 Sensitivity analyses, specified in advance
- 6.11 How this chapter advances the argument
- 6.12 Summary

**Chapter 7: Discussion**

- 7.0 The chapter's answer, stated first
- 7.1 Implications if H1 holds
- 7.2 Implications if H0 holds
- 7.3 Theoretical contribution back to each anchor framework
- 7.4 Rival explanations
- 7.5 External validity and scoped extensions
- 7.6 Relationship to the cost-model and tradespace literatures
- 7.7 What would falsify the contribution
- 7.8 Decision recommendation (management, not architecture)
- 7.9 How this chapter advances the argument
- 7.10 Summary

**Chapter 8: Conclusion**
- 8.1 The answer this dissertation gives
- 8.2 The contribution restated
- 8.3 What stands even if the hypothesis is not confirmed
- 8.4 The single falsifiable claim and its decision rule
- 8.5 Limitations, stated honestly
- 8.6 A concrete future-research program
- 8.7 Why both outcomes advance the portfolio
- 8.8 Closing: converting dollars into validated science

**References**

**Appendices**

- Appendix A. Variable-Construction Tables
- Appendix B. Instrument-Product Matching Protocol
- Appendix C. Pre-Registration Record (Frozen Before Execution)
- Appendix D. Brain and API Provenance Log


## List of Tables

- Table 3.1. The three literatures and the axes each possesses
- Table 3.2. What each literature contributes to and withholds from the dissertation
- Table 3.3. Confidence calibration on the chapter's principal claims
- Table 4.1. Measurement table: construct, operational definition, source, and scale
- Table 6.1 (shell). Balance diagnostics across cost terciles
- Table 6.2 (shell). Common-support trimming log
- Table 6.3 (shell). Model comparison
- Table 6.4 (shell). Over-specification test
- Table 6.5 (shell). Sensitivity analyses

No figures appear in this design-stage dissertation; all quantitative displays are specification tables and pre-registered result-table shells, which are listed above.


# Chapter 1: Introduction

## 1.1 Executive thesis: the answer this dissertation pursues

This dissertation advances a single, falsifiable answer to a question that sits at the heart of responsible stewardship, one NASA and the Jet Propulsion Laboratory ask implicitly every time they formulate an Earth-observing mission but have never answered with evidence: as the dollars committed to a radiometer rise, does the validated geophysical accuracy the instrument ultimately delivers rise in proportion, or does it bend over. The answer this work expects to find, and is built to test rather than to assert, is that a reduced-form hedonic frontier estimated across NASA-class passive radiometers will show validated retrieval accuracy to be a concave function of instrument development cost, with an identifiable over-specification spectral-channel count beyond which additional specification stops paying for itself in validated science. If the assembled data confirm that expectation under the decision rule fixed in this design, the result gives cost-capped Earth-science mission formulation a defensible stopping rule for spectral specification. If the data instead retain the null of linearity, the result removes diminishing returns as an unexamined assumption from instrument budgeting and justifies continued investment in specification where mission requirements demand it. Both outcomes are decision-relevant, and the dissertation is committed to reporting whichever the data support.

That sentence is the chapter thesis, and the rest of this chapter develops it rather than circling back to it. The claim deserves to stand at the front because the contribution is not a survey, a methodological refinement, or a data product. It is a directional, testable proposition about the shape of a relationship the field treats as monotone and proportional without ever having measured it. The expected finding is concavity; the action it would license is a per-instrument specification cap; the consequence of continuing without it is that mission teams keep buying spectral channels on the implicit belief that each one returns commensurate science, when the theory assembled here predicts that beyond a point they do not. Opening with the claim also sets the burden the chapter accepts. The argument that follows must show that the problem is real and that it is material, identify the mechanism the design addresses, explain why this design is preferable to the obvious alternatives, and bound the residual risk so that the contribution remains defensible. Those obligations shape the argument here and recur throughout the dissertation.

A note on register is owed at the outset. This is a design-stage dissertation. The estimator, the identification strategy, the threats to validity, and the decision rule are all specified in advance, but no result reported anywhere in this document has been executed on the full assembled dataset. Where the text describes the shape of an expected curve or the location of an expected over-specification edge, those descriptions are illustrations of the design, labeled as expectations under the contribution hypothesis, and they must not be read as empirical findings. Stating the falsifiable claim and the rule that would reject it, before any number is computed, is what separates this work from a search for a pleasing curve. That discipline is carried from this introduction through every later chapter.

## 1.2 The problem: cost and accuracy are never placed on the same axes

The problem this dissertation addresses is a gap between two well-developed bodies of practice that have never been joined. Today one community predicts what an Earth-science instrument will cost from its design, while a separate community measures how accurate the instrument's products turn out to be, and no one regresses the second quantity on the first. What the field needs, and lacks, is a population-level estimate of validated accuracy as a function of instrument cost, with the design attributes that drive both held fixed. Because no such estimate exists, mission budgets continue to set spectral specification without evidence on whether the marginal dollar still buys validated science.

Consider the choice an Earth-science program manager actually faces. Every radiometer NASA flies embodies a set of decisions about how much capability to buy. The manager decides how many spectral channels to carry, how wide a swath to image, how finely to resolve the surface, and how elaborate an on-board calibration subsystem to fly. Each of those decisions raises the instrument's development cost in a predictable way. The NASA Instrument Cost Model exists because these design attributes are structured, estimable cost drivers, and its successive versions are fit on curated databases of flown instruments to predict instrument cost from exactly such attributes [\[42\]](#ref-42), [\[37\]](#ref-37). The premise of the entire investment, however, is not cost. It is the validated geophysical accuracy of the products the instrument eventually delivers: the sea-surface temperature, the aerosol optical depth, the soil moisture, the precipitation rate that the science and applications communities will use as inputs to research and to operational decisions. That accuracy is measured, after launch, by calibration and validation programs that compare retrieved products against independent reference standards. The aerosol optical depth retrieved by MODIS is validated against the AERONET ground network with published expected-error envelopes [\[85\]](#ref-85), [\[87\]](#ref-87); sea-surface temperature carries validated bias and standard-deviation statistics built over decades of in-situ matchups [\[73\]](#ref-73); soil moisture from SMAP is validated against core validation sites with reported root-mean-square and unbiased root-mean-square error [\[77\]](#ref-77).

The two communities produce rigorous numbers, but on different axes. The cost community produces cost as a function of design and is silent on delivered accuracy. The validation community produces accuracy for one product, or one instrument, and is silent on the instrument's cost and on any population-level relationship. That the two are never jointly modeled follows from the structure of these literatures themselves: the cost models terminate their causal chain at cost [\[42\]](#ref-42), [\[46\]](#ref-46), and the validation papers terminate theirs at a product-specific error statistic [\[85\]](#ref-85), [\[77\]](#ref-77), [\[73\]](#ref-73). A relationship no published study estimates is, for the field's decision purposes, a relationship that does not exist; a program manager cannot cite a number that has never been computed. The strongest evidence is the absence, across the cost-modeling and cal/val corpora assembled for this work, of any entry that regresses validated accuracy on instrument cost across a population of radiometers. One caveat is appropriate and is preserved: the absence is to this candidate's knowledge and within the assembled corpus, not a proof of universal non-existence, and the possibility that some unpublished internal trade study has done this informally is acknowledged, which is precisely why the contribution is framed as the first defensible, externally documented estimate rather than the first thought of the idea.

## 1.3 The gap and why it persists

Three literatures bear on the accuracy-cost question, and the structural reason the gap persists is that each one stops exactly where the join would begin. Naming why each stops short is more useful than noting that the gap exists, because the reasons are what tell us the join is a genuine contribution rather than an oversight any of the three could have closed in passing.

The first literature is hedonic pricing, founded by Rosen, which shows that the implicit value of the individual attributes of a differentiated good can be recovered by regressing the good's price on its measurable characteristics, with the partial derivatives of the price function revealing the marginal implicit prices of each attribute [\[26\]](#ref-26). Hedonic methods are mature and are applied routinely to housing, environmental amenities, and differentiated manufactured goods. They have a deep apparatus for separating an attribute's contribution from confounders. But the hedonic literature regresses price on attributes; it has never been inverted to treat a performance metric, rather than market price, as the hedonic outcome, and so on its own terms it does not speak to the accuracy of an engineered instrument. It stops at price because price is the equilibrium object its theory is about.

The second literature is instrument cost modeling, exemplified by NICM and by the parametric telescope and payload cost models of Stahl and colleagues [\[42\]](#ref-42), [\[37\]](#ref-37), [\[46\]](#ref-46). This literature is hedonic in spirit already: it regresses cost on design attributes such as mass, power, aperture, and channel count, and it demonstrates that both single-variable and multivariable parametric forms carry real explanatory traction. It is the closest existing practice to what this dissertation does. But its dependent variable is cost, by construction and by purpose, because its job is to support cost estimation for proposal and budget planning. It cannot speak to returns because returns require accuracy on the left-hand side, and accuracy is not in its model. It stops at cost because cost is what its users need to predict.

The third literature is calibration and validation, which is large, rigorous, and deliberately product-specific [\[85\]](#ref-85), [\[77\]](#ref-77), [\[73\]](#ref-73), [\[83\]](#ref-83). It establishes the validated error of individual products to high standards, with traceable reference networks and formalized performance metrics [\[83\]](#ref-83). But it treats each instrument and each product in isolation, because its purpose is to certify a particular data record for scientific use, not to compare instruments against a population frontier. It stops at one product because one product is what each validation effort is responsible for.

The unfilled space is therefore the join, and the join is unfilled for a reason that is structural rather than accidental: no single one of these three literatures has both axes in scope at once. The cost models have cost and design but not accuracy. The validation studies have accuracy and design but not cost or a population. The hedonic apparatus has the method to relate an outcome to attributes but has never been pointed at this outcome. Closing the gap requires borrowing the dependent variable from the third literature, the regressor from the second, and the estimation logic, inverted, from the first. That triangulation is the contribution's structural novelty, and it is also why the gap has survived: closing it is no one community's job.

The kind of contribution this makes deserves to be stated precisely, because the design plan flags two evidence gaps that bear directly on the claim of novelty and should be acknowledged in the introduction rather than discovered later. The first is that the corpus assembled for this dissertation contains the NICM documentation but not the underlying instrument-level cost table itself, because those raw cost values are a JPL-maintained database rather than a public, citable artifact [\[42\]](#ref-42), [\[37\]](#ref-37). The dissertation therefore treats the NICM literature as the authority for the cost construct, and it states the acquisition of the actual cost values through JPL channels as a data-access dependency at execution, not as a citation. The second gap is that no corpus entry performs the exact join this work proposes, which is the expected consequence of the join being novel; the closest existing precedents are the cost-model family and the applied-hedonic literature, and the absence of a direct methodological precedent for inverting the hedonic surface onto instrument accuracy is itself part of what makes the contribution a first estimate. Naming both gaps here, rather than letting them surface as surprises in the data and design chapters, is consistent with the design-stage honesty the whole work is committed to.

### 1.3.1 Institutional and historical context
The institutional setting explains both why the gap has practical force and why the moment to close it has arrived. NASA's Earth Science Division formulates and operates a portfolio of observing missions whose instruments are, in large part, developed and managed through JPL and partner centers, and the cost-estimating discipline that supports that formulation is itself a JPL product: the NASA Instrument Cost Model is maintained at JPL and has been carried through successive versions to keep its cost-estimating relationships current with the flown-instrument record [\[42\]](#ref-42), [\[37\]](#ref-37). A mature, institutionally owned cost model is what makes the missing accuracy axis conspicuous. The institution can predict, with documented relationships, what an instrument will cost from its design; it cannot predict, with any comparable relationship, what validated accuracy that cost will return. The asymmetry is institutional, not academic. The cost side has a model, a database, and an owner; the accuracy-return side has none.

The historical arc of Earth observation makes the asymmetry more costly over time. For much of the discipline's history the dominant architecture was the large, multi-instrument flagship platform carrying highly specified sensors, an architecture in which the implicit answer to how much capability to buy per instrument was simply as much as the platform could carry and the budget could bear. In that regime, a frontier estimate would have been informative but not urgent, because the architecture itself fixed the specification choice. The contemporary trajectory differs. The observing community is moving toward distributed architectures of smaller instruments and toward commercial data buys, and both shifts dissolve the old default and force explicit, per-instrument decisions about specification [\[137\]](#ref-137), [\[130\]](#ref-130). A distributed architecture is, in effect, a bet that more instruments at lower individual specification deliver more total value than fewer at higher specification, and that bet is the proposition a concave frontier would support and a linear frontier would undercut. The value-of-investment framing that the space-sustainability and value-driven-design literatures bring to portfolio choice makes the same point at the level of strategy: when capability must be rationed against a ceiling, the right objective is value returned, not capability accumulated [\[134\]](#ref-134), [\[17\]](#ref-17), [\[139\]](#ref-139). The field is now making the specification choice explicitly and frequently for the first time, and it is making that choice without the accuracy-cost evidence that would discipline it. The convergence of an institutional asymmetry and a historical shift is what gives the gap its urgency.

## 1.4 The falsifiable contribution: H1 against H0

The dissertation states a single falsifiable contribution and a single null against which it is tested. These are carried verbatim from the approved prospectus and are not reworded anywhere in this work.

**H1 (contribution):** Validated geophysical-retrieval accuracy for Earth-observing radiometers is a concave function of instrument cost. The marginal accuracy gained per additional dollar of instrument investment declines as cost rises and collapses beyond an estimable spectral-channel count, identifying an over-specification region in which additional channels and the cost they carry do not produce a commensurate gain in validated accuracy.

**H0 (null):** Validated retrieval accuracy is linear in instrument cost. There are no diminishing returns; the marginal accuracy per dollar is constant, and no over-specification region exists.

The contribution is falsifiable in the strict sense, and the conditions under which H1 is rejected are stated in advance. H1 is rejected and H0 stands if the estimated cost term is statistically indistinguishable from a straight line, or if the second derivative of the fitted accuracy-cost function is not reliably negative over the supported range, or if the marginal channel-count contribution remains positive across the entire observed channel range so that no over-specification region exists. None of these rejection conditions can be satisfied by post hoc reasoning; each is a condition on an estimated quantity defined before the data are run.

The contribution makes a sharper prediction than bare concavity, and the sharpness is deliberate because it raises the bar for confirmation. A curve can bend for many reasons, several of which are rival explanations rather than the claimed frontier, and a finding of mere aggregate concavity would be weak evidence for the mechanism the theory proposes. H1 therefore predicts not only that the accuracy-cost surface is concave but that there is an identifiable channel count past which the marginal contribution of additional spectral channels to validated accuracy is not different from zero once other drivers are held fixed. That over-specification edge is a specific design margin, not a vague curvature, and it is testable as such. The reasoning that makes this the right sharper prediction, rather than an arbitrary embellishment, is developed in the theoretical framework: the same bounded-rationality and near-decomposability logic that predicts diminishing returns in the aggregate predicts a specific mechanism, channel-information redundancy, that should produce a locatable channel-count threshold rather than a smoothly distributed fade. Stating the sharper prediction commits the design to a harder test, the appropriate posture for a contribution that wants to be believed.

The notation that carries the test is fixed across the dissertation and is introduced here so that the reader meets it early. Validated accuracy is modeled as

\[ \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \qquad\qquad (1) \]

where \( g \) is an unknown smooth function estimated under a monotonicity-and-concavity-respecting smoother, \( \mathbf{X} \) is the vector of design and difficulty controls entered linearly, \( \boldsymbol{\beta} \) is the vector of their coefficients, and \( e \) is an instrument-clustered error. The function \( g \) carries the concavity test; the sign of its second derivative \( g'' \) over the supported range is the quantity H1 predicts to be reliably negative. The over-specification test enters spectral-channel count with a flexible term and locates the channel range over which its marginal contribution to accuracy is statistically indistinguishable from zero. The full specification, identification, and the shape constraint on \( g \) are the subject of Chapter 5; the notation appears here only so that the falsifiable claim is anchored to the object that tests it.

## 1.5 Why it matters for NASA, JPL, and the named stakeholders

The materiality of the problem is the second pillar of the argument, and it rests on a feature of the decision environment that holds regardless of which hypothesis the data support: Earth-science portfolios choose specification under a fixed topline. JPL's Earth Science portfolio competes for funding against a budget ceiling it does not control, and within that ceiling every dollar committed to elaborating one instrument is a dollar unavailable to another instrument or to the error sources that bind after launch. That structural fact turns an abstract question about a curve's shape into a live budgeting question, and it is why the contribution is decision-relevant under either outcome rather than merely interesting.

The mechanism connecting the frontier's shape to the budgeting decision runs as follows. If accuracy returns to instrument cost are concave, then the marginal validated accuracy bought by the last increment of specification on a heavily specified instrument is small, because that instrument is operating in the flat region of the frontier. A portfolio that concentrates budget in a few maximally specified instruments therefore spends its marginal dollars where they buy little science, while the same dollars spread across more, individually less elaborate instruments, each operating in the steep region of the frontier, would buy more total validated accuracy. The observable consequence of concavity is a reallocation logic: cap per-instrument specification at the edge of the over-specification region and redirect the saved budget either across more instruments or toward the error sources, principally calibration drift and geolocation error, that actually limit accuracy once specification is adequate. If instead returns are linear, the same chain runs the other way: the marginal dollar buys the same accuracy everywhere, concentration carries no penalty, and diminishing returns cannot be invoked as an argument in a descope. The shape of \( g \) is not a curiosity; it is the hinge on which a defensible allocation rule turns.

The timing sharpens the materiality. The Earth-observing community is moving toward distributed architectures of smaller instruments and toward commercial data buys, and both trends force explicit, near-term choices about how much capability to buy per instrument [\[137\]](#ref-137), [\[130\]](#ref-130). A frontier estimate would tell whether the distributed-architecture instinct is supported by the accuracy economics or is merely a response to cost ceilings, a different and weaker justification. The same estimate would inform the recurring trade between funding a new, more elaborate instrument and continuing to exploit an existing one, since the marginal accuracy of the new instrument is worth its marginal cost only if the portfolio is operating in the steep region of the frontier. The value-of-investment framing that the space-sustainability and value-driven-design literatures bring to portfolio choice reinforces the same point: capability is worth buying only up to the point where it still returns value [\[134\]](#ref-134), [\[17\]](#ref-17), [\[139\]](#ref-139). None of these decisions currently rests on a measured accuracy-cost relationship, and that deficiency is what the dissertation is built to remove.

The stakeholders for whom this matters are concrete rather than rhetorical. JPL mission formulation teams would gain an evidence-based stopping rule for spectral specification, replacing capability-maximizing instinct with a value-aware target. NASA Earth Science Division program managers, who set and defend toplines across competing missions, would gain a principled basis for descope arguments and for judging distributed-architecture proposals. The cost-estimating community that maintains NICM would gain the accuracy axis its models structurally lack, complementing rather than displacing its work [\[42\]](#ref-42). The validation community would see its product-specific error records put to a population-level use they were never designed for but are well suited to support [\[73\]](#ref-73), [\[83\]](#ref-83). Confidence in this materiality claim is high, because it rests not on the as-yet-untested empirical result but on the fixed-topline structure of the decision and on the documented near-term shift toward distributed and commercial architectures; what would lower that confidence is evidence that Earth-science budgets are in practice not constrained at the margin, which the funding history does not support.

## 1.6 Scope and what this dissertation does not claim

Keeping the contribution falsifiable requires keeping it narrow, and several things are deliberately out of scope. Naming them here is part of bounding the residual risk, the fifth obligation the argument carries, and it is also what keeps the single claim testable rather than diffuse.

First, the dissertation does not claim a structural causal model of how each design attribute produces accuracy through the physics of the retrieval. It estimates a reduced-form frontier and is honest that the cost effect it recovers is an embodied-investment effect, the joint consequence of the engineering effort, component quality, and calibration rigor that cost buys, rather than the isolated effect of any single mechanism. The justification for treating cost as a meaningful regressor despite this is that instrument cost is a near-sufficient statistic for embodied build quality, the same premise the cost-model literature already relies on when it predicts cost from design [\[42\]](#ref-42), [\[46\]](#ref-46); the reduced-form reading is the appropriate caveat on what the cost coefficient means.

Second, the dissertation does not claim that the over-specification channel count is universal across geophysical variables. The test is run within the supported population, and the estimate is conditional on the controls. Soil moisture under vegetation and clear-sky sea-surface temperature are not retrieved with the same channel economics, and the dissertation does not assert a single magic number that holds across them; it estimates an edge conditional on the difficulty control and reports it as such.

Third, the dissertation does not claim to value scientific accuracy in dollars or to perform a full cost-benefit analysis. It estimates the technical frontier that any such valuation would have to take as input. Converting validated accuracy into a dollar value of science is a separate exercise with its own large literature and its own assumptions, and folding it in would make the contribution diffuse and the claim unfalsifiable. The frontier is the input; the valuation is downstream and out of scope.

Fourth, the population is restricted to NASA and NASA-partnered passive radiometers in the modern era, roughly the MODIS era to the present. Active sensors such as radars and lidars are excluded, not for convenience but because their cost drivers, transmit power, antenna or telescope aperture, and pulse design, and their accuracy metrics are not commensurable with passive radiometry; pooling them would violate the comparability that identification requires. Non-NASA instruments built under different cost-accounting conventions and future instruments using technologies absent from the sample are likewise outside the estimand. These limits are stated rather than papered over, and the discussion in Chapter 7 returns to two of them, the active-sensor analogue and the commercial-radiometer analogue, as scoped next studies rather than as weaknesses of this one.

Narrowing the claim in these four ways is what makes the single contribution testable. A diffuse claim that instrument investment generally shows diminishing returns across all sensors and all variables and all cost regimes would be unfalsifiable and therefore useless to a program manager. The bounded claim, concavity of validated accuracy in development cost across NASA-class passive radiometers with an identifiable over-specification channel count, is sharp enough to be wrong, which is the property the contribution needs.

## 1.7 Definitions of key terms

Because the dissertation joins literatures that use the same words differently, the load-bearing terms are defined here and used consistently throughout. These definitions are fixed and are carried verbatim into every chapter.
**Validated accuracy** is the dependent variable. It is a standardized, sign-oriented, requirement-normalized retrieval-error metric, constructed from bias, root-mean-square error, unbiased root-mean-square error, and expected-error compliance, oriented so that the variable increases in accuracy and stays comparable across product families. It is drawn from independent calibration and validation records, the DAAC product documentation, and the peer-reviewed validation papers those records cite as authoritative, never from an instrument's design specifications. Insisting on independent validation records rather than self-reported specifications is what gives the dependent variable its construct validity. The credibility of the whole exercise rests on the accuracy metric being a real, externally validated number rather than a vendor's claim [\[85\]](#ref-85), [\[77\]](#ref-77), [\[73\]](#ref-73).

**Cost** is the regressor of central interest. It is the total instrument development cost in constant-year dollars, taken from NICM-class records. It is development cost specifically, not life-cycle cost; operations, reprocessing, and algorithm-maintenance spending are deliberately excluded, because the claim concerns instrument investment and development cost is the construct that measures it [\[42\]](#ref-42), [\[37\]](#ref-37). The boundary is stated so that the resulting frontier is not misread as a total-cost frontier.

**Spectral-channel count** is the number of spectral channels the instrument carries. It is the design attribute that carries the over-specification test, since the sharper prediction of H1 concerns the channel count past which marginal channel contribution to accuracy vanishes.

**Design controls**, denoted \( \mathbf{X} \), are the attributes entered linearly to absorb the systematic reasons an instrument received its cost: swath width, spatial resolution, calibration approach as a categorical variable (on-board blackbody, solar diffuser, vicarious, or lunar), instrument mass and power as built, and mission epoch to absorb technology vintage.

**Retrieval-difficulty control** captures the intrinsic hardness of the geophysical variable being retrieved, so that soil moisture under vegetation and clear-sky sea-surface temperature are not treated as equally easy regardless of instrument quality.

**Unit of analysis** is the instrument-product pair. A single radiometer often produces several validated products, for example a sounder that yields temperature, water-vapor, and trace-gas profiles. Because validated accuracy is defined per product, each instrument contributes one row per validated product, with cost attributed at the instrument level and shared across that instrument's products. The dependence this creates among rows from the same instrument is handled by instrument-clustered inference, specified in Chapter 5.

## 1.8 Design-stage statement

This dissertation is presented at the design stage, and the guardrail that governs every later chapter is stated plainly here. No quantitative result reported anywhere in this work has been executed on the full assembled dataset. The estimator in \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), the identification strategy, the covariate-balancing procedure, the over-specification test, and the decision rule are all specified in advance, but the coefficients, the sign of \( g'' \), and the location of any over-specification channel count are not reported as findings, because they have not been computed on the assembled population. Where later chapters describe an expected steep-then-flat curve under H1 or an expected straight line under H0, those descriptions illustrate the design, labeled as expectations conditional on a hypothesis and used only to make the procedure concrete. They are not empirical results, and the dissertation is committed to reporting whichever shape the data support once assembled and run under the pre-registered rule.

This posture is a deliberate methodological commitment, not a limitation to be apologized for. Specifying the falsifiable claim, the estimator, the threats to validity, and the rejection conditions before any number is computed is the discipline that protects the contribution from the most common failure mode of small-sample curve-fitting: finding concavity in the noise of an underpowered sample and presenting it as a frontier. The design is built so that in-sample curvature alone cannot support H1. The decision rule in Chapters 5 and 6 requires the concave model to beat the linear null in held-out prediction before concavity is credited at all. Stating that rule in advance is what makes the eventual result, in either direction, believable.

## 1.9 Roadmap of the dissertation

The argument proceeds through eight chapters and a backmatter, each carrying the argument forward and each obeying the fixed definitions, notation, and hypotheses set out above.

**Chapter 2, the theoretical framework,** builds the three pillars that make concavity the expected result rather than an arbitrary guess. It develops the inverted hedonic surface, in which Rosen's price-on-attributes logic is turned to regress accuracy on attributes with cost as the central attribute [\[26\]](#ref-26); it develops Simon's bounded-rationality, satisficing, and near-decomposability arguments as the prior that returns to elaboration should diminish and that an over-specification region should exist [\[19\]](#ref-19), [\[14\]](#ref-14); and it develops value-driven design and tradespace exploration as the aerospace operationalization in which value, not raw capability, is the objective and tradespaces routinely contain dominated, over-specified regions [\[17\]](#ref-17), [\[139\]](#ref-139). The chapter closes by assembling these into the named causal mechanism the design is built to detect.

**Chapter 3, the literature review,** treats the three bodies of work that bear on the question and names the join none of them closes. It covers the instrument cost-estimating relationships exemplified by NICM and the Stahl parametric models [\[42\]](#ref-42), [\[46\]](#ref-46), the cost-growth and optimism-bias literature that bears on the reliability of the cost regressor [\[38\]](#ref-38), and the calibration and validation literature treated as a body that defines what validated accuracy means [\[85\]](#ref-85), [\[73\]](#ref-73).

**Chapter 4, data and measurement,** constructs the three named data sources and the variables: validated accuracy from Earthdata DAACs and the peer-reviewed cal/val literature, NICM cost records, and NTRS design specifications. It gives the worked construction of the requirement-normalized dependent variable for each product family, including aerosol optical depth, sea-surface temperature, soil moisture, and precipitation [\[85\]](#ref-85), [\[77\]](#ref-77), [\[86\]](#ref-86), [\[79\]](#ref-79), and it states the coverage and the data limitations, including the survivorship and publication-bias concern and the development-cost-only boundary.

**Chapter 5, the research design,** is the methodological heart. It fixes the estimand as the shape of the conditional expectation of validated accuracy in the cost dimension over common support, specifies the partially linear semiparametric estimator in the notation above, develops the identification strategy in the selection-on-observables tradition with covariate balancing across cost strata [\[105\]](#ref-105), [\[94\]](#ref-94), details the over-specification test, and works through the threats to internal, external, construct, and statistical-conclusion validity, each paired with the design feature that answers it.

**Chapter 6, the analysis plan,** lays out the five pre-registered estimation steps, the decision rule that requires the concave model to beat the linear null out of sample and \( g'' \) to be reliably negative, and the illustrative, not-yet-executed expectations under each hypothesis. It grounds the over-specification test physically in the information content of additional spectral channels, so that the statistical edge maps to a physical redundancy onset rather than a fitted artifact.

**Chapter 7, the discussion,** works through the implications under each outcome, the rival explanations that could produce apparent concavity without the claimed frontier, the external-validity bounds and the scoped extensions to active sensors and commercial radiometers, the complementary relationship to the cost-model and tradespace literatures, and the explicit falsification conditions. It is where the single permitted decision mapping, the plain-language management recommendation to cap spectral specification at the over-specification edge and reallocate the saved budget, is stated.

**Chapter 8, the conclusion,** restates the contribution, the design discipline, and the decision relevance under both outcomes, and closes on the portfolio's central problem of converting dollars into validated science.

The backmatter renders the full reference list and the appendices, including the variable-construction tables, the instrument-product matching protocol, the pre-registration record, and the brain and API provenance log.

One further scope decision closes the roadmap. This dissertation does not field a capability, system, or data exchange; it estimates a frontier and recommends a decision rule. The single decision the work produces is the management recommendation in Chapter 7, stated as a recommendation rather than as a systems-engineering artifact, and the vocabulary of capability-to-system-function traceability is therefore absent throughout. What every chapter carries forward instead is a single disciplined sequence: the problem is real, the problem is material, the design addresses the causal mechanism, the design beats the alternatives, and the residual risk is bounded and acceptable. The introduction has now established the first two of these and previewed the remaining three, and the chapters that follow build them out.


# Chapter 2: Theoretical Framework

## 2.0 Chapter thesis and problem frame

This chapter's answer comes first. Concavity in the relationship between instrument development cost and validated retrieval accuracy is not an arbitrary empirical guess that the dissertation hopes the data will confirm; it is the prediction that follows once three established bodies of theory are brought to bear on the same object. An inverted hedonic surface gives the relationship a tractable functional structure in which cost enters as the central attribute of a differentiated good. A theory of bounded rationality and near-decomposable design supplies the substantive reason the marginal return to that attribute must eventually fall. The value-driven-design tradition in aerospace systems engineering operationalizes both, demonstrating that real tradespaces of space instruments routinely contain dominated, over-specified regions where additional capability no longer purchases proportional value. Read together, these pillars convert the central claim, that validated accuracy is a concave function of instrument cost with an identifiable over-specification spectral-channel count, from a curve someone might fit into a hypothesis with a theoretical pedigree. That is the work of this chapter: to build the conceptual model that the empirical design in later chapters will then test, and to make the concavity prior load-bearing rather than decorative.

The problem this chapter must solve is conceptual rather than empirical. As matters stand, each pillar lives in its own literature and speaks to its own object. Rosen's hedonic framework values the attributes of consumer and environmental goods through market prices [\[26\]](#ref-26), [\[24\]](#ref-24), [\[16\]](#ref-16); it has never been turned toward the performance of an engineered scientific instrument. Simon's account of bounded rationality and the architecture of complexity explains why organizations stop searching short of an optimum and why complex systems are near-decomposable [\[19\]](#ref-19), [\[14\]](#ref-14), [\[11\]](#ref-11), [\[22\]](#ref-22); it is rarely connected to the curvature of a cost-performance frontier. The value-driven-design and tradespace literature in aerospace knows that capability beyond a value threshold is dominated [\[17\]](#ref-17), [\[23\]](#ref-23), [\[20\]](#ref-20); it has reasoned about that threshold case by case rather than locating it across a population. What is wanted is a single conceptual model in which the three pillars compose, so that the hedonic surface carries the functional form, bounded rationality and near-decomposability supply the concavity, and value-driven design grounds the whole in the aerospace setting where the empirical work lives. No prior work has assembled these three into a joint prediction about an instrument-cost-to-accuracy frontier, and without that composition the dissertation's central hypothesis would rest on intuition alone, leaving a reviewer free to ask why concavity rather than linearity is the maintained expectation. This chapter supplies the composition so that H1 enters the empirical chapters already theoretically earned.

A note on register and scope is owed at the outset, because it disciplines everything that follows. The dissertation is a design-stage artifact. No coefficient, no second-derivative sign, and no over-specification channel count reported anywhere in this chapter is an executed empirical result; where the chapter speaks of what concavity would look like, it describes a theoretical prediction, not a finding. The chapter also respects the scope decision recorded earlier: this is an econometric study that estimates a frontier and recommends a decision rule, not a systems architecture. What the chapter does carry forward is the dissertation's disciplined sequence of establishing that the problem is real and material, that the proposed design addresses the underlying causal mechanism, that it is preferable to the alternatives, and that the residual risk is acceptable, with the theoretical pillars here supplying the reasoning behind the earliest of those propositions.
## 2.1 The hedonic framework and its deliberate inversion

The first pillar is Rosen's hedonic theory, adopted not in its original orientation but inverted. The hedonic apparatus, designed to recover the implicit prices of a differentiated good's attributes from that good's market price, can be turned around to recover the implicit accuracy contribution of an instrument's attributes from the instrument's validated performance, with development cost itself entering as the central attribute. The foundation is Rosen's result and its subsequent refinements. Rosen showed that a differentiated good is properly understood as a bundle of measurable attributes, and that in competitive equilibrium the good's price is a function of those attributes whose partial derivatives reveal the marginal implicit prices buyers pay and sellers receive for each one [\[26\]](#ref-26). Quigley and the identification literature that followed clarified how the underlying demand and supply functions could be separated from the observed hedonic surface, and catalogued the conditions under which the implicit prices are interpretable rather than merely descriptive [\[24\]](#ref-24). Coulson's retrospective documents how durable and how widely transported the framework has proven across half a century of applied work [\[16\]](#ref-16). The contemporary applied record confirms the framework's reach: hedonic models recover the implicit value of waterfront access in coastal property markets [\[13\]](#ref-13), of street-visible greenery in dense urban housing [\[15\]](#ref-15), of sustainability certifications in differentiated coffee [\[10\]](#ref-10), and of clean air through spatial welfare-loss estimation [\[8\]](#ref-8). The inversion is licensed because the hedonic logic is indifferent to the direction in which it is run. Rosen's result describes how the value of a bundle decomposes into the marginal contributions of its constituent attributes; nothing in the mathematics requires that the bundle's value be a market price rather than another scalar that the attributes jointly produce. If validated accuracy is the scalar that an instrument's attributes jointly produce, then the same decomposition recovers the marginal accuracy contribution of each attribute, and the hedonic surface becomes an accuracy surface.

Treating cost as the central attribute rather than as one regressor among many needs its own justification, because the move is the conceptual hinge of the entire dissertation. That justification comes from the instrument cost-modeling literature, which establishes that instrument cost is not noise but a structured index of build characteristics. The NASA Instrument Cost Model regresses development cost on design attributes such as mass, power, and channel count and fits that relationship on a curated database of flown instruments [\[42\]](#ref-42), [\[37\]](#ref-37). The parametric telescope cost models of Stahl and colleagues demonstrate the same systematic predictability for optical payloads, showing that single-variable and multivariable forms alike have explanatory traction and that cost rises in lawful ways with aperture, wavelength, and operating temperature [\[44\]](#ref-44), [\[46\]](#ref-46), [\[47\]](#ref-47). The interpretation that follows is this: because cost is systematically predictable from the engineering attributes of an instrument, cost is a near-sufficient statistic for the embodied engineering effort, component quality, and calibration rigor that a build represents. Those embodied qualities are what translate into delivered accuracy. Cost therefore stands in the inverted hedonic surface as a compressed index of build quality, and the curvature of the accuracy surface in the cost dimension is the object of central interest. The cost models are thus evidence not merely that cost can be predicted but that cost is a legitimate hedonic index, and that legitimacy is what makes the inversion defensible rather than a curiosity.

A caveat must be protected, because the inversion buys tractability at a price. The hedonic surface is reduced-form. It does not model the physics by which a particular spectral channel improves a particular retrieval; it models the statistical association between embodied investment and delivered accuracy across a population. The cost effect it isolates is an embodied-investment effect, not a single identified mechanism, and the dissertation is candid in Chapter 1 and again here that this is the intended estimand rather than a structural causal model of retrieval physics. A careful reader will object that an embodied-investment index could conflate distinct mechanisms, so that two instruments at the same cost embody very different mixes of channels, calibration, and integration rigor. The framework concedes this and answers it not within the hedonic theory itself but through the design controls and the identification strategy developed later, where the design attributes that the cost index compresses are reintroduced as explicit regressors and the common-support restriction confines comparison to instruments that are genuinely alike in their non-cost attributes. Confidence in the inversion as a framing device is therefore high, because the hedonic logic transfers cleanly and the cost-as-index premise is backed by an entire cost-modeling literature; confidence that the reduced-form cost effect is causally clean is held in reserve for the identification chapter, which is where that question belongs. What would raise confidence in the framing is the existence of a prior study that had already inverted a hedonic surface onto a performance metric; the corpus contains none, which is part of why the inversion is itself a contribution rather than a borrowed method, and the absence of a direct precedent is flagged here rather than papered over.

## 2.2 Identification of hedonic functions and their hazards

The hedonic framework does not arrive free of econometric danger, and a theoretical chapter that adopted it without naming its hazards would defer a debt the design chapter cannot fully repay. The purpose of this section is narrow and preparatory. The same three hazards that afflict any hedonic estimation, functional-form misspecification, omitted-attribute bias, and multicollinearity among characteristics, are present in the inverted accuracy surface, and the theoretical framework must acknowledge them now so that the research design can be built to answer them rather than to discover them. The methodological literature on hedonic identification establishes the point. The catalog of econometric hazards in estimating hedonic price functions is long-standing and explicit about how each hazard distorts the recovered implicit prices [\[24\]](#ref-24). The demand-and-supply identification problem, that an observed hedonic surface is the envelope of buyer and seller behavior and does not by itself reveal the structural functions beneath it, was central to the post-Rosen literature and motivated approaches that recover marginal willingness to pay without instrumental variables under stated conditions [\[18\]](#ref-18). The demand-estimation literature with unobserved product characteristics shows precisely how a single omitted attribute biases the recovered hedonic surface and what structure is required to identify preferences in its presence [\[21\]](#ref-21). The dynamic-hedonic critique adds that when an attribute is habit forming or otherwise inter-temporally linked, a static hedonic interpretation misreads the marginal value, because observed prices then reflect both contemporaneous value and continuation value [\[1\]](#ref-1).

These hazards carry into the present setting because the inversion does not exempt the accuracy surface from any of them; it merely changes the dependent scalar. Functional-form misspecification is in fact the hazard the dissertation most cares about, because the entire contribution is a claim about functional form: whether the cost term is linear or concave. This is a productive reframing rather than a threat to be eliminated, because the design responds to it directly by estimating the cost term under a flexible, shape-constrained smoother and testing the concave fit against a linear null out of sample, so that functional form is the object of inference rather than an assumption smuggled in. Omitted-attribute bias is the hazard that maps onto the identification problem the dissertation treats most seriously: an unobserved driver that raises both cost and accuracy would mimic a steeper cost effect and could mask concavity, while an unobserved driver that raises cost without raising accuracy would exaggerate concavity. The framework names this here and hands it to the design controls and the difficulty control in the research-design chapter, where the systematic reasons an instrument received its cost are reintroduced as observables. Multicollinearity among characteristics, that channel count, swath, resolution, and cost move together because elaborate instruments tend to be elaborate on every axis, is real and is the reason the design pre-commits to a limited set of pre-specified controls and to common-support trimming, so that the concavity estimate is interpolation among comparable instruments rather than extrapolation across a collinear ridge.

One caveat applies: this section does not resolve the hazards; it inventories them and assigns each to the chapter that will answer it. That division of labor is deliberate. A theoretical framework earns its keep by stating the conditions under which its central construct is identified, not by performing the identification, and the objection that the framework has merely deferred the hard problems is answered by the explicit forward pointers: functional form to the shape-constrained estimator and the out-of-sample test, omitted attributes to the design and difficulty controls, multicollinearity to common support and the pre-specified control set [\[12\]](#ref-12), [\[3\]](#ref-3). Confidence that these hazards are the right ones to worry about is very high, because they are the canonical hedonic hazards documented across the entire identification literature; confidence that the design fully neutralizes them is moderate and design-stage, because the sample is small and the controls are necessarily limited, which is itself carried as an explicit residual risk rather than hidden. What would lower confidence is evidence that a fourth, unanticipated hazard specific to the instrument setting dominates; the chapter cannot rule that out from theory alone, and says so.

## 2.3 Bounded rationality and satisficing

The second pillar supplies the reason the accuracy surface should curve rather than rise in a straight line. Simon's account of bounded rationality and satisficing predicts diminishing returns to instrument investment, because the organizations that design Earth-science radiometers do not optimize over a complete attribute space; they search until a design meets an aspiration level and then stop, and the structure of that search produces a concave relationship between effort expended and performance delivered. Simon's foundational position and its modern elaborations carry the argument. Simon held, in the form recovered and systematized in the history-of-thought literature, that rationality is bounded by the cognitive and informational limits of real decision-makers, so that procedural rationality, the rationality of the search process, replaces the substantive rationality of the optimizing agent [\[19\]](#ref-19). Satisficing is the operational form of this insight: decision-makers set aspiration thresholds and accept the first alternative that clears them rather than canvassing the full space for the global optimum. The contemporary literature has both formalized and extended this. A formal-verification treatment encodes satisficing through parameterized tolerance thresholds and proves its relationship to expected-utility maximization, establishing that satisficing is a mathematically coherent decision rule rather than a vague gesture at human limitation [\[4\]](#ref-4). A meta-synthesis traces the lineage from Simon's procedural rationality through ecological heuristics and dual-process theory, showing the construct's continuing analytic vitality across behavioral economics [\[6\]](#ref-6). The seventy-fifth-anniversary reassessment in the public-administration literature reaffirms that Simon's satisficing remains the dominant frame for understanding decision-making in real organizations, including the public and quasi-public organizations that fund and build scientific instruments [\[11\]](#ref-11). The construct has proven portable enough to be embedded in artificial-agent design as a model of realistic decision-making under uncertainty and information overload [\[5\]](#ref-5), and to anchor satisficing alignment procedures that optimize a primary objective while holding others to acceptable thresholds [\[9\]](#ref-9).

Bounded rationality connects to the curvature of the cost-accuracy frontier through the mechanism by which satisficing search produces diminishing returns. Consider an instrument design team operating under a fixed mission requirement, which is the aspiration threshold made concrete. The team adds capability, channels, calibration elaboration, finer resolution, until the design is expected to clear the requirement, and then it stops, because satisficing search terminates at the aspiration level rather than continuing toward an unbounded optimum. Two consequences follow for the shape of the frontier. First, the early, cheap increments of capability are the ones that move a design from well below the requirement to at or above it, so they carry large accuracy gains per dollar; this is the steep region of the frontier. Second, once the requirement is met, further investment is either not undertaken, because search has stopped, or is undertaken for reasons other than marginal accuracy, in which case it buys specification without commensurate validated-accuracy gain; this is the flat region. The driver is the addition of capability; the mechanism is satisficing search terminating at an aspiration threshold so that marginal capability past the threshold is decoupled from marginal accuracy; the observable effect is a flattening of the accuracy-versus-cost curve; the operational consequence is that dollars spent past the threshold buy specification rather than validated science; and the strategic implication, developed in later chapters, is that a portfolio operating in the flat region is leaving validated accuracy on the table. This is a named causal chain, not a bare correlation, which is the standard the chapter holds itself to.

A caveat protects the section from over-reach. Bounded rationality predicts that the frontier curves; it does not predict by itself where the bend occurs or how sharp it is, and it does not establish that the bend is the same across geophysical variables. Those are quantities the empirical work must estimate, and the framework claims only the qualitative prediction of concavity from this pillar. One objection worth taking seriously is that disciplined optimization, rather than satisficing, might govern flagship instrument design, in which case returns could remain linear up to a hard physical ceiling rather than bending gently. The framework's answer is that even a fully optimizing designer faces the near-decomposability limit developed in the next section, so concavity is over-determined: it follows from satisficing under the realistic account of how organizations decide, and it follows again from the architecture of complexity even under an idealized optimizer. The two pillars reinforce rather than substitute for one another, which is why the chapter treats them in sequence rather than collapsing them. Confidence in the satisficing prediction of concavity is high as a qualitative matter, because the construct is foundational, formally grounded, and repeatedly validated across organizational settings [\[4\]](#ref-4), [\[6\]](#ref-6), [\[11\]](#ref-11); confidence about the location and sharpness of the bend is deliberately withheld and assigned to estimation. What would raise confidence in the satisficing account specifically, as opposed to the near-decomposability account, is evidence that design teams demonstrably stop at requirement thresholds rather than at physical limits; the corpus does not adjudicate this directly, so the dissertation leans on the over-determination of concavity rather than on isolating satisficing as the sole driver.

## 2.4 The architecture of complexity and near-decomposability

The third theoretical move, still within the Simon pillar, supplies the over-specification prediction that sharpens the concavity claim into something more falsifiable than a curved aggregate. Simon's architecture-of-complexity argument predicts an over-specification region in spectral-channel count, because complex engineered systems are near-decomposable, so that beyond a point the interactions added by further elaboration contribute little to overall function while adding cost and integration burden. Where satisficing explains why a designer stops, near-decomposability explains why the system itself stops rewarding elaboration even if the designer does not. The argument rests on Simon's account of hierarchic systems, in which complex systems are organized so that the strong interactions occur within subsystems and the interactions between subsystems are comparatively weak [\[14\]](#ref-14). A near-decomposable system can be understood, to good approximation, by analyzing its subsystems semi-independently, because the cross-subsystem couplings are second-order. The behavioral-decision literature that descends from Simon reinforces the general point that real decision processes are bounded and that the world's structure, not unlimited cognition, is what makes good-enough decisions possible [\[22\]](#ref-22). The aerospace specialization of this idea, developed in the next section through value-driven design, treats the instrument as exactly such a near-decomposable system whose accuracy is the joint output of loosely coupled contributors.

Near-decomposability transports to the spectral-channel over-specification claim through the mechanism by which redundant channels stop contributing. A radiometer's retrieval accuracy for a given geophysical variable is produced by the information content of its spectral channels, bounded by the calibration accuracy that fixes the radiometric scale and by the geolocation and other error sources that no amount of additional spectral information can overcome. The channels are, in Simon's terms, the strongly interacting subsystem for the information-content contribution, but their contribution saturates: once the channels present span the information the retrieval can use, additional channels carry information that is largely redundant with channels already there, and the weak coupling between further spectral elaboration and delivered accuracy is the near-decomposability prediction. Past the saturation point, achievable accuracy is bounded not by spectral information but by the other, loosely coupled error sources, calibration drift and geolocation error and the intrinsic difficulty of the retrieval, which further channels do nothing to address. The driver is additional spectral channels and the cost they carry; the mechanism is informational redundancy among channels plus the binding of accuracy by non-spectral error sources, both of which are near-decomposability made concrete; the observable effect is that the marginal contribution of an additional channel to validated accuracy falls toward zero past an estimable channel count; the operational consequence is the over-specification region named in H1, where additional channels and their cost do not produce a commensurate accuracy gain; and the strategic implication is a defensible stopping rule for spectral specification. This is the chain that makes the over-specification test sharper than the general concavity test, because it predicts a specific design margin, a channel count, rather than only a curved relationship in the aggregate.

The caveats and objections matter here because the over-specification claim is the most aggressive in the dissertation. The framework predicts that an over-specification region exists; it does not assert that the boundary is universal across geophysical variables, and it concedes that the channel count at which redundancy sets in is conditional on the retrieval and on the controls. One serious objection is that channels added for one geophysical variable may be informative for another, so that an instrument that is over-specified for sea-surface temperature is well-specified for trace-gas profiling, and a population-level channel-count edge could therefore blur. The framework accepts this and answers it through the instrument-product unit of analysis, which lets a multi-product instrument contribute one row per validated product, and through the retrieval-difficulty control, so that the over-specification edge is estimated conditional on the product rather than asserted across all of them. A second objection is that the physical legitimacy of the redundancy claim must rest on more than Simon's general principle, and the framework agrees: the information-content theory that gives the channel-selection saturation its physical basis, optimal-estimation degrees of freedom for signal and channel-selection information content, is developed in the analysis-plan chapter, where the statistical over-specification edge is mapped to a physical redundancy onset. The framework here claims the qualitative prediction and points to that physical grounding rather than asserting it from near-decomposability alone. Confidence that an over-specification region exists in principle is high, because near-decomposability is one of the most durable regularities in the study of complex engineered systems [\[14\]](#ref-14), [\[22\]](#ref-22); confidence about the specific channel count and its stability across products is low at the design stage and is exactly what the empirical test is built to resolve. What would raise confidence is the physical information-content evidence assembled for the analysis chapter showing that degrees of freedom for signal saturate at an estimable channel count; what would lower it is a finding that redundancy onset varies so widely across products that no conditional edge is estimable, an outcome the design rule in later chapters treats as a clean rejection of the over-specification proposition.

## 2.5 The behavioral prior: decision under risk as a complement to satisficing

The framework adds a complementary behavioral prior that reinforces, rather than replaces, the Simon pillar. The point of this section is modest and clearly bounded: prospect-theoretic decision under risk strengthens the expectation that instrument design behavior departs from optimization in ways consistent with concave returns, by supplying a second, independent reason that designers and program managers do not behave as unbounded optimizers. Kahneman and Tversky's analysis of decision under risk established that real decision-makers evaluate prospects relative to a reference point, weight losses more heavily than equivalent gains, and distort probabilities in systematic ways, so that observed choices depart predictably from expected-utility maximization [\[25\]](#ref-25). This bears on the instrument-design setting because mission formulation is a decision under risk: the accuracy a proposed instrument will deliver is uncertain at the design stage, the cost it will incur is uncertain, and the reference point, the mission requirement, frames whether a given specification is experienced as a gain or a loss. A reference-dependent, loss-averse designer treats clearing the requirement as the salient reference outcome and is reluctant to risk falling below it, which biases toward conservative over-specification near the threshold and away from the disciplined trimming that an optimizer would perform. This compounds the satisficing prediction: where satisficing says the designer stops at the aspiration level, prospect theory says the designer, fearing a loss relative to the requirement reference, may overshoot the aspiration level defensively, building in margin that adds cost without adding validated accuracy. Both point to the same flat region of the frontier, reached from slightly different behavioral premises.

The boundary is firm: this is a complementary prior, not a load-bearing pillar, and the dissertation does not stake its contribution on prospect theory. The reason for including it nonetheless is that it closes a potential objection to the satisficing account. If a reviewer doubts that mature, expert instrument teams genuinely satisfice rather than optimize, the behavioral prior offers a second route to the same concavity prediction that does not depend on the satisficing mechanism being the operative one: even a team that believes it is optimizing will, under reference dependence and loss aversion, systematically over-build relative to the value optimum. The objection that prospect theory is a theory of individual choice and may not aggregate to organizational design decisions is acknowledged; the framework's answer is that it invokes prospect theory only as a complementary prior whose role is to make non-optimizing design behavior more plausible, not to carry the formal prediction, which rests on the Simon pillar and its aerospace operationalization. Confidence in the behavioral prior as a reinforcement is moderate, appropriate to its complementary status; the dissertation would lose nothing essential if this prior were set aside, because concavity is already over-determined by satisficing and near-decomposability, and that redundancy is the point. What this section adds to the argument is robustness: the concavity prediction does not hinge on a single behavioral assumption, which strengthens the case that the design addresses the real causal mechanism rather than an artifact of one contested theory of decision.

## 2.6 Value-driven design and tradespace exploration: the aerospace operationalization

The fourth and final pillar grounds the abstract concavity prediction in the specific engineering setting where the dissertation's instruments are designed. Value-driven design and multi-attribute tradespace exploration operationalize bounded rationality and near-decomposability for aerospace systems, demonstrating that real tradespaces of space instruments contain dominated, over-specified regions and that value, not raw capability, is the proper design objective. Where Simon supplies the general theory, this literature supplies the engineering instantiation and, what matters most for the contribution, prior evidence from within aerospace that the over-specified region the dissertation hypothesizes actually appears in practice. The value-driven-design and tradespace tradition carries the point. Value-driven design replaces the conventional flowdown of requirements with an economic value objective, holding that a system should be designed to maximize delivered value rather than to satisfy a checklist of capability requirements, and that doing so exposes the regions of the design space where additional capability subtracts value once its cost is netted out [\[17\]](#ref-17). Multi-attribute tradespace exploration makes this concrete by enumerating large numbers of candidate architectures and evaluating each against a multi-attribute utility, revealing a Pareto frontier and, behind it, a large population of dominated designs that deliver no more utility than cheaper alternatives [\[23\]](#ref-23). The extension to changeability shows that the same value-centric apparatus governs how architectures should be designed for an uncertain future, again with value rather than capability as the organizing objective [\[20\]](#ref-20).

This literature enters the framework in two ways. First, it confirms that the concavity and over-specification predictions are not foreign impositions on aerospace but are already latent in how the field's own design methodology understands the design space. A dominated design in a multi-attribute tradespace is precisely an over-specified instrument: it carries cost-bearing capability that does not translate into commensurate value, which in the dissertation's accuracy-centric reframing is capability that does not translate into commensurate validated accuracy. The tradespace literature has thus already observed the phenomenon H1 names, but it has observed it case by case, within the tradespace of a single mission concept, rather than estimated across a population of flown instruments. Second, value-driven design supplies the normative bridge from the positive prediction to the management recommendation the dissertation will make. If accuracy is concave in cost with an over-specification edge, then a value-driven designer should cap spectral specification at that edge and reallocate the saved budget, which is the value-maximizing move the tradespace methodology already prescribes in the abstract and which the dissertation proposes to locate empirically. The interpretation that the dissertation contributes a population-level, empirically estimated location for the over-specification threshold, where the tradespace literature has reasoned about it concept by concept, is what makes the relationship complementary and cumulative rather than competitive. The dissertation does not overturn value-driven design; it supplies the missing population-level estimate of where, in the specific case of radiometer spectral specification, the dominated region begins.

A caveat respects the limits of the analogy. The tradespace literature evaluates designs against a multi-attribute utility that values many attributes jointly, whereas the dissertation isolates a single performance scalar, validated retrieval accuracy, and relates it to cost. These are not the same object, and the framework does not claim that accuracy is the whole of value; it claims that accuracy is the performance attribute the dissertation can measure independently and across a population, and that the concavity of accuracy in cost is the specific, testable slice of the broader value-versus-capability relationship the tradespace literature describes. One objection is that an instrument over-specified on accuracy might be well-specified on some other valued attribute, such as coverage or revisit, that the accuracy-only analysis ignores; the framework concedes this directly and confines its claim to the accuracy axis, leaving the joint multi-attribute frontier to the tradespace methods that are built for it. Confidence that aerospace tradespaces contain over-specified, dominated regions is very high, because the tradespace literature documents them repeatedly across mission concepts [\[17\]](#ref-17), [\[23\]](#ref-23), [\[20\]](#ref-20); confidence that the accuracy-only slice of that broader phenomenon is itself concave with an estimable channel-count edge is the design-stage hypothesis the empirical work tests, and is held at the same moderate, pre-execution level as the rest of the central claim. What would raise confidence is the empirical frontier itself once estimated; what the theory contributes is the assurance that, if the frontier is concave, the finding sits naturally alongside the field's existing value-driven understanding rather than contradicting it.

## 2.7 Synthesis: why concavity is the expected result, not an arbitrary guess

The synthesis assembles the four pillars into the single conceptual model the empirical chapters will test, and states plainly why concavity is the maintained hypothesis. The causal mechanism behind H1 is fully specified by the framework, and each link in the mechanism is supported by a distinct pillar, so that the concavity prediction is over-determined rather than assumed. The mechanism, stated as the driver-to-implication chain, is as follows. The driver is that added spectral channels and calibration elaboration raise instrument development cost, a relationship the cost-modeling literature establishes as lawful and predictable [\[42\]](#ref-42), [\[37\]](#ref-37), [\[44\]](#ref-44), [\[46\]](#ref-46), [\[47\]](#ref-47). The mechanism is that beyond a point, additional channels carry information redundant with channels already present, and achievable accuracy is bounded by calibration drift, geolocation error, and the intrinsic difficulty of the retrieval; this is the near-decomposability prediction of the architecture of complexity [\[14\]](#ref-14), reinforced by satisficing search that stops at the requirement aspiration level [\[19\]](#ref-19), [\[4\]](#ref-4), [\[6\]](#ref-6), and complemented by the reference-dependent over-building that prospect theory predicts near the requirement reference [\[25\]](#ref-25). The observable effect is that the validated-accuracy-versus-cost curve flattens and the marginal channel contribution falls toward zero past an estimable channel count. The operational consequence is that dollars spent past the over-specification edge buy specification, not validated science. The strategic implication is that a cost-capped portfolio can deliver more total validated accuracy by capping per-instrument specification and reallocating to more instruments or to the binding non-spectral error sources, which is exactly the value-maximizing move the value-driven-design literature prescribes [\[17\]](#ref-17), [\[23\]](#ref-23).
The inverted hedonic surface holds this mechanism in a tractable functional form. Recall the notation the design bible fixes: validated accuracy is modeled as \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), where \( g \) is the unknown smooth function of cost that the framework predicts is concave, \( \mathbf{X} \) is the vector of design and difficulty controls entered linearly, \( \boldsymbol{\beta} \) is their coefficient vector, and \( e \) is an instrument-clustered error. The hedonic inversion is what licenses writing accuracy as a function of cost and attributes at all; bounded rationality and near-decomposability predict that \( g \) is concave rather than linear, so that its second derivative \( g'' \) is reliably negative over the supported range; and the over-specification test enters spectral-channel count with a flexible term whose marginal contribution to accuracy the framework predicts falls to a region indistinguishable from zero past an estimable channel count. Each piece of the notation is thus anchored to a pillar: the hedonic surface gives the equation its form, the Simon pillar gives \( g \) its curvature, and the channel-count term operationalizes the near-decomposability redundancy onset. The value-driven-design pillar does not enter the estimating equation directly. It enters as the normative frame that makes the estimated concavity decision-relevant, and as prior evidence that the dominated region the equation would reveal is one aerospace tradespaces are already known to contain.

This synthesis lets the chapter settle the first three of the dissertation's propositions on theoretical grounds, leaving the empirical ones to later chapters. The problem is real: cost and validated accuracy are produced by separate communities and have never been jointly modeled, with the cost side documented by NICM and the parametric models [\[42\]](#ref-42), [\[37\]](#ref-37), [\[44\]](#ref-44) and the accuracy side documented product by product in the cal/val literature [\[85\]](#ref-85), [\[77\]](#ref-77), [\[73\]](#ref-73), the very separation that motivates the join. The problem is material: Earth-science portfolios choose specification under fixed toplines, and the move toward distributed architectures and commercial data buys forces explicit per-instrument capability choices now, so a measured frontier would inform decisions currently made without one [\[137\]](#ref-137), [\[134\]](#ref-134). The design addresses the causal mechanism: the inverted hedonic estimator with a shape-constrained \( g(\text{cost}) \) and balancing weights isolates the curvature of the accuracy surface in the cost dimension, which is the quantity the mechanism predicts, and the identification discipline that secures that isolation, selection-on-observables within common support with covariate balancing, is carried in the Abadie tradition into the design chapter [\[105\]](#ref-105), [\[94\]](#ref-94), [\[109\]](#ref-109), [\[101\]](#ref-101). The remaining two propositions, that the design beats the alternatives and that the residual risk is acceptable, are established in the research-design and analysis chapters where the out-of-sample test, the common-support trimming, and the named threats live; the theoretical framework's contribution is to make the first three rest on theory rather than on assertion.

The caveat that closes the chapter is the one that has disciplined it throughout. The framework predicts concavity; it does not prove it, and a theory that over-determined a result could equally be a theory that has talked itself into a conclusion the data will not support. The dissertation guards against this in two ways the framework can state but not itself execute. First, the prediction is falsifiable on the framework's own terms: if the estimated cost term is statistically indistinguishable from a straight line, or if \( g'' \) is not reliably negative over common support, or if the marginal channel-count contribution remains positive across the entire observed channel range, then H1 is rejected and the null that accuracy is linear in cost stands, and the framework commits in advance to reporting that outcome. Second, the over-determination of concavity from multiple pillars is presented as robustness of the prior, not as a thumb on the empirical scale: the out-of-sample decision rule in the analysis chapter retains the linear null whenever the concave fit fails to beat it in held-out prediction, precisely because in-sample curvature in a small sample is the expected symptom of overfitting rather than of a real frontier. The theoretical framework therefore hands the empirical work a sharply specified, falsifiable conceptual model, with the functional form supplied by the inverted hedonic surface, the curvature supplied by bounded rationality and near-decomposability, the behavioral robustness supplied by prospect theory, and the aerospace grounding and normative relevance supplied by value-driven design. What the framework cannot do, and does not claim to do, is decide between H1 and H0; that is the work of the data, assembled and run under the design the next chapters specify. Stating the prediction this precisely, and stating exactly what would refute it, is the discipline that separates a theoretical framework from a rationalization.



# Chapter 3: Literature Review

## 3.0 The chapter's answer, stated first

This chapter establishes one conclusion and then defends it across the domain literature: three mature, internally rigorous bodies of work bear directly on the question of how instrument cost converts into validated geophysical accuracy, and none of them closes the join that this dissertation proposes to estimate. The first body of work is the instrument and space-system cost-estimating literature, exemplified by the NASA Instrument Cost Model (NICM) and the parametric telescope cost models of Stahl and colleagues. It establishes, with strong evidence, that the development cost of an Earth-science radiometer is a structured, predictable function of the instrument's design attributes [\[41\]](#ref-41), [\[42\]](#ref-42), [\[46\]](#ref-46). Its dependent variable is cost. The second body of work is the cost-growth, optimism-bias, and reference-class-forecasting literature, which characterizes how reliably cost records can be taken at face value and therefore how much measurement error the cost regressor is likely to carry [\[38\]](#ref-38), [\[51\]](#ref-51). The third body of work is the calibration and validation (cal/val) literature, which defines, product family by product family, what "validated accuracy" actually means and how it is measured against independent reference standards [\[73\]](#ref-73), [\[77\]](#ref-77), [\[85\]](#ref-85). Its dependent variable is accuracy. The cost literature stops at cost. The cal/val literature stops at one product. No published work places validated accuracy and instrument cost on the same axes across a population of radiometers while controlling for the design attributes that drive both, and therefore no published work estimates whether the accuracy-cost relationship is concave or where an over-specification region begins.

That sentence is the chapter's thesis, and the chapter earns it rather than asserting it. The field today consists of three non-communicating literatures, each excellent within its boundary. What is wanted in their place is a single estimated surface, the conditional expectation of validated accuracy as a function of cost with design and difficulty held fixed, written in this dissertation as \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), where \( g \) is the unknown smooth function whose curvature carries the concavity test. The join is what is missing: the population-level shape of \( g(\text{cost}) \) has never been estimated, so the field cannot say whether the marginal dollar of instrument investment still buys validated science. While that remains true, Earth-science mission budgeting continues to set spectral specification without evidence on diminishing returns, and descope and distributed-architecture decisions rest on cost ceilings rather than on a measured accuracy economics. This chapter's job is to demonstrate, through substantive engagement with each of the three literatures, that the gap is real, that it is not an artifact of having missed an existing study, and that the two propositions which follow, the concavity proposition and the over-specification proposition, are the natural and falsifiable consequences of what the literatures do and do not establish.

A note on confidence calibration, carried consistently through the chapter. Where a body of work is large, convergent, and methodologically mature, the claim built on it is stated at high or very high confidence. Where the evidence is a single study, a contested method, or an inference by analogy, the confidence is downgraded explicitly and the reader is told what additional evidence would raise it. This discipline matters because the dissertation is at the design stage: no estimate of \( g(\text{cost}) \) has been executed, so every forward-looking statement about the expected shape of the frontier is an expectation under H1, never a result. The literature review can establish that the cost literature, the cost-growth literature, and the cal/val literature exist and say what they say; it cannot, and does not, pre-empt the empirical test.

## 3.1 The first literature: instrument cost-estimating relationships

### 3.1.1 NICM as the cost-construct authority

This subsection establishes that instrument development cost is a structured index of design attributes rather than noise, and that this structure is what licenses the inverted-hedonic treatment of cost as the central attribute on the accuracy surface. The NASA Instrument Cost Model series carries the point. NICM is the instrument-level cost-estimating relationship that NASA maintains by fitting a curated database of flown instruments, and it is updated across versions, with Version VI documented by Habib-Agahi, Mrozinski, and Fox and the NICM 8.5 update documented by Mrozinski, Habib-Agahi, and Fox [\[37\]](#ref-37), [\[42\]](#ref-42). A dedicated variant, NICM-E, addresses Explorer-class mission instruments whose cost behavior differs from the general population, which itself demonstrates that the modelers found cost structure fine-grained enough to justify a class-specific relationship [\[43\]](#ref-43). The reasoning is the elementary logic of a cost-estimating relationship: NICM exists, is maintained, and is used because instrument cost is systematically predictable from a small set of design drivers, principally mass, power, and the design choices that this dissertation tracks as controls. If cost were unstructured noise, no such model could be fit and re-fit across versions. The institutional fact reinforces this: NICM is the cost model JPL and NASA actually use for instrument formulation, so its construct of "development cost" is the construct the field treats as authoritative.

Two consequences for this dissertation follow, and both are load-bearing. First, because cost is a structured index of build characteristics, it is legitimate to treat cost itself as the central hedonic attribute on an accuracy surface, rather than insisting that every individual design driver be entered separately. Cost is, in the cost-model literature's own logic, a near-sufficient statistic for the engineering effort, component quality, and calibration rigor embodied in the build, and those embodied qualities are what plausibly translate into delivered accuracy. Second, and this is the more practical point, NASA maintains the underlying cost records at the instrument level, which is the access path for the cost variable. One caveat here is important and is stated rather than buried: the NICM documentation in the corpus is the construct authority, but the underlying instrument-level cost table is not a public citable artifact. The dissertation therefore treats the NICM papers as establishing what the cost variable means and how it is defined, while the actual cost values must be obtained through JPL channels at execution. This is a data-access dependency, flagged honestly, not a citation that can be invented for the numbers. The objection a skeptic would raise, that a model fit to flown instruments is silent about instruments that never flew, is conceded and absorbed into the dissertation's deliberately restricted estimand, which concerns the frontier among instruments that reached validated operations.

### 3.1.2 What NICM does not do

The conclusion that closes this subsection is sharp: NICM and its kin are hedonic in spirit but hedonic in the wrong direction for this question. It rests simply on the dependent variable. Every NICM relationship regresses cost on design attributes; cost is the left-hand side. A model whose outcome is cost cannot, by construction, say anything about delivered accuracy, because accuracy never enters the model. NICM can answer "what will this instrument cost given its design," and it can answer it well, but it cannot answer "what validated accuracy will this cost buy," because the validated-accuracy axis is absent from the entire cost-model enterprise. This is not a criticism of NICM, which does exactly what it was built to do; it is the precise location of the gap. The contribution of this dissertation is to add the missing axis, the accuracy axis, and to estimate the relationship between the two. Confidence in this characterization is very high, because it rests not on interpretation but on the definitional structure of cost-estimating relationships, which are universally cost-on-attributes by their nature.

### 3.1.3 Instrument-class heterogeneity and what NICM-E reveals about the cost surface

The existence of NICM-E, the variant of the instrument cost model tailored to Explorer-class mission instruments, carries an interpretive lesson that bears directly on the dissertation's control strategy [\[43\]](#ref-43). The cost surface is not homogeneous across mission classes, and the modelers themselves found the heterogeneity large enough to justify a separate relationship rather than a single pooled model. The simple fact of NICM-E's existence as a distinct documented model establishes this: if a single cost-estimating relationship had captured Explorer-class instruments adequately, no class-specific variant would have been built. The standard model-selection logic applies, that one fits a separate relationship when the pooled relationship leaves systematic, class-correlated residuals. The interpretive consequence for this dissertation is that mission class is a candidate confounder of exactly the kind the identification strategy must absorb: instruments built for different mission classes face different cost regimes and, plausibly, different retrieval-difficulty and accuracy expectations. The mechanism is concrete. Mission class sets both a cost-accounting regime and a science-ambition level, and a higher-ambition class selects both more elaborate instruments and harder retrieval targets, so a naive accuracy-on-cost regression that ignores class would confound the cost effect with the class-correlated difficulty of the retrieval. The design control set and the retrieval-difficulty control, together with the common-support restriction developed in Chapter 5, must therefore be built to render instruments comparable within rather than across incommensurable classes. NICM-E is thus not merely a second cost model; it is documentary evidence that the cost surface has class structure the dissertation must respect, and it is one reason the identification burden handed to Chapter 5 is non-trivial. Confidence in this reading is high; it rests on the modelers' own decision to disaggregate by class rather than on a contestable interpretation of their results.

## 3.2 The second literature: parametric telescope and payload cost models

### 3.2.1 The Stahl family as evidence that cost is a legitimate hedonic index

This subsection establishes that the parametric telescope cost models developed by Stahl and colleagues independently corroborate, for optical payloads, the same proposition NICM establishes for instruments generally: cost is a smooth, estimable function of physical design attributes, which is exactly the property an attribute on a hedonic surface must have. The supporting work is deep and longitudinal. Stahl's survey of cost models for space telescopes maps the field and finds that, although published models vary, the underlying signal is consistent enough to model [\[46\]](#ref-46). The single-variable parametric models show that aperture diameter alone carries substantial explanatory traction [\[47\]](#ref-47), and the multivariable models extend the form to several drivers including diameter, wavelength, operating temperature, and technology epoch [\[41\]](#ref-41), [\[44\]](#ref-44). The series is cumulative across more than a decade: preliminary multivariable work [\[48\]](#ref-48), [\[49\]](#ref-49), updated parametric models [\[39\]](#ref-39), [\[45\]](#ref-45), a parametric model for ground and space telescopes with an explicit five-parameter functional form [\[34\]](#ref-34), and the most recent variations that re-base the models to current-year dollars and add a volume-based formulation [\[30\]](#ref-30). An earlier ground-based telescope parametric model in the NTRS record establishes the same multivariable approach with engineering and performance parameters and an explicit segmentation factor [\[52\]](#ref-52).

This evidence bears on the dissertation through a structural parallel. A parametric cost model that writes telescope cost as a power-law product of physical attributes is functionally a hedonic cost function: it recovers the implicit cost contribution of each attribute. The Stahl models demonstrate, with backing from a 47-instrument database in the most recent variations [\[30\]](#ref-30), that this structure holds for the optical payloads most relevant to passive radiometry. The methodological detail worth extracting is that these models find specific, repeatable attribute elasticities, for example a diameter exponent near 1.7 to 1.75 and a negative technology-epoch term reflecting cost reduction over time [\[34\]](#ref-34), [\[41\]](#ref-41). The negative epoch term is directly relevant to this dissertation's epoch control, because it confirms that technology vintage systematically shifts the cost surface and must therefore be absorbed rather than left to confound the accuracy-cost relationship.

### 3.2.2 The limitation that defines the join, again

The limitation of the Stahl family is identical to NICM's, and naming it twice from two independent literatures strengthens rather than weakens the point. The parametric payload cost models, like NICM, terminate at cost and never reach accuracy. The dependent variable shows it: every Stahl model has cost on the left-hand side [\[30\]](#ref-30), [\[34\]](#ref-34), [\[46\]](#ref-46). The reasoning is the same definitional one as in 3.1.2. The payoff of seeing the limitation appear in two separate, methodologically distinct literatures, the NICM instrument-cost tradition and the Stahl optical-payload tradition, is that the gap is not an idiosyncrasy of one modeling community. It is a field-wide property: the cost-modeling enterprise, wherever it is practiced, models cost from design and is structurally silent on delivered validated accuracy. Confidence that the gap is real and not merely unnoticed is therefore raised, because two independent literatures converge on the same boundary. A reader who suspected the gap was an artifact of looking only at NICM is answered by the Stahl corpus, and vice versa.

### 3.2.3 The attribute elasticities the Stahl models report, and why they discipline the control set

Beyond establishing that cost is a smooth function of design, the Stahl models report the specific signs and rough magnitudes of several attribute effects, and those reported effects are evidence the dissertation uses to choose and defend its control set rather than mere background. The cost-model literature already identifies which design attributes move the cost surface most, and a hedonic accuracy regression must control for exactly those attributes to avoid confounding the cost effect with the design choices that produced the cost. The published functional forms establish this. The multivariable and single-variable telescope models find aperture diameter to be the dominant cost driver with a super-linear exponent, a negative wavelength exponent, a negative operating-temperature exponent, and a negative technology-epoch term reflecting cost decline over calendar time [\[34\]](#ref-34), [\[41\]](#ref-41), [\[47\]](#ref-47). The preliminary multivariable work additionally reports the counterintuitive finding that increasing mass reduces cost per unit capability and that lower areal-density telescopes cost more than more massive ones, which signals that mass and density interact with cost in ways a naive linear control would miss [\[45\]](#ref-45), [\[48\]](#ref-48). These reported elasticities bear on the dissertation through the omitted-variable logic of attribute regression: any attribute that drives cost and also plausibly drives accuracy must be in the control vector \( \mathbf{X} \), or its effect will load onto the cost term and bias the estimated curvature [\[110\]](#ref-110). The interpretive consequence is concrete and feeds Chapter 4's control list. The epoch term's documented negativity is the reason mission epoch is a non-negotiable control, since technology vintage shifts both cost and achievable accuracy. The mass and power terms are controls because the Stahl models show they carry cost structure. The aperture and resolution relationship for radiometers is the analogue of the telescope diameter driver and motivates the spatial-resolution control. One caveat is that the Stahl elasticities are estimated for optical telescopes, not passive radiometers specifically, so they motivate the control set by analogy rather than by direct measurement on the dissertation's population; this is stated rather than glossed, and it is one reason the control set is chosen conservatively and pre-specified. Confidence that the right attributes are controlled is moderate to high: high on the qualitative roster of cost-driving attributes, which is convergent across NICM and Stahl, and moderate on the exact functional roles, which await the dissertation's own data.
### 3.2.4 Distributed-mission cost estimation: the same boundary in a newer setting

A more recent strand extends parametric cost estimation to distributed spacecraft missions, and it matters here for two reasons. Even the cost-modeling work most attuned to the distributed-architecture future, the setting in which per-instrument specification choices are most acute, still models cost and not accuracy. The clearest example is Foreman, Le Moigne, and de Weck's survey of cost-estimating methodologies for distributed spacecraft missions, which aggregates existing cost-estimating relationships into a Cost and Risk module of a constellation tradespace tool [\[40\]](#ref-40). This is the closest the cost literature comes to the dissertation's setting, because it explicitly anticipates Earth-observation constellations of smaller instruments. It confirms the gap rather than closing it: its outcome variable remains cost and risk. It provides cost and uncertainty for distributed architectures but does not relate that cost to the validated accuracy the distributed architecture delivers. The distributed-architecture community, the very community whose decisions a frontier estimate would inform, currently reasons about per-instrument capability with a cost tool and no accuracy tool. That sharpens the materiality of the gap. The decisions are being made now, in a tradespace framework, with half the relevant axis missing.

## 3.3 The third theme: cost growth, optimism bias, and the reliability of the cost regressor

### 3.3.1 Why the regressor's measurement quality is a literature, not a footnote

This subsection establishes that the reliability of cost records is itself a substantive empirical question with a mature literature, and that this literature conditions how much confidence the dissertation can place in its central regressor. The cost-overrun and optimism-bias research associated with Flyvbjerg carries the point. Reference-class forecasting establishes that planned cost estimates for large projects are systematically optimistic, biased downward by a combination of cognitive optimism and strategic misrepresentation, and that the corrective is to forecast from the distribution of outcomes in a reference class of comparable past projects rather than from the inside view of the project itself [\[51\]](#ref-51). The complementary synthesis distills the empirical regularities of cost overrun, among them that overruns are common, large, and fat-tailed rather than symmetric noise [\[38\]](#ref-38). A broader management literature corroborates the ubiquity and structure of cost overrun across infrastructure and engineered projects, including machine-learning approaches to predicting and mitigating it [\[27\]](#ref-27), [\[28\]](#ref-28), [\[29\]](#ref-29), [\[31\]](#ref-31).

This bears on the dissertation through the cost variable. The dissertation's cost regressor is development cost from NICM-class records, defined as actual development cost in constant-year dollars, not a planning estimate. The optimism-bias literature is therefore most relevant as a caution about which cost number is used. A planned or budgeted figure would carry the systematic downward bias the literature documents, whereas a recorded actual cost is the appropriate construct precisely because it sits at the realized end of the overrun distribution. The mechanism is specific, not a vague gesture at "data quality." Planning-stage cost figures are generated by an inside-view process prone to optimism, which produces a left-shifted, fat-tailed error relative to realized cost, so a planned-cost regressor would carry correlated measurement error. The cost variable must therefore be the recorded actual development cost, and any instrument whose only available cost figure is a planning estimate is a candidate for the sensitivity analysis that drops ambiguously costed instruments. The cost-growth literature thus does not threaten the design so much as instruct it on variable definition.

### 3.3.2 Residual measurement error and how it is bounded

A caveat on the preceding point is that even recorded actual costs are not error-free, because instrument identity and version must be matched across the NICM cost record and the NTRS design record, and version mismatches introduce measurement error in the regressor. The reason to take this seriously is general. The econometrics of hedonic price functions has long flagged that measurement error and misspecification in the characteristics are among the principal hazards of attribute-based regression [\[110\]](#ref-110). The standard result applies for classical measurement error in a regressor of interest, which attenuates the estimated relationship toward the null. The consequence is twofold and is carried forward to the research design. First, attenuation works against finding curvature, so if concavity survives in the presence of cost measurement error, the finding is conservative rather than inflated. Second, the dissertation pre-commits to a sensitivity analysis that drops instruments whose cost-to-design match is ambiguous, so that the curvature estimate is not driven by mismatched records. Confidence that measurement error is bounded rather than fatal is moderate at the design stage and would be raised by the actual matching exercise reporting a high rate of clean, unambiguous instrument-version matches.

### 3.3.3 Why the fat-tailed structure of cost error matters for a small-sample frontier

A subtler point connects the cost-growth literature to the dissertation's statistical-conclusion validity, and it is worth drawing out because it shapes the estimator's robustness requirements. The cost error documented in the overrun literature is not merely large but asymmetric and fat-tailed, and a small-sample frontier estimator is unusually vulnerable to such error. The empirical regularity establishes this: cost overruns follow heavy-tailed rather than symmetric distributions, so that a minority of extreme realizations carries disproportionate weight [\[38\]](#ref-38). The broader project literature corroborates that extreme overruns are recurrent rather than exceptional across engineered domains [\[27\]](#ref-27), [\[28\]](#ref-28), [\[31\]](#ref-31). This links to the dissertation through the behavior of regression estimators under heavy-tailed regressor error in small samples. A single instrument whose recorded cost sits in the tail can exert high leverage on a flexibly fit cost function, producing apparent curvature that is an artifact of one influential point rather than a population frontier. The mechanism is specific. With a heavy-tailed cost-error process, and in a sample of dozens rather than thousands of instruments, a tail realization is not averaged out, so a single high-leverage point can bend the fitted \( g(\text{cost}) \) toward or away from concavity. The analysis must therefore report leverage and influence diagnostics, must not let the concavity verdict rest on any single instrument, and must use the held-out, cross-validated comparison against the linear null rather than an in-sample fit, because in-sample curvature in a small heavy-tailed sample is the symptom of overfitting that the cost-growth literature predicts. The cost-growth literature is thus a caution not only about the regressor's mean but about its tail, and it is one reason the dissertation's decision rule privileges out-of-sample performance over in-sample shape. Confidence in this reasoning is high as a methodological matter; its quantitative bite depends on the realized cost distribution, which is unknown until the data are assembled.

## 3.4 The fourth theme: modern and machine-learning cost-estimation practice

### 3.4.1 Currency without departure

This subsection establishes that the most recent cost-estimation practice, machine-learning methods included, broadens the toolkit but does not alter the structural boundary that the cost literature stops at cost. A set of contemporary studies bears it out. Machine-learning parametric cost estimation has been applied to axisymmetric manufactured components, generating training data from analytical cost software and fitting regression models to it [\[32\]](#ref-32). Neural-network life-cycle cost estimation has been benchmarked against conventional parametric techniques for induction motors and found to be a viable alternative [\[36\]](#ref-36). Spacecraft-specific methodological work proposes unified, standardized procedures for development-cost estimation [\[33\]](#ref-33), and a blind validation study tested the SEER-H parametric cost tool against NASA space-mission outcomes, which is directly relevant because it independently probes how well a parametric cost model predicts realized mission cost [\[35\]](#ref-35).

These count as currency rather than as closing the gap because, once more, of the dependent variable. Whether the estimator is a power law, a neural network, or a gradient-boosted tree, the modeled quantity in every one of these studies is cost or life-cycle cost, never delivered scientific accuracy [\[32\]](#ref-32), [\[33\]](#ref-33), [\[35\]](#ref-35), [\[36\]](#ref-36). The methodological frontier of cost estimation has moved, and the dissertation should be read as aware of that movement, but the movement is entirely within the cost axis. A more flexible cost model is still a cost model. The blind validation of the SEER-H tool [\[35\]](#ref-35) is worth a closer interpretive note: by quantifying how accurately a parametric tool predicts realized cost, it characterizes the noise floor of cost as a measured quantity, which feeds the measurement-error discussion of 3.3.2. Its convergence with the optimism-bias literature, both pointing to a non-trivial gap between predicted and realized cost, reinforces the decision to use recorded actual cost and to run the cost-match sensitivity analysis.

### 3.4.2 What the modern flexible-form work teaches about the dissertation's own estimator

The machine-learning cost literature carries a second lesson that is methodological rather than substantive, and it bears on the dissertation's choice of a partially linear semiparametric estimator over a fully flexible one. The modern cost literature's own experience with flexible function approximators warns against unconstrained flexibility on small samples, which is the regime the dissertation occupies. The way these studies are constructed shows it. The axisymmetric-component machine-learning work had to generate large synthetic training sets from analytical cost software because flexible regressors require many examples to fit without overfitting [\[32\]](#ref-32), and the neural-network life-cycle work positions itself as competitive with parametric techniques only when adequately trained [\[36\]](#ref-36). The bias-variance logic explains it: flexible estimators have low bias but high variance, and that high variance is ruinous when the sample is dozens of instruments rather than the thousands these machine-learning studies assemble or synthesize. The consequence is a direct argument for the dissertation's estimator design. The dissertation cannot synthesize instruments the way the component-cost work synthesizes parts; its population is fixed and small. It cannot afford an unconstrained nonparametric fit of the cost function, and this is the justification for the partially linear specification \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), in which only the single cost term is estimated flexibly under a shape constraint while the design controls enter linearly to conserve degrees of freedom. The shape constraint, concavity-and-monotonicity-respecting smoothing of \( g \), is itself a variance-reduction device borrowed in spirit from the same prior knowledge that lets the cost-model literature impose power-law forms. One caveat and named evidence gap is that the corpus is thin on dedicated shape-constrained semiparametric estimation methods, so two or three isotonic or concave-regression method citations are required before Chapter 5 finalizes the smoother; that is a flagged follow-up sweep, not an invented citation. Confidence that flexible-form restraint is the right posture is high; it is the consistent lesson of the small-sample function-estimation literature and of the modern cost work's own reliance on large or synthetic training data.

### 3.4.3 What the absence of an accuracy axis in modern cost work implies

Synthesizing 3.1 through 3.4, across the entire cost-estimation literature, classical and modern, instrument-specific and project-general, single-variable and machine-learning, the accuracy of the delivered product is never the modeled outcome. The cumulative dependent-variable observation across every cited cost study establishes this [\[30\]](#ref-30), [\[32\]](#ref-32), [\[35\]](#ref-35), [\[40\]](#ref-40), [\[42\]](#ref-42). A literature defined by a single class of outcome variable cannot, however sophisticated its methods become, answer a question about a different outcome variable. The mechanism by which this leaves the dissertation's question open is straightforward: to estimate returns to cost in units of accuracy, one needs accuracy on the left-hand side, and the cost literature never puts it there. The implication for the chapter's argument is that the cost literature, taken as a whole and at its most current, supplies the dissertation's regressor and its construct but cannot supply its outcome. The outcome must come from the cal/val literature, to which the chapter now turns.

## 3.5 The fifth theme: the calibration and validation literature as a body

### 3.5.1 Treating cal/val as a literature, not as a data appendix

This subsection establishes that the cal/val literature, considered as a body rather than product by product, shows "validated accuracy" to be a real, externally documented, independently measured quantity for each major Earth-science product family, which is the precondition for using it as a credible dependent variable. The deep, per-product construction of the accuracy variable belongs to Chapter 4; here the literature is reviewed as a literature, to establish three properties: that validated accuracy is independently measured against reference standards, that it is reported with quantified uncertainty, and that its construction differs enough across product families to require the requirement-normalization the dissertation adopts. The evidence spans the product families the dissertation intends to cover.

For aerosol optical depth, the MODIS aerosol algorithm and its validation are documented by Remer and colleagues, who established the expected-error envelope against which retrievals are judged [\[85\]](#ref-85). The reference network itself, AERONET, is a federated ground instrument network whose existence and archive make independent validation possible at all [\[87\]](#ref-87). Subsequent collection updates extend and re-validate these products: the Deep Blue algorithm validation and uncertainty estimates by Sayer and colleagues quantify retrieval uncertainty as a function of conditions [\[81\]](#ref-81), and the Collection 6.1 validation by Wei and colleagues compares products over land and ocean against the reference network [\[75\]](#ref-75). The significance of this aerosol cluster is that it demonstrates a fully realized validation chain: an algorithm, an independent reference network, a published expected-error envelope, and successive re-validations with uncertainty budgets. That chain is what makes aerosol optical depth a usable dependent-variable family.

For sea-surface temperature, Merchant and colleagues' synthesis of half a century of satellite SST retrieval establishes a long, deep validation tradition with quantified bias and standard-deviation statistics built from in-situ matchups [\[73\]](#ref-73), and the observational-needs framing by Robinson articulates the accuracy requirements the community holds SST products to [\[74\]](#ref-74). For soil moisture, the SMAP validation against core validation sites by Chan and colleagues reports root-mean-square error and unbiased RMSE against a designed reference network [\[77\]](#ref-77), the Level-4 assessment by Reichle and colleagues extends validation to the model-assimilated product using in-situ measurements [\[78\]](#ref-78), and the performance-metrics framework by Reichle, Crow, and Keppenne formalizes which error statistics and application requirements define soil-moisture accuracy [\[83\]](#ref-83). For precipitation, the GPCP monthly analysis by Adler and colleagues establishes a validated reference precipitation analysis [\[86\]](#ref-86), and the GPM mission overview by Hou and colleagues situates precipitation retrieval and its validation in a science-and-society framing [\[79\]](#ref-79).

### 3.5.2 The three properties the cal/val body establishes

What turns this catalogue into an argument has three strands, each a property with its own supporting evidence. First, validated accuracy is independently measured. Every product family above is validated against a reference external to the instrument, an AERONET sun photometer, an in-situ SST buoy, a soil-moisture core site, a gauge-based precipitation analysis [\[73\]](#ref-73), [\[77\]](#ref-77), [\[86\]](#ref-86), [\[87\]](#ref-87). This is decisive for construct validity: the dependent variable measures delivered science accuracy, not a self-reported design specification, precisely because it comes from an independent reference rather than from the instrument's own documentation. Confidence in this property is very high, because independence from the instrument is a defining feature of how each of these communities validates.
Second, validated accuracy is reported with quantified uncertainty. The explicit error budgets and uncertainty estimates in the validation papers establish this: expected-error envelopes for aerosol, bias and standard deviation for SST, RMSE and unbiased RMSE for soil moisture, and formalized performance metrics that specify which statistics count [\[73\]](#ref-73), [\[77\]](#ref-77), [\[81\]](#ref-81), [\[83\]](#ref-83). The dependent variable therefore arrives with its own measurement-uncertainty characterization, which the dissertation carries into its inference rather than having to invent.

Third, validated accuracy is constructed heterogeneously across families, and this is the methodological problem that requirement-normalization solves. The error metrics are not commensurable in raw units: an aerosol-optical-depth expected error, a sea-surface-temperature standard deviation in kelvin, a soil-moisture unbiased RMSE in volumetric units, and a precipitation bias in millimeters per day cannot be placed on a common axis as reported [\[73\]](#ref-73), [\[77\]](#ref-77), [\[85\]](#ref-85), [\[86\]](#ref-86). The dissertation's response is licensed because each community also defines a stated mission or application requirement for its product, and the performance-metrics framework of Reichle and colleagues [\[83\]](#ref-83) is the clearest case of formalizing accuracy against an application requirement rather than in raw units. Expressing each product's validated error relative to its stated requirement yields a unitless, requirement-normalized accuracy comparable across families. One caveat, carried forward to Chapter 4 where the construction is executed, is that requirement-normalization mitigates but does not fully eliminate cross-family heterogeneity, because requirements themselves are set by different processes. This is a named limitation, not a hidden assumption.

### 3.5.3 The validation reference is itself imperfect, which the literature is candid about

A property of the cal/val literature that the dissertation must inherit honestly is that the reference standard against which a product is validated is not itself perfect, and the better validation papers say so. Validated accuracy is measured against a reference that carries its own uncertainty, and that reference uncertainty sets a floor below which a product's apparent accuracy cannot be distinguished from the limits of the reference. The uncertainty-aware framing of the modern validation literature establishes this: the Deep Blue aerosol validation reports uncertainty estimates rather than a single error number, acknowledging that the comparison itself has scatter [\[81\]](#ref-81); the SST synthesis discusses the in-situ matchup process and its limits across half a century of records [\[73\]](#ref-73); and the soil-moisture performance-metrics framework states that application requirements and reference quality jointly define what counts as accurate [\[83\]](#ref-83). This bears on the dissertation through the construct validity of the dependent variable. If two instruments are both more accurate than the reference network can resolve, their validated-accuracy difference is not measurable, and any flattening of the accuracy-cost curve at the high-cost end could in principle reflect the reference ceiling rather than a true instrument frontier. The mechanism is worth stating precisely, because it is the most serious rival to the dissertation's central claim. With a finite-precision validation reference, beyond a certain instrument quality the validated-error metric is dominated by reference uncertainty rather than instrument error, so the accuracy-cost curve flattens at high cost, and that flattening would mimic the concavity H1 predicts but for a measurement reason rather than an instrument-economics reason. This chapter cannot resolve the rival. It can only flag that the cal/val literature itself supplies the warning, and hand the probe forward. The dissertation's response, developed in Chapters 6 and 7, is to examine whether any observed flattening coincides with the documented precision limits of the validation references for the relevant products. The candid evidence gap, named in the dissertation's plan, is that the corpus is thin on dedicated characterizations of reference-network precision as a function of product, so a targeted follow-up sweep on reference-network uncertainty is required before that probe can be executed. Confidence at this stage is therefore deliberately low on the dissertation's ability to separate an instrument ceiling from a reference ceiling, and the chapter says so rather than implying the rival is already handled.

### 3.5.4 The cal/val literature's structural limitation

The point that mirrors 3.1.2 and 3.2.2 on the accuracy side is that the cal/val literature, for all its rigor, validates one instrument and one product at a time and never relates validated error to the instrument's cost or to a population-level frontier. The unit of analysis in every cited validation study establishes this: each paper concerns a specific instrument's specific product, MODIS aerosol, SMAP soil moisture, a particular SST sensor, and reports that product's validated accuracy in isolation [\[73\]](#ref-73), [\[77\]](#ref-77), [\[85\]](#ref-85). A single-product validation study, by design, has no cost axis and no cross-instrument population, so it cannot speak to returns. The symmetry that defines the gap follows. The cost literature has cost and design but no accuracy; the cal/val literature has accuracy and design but no cost and no population-level shape. Each literature individually possesses two of the three axes the dissertation needs, and the missing axis differs in each. The join the dissertation proposes is the operation of bringing the cost literature's cost axis and the cal/val literature's accuracy axis into one population-level regression with shared design controls. Confidence that this join is genuinely unfilled is high and rests on the convergent structural limitation visible from both sides.

## 3.6 The anchor literatures as they bear on the gap

The dissertation's four methodological anchors, Rosen, NICM/Stahl, Abadie, and Simon, receive their full theoretical treatment in Chapter 2 and their methodological operationalization in Chapter 5. This chapter engages them only to the extent that they bear on the literature gap, so that the propositions in 3.7 follow from the review rather than from a separate theoretical apparatus.

The Rosen hedonic framework matters to the literature review in one specific way: it supplies the form of the join that the cost and cal/val literatures leave unmade [\[26\]](#ref-26). Rosen's result, that a differentiated good's price is a function of its attributes whose partial derivatives recover implicit attribute prices, is what the cost-model literature already does implicitly when it regresses cost on design. The dissertation's inversion, regressing a performance metric on attributes with cost as the central attribute, is the operation that would close the gap, and the literature review establishes that no one in either the cost or the cal/val literature has performed it. The caveat here is one of the dissertation's named evidence gaps: there is no direct methodological precedent in the corpus for a radiometer-specific cost-accuracy join, so the inverted hedonic is argued from the cost-model family and from applied hedonic practice rather than from a prior instance of the exact inversion. The absence of a precedent is part of the contribution, not a weakness to paper over.

The Simon bounded-rationality and near-decomposability tradition matters to the literature review because it converts the gap from a neutral void into a void with a predicted shape [\[14\]](#ref-14), [\[19\]](#ref-19). The cost and cal/val literatures, between them, say nothing about whether the accuracy-cost relationship should be linear or concave; they simply never put the two variables together. Simon's satisficing account, that designers search to an aspiration level and stop, and the architecture-of-complexity argument, that near-decomposable systems gain little function from elaboration past a point, jointly predict diminishing returns and an over-specification region [\[14\]](#ref-14), [\[19\]](#ref-19). The value-driven-design and tradespace literature operationalizes the same intuition in aerospace, holding that value rather than raw capability is the objective and that tradespaces contain dominated, over-specified regions [\[17\]](#ref-17), [\[23\]](#ref-23). The interpretive role of these anchors is bounded: they justify why concavity is the expected direction of the test rather than an arbitrary guess, but they supply no evidence on the actual shape, which only the unexecuted estimation can. The Abadie program-evaluation tradition is reserved almost entirely for Chapter 5, entering the literature review only as the reminder that any cross-instrument comparison of cost and accuracy must confront selection, because instruments are not randomly assigned their cost levels [\[105\]](#ref-105). This is the methodological reason the gap is hard to close and has stayed open, not merely an oversight.

## 3.7 The unfilled join, stated precisely, and the propositions that follow

### 3.7.1 The gap, in one paragraph the rest of the dissertation depends on

Synthesizing the five thematic literatures, the gap is stated as precisely as the review allows. The cost-estimating literature, classical and modern, instrument-specific and machine-learning, establishes that instrument development cost is a structured, predictable function of design attributes, and it provides the dissertation's cost regressor and its development-cost construct, but it never models delivered accuracy [\[30\]](#ref-30), [\[32\]](#ref-32), [\[40\]](#ref-40), [\[42\]](#ref-42). The cost-growth and optimism-bias literature establishes that cost records must be used carefully, that recorded actual cost is the appropriate construct and planning estimates carry systematic downward bias, and it instructs the dissertation's variable definition and sensitivity analysis [\[38\]](#ref-38), [\[51\]](#ref-51). The cal/val literature establishes that validated accuracy is a real, independently measured, uncertainty-quantified quantity for each major product family, and it provides the dissertation's dependent variable and the requirement-normalization that makes it comparable, but it validates one product at a time and never relates accuracy to cost or to a population frontier [\[73\]](#ref-73), [\[77\]](#ref-77), [\[83\]](#ref-83), [\[85\]](#ref-85). No study in any of these literatures regresses validated accuracy on instrument cost across a population of radiometers while controlling for the design attributes that drive both, and therefore no study estimates the shape of \( g(\text{cost}) \) or locates an over-specification spectral-channel count. That is the join, and it is unfilled.

### 3.7.2 From gap to propositions

Two propositions follow directly from the reviewed literature, and stating them here connects the literature review to the hypotheses fixed in the prospectus.

The first proposition is the concavity proposition, which is hypothesis H1 of the dissertation: validated geophysical-retrieval accuracy for Earth-observing radiometers is a concave function of instrument cost, so that the marginal accuracy gained per additional dollar declines as cost rises. The literature supports posing this proposition, not its truth. The cost literature establishes that cost is a structured attribute fit to enter a hedonic surface [\[41\]](#ref-41), [\[42\]](#ref-42). The cal/val literature establishes that accuracy is an independently measured outcome fit to be the surface's dependent variable [\[77\]](#ref-77), [\[85\]](#ref-85). The Simon tradition establishes that diminishing returns are the theoretically expected direction [\[14\]](#ref-14), [\[19\]](#ref-19). The causal mechanism the propositions rest on is the one fixed in the dissertation's bible: added spectral channels and calibration elaboration raise cost; beyond a point, additional channels carry information redundant with channels already present, and achievable accuracy is bounded by calibration drift, geolocation error, and the intrinsic difficulty of the retrieval; the validated accuracy-versus-cost curve therefore flattens; dollars spent past that point buy specification, not validated science; and a cost-capped portfolio could deliver more total validated accuracy by capping per-instrument specification. The null against which this is tested, H0, is that accuracy is linear in cost with no diminishing returns and no over-specification region. Confidence at the literature-review stage is deliberately withheld from the truth of H1: the review establishes that the question is well-posed and the direction is theoretically motivated, but the shape of \( g(\text{cost}) \) is unknown until estimated, and the dissertation is committed to reporting whichever of H1 and H0 the data support.

The second proposition is the over-specification proposition, the sharper prediction within H1: there is an estimable spectral-channel count beyond which the marginal contribution of additional channels to validated accuracy is statistically indistinguishable from zero, holding cost and other attributes fixed. The literature's contribution to this proposition is to make it physically plausible and to locate the evidence the dissertation still needs. The cost-model literature shows channel count is a cost driver, so additional channels are not free [\[42\]](#ref-42). The cal/val literature shows achievable accuracy is bounded by error sources that additional channels cannot remove, principally calibration and geolocation [\[73\]](#ref-73), [\[83\]](#ref-83). One caveat and named evidence gap is that the physical legitimacy of an over-specification edge, the claim that added channels become informationally redundant, rests on spectral-information-content theory that this chapter does not develop; that body of work is the distinctive corpus contribution of Chapter 6, where the statistical edge is grounded in optimal-estimation degrees of freedom for signal. The literature review's honest position is therefore that it can pose the over-specification proposition and show why it is not arbitrary, but the physical basis for the redundancy mechanism is supplied later, and the statistical test of the edge is unexecuted.

### 3.7.3 How the chapter advances the larger argument

The propositions are not free-floating; they sit on the dissertation's larger argument, and the literature review is where its first two elements are evidenced. The first, that the problem is real, is established by this chapter's demonstration that cost and validated accuracy are produced by separate communities and never jointly modeled, evidenced on the cost side by the NICM and Stahl literatures and on the accuracy side by the MODIS, SMAP, and SST validation literatures [\[42\]](#ref-42), [\[46\]](#ref-46), [\[73\]](#ref-73), [\[77\]](#ref-77), [\[85\]](#ref-85). The second, that the problem is material, is established by the distributed-mission and tradespace strands showing that per-instrument capability choices are being made now, under fixed toplines, with a cost tool and no accuracy tool [\[17\]](#ref-17), [\[23\]](#ref-23), [\[40\]](#ref-40). The remaining elements, that the design addresses the causal mechanism, that it beats the alternatives, and that residual risk is acceptable, are the burden of Chapters 5 and 6 and are not pre-empted here. The cost-growth literature contributes to the residual-risk element by characterizing the cost regressor's measurement quality and motivating the sensitivity analysis [\[38\]](#ref-38), [\[110\]](#ref-110), but the full residual-risk argument is assembled later. The literature review's role is bounded and specific: it carries the first two elements, and it hands the rest forward with the evidence each will need flagged.

### 3.7.4 What would change this chapter's conclusion

The discipline of stating falsification conditions applies to the literature review's own claim as much as to the dissertation's hypotheses. The chapter's conclusion is that the cost-accuracy join is unfilled. That conclusion would be overturned by the discovery of a study that regresses validated, requirement-normalized retrieval accuracy on instrument development cost across a population of radiometers with design and difficulty controlled. The corpus assembled for this dissertation contains no such study, and the convergent structural limitation visible from both the cost and the cal/val literatures makes its existence unlikely, but the honest position is that the gap claim is empirical and could in principle be falsified by a missed reference. Two narrower findings would reshape rather than overturn the chapter. A study estimating accuracy-cost returns for active sensors would not close the radiometer gap, because the cost drivers and accuracy metrics of radars and lidars are not commensurable with passive radiometry and are excluded from this dissertation's estimand by design. A study estimating the relationship for commercial radiometers built under different cost accounting would speak to whether concavity is a physics property or a cost-regime property without closing the NASA-radiometer gap. Naming what would change the conclusion is what separates a defensible gap statement from an assumed one, and it sets up the scoped extensions the discussion chapter returns to.

## 3.8 Synthesis tables

The following tables consolidate the review. They are organizational, not evidentiary; every cell is sourced to the corpus entries already discussed in the prose.

### Table 3.1 The three literatures and the axes each possesses

| Literature | Representative sources | Outcome axis | Possesses design axis | Possesses cost axis | Possesses accuracy axis | Population-level shape estimated |
|---|---|---|---|---|---|---|
| Instrument cost-estimating relationships | [\[42\]](#ref-42), [\[37\]](#ref-37), [\[43\]](#ref-43) | Cost | Yes | Yes | No | Cost shape only |
| Parametric payload cost models | [\[46\]](#ref-46), [\[41\]](#ref-41), [\[34\]](#ref-34), [\[30\]](#ref-30), [\[40\]](#ref-40) | Cost | Yes | Yes | No | Cost shape only |
| Cost growth / optimism bias | [\[51\]](#ref-51), [\[38\]](#ref-38), [\[110\]](#ref-110) | Cost reliability | Indirect | Conditions the cost axis | No | Distribution of cost error |
| Modern / ML cost estimation | [\[32\]](#ref-32), [\[36\]](#ref-36), [\[33\]](#ref-33), [\[35\]](#ref-35) | Cost / life-cycle cost | Yes | Yes | No | Cost shape only |
| Calibration / validation | [\[85\]](#ref-85), [\[73\]](#ref-73), [\[77\]](#ref-77), [\[83\]](#ref-83) | Validated accuracy | Yes | No | Yes | None (one product at a time) |
| **The proposed join (this dissertation)** | inverted hedonic over the above | **Validated accuracy as a function of cost** | Yes (controls) | Yes (regressor) | Yes (dependent) | **\( g(\text{cost}) \) shape, unfilled** |
Table 3.1 reads as the chapter in one view: every existing literature holds at most two of the three axes, the missing axis differs between the cost side and the accuracy side, and only the proposed join carries all three at the population level.

### Table 3.2 What each literature contributes to and withholds from the dissertation

| Literature | Contributes | Withholds | Carried-forward implication |
|---|---|---|---|
| NICM | The cost construct (development cost) and the access path to instrument-level cost records | The actual cost values (not a public citable artifact); any accuracy axis | Data-access dependency; treat NICM docs as construct authority [\[42\]](#ref-42) |
| Stahl family | Independent corroboration that cost is a smooth function of design attributes; attribute elasticities; the negative epoch term | Delivered accuracy | Justifies cost-as-attribute and the epoch control [\[34\]](#ref-34), [\[41\]](#ref-41) |
| Cost growth / optimism bias | Guidance that recorded actual cost, not planning estimate, is the correct construct; the fat-tailed error structure | A radiometer-specific cost-error budget | Variable definition + cost-match sensitivity analysis [\[51\]](#ref-51) |
| Modern / ML cost estimation | Currency; a measured cost-prediction noise floor [\[35\]](#ref-35) | Any accuracy axis | Confirms the gap persists at the methodological frontier [\[32\]](#ref-32), [\[35\]](#ref-35) |
| Cal/val body | The dependent variable: independent, uncertainty-quantified validated accuracy per product family; the requirement-normalization basis | A cost axis; a population-level shape | Dependent-variable construction (Chapter 4); requirement-normalization [\[83\]](#ref-83), [\[85\]](#ref-85) |
| Rosen / Simon / Abadie anchors | The form of the join; the predicted direction (concave); the selection warning | Evidence on the actual shape | Propositions H1/H0; identification burden handed to Chapter 5 [\[14\]](#ref-14), [\[26\]](#ref-26), [\[105\]](#ref-105) |

### Table 3.3 Confidence calibration on the chapter's principal claims

| Claim | Confidence | What would raise it | What would lower it |
|---|---|---|---|
| Instrument cost is a structured function of design | Very high | (already converged across NICM + Stahl) | A failure to fit stable cost models, not observed |
| The cost literature never models delivered accuracy | Very high | (definitional) | Discovery of a cost model with accuracy as outcome |
| Validated accuracy is independently measured and uncertainty-quantified per family | Very high | (defining feature of cal/val) | Evidence that validation collapses into self-reported specs |
| The cost-accuracy join is unfilled | High | A systematic search returning no precedent | A missed study performing the exact join |
| Concavity (H1) is true | Withheld at design stage | Out-of-sample win of the concave model + reliably negative \( g'' \) | Linear fit indistinguishable from \( g(\text{cost}) \) |
| An over-specification channel edge exists | Withheld; physically motivated only | Information-content backing (Chapter 6) + a marginal-channel region indistinguishable from zero | Marginal channel contribution positive across the observed range |

## 3.9 Conclusion of the chapter

This chapter set out to show that the cost-accuracy join is real, unfilled, and not an artifact of a missed study, and it did so by engaging each of the three bearing literatures substantively rather than by listing them. The instrument cost-estimating literature, anchored by NICM and corroborated by the Stahl parametric payload models, establishes with very high confidence that instrument development cost is a structured function of design attributes; it supplies the dissertation's cost regressor and its construct while withholding any accuracy axis [\[30\]](#ref-30), [\[40\]](#ref-40), [\[41\]](#ref-41), [\[42\]](#ref-42). The cost-growth and optimism-bias literature establishes that recorded actual cost is the construct to use, and it instructs the dissertation's variable definition and its measurement-error sensitivity analysis [\[38\]](#ref-38), [\[51\]](#ref-51), [\[110\]](#ref-110). The modern and machine-learning cost-estimation literature confirms that the structural boundary, cost-on-design, persists at the methodological frontier and supplies a measured noise floor for cost prediction [\[32\]](#ref-32), [\[35\]](#ref-35), [\[36\]](#ref-36). The cal/val literature, treated as a body, establishes that validated accuracy is a real, independently measured, uncertainty-quantified quantity for each major product family; it supplies the dissertation's dependent variable and the basis for requirement-normalization, while validating one product at a time and never reaching a cost axis or a population frontier [\[73\]](#ref-73), [\[74\]](#ref-74), [\[75\]](#ref-75), [\[77\]](#ref-77), [\[78\]](#ref-78), [\[79\]](#ref-79), [\[81\]](#ref-81), [\[83\]](#ref-83), [\[85\]](#ref-85), [\[86\]](#ref-86), [\[87\]](#ref-87).

The convergent structural limitation, visible from both the cost side and the accuracy side, is the chapter's central finding. Each literature holds two of the three axes the question needs, the missing axis differs between them, and no study brings validated accuracy and instrument cost into one population-level regression with shared design controls. The unfilled join is the gap, and from it follow the two propositions the dissertation tests: the concavity proposition H1, that validated accuracy is a concave function of instrument cost, against the linear null H0; and the sharper over-specification proposition, that an estimable spectral-channel count exists beyond which additional channels stop paying for themselves in validated accuracy. The literature motivates posing both propositions and supplies the predicted direction through the Simon tradition [\[14\]](#ref-14), [\[19\]](#ref-19), but it does not, and at the design stage cannot, supply the answer: the shape of \( g(\text{cost}) \) is unknown until estimated, and the dissertation is committed to the decision rule, an out-of-sample win for the concave model and a reliably negative \( g'' \), that will discriminate H1 from H0. The two elements of the argument this chapter carries, that the problem is real and that it is material, are now evidenced [\[17\]](#ref-17), [\[23\]](#ref-23), [\[40\]](#ref-40), [\[42\]](#ref-42), [\[85\]](#ref-85). The remaining elements, the design's address of the causal mechanism, its advantage over alternatives, and the acceptability of residual risk, pass forward to the theoretical framework, the data and measurement chapter, the research design, and the analysis plan, each with the evidence it will need already flagged. The chapter's work is to locate the gap precisely enough that the rest of the dissertation knows exactly what it must estimate and why no prior study has estimated it.


# Chapter 4: Data and Measurement

## 4.1 The chapter's answer: a defensible, three-source instrument-product table

This chapter's thesis is that the join at the heart of the dissertation can be built, and built honestly. The argument the dissertation makes stands or falls on a single empirical object: a table whose rows are instrument-product pairs and whose columns are a requirement-normalized validated accuracy metric, an instrument development cost, and the design and difficulty attributes that drive both. If that table cannot be assembled from real, independently produced records, the hedonic frontier of Chapter 5 is an abstraction with nothing to estimate. The answer this chapter defends is that the table is assemblable from three named, externally documented data sources, that every variable in it has an operational definition that maps to a real measurement, and that the known biases in the assembly are nameable, bounded, and either mitigated by construction or carried forward as scoped limitations rather than hidden. The measurement of validated accuracy is drawn from independent calibration-and-validation (cal/val) records rather than from design specifications, the single most consequential construct-validity decision in the entire design.

The chapter does not claim that the assembly is free of difficulty. It claims the opposite: that the difficulties are exactly the ones a careful observational study should expect when it joins records produced by communities that never intended their products to be linked, and that naming each difficulty is part of what makes the contribution defensible rather than merely suggestive. The cost community and the validation community do not share an instrument identifier, a version convention, or a unit of analysis. The aerosol community reports an expected-error envelope, the sea-surface-temperature community reports a bias and a robust standard deviation against drifting-buoy matchups, and the soil-moisture community reports an unbiased root-mean-square error against core validation sites. None of these numbers is comparable to another in raw form. The requirement-normalization described in this chapter is the device that makes them comparable, and the limitations section is candid that normalization mitigates but does not erase metric heterogeneity. Confidence in the assemblability of the table is moderate-to-high: the source records demonstrably exist and are cited here from real validation papers, but the linkage step has not yet been executed on the full population, so the count of successfully matched instrument-product rows is itself an expected quantity, not a result.

### 4.1.1 Problem frame for the measurement layer

The current state of measurement practice is two mature but disconnected reporting traditions. On the cost side, NASA maintains instrument-level development-cost records and the NASA Instrument Cost Model (NICM) that fits cost to design attributes [\[37\]](#ref-37), [\[42\]](#ref-42), [\[43\]](#ref-43). On the accuracy side, the cal/val literature reports validated retrieval error product by product, to high and externally audited standards [\[73\]](#ref-73), [\[77\]](#ref-77), [\[83\]](#ref-83), [\[85\]](#ref-85). The desired state is a single instrument-product table in which a cost and a validated accuracy sit in the same row, with the design attributes that confound their relationship held as controls. The gap is that no shared identifier, unit, or metric links the two traditions, so the table does not exist and has never been built. Leaving the gap unaddressed means the entire research question, whether validated accuracy is concave in instrument cost, cannot be posed empirically at all; it remains a conceptual conjecture with no data layer beneath it. This chapter closes the gap by specifying, source by source and variable by variable, how the table is constructed, and by being explicit about where the construction is solid and where it is a documented data-access dependency.

### 4.1.2 What this chapter carries forward from the prospectus

The prospectus fixed the three named data sources, the instrument-product unit of analysis, the requirement-normalized and sign-oriented dependent variable, the development-cost definition of the regressor, the design and difficulty control set, the coverage envelope, and the five limitations. This chapter does not revise any of those commitments; it elaborates each into an operational procedure with a worked construction for every product family and a measurement table that ties each construct to a definition, a source, and a scale. The notation is the prospectus notation, used unchanged: the estimating equation is \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), where \( g \) is the unknown smooth function whose curvature carries the concavity test, \( \mathbf{X} \) is the vector of design and difficulty controls entered linearly, \( \boldsymbol{\beta} \) is their coefficient vector, and \( e \) is an instrument-clustered error. Chapter 4 builds the data that populate `accuracy`, `cost`, and \( \mathbf{X} \); it does not estimate \( g \), and it reports no coefficient, no second derivative, and no over-specification channel count. Those belong to Chapters 5 and 6, and any number that appears in this chapter is an illustrative placeholder used to specify a procedure, labeled as such.

## 4.2 Named data source one: validated accuracy from Earthdata DAACs and the peer-reviewed cal/val literature

### 4.2.1 Provenance and access

The dependent variable originates in the validation records that NASA's Earthdata Distributed Active Archive Centers (DAACs) and the peer-reviewed cal/val literature maintain for each Level-2 and Level-3 retrieval product. The provenance of an accuracy number matters as much as its value, because the construct-validity claim of the dissertation is that the dependent variable measures delivered science accuracy and not a self-reported specification. A validated accuracy statistic earns its place in the table only when an independent comparison of the retrieved product against a reference standard produces it, documented either in DAAC product documentation or in the validation paper that the DAAC cites as authoritative for that product. The access path is the published record. For aerosol optical depth, the authoritative validation is the comparison of Moderate Resolution Imaging Spectroradiometer (MODIS) retrievals against the Aerosol Robotic Network (AERONET), whose expected-error envelope and federated-network construction are documented in the foundational algorithm and network papers [\[85\]](#ref-85), [\[87\]](#ref-87) and refined across collection updates and the Deep Blue algorithm [\[75\]](#ref-75), [\[81\]](#ref-81). For sea-surface temperature, the validation record is built from decades of in-situ matchups summarized in the half-century synthesis of satellite SST and its observational-needs companion [\[73\]](#ref-73), [\[74\]](#ref-74). For soil moisture, the authoritative record is the comparison of Soil Moisture Active Passive (SMAP) products against core validation sites with reported root-mean-square error and unbiased RMSE [\[77\]](#ref-77), [\[78\]](#ref-78), with the performance metrics themselves formalized by the soil-moisture community [\[83\]](#ref-83). For precipitation, the validation tradition runs from the Global Precipitation Climatology Project analysis to the Global Precipitation Measurement mission [\[86\]](#ref-86), [\[79\]](#ref-79).

These count as the access path because each is a real, resolvable publication with a digital object identifier, and each reports a validated error statistic for a named product. The connection to the construct is that an error statistic produced by an independent reference comparison is, by construction, a measure of delivered accuracy and not of design intent, precisely the property the dependent variable requires. The cal/val community's own institutional practice reinforces this: validation is a defined mission phase with stated objectives to calibrate, verify, and validate science-product accuracy against Level-1 mission science requirements, as the SMAP cal/val record states explicitly [\[71\]](#ref-71). One caveat is that the access path is the published record rather than a single machine-readable accuracy database; assembling the dependent variable therefore requires extraction from heterogeneous documents, a labor cost and a source of transcription risk rather than a conceptual obstacle. The objection a skeptic would raise, that DAAC-cited validation papers might over-report accuracy for products that met requirements, is the publication-bias threat treated in Section 4.8 and carried forward as a named limitation, not a reason to abandon the source.

### 4.2.2 Coverage and the unit at which accuracy is reported

Coverage on the accuracy side is product-family-wide and deep within each family, but uneven across families, and the chapter is candid about that unevenness. Aerosol optical depth is among the most heavily validated geophysical variables in the entire Earth-observing record, with validation studies spanning sensors, collections, and regions, including intercomparisons of MODIS against AERONET at hundreds of ground stations [\[75\]](#ref-75), regional validations of MODIS aerosol products [\[62\]](#ref-62), [\[61\]](#ref-61), and cross-sensor validations of Spinning Enhanced Visible Infrared Radiometer aerosol retrievals against both AERONET and MODIS [\[69\]](#ref-69). Sea-surface temperature is similarly deep, with multi-source validations against Argo floats and drifting buoys reporting root-mean-square errors by sensor class, infrared versus passive-microwave [\[63\]](#ref-63), and operational near-real-time products carrying their own accuracy characterizations [\[58\]](#ref-58). Soil moisture is well covered for the SMAP era through core-validation-site comparisons and independent regional assessments [\[77\]](#ref-77), [\[54\]](#ref-54), [\[59\]](#ref-59). Precipitation and land-surface temperature are covered but with fewer instrument-product rows in the radiometer-relevant population [\[65\]](#ref-65), [\[55\]](#ref-55). The unit at which accuracy is reported is the product, not the instrument: a single radiometer that yields several validated products contributes one validated accuracy number per product, which is why the unit of analysis is the instrument-product pair and not the instrument. This reporting convention is a feature, not a flaw, because it supplies multiple accuracy observations per expensive instrument and gives the regression more rows than instruments, at the cost of a within-instrument dependence structure that Chapter 5 addresses by clustering.

### 4.2.3 Known biases in the accuracy source

Three biases are known at the outset and stated here so they are not discovered later as surprises. The first is metric heterogeneity: the aerosol community reports expected-error compliance and the fraction of retrievals within an envelope [\[85\]](#ref-85), [\[81\]](#ref-81), the SST community reports a bias and a robust standard deviation [\[73\]](#ref-73), and the soil-moisture community reports RMSE and unbiased RMSE against core sites [\[77\]](#ref-77), [\[83\]](#ref-83). These are not the same quantity, and averaging them in raw form would be meaningless. The requirement-normalization of Section 4.4 is the response. The second is reference-network heterogeneity: AERONET, drifting buoys, and soil-moisture core sites are themselves imperfect references with their own uncertainty budgets, and a product validated against a noisier reference will appear less accurate for reasons of the reference rather than the instrument. This is the validation-reference-ceiling concern, named here and probed analytically in Chapters 6 and 7. The third is selection in which products get validation papers written about them, which correlates with whether the product met its requirement; this is the publication-bias component of the survivorship threat in Section 4.8. Naming these three biases at the source level, rather than at the end, is the discipline that lets the later chapters treat each as a named objection with a specific design feature attached.
## 4.3 Named data sources two and three: NICM cost records and NTRS design specifications

### 4.3.1 NICM as the cost regressor: provenance, access, and a documented dependency

The cost regressor originates in NICM-class instrument development-cost records. NICM is the instrument-level cost-estimating relationship NASA maintains, fit on a curated database of flown instruments and updated across versions. The published documentation establishes two things: that instrument cost is systematically predictable from design attributes, and that NASA holds the underlying records at the instrument level [\[37\]](#ref-37), [\[42\]](#ref-42), [\[43\]](#ref-43). The provenance of the cost variable is a maintained NASA model and its supporting database; the access path is JPL and NASA cost channels rather than a public citable artifact. This distinction carries weight, so it is stated plainly. The corpus contains the NICM documentation, which is the authority for the cost construct, but it does not and cannot contain the instrument-level cost values themselves, which are not a public dataset. The dissertation treats this as a data-access dependency, not as a citation. No number here is attributed to a NICM paper as if the paper reported that instrument's cost. The papers are cited as the authority for what the cost construct is and for the claim that the records exist and are maintained; the values are obtained at execution through JPL channels. Stating this as an explicit dependency, rather than papering over it with a pseudo-citation, is required by the design-stage honesty that governs every chapter.

NICM is the appropriate cost source because it is the canonical NASA instrument-cost authority, defines cost at the instrument level, and normalizes to constant-year dollars, all of which the documentation establishes [\[37\]](#ref-37), [\[42\]](#ref-42). Instrument development cost, so defined, is a near-sufficient statistic for the embodied engineering effort, component quality, and calibration rigor of the build, and those embodied qualities are what the hedonic argument expects to translate into accuracy. The wider parametric-cost-model literature reinforces the point, demonstrating independently that cost is a structured index of design attributes rather than noise, both for instruments through NICM and for optical payloads through the telescope-cost family surveyed by Stahl [\[46\]](#ref-46). Two caveats apply. NICM cost is development cost, not life-cycle cost, so operations, reprocessing, and algorithm maintenance fall outside the variable by construction. Cost records are also subject to the optimism bias and cost-growth dynamics documented in the project-cost literature [\[38\]](#ref-38), [\[51\]](#ref-51), which is the source of the measurement-error-in-the-regressor concern of Section 4.8. A reviewer would press the objection that development cost omits the substantial post-launch spending that also buys accuracy through reprocessing and algorithm improvement. That objection is conceded and bounded: because the claim concerns instrument investment specifically, development cost is the appropriate construct, and the boundary is stated so the estimate is never misread as a total-cost frontier.

### 4.3.2 NTRS design specifications: provenance, access, and coverage

The design control set and the channel-count variable that carries the over-specification test originate in the NASA Technical Reports Server (NTRS) and in mission instrument handbooks. NTRS is a public, resolvable archive, and the corpus includes NTRS records that document instrument design and radiometric-calibration characteristics directly, including vicarious and on-board calibration assessments for the Visible Infrared Imaging Radiometer Suite [\[76\]](#ref-76), [\[56\]](#ref-56), MODIS radiometric-calibration improvements [\[80\]](#ref-80), and CubeSat radiometer calibration and validation [\[66\]](#ref-66). The provenance of the design variables is therefore the engineering and calibration literature for each instrument, and the access path is the public NTRS archive plus published instrument handbooks. Coverage is strong for the design attributes that NTRS and handbooks document well, principally spectral-channel count and center wavelengths, swath width, spatial resolution, and calibration approach, the last of which NTRS calibration assessments describe explicitly as on-board blackbody, solar-diffuser, vicarious, and lunar methods [\[76\]](#ref-76), [\[56\]](#ref-56), [\[80\]](#ref-80). Coverage is thinner for as-built mass and power on some older instruments. The matching protocol of Chapter 6 handles that gap rather than fabrication: an instrument whose mass or power cannot be confirmed from a primary record is flagged in the unmatched log, not assigned an invented value.

NTRS is the appropriate design source because it is the authoritative public archive for NASA instrument engineering documentation and documents the specific attributes the control set requires. Design attributes drawn from engineering records, rather than from the cost model or the validation paper, are independent of both the regressor and the dependent variable, which is the independence the control set needs to absorb confounding rather than to induce it. One caveat is that NTRS documents are heterogeneous in completeness and format, so extraction is per-instrument and auditable rather than automatic. The chapter's confidence that the design control set can be populated is high for channel count, swath, resolution, and calibration approach, and moderate for as-built mass and power, with the gap logged rather than smoothed over.

## 4.4 The dependent variable: requirement-normalized, sign-oriented validated accuracy

### 4.4.1 Why raw error is not usable and what replaces it

The dependent variable cannot be raw retrieval error, because raw error units differ across geophysical variables and are therefore not comparable across product families. An aerosol optical depth error is dimensionless and on the order of hundredths; a sea-surface-temperature error is in kelvin and on the order of tenths; a soil-moisture error is in volumetric water content and on the order of hundredths of cubic-meters-per-cubic-meter; a precipitation error is in millimeters per unit time. Regressing a stacked column of such incommensurable numbers on cost would be meaningless. The construct that replaces raw error is requirement-normalized, sign-oriented validated accuracy: each product's validated error is expressed relative to that product's stated mission accuracy requirement, yielding a unitless quantity, and the sign is oriented so that the variable increases in accuracy. A product that meets its requirement exactly sits at the requirement boundary; a product that beats its requirement sits on the accurate side; a product that misses its requirement sits on the inaccurate side. The construct is therefore not raw error and not raw accuracy but requirement compliance expressed as a continuous, comparable, increasing-in-accuracy score.

This construction is sound because mission accuracy requirements are themselves documented, externally, in the same engineering and validation records that report the error, and the validation communities already think in requirement-compliance terms. The aerosol community's expected-error envelope is itself a requirement-referenced construct [\[85\]](#ref-85), [\[81\]](#ref-81), the SST observational-needs literature states accuracy requirements explicitly [\[74\]](#ref-74), and the soil-moisture community formalized application requirements alongside its performance metrics [\[83\]](#ref-83). Normalizing each error to its own product's requirement makes meeting-the-requirement the common construct across families, which is comparable in a way that raw error is not. The requirement is also the quantity the mission was actually built to achieve, so a frontier defined in requirement-compliance units is a frontier in the units the investment decision itself uses. One caveat is that requirement-normalization makes the dependent variable comparable in a relative sense but does not make the underlying references equally precise across families. A kelvin of SST error against a drifting buoy and a hundredth of soil moisture against a core site are normalized to a common scale, but the references behind them carry different fractional uncertainties, which is the reference-ceiling caveat carried to Chapter 6. The objection that requirement-normalization could distort the frontier if requirements were set with inconsistent strictness across families is acknowledged, and it is one motivation for the difficulty control of Section 4.6 and for the family-level sensitivity analysis planned in Chapter 6.

### 4.4.2 Worked construction by product family

The construction is specified per family so that it is auditable rather than abstract.

**Aerosol optical depth (MODIS validated against AERONET).** The validated accuracy is the agreement of retrieved aerosol optical depth with co-located AERONET observations, expressed through the published expected-error envelope and the fraction of retrievals falling within it [\[85\]](#ref-85), [\[87\]](#ref-87). The error is the deviation of MODIS aerosol optical depth from the AERONET reference at matched space and time, summarized as a root-mean-square error and an expected-error compliance fraction in the validation literature [\[75\]](#ref-75), [\[81\]](#ref-81), [\[62\]](#ref-62). The requirement reference is the mission expected-error specification for the product. The sign orientation places higher compliance and lower deviation on the accurate side. The Deep Blue algorithm's per-retrieval uncertainty estimate [\[81\]](#ref-81) and the cross-sensor validations [\[69\]](#ref-69) supply the breadth of matchups that make the family's accuracy number stable.

**Sea-surface temperature (infrared and passive-microwave radiometers validated against in-situ).** The validated accuracy is the bias and robust standard deviation of retrieved SST against drifting buoys and Argo floats, the quantities the SST validation tradition reports [\[73\]](#ref-73). The multi-source validation of infrared and passive-microwave radiometers against Argo reports root-mean-square errors by sensor class [\[63\]](#ref-63), which is the raw error that requirement-normalization converts to a comparable score against the SST observational requirement [\[74\]](#ref-74). The sign orientation places smaller bias and smaller robust standard deviation on the accurate side.

**Soil moisture (SMAP validated against core validation sites).** The validated accuracy is the unbiased root-mean-square error of retrieved soil moisture against spatially averaged core-validation-site measurements, the SMAP cal/val standard [\[77\]](#ref-77), [\[78\]](#ref-78). The community's formalized performance metrics, RMSE and unbiased RMSE with stated application requirements, supply both the error and the requirement against which it is normalized [\[83\]](#ref-83). Independent regional assessments and passive-only retrievals provide additional instrument-product rows [\[54\]](#ref-54), [\[59\]](#ref-59), [\[68\]](#ref-68). The sign orientation places smaller unbiased RMSE on the accurate side.

**Precipitation (GPCP and GPM-era products validated against gauges and ground radar).** The validated accuracy is the agreement of retrieved precipitation with gauge and ground-radar references, as in the validation of integrated multi-satellite retrievals against polarimetric ground radar [\[65\]](#ref-65), normalized to the precipitation product's accuracy requirement [\[86\]](#ref-86), [\[79\]](#ref-79). The sign orientation places smaller error against the reference on the accurate side.

**Land-surface temperature and emissivity (validated against in-situ and water-surface sites).** The validated accuracy is the agreement of retrieved land-surface temperature with reference measurements, drawing on coastal LST retrieval validation [\[55\]](#ref-55) and on automated water-surface validation sites for thermal-infrared products [\[84\]](#ref-84), normalized to the LST accuracy requirement. The sign orientation places smaller temperature error on the accurate side.

Across all families the construction is identical in form: take the validated error from the independent reference comparison, divide by the product's stated requirement to obtain a unitless compliance score, and orient the sign so the variable increases in accuracy. The per-family worked formulas are collected in Appendix A of the backmatter so the construction is reproducible.

### 4.4.3 Confidence in the dependent variable

Confidence that the dependent variable can be constructed as specified is high for the four best-covered families, aerosol, SST, soil moisture, and precipitation, because each has a documented requirement and a documented validated error in real publications cited above. Confidence is moderate for land-surface temperature and any thinner family, where fewer instrument-product rows are available and the requirement reference is less uniformly stated. The evidence that would raise confidence is a completed extraction pass that confirms a validated error and a stated requirement for every product in the population; the evidence that would lower it is the discovery that a family reports validated error in a form that resists requirement-normalization, in which case that family would be flagged and either reconstructed or excluded with the exclusion logged. No family's accuracy number is invented; a family that cannot be normalized is dropped, not filled.

## 4.5 The cost variable: development cost in constant-year dollars

### 4.5.1 Operational definition and boundary

The cost regressor is total instrument development cost in constant-year dollars, taken from NICM-class records [\[37\]](#ref-37), [\[42\]](#ref-42). The operational definition is deliberately narrow. It is development cost, the cost of designing, building, integrating, and testing the instrument through delivery, not life-cycle cost. Operations, ground-segment costs, reprocessing campaigns, and algorithm-maintenance spending are excluded by construction. The constant-year-dollar normalization removes inflation so that an instrument built in one era is comparable in cost to one built in another, which the NICM documentation supports as standard practice [\[37\]](#ref-37). The boundary is stated as a construct decision, not as an oversight: because the dissertation's claim concerns returns to instrument investment specifically, development cost is the correct construct, and the wider life-cycle spending that also contributes to delivered accuracy through post-launch algorithm work is held out of the regressor and named as a boundary in Section 4.8.

The development-cost definition is appropriate because NICM defines and maintains cost at exactly this boundary and at the instrument level [\[37\]](#ref-37), [\[42\]](#ref-42), [\[43\]](#ref-43). The embodied build quality the hedonic argument cares about is purchased during development, so development cost is the dollar quantity most tightly coupled to the embodied accuracy-relevant qualities of the instrument. The parametric-cost-model literature reinforces this through its consistent treatment of development cost as the quantity predicted from design attributes [\[46\]](#ref-46). One caveat is the boundary itself: a frontier estimated on development cost is a development-cost frontier, and it would understate the total dollars behind a product's accuracy to the extent that post-launch spending matters. The objection that two instruments with identical development cost might deliver very different accuracy because one received far more post-launch algorithm investment is conceded, and it is one reason the design is reduced-form and honest that the cost effect is an embodied-investment effect rather than a single clean mechanism.
### 4.5.2 The cost-record-reliability concern as a measurement property

Cost records are not error-free, and treating them as if they were would be a measurement-validity failure. The project-cost literature documents systematic optimism bias and cost growth in large engineering projects, with reference-class forecasting proposed as the corrective [\[51\]](#ref-51), and characterizes the distribution of cost overruns directly [\[38\]](#ref-38). For this dissertation the implication is specific: the cost regressor carries measurement error, partly from version mismatches between the cost record and the design record, and partly from the optimism-and-growth dynamics that make a recorded cost an imperfect measure of true embodied investment. This is not a reason to distrust the variable but a property to be managed. The management has three parts: instrument-version matching in the assembly step so that the cost record and the design record refer to the same build, sensitivity analysis that drops ambiguously matched instruments to test whether the frontier shape survives their removal, and treatment of cost measurement error as an internal-validity threat in Chapter 5. Stating the reliability concern here, where the variable is defined, lets Chapter 5 treat it as a known and bounded threat rather than as a discovered defect.

## 4.6 Design and difficulty controls: the X vector

### 4.6.1 The design controls

The control vector \( \mathbf{X} \) absorbs the systematic reasons an instrument received its cost, so that the cost effect estimated by \( g \) is not confounded with the design choices that drive cost. The design controls are spectral-channel count, swath width, spatial resolution, calibration approach as a categorical, instrument mass and power as built, and mission epoch. Spectral-channel count carries the over-specification test of Chapters 5 and 6 and is therefore both a control and the object of a dedicated flexible term; it is the number of spectral channels the instrument carries, taken from NTRS design records and instrument handbooks [\[76\]](#ref-76), [\[56\]](#ref-56). Swath width and spatial resolution are standard imaging-geometry attributes from the same records. Calibration approach is a categorical coded as on-board blackbody, solar diffuser, vicarious, or lunar, a coding the NTRS calibration literature supports directly, since those records describe instruments carrying solar diffusers and V-groove blackbodies for reflective and thermal bands [\[76\]](#ref-76) and instruments calibrated vicariously against stable Earth and lunar targets [\[56\]](#ref-56), [\[80\]](#ref-80), [\[66\]](#ref-66). Instrument mass and power as built are the standard NICM design attributes [\[37\]](#ref-37), used here as controls because they index instrument scale independently of channel count. Mission epoch is a technology-vintage control that absorbs the secular improvement in radiometer technology over time, which the cost-model literature documents as a real effect, with telescope cost falling and capability rising as a function of year [\[46\]](#ref-46); the same vintage effect on the accuracy side is exactly the rival explanation that Chapter 7 must hold off, and the epoch control is the design feature that does so.

This control set is justified because each attribute is documented in independent engineering records and each is a plausible driver of both cost and accuracy. Conditioning on these attributes removes the most plausible confounders of the cost-accuracy relationship, which is the selection-on-observables requirement the identification strategy depends on. One caveat is that the control set is finite and pre-specified to preserve degrees of freedom in a small sample, so it cannot absorb an unobserved driver that is orthogonal to all of these attributes; that residual is the omitted-variable threat of Chapter 5. The objection that some confounder, for instance an unmeasured difference in team experience, raises both cost and accuracy and would masquerade as a steeper cost effect is acknowledged, and it is precisely why the design is honest that identification rests on selection-on-observables within common support and not on randomization.

### 4.6.2 The retrieval-difficulty control

The retrieval-difficulty control captures the intrinsic hardness of the geophysical variable being retrieved, independent of the instrument. Soil moisture under dense vegetation is harder to retrieve accurately than clear-sky sea-surface temperature, regardless of how much the instrument cost, because vegetation attenuates and confounds the L-band signal in ways the retrieval must model and partly cannot [\[59\]](#ref-59), [\[68\]](#ref-68), and because the soil-moisture community's own performance-metrics framework recognizes that achievable accuracy is bounded by retrieval conditions and not only by instrument quality [\[83\]](#ref-83). Without a difficulty control, an estimator would confound the cost effect with the difficulty of the problems that expensive instruments were built to solve: if harder retrievals were systematically assigned to more expensive instruments, naive estimation would understate the cost effect, and if easier retrievals were assigned to cheaper instruments, it would overstate concavity. The difficulty control, operationalized as a categorical or ordinal hardness index tied to the geophysical variable and its retrieval conditions, is the design feature that breaks this confound. The documented dependence of achievable accuracy on retrieval conditions across families supports it [\[83\]](#ref-83), [\[59\]](#ref-59), [\[55\]](#ref-55). Conditioning on difficulty removes the difficulty-assignment confound from the cost coefficient. One caveat is that difficulty is itself measured coarsely, as an index rather than a continuous physical quantity, so it absorbs the gross difficulty differences across families and conditions but not fine within-family gradients; the residual is a named limitation and a target for the common-support restriction of Chapter 5, which keeps comparisons within regions where difficulty is genuinely comparable.

## 4.7 Coverage of the assembled table

The intended population is NASA and NASA-partnered Earth-observing passive radiometers that have both a NICM-class development-cost record and a documented Level-2 or Level-3 validation record, spanning roughly the MODIS era to the present. This envelope is a deliberate intersection of three conditions, and each condition narrows the population for a stated reason. The first condition, a NICM-class cost record, restricts the set to instruments NASA tracked in its cost database, which is the only way to populate the regressor. The second condition, a documented validation record, restricts it to instruments whose products were independently validated, which is the only way to populate the dependent variable. The third condition, passive radiometry, excludes active sensors such as radars and lidars, because their cost drivers, transmit power, antenna or telescope aperture, and pulse design, and their accuracy metrics are not commensurable with passive radiometry; pooling them would violate the comparability that identification requires. The result is a population on the order of dozens of instruments and a larger number of instrument-product rows, since each multi-product radiometer contributes several rows.

This coverage envelope follows because the three conditions are jointly necessary to build a row of the table: an instrument missing any one of them cannot supply a complete observation and therefore cannot enter the regression honestly. The radiometer-only boundary rests on the cost-model literature's own recognition that different instrument classes have different cost drivers, with telescope and optical-payload cost driven by aperture and wavelength [\[46\]](#ref-46) in ways that do not transfer to active microwave sensors. One caveat is that the population is small by econometric standards, which constrains how flexibly \( g \) can be estimated and is one reason the estimator of Chapter 5 is partially linear and semiparametric rather than fully nonparametric. The objection that excluding active sensors limits generality is conceded and converted into a scoped extension in Chapter 7: a parallel frontier for active sensors is a companion study, not a defect of this one, because pooling incommensurable classes would buy breadth at the cost of identification.

The coverage also has a temporal lower bound at roughly the MODIS era. The reason is practical and is stated as such: the modern, well-documented combination of a maintained instrument-level cost record and a rigorous, requirement-referenced validation record is reliably available for instruments of that era and after, and becomes patchy before it. Extending the population earlier would add instruments for which either the cost record or the validation record is incomplete, which would either introduce missing-data bias or force fabrication, neither of which is acceptable. The lower bound is therefore a data-quality boundary, not an arbitrary cutoff, and it is reported so the external-validity claim of Chapter 7 is correctly scoped to the modern era.

## 4.8 Data quality, validation against known values, and the named biases

### 4.8.1 Validation of the assembled variables against known values

Before the table is used, each variable is validated against externally known values, the data-quality discipline that catches assembly errors. The cost variable is validated by checking that the constant-year-dollar development costs are monotone-consistent with the NICM design-attribute relationships: an instrument with more channels, larger mass, and more elaborate calibration should not record a development cost wildly below a simpler instrument once epoch is accounted for, because the cost model itself predicts the opposite [\[37\]](#ref-37), [\[42\]](#ref-42). A row that violates this expectation flags a likely version-mismatch or transcription error for re-checking rather than being silently retained. The accuracy variable is validated by checking each extracted validated-error value against the value reported in the source publication, so that the requirement-normalized score traces back to a real published number; an SST root-mean-square error of roughly half a kelvin for an infrared radiometer against Argo, for instance, is consistent with the multi-source validation record [\[63\]](#ref-63), and an extracted value far outside that family's published range is re-checked before it enters the table. The design variables are validated against instrument handbooks and NTRS calibration assessments [\[76\]](#ref-76), [\[56\]](#ref-56), [\[80\]](#ref-80), so that a recorded channel count or calibration approach matches the primary engineering record. This three-way validation, cost against the cost model's qualitative predictions, accuracy against the source publication's reported value, and design against the engineering record, is the data-quality gate, and every value that fails it is re-checked or logged, never imputed by fiat.

### 4.8.2 The five named biases, carried forward from the prospectus and elaborated

The prospectus named five limitations, and this chapter elaborates each into a concrete data-quality property with a mitigation.

**Small sample.** The population is dozens of instruments and a larger but still modest number of instrument-product rows. The consequence is that the cost function \( g \) cannot be estimated with full nonparametric flexibility without overfitting. The mitigation, specified here and executed in Chapters 5 and 6, is the partially linear semiparametric form with a shape-constrained smoother for \( g \), a limited pre-specified control set to preserve degrees of freedom, and a held-out predictive test so that in-sample curvature alone cannot be mistaken for a real frontier. The small sample is a constraint on method, not a reason the question cannot be asked.

**Metric heterogeneity.** Validated accuracy is reported differently across families, expected-error compliance for aerosol [\[85\]](#ref-85), [\[81\]](#ref-81), bias and robust standard deviation for SST [\[73\]](#ref-73), unbiased RMSE for soil moisture [\[77\]](#ref-77), [\[83\]](#ref-83). The requirement-normalization of Section 4.4 is the primary mitigation, converting each to a comparable compliance score, and a family-level sensitivity analysis in Chapter 6 tests whether the frontier shape is robust to dropping any single family. Normalization mitigates but does not eliminate the heterogeneity, which is stated rather than hidden.

**Cross-community linkage error.** The cost records and the validation records were produced by different communities and were never designed to be joined, so linking them requires matching instrument identity and version across record systems that share no common key. This is a documented source of potential error, addressed by the explicit NICM-to-NTRS matching protocol of Chapter 6, by logging every unmatched or ambiguously matched instrument, and by sensitivity analysis that drops ambiguous matches. The linkage error is named as a property of joining cross-community records, which is what makes it manageable.

**Survivorship and publication bias.** Instruments that flew, validated, and published are over-represented relative to instruments that failed or underperformed, and validation papers are more likely to be written for products that met requirements [\[38\]](#ref-38). If failure correlates with cost, this could bias the frontier. The mitigation is definitional: the population is restricted by construction to flown instruments with a validation record, so the estimand is explicitly the frontier among instruments that reached validated operations, and the claim is not extended to the design-and-fail population. The bias is bounded by being made part of the estimand's definition rather than left to contaminate a broader claim.

**Development-cost-only boundary.** Cost is development cost, not life-cycle cost, so post-launch operations, reprocessing, and algorithm maintenance fall outside the variable [\[37\]](#ref-37). Because the claim concerns instrument investment, this is the correct construct, but the boundary means the frontier is a development-cost frontier and must not be read as a total-cost frontier. The boundary is stated as a scope condition on interpretation.

A sixth property, the validation-reference ceiling, is elevated here from the prospectus's discussion because it is fundamentally a measurement issue. The in-situ references, AERONET for aerosol [\[87\]](#ref-87), drifting buoys and Argo for SST [\[73\]](#ref-73), [\[63\]](#ref-63), and core sites for soil moisture [\[77\]](#ref-77), [\[83\]](#ref-83), are themselves imperfect, with their own uncertainty budgets. A very accurate instrument validated against a reference that is itself only so precise will appear to plateau in accuracy for reasons of the reference rather than the instrument, which could masquerade as concavity at the high-cost end. This is a genuine alternative to the H1 mechanism and is treated as such: Chapter 6 probes whether any observed flattening coincides with the precision limits of the validation references, and Chapter 7 carries it as the leading rival explanation. Naming it as a measurement property in the data chapter, rather than only as a discussion-section caveat, is what gives the later probe a concrete target.

### 4.8.3 How the measurement layer advances the argument

The measurement layer carries two of the dissertation's five argument elements directly. It evidences that the problem is real, because it documents that cost and validated accuracy are produced by separate communities, NICM on the cost side [\[37\]](#ref-37), [\[42\]](#ref-42) and the cal/val literature on the accuracy side [\[73\]](#ref-73), [\[77\]](#ref-77), [\[85\]](#ref-85), and are never jointly modeled, which is the gap the dissertation fills. It also carries much of the residual-risk element, because the small-sample, metric-heterogeneity, linkage, survivorship, and reference-ceiling risks are exactly the risks this chapter names, bounds, and attaches mitigations to. The chapter does not by itself establish that the design addresses the causal mechanism or that it beats alternatives; those are the work of Chapters 5 and 6. But it establishes that the data layer beneath those chapters is real, that every variable maps to a documented measurement, and that the known biases are managed rather than ignored. That is the precondition for everything downstream, and it is the standard this chapter holds itself to.
## 4.9 Ethics, access, and provenance transparency

The data are non-human-subjects engineering and Earth-observation records, so the ethics of this study are not the ethics of human-subjects research but the ethics of access, attribution, and transparency. Three commitments govern the data work. The first is provenance transparency: every accuracy value traces to a published validation record with a resolvable identifier, every design value traces to an NTRS or handbook engineering record, and every cost value traces to a NICM-class record obtained through the appropriate JPL and NASA channel. No value enters the table without a documented source, and the assembled table records its provenance per cell so that any number can be audited back to its origin. The second commitment concerns the cost-access dependency: because instrument-level NICM cost values are not a public artifact, the dissertation is explicit that the cost variable is obtained through institutional channels rather than from the literature, and it does not represent any published paper as the source of a specific instrument's cost. This is both an honesty requirement and an access requirement, stated so that a reader understands the cost column is a documented data-access dependency to be satisfied at execution, not a public download. The third commitment is attribution: the validation communities whose published records supply the dependent variable are cited as the authorities for those values, because the credibility of the dependent variable rests entirely on the independence and rigor of their work [\[73\]](#ref-73), [\[77\]](#ref-77), [\[83\]](#ref-83), [\[85\]](#ref-85), [\[87\]](#ref-87).

A final transparency point concerns the boundary between what this chapter has established and what remains a dependency. The chapter has established that the three named sources exist, that each variable has an operational definition mapping to a documented measurement, and that the known biases are named and bounded. It has not executed the assembly, so the count of successfully matched instrument-product rows, the realized common-support region in cost, and the realized distribution of channel counts are expected quantities to be determined at execution, not results reported here. Any number in this chapter that looks like a finding, a representative SST error of about half a kelvin, a population on the order of dozens of instruments, is an illustrative or order-of-magnitude statement used to make the construction concrete. Such numbers stay consistent with the published ranges cited and are explicitly not empirical results of the assembled dataset. The design-stage guardrail that governs every chapter governs this one: the data layer is specified in full, its quality controls and biases are stated in full, and the realized numbers wait for the assembly that Chapter 6 pre-registers and that execution will run.

## 4.10 Measurement table

The following table operationalizes every variable in the instrument-product table, tying each construct to its operational definition, its source, and its scale. It is the chapter's consolidated measurement specification and the reference that Chapters 5 and 6 inherit.

**Table 4.1. Measurement table: construct, operational definition, source, and scale.**

| Construct | Operational definition | Source | Scale |
|-----------|------------------------|--------|-------|
| Validated accuracy (dependent) | Validated retrieval error from an independent reference comparison, divided by the product's stated mission accuracy requirement, sign-oriented to increase in accuracy (requirement-compliance score) | Earthdata DAAC documentation and peer-reviewed cal/val papers per family: aerosol [\[85\]](#ref-85), [\[87\]](#ref-87), [\[75\]](#ref-75), [\[81\]](#ref-81); SST [\[73\]](#ref-73), [\[63\]](#ref-63); soil moisture [\[77\]](#ref-77), [\[78\]](#ref-78), [\[83\]](#ref-83); precipitation [\[86\]](#ref-86), [\[79\]](#ref-79), [\[65\]](#ref-65); LST [\[55\]](#ref-55), [\[84\]](#ref-84) | Unitless, continuous, increasing in accuracy |
| Cost (regressor of interest) | Total instrument development cost in constant-year dollars; excludes operations, reprocessing, algorithm maintenance | NICM-class instrument records (construct authority [\[37\]](#ref-37), [\[42\]](#ref-42), [\[43\]](#ref-43)); values via JPL/NASA channels (data-access dependency) | Constant-year US dollars, continuous |
| Spectral-channel count | Number of spectral channels carried by the instrument; carries the over-specification test | NTRS design records and instrument handbooks [\[76\]](#ref-76), [\[56\]](#ref-56) | Count, integer |
| Swath width | Cross-track imaging swath of the instrument | NTRS design records and handbooks [\[76\]](#ref-76), [\[56\]](#ref-56) | Kilometers, continuous |
| Spatial resolution | Nominal ground sampling distance of the product | NTRS design records and handbooks [\[76\]](#ref-76), [\[56\]](#ref-56) | Meters or kilometers, continuous |
| Calibration approach | Primary radiometric-calibration method | NTRS calibration assessments [\[76\]](#ref-76), [\[56\]](#ref-56), [\[80\]](#ref-80), [\[66\]](#ref-66) | Categorical: on-board blackbody / solar diffuser / vicarious / lunar |
| Instrument mass (as built) | Delivered instrument mass | NICM-class design attributes [\[37\]](#ref-37) | Kilograms, continuous |
| Instrument power (as built) | Delivered instrument power | NICM-class design attributes [\[37\]](#ref-37) | Watts, continuous |
| Mission epoch | Technology-vintage year of the instrument; absorbs secular technology improvement | NTRS records and handbooks; cost-model vintage effect [\[46\]](#ref-46) | Year, continuous or binned |
| Retrieval difficulty | Intrinsic hardness of the geophysical variable and its retrieval conditions, independent of the instrument | Family cal/val literature and performance-metrics frameworks [\[83\]](#ref-83), [\[59\]](#ref-59), [\[55\]](#ref-55) | Ordinal/categorical hardness index |
| Unit of analysis | Instrument-product pair; cost attributed at instrument level and shared across that instrument's products; within-instrument dependence handled by clustering (Chapter 5) | Construction across the three sources | One row per validated product |

The table is the operational core of the chapter. Each row converts a construct named in the prospectus into a measurement with a real source and a defined scale, and the citations in the source column are all real entries in the assembled corpus. The variables `accuracy`, `cost`, and the columns of \( \mathbf{X} \) in the estimating equation \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \) are exactly the constructs in this table, populated from exactly these sources at exactly these scales. With the data layer specified to this level, Chapter 5 can take the table as given and turn to the estimand, the estimator, and the identification strategy that recover the curvature of \( g \) from it.


# Chapter 5: Research Design and Identification

## 5.1 The answer this chapter delivers

The methodological claim of this chapter is that the shape of the accuracy-cost relationship for Earth-science radiometers can be estimated credibly, from observational data and at small sample size, by a partially linear semiparametric regression in which instrument development cost enters through a shape-constrained smooth function while design and difficulty attributes enter linearly, identified by selection-on-observables within a region of common support and made comparable by covariate balancing across cost strata. That is the answer; the rest of the chapter develops it rather than building up to it. The estimand is the curvature of the conditional expectation of validated accuracy in the cost dimension, the estimator is \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \) with \( g \) carrying the concavity test, and identification rests on the argument that conditional on the control set the variation in cost is as good as random with respect to accuracy. Every threat that could break that argument is named in advance and given a mitigation that is part of the design rather than a repair applied after the fact. The over-specification proposition is tested by a sharper instrument than aggregate concavity: a flexible spectral-channel-count term whose marginal contribution to accuracy is traced as a function of channel count, with the over-specification edge defined as the lower bound of the range over which that marginal contribution is statistically indistinguishable from zero.

Stating the design answer first fixes the standard this chapter holds itself to. A research design for a single, falsifiable contribution is judged not by how elaborate its machinery is but by whether the machinery actually isolates the quantity the contribution is about and rejects the quantity it is not about. The contribution is the second derivative of \( g \) over common support and the channel-count edge; everything in the estimator and the identification strategy exists to estimate those two objects without confounding them with the difficulty of the retrieval problem, the technology epoch in which the instrument was built, or the publication and survivorship filters that placed the instrument in the sample at all. Where the design cannot fully neutralize a threat, the chapter says so and downgrades the confidence of the resulting estimate rather than overstating what the design buys. That honesty is not a concession; it is the discipline that makes a design-stage methodological chapter worth reading before any number has been computed.

The problem this chapter addresses can be framed in the same current-state, desired-state, gap, consequence structure that organizes the dissertation. The current state of empirical practice, were one to attempt this estimate naively, would be to regress validated accuracy on instrument cost directly, read the slope, and call a curved fit a frontier. The desired state is an estimate of the curvature that survives the obvious objection that expensive instruments are expensive for reasons that also make them accurate, so that a curved fit might reflect the sorting of instruments to cost levels rather than any return to the dollars themselves. The gap is that no design tailored to this specific inversion of the hedonic problem yet exists; the closest precedents are the cost-model literature, which regresses cost on attributes rather than accuracy on cost [\[42\]](#ref-42), [\[46\]](#ref-46), and the program-evaluation literature, which supplies the identification discipline but was developed for treatment effects rather than for the curvature of a continuous dose-response surface [\[105\]](#ref-105). The consequence of closing the gap badly, with a naive regression, is an estimate that would be rejected by any careful reader the moment selection was raised, and so would fail the decision-relevance standard the dissertation sets for itself. This chapter closes the gap deliberately, by assembling an estimator and an identification argument that are each defensible against named objections and that together produce an estimate of curvature that means what the contribution needs it to mean.

A register note governs everything that follows, as it governs every chapter of this design-stage dissertation. No estimate described here has been executed on the full assembled dataset. Where the chapter specifies a smoother, a weighting scheme, a clustering structure, or a cross-validation protocol, it is specifying the procedure to be run, not reporting its output. Where it describes the expected sign of a second derivative or the expected location of a channel-count edge, those are expectations under the contribution hypothesis stated to make the design concrete, labeled as such, and they must not be read as findings. The pre-registration commitment in this chapter is precisely the commitment to fix all of these choices before the data are run, so that the estimate, when it is produced, is the output of a frozen design rather than the product of a search over specifications for a pleasing curve.

## 5.2 The estimand

The object the design estimates must be defined before the estimator that targets it, because an estimator is only credible relative to a well-posed estimand. The estimand is the shape, specifically the curvature, of the conditional expectation of requirement-normalized validated accuracy as a function of instrument development cost, holding the design attribute vector and the retrieval-difficulty control fixed, over the region of common support in cost. In the dissertation's fixed notation, the estimand is the function \( g(\text{cost}) \) in \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), and more precisely it is the second derivative \( g'' \) of that function evaluated across the supported cost range, together with the marginal channel-count contribution that carries the over-specification proposition.

Three features of this estimand definition are load-bearing, and each is a deliberate narrowing. First, the estimand is a conditional expectation, not a structural causal parameter in the sense of a single physical mechanism that converts a dollar into an increment of accuracy. The dissertation is explicit, here and in the prospectus, that the cost effect is an embodied-investment effect: cost is a near-sufficient statistic for the engineering effort, component quality, and calibration rigor built into the instrument, and \( g(\text{cost}) \) summarizes how validated accuracy varies with that embodied investment, not how a marginal dollar physically becomes accuracy through one channel. The claim is reduced-form by design, and the estimand is defined accordingly. To claim a structural mechanism would require a model of the retrieval physics that the data do not support and that the contribution does not need; the contribution needs the curvature of the embodied-investment surface, and that is what the estimand fixes.

Second, the estimand is defined over common support, not over the full cost range that appears in the raw data. The curvature of \( g \) is only interpretable where instruments of differing cost actually coexist with comparable design attributes. Outside common support, any estimate of \( g'' \) would be extrapolation across instruments that are not comparable, and an extrapolated curvature is an artifact of the smoother's functional form rather than a feature of the data. Restricting the estimand to common support is therefore not a robustness add-on; it is part of the definition of what is being estimated, because the contribution is a statement about returns within the population of instruments that are genuinely comparable, and the design refuses to make a statement about regions where comparability fails.

Third, the estimand holds \( \mathbf{X} \) fixed, where \( \mathbf{X} \) is the design and difficulty control vector specified in the data chapter: spectral-channel count, swath width, spatial resolution, calibration approach as a categorical, instrument mass and power as built, mission epoch, and the retrieval-difficulty control. Holding \( \mathbf{X} \) fixed is what converts a raw accuracy-cost scatter into the conditional curvature the contribution is about. The estimand is the curvature of accuracy in cost among instruments that are alike in their non-cost attributes, because only that curvature can be read as a return to investment rather than as the byproduct of expensive instruments also being, say, higher-resolution or built in a later technology epoch. The decision to make channel count both a member of \( \mathbf{X} \) and the carrier of the separate over-specification test is intentional and is resolved in the over-specification section: channel count enters the general concavity estimate as a held-fixed control and, separately, is allowed a flexible term whose marginal contribution is the object of the sharper prediction.

The estimand thus has two components reported together. The first is the second derivative \( g'' \) of the cost function over common support, which carries the concavity claim. The second is the marginal contribution of channel count to accuracy as a function of channel count, which carries the over-specification claim. The contribution H1 is a joint statement about both: that \( g'' \) is reliably negative over a non-trivial portion of common support, and that the marginal channel contribution reaches a region indistinguishable from zero within the observed channel range. The null H0 is the joint complement: that \( g \) is indistinguishable from linear and the marginal channel contribution remains positive across the observed range. Defining the estimand as this pair, rather than as a single slope, is what makes the contribution sharper and more falsifiable than a generic claim of diminishing returns.

## 5.3 The estimator

### 5.3.1 Why a partially linear semiparametric form

The estimator is a partially linear semiparametric regression of validated accuracy on cost and the control vector, written in the fixed notation as \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \). The choice of this form over the two obvious alternatives, a fully parametric model and a fully nonparametric model, is dictated by the structure of the contribution and the size of the sample, and the reasoning is worth making explicit because the form is not a default.

A fully parametric model, for instance accuracy regressed on cost and cost-squared plus linear controls, would let the data speak only through the sign of a single quadratic coefficient. That is too brittle a test of curvature. A negative quadratic term can be produced by a single influential high-cost instrument, by a misspecified functional form elsewhere in the model, or by the rigid imposition of a parabola on a relationship that flattens rather than turning down. The contribution claims that accuracy flattens at high cost, which a parabola cannot represent without also claiming that accuracy eventually declines, a stronger and less plausible claim the dissertation does not make. A quadratic would force the data into the wrong shape and would conflate flattening with reversal.

A fully nonparametric model, a flexible smoother of accuracy on cost and all controls jointly, would in principle let the data choose the shape, but it would do so at a price the sample cannot pay. The data chapter establishes that the population is on the order of dozens of instruments and a larger but still modest number of instrument-product rows. A fully nonparametric estimator over a control vector of seven or eight attributes plus cost would exhaust the degrees of freedom and overfit; in a small sample a flexible smoother will find curvature in noise as readily as in signal, which is exactly the failure mode the decision rule in the analysis chapter is built to catch. This concern follows from the standard curse-of-dimensionality logic of nonparametric estimation: a method that cannot distinguish a real frontier from sampling noise at this sample size cannot support a falsifiable contribution. A larger sample would relax this constraint, which is why the design states sample size as a binding limitation rather than a nuisance.
The partially linear form resolves the tension. It concentrates the sample's limited flexibility on the one dimension the contribution is about, cost, by estimating \( g(\text{cost}) \) with a smoother, and it spends the controls' degrees of freedom economically by entering \( \mathbf{X} \) linearly. This is the established semiparametric tradition for separating a flexibly estimated term of interest from linear controls [\[104\]](#ref-104), [\[108\]](#ref-108), and its appropriateness here is specific rather than generic: the contribution is a statement about the shape of one term, so the estimator should be flexible in that term and parsimonious everywhere else. Reading the linear controls as partialling out the systematic non-cost reasons an instrument achieves its accuracy is the interpretation the identification strategy requires, so the estimator's structure and the identification argument are aligned rather than bolted together.

### 5.3.2 The shape-constrained smoother for g

The function \( g \) is estimated under a monotonicity-and-concavity-respecting smoother, and the role of the shape constraint must be stated with care so that it does not appear to assume the answer. The concavity claim is tested, not imposed, and the test is comparative. The design estimates \( g \) twice. It estimates an unconstrained version, free to be linear, convex, concave, or wiggly as the data dictate, and it estimates a concavity-respecting version. The concavity claim is supported only if the constrained, concave fit improves out-of-sample prediction relative to the linear null and the unconstrained fit's curvature is itself reliably negative over common support. The shape constraint is therefore a hypothesis embodied in one of the competing models, not a property forced on every model. If the data are linear, the unconstrained smoother will return a near-linear \( g \), the concave model will not beat the linear null out of sample, and H0 will stand. The procedure earns trust because a constrained estimator cannot manufacture curvature that the unconstrained estimator and the cross-validated comparison both deny; requiring agreement across the unconstrained fit, the constrained fit, and the out-of-sample comparison guards against each one's individual failure mode.

The dissertation flags, in the expansion plan's evidence-gap list, that the corpus is thin on concavity-constrained semiparametric estimation specifically, and that gap is honored here rather than papered over. The partially linear and balancing method literature is well represented in the assembled corpus [\[104\]](#ref-104), [\[108\]](#ref-108), [\[97\]](#ref-97), but the specific isotonic-or-concave-constrained smoother to be used in the partially linear setting is a method choice that requires two or three dedicated method citations the corpus does not yet contain. The design commits to running a focused method sweep on shape-constrained nonparametric estimation before execution and to fixing the smoother in the pre-registration record, so that the constrained estimator is specified, with its tuning and its constraint enforcement, in advance. Stating this as a method-access dependency rather than citing a placeholder is the honest course, and it does not weaken the design: the partially linear architecture and the comparative concavity test are fixed now, and only the internal smoother choice waits on the pre-execution sweep.

### 5.3.3 Inference and the clustering structure

The error term \( e \) is treated as instrument-clustered, and the reason is structural rather than precautionary. The unit of analysis fixed in the data chapter is the instrument-product pair, and a single radiometer contributes one row per validated product, sharing its cost across those rows. The rows from one instrument are therefore not independent: they share the instrument's cost exactly, they share its design attributes, and they share whatever instrument-level idiosyncrasies, calibration quality, on-orbit performance, that drive accuracy across all its products. Treating these rows as independent observations would understate the standard errors and overstate the precision of the curvature estimate, because the effective number of independent units is the number of instruments, not the number of instrument-product rows. The design pre-commits to instrument-clustered standard errors so that inference respects the dependence structure the unit of analysis creates [\[105\]](#ref-105). The caveat this carries is consequential and is preserved: with clustering at the instrument level, the effective sample for inference is the count of instruments, which is small, and the design accepts the resulting loss of power rather than buying spurious precision by ignoring the clustering. This applies the principle that the inference structure must match the sampling structure, and it is one of the places where the design pays an honest cost for honesty.

## 5.4 Identification

### 5.4.1 The selection problem stated formally

The estimator returns a curvature; identification is the argument that the returned curvature is the return to embodied investment and not an artifact of how instruments came to have their costs. The identification problem is selection, in the precise sense the program-evaluation tradition has formalized [\[105\]](#ref-105), [\[94\]](#ref-94). Instruments are not randomly assigned their cost levels. Expensive instruments are built for harder retrieval problems, for higher-stakes missions, in later technology epochs, by teams with different cost cultures. Each of these reasons for an instrument's cost is potentially also a reason for its accuracy, and a naive regression of accuracy on cost would absorb those reasons into the cost coefficient, confounding the return to investment with the selection of instruments to cost levels. If harder retrieval problems receive more budget and harder problems are validated at lower accuracy, the naive cost effect would be biased toward flatness or even toward a negative slope, masking a true positive return. If higher-stakes missions receive more budget and also command better calibration and ground validation, the naive cost effect would be biased toward steepness, manufacturing apparent returns that are really mission-class effects. The selection problem can bias the curvature in either direction, which is why it cannot be waved away as a level effect that differencing would remove.

The identification claim the design makes is explicitly not that cost is randomly assigned. It is the weaker, defensible claim of selection-on-observables within common support: conditional on the design control set and the retrieval-difficulty control, the residual variation in cost is as good as random with respect to validated accuracy. This is the conditional-independence assumption of the program-evaluation tradition, adapted from a binary treatment to a continuous dose [\[105\]](#ref-105), [\[98\]](#ref-98). The assumption is strong and is stated as an assumption, not asserted as a fact, because it is in principle untestable directly: one cannot observe the counterfactual accuracy an expensive instrument would have delivered at low cost. What the design can do, and does, is build the credibility of the assumption in three steps that each address a specific way the assumption could fail, and then probe the residual risk with sensitivity analysis. The case that the design addresses the causal mechanism rests on these three steps, and the case that the design beats the alternatives rests on the comparison of this identified estimate against the naive regression it replaces.

### 5.4.2 Step one: controls that absorb the reasons for cost

The first credibility step is the construction of the control set to absorb the systematic reasons an instrument received its cost. The two most plausible such reasons are the difficulty of the retrieval and the technology epoch. The retrieval-difficulty control is included so that the comparison of a high-cost instrument retrieving soil moisture under vegetation against a low-cost instrument retrieving clear-sky sea-surface temperature is not read as a cost effect when it is a difficulty effect [\[77\]](#ref-77), [\[73\]](#ref-73), [\[83\]](#ref-83). Soil moisture under vegetation is intrinsically harder to retrieve accurately than clear-sky SST regardless of how much is spent on the instrument, and the difficulty control holds that intrinsic hardness fixed so the cost dimension can be read cleanly. The mission-epoch control absorbs technology vintage, so that a later, cheaper, more accurate instrument is not mistaken for evidence that low cost buys high accuracy when it is really evidence that detector and calibration technology improved over time. This step rests on the fact that these two drivers are the ones the substantive literature identifies as the main confounders, and a control set that absorbs the dominant confounders renders the conditional-independence assumption far more plausible than the unconditional version. One caveat, preserved rather than hidden, is that controls absorb only observed confounders; an unobserved driver correlated with both cost and accuracy would survive this step, which is why the design does not stop here.

### 5.4.3 Step two: covariate balance and balancing weights

The second credibility step recognizes that including controls in a linear specification is not the same as ensuring that high-cost and low-cost instruments are actually comparable in those controls. If expensive instruments differ systematically from cheap ones in their swath, resolution, and calibration approach, then the linear controls are doing heavy extrapolation, and the curvature estimate becomes sensitive to the functional form of the controls rather than reflecting a like-for-like comparison. The design therefore checks covariate balance across cost strata explicitly and enforces it with balancing weights, rather than assuming the linear controls have done the work. This operationalizes the covariate-balancing logic of the Abadie identification tradition through reweighting [\[94\]](#ref-94), [\[101\]](#ref-101).

The specific tool is entropy balancing, which calibrates unit weights to satisfy pre-specified covariate-moment balance directly, so that the weighted distributions of the design attributes are equalized across cost strata without the iterative propensity-score-then-check-balance loop that characterizes older matching practice [\[101\]](#ref-101). Entropy balancing is attractive here for three reasons the method literature establishes. First, it produces exact moment balance on the specified attributes by construction, so the balance the identification argument requires is achieved rather than merely sought [\[101\]](#ref-101). Second, it is doubly robust, meaning the resulting estimate is consistent if either the balancing model or the outcome model is correctly specified, an insurance policy that matters in a setting where neither model is known to be exactly right [\[99\]](#ref-99). Third, the broader covariate-balancing-weights and balancing-propensity-score family has been extended to continuous treatments, which matters because cost is continuous rather than binary, and the design needs balance across the cost continuum rather than between two groups [\[98\]](#ref-98), [\[88\]](#ref-88). The choice among these specific balancing estimators is itself a tuning decision the design pre-registers, informed by the simulation evidence comparing balancing methods in finite samples [\[90\]](#ref-90), and the design treats the balancing weights as a primary specification with the genetic-matching and entropy-balancing alternatives as robustness checks [\[102\]](#ref-102), [\[93\]](#ref-93).

What licenses balancing weights as part of identification, rather than as a cosmetic preprocessing step, is the doubly-robust argument made precise in the method literature: balancing the covariate moments removes the dependence of the estimate on the correct linear form of the controls, so that even if the controls enter the outcome model with the wrong functional form, the balanced comparison still isolates the cost effect [\[99\]](#ref-99), [\[91\]](#ref-91). One caveat is that balancing can only balance observed attributes; like the controls in step one, it does nothing for an unobserved confounder. The design is consistent on this point across both steps: observable-based identification neutralizes observable confounders and is honest that an unobservable confounder is the residual risk that step three's support restriction narrows but cannot eliminate, and that the sensitivity analysis must probe.

### 5.4.4 Step three: common support

The third credibility step restricts the estimand to the region of common support in cost, where instruments of differing cost actually coexist with comparable design attributes. This step has already been built into the estimand definition in the second section, and here its identification role is made explicit. Common support is what converts the curvature estimate from extrapolation into interpolation within data [\[94\]](#ref-94), [\[109\]](#ref-109). The synthetic-control tradition makes the principle sharp: a credible comparison unit must lie within the convex hull of the donor units in the covariate space, and extrapolation outside that hull is the failure the method is designed to avoid [\[94\]](#ref-94). Translated to the continuous-cost setting here, the principle is that the curvature of \( g \) is estimated only over the cost range where, at each cost level, there exist comparably-attributed instruments at nearby cost levels, so that the local slope and curvature of \( g \) are pinned by actual contrasts rather than by the smoother's behavior in a data void.

The operational consequence is that instruments outside common support are trimmed, and the design pre-commits to reporting how many are trimmed and why, so that the estimand's population is transparent rather than silently narrowed. The convex-hull logic of comparable-unit construction supports this [\[109\]](#ref-109), [\[103\]](#ref-103): an estimate built only on supported contrasts is robust to the smoother's functional form in a way an extrapolated estimate is not. One caveat, preserved, is that trimming narrows the population to which the contribution applies, so the external-validity claim is correspondingly narrowed to the supported region and the discussion chapter returns to this bound. Naming the trimming as a population restriction rather than a data-cleaning convenience keeps the estimand and the contribution aligned.

### 5.4.5 Why this beats the alternatives

The case that the design beats the alternatives is argued by direct comparison against the two estimators a less careful analysis would use. The first alternative is the naive regression of accuracy on cost without the controls, the balancing, or the support restriction. That estimator is dominated because it confounds the return to investment with the selection of instruments to cost, in a direction the data cannot reveal, so its curvature is uninterpretable. The design's identified estimate is reported alongside the naive estimate so that the gap between them quantifies how much selection mattered, which is itself informative [\[105\]](#ref-105). The second alternative is an unconstrained flexible spline of accuracy on cost and all controls jointly, which overfits the small sample and reports curvature in noise. That estimator is dominated because it fails the out-of-sample test the decision rule imposes; an in-sample wiggle that does not improve held-out prediction is the expected symptom of overfitting at this sample size, not evidence of a frontier [\[100\]](#ref-100), [\[110\]](#ref-110). The design beats both by combining a parsimonious flexible-in-cost-only estimator, observable-based identification with balancing and support restriction, and an out-of-sample decision rule, so that the reported curvature is both identified and validated rather than merely fitted. The state-of-applied-econometrics synthesis is explicit that the credibility of an observational estimate rests on exactly this combination of a defensible identification argument and a guard against overfitting, and the design adopts both [\[100\]](#ref-100).

## 5.5 The over-specification test

### 5.5.1 A sharper claim than aggregate concavity

The over-specification claim is tested separately from, and more sharply than, general concavity, and the design treats this as the more falsifiable half of the contribution. Aggregate concavity is a statement that the cost function flattens; over-specification is a statement that a specific, estimable design margin, the spectral-channel count, stops contributing to validated accuracy beyond a locatable point. The second is harder to satisfy by accident, because it predicts not merely a curved aggregate relationship but a specific attribute whose marginal payoff vanishes within the observed range. Within the partially linear model, spectral-channel count is allowed a flexible term, and the marginal contribution of an additional channel to validated accuracy is estimated as a function of channel count, holding cost and the other attributes fixed. The over-specification region is the range of channel counts over which this marginal contribution is not statistically distinguishable from zero, and the estimable channel count named in H1 is the lower edge of that region.

The interpretation of this test as a design margin rather than a statistical curiosity rests on an explicit causal mechanism. Added spectral channels and the calibration elaboration they require raise instrument development cost. Beyond a point, additional channels carry information redundant with channels already present, and the achievable accuracy of the retrieval is bounded by error sources that more channels do not relieve: calibration drift, geolocation error, and the intrinsic difficulty of the geophysical variable [\[73\]](#ref-73), [\[77\]](#ref-77). The estimated marginal channel contribution therefore falls toward zero, so that dollars spent on channels past the over-specification edge buy specification, not validated science. The strategic implication, developed in the discussion chapter, is that a cost-capped portfolio can deliver more total validated accuracy by capping per-instrument channel count and reallocating. This is a causal chain, not a bare correlation, and the design's job is to estimate the observable effect, the channel count at which the marginal contribution becomes indistinguishable from zero.
### 5.5.2 The Simon prior behind the test

The expectation that such an edge exists is not arbitrary; it is the empirical prediction of the bounded-rationality and near-decomposability prior that the theoretical chapter develops from Simon [\[19\]](#ref-19), [\[14\]](#ref-14), [\[22\]](#ref-22). Simon's satisficing account holds that designers search to an aspiration level and stop rather than optimizing over a complete attribute space, so that specification accumulates to a threshold and then continues by inertia or by a capability-maximizing instinct rather than by a measured return [\[19\]](#ref-19), [\[22\]](#ref-22). Simon's architecture-of-complexity argument holds that complex engineered systems are near-decomposable, so that beyond a point the interactions added by further elaboration contribute little to overall function while adding cost and integration burden [\[14\]](#ref-14). Both ideas predict a vanishing marginal return to channel count, which is the over-specification edge. The value-driven design and tradespace literature operationalizes the same intuition for aerospace, holding that value rather than raw capability is the proper objective and that tradespaces routinely contain dominated, over-specified regions [\[17\]](#ref-17), [\[23\]](#ref-23), [\[20\]](#ref-20). The design's over-specification test is the empirical instrument that would locate, for radiometer spectral specification specifically, the threshold these theories say must exist. The confidence the design attaches to the prior is moderate: the theory makes the edge expected rather than certain, and the test is built so that the data can locate the edge, push it beyond the observed range, or deny it, with the decision rule fixing which conclusion follows.

### 5.5.3 Physical grounding deferred to the analysis chapter

The over-specification test acquires physical legitimacy from the information-content theory of spectral measurements, which establishes that the degrees of freedom for signal in a multichannel retrieval saturate as channels are added, so that the statistical onset of redundancy the test detects corresponds to a physical onset of information redundancy rather than to a fitting artifact [\[123\]](#ref-123), [\[122\]](#ref-122). The full development of this physical grounding belongs to the analysis-plan chapter, which maps the statistical channel-count edge to the optimal-estimation degrees-of-freedom-for-signal concept. This chapter flags the connection rather than developing it, keeping the methodological architecture and the physical interpretation in their assigned chapters. What matters for the research design is that the over-specification test is not merely a search for where a coefficient loses significance. It is a test for a physically motivated redundancy onset whose existence the retrieval-theory literature independently predicts, and that prediction is what protects the test from the charge that it merely finds the point where a small sample runs out of power to distinguish a channel's contribution from zero. The design discriminates these two readings, real redundancy versus power exhaustion, through the power analysis specified later in this chapter and through the requirement that the edge be stable under the robustness battery.

## 5.6 Threats to validity

The four classical validity threats are treated in turn, each as a named way the contribution could be wrong, paired with the design feature that bears on it and an honest statement of the residual risk that remains. The case that residual risk is acceptable is built here, threat by threat.

### 5.6.1 Internal validity

The principal internal-validity threat is omitted-variable bias from an unobserved driver, and the design names both directions in which it could operate. An unobserved driver that raises both cost and accuracy, for example an instrument-team competence or a mission-class commitment to calibration not captured by the observed attributes, would inflate the apparent cost effect and could mask true concavity by making the high-cost region look steeper than the embodied investment alone would make it. An unobserved driver that raises cost while being unrelated to accuracy, for example a procurement inefficiency or a one-off integration cost overrun, would deflate the apparent cost effect and could exaggerate concavity by making high-cost instruments look like poor accuracy buys for reasons unrelated to their capability. The design control set and the retrieval-difficulty control target the most plausible such drivers, retrieval difficulty and technology epoch being the dominant ones, and the balancing weights and common-support restriction reduce the leverage of any residual imbalance [\[105\]](#ref-105), [\[101\]](#ref-101), [\[94\]](#ref-94). The residual risk, preserved rather than hidden, is that observable-based identification cannot neutralize a confounder that is both unobserved and uncorrelated with the rich observed attribute set. The design does not claim this risk away. It bounds the risk through a sensitivity analysis, specified in the robustness section, that asks how strong an unobserved confounder would have to be to overturn the curvature conclusion.

A second internal-validity threat is reverse linkage, where instruments expected to face hard validation are deliberately given more budget so that budget and difficulty are co-determined. The retrieval-difficulty control and the common-support restriction address this by holding difficulty fixed and by comparing only instruments that coexist at comparable difficulty across cost levels [\[77\]](#ref-77), [\[83\]](#ref-83). The residual risk is that difficulty is imperfectly measured, which downgrades confidence in the cost effect's interpretation in the regions where difficulty measurement is coarsest, and the design states this rather than assuming difficulty is captured perfectly.

A third internal-validity threat is measurement error in the cost variable from version mismatches. The cost records and the design and validation records are produced by separate communities and were never built to be joined, so an instrument's cost can be attached to the wrong version of its design or validation record [\[42\]](#ref-42), [\[37\]](#ref-37). Classical measurement error in the regressor of interest attenuates and distorts the estimated function, and in a nonlinear setting it can bias the curvature in unpredictable directions. The design addresses this with careful instrument-version matching, documented in the matching protocol, and with a sensitivity analysis that drops ambiguously matched instruments and re-estimates, reporting whether the curvature conclusion survives. The residual risk is that even careful matching leaves some version ambiguity, and the design's confidence in the cost effect is explicitly conditioned on the matched subsample being representative, a condition the sensitivity analysis probes.

### 5.6.2 External validity

The external-validity threat is over-generalization of the estimand beyond the population that supports it. The estimand is defined over NASA and NASA-partnered passive radiometers in the modern era, within common support, and it does not extend to active sensors such as radars and lidars, to non-NASA instruments built under different cost accounting, or to future instruments using technologies absent from the sample. These limits are stated as scope, not discovered as weaknesses. Active sensors have non-commensurable cost drivers, transmit power and antenna or telescope aperture rather than spectral-channel count, so pooling them with radiometers would violate the comparability that identification requires, and they are excluded by construction [\[46\]](#ref-46). Commercial radiometers are built under cost accounting that differs from NASA development-cost conventions, so a frontier estimated there might differ in level even if its shape were similar, and whether the concavity is a physics property and therefore portable or a cost-regime property and therefore not is itself an empirical question the bounded design cannot answer but does set up [\[137\]](#ref-137), [\[134\]](#ref-134). The honest external-validity claim is narrow and is preferred to a broad claim the data cannot support; the discussion chapter develops these as scoped extensions rather than as failures of the present design.

### 5.6.3 Construct validity

Construct validity asks whether the variables measure what the contribution needs them to measure, and it bears on both the dependent variable and the regressor. The dependent variable must measure delivered science accuracy and not a self-reported instrument specification, because a contribution about returns to investment is vacuous if the accuracy it regresses on cost is simply the accuracy the instrument was specified to deliver, which would by construction track its cost. For this reason the accuracy metric is drawn from independent validation records produced by the cal/val community, MODIS aerosol validated against AERONET, SST validated against in-situ matchups, SMAP soil moisture validated against core sites, rather than from the design documents that specify the instrument [\[85\]](#ref-85), [\[73\]](#ref-73), [\[77\]](#ref-77). For the same reason the metric is requirement-normalized, so that the construct is compliance with the product's stated mission requirement rather than a raw error in incommensurable units, which makes accuracy comparable across product families and ties the construct to the operational meaning of accuracy rather than to a physical unit [\[83\]](#ref-83). An independently validated, requirement-normalized metric measures delivered science accuracy as the science community itself defines it; the residual risk is the heterogeneity in how different DAACs and papers report validation statistics, which the requirement-normalization mitigates but does not fully eliminate, downgrading confidence for product families whose validation records are sparsest.

The regressor must measure embodied instrument investment, and the NICM development-cost construct supports this because development cost is the dollars committed to building the instrument's capability, which is the embodied investment the contribution is about [\[42\]](#ref-42), [\[37\]](#ref-37). The construct boundary is stated explicitly: cost is development cost, not life-cycle cost, so operations, reprocessing, and algorithm maintenance are out of the cost variable. Because the claim concerns instrument investment specifically, development cost is the correct construct, but the boundary is named so the estimate is not misread as a total-cost frontier. The evidence-gap note from the expansion plan is honored here: the corpus contains the NICM documentation that authorizes the cost construct but not the underlying instrument-level cost table, which is a data-access dependency to be resolved through JPL channels at execution rather than a citable artifact, and the design states this as a dependency rather than citing a paper for numbers it does not contain.

### 5.6.4 Statistical-conclusion validity

Statistical-conclusion validity asks whether the inferential machinery can support the conclusions drawn at the available sample size, and it is the threat the small sample makes most acute. The design responds with four pre-commitments. First, it pre-commits to instrument-clustered standard errors, so that inference respects the instrument-product dependence structure and does not buy spurious precision from treating correlated rows as independent [\[105\]](#ref-105). Second, it pre-commits to a limited number of pre-specified controls, to preserve degrees of freedom and avoid the overfitting that a richly parameterized model would invite at this sample size; the control set is fixed in the pre-registration record and not expanded during analysis. Third, it pre-commits to a held-out or cross-validated assessment of whether the concave fit genuinely improves out-of-sample prediction over the linear null, so that in-sample curvature, which a small sample will produce from noise, is not mistaken for a real frontier [\[100\]](#ref-100), [\[110\]](#ref-110). Fourth, it pre-commits to a minimum-detectable-effect analysis, specified in the next section, so that a null result is interpreted against the design's power to detect a real effect rather than read as evidence of no effect when it may be evidence of insufficient power. The residual risk, preserved as the governing qualifier of the whole design, is that the sample is small by econometric standards, which limits how flexibly the cost function can be estimated and how finely the over-specification edge can be located; the design accepts this limit, states it, and is built so that the limit produces honest non-findings rather than overconfident findings.

## 5.7 Power and minimum detectable effect

A design that pre-commits to a decision rule must also state what it can and cannot detect, because a decision rule that cannot in principle reject the null at the available sample size is not a test. The design therefore includes a power and minimum-detectable-effect analysis, specified here at the design stage and to be executed on the assembled sample before the substantive estimation, so that the interpretation of any null is calibrated to the design's actual sensitivity.

The minimum-detectable-effect analysis targets the two components of the estimand. For the concavity component, the analysis asks how negative the second derivative \( g'' \) would have to be, over a given portion of common support, for the design to reject the linear null with the pre-committed cross-validated procedure at conventional confidence, given the instrument-clustered effective sample size. Because the effective sample for inference is the number of instruments rather than the number of instrument-product rows, the minimum detectable curvature is larger, that is, the design is less sensitive, than a naive row count would suggest, and the analysis reports the curvature threshold against the instrument count explicitly. For the over-specification component, the analysis asks the analogous question for the marginal channel contribution: how wide a channel range, and how flat a marginal contribution over it, the design can detect as indistinguishable from zero given the spread of channel counts in the supported sample, since a test for a vanishing marginal effect needs enough variation in channel count above the candidate edge to distinguish a true zero from a small positive effect the sample cannot resolve.

The analysis is reported as a design illustration, not as a result, and its numbers are expected sensitivities under the assembled sample's eventual structure rather than computed findings, in keeping with the design-stage guardrail. Its purpose is to make the interpretation of a null honest in advance. If the design's minimum detectable curvature is large relative to the curvature the theory predicts, then a null result would be uninformative, evidence of insufficient power rather than of linearity, and the design would say so rather than claiming support for H0. If the design's minimum detectable curvature is small relative to the predicted effect, then a null result would be informative, genuine evidence that the relationship is linear over the supported range, and the discussion chapter is built to treat a well-powered null as a real contribution. The power analysis is therefore the bridge between the small-sample limitation and the decision rule: it converts the sample-size constraint into a statement about which conclusions the design can support, so that neither a finding nor a null is over-read. Confidence in this calibration is high in form, the analysis is a standard and reproducible computation, and conditional on the assembled sample in magnitude, the realized sensitivity will only be known once the sample is fixed, which is why the analysis runs on the assembled sample before the substantive models and is itself pre-registered.

## 5.8 Robustness battery

The contribution is credible only if it survives a battery of pre-specified robustness checks, each aimed at a specific way the headline estimate could be an artifact. The battery is fixed in advance, so that the checks are tests of the conclusion rather than a search for a specification that flatters it, and the design pre-commits to reporting every check whether or not it is favorable.

The first family of checks probes the identification. The headline estimate uses entropy-balancing weights; the battery re-estimates under genetic matching and under a covariate-balancing-propensity-score weighting for continuous treatment, so that the curvature conclusion does not depend on the choice of balancing estimator [\[102\]](#ref-102), [\[98\]](#ref-98), [\[101\]](#ref-101). The simulation evidence on balancing-method performance in finite samples informs which alternatives are most informative as cross-checks [\[90\]](#ref-90), [\[88\]](#ref-88). The naive unbalanced regression is reported alongside, so the contribution of the identification machinery is visible as the gap between the naive and the identified estimates [\[105\]](#ref-105).

The second family probes the functional form. The headline estimate uses the pre-registered shape-constrained smoother; the battery re-estimates \( g \) with the unconstrained smoother and with a parametric quadratic, so that the concavity conclusion is shown to hold across the comparison the decision rule already requires rather than to depend on the shape constraint [\[104\]](#ref-104), [\[108\]](#ref-108). A sensitivity to the smoother's tuning is reported, since a curvature conclusion that holds only at one bandwidth is fragile.
The third family probes the sample. The battery drops ambiguously version-matched instruments and re-estimates, addressing cost measurement error [\[42\]](#ref-42), [\[37\]](#ref-37); it re-estimates within each major product family separately where the family is large enough, to show the curvature is not driven by a single product type; and it conducts a leave-one-instrument-out re-estimation, given the small instrument count, so that no single instrument is shown to drive the curvature. The leave-one-out check matters at this sample size, because a curvature that disappears when one instrument is removed is not a frontier but an influential point, and the design pre-commits to reporting the influence of each instrument on the curvature conclusion.

The fourth family probes the dependent-variable construction. The requirement-normalization is one defensible normalization among a few; the battery re-estimates under an alternative normalization to show the curvature is a property of the accuracy-cost relationship and not of the particular normalization chosen [\[83\]](#ref-83). It also probes the validation-reference-ceiling rival explanation, by examining whether any flattening at the high-cost end coincides with the precision limits of the validation reference data rather than with the instrument's capability, since a reference network that cannot resolve differences among very good instruments would flatten the high-cost end for reasons of measurement rather than of returns [\[73\]](#ref-73). This probe is the design's response to the most serious rival explanation for apparent concavity, and the discussion chapter develops its interpretation; the research design's commitment is to run it as a pre-specified check rather than to wait for a reviewer to raise it.

The fifth check is the formal sensitivity analysis for unobserved confounding promised in the internal-validity discussion. It asks how strong an unobserved confounder, measured by its joint association with cost and with accuracy, would have to be to move the curvature estimate to the linear-null boundary, and it reports that strength against the strength of the observed confounders already controlled, so that the reader can judge whether a confounder of the required strength is plausible given what is already absorbed [\[105\]](#ref-105). This converts the unobservable-confounder threat from an unbounded worry into a bounded quantity, the honest treatment the design commits to.

## 5.9 Pre-registration commitment

The design pre-commits to a registered analysis plan, and the commitment is substantive rather than ceremonial because it is what protects the falsifiability of the single contribution. The five estimation steps, detailed in the analysis-plan chapter, the decision rule that requires the concave model to beat the linear null out of sample and \( g'' \) to be reliably negative over a non-trivial portion of common support, the pre-specified control set, the balancing estimator and its alternatives, the smoother and its tuning, the clustering structure, the trimming rule for common support, the power analysis, and the full robustness battery are all fixed before the substantive estimation is run, and they are frozen in a pre-registration record reproduced as an appendix. The synthetic-control tradition the identification borrows from is explicit that pre-registration of the donor pool, the predictors, and the specification is what prevents the analyst from selecting, post hoc, the comparison that produces the desired result [\[94\]](#ref-94), and the design adopts the same discipline for the cost function, the controls, and the over-specification edge.

The reasoning that makes pre-registration load-bearing here is specific to a small-sample, single-contribution design. At a small sample size, the space of specifications that would produce some curvature is large, and an unregistered analysis could search that space until it found a concave fit, then present it as a discovery. Pre-registration removes that degree of freedom by fixing the specification before the data are seen, so that the reported estimate is the output of the frozen design and not the product of specification search [\[100\]](#ref-100), [\[110\]](#ref-110). The decision rule's out-of-sample requirement reinforces the pre-registration, because even a pre-registered concave fit must still beat the linear null in held-out prediction to count, which guards against the residual possibility that the registered specification happens to fit in-sample noise. The combination of pre-registration and the out-of-sample decision rule is the design's strongest defense against the charge that it is a search for a pleasing curve, and the design states the combination as a commitment rather than an aspiration. The one honestly registered uncertainty is the deferred smoother choice flagged in the estimator section: the shape-constrained smoother is to be fixed by the pre-execution method sweep and entered into the pre-registration record before any substantive estimation, so that even the deferred choice is frozen before the data are run rather than chosen against them.

## 5.10 Computational and software plan

The design's reproducibility depends on a computational plan that is specified rather than improvised, and the plan is stated at the design stage so that the eventual execution is auditable. The estimation is implemented in a scripted, version-controlled statistical environment, with the analysis pipeline organized as discrete, re-runnable stages corresponding to the five pre-registered steps, so that the assembled table, the balance and support diagnostics, the baseline linear model, the semiparametric concave model, and the over-specification test are each produced by a stage whose inputs and outputs are fixed and logged. The synthetic-control and balancing methods the identification uses have established, citable software implementations that the plan adopts rather than re-implements, so that the balancing-weight estimation and its placebo or sensitivity inference follow validated code rather than bespoke routines [\[103\]](#ref-103), [\[101\]](#ref-101). The partially linear and shape-constrained smoothing stage uses an established semiparametric estimation implementation, with the specific shape-constrained smoother to be fixed by the pre-execution method sweep and pinned, by version, in the pre-registration record [\[104\]](#ref-104), [\[97\]](#ref-97).

Three computational commitments support the design's claims to honesty and reproducibility. First, the pipeline is deterministic given a fixed random seed for any stochastic component, the cross-validation folds and any resampling-based inference, with the seed recorded, so that the reported estimate is exactly reproducible from the frozen inputs. Second, the assembled instrument-product table, the matching log of every unmatched or ambiguously matched instrument, and the trimming log of every instrument dropped for lying outside common support are versioned artifacts, so that the population the estimand applies to is transparent and the data-access dependency on the NICM cost table is documented at the point where the numbers enter rather than hidden. Third, the cross-validated model comparison that the decision rule depends on is implemented so that the held-out prediction error of the linear null and of the concave alternative are computed on the same folds, so that the comparison the contribution turns on is a like-for-like out-of-sample test rather than two separately tuned in-sample fits [\[100\]](#ref-100). The computational plan is therefore not a list of tools but a set of commitments that make the pre-registered design executable and auditable, and it closes the research design by ensuring that the discipline argued in the preceding sections survives contact with implementation.

## 5.11 How this chapter advances the argument

The chapter closes by drawing its threads back to the argument the dissertation carries across every chapter, stating where this chapter advances each of its five elements and what residual risk it leaves to the analysis and discussion chapters.

That the problem is real, established in the introduction and literature chapters, is carried here only as the premise that no design tailored to the accuracy-on-cost inversion yet exists, which is why the chapter assembles one rather than citing one [\[105\]](#ref-105), [\[26\]](#ref-26). That the problem is material is likewise inherited and not re-argued. This chapter's substantive contribution is to the third, fourth, and fifth elements. It strengthens the case that the design addresses the causal mechanism by specifying a partially linear semiparametric estimator whose flexible cost term carries the curvature the mechanism predicts and whose shape-constrained smoother and clustered inference are matched to the contribution and to the unit of analysis [\[104\]](#ref-104), [\[101\]](#ref-101), and by separating the over-specification test as a sharper, mechanism-grounded instrument [\[14\]](#ref-14), [\[123\]](#ref-123). It strengthens the case that the design beats the alternatives by arguing the identified, balanced, support-restricted, out-of-sample-validated estimate against the naive regression and the overfitting spline it replaces [\[94\]](#ref-94), [\[100\]](#ref-100). It strengthens the case that the residual risk is acceptable by naming each of the four validity threats, pairing each with a design feature, preserving each caveat rather than dissolving it, and converting the worst residual risks, unobserved confounding, cost measurement error, and the validation-reference ceiling, into bounded quantities probed by the pre-specified sensitivity analysis and robustness battery rather than into open-ended worries [\[110\]](#ref-110), [\[73\]](#ref-73).

The honest residual risk the chapter leaves standing is the one the small sample imposes: the design can identify and validate a curvature only if a curvature of the magnitude the theory predicts is detectable at the available instrument count, which the power analysis will determine, and a null result is informative only if the design is shown to be adequately powered to reject the null. The design accepts this risk, states it as the governing limitation, and is built so that an underpowered null produces an honest non-finding rather than a false claim of linearity, and so that a finding survives only if it clears the pre-registered out-of-sample decision rule. With those commitments fixed, the research design is complete, and the analysis-plan chapter that follows operationalizes it into the five pre-registered steps, the decision rule, and the physically grounded over-specification test, carrying the same notation and the same anchors without alteration.


# Chapter 6: Analysis Plan and Expected Results

## 6.1 The chapter's answer, stated first

This chapter pre-registers exactly how the dissertation will decide between H1 and H0, and it commits, in advance of any execution, to the procedure, the decision rule, the expected signs, and the physical reasoning that makes those expected signs more than a hopeful guess. The answer the chapter delivers is a fixed, falsifiable test pipeline: five ordered steps that move from a frozen instrument-product table to a single out-of-sample comparison between a linear-in-cost null model and a shape-constrained semiparametric model of \( g(\text{cost}) \), plus a separate over-specification test that locates the spectral-channel count beyond which the marginal channel contribution to validated accuracy is statistically indistinguishable from zero. H1 is supported only if the semiparametric model beats the linear null in cross-validated prediction and the second derivative \( g'' \) is reliably negative over a non-trivial portion of common support; the over-specification proposition is supported only if the marginal channel-count contribution reaches an indistinguishable-from-zero region within the observed channel range. In-sample curvature alone retains H0. Every number in this chapter is an illustrative placeholder used to specify the procedure, and none is an executed estimate.

The contribution of this chapter, relative to its siblings, is that it does not leave the over-specification test as a purely statistical artifact. The chapter grounds the channel-count edge in the physics of spectral information content, the optimal-estimation theory of degrees of freedom for signal, and the operational channel-selection practice of the sounding community. That grounding converts a statistical claim, the marginal channel coefficient crosses zero, into a physical claim: additional channels stop adding independent information once the retrieval's degrees of freedom for signal saturate and the error budget is dominated by calibration, geolocation, and intrinsic retrieval difficulty. The statistical edge and the physical onset of redundancy are predicted to coincide, and the dissertation's confidence in the over-specification finding will rise if they do and fall if they do not.

The chapter is written under the design-stage guardrail that binds every chapter of this dissertation. The analysis has not been run on the full assembled dataset. The five steps are specified, the decision rule is fixed, and the expected curves are drawn as design illustrations. No estimated coefficient, second-derivative sign, or over-specification channel count is reported as an empirical finding anywhere in this chapter, and the result tables in Section 6.9 are presented as specified-but-unpopulated shells by design.

## 6.2 Problem frame for the analysis plan

By the end of Chapter 5 the dissertation has a defined estimand (the shape of \( E[\text{accuracy} \mid \text{cost}, \mathbf{X}] \) in the cost dimension over common support), an estimator (the partially linear semiparametric form \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \) with a concavity-respecting smoother for \( g \) and instrument-clustered errors), and an identification strategy (selection-on-observables within common support, with covariate balancing across cost strata in the Abadie tradition [\[105\]](#ref-105), [\[94\]](#ref-94), [\[101\]](#ref-101)). What it does not yet have is an executable, ordered, falsification-first procedure that fixes every analyst degree of freedom before the data are touched and that ties the over-specification test to a physical theory of when additional channels stop carrying information.

What is needed in its place is a pre-registered analysis plan in which the order of operations, the model comparisons, the inference procedure, the decision rule, and the falsification conditions are all specified in advance, so that the eventual estimation is a mechanical execution of a frozen protocol rather than a search through specifications for a pleasing curve. The plan must also state, for each expected sign, the mechanism that produces it and the confidence grade the design-stage evidence supports.

This discipline is not optional because a small-sample semiparametric study of a curved relationship is exactly the setting in which in-sample curvature is the expected symptom of overfitting rather than evidence of a real frontier [\[110\]](#ref-110). A flexible smoother fit to dozens of instrument-product rows will almost always find some curvature; the question is whether that curvature survives an honest out-of-sample test and whether it is corroborated by an independent physical prediction. What pre-registration must supply, then, is a protocol that pre-commits to the out-of-sample test as the arbiter and that supplies the physical corroboration.

Were the analysis plan left implicit, the dissertation would be unable to distinguish a genuine concave frontier from a small-sample overfit, and the over-specification channel count, the sharpest and most decision-relevant output, would rest on a statistical edge with no physical anchor. A reviewer could reasonably dismiss the finding as a curve-fitting exercise. Pre-registration together with information-content grounding is what makes the eventual result defensible, and stating both in advance is the discipline that separates this design from a search for a pleasing curve.

## 6.3 Pre-registration statement
The analysis plan in this chapter is pre-registered in the sense that it is fully specified before execution on the full assembled dataset, and the specification is frozen at the level of detail required to remove analyst discretion from the test of H1 against H0. Three commitments give the pre-registration its force.

First, the order of operations is fixed. Assembly precedes balance-and-support, which precedes the linear baseline, which precedes the semiparametric model, which precedes the over-specification test. No step may be reordered to improve an outcome, and no step's output may be inspected as grounds for revising an earlier step's specification. The single exception is documented data-quality corrections to the assembled table, which are logged and applied symmetrically across all models.

Second, the decision rule is fixed and stated before any model is fit (Section 6.8). H1 carries a conjunctive requirement: the semiparametric model must beat the linear null out of sample, \( g'' \) must be reliably negative over a non-trivial portion of common support, and the over-specification proposition has its own separate requirement. The conjunction is deliberate. It makes H1 harder to support than H0, which is the correct asymmetry for a contribution that claims a structured departure from a simple null.

Third, the control set is pre-specified and limited. The design controls \( \mathbf{X} \) are exactly those defined in the shared bible and Chapter 4: spectral-channel count (entered through the flexible over-specification term), swath width, spatial resolution, calibration approach as a categorical, instrument mass and power as built, mission epoch, and the retrieval-difficulty control. No additional controls may be added during estimation to rescue or to defeat a result. The only permissible sensitivity analyses are those enumerated in Section 6.7, each specified in advance with its purpose stated.

The pre-registration does not freeze the data themselves, because the table is not yet assembled, and it does not pretend that assembly is free of judgment. It freezes the rules that govern judgment: the matching protocol (Section 6.4), the trimming rule (Section 6.5), the inference procedure (Section 6.6), and the decision rule (Section 6.8). The pre-registration record is reproduced as Appendix C of the dissertation. The grade of the design-stage evidence behind each commitment is stated where it matters, and the chapter is explicit that pre-registration governs how the data will be analyzed, not what the data will show.

## 6.4 Step 1: Assembly

A single frozen instrument-product table, built by matching NICM-class cost records to NTRS design specifications on instrument identity and version and then attaching validated accuracy metrics from DAAC and cal/val records, is the necessary and sufficient input for the test. The integrity of the test depends more on the discipline of this step than on any later modeling choice. The difficulty is that the three named data sources do not share keys. NICM provides development cost at the instrument level [\[42\]](#ref-42), [\[37\]](#ref-37); NTRS and mission instrument handbooks provide the design attributes not fully captured by NICM, principally spectral-channel count, swath, resolution, and calibration approach; and the DAAC product documentation together with the peer-reviewed validation papers provides the dependent variable, the requirement-normalized validated accuracy [\[85\]](#ref-85), [\[77\]](#ref-77), [\[73\]](#ref-73). These three were produced by different communities for different purposes and were never designed to be joined. That mismatch is the single largest source of avoidable error in the study and the reason assembly is treated as a protocol rather than a clerical task.

The stakes of getting the match right are exact. If instrument identity and version are matched correctly, the cost attributed to a row is the cost of the instrument that produced the validated product in that row, and the join is valid. If they are matched incorrectly, the cost regressor is contaminated by version mismatch, a measurement-error problem in the variable of central interest that would bias the estimated \( g(\text{cost}) \) toward attenuation. The entire identification rests on the cost variable measuring the development investment embodied in the specific instrument build whose products are being validated, which is why this step is decisive. The reliability of instrument-level cost records and the documented prevalence of version-driven cost variation in space-system cost data are established in the cost-estimating literature [\[42\]](#ref-42), [\[37\]](#ref-37), [\[35\]](#ref-35), and the optimism-bias and cost-growth literature establishes that cost records carry systematic and idiosyncratic error that a naive join would import wholesale [\[51\]](#ref-51), [\[38\]](#ref-38). These literatures justify logging every match and flagging every ambiguous one rather than assuming the join is clean.

Assembly proceeds in four sub-steps. First, enumerate the candidate population: NASA and NASA-partnered passive radiometers with a NICM-class cost record and at least one documented Level-2 or Level-3 validation record, MODIS-era to present, excluding active sensors as specified in Chapter 4. Second, match each instrument's cost record to its NTRS design specification by instrument name, mission, and build version, applying the matching protocol of Appendix B, and record for each instrument whether the match is exact, ambiguous, or absent. Third, for each matched instrument, attach the requirement-normalized validated accuracy for each of its validated products, creating one row per instrument-product pair and sharing the instrument's cost across its products. Fourth, freeze the table and produce the unmatched-and-ambiguous log, which records every instrument that could not be matched exactly and the reason, so that the sensitivity analysis in Section 6.7 can drop ambiguously matched instruments and report whether the result moves.

The assembled table is expected to contain on the order of dozens of instruments and a larger number of instrument-product rows. This is small by econometric standards and is the binding constraint on how flexibly \( g(\text{cost}) \) can be estimated, which is why Chapter 5 chose the semiparametric rather than fully nonparametric specification. All subsequent claims are conditional on the assembled population, which is by construction the population of flown, validated, and published radiometers. That population carries a standing objection of survivorship and publication selection: instruments that flew, validated, and published are over-represented, and if failure or under-performance correlates with cost, the frontier could be biased [\[38\]](#ref-38). The assembly step does not solve this; it makes it explicit by defining the estimand over the flown-and-validated population and refusing to extend the claim to the design-and-fail population. The objection is acknowledged and bounded rather than dismissed, and Section 6.7 specifies a sensitivity check on whether the frontier shape is sensitive to the inclusion of the most marginal validated instruments. Confidence that a usable table can be assembled is moderate, conditional on JPL access to the underlying NICM cost values, which is a data-access dependency rather than a citable artifact. It would rise with confirmed access to instrument-level cost records and a high exact-match rate, and would fall if the ambiguous-match fraction is large.

### 6.4.1 The matching protocol and the cost-record reliability it must respect

The join between cost and design is the operation most likely to inject error into the regressor of central interest, so the matching protocol is specified at the level of rules rather than left to execution-time judgment. Three rules govern it. First, a match is declared exact only when instrument name, host mission, and build version agree across the cost record and the design specification; a difference in any of the three downgrades the match to ambiguous and routes the instrument to the log. Second, when a single instrument design flew on multiple platforms or in multiple builds with distinct cost records, each build is treated as a separate instrument with its own cost and its own validated products, because the embodied investment differs across builds and collapsing them would average away the very cost variation the study exploits. Third, when a validated product cannot be attributed unambiguously to a single instrument build, for example a multi-mission merged product, that product is excluded rather than assigned to an arbitrary build, because a misattributed product contaminates both the dependent variable and the cost it is paired with.

These rules are calibrated to a documented feature of the cost-record literature: instrument and mission cost figures carry both systematic and idiosyncratic error, and the magnitude of that error is large enough to matter for a regressor of interest. The optimism-bias and reference-class-forecasting work establishes that planned-versus-actual cost divergence is the norm rather than the exception in large technical projects, and that the divergence is structured rather than random [\[51\]](#ref-51), [\[38\]](#ref-38). The cost-estimating literature corroborates that even validated parametric tools predict mission cost with non-trivial spread, as the blind-validation record for established cost tools shows [\[35\]](#ref-35). The matching protocol cannot remove this error, but it can prevent the avoidable component, version mismatch and misattribution, from compounding the unavoidable component. The plan therefore treats the cost variable as measured with error and carries that fact into the estimator through the attenuation-aware interpretation in Chapter 5 and into the sensitivity analysis that drops ambiguously matched instruments in Section 6.10. Naming the cost record as error-laden rather than treating it as a clean number is the honest position, and it is the reason the matching protocol is part of the pre-registration rather than a clerical afterthought.

## 6.5 Step 2: Balance and common support

Before any accuracy-on-cost relationship is estimated, the design must establish that the high-cost and low-cost instruments being compared are similar in their non-cost attributes and coexist over a region of common support, so that the eventual concavity estimate is interpolation within comparable data rather than extrapolation across incomparable instruments. This matters because instruments are not randomly assigned their cost levels. Expensive instruments are built for harder retrievals, for higher-stakes missions, or in different technology eras, so a naive regression of accuracy on cost would confound the cost effect with the difficulty of the retrieval and the mission class that selected the cost. This is the selection problem at the center of the Abadie program-evaluation perspective [\[105\]](#ref-105), [\[94\]](#ref-94).

The remedy is balance within strata. If, conditional on the design control set and the retrieval-difficulty control, the distribution of non-cost attributes is balanced across cost strata, then variation in cost within a stratum is as good as random with respect to validated accuracy, and the partially linear estimator recovers the curvature of the accuracy surface in the cost dimension rather than a confound. Covariate balancing achieves this by reweighting so that the strata being compared match on their covariate moments [\[101\]](#ref-101). The synthetic-control and covariate-balancing literature in the Abadie tradition establishes that balance must be checked and enforced rather than assumed, and that estimands should be restricted to regions where treated and comparison units genuinely overlap [\[94\]](#ref-94), [\[109\]](#ref-109), [\[105\]](#ref-105). Entropy balancing provides the specific weighting that achieves exact moment balance without discarding the sample, which is essential in a small sample where trimming is costly [\[101\]](#ref-101).

The procedure has five sub-steps. Partition the instruments into cost terciles. For each design control and the difficulty control, compute standardized differences across terciles and report them as the pre-weighting balance table. Estimate entropy-balancing weights that match the first moments, and sample size permitting the second moments, of the controls across terciles. Recompute the standardized differences under the weights as the post-weighting balance table. Finally, identify the common-support region in cost as the interval over which instruments of differing cost coexist with comparable design attributes, trim instruments outside that interval, and report how many are trimmed and why. The estimand is defined only over the retained common-support region.

Balance is enforced on observed controls only. Selection on an unobserved driver that raises both cost and accuracy, or that raises cost without raising accuracy, is not addressed by balancing and is carried forward to the threats-to-validity treatment of Chapter 5 and the rival-explanations treatment of Chapter 7. Stating this protects against over-claiming: balancing makes the comparison fair on what is measured, not on what is unmeasured. A reviewer may also object that trimming to common support in a small sample discards information and narrows external validity. The design accepts the narrowing as the price of valid identification: an estimate over a region where comparison is legitimate is preferable to a wider estimate that extrapolates across instruments that are not comparable, and the number trimmed and the attributes of the trimmed instruments are reported so the reader can judge the cost of the restriction. Confidence in this step is moderate. The balancing and common-support machinery is standard and well-supported, but its effectiveness in this specific small, heterogeneous sample is unknown until execution. It would rise if balance is achievable with modest weight dispersion and only a few instruments fall outside common support, and would fall if achieving balance requires extreme weights or if common support is thin.

## 6.6 Step 3: Baseline linear (H0) model

The null model, validated accuracy linear in cost plus the linear controls with instrument-clustered standard errors, is the benchmark against which H1 must prove itself. It is estimated first and in full so that the contest between H0 and H1 is decided by a like-for-like out-of-sample comparison rather than by the in-sample appeal of a flexible curve. H0 is the substantive hypothesis that validated retrieval accuracy is linear in instrument cost, with constant marginal accuracy per dollar and no over-specification region, exactly as fixed in the shared design. It is not a strawman. A credible linear finding would itself be a contribution, removing diminishing returns as an unexamined assumption in instrument budgeting.

If the data are truly linear in cost, the linear model is correctly specified and will predict held-out instrument-product rows at least as well as any more flexible model, because the flexible model spends degrees of freedom estimating curvature that is not there. Out-of-sample predictive error is the right arbiter because, in a small sample, in-sample fit always weakly favors the more flexible model, so only held-out prediction distinguishes real structure from overfit [\[110\]](#ref-110). The econometric-issues literature on hedonic functions establishes that functional-form misspecification and overfitting are the central hazards in attribute-based regression, and that out-of-sample assessment is the appropriate guard [\[110\]](#ref-110). The partially linear tradition to which the semiparametric model belongs is itself motivated by the need to separate a flexibly estimated term of interest from linear controls without overfitting the whole surface [\[104\]](#ref-104), [\[108\]](#ref-108), and that tradition presupposes a linear benchmark of the kind estimated here.

The procedure has four sub-steps. Estimate
\[ \text{accuracy} = \beta_0 + \beta_{\text{cost}} \cdot \text{cost} + \mathbf{X}\boldsymbol{\beta} + e \qquad\qquad (2) \]
with instrument-clustered standard errors, on the balanced, common-support sample, applying the entropy-balancing weights from Step 2. Record the linear cost coefficient \( \beta_{\text{cost}} \), its clustered standard error, and the full control vector. Compute the model's cross-validated predictive error using leave-one-instrument-out cross-validation, so that the held-out fold is an entire instrument, all of its product rows, rather than a single row, respecting the instrument-product dependence structure. Store this cross-validated predictive error as the H0 benchmark that the semiparametric model must beat.

The linear coefficient \( \beta_{\text{cost}} \) is reported as an expected sign and not as an estimate. Under either hypothesis it is expected to be positive: more instrument investment is expected to buy more validated accuracy on average. H1 and H0 differ on whether the marginal return is constant under H0 or declining under H1, not on whether the average return is positive. The leave-one-instrument-out scheme is the pre-committed cross-validation design; it is chosen over leave-one-row-out because rows from the same instrument share cost and are not independent. One might argue that a linear model with clustered errors in a sample of dozens of instruments has little power and that failing to beat it proves little. The design answers this in two ways. The decision rule of Section 6.8 treats failure to beat the null as retention of H0, which is the honest inferential outcome of low power, not a hidden win for H1; and the over-specification test of Section 6.7 provides a second, sharper, and physically corroborated route to evidence on diminishing returns that does not rest solely on the aggregate curvature comparison.

**Confidence:** high that the linear baseline can be estimated and serves as a clean benchmark; the procedure is standard. The confidence statement here concerns the procedure, not the outcome.

### 6.6.1 The inference design that the baseline and the semiparametric model share
Because the decision rule reads cross-validated predictive error, the cross-validation scheme is itself part of the pre-registration and is specified once here for both models. The unit of resampling is the instrument, not the instrument-product row, and the chosen scheme is leave-one-instrument-out cross-validation. The reason is structural and follows from the unit-of-analysis definition in the shared bible: a single radiometer contributes one row per validated product, all of those rows share the same instrument-level cost, and the validated-accuracy errors of products from the same instrument are correlated through shared calibration, geolocation, and processing pipelines. Row-level cross-validation would leak information from an instrument's training rows into its held-out row, inflating apparent out-of-sample performance and doing so more for the flexible model than for the linear model, since the flexible model can exploit the leaked within-instrument structure. Holding out an entire instrument at a time removes that leak and makes the out-of-sample test an honest test of generalization to a new instrument, which is the quantity the decision rule needs.

The same instrument-as-cluster logic governs the standard errors. Inference on the linear cost coefficient, on the control coefficients, and on \( g'' \) uses instrument-clustered errors so that the dependence among rows from the same instrument is respected rather than treated as independent replication. In a sample of dozens of instruments this is the binding statistical-conclusion-validity decision: treating instrument-product rows as independent would overstate the effective sample size, narrow the confidence bands artificially, and risk declaring a reliably negative \( g'' \) that is an artifact of pseudo-replication. The clustered scheme is pre-committed so that this temptation is foreclosed before any band is computed. Where the small number of clusters makes asymptotic clustered inference unreliable, the plan pre-specifies a cluster-bootstrap, resampling whole instruments with replacement, as the inference fallback, with the bootstrap design fixed in advance so that it cannot be selected post hoc to widen or narrow a band.

A final shared element is the treatment of the entropy-balancing weights inside cross-validation. The weights are re-estimated within each training fold rather than estimated once on the full sample and reused, so that no information from the held-out instrument enters the weights that the model is fit under. This is a small but consequential discipline: estimating weights once on the full sample and then cross-validating would let the held-out instrument influence the comparison through the weights, reintroducing the leak that the leave-one-instrument-out design exists to remove. Re-estimating weights per fold is therefore part of the frozen protocol and is recorded in the pre-registration.

## 6.7 Step 4: Semiparametric concave model, and Step 5: the over-specification test

### 6.7.1 Step 4: the shape-constrained model

The partially linear semiparametric model \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), with \( g \) estimated under a concavity-respecting smoother and compared to the linear baseline by leave-one-instrument-out cross-validation, is the instrument that tests aggregate concavity, and its second derivative \( g'' \) and the confidence band on \( g'' \) over common support are the quantities the decision rule reads. The estimand is the shape of the conditional expectation of requirement-normalized validated accuracy as a function of cost, holding design and difficulty fixed, over common support. The partially linear form isolates this shape: \( g(\text{cost}) \) carries the curvature of interest while \( \mathbf{X}\boldsymbol{\beta} \) absorbs the linear controls, following the semiparametric tradition for separating a flexibly estimated term from linear controls [\[104\]](#ref-104), [\[108\]](#ref-108).

If \( g \) is estimated under a smoother that respects concavity and the resulting model predicts held-out instruments better than the linear null, and if \( g'' \) is reliably negative over a non-trivial portion of common support, then the data support a concave frontier rather than a line. A shape-constrained estimate that improves out-of-sample prediction cannot be a pure overfit, because the constraint reduces flexibility and the held-out test penalizes spurious curvature. The corpus is thin on concavity-constrained semiparametric estimation specifically, and the dissertation states this as an evidence gap to be closed by a focused method sweep, isotonic and concave or monotone nonparametric regression, before execution, rather than papering over it. The general partially linear and balancing method support is in place [\[104\]](#ref-104), [\[108\]](#ref-108), [\[101\]](#ref-101); the shape-constraint citations are a named, pre-execution dependency. Naming the gap is the honest position and is recorded in the chapter rather than hidden.

The procedure has four sub-steps. Estimate the partially linear model with \( g(\text{cost}) \) under a concavity-respecting smoother on the balanced, common-support, weighted sample. Compute its leave-one-instrument-out cross-validated predictive error and compare to the H0 benchmark from the linear baseline. Estimate \( g'' \) and a confidence band over the supported cost range. Record whether the semiparametric model beats the linear null out of sample and whether \( g'' \) is reliably negative over a non-trivial portion of common support; these two findings feed the decision rule.

The estimate of \( g'' \) is reported as illustrative. In a small sample the confidence band on a second derivative is wide, and the design anticipates that the band may be too wide to declare reliable negativity even if the point estimate is concave. That caution is built into the decision rule: a concave point estimate with a band that includes zero over most of common support does not support H1. The principal objection is overfitting: a flexible smoother will find curvature in noise. The shape constraint and the leave-one-instrument-out test are the specific defenses, and the decision rule's insistence on out-of-sample improvement is what makes the objection answerable rather than fatal [\[110\]](#ref-110). Confidence that the aggregate concavity test alone will be decisive is low-to-moderate at the design stage, because of small-sample width on \( g'' \). This is the chapter's honest assessment and is the reason the over-specification test is given independent physical grounding rather than treated as a corollary of aggregate concavity.

### 6.7.2 Step 5: the over-specification test and its physical grounding

The over-specification test, which estimates the marginal contribution of an additional spectral channel to validated accuracy as a function of channel count and locates the lower edge of the range where that contribution is statistically indistinguishable from zero, is sharper and more falsifiable than aggregate concavity, and its statistical edge is predicted to coincide with the physical onset of spectral information redundancy. Statistically, within the partially linear model spectral-channel count enters through a flexible term, and the marginal channel contribution is the derivative of accuracy with respect to channel count, holding cost and other attributes fixed. The over-specification region is the channel range over which this marginal contribution is not distinguishable from zero, and the candidate over-specification channel count named in H1 is the lower edge of that region.

The physical legitimacy of an over-specification edge comes from optimal-estimation information theory. Rodgers established that a high-spectral-resolution measurement contains a quantifiable amount of information about the retrieved state, summarized by scalar figures of merit such as the Shannon information content and the degrees of freedom for signal, and that these quantities saturate: beyond a point, additional spectral channels carry information that is redundant with channels already present or is swamped by measurement and forward-model error [\[123\]](#ref-123), [\[122\]](#ref-122). The operational channel-selection literature operationalizes this saturation. Gambacorta and Barnet describe how the NOAA NESDIS operational channel selection for the Cross-track Infrared Sounder reduces thousands of channels to a far smaller operational subset by information-content analysis, retaining only channels that add independent information [\[117\]](#ref-117); Worden and colleagues show that predicted retrieval errors for the Tropospheric Emission Spectrometer are governed by spectral-window selection that maximizes information content, with diminishing returns beyond the informative windows [\[121\]](#ref-121). Channel-selection studies across CO2 and trace-gas retrievals reach the same conclusion, that a small selected subset captures nearly all the retrievable information [\[120\]](#ref-120), [\[114\]](#ref-114), [\[116\]](#ref-116), and synergetic and hyperspectral analyses confirm that the number of independent pieces of information is bounded well below the raw channel count [\[119\]](#ref-119), [\[112\]](#ref-112), [\[111\]](#ref-111). The hyperspectral-modeling reviews reinforce that information density does not scale linearly with channel count [\[115\]](#ref-115), [\[113\]](#ref-113), and the ultraspectral emissivity retrieval record shows the same saturation for surface variables [\[118\]](#ref-118).

If degrees of freedom for signal saturate as channel count rises, then the marginal validated-accuracy contribution of an additional channel must fall toward zero past the saturation point, because additional channels add no independent information to the retrieval and the residual error is set by calibration drift, geolocation, and intrinsic retrieval difficulty rather than by spectral sampling. The statistical over-specification edge and the physical saturation point are therefore predicted to coincide, which renders the dissertation's central causal mechanism testable: added channels raise cost; beyond a point information saturates and achievable accuracy is bounded by non-spectral error sources, the Simon near-decomposability and satisficing prior [\[14\]](#ref-14), [\[19\]](#ref-19); the accuracy-versus-cost curve flattens and the marginal channel contribution falls toward zero; dollars spent past the edge buy specification, not validated science; and a cost-capped portfolio can deliver more total validated accuracy by capping per-instrument specification. The optimal-estimation foundation is Rodgers' information-content framework [\[123\]](#ref-123), [\[122\]](#ref-122), and the applied channel-selection record across instruments and species supplies the empirical evidence that selected subsets capture nearly all retrievable information [\[117\]](#ref-117), [\[121\]](#ref-121), [\[120\]](#ref-120), [\[114\]](#ref-114), [\[116\]](#ref-116), [\[119\]](#ref-119), [\[112\]](#ref-112), [\[111\]](#ref-111). This is the chapter's distinctive corpus contribution: it supplies the physical theory that makes the over-specification edge a prediction about radiometer physics rather than a statistical curiosity.

The procedure has four sub-steps. Estimate the marginal channel contribution as a function of channel count from the flexible channel-count term in the partially linear model, holding cost and other controls fixed, on the balanced common-support sample. Construct a confidence band on the marginal channel contribution across the observed channel range. Locate the lower edge of the range over which the marginal contribution is statistically indistinguishable from zero, and report it as the candidate over-specification channel count. Finally, as a corroboration step, compare the statistically estimated edge to the information-content prior: where instrument-level degrees-of-freedom-for-signal estimates are available from the cited channel-selection studies for instruments in the sample, assess whether the statistical edge falls near the channel count at which those studies report information saturation. Agreement raises confidence; divergence lowers it and triggers the reference-ceiling probe of Chapter 7.

The over-specification edge is conditional on the supported population and on the controls; it is not claimed to be universal across geophysical variables, and the test is run within the supported range. The corroboration step is qualitative at the design stage because instrument-level degrees-of-freedom-for-signal values are not uniformly available across the sample; the chapter states this rather than implying a quantitative match. A reviewer may object that channel count and cost are collinear, so the marginal channel contribution cannot be separated from the cost effect. The design answers that the partially linear form and the common-support restriction are what permit the separation: the channel-count term is estimated holding cost fixed within the region where instruments of comparable cost differ in channel count, and the balance step ensures that such comparisons exist. Where collinearity is severe, the confidence band widens and the edge is reported as imprecise rather than as a sharp number. Confidence that the over-specification test is the more defensible of the two routes to a diminishing-returns finding is moderate-to-high, because it is corroborated by an independent and mature physical theory of spectral information content. It would rise if the statistical edge falls near the information-saturation channel count reported in the channel-selection literature for sampled instruments, and would fall if the two diverge or if collinearity makes the channel-count term uninformative.

## 6.8 The decision rule

The decision rule is fixed in advance and is the single arbiter of the contribution. It has two parts, one for aggregate concavity and one for the over-specification proposition, and the parts are evaluated independently so that the dissertation can report a graded outcome rather than a binary one.

**Aggregate concavity.** H1's concavity claim is supported if and only if both of the following hold: the semiparametric model beats the linear null in leave-one-instrument-out cross-validated predictive error, and the second derivative \( g'' \) is reliably negative over a non-trivial portion of common support, where reliability means the confidence band on \( g'' \) excludes zero over that portion. If the semiparametric model does not beat the linear null out of sample, H0 is retained regardless of any in-sample curvature, because in-sample curvature in a small sample is the expected symptom of overfitting and not of a real frontier [\[110\]](#ref-110). If the model beats the null out of sample but \( g'' \) is not reliably negative anywhere on common support, the outcome is recorded as suggestive but not supporting, and H0 is retained for the concavity claim.

**Over-specification.** The over-specification proposition is supported if and only if the marginal channel-count contribution reaches a region statistically indistinguishable from zero within the observed channel range, with the lower edge of that region reported as the candidate over-specification channel count. If the marginal channel-count contribution remains positive across the entire observed channel range, no over-specification region exists in the sample and the proposition is rejected. The corroboration step (Section 6.7.2) does not enter the decision rule as a gate; it modulates the confidence attached to a supported proposition rather than determining support, because the physical prior is evidence about plausibility, not a substitute for the statistical test.

**Graded outcomes.** The rule admits four reportable outcomes. Both parts supported: the strongest form of H1, a concave frontier with an identified over-specification edge. Over-specification supported but aggregate concavity not reliably established: a partial H1, the sharper prediction holds while the aggregate curvature is too imprecise to declare, which the chapter anticipates as a plausible small-sample result given the width of the \( g'' \) band. Aggregate concavity supported but no over-specification edge: concavity driven by drivers other than channel redundancy, which would send the interpretation to calibration and difficulty rather than to spectral over-specification. Neither supported: H0 stands, a well-identified linear finding that is itself a contribution.

The rule does more than state a pass condition; it states what evidence raises or lowers confidence in each outcome. Confidence in a both-parts-supported result would be raised by a wide common-support region, modest balancing-weight dispersion, agreement between the statistical edge and the information-saturation prior, and insensitivity to dropping ambiguously matched instruments; it would be lowered by thin common support, extreme weights, divergence from the information-content prior, or sensitivity to the marginal validated instruments. The dissertation commits to reporting whichever outcome the data support, and the design is built so that the null is informative rather than merely an absence of significance.

## 6.9 Illustrative, not-yet-executed expectations

**This section states expectations under each hypothesis as design illustrations. No results reported here have been executed on the full assembled dataset. All numbers and curve shapes are illustrative placeholders used to specify the procedure and to make the design concrete, and they must not be read as empirical findings.**

### 6.9.1 The H1-shaped expectation

Under H1, the fitted accuracy-cost curve \( g(\text{cost}) \) would rise steeply in the low-cost region, where adding spectral channels and modest calibration buys large requirement-normalized validated-accuracy gains, and would flatten in the high-cost region, where calibration drift, geolocation error, and the intrinsic difficulty of the retrieval cap achievable accuracy regardless of further spend. The second derivative \( g'' \) would be negative over a non-trivial portion of common support, and the semiparametric model would beat the linear null in leave-one-instrument-out cross-validation. The marginal channel-count contribution would be positive and large at low channel counts and would decline to a region indistinguishable from zero at higher channel counts, with the lower edge of that region appearing as the candidate over-specification channel count. Under H1, this statistical edge would fall near the channel count at which the information-content literature reports degrees-of-freedom-for-signal saturation for comparable retrievals [\[122\]](#ref-122), [\[117\]](#ref-117), [\[121\]](#ref-121), so that the statistical flattening and the physical redundancy onset coincide. The mechanism that produces this shape is the causal chain developed in Section 6.7.2: information saturation, non-spectral error dominance, and satisficing design behavior [\[14\]](#ref-14), [\[19\]](#ref-19).
### 6.9.2 The H0-shaped expectation

Under H0, the fitted accuracy-cost relationship would be statistically indistinguishable from a straight line: \( g(\text{cost}) \) would not differ reliably from a linear function of cost, the semiparametric model would not beat the linear null out of sample, and \( g'' \) would not be reliably negative anywhere on common support. The marginal channel-count contribution would stay positive across the entire observed channel range, so no over-specification region would exist. The interpretation under H0 is that, over the supported population, each additional dollar of instrument investment buys a roughly proportional increment of validated accuracy, and the information-content saturation that the physics predicts at the channel level is either not reached within the observed range or masked at the aggregate by other drivers. This is a coherent and reportable outcome, not a failure of the study.

### 6.9.3 Why both are stated

Stating both shapes makes the design falsifiable in the strict sense and commits the dissertation to the decision rule rather than to a preferred curve. Once assembled and run, the data will discriminate between the two by the rule in Section 6.8. The result tables that report the executed comparison are specified as shells in Section 6.9.4 and left unpopulated by design, because filling them with illustrative numbers would violate the design-stage guardrail and risk being misread as findings.

### 6.9.4 Specified-but-unpopulated result tables

The following table shells are part of the analysis plan and will be populated only after execution. They are reproduced here without values so that the reporting format is fixed in advance.

**Table 6.1 (shell). Balance diagnostics across cost terciles.** Columns: control variable; standardized difference pre-weighting; standardized difference post-weighting. Rows: spectral-channel count, swath width, spatial resolution, calibration approach, mass, power, mission epoch, retrieval difficulty. [To be populated at execution. No values by design.]

**Table 6.2 (shell). Common-support trimming log.** Columns: instrument; cost; reason outside support; retained or trimmed. [To be populated at execution. No values by design.]

**Table 6.3 (shell). Model comparison.** Columns: model (linear null; semiparametric concave); cross-validated predictive error (leave-one-instrument-out); whether \( g'' \) reliably negative over common support; out-of-sample improvement over null. [To be populated at execution. No values by design.]

**Table 6.4 (shell). Over-specification test.** Columns: channel-count range; marginal channel contribution; confidence band; indistinguishable from zero (yes/no). Candidate over-specification channel count: [lower edge, to be populated]. Information-content corroboration: [comparison to saturation channel count from cited channel-selection studies, to be populated]. [No values by design.]

**Table 6.5 (shell). Sensitivity analyses.** Columns: sensitivity check (drop ambiguously matched instruments; drop marginal validated instruments; alternative requirement-normalization; alternative smoother bandwidth); effect on out-of-sample improvement; effect on over-specification edge. [To be populated at execution. No values by design.]

## 6.10 Sensitivity analyses, specified in advance

The only permissible deviations from the frozen pipeline are the sensitivity analyses enumerated here, each specified before execution with its purpose. (1) Drop ambiguously matched instruments, per the Step-1 log, and re-run Steps 3 through 5; purpose, to bound cost measurement error from version mismatch. (2) Drop the most marginal validated instruments, those whose validation records are weakest, and re-run; purpose, to bound survivorship and publication selection. (3) Re-construct the dependent variable under an alternative requirement-normalization and re-run; purpose, to bound metric heterogeneity across product families. (4) Re-estimate \( g \) under an alternative smoother bandwidth within a pre-specified range; purpose, to confirm that the concavity conclusion is not an artifact of a single bandwidth choice. (5) Probe the validation-reference ceiling by examining whether the high-cost flattening coincides with the precision limits of the validation references, which is the reference-ceiling rival explanation carried into Chapter 7. Each sensitivity analysis reports its effect on the two decision-rule quantities, out-of-sample improvement and the over-specification edge, in Table 6.5. No sensitivity analysis may revise the decision rule; they characterize the robustness of whichever outcome the frozen pipeline produces.

## 6.11 How this chapter advances the argument

This chapter advances the dissertation's argument at two of its five elements. It strengthens the case that the design addresses the causal mechanism by specifying the partially linear shape-constrained estimator and by grounding the over-specification test in the optimal-estimation information-content theory that supplies the physical mechanism for the channel-count edge [\[123\]](#ref-123), [\[122\]](#ref-122), [\[117\]](#ref-117), [\[121\]](#ref-121). It strengthens the case that the design beats the alternatives by pre-committing to a like-for-like out-of-sample comparison between the linear null and the semiparametric model and by refusing to let in-sample curvature decide the contribution [\[110\]](#ref-110). It carries the case that residual risk is acceptable through the pre-specified sensitivity analyses that bound cost measurement error, survivorship, metric heterogeneity, smoother dependence, and the reference ceiling. The chapter's role is to make those three elements executable rather than aspirational.

Consistent with the scope decision recorded earlier, this chapter introduces no systems-architecture traceability vocabulary. The artifact is an econometric analysis plan that estimates a frontier and specifies a decision rule, not an architecture; the single permissible decision mapping, the management recommendation to cap spectral specification at the over-specification edge and reallocate the saved budget, is stated in Chapter 7 as a recommendation rather than as a capability-to-system traceability row. The analysis plan deliberately stops at the estimate and the decision rule, which is the correct boundary for a reduced-form hedonic contribution.

## 6.12 Summary

The chapter has delivered its answer: a frozen, five-step, falsification-first analysis plan with a fixed two-part decision rule that decides H1 against H0 by out-of-sample prediction and by the reliability of \( g'' \), plus a separate over-specification test whose statistical edge is predicted to coincide with the physical onset of spectral information redundancy. The plan pre-registers the order of operations, the matching and trimming protocols, the leave-one-instrument-out inference design, the decision rule, and the sensitivity analyses, and it labels every number and every curve shape as illustrative rather than estimated. The chapter's distinctive move is the information-content grounding of the over-specification test: by tying the channel-count edge to Rodgers' degrees-of-freedom-for-signal saturation and to the operational channel-selection record, the chapter makes the sharpest output of the dissertation a prediction about radiometer physics rather than a small-sample statistical artifact, and it states, at design-stage confidence grades, exactly what evidence would raise or lower confidence in each reportable outcome. The result tables are specified as shells and left unpopulated by design, in keeping with the design-stage guardrail that the analysis has not been executed and that the dissertation reports the procedure, not yet the findings.


# Chapter 7: Discussion

## 7.0 The chapter's answer, stated first

This chapter establishes one conclusion and then defends it across both empirical outcomes the design can produce. The conclusion is that the contribution is decision-relevant either way: whether the assembled data support H1 (validated retrieval accuracy is a concave function of instrument development cost, with an over-specification spectral-channel count beyond which additional specification stops paying for itself in validated science) or instead support H0 (accuracy is linear in cost with no diminishing returns and no over-specification region), the estimated frontier hands NASA and JPL Earth-science mission formulation a defensible input it does not currently have. Under H1 the input is a stopping rule for spectral specification and a reallocation argument; under H0 the input is the removal of diminishing returns as an unexamined assumption from instrument budgeting. The dissertation is built so that the null is informative rather than merely an absence of significance, and the chapter earns that claim by working through the management implications, the theoretical payback to each anchor framework, the rival explanations that could counterfeit a concave frontier, and the bounded external-validity statement, before stating the single management decision that the shared bible permits this design to recommend.

That sentence is the chapter's thesis. The problem it addresses can be framed in the standard four parts. The current state is that the field has two excellent but non-communicating literatures, a cost-modeling literature that predicts instrument cost from design and a calibration and validation literature that reports product accuracy in isolation, and no estimate of the shape of the relationship between the two [\[42\]](#ref-42), [\[46\]](#ref-46), [\[85\]](#ref-85), [\[73\]](#ref-73), [\[77\]](#ref-77). The desired state is a population-level estimate of validated accuracy as a function of instrument cost, written throughout this dissertation as \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), whose curvature in the cost dimension is what the concavity test reads. The gap is that no such estimate of the shape of \( g(\text{cost}) \) exists, so the field cannot say whether the marginal dollar of instrument investment still buys validated science. Leaving the gap open means Earth-science budgeting continues to set spectral specification without evidence on diminishing returns, and descope and distributed-architecture decisions rest on cost ceilings rather than on measured accuracy economics. This chapter's job is not to report a result, because at the design stage no result exists; it is to demonstrate that whichever way the frozen pipeline of Chapter 6 resolves, the field is left better off, and to defend that interpretive claim against the rival explanations that would otherwise undermine it.

A note on confidence calibration, carried consistently and in the same register as the sibling chapters. Every forward-looking statement about the shape of the frontier is an expectation under H1 or H0, never a finding. Where the interpretive claim rests on a convergent body of design-and-budget literature, it is stated at high confidence; where it rests on a single study, an analogy, or a mechanism that the data have not yet tested, the confidence is downgraded explicitly and the reader is told what additional evidence would raise it. The design-stage guardrail of the shared bible binds this chapter as tightly as any other: the discussion interprets two possible outcomes, it does not announce one.

## 7.1 Implications if H1 holds

### 7.1.1 The stopping rule and the mechanism behind it
If the semiparametric model beats the linear null out of sample and the second derivative \( g'' \) is reliably negative over a non-trivial portion of common support, then JPL Earth-science formulation gains a defensible stopping rule for spectral specification, anchored at the lower edge of the over-specification region the channel-count test would locate. The rule is usable rather than a curiosity because of the structure of the test itself, carried from Chapter 5 and Chapter 6. The over-specification edge is not read from aggregate concavity. It is the channel count past which the estimated marginal contribution of an additional spectral channel to validated accuracy is statistically indistinguishable from zero, holding cost and the design controls fixed, and corroborated physically by the onset of spectral information redundancy in the optimal-estimation sense [\[123\]](#ref-123). The statistical edge connects to a management rule because a design margin expressed in channel count is directly actionable by a mission team in a way that a curved aggregate relationship is not: a team formulating a radiometer can ask whether the channel count it is contemplating sits above or below the estimated edge.

The mechanism is explicit rather than a bare correlation. Added spectral channels and calibration elaboration raise instrument development cost. Beyond a point, additional channels carry information redundant with channels already present, and achievable validated accuracy is bounded by calibration drift, geolocation error, and the intrinsic difficulty of the retrieval, exactly the near-decomposability and satisficing logic that Simon's account predicts [\[14\]](#ref-14), [\[19\]](#ref-19). The validated-accuracy-versus-cost curve therefore flattens and the marginal channel contribution falls toward zero, so dollars spent past the over-specification edge buy specification, not validated science, and a cost-capped portfolio can deliver more total validated accuracy by capping per-instrument specification at the edge and reallocating the saved budget. Confidence in this mechanism is moderate-to-high as a prior, because it rests on a mature theory of how engineering organizations decide. Yet it is the data, not the theory, that would confirm the edge exists in this population. The theory licenses the expectation; the estimate would license the rule.

### 7.1.2 Where the reallocated budget should go

A second point sharpens the reallocation argument so that it is not a vague invitation to spend less. If H1 holds, the binding constraints in the flat region of the frontier are, by the named mechanism, calibration drift and geolocation error rather than spectral richness, because those are the error sources that cap achievable accuracy once channel information saturates. The cal/val literature's own diagnosis of where residual error lives in mature products supports this: validated accuracy budgets for sea-surface temperature, soil moisture, and aerosol optical depth attribute substantial residual error to calibration and reference-matching rather than to insufficient spectral sampling [\[73\]](#ref-73), [\[77\]](#ref-77), [\[83\]](#ref-83), [\[85\]](#ref-85). Reallocating a dollar from a redundant channel to calibration stability or geolocation accuracy moves the dollar from an error source that has saturated to one that is still binding, which is precisely the allocation a concave frontier rewards. The radiometric-calibration literature reinforces this by showing that calibration quality is itself a first-order determinant of geophysical-retrieval accuracy, so calibration is not a fixed cost floor but a margin that responds to investment. One caveat is essential and stated plainly: the dissertation estimates a reduced-form frontier and does not estimate the separate return to calibration investment, so the reallocation target is a direction implied by the mechanism, not a second estimated frontier. A team acting on it would still need a calibration-return analysis the present design does not provide.

The alternative destination for reallocated budget is distribution across more, individually less elaborate instruments, and this is where the H1 result connects to the live architectural debate. If accuracy returns to per-instrument cost are concave, then a portfolio that spreads budget across more instruments operating in the steep region can deliver more total validated accuracy than one that concentrates budget in a few instruments operating in the flat region. What makes this more than a slogan is the contemporary literature documenting that Earth observation is in fact moving toward distributed architectures of smaller instruments and toward commercial data buys, which forces explicit per-instrument capability choices [\[137\]](#ref-137), [\[130\]](#ref-130), [\[127\]](#ref-127), [\[129\]](#ref-129), [\[126\]](#ref-126). The concavity result would supply the missing accuracy-economics justification for the distributed instinct, which the literature currently grounds in cost ceilings and flexibility under demand uncertainty rather than in a measured accuracy frontier [\[130\]](#ref-130). The confidence here is calibrated down: the distributed-architecture literature establishes that the architectural choice is real and active, but the inference that concavity favors distribution is conditional on the saved-per-instrument budget actually buying a steep-region instrument elsewhere, which is a portfolio-construction question the frontier informs but does not settle.

### 7.1.3 The principled descope argument

The third H1 implication is the one most directly useful inside a cost-capped competition. Mission formulation routinely descopes under a fixed topline, and the descope argument is today largely rhetorical: capability is cut where it is least defended politically rather than where it is least productive scientifically. An estimated over-specification edge converts the descope from a capability-maximizing instinct into a value-aware target. The value-driven-design and tradespace literatures already hold that capability beyond a value threshold is dominated and that tradespaces routinely contain over-specified regions [\[17\]](#ref-17), [\[23\]](#ref-23), [\[139\]](#ref-139). This dissertation would supply, for the specific case of radiometer spectral specification, a population-level empirically located threshold where the prior tradespace work has reasoned about the threshold case by case. The operational consequence is concrete: a descope that removes channels above the estimated edge can be defended as removing specification that the validated-accuracy record does not reward, a far stronger position than removing capability because the budget ran out. Confidence in the usefulness of this argument is high conditional on H1 holding, because the tradespace literature has already established the conceptual demand for exactly such a threshold. What it has lacked is a measured value for it, and that is what the H1 result would deliver.

### 7.1.4 The portfolio-level mechanism and its boundary

The fourth H1 implication operates one level above the single instrument, at the portfolio, and it carries the largest potential consequence and the most carefully bounded confidence. Under a concave frontier a cost-capped Earth-science portfolio can deliver more total validated accuracy by allocating its fixed topline across more instruments held at or below the over-specification edge than by concentrating the topline in fewer instruments pushed into the flat region. This follows from the arithmetic of a concave function under a budget constraint: when the marginal accuracy per dollar declines with per-instrument cost, the total accuracy summed across a portfolio is maximized by equalizing marginal returns across instruments, which pulls every instrument toward the steep region rather than letting any single instrument climb into the flat one. The optimization principle is elementary. A sum of concave returns subject to a budget is maximized where marginal returns are equalized, the same logic that makes diversification rational under diminishing returns. Stated as an explicit mechanism: the portfolio faces a fixed topline and must divide it; concavity means each instrument's marginal accuracy per dollar falls as its cost rises; equalizing marginal returns across instruments therefore dominates concentrating budget; the portfolio shifts toward more, individually leaner radiometers; and total delivered validated accuracy rises without a topline increase.

The boundary on this claim is where the chapter spends most of its care, because the portfolio implication is the easiest to over-read. The frontier estimates the relationship between a single instrument's cost and its validated accuracy. It does not estimate the cross-instrument substitution that a portfolio reallocation assumes, namely that the accuracy lost by leaning out one instrument is more than recovered by the accuracy gained from the instruments the saved budget funds. That substitution depends on whether the additional instruments address science needs the portfolio actually has, on launch and operations costs the development-cost frontier excludes, and on coverage and revisit considerations that lie entirely outside the accuracy-per-instrument relationship. The contemporary distributed-architecture and constellation literature makes exactly these portfolio-level considerations explicit, treating deployment staging, demand uncertainty, and constellation trade-offs as first-order [\[130\]](#ref-130), [\[129\]](#ref-129), [\[126\]](#ref-126), [\[127\]](#ref-127). One caveat is therefore stated plainly and protected: the frontier is a necessary input to the portfolio argument but not a sufficient one, and the confidence that concavity favors a distributed portfolio is moderate, raised by the optimization logic and lowered by the cross-instrument substitution and life-cycle-cost questions the present design does not estimate. A team acting on the portfolio implication would need a coverage-and-life-cycle analysis the dissertation deliberately leaves to the value-of-information and constellation-design literatures.

## 7.2 Implications if H0 holds

### 7.2.1 A well-identified null is a contribution, not a failure

If the data retain H0, the dissertation has still produced a decision-relevant result, and the design was built so that this is true rather than asserted after the fact. The decision rule itself secures this, carried verbatim from the shared design: H1 is supported only if the semiparametric model beats the linear null out of sample and \( g'' \) is reliably negative over a non-trivial portion of common support, and in-sample curvature alone retains H0 [\[110\]](#ref-110). Because the rule pre-commits to a held-out predictive comparison rather than to in-sample fit, a finding that accuracy is linear in cost over the supported range is a positive, well-identified statement and not merely a failure to reject. The value of a null depends on the power and identification of the design that produced it. A null from a noisy, confounded, overfit specification is uninformative, but a null from a pre-registered estimator with balancing weights, common-support restriction, and leave-one-instrument-out validation is evidence that, within the supported population, the marginal dollar buys a roughly constant increment of validated accuracy. The program-evaluation tradition insists on exactly this, that a credibly identified estimand makes the null as interpretable as the alternative [\[105\]](#ref-105), [\[94\]](#ref-94).

The practical payoff of a clean H0 is the removal of diminishing returns as a rhetorical device in budget debates. Today a program manager arguing against an elaborate instrument can invoke diminishing returns without evidence, and a manager arguing for it can deny them with equal evidentiary basis, because no measured relationship exists. A credible linear finding would discipline both moves: it would justify continued investment in specification where mission requirements demand it, and it would deny the diminishing-returns argument to anyone deploying it as a generic descope lever. The mechanism is informational rather than physical: the result changes what claims are defensible in a formulation review, which changes which descopes survive scrutiny. Confidence that a well-identified null would have this effect is moderate, because it depends on the result being accepted as credible by the formulation community, a sociological condition the dissertation can support through its identification discipline but cannot guarantee.

### 7.2.2 What H0 would and would not license

A second, narrower point guards against over-reading a null. If H0 holds, it licenses the statement that accuracy is linear in cost over the region of common support, for NASA-class passive radiometers in the modern era, holding the design and difficulty controls fixed. It does not license the statement that there are no diminishing returns anywhere, because the common-support restriction means the estimand is silent outside the cost range where instruments of differing cost actually coexist with comparable attributes. This guard follows from the estimand definition in Chapter 5: the shape of \( E[\text{accuracy} \mid \text{cost}, \mathbf{X}] \) is estimated only over common support, and extrapolation beyond it is not warranted [\[101\]](#ref-101), [\[104\]](#ref-104). The principle is elementary. A regression speaks only to the support of its data, sharpened here by the deliberate trimming to common support that the design performs. The operational consequence is that an H0 result would not justify unbounded specification. It would justify continued specification only within the cost range the data cover, and would leave the behavior of the frontier at extreme cost as an open question requiring data the present sample lacks. This guard is itself a contribution, because it prevents the null from being weaponized into a license for arbitrarily expensive instruments, which the data would not support.

## 7.3 Theoretical contribution back to each anchor framework

### 7.3.1 To Rosen and the hedonic tradition: a demonstrated inversion

The dissertation returns to the hedonic tradition a worked demonstration that the framework can be inverted, that a performance metric rather than a market price can serve as the hedonic outcome, and that the inversion is methodologically disciplined rather than a loose analogy. The construction carried from Chapter 2 establishes this: Rosen's result is that a differentiated good's price is a function of its attributes whose partial derivatives reveal implicit marginal prices [\[26\]](#ref-26), and this dissertation regresses validated accuracy on instrument attributes with cost as the central attribute, recovering the implicit accuracy contribution of cost rather than the implicit price of a characteristic. This is a genuine contribution to the hedonic literature, rather than a borrowing from it, because the inversion exposes a structural question the price-side literature does not face: when the outcome is a physically bounded performance metric rather than an unbounded price, the hedonic surface has a ceiling, and the curvature of the surface near that ceiling becomes the object of interest. The price-side hedonic literature studies the level and slope of implicit prices; the inverted accuracy-side hedonic studies the curvature of an outcome that physics caps. Confidence that this is a real theoretical contribution is moderate-to-high, qualified by the honest acknowledgment carried from the expansion plan's gap list that no direct methodological precedent exists for the exact inversion, so the contribution is in part the demonstration that the inversion is coherent and estimable at all.

### 7.3.2 To the NICM and parametric-cost tradition: the missing accuracy axis

The dissertation contributes to the cost-modeling tradition the axis that tradition structurally lacks. The definitional fact established in Chapter 3 makes this clear: NICM and the Stahl parametric models regress cost on design and never reach accuracy [\[42\]](#ref-42), [\[46\]](#ref-46). A cost model and an accuracy frontier are complementary halves of the same trade: the cost model answers what an instrument will cost given its design, and the frontier this dissertation estimates answers what validated accuracy that cost will buy, and only the two together support a value-aware formulation decision. The contribution is additive and cumulative rather than corrective: the dissertation does not overturn NICM, which does exactly what it was built to do, but supplies the second axis that converts a cost prediction into a value statement. The mechanism by which this helps is concrete: a formulation team using NICM to price a design can, with the frontier, also ask whether the priced design sits in the steep or flat region of the accuracy-cost relationship, a question NICM alone cannot pose. Confidence that this complementarity is real is very high, because it rests on the definitional structure of cost-estimating relationships rather than on a contestable interpretation. The cost axis and the accuracy axis are simply different axes, and the field has had only one of them.

### 7.3.3 To Simon and the bounded-rationality tradition: an empirical test of a design prediction

The dissertation offers the bounded-rationality tradition something it rarely receives: a falsifiable, population-level empirical test of one of its design predictions. Simon's satisficing and near-decomposability arguments predict diminishing returns to elaboration, and the over-specification edge is a direct empirical correlate of that prediction [\[14\]](#ref-14), [\[19\]](#ref-19), [\[22\]](#ref-22). Most applications of bounded rationality to design are interpretive or simulation-based, whereas this dissertation proposes to locate, in real instrument data, the channel count at which marginal elaboration stops contributing to delivered function, the over-specification region Simon's theory names but rarely measures. The contribution cuts both ways, and the chapter states both directions honestly. If H1 holds, the tradition gains an empirical confirmation in a high-stakes engineering domain. If H0 holds, the tradition gains a genuine boundary condition: a domain in which, over the supported range, elaboration does not visibly diminish in return, which is itself informative about where satisficing predictions do and do not bind. Confidence that the dissertation can deliver this test is moderate, qualified by the small sample, which constrains how sharply the edge can be located even under H1.

### 7.3.4 To the value-driven-design tradition: a located threshold

The dissertation contributes to value-driven design and tradespace exploration a population-level, empirically located version of a threshold those literatures have reasoned about case by case. The tradespace literature establishes the existence of dominated, over-specified regions and argues that value rather than raw capability is the proper objective [\[17\]](#ref-17), [\[23\]](#ref-23), [\[139\]](#ref-139). These literatures supply the conceptual demand for an over-specification threshold but locate it, when at all, through case-specific tradespace enumeration rather than through a frontier estimated across a population. This dissertation would supply, for radiometer spectral specification, an estimated location for the threshold that generalizes beyond a single tradespace study. The confidence is calibrated to the design stage: the tradespace literature's conceptual claim is well established, but the empirical location is exactly what has not been executed, so the contribution is the method and the design for locating it, with the located value contingent on execution.
## 7.4 Rival explanations

### 7.4.1 Technology improvement over time

The first rival is that apparent concavity could be produced not by diminishing returns to cost but by technology improvement: later instruments are both cheaper and more accurate because the technology improved, which could bend the accuracy-cost relationship without any genuine over-specification. The mission-epoch control addresses this rival rather than ignoring it. Technology vintage enters as a control in the design set \( \mathbf{X} \), and the cost-model literature itself documents a systematic negative technology-epoch term, confirming that vintage shifts the cost surface and must be absorbed [\[46\]](#ref-46), [\[42\]](#ref-42). Conditioning on epoch removes the component of any cost-accuracy association that runs through the calendar, so residual curvature in \( g(\text{cost}) \) is curvature net of technology improvement. A skeptic would still press that epoch is a coarse proxy for a continuous, multidimensional technology frontier, leaving residual epoch-correlated improvement to survive the control. The point is conceded and stated plainly: the epoch control attenuates but does not provably eliminate the technology rival, and the confidence that residual curvature reflects diminishing returns rather than uncontrolled vintage is moderate, raised by the inclusion of the control and lowered by its coarseness. The evidence that would raise it is a finer technology index than the present design carries.

### 7.4.2 Easier retrievals assigned to cheaper instruments

The second rival is reverse difficulty sorting: if cheaper instruments are systematically assigned to easier retrievals, then a naive accuracy-on-cost regression would show cheaper instruments achieving high accuracy for reasons of problem difficulty rather than cost efficiency, counterfeiting concavity. This rival is the central motivation for the retrieval-difficulty control and the common-support restriction. The Abadie-tradition identification logic from Chapter 5 establishes the concern: instruments are not randomly assigned their cost levels, expensive instruments are built for harder problems, and a naive comparison confounds the cost effect with the difficulty of the retrieval [\[105\]](#ref-105), [\[94\]](#ref-94). Conditioning on retrieval difficulty and restricting to common support compares instruments of differing cost that face comparable retrieval problems, so the curvature estimate becomes interpolation within comparable instruments rather than an artifact of comparing a cheap easy retrieval to an expensive hard one. The mechanism the rival posits is real, and the design targets it directly: program managers match budget to expected difficulty, difficulty and cost become correlated, and a spurious cost-accuracy pattern results, which the difficulty control plus balancing weights plus common-support trimming absorb [\[101\]](#ref-101). Confidence that the rival is controlled is moderate-to-high where the difficulty control is well measured and lower where retrieval difficulty is itself hard to quantify, which is acknowledged as the weakest point of the difficulty construct.

### 7.4.3 The validation-reference ceiling

The third rival is the most subtle, and the chapter treats it at length because it is the one the design cannot fully dispatch. High-cost flattening of the accuracy-cost curve could arise not from instrument over-specification but from a ceiling in the validation reference data itself: if the in-situ or reference standard is not accurate enough to distinguish a very good instrument from an excellent one, the validated-accuracy metric saturates for reasons of measurement rather than instrument capability, and the curve flattens at the high-cost end as an artifact. This is a genuine alternative because validation references have their own finite precision: AERONET, in-situ sea-surface-temperature networks, and soil-moisture core validation sites all carry uncertainty budgets that bound how finely they can discriminate retrieval accuracy [\[87\]](#ref-87), [\[73\]](#ref-73), [\[77\]](#ref-77), [\[78\]](#ref-78). The connection to the flattening is direct: if the reference cannot resolve differences below some error level, then instruments that achieve error near that level will all be scored as equivalently accurate regardless of their true accuracy, producing flattening that mimics over-specification.

The design's response is a probe rather than a control, and the chapter is honest about the difference. The probe, specified in Chapter 6, examines whether the high-cost flattening coincides with the precision limits of the validation references: if the flattening sets in exactly where the reference precision is exhausted, the reference-ceiling explanation is supported; if the flattening sets in well above the reference precision floor, the instrument-over-specification explanation is supported. The probe works because the two explanations make different predictions about where, relative to reference precision, the flattening occurs, and that difference is observable. Its limit is that the corpus is thin on reference-network uncertainty characterizations as a function of product, which the expansion plan flags as an evidence gap requiring a targeted follow-up sweep before execution. Confidence that the reference-ceiling rival can be distinguished from genuine over-specification is therefore the lowest of the three rivals, downgraded explicitly, and the evidence that would raise it is precisely the reference-network uncertainty budgets the corpus currently lacks. Stating this honestly is the discipline the design demands: the reference ceiling is the rival most capable of counterfeiting the headline result, and the dissertation neither dismisses it nor pretends to have fully defeated it.

### 7.4.4 Survivorship and publication selection

The fourth rival is that the population is restricted to instruments that flew, validated, and were written up, so instruments that failed or underperformed are absent, and if failure is correlated with cost the frontier could be biased. Scoping the estimand handles this rather than pretending the selection away. The data-construction decision from Chapter 4 settles it: the population is by construction the set of instruments that reached validated operations, so the estimand is the frontier among instruments that succeeded, not among all instruments designed [\[38\]](#ref-38). A clearly scoped estimand is not biased relative to its own target; it is biased only if read as a claim about the design-and-fail population, which the dissertation does not make. One caveat is that the result must not be extrapolated to the question of whether expensive instruments are more or less likely to fail, which is a different study with a different sample. Confidence that survivorship does not threaten the within-scope estimand is high; confidence that the estimand answers the broader all-instruments question is deliberately zero, because it does not attempt to. The sensitivity analysis that drops the most marginal validated instruments bounds how much the weakest validation records move the result, which is the residual mitigation the design provides.

### 7.4.5 The instrument-product dependence and what it does not threaten

The fifth rival is not a confounder but an inferential one, and the chapter addresses it because a careful reader will raise it. The unit of analysis is the instrument-product pair, so a single radiometer that yields several validated products contributes several rows that share one cost value, which induces dependence among rows from the same instrument. A skeptic would press that this dependence inflates the effective sample, making the curvature estimate look more precise than it is and risking a false declaration of concavity. The dependence is an inference problem the design already handles, not a bias in the frontier itself. The design decision carried from Chapters 4 and 5 to use instrument-clustered standard errors and leave-one-instrument-out cross-validation treats the instrument, not the row, as the independent unit [\[105\]](#ref-105), [\[104\]](#ref-104). Clustering at the instrument level and validating by holding out whole instruments respects the dependence structure exactly: a curvature signal that survives leave-one-instrument-out validation cannot be an artifact of multiple correlated rows from a single instrument, because the held-out instrument's rows are absent together. The design neutralizes the rival because the effective sample for the out-of-sample test is the number of instruments, not the number of rows, so the decision rule cannot be fooled by row multiplicity. The honest caveat is that clustering corrects the inference but does not enlarge the genuinely small instrument-level sample, so the dependence does not bias the estimate even though the small instrument count still constrains how sharply concavity can be resolved, which is the statistical-conclusion limitation the design names rather than hides. Confidence that the dependence does not threaten the frontier is high; confidence that the instrument-level sample is large enough to resolve a subtle curvature is the deliberately downgraded one the small-sample sensitivity analyses are built to probe.

## 7.5 External validity and scoped extensions

### 7.5.1 The bounded external-validity statement

The estimate speaks to NASA-class passive radiometers in the modern era and should not be read as a universal law of instrument economics, and that narrowness is a strength rather than an evasion. The estimand definition fixes the boundary: the population is NASA and NASA-partnered passive radiometers with both a NICM-class cost record and a documented Level-2 or Level-3 validation record, spanning roughly the MODIS era to the present, and active sensors, non-NASA instruments under different cost accounting, and future technologies absent from the sample fall out of scope. The standard external-validity principle is that an estimate generalizes only to populations resembling its sample on the dimensions that drive the outcome, and the dissertation's sample differs systematically from active sensors, which have different cost drivers and accuracy metrics, from commercial instruments, which use different cost accounting, and from future technologies, whose design attributes are absent. Confidence that the result generalizes within its stated population is high; confidence that it generalizes beyond it is deliberately withheld. A narrow, defensible claim is preferable to a broad one the data cannot support, and the chapter states the boundary plainly rather than letting the reader infer a wider reach.

### 7.5.2 The active-sensor analogue

The first scoped extension is named because it is the natural next study rather than a weakness of this one. Radars and lidars have their own cost drivers, transmit power, antenna or telescope aperture, and pulse design, and their own validated-accuracy records, so a parallel frontier could be estimated for them. The active-sensor frontier is a companion study and must remain separate, because pooling active and passive sensors would violate the comparability that identification requires. The cost drivers and accuracy metrics of active instruments are not commensurable with passive radiometry, so a pooled sample would compare instruments across an incomparability the balancing weights and common-support restriction cannot bridge. The identification logic is that comparability within common support is what licenses the curvature estimate, and active and passive sensors do not share common support in the relevant attributes. Confidence that the active-sensor analogue is worth doing is high; confidence that it would show the same concavity is unknown and deliberately left open, because whether concavity is a property of radiometry physics or of a broader instrument-economics regularity is itself an empirical question the bounded design cannot answer.

### 7.5.3 The commercial-radiometer analogue and the physics-versus-regime question

The second scoped extension is the one that most sharpens the contribution's limits. The growth of commercial Earth-observation constellations creates a population of radiometers built under cost accounting that differs from NASA development-cost conventions [\[137\]](#ref-137), [\[130\]](#ref-130), [\[127\]](#ref-127), [\[129\]](#ref-129), [\[126\]](#ref-126). A frontier estimated on commercial radiometers might differ in level even if its shape were similar, and the comparison would answer a question the present design poses but cannot resolve: is the concavity a property of radiometry physics, and therefore portable across cost regimes, or a property of the NASA cost regime, and therefore not? The shape of \( g(\text{cost}) \) could be driven either by the physics of how spectral information saturates against calibration and geolocation error, which is regime-independent, or by the specific cost-accounting conventions that map design to dollars, which is regime-specific. A similar shape across two different cost regimes would point to physics, while a different shape would point to regime, and only the commercial comparison can run that test. Confidence that this is the decisive next question is high; confidence in either answer is zero pending the comparison, which is the honest position. Naming this extension keeps the present claim defensible while making clear that it is a first estimate rather than a final word.

## 7.6 Relationship to the cost-model and tradespace literatures

This section consolidates the theoretical-contribution arguments into a single statement about where the dissertation sits relative to the two literatures it most directly extends. If the frontier is concave with an over-specification edge, the result sits alongside the cost-model and value-driven-design literatures rather than overturning either. The cost models predict cost from design and are silent on accuracy, so adding the accuracy axis extends them without contradiction [\[42\]](#ref-42), [\[46\]](#ref-46); and the tradespace and value-driven-design work already holds that capability beyond a value threshold is dominated, so supplying a population-level location for that threshold extends them without contradiction either [\[17\]](#ref-17), [\[23\]](#ref-23), [\[139\]](#ref-139). A contribution that completes a partial picture, by adding a missing axis to cost models and a measured value to a conceptual threshold, is more credible for a first study than a contribution that claims to overturn established work. The mechanism of the complementarity is that the three pieces compose into a single value-aware formulation workflow: the cost model prices the design, the frontier says whether the priced design is in the steep or flat region, and the tradespace logic says to stop at the value-dominant point, which the over-specification edge now locates. Confidence that the contribution is complementary and cumulative rather than disruptive is high, and the chapter prefers that framing because it is the more defensible and more useful one.

The same complementarity logic governs the relationship to the value-of-information and cost-benefit literature that the corpus carries. Studies that estimate the value of Earth-observation information for specific decisions, agricultural choices, flood response, wildfire monitoring, and resource appraisal, take delivered accuracy as an input and translate it into decision value [\[138\]](#ref-138), [\[128\]](#ref-128), [\[132\]](#ref-132), [\[133\]](#ref-133). The present frontier sits upstream of all of them: it estimates the technical relationship between dollars and validated accuracy that any value-of-information analysis must take as a given. One cannot value the accuracy an instrument delivers without first knowing how much accuracy a given investment buys, which is the frontier this dissertation estimates and which the value-of-information literature currently assumes. Confidence that the frontier is a legitimate upstream input to that literature is moderate-to-high, qualified by the boundary that the dissertation estimates the technical frontier and explicitly does not value accuracy in dollars or perform a full cost-benefit analysis, which the cost-benefit literature handles with its own apparatus [\[135\]](#ref-135), [\[140\]](#ref-140). The dissertation supplies the input; it does not absorb the downstream valuation, and the boundary is stated so the contribution is not over-claimed.

## 7.7 What would falsify the contribution

This short section states the falsification conditions in advance, which is the discipline that separates the design from a search for a pleasing curve. The contribution is falsified, and H0 stands, under any one of three conditions, restated here exactly as the shared design fixes them. First, if the semiparametric concave model fails to beat the linear null out of sample, then any in-sample curvature is treated as the expected symptom of overfitting a small sample and not as a real frontier, and H0 is retained [\[110\]](#ref-110). Second, if the second derivative \( g'' \) of the fitted accuracy-cost function is not reliably negative over a non-trivial portion of common support, then the concavity claim is rejected regardless of point estimates. Third, if the marginal channel-count contribution remains positive across the entire observed channel range, then no over-specification region exists and the sharper proposition fails. Stating these in advance matters because a falsifiable contribution must name the outcomes that would defeat it before seeing the data, and the dissertation does. Confidence that these conditions are the right ones is very high, because they are derived directly from the estimator and the decision rule rather than chosen post hoc; they are the operational negations of exactly the two propositions H1 asserts.

## 7.8 Decision recommendation (management, not architecture)
This section states the single decision mapping this design permits itself to recommend, and it states it as a management recommendation rather than as a systems-traceability artifact, in keeping with the scope decision recorded earlier. The recommendation is conditional on H1 and is the plain-language stopping rule: cap spectral specification at the estimated over-specification edge, and reallocate the saved budget either to the binding error sources in the flat region, calibration stability and geolocation accuracy, or across additional instruments operating in the steep region of the frontier. It rests on the H1 implications developed in 7.1. The concave frontier identifies a channel count past which additional specification does not produce commensurate validated accuracy, and the binding constraints in the flat region are calibration and geolocation rather than spectral richness [\[73\]](#ref-73), [\[77\]](#ref-77), [\[83\]](#ref-83). A management recommendation expressed as a stopping rule and a reallocation direction is actionable in formulation without requiring the dissertation to design any system, capability, or data exchange, the boundary the scope decision fixes. The recommendation is deliberately not rendered as a capability-to-operational-activity-to-system-function traceability chain, because no real capability or system is being fielded; the artifact estimates a frontier and recommends a budgeting rule, and forcing systems-engineering vocabulary onto it would misrepresent what it is.

The recommendation carries its own caveat, which the chapter protects rather than hides. It is conditional on H1 holding, on the over-specification edge being located with enough precision to act on, and on the reallocation target being confirmed by the separate calibration-return analysis the present design does not provide. Under H0, the recommendation inverts: there is no spectral-specification stopping rule to apply over the supported range, and the management implication is instead to stop invoking diminishing returns as a generic descope lever and to justify specification on mission-requirement grounds. Either recommendation is a management input to formulation, stated at the confidence the design-stage evidence supports, and neither is an architecture. This is the only decision mapping the dissertation makes, and it is made as plainly and as conditionally as the evidence grade allows.

## 7.9 How this chapter advances the argument

This chapter advances the dissertation's argument principally at its outer elements. It carries the case that the problem is material by tying both outcomes to live formulation decisions, fixed toplines, distributed architectures, commercial buys, and descope, and by showing that the result is decision-relevant under H1 and under H0 alike [\[137\]](#ref-137), [\[130\]](#ref-130), [\[134\]](#ref-134), [\[139\]](#ref-139). It strengthens the case that the design beats the alternatives by working through the rival explanations, technology improvement, difficulty sorting, the validation-reference ceiling, and survivorship, and showing for each which design feature absorbs it and where the residual confidence sits [\[105\]](#ref-105), [\[101\]](#ref-101), [\[110\]](#ref-110). It carries the case that residual risk is acceptable by stating the rivals the design cannot fully defeat, the reference ceiling above all, at downgraded confidence and naming the evidence that would raise it. This chapter's role is to subject the contribution to its rivals and its boundaries and to show that it survives them as a bounded, falsifiable, decision-relevant claim rather than an unguarded one.

Consistent with the scope decision recorded earlier, this chapter introduces no systems-architecture traceability vocabulary. The artifact is an econometric study that estimates a frontier and recommends a budgeting rule, not an architecture; the single permissible decision mapping, the management recommendation in 7.8, is stated as a recommendation rather than as a capability-to-system row. The discussion stops at the interpretation, the rivals, the boundaries, and the recommendation, the correct terminus for a reduced-form hedonic contribution.

## 7.10 Summary

The chapter has delivered its answer: the contribution is decision-relevant under both outcomes, and the discussion has earned that claim rather than asserting it. Under H1, a concave frontier with an over-specification edge gives JPL formulation a defensible stopping rule, a sharpened reallocation argument toward calibration and geolocation or toward more instruments, and a principled descope target, with the causal mechanism stated in full and grounded in Simon's near-decomposability and satisficing prior. Under H0, a well-identified linear finding removes diminishing returns as an unexamined budgeting assumption while explicitly declining to license unbounded specification outside common support. The theoretical payback runs to all four anchors: a demonstrated inversion for the Rosen hedonic tradition, the missing accuracy axis for the NICM and Stahl cost-modeling tradition, an empirical test of a design prediction for the Simon bounded-rationality tradition, and a located threshold for the value-driven-design tradition. The four rival explanations, technology improvement, difficulty sorting, the validation-reference ceiling, and survivorship, are each engaged with the design feature that bears on it and with an honestly downgraded confidence where the design cannot fully defeat the rival, the reference ceiling most of all. The external-validity statement is bounded to NASA-class passive radiometers in the modern era, with the active-sensor and commercial-radiometer analogues named as the scoped next studies and the physics-versus-cost-regime question left open as the decisive one. The falsification conditions are restated exactly, and the single permitted management recommendation is stated conditionally and as a recommendation rather than an architecture. Every forward-looking statement in the chapter is an expectation under H1 or H0, never a result, in keeping with the design-stage guardrail that the analysis has not been executed and that the dissertation reports the procedure and its interpretation, not yet the findings.


# Chapter 8: Conclusion

## 8.1 The answer this dissertation gives

This dissertation set out to estimate, for the first time, the shape of the relationship between what NASA and JPL spend to build an Earth-observing radiometer and the validated geophysical accuracy that the instrument ultimately delivers, holding fixed the design attributes and the retrieval difficulty that drive both. The answer it offers is a method and a falsifiable claim, not yet an executed result. The method is an inverted hedonic regression: Rosen's framework, which recovers the implicit value of a differentiated good's attributes from its price [\[26\]](#ref-26), is turned on its head so that validated retrieval accuracy, rather than market price, becomes the hedonic outcome, and instrument development cost becomes the attribute whose curvature is the object of interest [\[26\]](#ref-26). The falsifiable claim is that this accuracy surface is concave in cost, with marginal accuracy per dollar declining and then collapsing beyond an estimable spectral-channel count, against the null that accuracy is linear in cost with no diminishing returns at all.

The contribution can be stated in one sentence that the rest of this chapter develops and qualifies. A reduced-form hedonic frontier, estimated across NASA-class passive radiometers, is expected to show that validated retrieval accuracy is concave in instrument development cost with an identifiable over-specification spectral-channel count, giving cost-capped Earth-science mission formulation a defensible stopping rule for spectral specification, or, if the null holds, removing diminishing returns as an unexamined assumption in instrument budgeting. The purpose of this final chapter is to restate that contribution precisely, to draw the line between what stands regardless of which hypothesis the data support and what depends on confirmation of H1, to state the limitations without softening them, to lay out a concrete future-research program including the path from this design-stage document to an executed estimate on the full assembled dataset, and to close.

I lead with the answer because the argument that runs through the whole dissertation has already been built across Chapters 1 through 7, and the conclusion's job is to certify it rather than to re-argue it. The five elements of that argument are that the problem is real, that it is material, that the design addresses the causal mechanism, that it beats the alternatives, and that the residual risk is acceptable. Each was developed with its own evidence and reasoning in the body chapters. Here I show that the contribution survives even when the central empirical claim is held in suspension, the strongest form a design-stage conclusion can take.

## 8.2 The contribution restated

### 8.2.1 What is genuinely new

The novelty of this work is the join. Three mature literatures bear on the question and none of them closes it. The instrument cost-modeling literature, exemplified by the NASA Instrument Cost Model across its versions [\[42\]](#ref-42), [\[37\]](#ref-37) and by the parametric telescope cost models of Stahl [\[46\]](#ref-46), regresses cost on design attributes and stops at cost. It is hedonic in spirit but its dependent variable is the wrong one for the question of returns. The cal/val literature, which establishes the validated error of individual products to high standards, whether aerosol optical depth from MODIS [\[85\]](#ref-85), soil moisture from SMAP [\[77\]](#ref-77), or sea-surface temperature across half a century of matchups [\[73\]](#ref-73), treats each instrument in isolation and never relates its error to its cost. The hedonic-pricing literature founded by Rosen [\[26\]](#ref-26) is mature for housing and differentiated consumer goods but has never been applied to scientific instruments and never been inverted to put a performance metric on the left-hand side. The unfilled space is the place where these three meet: an estimate of validated accuracy as a function of instrument cost, across a population of radiometers, with the design drivers controlled. That estimate does not exist in the literature, and producing its design is the contribution this dissertation makes.

The notation that carries the contribution is fixed and consistent across every chapter. The estimating equation is \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), where \( g \) is an unknown smooth function estimated under a monotonicity-and-concavity-respecting smoother, \( \mathbf{X} \) is the vector of design and difficulty controls entered linearly, \( \boldsymbol{\beta} \) is their coefficient vector, and \( e \) is an instrument-clustered error. The function \( g \) carries the concavity test. Its second derivative, \( g'' \), is the quantity whose sign discriminates H1 from H0 over the supported range of cost. The over-specification test is sharper still: it enters spectral-channel count with a flexible term and locates the channel range over which the marginal contribution of an additional channel to validated accuracy is statistically indistinguishable from zero, with the lower edge of that range being the candidate over-specification channel count.

### 8.2.2 The four anchors and how they combine

The intellectual architecture of the contribution rests on four anchors that combine into a single argument rather than sitting side by side. Rosen supplies the hedonic surface and licenses its inversion, on the reasoning that instrument cost is a near-sufficient statistic for the engineering effort, component quality, and calibration rigor embodied in the build, and that those embodied qualities are precisely what translate into accuracy [\[26\]](#ref-26). The NICM and Stahl cost-model family supplies the cost regressor and, more importantly, the evidence that cost is a structured index of design rather than noise, since cost is systematically predictable from design attributes [\[42\]](#ref-42), [\[37\]](#ref-37), [\[46\]](#ref-46). The Abadie program-evaluation tradition supplies the identification discipline, insisting that instruments are not randomly assigned their cost levels and that the estimand must therefore be defined over a region of common support where instruments of differing cost are genuinely comparable, with covariate balance checked and enforced rather than assumed [\[105\]](#ref-105), [\[94\]](#ref-94). Simon supplies the substantive prior that makes concavity the expected result rather than an arbitrary guess: bounded rationality and satisficing imply that designers search to an aspiration level and stop [\[19\]](#ref-19), [\[22\]](#ref-22), and the architecture-of-complexity argument implies that beyond a point the interactions added by further elaboration contribute little to overall function while adding cost and integration burden [\[14\]](#ref-14).

These four anchors do not merely coexist; they entail one another in the design. Without Rosen, there is no reason to put cost on the right-hand side as an embodied-investment index. Without the cost-model evidence, the Rosen inversion would rest on an asserted rather than a demonstrated link between cost and build quality. Without Abadie, the regression would confound the cost effect with the difficulty of the retrieval and the mission class that selected the cost, and the concavity estimate would be an artifact of comparing dissimilar instruments. Without Simon, concavity would be a curve one hoped to find rather than a mechanism one predicted in advance. The contribution is the assembly, and the assembly is what makes the single claim both motivated and testable.

## 8.3 What stands even if the hypothesis is not confirmed

The most important property of this design is that its value does not hinge on H1 being confirmed. This is deliberate, and it is the discipline that separates a defensible contribution from a search for a pleasing curve. Three things stand regardless of which hypothesis the data ultimately support, and I state them with calibrated confidence because the body chapters established their grounds.

### 8.3.1 The frontier estimate itself, in either direction

Whether the fitted \( g(\text{cost}) \) turns out concave or linear, the field gains its first population-level estimate of the accuracy-cost relationship for radiometers, which it did not have before. Confidence in this claim is high, because it follows from the construction rather than from the result: the estimand is the shape of the conditional expectation of requirement-normalized accuracy in the cost dimension over common support, and that shape is estimated and reported whichever way it comes out. A credible finding that returns are linear over the supported range is not a failure. It would remove diminishing returns as a rhetorical device in budget debates and would justify continued investment in specification where mission requirements demand it. The decision rule is built so that the null is informative rather than merely an absence of significance: H0 is retained only when the semiparametric model fails to beat the linear baseline out of sample, a positive evidentiary statement about the data, not a default. What would raise confidence in the linear conclusion is convergence of the cross-validated predictive comparison and the second-derivative band on the same answer; what would lower it is a held-out test that is underpowered because the assembled sample is too small to discriminate the two curves, a contingency Chapter 5 names explicitly.

### 8.3.2 The measurement apparatus and the requirement-normalization
The second thing that stands is the apparatus for making validated accuracy comparable across product families. Raw retrieval-error units differ across geophysical variables, so the dissertation expresses accuracy relative to each product's stated mission requirement, yielding a unitless requirement-normalized accuracy that is comparable across families [\[83\]](#ref-83). This construction is independent of the hypothesis. It draws the dependent variable from independent DAAC and cal/val validation records rather than from design specifications, the move that gives the construct its credibility, and it is reusable by any later study that wishes to place accuracy and another instrument attribute on the same axes. Confidence here is moderate to high. It rests on the per-product validation records, which are externally documented and authoritative [\[85\]](#ref-85), [\[77\]](#ref-77), [\[73\]](#ref-73), [\[83\]](#ref-83). The one caveat is that requirement-normalization reduces but does not fully remove the heterogeneity in how DAACs and papers report accuracy, and the residual heterogeneity is a named limitation rather than a solved problem.

### 8.3.3 The identification template for joining cross-community data

The third thing that stands is the identification template. Cost records and validation records are produced by different communities and were never designed to be joined. The dissertation treats the linkage not as a hidden hazard but as a documented procedure with its own matching protocol and its own log of unmatched and ambiguously matched instruments. The selection-on-observables-within-common-support strategy, with balancing weights across cost strata [\[101\]](#ref-101) and a held-out predictive test, is a template for any cross-community observational join in the space-systems domain, not only for this one. Its value is methodological and survives the empirical outcome. Confidence is moderate. The design controls are chosen to absorb the systematic reasons an instrument received its cost, but the objection, that an unobserved driver could raise both cost and accuracy and mimic a steeper cost effect, is a genuine residual risk that the template bounds but cannot eliminate without an instrument or an experiment the observational setting does not provide.

Stated together, these three standing contributions mean that the dissertation is robust to its own central uncertainty. Even in the world where H0 is retained and there is no over-specification edge to report, the field is left with a frontier estimate, a reusable accuracy-normalization, and a transferable identification template. This is what makes the residual risk acceptable: the cost of being wrong about concavity is bounded, because the apparatus that produced the test is useful independent of the test's verdict.

## 8.4 The single falsifiable claim and its decision rule

A conclusion should not let the central claim drift, so I restate the hypotheses verbatim and the rule that adjudicates them. H1, the contribution, is that validated geophysical-retrieval accuracy for Earth-observing radiometers is a concave function of instrument cost, with marginal accuracy per additional dollar declining as cost rises and collapsing beyond an estimable spectral-channel count, identifying an over-specification region in which additional channels and the cost they carry do not produce a commensurate gain in validated accuracy. H0, the null, is that validated retrieval accuracy is linear in instrument cost, with no diminishing returns, constant marginal accuracy per dollar, and no over-specification region.

The decision rule has two prongs and pre-commits to both before any data are run. H1 is supported only if the semiparametric model beats the linear null in cross-validated prediction and the second derivative \( g'' \) is reliably negative over a non-trivial portion of common support. The over-specification proposition is supported only if the marginal channel-count contribution reaches a region indistinguishable from zero within the observed channel range. If the semiparametric model does not beat the linear null out of sample, H0 is retained regardless of any in-sample curvature, because in-sample curvature in a small sample is the expected symptom of overfitting and not of a real frontier [\[110\]](#ref-110). The mechanism behind the prediction is explicit rather than a bare correlation. Added spectral channels and calibration elaboration raise development cost; beyond a point additional channels carry information redundant with channels already present, and achievable accuracy is bounded by calibration drift, geolocation error, and the intrinsic difficulty of the retrieval, which is the near-decomposability and satisficing logic Simon supplies [\[14\]](#ref-14), [\[19\]](#ref-19); the accuracy-cost curve therefore flattens and the marginal channel contribution falls toward zero, so dollars spent past the over-specification edge buy specification rather than validated science, and a cost-capped portfolio can deliver more total validated accuracy by capping per-instrument specification. The physical legitimacy of the channel-count edge is anchored in optimal-estimation information-content theory, which formalizes the degrees of freedom for signal that a set of spectral channels can support and the point at which additional channels add little independent information [\[122\]](#ref-122). That the statistical over-specification edge should coincide with a physical redundancy onset is what keeps the test from being a purely numerical artifact.

## 8.5 Limitations, stated honestly

A conclusion earns its claims by being candid about what bounds them. Five limitations were carried through the dissertation and none of them is dissolved here.

First, the sample is small by econometric standards. The intended population is NASA and NASA-partnered passive radiometers with both a NICM-class cost record and a documented Level-2 or Level-3 validation record, on the order of dozens of instruments and a larger but still modest number of instrument-product rows. This constrains how flexibly \( g(\text{cost}) \) can be estimated. It is the direct reason the design chooses a partially linear semiparametric specification rather than a fully nonparametric one, and the reason the held-out predictive test rather than in-sample fit is the arbiter. The limitation is real, and the design is shaped around it rather than pretending it away.

Second, accuracy metrics are heterogeneous across DAACs and papers, and requirement-normalization reduces but does not remove that heterogeneity. The construct validity of the dependent variable rests on the validation records being real, independent, and authoritative [\[85\]](#ref-85), [\[77\]](#ref-77), [\[73\]](#ref-73), [\[83\]](#ref-83), and on the normalization expressing each as compliance against a stated requirement, but reporting conventions still differ across product families and the residual differences enter as noise.

Third, the cost and validation records were produced by different communities and never designed to be joined, so the linkage requires careful matching of instrument identity and version and is a documented source of potential error rather than a hidden one. Measurement error in the cost regressor from version mismatches is addressed by careful matching and by sensitivity analysis that drops ambiguously matched instruments, but it is not eliminated.

Fourth, the estimand is restricted to flown-and-validated instruments by construction, which means survivorship and publication selection are inside the population definition, not corrected away. Instruments that flew, validated, and published are over-represented relative to those that failed or underperformed, and validation papers are more likely to be written for products that met requirements. The honest statement is that the frontier estimated here is the frontier among instruments that reached validated operations, and the claim is not extended to the design-and-fail population.

Fifth, cost in NICM is development cost, not life-cycle cost, so operations, reprocessing, and algorithm-maintenance spending are outside the cost variable [\[42\]](#ref-42). Because the claim concerns instrument investment specifically, development cost is the appropriate construct, but the boundary is stated so that the estimate is not misread as a total-cost frontier.

To these five I add a sixth specific to the design stage. There is no direct methodological precedent for the exact inversion this dissertation performs, namely validated accuracy regressed on instrument cost across radiometers. The absence of a precedent is part of the contribution, but it also means the inversion's plausibility rests on the inverted-hedonic argument and the cost-model evidence rather than on a prior demonstration that the join behaves as expected. Confidence in the inversion is therefore moderate rather than high, and the future program below is designed in part to convert that moderate confidence into something testable on real data.

## 8.6 A concrete future-research program

The future program has two parts. The first is the path from this design-stage document to an executed estimate on the full assembled dataset, the obligation this dissertation owes its own design. The second is the set of scoped extensions that the bounded present claim sets up but cannot answer.

### 8.6.1 Path to execution on the full data

Execution follows the five pre-registered steps the analysis plan fixes, and the future work is to run them in order without altering the frozen specification. Step one is assembly: build the instrument-product table by matching NICM cost records to NTRS design specifications by instrument identity and version, then attach validated accuracy metrics from the DAAC and cal/val records for each product, freeze the matched table, and document every unmatched or ambiguously matched instrument. The binding dependency here is data access. The NICM documentation establishes the cost construct and confirms that NASA maintains instrument-level cost records [\[42\]](#ref-42), [\[37\]](#ref-37), but the underlying cost table is not a public citable artifact, so the actual cost values must be obtained through JPL channels at execution rather than read from the literature. This is a data-access dependency, not a citation, and naming it as such is part of the design-stage honesty.

Step two is balance and support: estimate covariate balance of the design controls across cost terciles, compute balancing weights [\[101\]](#ref-101), identify the common-support region in cost, trim instruments outside common support, and report how many are trimmed and why. Step three estimates the H0 benchmark, accuracy linear in cost plus the linear controls with instrument-clustered standard errors, and records its cross-validated predictive error. Step four estimates the partially linear model with \( g(\text{cost}) \) under a concavity-respecting smoother and compares its cross-validated predictive error against the linear baseline, reporting \( g'' \) and its confidence band over the supported cost range. Step five estimates the marginal contribution of channel count to accuracy as a function of channel count and locates the range where it is indistinguishable from zero, reporting the lower edge as the candidate over-specification channel count.

Two targeted evidence sweeps should precede execution because the design depends on them and the present corpus is thin in both places. The first is a focused method sweep on shape-constrained semiparametric estimation, specifically isotonic and concave or monotone nonparametric regression in the partially linear setting, so that the concavity-respecting smoother in step four rests on dedicated method citations beyond the general partially linear references the design currently carries [\[104\]](#ref-104). The second is a sweep on the precision limits of the in-situ reference networks themselves as a function of product, because the reference-ceiling rival explanation, that the validation standard is not accurate enough to distinguish very good instruments and so flattens the high-cost end for reasons of measurement rather than instrument capability, can only be probed if the uncertainty budgets of the reference networks are characterized. Both sweeps are bounded and specific, and both should be completed before the corresponding step is run rather than after.

### 8.6.2 Scoped extensions

Two extensions are natural next studies rather than weaknesses of this one, and naming them keeps the present claim defensible while making clear that it is a first estimate. The first is the active-sensor analogue. Radars and lidars have their own cost drivers, transmit power, antenna or telescope aperture, and pulse design, and their own validated-accuracy records, and a parallel frontier could be estimated for them. Pooling them with radiometers would violate the comparability that identification requires, so they are excluded here and left to a companion analysis that estimates their frontier on its own terms. The second is the commercial-radiometer analogue. The growth of commercial Earth-observation constellations creates a population of instruments built under cost accounting that differs from NASA development-cost conventions [\[137\]](#ref-137), and a frontier estimated there might differ in level even if its shape were similar. Whether the concavity, if found, is a property of radiometry physics and therefore portable across cost regimes, or a property of the NASA cost regime and therefore not, is itself an empirical question that the bounded design here cannot answer but does set up. The same distributed-architecture and space-sustainability pressures that make the present question timely are what make these extensions worth doing [\[137\]](#ref-137), [\[134\]](#ref-134).

A third extension follows from the standing contributions of Section 8.3. Because the requirement-normalization and the cross-community identification template survive the empirical outcome, they can be carried to other instrument attributes. The same apparatus that places accuracy and cost on the same axes can place accuracy and mass, or accuracy and power, or accuracy and revisit on the same axes, each of which is a budget-relevant trade that currently rests on engineering judgment rather than a measured frontier. The value-driven-design and tradespace literature has reasoned about these trades case by case [\[17\]](#ref-17), [\[23\]](#ref-23); the contribution of the present method is to supply a population-level, empirically estimated location for the value threshold, and that contribution generalizes beyond the single accuracy-cost pair this dissertation estimates first.

## 8.7 Why both outcomes advance the portfolio
The decision relevance of the work does not depend on which hypothesis the data support, and this is worth stating plainly at the close because it is the standard the dissertation held itself to throughout. If H1 holds, JPL Earth Science formulation gains a defensible stopping rule: mission teams would have an evidence-based basis for capping spectral specification at the edge of the over-specification region and reallocating the saved budget either across more, individually less elaborate instruments or toward the error sources, calibration and geolocation, that actually bind in the flat region of the frontier. The result would give cost-capped competitions a principled descope argument, replacing capability-maximizing instincts with a value-aware target. This is the single management decision the design permits as an output, and it is stated as a recommendation rather than as an architecture, because the artifact is an econometric study that estimates a frontier and recommends a rule, not a system being fielded.

If H0 holds, the contribution is still real and still useful. A well-identified finding that accuracy returns to cost are linear over the supported range would remove diminishing returns as an unexamined assumption from instrument budgeting and would justify continued investment in specification where mission requirements demand it. The portfolio gains a cleaner basis for its choices either way, which is why the dissertation is committed to reporting whichever outcome the data support rather than to confirming a preferred curve. The broader portfolio context, a community moving toward distributed architectures of smaller instruments and toward commercial data buys, forces explicit per-instrument capability choices now [\[137\]](#ref-137), [\[134\]](#ref-134), and an estimate of the accuracy-cost shape informs whether the distributed-architecture instinct is supported by the accuracy economics or merely by cost ceilings. That question is currently answered by instinct; the contribution is to let it be answered by evidence.

## 8.8 Closing: converting dollars into validated science

Every Earth-science radiometer NASA flies is a decision about how much capability to buy, and the premise of the entire investment is not cost but the validated science the instrument delivers after launch. The field has long had cost models that predict what an instrument will cost from its design [\[42\]](#ref-42), [\[46\]](#ref-46) and validation programs that report how accurate its products are [\[85\]](#ref-85), [\[77\]](#ref-77), [\[73\]](#ref-73), yet it has never placed those two quantities on the same axes and asked whether each additional dollar still buys validated accuracy. This dissertation builds the apparatus to ask that question and states, in advance, the answer that would confirm a frontier and the answer that would deny one. It does so at the design stage, with a pre-registered estimator, an explicit identification strategy, a named threat analysis, and a decision rule fixed before any data are run, and with every numerical expectation labeled illustrative and not executed on the full assembled dataset.

The discipline of that honesty is the point. A frontier claimed without a held-out test, or an over-specification edge reported from in-sample curvature in a small sample, would be worse than no claim at all, because it would lend a number's authority to an artifact. By committing to the rule that H0 stands unless the concave model beats the linear null out of sample, and by naming the survivorship boundary, the reference-ceiling rival, and the data-access dependency as limits rather than hiding them, the work makes itself the kind of first study that the next study can build on rather than has to correct. If the frontier is concave, NASA and JPL gain a stopping rule for spectral specification and a way to convert the same budget into more total validated science. If it is linear, the field gains the right to stop invoking diminishing returns it has never measured. Either way, the dissertation moves the Earth Science Missions portfolio one estimate closer to converting dollars into validated science by evidence rather than by instinct. That is the contribution it set out to make, and it is offered in a spirit of service to the institutions and the public the work exists to serve, as the standard against which it asks to be judged.
## References and Appendices

This back matter makes every claim in the dissertation traceable to a real, resolvable source and every measurement, derivation, and procedural decision reproducible by an analyst who has only this document and access to the named data sources. The consolidated reference list is rendered in a single consistent IEEE style from the assembled bibliography (research/corpus.jsonl), numbered in order of first assembly by theme, with every in-text marker keyed to its numbered entry and every entry carrying a clickable DOI or a resolvable URL. The appendices externalize what the main chapters compress: the variable-construction formulas (Appendix A), the instrument-product matching protocol (Appendix B), the frozen pre-registration record (Appendix C), and the brain-and-API provenance log that documents how the corpus itself was assembled (Appendix D). Consistent with the design-stage guardrail that binds every chapter, nothing here reports an executed empirical result; the appendices specify procedures and label all numerical content as illustrative.

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## Appendix A. Variable-Construction Tables

Appendix A externalizes the construction of every variable that enters the estimator \( \text{accuracy} = g(\text{cost}) + \mathbf{X}\boldsymbol{\beta} + e \), because the credibility of the whole exercise rests on the dependent variable being a real, independently validated number rather than a self-reported design specification. The appendix gives the requirement-normalization formula, the per-product instantiation of that formula, the calibration-approach coding scheme, and the construction of the cost regressor and the control vector \( \mathbf{X} \). All quantities are construction rules; no value reported here is an executed measurement.

**A.1 The requirement-normalized accuracy metric.** Raw retrieval error is reported in incommensurable physical units across product families (kelvin for sea-surface temperature, volumetric water content for soil moisture, an unitless optical depth for aerosol, millimeters per hour for precipitation), so the dependent variable cannot be the raw error itself. The construction proceeds in three steps. First, for each instrument-product row, extract the validated error statistic that the responsible Distributed Active Archive Center (DAAC) or the cal/val paper it cites treats as authoritative, preferring unbiased root-mean-square error where reported and falling back to root-mean-square error or to expected-error compliance fraction where it is not. Second, divide that validated error by the product's stated mission accuracy requirement to form a unitless requirement-normalized error \( r = \text{error} / \text{requirement} \), so that \( r < 1 \) means the product meets requirement and \( r > 1 \) means it does not. Third, sign-orient the metric so that higher means better by defining accuracy as \( \text{accuracy} = -\ln(r) \), a monotone decreasing transform of normalized error that is increasing in delivered accuracy, symmetric in over- and under-performance on the log scale, and defined for all positive \( r \). The logarithmic form is a construction choice, not a fitted result; it is adopted so that proportional improvements in error map to equal increments of the dependent variable, which is the natural scale for a returns analysis. Where a product reports only an expected-error envelope and a compliance fraction rather than a continuous error, the compliance fraction is mapped to `r` through the product's stated envelope width, and the row is flagged in the matched table as envelope-derived so that sensitivity analysis can drop it.

**A.2 Per-product instantiation.** The general formula is instantiated separately for each product family, drawing the requirement and the authoritative validated error from the cited records. For aerosol optical depth, the validated error is the AERONET-matchup expected-error compliance reported for the MODIS and Deep Blue algorithms [\[85\]](#ref-85), [\[81\]](#ref-81), [\[75\]](#ref-75), with the network and its uncertainty role defined by [\[87\]](#ref-87) and the requirement taken from the product's stated expected-error envelope. For sea-surface temperature, the validated bias and standard deviation are drawn from the half-century synthesis and the operational-product validations [\[73\]](#ref-73), [\[58\]](#ref-58), [\[63\]](#ref-63), normalized to the product's stated accuracy requirement. For soil moisture, the unbiased root-mean-square error against core validation sites and in-situ measurements is the validated error [\[77\]](#ref-77), [\[78\]](#ref-78), with the metric definitions and application requirements taken from [\[83\]](#ref-83) and the disaggregation and flagging assessments [\[64\]](#ref-64), [\[67\]](#ref-67), [\[72\]](#ref-72) contributing rows where they report independent validation. For precipitation, the validated statistics are taken from the GPCP and GPM/IMERG records [\[86\]](#ref-86), [\[79\]](#ref-79), [\[65\]](#ref-65). For land-surface temperature and emissivity, the validated error is drawn from the coastal-retrieval and ultraspectral-emissivity records [\[55\]](#ref-55), [\[118\]](#ref-118). Each instantiation records the exact requirement value used and its source, so that the normalization is auditable per row.

**A.3 Calibration-approach coding.** Calibration approach enters \( \mathbf{X} \) as a categorical control with four mutually exclusive levels, coded from the NTRS design record and the validation literature: on-board blackbody, solar diffuser, vicarious, and lunar. Instruments carrying more than one calibration path are coded by their primary radiometric reference for the product in question, and the secondary path is recorded in a free-text note for sensitivity analysis. The vicarious and lunar categories are populated from the radiometric-assessment records [\[56\]](#ref-56), [\[76\]](#ref-76), [\[53\]](#ref-53), the on-board and deep-learning calibration records [\[57\]](#ref-57), [\[66\]](#ref-66), and the early-mission radiometric assessments, so that the coding reflects how each instrument's radiometric scale is actually maintained rather than a nominal design intent.

**A.4 Cost regressor and control vector.** The cost regressor is total instrument development cost in constant-year dollars, defined by the NICM construct [\[42\]](#ref-42), [\[37\]](#ref-37), [\[43\]](#ref-43) and explicitly bounded to exclude operations, reprocessing, and algorithm maintenance, so the variable measures embodied instrument investment and not life-cycle spend. Constant-year normalization uses a single published deflator applied uniformly; the deflator choice is recorded so the cost series is reproducible. The control vector \( \mathbf{X} \) comprises spectral-channel count (which separately carries the over-specification test), swath width, spatial resolution, the calibration-approach categorical of A.3, instrument mass and power as built, mission epoch as a technology-vintage control, and a retrieval-difficulty control that orders geophysical variables by intrinsic hardness (for example, soil moisture under vegetation above clear-sky sea-surface temperature), drawn from the validation literature's own characterizations of retrieval difficulty.


## Appendix B. Instrument-Product Matching Protocol

Appendix B specifies how the three named data sources are joined, because the linkage is the single most error-prone step in the design: the cost records and the validation records were produced by separate communities and were never built to be joined. The protocol is stated as a reproducible rule set with an explicit log template, so that every matched, unmatched, and ambiguous instrument is documented rather than silently dropped.

**B.1 Matching keys and rules.** The primary join is NICM cost record to NTRS design specification, keyed on instrument identity and version. Identity is matched on the canonical instrument acronym plus the host platform and the build serial where a sensor flew on multiple platforms (for example, a radiometer flown on successive satellites is one identity per build). Version is matched on the design freeze that the cost record refers to, so that a re-flight with modified channels is not silently merged with its predecessor. Where the cost record and the design record disagree on a channel count or a mass, the design record governs the control variable and the discrepancy is logged. The secondary join attaches validated accuracy: each design-matched instrument is linked to the DAAC product documentation and the cal/val paper the DAAC cites as authoritative for each of its validated products, producing one instrument-product row per validated product.

**B.2 Unmatched and ambiguous log template.** Every instrument that fails to match is recorded in a log with fields: instrument acronym, platform, build, the source that has it (cost-only, design-only, or validation-only), the reason for the failure (no cost record, no validation record, version ambiguity, identity collision), and the disposition (excluded, held for manual resolution, or resolved with a documented rationale). Ambiguously matched instruments, principally version mismatches, are not used in the primary estimate; they are retained only for the sensitivity analysis that re-runs the estimator with and without them, so that the contribution of ambiguous matches to any apparent curvature can be isolated.

**B.3 Dependence and clustering.** Because one instrument contributes one row per validated product and the cost is attributed at the instrument level and shared across that instrument's products, rows from the same instrument are not independent. The protocol therefore tags every row with its instrument identifier, and all inference clusters standard errors at that identifier, as fixed in the research design. The matching protocol thus produces not only the analysis table but the clustering structure that the estimator requires.


## Appendix C. Pre-Registration Record (Frozen Before Execution)

Appendix C is the frozen pre-registration. It is reproduced here so that the analysis plan is fixed before any estimate is computed and cannot be revised after seeing the data; this is the discipline that separates the design from a search for a pleasing curve. The five steps, the decision rule, and the pre-specified control set are stated exactly as they bind execution.

**C.1 The five pre-registered steps.** Step 1, assembly: build the instrument-product table by the Appendix B protocol, freeze it, and document every unmatched or ambiguous instrument. Step 2, balance and support: estimate covariate balance of the design controls across cost terciles, compute balancing weights, identify the common-support region in cost, trim instruments outside common support, and report how many are trimmed and why. Step 3, baseline linear (H0) model: estimate accuracy linear in cost plus the linear controls with instrument-clustered standard errors, and record the linear cost coefficient and the cross-validated predictive error as the H0 benchmark. Step 4, semiparametric concave model: estimate the partially linear model with \( g(\text{cost}) \) under a concavity-respecting smoother, compare its cross-validated predictive error against the linear baseline, and estimate the second derivative \( g'' \) and its confidence band over the supported cost range. Step 5, over-specification test: estimate the marginal contribution of spectral-channel count to accuracy as a function of channel count and locate the range where it is statistically indistinguishable from zero, reporting the lower edge as the candidate over-specification channel count.

**C.2 The decision rule.** H1 is supported only if both conditions hold: the semiparametric model beats the linear null in cross-validated prediction, and \( g'' \) is reliably negative over a non-trivial portion of common support. The over-specification proposition is supported only if the marginal channel-count contribution reaches a region indistinguishable from zero within the observed channel range. If the semiparametric model does not beat the linear null out of sample, H0 is retained regardless of any in-sample curvature, because in a small sample in-sample curvature is the expected symptom of overfitting rather than evidence of a real frontier. The rule is committed in advance and is not contingent on the realized estimates.

**C.3 The pre-specified control set.** The controls are fixed at: spectral-channel count, swath width, spatial resolution, calibration-approach categorical, instrument mass, instrument power, mission epoch, and retrieval difficulty. No control may be added after seeing the data; if an omitted driver is discovered, it is reported as a named limitation rather than introduced post hoc, to preserve the degrees of freedom the small sample affords and to keep the test honest.


## Appendix D. Brain and API Provenance Log

Appendix D documents how the corpus in `research/corpus.jsonl` was assembled, in keeping with the transparency rule that any research output must list the sources it swept. The 141 entries were drawn through a two-sweep discovery process and then screened for relevance, deduplicated by DOI and title, graded, and theme-assigned to the chapter each best serves. Sweep one queried open and keyed scholarly sources: OpenAlex and Crossref for broad coverage and DOI resolution, arXiv for preprints in econometrics and bounded rationality, Semantic Scholar for citation tracing, and the NASA Technical Reports Server (NTRS) for the instrument cost-model documentation and the validation and radiometric-calibration reports that no commercial index carries. Sweep two queried the local research brains relevant to the topic: the Acta Astronautica corpus for the value-driven-design and Earth-observation-markets entries, the space-economy and AMOS holdings for portfolio and sustainability context, and the doctorate libraries for the methodological anchors. Entries that did not bear on attribute-based valuation, bounded-rationality design, instrument cost estimation, validated retrieval accuracy, program-evaluation identification, spectral information content, or Earth-observation portfolio value were dropped before the corpus was frozen.

Every entry carries a grade reflecting source quality and fit: grade A entries are peer-reviewed venue articles or canonical methodological works directly on point; grade B entries are NTRS technical reports and working papers that are real and resolvable but carry less editorial weight or, in several cases, lost author metadata in harvesting and are rendered here as anonymous with their NTRS identifier; grade C entries are discussion-stage or supplementary records retained because they uniquely cover a needed facet. The anonymous NTRS entries were retained only where their titles and NTRS identifiers were confirmed to match their assigned chapter's evidentiary need, and they are clustered in the data-and-measurement and information-content families where the validation and calibration record genuinely lives. Two data-access dependencies are recorded here rather than papered over. First, the NICM documentation is in the corpus but the underlying instrument-level cost table is not a public citable artifact; the cost values must be obtained through JPL channels at execution, and the corpus supplies the cost construct authority, not the numbers. Second, the precision-limit characterizations of the in-situ reference networks, needed for the reference-ceiling probe, are thin in the present corpus and are flagged for a targeted follow-up sweep before that probe is run. Logging these dependencies as named gaps, rather than filling them with invented citations, is the provenance discipline this dissertation commits to.