# Retrieval-Accuracy Returns to Instrument Investment in Earth-Science Radiometers: a Hedonic Regression of Validated Science Accuracy on Cost Drivers **Candidate:** JPL_ASTRO_EARTH_10 **Program:** COLLEGIUM 1st Battalion **Category:** Earth Science Missions **Date:** 2026-06-15 --- ## Abstract NASA and JPL allocate large fractions of Earth-observing mission budgets to instrument development, yet the relationship between dollars spent on a radiometer and the validated geophysical accuracy that the instrument ultimately delivers is not well characterized 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 cal/val programs report how accurate the retrieved products are, but the two literatures have not been joined to ask whether accuracy returns to cost are linear or concave. This dissertation proposes a hedonic regression of validated Level-2 and Level-3 retrieval-error metrics on instrument cost and on the design attributes that drive both cost and accuracy, principally spectral-channel count, swath, spatial resolution, and calibration approach. The central falsifiable claim is that validated retrieval accuracy is a concave function of instrument cost, so that marginal accuracy gained per additional dollar declines and eventually collapses beyond an estimable spectral-channel count, identifying an over-specification region. The null hypothesis is that accuracy is linear in cost with no diminishing returns. The method adapts Rosen's hedonic price framework, treats accuracy rather than market price as the dependent attribute, and uses a partially linear semiparametric specification so that the cost term enters through a flexible concave function while design controls enter linearly. Identification draws on Abadie's program-evaluation perspective on selection and on covariate balancing across instrument classes. The data are validated accuracy metrics published by Earthdata DAACs and in the peer-reviewed cal/val literature, NICM instrument cost records, and NTRS design specifications, assembled at the instrument-product level. This document is a design-stage dissertation. It states the estimator, the identification strategy, the threats to validity, and a pre-registered analysis plan, and it labels all numerical results 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 channel count beyond which additional spectral specification stops paying for itself in validated science. --- ## 1. Introduction and Contribution ### 1.1 The problem Every Earth-science radiometer that NASA flies represents a choice about how much capability to buy. Program managers decide how many spectral channels to include, how wide a swath to image, how finely to resolve the surface, and how elaborate an on-board calibration subsystem to carry. Each of these choices raises the instrument's development cost, and the NASA Instrument Cost Model (NICM) exists precisely because those choices are predictable cost drivers [1], [2], [3]. The premise of the entire investment, however, is not cost. It is the validated geophysical accuracy of the products that 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. That accuracy is measured, after launch, by cal/val programs that compare retrieved products against reference standards [4], [5], [6], [7], [8]. The gap is that these two quantities, cost and validated accuracy, are almost never placed on the same axes. Cost models predict cost from design. Validation studies report accuracy for one instrument or one product. No published work, to this candidate's knowledge, estimates validated retrieval accuracy as a function of instrument cost across a population of radiometers while controlling for the design attributes that drive both. As a result, the field has no defensible answer to a question that directly affects how mission budgets are set: does each additional dollar of instrument investment buy a proportional increment of validated accuracy, or do the returns diminish, and if they diminish, where does the marginal dollar stop paying for itself? ### 1.2 The gap in the literature Three literatures bear on this question and none closes it. The first is the hedonic-pricing literature founded by Rosen, which shows how the implicit value of the individual attributes of a differentiated good can be recovered by regressing the good's price on its measurable characteristics [9], [10], [11]. Hedonic methods are mature and are routinely applied to housing, environmental amenities, and differentiated products [12], [13]. They have not been applied to scientific instruments, and critically they have not been inverted to treat a performance metric, rather than market price, as the hedonic outcome. The second is the instrument cost-modeling literature, exemplified by NICM [1], [2], [3] and by the parametric telescope cost models of Stahl and colleagues [14], [15], [16], [17]. This literature is explicitly hedonic in spirit. It regresses cost on design attributes such as mass, power, aperture, and channel count. But its dependent variable is cost, not delivered accuracy, so it cannot speak to returns. The third is the cal/val literature, which is large, rigorous, and product-specific [4], [5], [6], [7], [8], [18]. It establishes the validated error of individual products to high standards but treats each instrument in isolation and does not relate error to the instrument's cost or to a population-level frontier. The unfilled space is the join. No estimate exists of the shape of the accuracy-cost relationship across instruments, and therefore no estimate exists of whether that relationship is concave or where an over-specification region begins. ### 1.3 The falsifiable contribution This dissertation states a single falsifiable contribution. **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 claim is falsifiable in the strict sense. 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, H1 is rejected and H0 stands. The claim also makes a sharper prediction than mere concavity: it predicts 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. ### 1.4 Why it matters for NASA and JPL JPL's Earth Science portfolio competes for funding against a fixed top line. If accuracy returns to instrument cost are concave, then a portfolio that distributes budget across more, individually less elaborate instruments can deliver more total validated accuracy than a portfolio that concentrates budget in a few highly specified instruments operating in the flat region of the frontier. An estimate of the over-specification channel count would give cost-capped mission formulation a defensible stopping rule for spectral specification. If, instead, returns are linear, the analysis would justify continued investment in maximal specification and would remove diminishing returns as an argument in descopes. Either result is decision-relevant, which is the standard this dissertation holds itself to. The timing is also relevant. The Earth-observing community is moving toward distributed architectures of smaller instruments and toward commercial data buys, both of which force explicit choices about how much capability to buy per instrument. A frontier estimate would inform whether the distributed-architecture instinct is supported by the accuracy economics or merely by cost ceilings. The same estimate would inform the trade between a new, more elaborate instrument and the continued exploitation of an existing one, since the marginal accuracy of the new instrument is only worth its marginal cost if the portfolio is operating in the steep region of the frontier. None of these decisions currently rests on a measured accuracy-cost relationship, which is the deficiency this dissertation addresses. ### 1.5 Scope and what this dissertation does not claim To keep the contribution falsifiable, several things are deliberately out of scope. 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 is an embodied-investment effect rather than a single mechanism. It 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. It 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. Narrowing the claim in these ways is what makes the single contribution testable rather than diffuse. --- ## 2. Background and Literature ### 2.1 The hedonic framework and its inversion Rosen's 1974 result is the foundation [9]. A differentiated good is a bundle of attributes, and in competitive equilibrium the good's price is a function of those attributes whose partial derivatives reveal the marginal implicit prices that buyers pay and sellers receive for each attribute. The subsequent literature refined identification of the underlying demand and supply functions [10], [11] and catalogued the econometric hazards of estimating hedonic functions, including functional-form misspecification, omitted attributes, and multicollinearity among characteristics [18]. This dissertation performs a deliberate inversion. Instead of regressing the market price of a good on its attributes, it regresses a performance metric, validated retrieval accuracy, on the attributes of the instrument, with instrument cost itself entering as the attribute of central interest. The logic that licenses this is the same logic the cost-model literature already uses implicitly: instrument cost is a near-sufficient statistic for the engineering effort, component quality, and calibration rigor embodied in the build, and those embodied qualities are what translate into accuracy. The hedonic surface here is an accuracy surface, and the object of interest is the curvature of that surface in the cost dimension. ### 2.2 Cost as a hedonic index: NICM and parametric cost models NICM is the instrument-level cost-estimating relationship maintained by NASA, fit on a curated database of flown instruments and updated across versions VI through VIII and beyond [1], [2], [3]. Its existence establishes two facts this dissertation relies on. First, instrument cost is systematically predictable from design attributes, which means cost is not noise but a structured index of build characteristics. Second, NASA maintains the underlying cost records at the instrument level, which is the access path for the cost variable. The parametric telescope cost models of Stahl and colleagues make the same point for optical payloads and demonstrate that single-variable and multivariable parametric forms both have explanatory traction [14], [15], [16], [17]. The present work treats these cost models as the source of the cost regressor and as evidence that cost is a legitimate hedonic index rather than a fitting these models in the cost direction. ### 2.3 Validated accuracy as the dependent attribute The dependent variable is validated retrieval accuracy, and the cal/val literature defines it product by product. Aerosol optical depth from MODIS is validated against the AERONET ground network with published expected-error envelopes [4], [5]. Sea-surface temperature retrievals carry validated bias and standard-deviation statistics built over decades of in-situ matchups [6], [7]. Soil moisture from SMAP is validated against core validation sites with reported root-mean-square error and unbiased RMSE [8], and the soil-moisture community has formalized performance metrics and application requirements [19]. Precipitation products are validated against gauge and combined reference analyses [20], [21]. This literature gives the dependent variable a defensible, externally documented construction for each product family, which is essential because the credibility of the whole exercise rests on the accuracy metric being a real, validated number rather than a self-reported specification. ### 2.4 The Abadie lens: identification and selection The anchor methodologist Abadie contributes the identification discipline. Abadie's program-evaluation work treats the central problem of observational inference as selection: units are not randomly assigned to treatment levels, so naive comparisons confound the treatment with the reasons units received it [22]. The translation to this setting is direct. Instruments are not randomly assigned their cost levels. Expensive instruments are built for harder retrieval problems, or for higher-stakes missions, or in eras with different technology. A naive regression of accuracy on cost would confound the cost effect with the difficulty of the retrieval problem and with the mission class that selected the cost. The Abadie perspective insists that the design control set must absorb the systematic reasons an instrument received its cost, that covariate balance across cost strata be checked and enforced rather than assumed, and that the estimand be defined over a region of common support where instruments of different cost are genuinely comparable. The covariate-balancing logic in the Abadie tradition motivates the use of balancing weights across instrument classes so that the concavity estimate is not an artifact of comparing dissimilar instruments. ### 2.5 The Simon lens: bounded rationality, satisficing, and over-specification The anchor methodologist Simon supplies the substantive prior that makes concavity the expected result rather than an arbitrary guess. Simon's account of bounded rationality and satisficing holds that designers and organizations do not optimize over a complete attribute space; they search until a design meets an aspiration level and then stop [23], [24]. Simon's architecture-of-complexity argument adds 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 [25]. Applied here, both ideas predict diminishing returns. Additional spectral channels improve a retrieval only until the information they add is redundant with channels already present or is swamped by other error sources such as calibration drift and geolocation error. Past that point the instrument is over-specified relative to the validated accuracy it can deliver, which is exactly the over-specification region H1 names. The value-driven design and multi-attribute tradespace exploration literature operationalizes the same intuition in aerospace, showing that value, not raw capability, is the proper objective and that tradespaces routinely contain dominated, over-specified regions [26], [27], [28]. The Simon lens thus converts the concavity hypothesis from a statistical curiosity into a prediction grounded in a theory of how engineering organizations actually decide. --- ## 3. Data ### 3.1 Named datasets and sources The analysis joins three named data sources at the instrument-product level. 1. **Validated accuracy metrics from NASA Earthdata DAACs and the peer-reviewed cal/val literature.** Level-2 and Level-3 retrieval-accuracy statistics, principally bias, RMSE, unbiased RMSE, and expected-error compliance, are extracted from DAAC product documentation and from the published validation papers that the DAACs cite as the authoritative validation record for each product [4], [5], [6], [7], [8], [19], [20], [21]. These provide the dependent variable. 2. **NASA Instrument Cost Model (NICM) records.** The NICM database and its published documentation provide development cost at the instrument level, normalized to constant-year dollars, together with the design attributes NICM tracks [1], [2], [3]. These provide the cost regressor and several design controls. 3. **NTRS instrument design specifications.** NASA Technical Reports Server records and mission instrument handbooks provide the design attributes not fully captured by NICM, principally spectral-channel count and center wavelengths, swath width, spatial resolution, and calibration approach (on-board blackbody, solar diffuser, vicarious, or lunar) [14], [15], [16], [17]. These provide the design control set and the channel-count variable that defines the over-specification test. ### 3.2 Unit of analysis The 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, the instrument contributes one row per validated product, and the cost is attributed at the instrument level and shared across that instrument's products. The dependence this creates among rows from the same instrument is addressed in the research design through clustered inference. ### 3.3 Variable construction The dependent variable, validated accuracy, is constructed as a standardized, sign-oriented error metric so that lower error means worse and the variable is increasing in accuracy. Because raw error units differ across geophysical variables, accuracy is expressed relative to the product's stated mission requirement, yielding a unitless requirement-normalized accuracy that is comparable across product families. The cost regressor is total instrument development cost in constant-year dollars from NICM. Design controls are spectral-channel count, swath width, spatial resolution, calibration approach as a categorical, instrument mass and power as built, and mission epoch to absorb technology vintage. A retrieval-difficulty control is included to capture the intrinsic hardness of the geophysical variable being retrieved, since soil moisture under vegetation is harder than clear-sky SST regardless of instrument cost. ### 3.4 Coverage The intended population is NASA and NASA-partnered Earth-observing 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. This yields a population on the order of dozens of instruments and a larger number of instrument-product rows. The sample is deliberately bounded to radiometers, excluding active sensors such as radars and lidars, because the cost drivers and accuracy metrics of active instruments are not commensurable with passive radiometry. ### 3.5 Limitations of the data Three limitations are acknowledged at the outset. First, the sample is small by econometric standards, which constrains how flexibly the cost function can be estimated and motivates the semiparametric rather than fully nonparametric specification. Second, accuracy metrics are heterogeneous in how they are reported across DAACs and papers; the requirement-normalization mitigates but does not eliminate this. Third, the cost records and the validation records are produced by different communities and were never designed to be joined, so the linkage requires careful matching of instrument identity and version, which is a documented source of potential error rather than a hidden one. A fourth limitation concerns survivorship and publication. 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. If failure and under-performance are correlated with cost, this could bias the frontier. The dissertation treats this as a named threat rather than an obstacle: the population is restricted to flown instruments with a validation record by construction, so the estimand is explicitly the frontier among instruments that reached validated operations, and the discussion does not extend the claim to the design-and-fail population. A fifth limitation is that cost in NICM is development cost, not life-cycle cost, so operations, reprocessing, and algorithm-maintenance spending are not in the cost variable. 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. --- ## 4. Research Design and Identification ### 4.1 Estimand and estimator The estimand is the shape of the conditional expectation of requirement-normalized validated accuracy as a function of instrument cost, holding design attributes and retrieval difficulty fixed, over the region of common support. The estimator is a partially linear semiparametric regression. Validated accuracy is modeled as accuracy = g(cost) + X beta + e, where g is an unknown smooth function estimated under a monotonicity-and-concavity-respecting smoother, X is the vector of design and difficulty controls entered linearly, beta is the vector of their coefficients, and e is an instrument-clustered error. The partially linear form follows the semiparametric tradition for separating a flexibly estimated term of interest from linear controls [29], [30]. The function g carries the test. Concavity is assessed by estimating g under a shape-constrained smoother and comparing fit and curvature against an unconstrained linear-in-cost alternative. ### 4.2 Identification strategy Identification rests on selection-on-observables within common support, in the Abadie tradition [22]. The claim is not that cost is randomly assigned. It is that, conditional on the design control set and the retrieval-difficulty control, variation in cost is as good as random with respect to validated accuracy. The credibility of this claim is built, not asserted, in three steps. First, the design controls are chosen to absorb the systematic reasons an instrument received its cost, principally the difficulty of the retrieval and the technology epoch. Second, covariate balance across cost strata is checked, and balancing weights are applied so that high-cost and low-cost instruments being compared are similar in their non-cost attributes. Third, the estimand is restricted to the region of common support in cost where instruments of differing cost actually coexist with comparable design attributes, so that the concavity estimate is interpolation within data rather than extrapolation across incomparable instruments. ### 4.3 The over-specification test The over-specification claim is tested separately from general concavity. Within the partially linear model, spectral-channel count enters with a flexible term, and the marginal contribution of an additional channel to validated accuracy is estimated as a function of channel count. The over-specification region is the range of channel counts over which this marginal contribution is not statistically distinguishable from zero, holding cost and other attributes fixed. The estimable channel count named in H1 is the lower edge of that region. This is a sharper and more falsifiable test than overall concavity because it predicts a specific design margin rather than only a curved aggregate relationship. ### 4.4 Threats to validity **Internal validity.** The principal threat is omitted-variable bias from an unobserved driver that raises both cost and accuracy, which would mimic a steeper cost effect and could mask concavity, or an unobserved driver that raises cost while being unrelated to accuracy, which would exaggerate concavity. The design control set and the retrieval-difficulty control target the most plausible such drivers. A second threat is reverse linkage, where instruments expected to face hard validation are deliberately given more budget; the difficulty control and the common-support restriction address this. A third threat is measurement error in the cost variable from version mismatches, addressed by careful instrument-version matching and by sensitivity analysis that drops ambiguously matched instruments. **External validity.** The estimand is defined over NASA and NASA-partnered passive radiometers in the modern era. It does not extend to active sensors, to non-NASA instruments built under different cost accounting, or to future instruments using technologies absent from the sample. These limits are stated rather than papered over, and the discussion returns to them. **Construct validity.** The dependent variable must actually measure delivered science accuracy and not a self-reported specification. This is why the accuracy metric is drawn from independent validation records rather than from design documents, and why it is requirement-normalized so that meeting a stated requirement, not raw error, is the construct. The cost variable must measure embodied instrument investment, which NICM's development-cost definition supports. **Statistical-conclusion validity.** The sample is small, so the analysis pre-commits to instrument-clustered standard errors to respect the instrument-product dependence structure, to a limited number of pre-specified controls to preserve degrees of freedom, and to a held-out or cross-validated assessment of whether the concave fit genuinely improves out-of-sample prediction over the linear null rather than merely fitting in-sample noise. --- ## 5. Analysis Plan and Findings **This section is a design-stage analysis plan. No results reported here have been executed on the full assembled dataset. All numbers are illustrative placeholders used to specify the procedure, and they must not be read as empirical findings.** ### 5.1 Estimation procedure The procedure proceeds in five pre-registered steps. Step 1, 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. Step 2, balance and support. Estimate covariate balance of the design controls across cost terciles. Compute balancing weights and identify the common-support region in cost. Trim instruments outside common support and report how many are trimmed and why. Step 3, baseline linear model. Estimate the null model with accuracy linear in cost plus the linear controls, using instrument-clustered standard errors. Record the linear cost coefficient and the model's cross-validated predictive error. This is the H0 benchmark. Step 4, semiparametric concave model. Estimate the partially linear model with g(cost) under a concavity-respecting smoother. Compare its cross-validated predictive error against the linear baseline. Estimate the second derivative of g and its confidence band over the supported cost range. Step 5, over-specification test. Estimate the marginal contribution of channel count to accuracy as a function of channel count and locate the range where it is not distinguishable from zero. Report the lower edge as the candidate over-specification channel count. ### 5.2 Decision rule H1 is supported only if both of the following hold. The semiparametric model must beat the linear null in cross-validated prediction, and the second derivative of g must be reliably negative over a non-trivial portion of common support. The over-specification sub-claim 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. ### 5.3 Illustrative, not-yet-executed expectations The following are expectations under H1, stated to make the design concrete, and are explicitly not results. Under H1, the fitted accuracy-cost curve would rise steeply in the low-cost region, where adding channels and modest calibration buys large 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 illustrative over-specification edge would appear as a channel count past which the estimated marginal channel contribution crosses into statistical insignificance. Under H0, the curve would instead be indistinguishable from a straight line and the marginal channel contribution would remain positive across the observed range. The point of stating both is that the data, once assembled and run, will discriminate between them by the decision rule in 5.2, and the dissertation is committed to reporting whichever the data support. --- ## 6. Discussion ### 6.1 Implications if H1 holds If validated accuracy is concave in cost with an identifiable over-specification channel count, the practical implication for JPL Earth Science formulation is 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 instruments or toward the error sources, calibration and geolocation, that actually bind in the flat region. The result would also give cost-capped competitions a principled descope argument, replacing capability-maximizing instincts with a value-aware target. ### 6.2 Implications if H0 holds If the data retain H0, the contribution is still real and still useful. A credible finding that accuracy returns to cost are linear over the supported range would remove diminishing returns as a rhetorical device in budget debates and would justify continued investment in specification where mission requirements demand it. A null result that is well identified and honestly reported is a contribution, and the design is built so that the null is informative rather than merely an absence of significance. ### 6.3 Rival explanations Several rival explanations could produce apparent concavity that is not the claimed frontier. Technology improvement over time could make later, cheaper instruments more accurate, which the mission-epoch control absorbs. Easier retrievals could be assigned to cheaper instruments, which the retrieval-difficulty control and common-support restriction address. A ceiling in the validation reference data itself, where the in-situ standard is not accurate enough to distinguish very good instruments, could flatten the high-cost end for reasons of measurement rather than instrument capability; this is a genuine alternative and would be probed by examining whether the flattening coincides with the precision limits of the validation references. Naming these rivals and the design features that bear on each is part of what makes the contribution defensible rather than merely suggestive. ### 6.4 External validity The estimate would speak to NASA-class passive radiometers in the modern era and should not be read as a universal law of instrument economics. Active sensors, commercial smallsat radiometers built under different cost regimes, and future technologies are out of scope. The honest external-validity claim is narrow and bounded, which is preferable to a broad claim the data cannot support. Two extensions are worth naming because they are the natural next studies rather than weaknesses of this one. The first is the active-sensor analogue. Radars and lidars have their own cost drivers, transmit power, antenna or telescope aperture, pulse design, and their own validated-accuracy records. A parallel frontier could be estimated for them, but pooling them with radiometers would violate the comparability that identification requires, so they are excluded here and left to a companion analysis. 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, and a frontier estimated there might differ in level even if its shape were similar. Whether the concavity is a property of radiometry physics, and therefore portable, 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. Stating these as scoped extensions keeps the present claim defensible while making clear that it is a first estimate rather than a final word. ### 6.5 Relationship to the cost-model and tradespace literatures If the frontier is concave with an over-specification edge, the result would sit naturally alongside the existing cost-model and value-driven-design literatures rather than overturning them. The cost models predict cost from design and are silent on accuracy; this work would add the accuracy axis they lack. The tradespace and value-driven-design work already holds that capability beyond a value threshold is dominated; this work would supply a population-level, empirically estimated location for that threshold in the specific case of radiometer spectral specification, where prior work has reasoned about it case by case. The contribution is therefore complementary and cumulative, which is the more credible kind of contribution for a first study to make. ### 6.5 What would falsify the contribution The contribution is falsified if the semiparametric concave model fails to beat the linear null out of sample, or if the second derivative of the fitted cost function is not reliably negative over common support, or if the marginal channel-count contribution remains positive across the entire observed channel range so that no over-specification region exists. Any one of these outcomes returns the field to H0. Stating the falsification conditions in advance is the discipline that separates this design from a search for a pleasing curve. --- ## 7. Contribution and Conclusion This dissertation proposes to estimate, for the first time, the shape of the relationship between instrument cost and validated geophysical-retrieval accuracy across a population of Earth-observing radiometers. It inverts the hedonic framework of Rosen to treat validated accuracy rather than market price as the hedonic outcome, draws the cost regressor from the established NICM and parametric cost-model literature, draws the dependent variable from independent DAAC and cal/val validation records, and identifies the cost effect using the selection-on-observables discipline of the Abadie program-evaluation tradition, with the Simon theory of bounded rationality and near-decomposable design supplying the prior that returns should diminish and that an over-specification region should exist. The single falsifiable contribution is that validated retrieval accuracy is a concave function of instrument cost whose marginal accuracy-per-dollar collapses beyond an estimable spectral-channel count, against the null that accuracy is linear in cost with no diminishing returns. The work is presented at the design stage, with a pre-registered estimator, identification strategy, threat analysis, and decision rule, and with all numerical expectations explicitly labeled as illustrative and not yet executed. If confirmed, the contribution gives NASA and JPL a defensible accuracy-per-dollar frontier and an over-specification stopping rule for spectral specification; if rejected, it removes diminishing returns as an unexamined assumption from instrument budgeting. Both outcomes advance the Earth Science Missions portfolio's ability to convert dollars into validated science. --- ## References [1] H. Habib-Agahi, J. Mrozinski, and G. Fox, "Latest NASA Instrument Cost Model (NICM): Version VI," NASA Jet Propulsion Laboratory, NTRS 20160008251, 2014. https://ntrs.nasa.gov/citations/20160008251 [2] J. Mrozinski, H. Habib-Agahi, G. Fox, and others, "NASA Instrument Cost Model: NICM 8.5," NASA Jet Propulsion Laboratory, NTRS 20210012565, 2019. https://ntrs.nasa.gov/citations/20210012565 [3] H. Habib-Agahi and J. Mrozinski, "NASA Instrument Cost Model for Explorer-Like Mission Instruments (NICM-E)," NASA Jet Propulsion Laboratory, NTRS 20150007881, 2013. https://ntrs.nasa.gov/citations/20150007881 [4] L. A. Remer, Y. J. Kaufman, D. Tanre, and others, "The MODIS Aerosol Algorithm, Products, and Validation," Journal of the Atmospheric Sciences, vol. 62, no. 4, pp. 947-973, 2005. doi: 10.1175/JAS3385.1. https://doi.org/10.1175/jas3385.1 [5] B. N. Holben, T. F. Eck, I. Slutsker, and others, "AERONET, A Federated Instrument Network and Data Archive for Aerosol Characterization," Remote Sensing of Environment, vol. 66, no. 1, pp. 1-16, 1998. doi: 10.1016/S0034-4257(98)00031-5. https://doi.org/10.1016/s0034-4257(98)00031-5 [6] C. J. Merchant, O. Embury, C. E. Bulgin, and others, "Half a century of satellite remote sensing of sea-surface temperature," Remote Sensing of Environment, vol. 233, 111366, 2019. doi: 10.1016/j.rse.2019.111366. https://doi.org/10.1016/j.rse.2019.111366 [7] A. R. Robinson and others, "Observational Needs of Sea Surface Temperature," Frontiers in Marine Science, vol. 6, 420, 2019. doi: 10.3389/fmars.2019.00420. https://doi.org/10.3389/fmars.2019.00420 [8] S. K. Chan, R. Bindlish, P. E. O'Neill, and others, "Validation of SMAP surface soil moisture products with core validation sites," Remote Sensing of Environment, vol. 191, pp. 215-231, 2017. doi: 10.1016/j.rse.2017.01.021. https://doi.org/10.1016/j.rse.2017.01.021 [9] S. Rosen, "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, vol. 82, no. 1, pp. 34-55, 1974. doi: 10.1086/260169. https://doi.org/10.1086/260169 [10] J. M. Quigley and others, "Hedonic Prices and Implicit Markets: Estimating Demand and Supply Functions for Differentiated Products," Journal of Political Economy, vol. 95, no. 1, 1987. doi: 10.1086/261441. https://doi.org/10.1086/261441 [11] N. E. Coulson, "The Continuing Impact of Sherwin Rosen's Hedonic Prices and Implicit Markets," Journal of Political Economy, vol. 125, no. 6, 2017. doi: 10.1086/694645. https://doi.org/10.1086/694645 [12] B. Bishop and others, "A hedonic pricing method to estimate the value of waterfronts in the Gulf of Mexico," Urban Forestry and Urban Greening, vol. 41, pp. 96-106, 2019. doi: 10.1016/j.ufug.2019.04.004. https://doi.org/10.1016/j.ufug.2019.04.004 [13] Y. Wu and others, "Impacts of Street-Visible Greenery on Housing Prices: Evidence from a Hedonic Price Model and a Massive Street View Image Dataset in Beijing," ISPRS International Journal of Geo-Information, vol. 7, no. 3, 104, 2018. doi: 10.3390/ijgi7030104. https://doi.org/10.3390/ijgi7030104 [14] H. P. Stahl, T. Henrichs, A. Luedtke, and M. West, "Update on multivariable parametric cost models for ground and space telescopes," Proc. SPIE, vol. 8442, 84421C, 2012. doi: 10.1117/12.926363. https://doi.org/10.1117/12.926363 [15] H. P. Stahl, "Survey of cost models for space telescopes," Optical Engineering, vol. 49, no. 5, 053005, 2010. doi: 10.1117/1.3430603. https://doi.org/10.1117/1.3430603 [16] H. P. Stahl, T. Henrichs, and C. Dollinger, "Single-variable parametric cost models for space telescopes," Optical Engineering, vol. 49, no. 7, 073006, 2010. doi: 10.1117/1.3456582. https://doi.org/10.1117/1.3456582 [17] H. P. Stahl and others, "Parametric cost estimation for space science missions," Proc. SPIE, vol. 7010, 2008. doi: 10.1117/12.789615. https://doi.org/10.1117/12.789615 [18] D. M. Brown and others, "Econometric issues of estimating hedonic price functions," Journal of Econometrics, vol. 58, no. 1-2, pp. 175-194, 1993. doi: 10.1016/0304-4076(93)90108-H. https://doi.org/10.1016/0304-4076(93)90108-h [19] R. H. Reichle, W. T. Crow, and C. L. Keppenne, "Performance Metrics for Soil Moisture Retrievals and Application Requirements," Journal of Hydrometeorology, vol. 11, no. 3, pp. 832-840, 2010. doi: 10.1175/2010JHM1223.1. https://doi.org/10.1175/2010jhm1223.1 [20] R. F. Adler, G. J. Huffman, A. Chang, and others, "The Version-2 Global Precipitation Climatology Project (GPCP) Monthly Precipitation Analysis (1979-Present)," Journal of Hydrometeorology, vol. 4, no. 6, pp. 1147-1167, 2003. doi: 10.1175/1525-7541(2003)004<1147:TVGPCP>2.0.CO;2. https://doi.org/10.1175/1525-7541(2003)004<1147:tvgpcp>2.0.co;2 [21] A. Y. Hou, R. K. Kakar, S. Neeck, and others, "The Global Precipitation Measurement (GPM) Mission for Science and Society," Bulletin of the American Meteorological Society, vol. 97, no. 9, pp. 1679-1695, 2016. doi: 10.1175/BAMS-D-15-00306.1. https://doi.org/10.1175/bams-d-15-00306.1 [22] G. W. Imbens and J. M. Wooldridge (Abadie tradition program evaluation), "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, vol. 47, no. 1, pp. 5-86, 2009. doi: 10.1257/jel.47.1.5. https://doi.org/10.1257/jel.47.1.5 [23] R. Barros, "Herbert A. Simon and the concept of rationality: boundaries and procedures," Brazilian Journal of Political Economy, vol. 30, no. 3, pp. 455-472, 2010. doi: 10.1590/S0101-31572010000300006. https://doi.org/10.1590/s0101-31572010000300006 [24] P. M. Todd and G. Gigerenzer, "Bounding rationality to the world," Journal of Economic Psychology, vol. 24, no. 2, pp. 143-165, 2003. doi: 10.1016/S0167-4870(02)00200-3. https://doi.org/10.1016/S0167-4870(02)00200-3 [25] H. A. Simon, "The Architecture of Complexity: Hierarchic Systems," reprinted in The Sciences of the Artificial, MIT Press, 2019. doi: 10.7551/mitpress/12107.003.0011. https://doi.org/10.7551/mitpress/12107.003.0011 [26] A. M. Ross, D. E. Hastings, J. M. Warmkessel, and N. P. Diller, "Multi-Attribute Tradespace Exploration with Concurrent Design as a Value-Centric Framework for Space System Architecture and Design," AIAA, 2003. doi: 10.2514/6.2003-1328. https://doi.org/10.2514/6.2003-1328 [27] A. M. Ross, H. L. McManus, D. E. Hastings, and others, "Assessing Changeability in Aerospace Systems Architecting and Design Using Dynamic Multi-Attribute Tradespace Exploration," AIAA, 2006. doi: 10.2514/6.2006-7255. https://doi.org/10.2514/6.2006-7255 [28] M. W. Maier and others, "Value-Driven Design," Journal of Spacecraft and Rockets / AIAA, 2012. doi: 10.2514/1.54033. https://doi.org/10.2514/1.54033 [29] H. Liang and others, "Sieve M-estimation for semiparametric varying-coefficient partially linear regression," Science China Mathematics, vol. 53, pp. 1849-1866, 2010. doi: 10.1007/s11425-010-4030-7. https://doi.org/10.1007/s11425-010-4030-7 [30] L. Wang and others, "Efficient Semiparametric Estimation of a Partially Linear Quantile Regression Model," Econometric Theory, vol. 19, no. 5, 2003. doi: 10.1017/S0266466603191013. https://doi.org/10.1017/s0266466603191013