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NASA NTRS2002

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Howell, L. W.↗

NASA NTRS2004

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry: Evaluation of Estimates Using Independent Data - Part 2

Rainfall rate estimates from space-borne k&ents are generally accepted as reliable by a majority of the atmospheric science commu&y. One-of the Tropical Rainfall Measuring Mission (TRh4M) facility rain rate algorithms is based upon passive microwave observations fiom the TRMM Microwave Imager (TMI). Part I of this study describes improvements in the TMI algorithm that are required to introduce cloud latent heating and drying as additional algorithm products. Here, estimates of surface rain rate, convective proportion, and latent heating are evaluated using independent ground-based estimates and satellite products. Instantaneous, OP5resolution estimates of surface rain rate over ocean fiom the improved TMI algorithm are well correlated with independent radar estimates (r approx. 0.88 over the Tropics), but bias reduction is the most significant improvement over forerunning algorithms. The bias reduction is attributed to the greater breadth of cloud-resolving model simulations that support the improved algorithm, and the more consistent and specific convective/stratiform rain separation method utilized. The bias of monthly, 2.5 deg. -resolution estimates is similarly reduced, with comparable correlations to radar estimates. Although the amount of independent latent heating data are limited, TMI estimated latent heating profiles compare favorably with instantaneous estimates based upon dual-Doppler radar observations, and time series of surface rain rate and heating profiles are generally consistent with those derived from rawinsonde analyses. Still, some biases in profile shape are evident, and these may be resolved with: (a) additional contextual information brought to the estimation problem, and/or; (b) physically-consistent and representative databases supporting the algorithm. A model of the random error in instantaneous, 0.5 deg-resolution rain rate estimates appears to be consistent with the levels of error determined from TMI comparisons to collocated radar. Error model modifications for non-raining situations will be required, however. Sampling error appears to represent only a fraction of the total error in monthly, 2S0-resolution TMI estimates; the remaining error is attributed to physical inconsistency or non-representativeness of cloud-resolving model simulated profiles supporting the algorithm.

Yang, Song↗

NASA NTRS2006

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry. Part II: Evaluation of Estimates Using Independent Data

Rainfall rate estimates from spaceborne microwave radiometers are generally accepted as reliable by a majority of the atmospheric science community. One of the Tropical Rainfall Measuring Mission (TRMM) facility rain-rate algorithms is based upon passive microwave observations from the TRMM Microwave Imager (TMI). In Part I of this series, improvements of the TMI algorithm that are required to introduce latent heating as an additional algorithm product are described. Here, estimates of surface rain rate, convective proportion, and latent heating are evaluated using independent ground-based estimates and satellite products. Instantaneous, 0.5 deg. -resolution estimates of surface rain rate over ocean from the improved TMI algorithm are well correlated with independent radar estimates (r approx. 0.88 over the Tropics), but bias reduction is the most significant improvement over earlier algorithms. The bias reduction is attributed to the greater breadth of cloud-resolving model simulations that support the improved algorithm and the more consistent and specific convective/stratiform rain separation method utilized. The bias of monthly 2.5 -resolution estimates is similarly reduced, with comparable correlations to radar estimates. Although the amount of independent latent heating data is limited, TMI-estimated latent heating profiles compare favorably with instantaneous estimates based upon dual-Doppler radar observations, and time series of surface rain-rate and heating profiles are generally consistent with those derived from rawinsonde analyses. Still, some biases in profile shape are evident, and these may be resolved with (a) additional contextual information brought to the estimation problem and/or (b) physically consistent and representative databases supporting the algorithm. A model of the random error in instantaneous 0.5 deg. -resolution rain-rate estimates appears to be consistent with the levels of error determined from TMI comparisons with collocated radar. Error model modifications for nonraining situations will be required, however. Sampling error represents only a portion of the total error in monthly 2.5 -resolution TMI estimates; the remaining error is attributed to random and systematic algorithm errors arising from the physical inconsistency and/or nonrepresentativeness of cloud-resolving-model-simulated profiles that support the algorithm.

Yang, Song↗

NASA NTRS2006

Bayesian Estimation of Precipitation from Satellite Passive Microwave Observations Using Combined Radar-Radiometer Retrievals

Precipitation estimation from satellite passive microwave radiometer observations is a problem that does not have a unique solution that is insensitive to errors in the input data. Traditionally, to make this problem well posed, a priori information derived from physical models or independent, high-quality observations is incorporated into the solution. In the present study, a database of precipitation profiles and associated brightness temperatures is constructed to serve as a priori information in a passive microwave radiometer algorithm. The precipitation profiles are derived from a Tropical Rainfall Measuring Mission (TRMM) combined radar radiometer algorithm, and the brightness temperatures are TRMM Microwave Imager (TMI) observed. Because the observed brightness temperatures are consistent with those derived from a radiative transfer model embedded in the combined algorithm, the precipitation brightness temperature database is considered to be physically consistent. The database examined here is derived from the analysis of a month-long record of TRMM data that yields more than a million profiles of precipitation and associated brightness temperatures. These profiles are clustered into a tractable number of classes based on the local sea surface temperature, a radiometer-based estimate of the echo-top height (the height beyond which the reflectivity drops below 17 dBZ), and brightness temperature principal components. For each class, the mean precipitation profile, brightness temperature principal components, and probability of occurrence are determined. The precipitation brightness temperature database supports a radiometer-only algorithm that incorporates a Bayesian estimation methodology. In the Bayesian framework, precipitation estimates are weighted averages of the mean precipitation values corresponding to the classes in the database, with the weights being determined according to the similarity between the observed brightness temperature principal components and the brightness temperature principal components of the classes. Because the classes are stratified by the sea surface temperature and the echo-top-height estimator, the number of classes that are considered for retrieval is significantly smaller than the total number of classes, making the algorithm computationally efficient. The radiometer-only algorithm is applied to TMI observations, and precipitation estimates are compared with combined TRMM precipitation radar (PR) TMI reference estimates. The TMI-only algorithm, supported by the empirically derived database, produces estimates that are more consistent with the reference values than the precipitation estimates from the version-6 TRMM facility TMI algorithm. Cloud-resolving model simulations are used to assign a latent heating profile to each precipitation profile in the empirically derived database, making it possible to estimate latent heating using the radiometer-only algorithm. Although the evaluation of latent heating estimates in this study is preliminary, because realistic conditional probability distribution functions are attached to latent heating structures in the algorithm s database, a generally positive impact on latent heating estimation from passive microwave observations is expected.

Grecu, Mircea↗

NASA NTRS2011

Space Radiation Cancer, Circulatory Disease and CNS Risks for Near Earth Asteroid and Mars Missions: Uncertainty Estimates for Never-Smokers

The uncertainties in estimating the health risks from galactic cosmic rays (GCR) and solar particle events (SPE) are a major limitation to the length of space missions and the evaluation of potential risk mitigation approaches. NASA limits astronaut exposures to a 3% risk of exposure induced cancer death (REID), and protects against uncertainties in risks projections using an assessment of 95% confidence intervals after propagating the error from all model factors (environment and organ exposure, risk coefficients, dose-rate modifiers, and quality factors). Because there are potentially significant late mortality risks from diseases of the circulatory system and central nervous system (CNS) which are less well defined than cancer risks, the cancer REID limit is not necessarily conservative. In this report, we discuss estimates of lifetime risks from space radiation and new estimates of model uncertainties are described. The key updates to the NASA risk projection model are: 1) Revised values for low LET risk coefficients for tissue specific cancer incidence, with incidence rates transported to an average U.S. population to estimate the probability of Risk of Exposure Induced Cancer (REIC) and REID. 2) An analysis of smoking attributable cancer risks for never-smokers that shows significantly reduced lung cancer risk as well as overall cancer risks from radiation compared to risk estimated for the average U.S. population. 3) Derivation of track structure based quality functions depends on particle fluence, charge number, Z and kinetic energy, E. 4) The assignment of a smaller maximum in quality function for leukemia than for solid cancers. 5) The use of the ICRP tissue weights is shown to over-estimate cancer risks from SPEs by a factor of 2 or more. Summing cancer risks for each tissue is recommended as a more accurate approach to estimate SPE cancer risks. 6) Additional considerations on circulatory and CNS disease risks. Our analysis shows that an individual s history of smoking exposure has a larger impact on GCR risk estimates than amounts of radiation shielding or age at exposure (amongst adults). Risks for never-smokers compared to the average U.S. population are estimated to be reduced between 30% and 60% dependent on model assumptions. Lung cancer is the major contributor to the reduction for never-smokers, with additional contributions from circulatory diseases and cancers of the stomach, liver, bladder, oral cavity and esophagus, and leukemia. The relative contribution of CNS risks to the overall space radiation detriment is potentially increased for never-smokers such as most astronauts. Problems in estimating risks for former smokers and the influence of second-hand smoke are discussed. Compared to the LET approximation, the new track structure derived radiation quality functions lead to a reduced risk for relativistic energy particles and increased risks for intermediate energy particles. Revised estimates for the number of safe days in space at solar minimum for heavy shielding conditions are described for never-smokers and the average U.S. population. Results show that missions to near Earth asteroids (NEA) or Mars violate NASA's radiation safety standards with the current levels of uncertainties. Greater improvements in risk estimates for never-smokers are possible, and would be dependent on improved understanding of risk transfer models, and elucidating the role of space radiation on the various stages of disease formation (e.g. initiation, promotion, and progression).

Cucinotta, Francis A.↗

NASA NTRS2012

Combining Ratio Estimation for Low Density Parity Check (LDPC) Coding

The Low Density Parity Check (LDPC) Code decoding algorithm make use of a scaled receive signal derived from maximizing the log-likelihood ratio of the received signal. The scaling factor (often called the combining ratio) in an AWGN channel is a ratio between signal amplitude and noise variance. Accurately estimating this ratio has shown as much as 0.6 dB decoding performance gain. This presentation briefly describes three methods for estimating the combining ratio: a Pilot-Guided estimation method, a Blind estimation method, and a Simulation-Based Look-Up table. The Pilot Guided Estimation method has shown that the maximum likelihood estimates of signal amplitude is the mean inner product of the received sequence and the known sequence, the attached synchronization marker (ASM) , and signal variance is the difference of the mean of the squared received sequence and the square of the signal amplitude. This method has the advantage of simplicity at the expense of latency since several frames worth of ASMs. The Blind estimation method s maximum likelihood estimator is the average of the product of the received signal with the hyperbolic tangent of the product combining ratio and the received signal. The root of this equation can be determined by an iterative binary search between 0 and 1 after normalizing the received sequence. This method has the benefit of requiring one frame of data to estimate the combining ratio which is good for faster changing channels compared to the previous method, however it is computationally expensive. The final method uses a look-up table based on prior simulated results to determine signal amplitude and noise variance. In this method the received mean signal strength is controlled to a constant soft decision value. The magnitude of the deviation is averaged over a predetermined number of samples. This value is referenced in a look up table to determine the combining ratio that prior simulation associated with the average magnitude of the deviation. This method is more complicated than the Pilot-Guided Method due to the gain control circuitry, but does not have the real-time computation complexity of the Blind Estimation method. Each of these methods can be used to provide an accurate estimation of the combining ratio, and the final selection of the estimation method depends on other design constraints.

Mahmoud, Saad↗

NASA NTRS2012

A Probabilistic Mass Estimation Algorithm for a Novel 7- Channel Capacitive Sample Verification Sensor

A document describes an algorithm created to estimate the mass placed on a sample verification sensor (SVS) designed for lunar or planetary robotic sample return missions. A novel SVS measures the capacitance between a rigid bottom plate and an elastic top membrane in seven locations. As additional sample material (soil and/or small rocks) is placed on the top membrane, the deformation of the membrane increases the capacitance. The mass estimation algorithm addresses both the calibration of each SVS channel, and also addresses how to combine the capacitances read from each of the seven channels into a single mass estimate. The probabilistic approach combines the channels according to the variance observed during the training phase, and provides not only the mass estimate, but also a value for the certainty of the estimate. SVS capacitance data is collected for known masses under a wide variety of possible loading scenarios, though in all cases, the distribution of sample within the canister is expected to be approximately uniform. A capacitance-vs-mass curve is fitted to this data, and is subsequently used to determine the mass estimate for the single channel s capacitance reading during the measurement phase. This results in seven different mass estimates, one for each SVS channel. Moreover, the variance of the calibration data is used to place a Gaussian probability distribution function (pdf) around this mass estimate. To blend these seven estimates, the seven pdfs are combined into a single Gaussian distribution function, providing the final mean and variance of the estimate. This blending technique essentially takes the final estimate as an average of the estimates of the seven channels, weighted by the inverse of the channel s variance.

Wolf, Michael↗

NASA NTRS2016

A Survey of Cost Estimating Methodologies for Distributed Spacecraft Missions

Satellite constellations and Distributed Spacecraft Mission (DSM) architectures offer unique benefits to Earth observation scientists and unique challenges to cost estimators. The Cost and Risk (CR) module of the Tradespace Analysis Tool for Constellations (TAT-C) being developed by NASA Goddard seeks to address some of these challenges by providing a new approach to cost modeling, which aggregates existing Cost Estimating Relationships (CER) from respected sources, cost estimating best practices, and data from existing and proposed satellite designs. Cost estimation through this tool is approached from two perspectives: parametric cost estimating relationships and analogous cost estimation techniques. The dual approach utilized within the TAT-C CR module is intended to address prevailing concerns regarding early design stage cost estimates, and offer increased transparency and fidelity by offering two preliminary perspectives on mission cost. This work outlines the existing cost model, details assumptions built into the model, and explains what measures have been taken to address the particular challenges of constellation cost estimating. The risk estimation portion of the TAT-C CR module is still in development and will be presented in future work. The cost estimate produced by the CR module is not intended to be an exact mission valuation, but rather a comparative tool to assist in the exploration of the constellation design tradespace. Previous work has noted that estimating the cost of satellite constellations is difficult given that no comprehensive model for constellation cost estimation has yet been developed, and as such, quantitative assessment of multiple spacecraft missions has many remaining areas of uncertainty. By incorporating well-established CERs with preliminary approaches to approaching these uncertainties, the CR module offers more complete approach to constellation costing than has previously been available to mission architects or Earth scientists seeking to leverage the capabilities of multiple spacecraft working in support of a common goal.

0↗

NASA NTRS2016

A Survey of Cost Estimating Methodologies for Distributed Spacecraft Missions

Foreman, Veronica L.↗

NASA NTRS2015

Rule-Based Flight Software Cost Estimation

This paper discusses the fundamental process for the computation of Flight Software (FSW) cost estimates. This process has been incorporated in a rule-based expert system [1] that can be used for Independent Cost Estimates (ICEs), Proposals, and for the validation of Cost Analysis Data Requirements (CADRe) submissions. A high-level directed graph (referred to here as a decision graph) illustrates the steps taken in the production of these estimated costs and serves as a basis of design for the expert system described in this paper. Detailed discussions are subsequently given elaborating upon the methodology, tools, charts, and caveats related to the various nodes of the graph. We present general principles for the estimation of FSW using SEER-SEM as an illustration of these principles when appropriate. Since Source Lines of Code (SLOC) is a major cost driver, a discussion of various SLOC data sources for the preparation of the estimates is given together with an explanation of how contractor SLOC estimates compare with the SLOC estimates used by JPL. Obtaining consistency in code counting will be presented as well as factors used in reconciling SLOC estimates from different code counters. When sufficient data is obtained, a mapping into the JPL Work Breakdown Structure (WBS) from the SEER-SEM output is illustrated. For across the board FSW estimates, as was done for the NASA Discovery Mission proposal estimates performed at JPL, a comparative high-level summary sheet for all missions with the SLOC, data description, brief mission description and the most relevant SEER-SEM parameter values is given to illustrate an encapsulation of the used and calculated data involved in the estimates. The rule-based expert system described provides the user with inputs useful or sufficient to run generic cost estimation programs. This system's incarnation is achieved via the C Language Integrated Production System (CLIPS) and will be addressed at the end of this paper.

computational intelligence↗

NASA NTRS1977

The use of parametric cost estimating relationships for transport aircraft systems in establishing initial Design to Cost Targets

This paper provides a brief overview of Design to Cost (DTC). Problems inherent in attempting to estimate costs are discussed, along with techniques and types of models that have been developed to estimate aircraft costs. A set of cost estimating relationships that estimate the total production cost of commercial and military transport aircraft at the systems level is presented and the manner in which these equations might be used effectively in developing initial DTC targets is indicated. The principal point made in this paper is that, by using a disagregated set of equations to estimate transport aircraft costs at the systems level, reasonably accurate preliminary cost estimates may be achieved. These estimates may serve directly as initial DTC targets, or adjustments may be made to the estimates obtained for some of the systems to estimate the production cost impact of alternative designs or manufacturing technologies. The relative ease by which estimates may be made with this model, the flexibility it provides by being disaggregated, and the accuracy of the estimates it provides make it a unique and useful tool in establishing initial DTC targets.

Beltramo, M. N.↗

NASA NTRS1987

Robust time and frequency domain estimation methods in adaptive control

A robust identification method was developed for use in an adaptive control system. The type of estimator is called the robust estimator, since it is robust to the effects of both unmodeled dynamics and an unmeasurable disturbance. The development of the robust estimator was motivated by a need to provide guarantees in the identification part of an adaptive controller. To enable the design of a robust control system, a nominal model as well as a frequency-domain bounding function on the modeling uncertainty associated with this nominal model must be provided. Two estimation methods are presented for finding parameter estimates, and, hence, a nominal model. One of these methods is based on the well developed field of time-domain parameter estimation. In a second method of finding parameter estimates, a type of weighted least-squares fitting to a frequency-domain estimated model is used. The frequency-domain estimator is shown to perform better, in general, than the time-domain parameter estimator. In addition, a methodology for finding a frequency-domain bounding function on the disturbance is used to compute a frequency-domain bounding function on the additive modeling error due to the effects of the disturbance and the use of finite-length data. The performance of the robust estimator in both open-loop and closed-loop situations is examined through the use of simulations.

Lamaire, Richard Orville↗

NASA NTRS1989

A Doppler centroid estimation algorithm for SAR systems optimized for the quasi-homogeneous source

Radar signal processing applications frequently require an estimate of the Doppler centroid of a received signal. The Doppler centroid estimate is required for synthetic aperture radar (SAR) processing. It is also required for some applications involving target motion estimation and antenna pointing direction estimation. In some cases, the Doppler centroid can be accurately estimated based on available information regarding the terrain topography, the relative motion between the sensor and the terrain, and the antenna pointing direction. Often, the accuracy of the Doppler centroid estimate can be improved by analyzing the characteristics of the received SAR signal. This kind of signal processing is also referred to as clutterlock processing. A Doppler centroid estimation (DCE) algorithm is described which contains a linear estimator optimized for the type of terrain surface that can be modeled by a quasi-homogeneous source (QHS). Information on the following topics is presented: (1) an introduction to the theory of Doppler centroid estimation; (2) analysis of the performance characteristics of previously reported DCE algorithms; (3) comparison of these analysis results with experimental results; (4) a description and performance analysis of a Doppler centroid estimator which is optimized for a QHS; and (5) comparison of the performance of the optimal QHS Doppler centroid estimator with that of previously reported methods.

Jin, Michael Y.↗

NASA NTRS2008

Estimating Software-Development Costs With Greater Accuracy

COCOMOST is a computer program for use in estimating software development costs. The goal in the development of COCOMOST was to increase estimation accuracy in three ways: (1) develop a set of sensitivity software tools that return not only estimates of costs but also the estimation error; (2) using the sensitivity software tools, precisely define the quantities of data needed to adequately tune cost estimation models; and (3) build a repository of software-cost-estimation information that NASA managers can retrieve to improve the estimates of costs of developing software for their project. COCOMOST implements a methodology, called '2cee', in which a unique combination of well-known pre-existing data-mining and software-development- effort-estimation techniques are used to increase the accuracy of estimates. COCOMOST utilizes multiple models to analyze historical data pertaining to software-development projects and performs an exhaustive data-mining search over the space of model parameters to improve the performances of effort-estimation models. Thus, it is possible to both calibrate and generate estimates at the same time. COCOMOST is written in the C language for execution in the UNIX operating system.

Baker, Dan↗

NASA NTRS2011

Local Estimators for Spacecraft Formation Flying

A formation estimation architecture for formation flying builds upon the local information exchange among multiple local estimators. Spacecraft formation flying involves the coordination of states among multiple spacecraft through relative sensing, inter-spacecraft communication, and control. Most existing formation flying estimation algorithms can only be supported via highly centralized, all-to-all, static relative sensing. New algorithms are needed that are scalable, modular, and robust to variations in the topology and link characteristics of the formation exchange network. These distributed algorithms should rely on a local information-exchange network, relaxing the assumptions on existing algorithms. In this research, it was shown that only local observability is required to design a formation estimator and control law. The approach relies on breaking up the overall information-exchange network into sequence of local subnetworks, and invoking an agreement-type filter to reach consensus among local estimators within each local network. State estimates were obtained by a set of local measurements that were passed through a set of communicating Kalman filters to reach an overall state estimation for the formation. An optimization approach was also presented by means of which diffused estimates over the network can be incorporated in the local estimates obtained by each estimator via local measurements. This approach compares favorably with that obtained by a centralized Kalman filter, which requires complete knowledge of the raw measurement available to each estimator.

Fathpour, Nanaz↗

NASA NTRS2013

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗

NASA NTRS2019

Prior biosphere model impact on global terrestrial CO2 fluxes estimated from OCO-2 retrievals

This study assesses the impact of different state of the art global biospheric CO2 flux models, when applied as prior information, on inverse model “top-down” estimates of terrestrial CO2 fluxes obtained when assimilating Orbiting Carbon Observatory 2 (OCO-2) observations. This is done with a series of observing system simulation experiments (OSSEs) using synthetic CO2 column-average dry air mole fraction (XCO2) retrievals sampled at the OCO-2 satellite spatiotemporal frequency. The OSSEs utilized a 4-D variational (4D-Var) assimilation system with the GEOS-Chem global chemical transport model (CTM) to estimate CO2 net ecosystem exchange (NEE) fluxes using synthetic OCO-2 observations. The impact of biosphere models in inverse model estimates of NEE is quantified by conducting OSSEs using the NASA-CASA, CASA-GFED, SiB-4, and LPJ models as prior estimates and using NEE from the multi-model ensemble mean of the Multiscale Synthesis and Terrestrial Model Intercomparison Project as the “truth”. Results show that the assimilation of simulated XCO2 retrievals at OCO-2 observing modes over land results in posterior NEE estimates which generally reproduce “true” NEE globally and over terrestrial TransCom-3 regions that are well-sampled. However, we find larger spread among posterior NEE estimates, when using different prior NEE fluxes, in regions and seasons that have limited OCO-2 observational coverage and a large range in “bottom-up” NEE fluxes. Seasonally averaged posterior NEE estimates had standard deviations (SD) of ∼10 % to ∼50 % of the multi-model-mean NEE for different TransCom-3 land regions with significant NEE fluxes (regions/seasons with a NEE flux ≥0.5 PgC/yr). On a global average, the seasonally averaged residual impact of the prior model NEE assumption on the posterior NEE spread is ∼10 %–20 % of the posterior NEE mean. Additional OCO-2 OSSE simulations demonstrate that posterior NEE estimates are also sensitive to the assumed prior NEE flux uncertainty statistics, with spread in posterior NEE estimates similar to those when using variable prior model NEE fluxes. In fact, the sensitivity of posterior NEE estimates to prior error statistics was larger than prior flux values in some regions/times in the tropics and Southern Hemisphere where sufficient OCO-2 data were available and large differences between the prior and truth were evident. Overall, even with the availability of spatiotemporally dense OCO-2 data, noticeable residual differences (up to ∼20 %–30 % globally and 50 % regionally) in posterior NEE flux estimates remain that were caused by the choice of prior model flux values and the specification of prior flux uncertainties.

Sajeev Philip↗

NASA NTRS2019

Blind Validation Study of Parametric Cost Estimation Tool SEER-H for NASA Space Missions

One of the primary parametric cost modeling tools used by NASA and the aerospace industry to estimate the development and production cost of future spacecraft hardware is SEER-H by Galorath. To date, no independent validation of this tool for cost estimation of space missions has been reported in the literature. In the present validation study, cost estimators used SEER-H to estimate the cost of twelve different past NASA science missions. The estimators were prevented from knowing the actual cost of the missions in an effort to minimize cognitive biases. The point estimates of SEER-H had an average error of 23%, median error of -0.3%, and a standard deviation of 43%. Nine of the twelve mission's actual costs fell within the 80% confidence interval of SEER's probabilistic estimates. Several factors independent of SEER that may have affected the accuracy of the results have been identified and are discussed; these include: uncertainty in the technical data used for the estimates, the methods used to estimate uncertainty in spacecraft component mass and numbers of prototypes, and the experience of the estimators.

SEER-H↗