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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement

This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm bounds for finite element and graph-based discretizations of Matérn-type priors and deconvolution forward models. For linear-Gaussian inverse problems, we develop a general theory to characterize the error in the approximation to the posterior. We also embed the computational framework into ensemble Kalman methods and MAP estimators for nonlinear inverse problems. Furthermore, our operator-norm bounds for prior discretizations guarantee the scalability and accuracy of these algorithms under mesh refinement.

Bayesian inverse problem↗
DOE OSTI2023

Modeled production, oxidation, and transport processes of wetland methane emissions in temperate, boreal, and Arctic regions

Abstract Wetlands are the largest natural source of methane (CH 4 ) to the atmosphere. The eddy covariance method provides robust measurements of net ecosystem exchange of CH 4 , but interpreting its spatiotemporal variations is challenging due to the co‐occurrence of CH 4 production, oxidation, and transport dynamics. Here, we estimate these three processes using a data‐model fusion approach across 25 wetlands in temperate, boreal, and Arctic regions. Our data‐constrained model—iPEACE—reasonably reproduced CH 4 emissions at 19 of the 25 sites with normalized root mean square error of 0.59, correlation coefficient of 0.82, and normalized standard deviation of 0.87. Among the three processes, CH 4 production appeared to be the most important process, followed by oxidation in explaining inter‐site variations in CH 4 emissions. Based on a sensitivity analysis, CH 4 emissions were generally more sensitive to decreased water table than to increased gross primary productivity or soil temperature. For periods with leaf area index (LAI) of ≥20% of its annual peak, plant‐mediated transport appeared to be the major pathway for CH 4 transport. Contributions from ebullition and diffusion were relatively high during low LAI (<20%) periods. The lag time between CH 4 production and CH 4 emissions tended to be short in fen sites (3 ± 2 days) and long in bog sites (13 ± 10 days). Based on a principal component analysis, we found that parameters for CH 4 production, plant‐mediated transport, and diffusion through water explained 77% of the variance in the parameters across the 19 sites, highlighting the importance of these parameters for predicting wetland CH 4 emissions across biomes. These processes and associated parameters for CH 4 emissions among and within the wetlands provide useful insights for interpreting observed net CH 4 fluxes, estimating sensitivities to biophysical variables, and modeling global CH 4 fluxes.

Ueyama, Masahito↗
DOE OSTI2020

Remote Radiation Sensing Using Aerial and Ground Platforms

Remote sensing of ionizing radiation has a significant role in waste management, nuclear material management and nonproliferation, and radiation safety. Robotic platforms can surpass the number of tasks that are achieved by humans. With this technique, the operator's radiation exposure can be decreased. Remote sensing allows for the evaluation and monitoring of radiological contamination. Gamma-ray and neutron sensors were integrated onto the robotic platforms. This approach allows for the radiation sensor data to be dynamically tracked and mapped thus enabling further analysis of the radiation flux in temporal and spatial domains. The goal is to complete scheduled tasks while the robot is being irradiated. To achieve this, electronic components must be shielded and radiation hardened. CZT Detector: Cadmium Zinc Telluride (CZT) detector technology has been a promising solution for gamma-ray and x-ray measurements. Detector data is transferred to the Odroid minicomputer that controls and powers the module via the USB. Robot Operating System (ROS) was utilized for data acquisition and data fusion. The Mariscotti method was employed for the spectrum analysis. A function was programmed in ROS for the automatic identification of photopeaks. CLYC Detector: A Cs{sub 2}LiYCl{sub 6}:Ce{sup 3+} (CLYC) detector was used for simultaneous medium-resolution gamma-ray measurements and neutron counting. A 2.54 cm diameter photomultiplier tube (PMT) was equipped with a high voltage supply and a miniature digitizer. Gamma-ray excitation: fast core-to-valence luminescence (CVL) with 1 ns decay constant, and prompt Ce{sup 3+} emission with 50 ns decay constant. Neutron excitation: slow cerium self-trapped excitation (Ce{sup 3+} STE), 1000 ns decay constant. Radiation Source Localization: Maximum Likelihood Estimation (MLE) and gradient-based methods were used to locate the position of a radiation source based on measured radiation intensities. Multi-Particle Transport Code FLUKA: Estimation of radiation damage of the electronic components is important in order to optimize the robot's operational time while it is irradiated. Displacement per atom (DPA) represents the radiation damage in materials exposed to the ionizing radiation. Various shielding layers of different thickness t were analyzed (< 5% statistical error). The model of the controller of the UAS was designed in FLUKA. Conclusion: CZT and CLYC detectors were integrated onto the robotic platforms. Radiation source localization and contour mapping using robotic platforms were studied. Functions for data analysis and fusion were developed in ROS. FLUKA code was utilized to analyze DPA values. Layers of low-density and high-density materials were used to shield the UAS electronics.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1978

Secondary error analysis: The evaluation of analyst dot labeling

The author has identified the following significant results. From this examination of 25 test segments using Al labeling and ground truth labeling, the PCC on type 1 dots was found to be signficantly better for both types of ground truth labeled procedures than the PCC obtained using Al labeling. No significant difference in the PCC was found for type 2 dots. However, in all three treatments, the type 2 dots included pixels which fell on boundaries or were mixed pixels. This accounted for all PCC2 values being equally low. The proportion estimates achieved in these classifications showed no significant differences between procedures.

Havens, K. A.↗
DOE OSTI2022

Regression of exchangeable relational arrays

Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modelled as a linear function of observable covariates. Uncertainty estimates for regression coefficient estimators, and ideally the coefficient estimators themselves, must account for dependence between elements of the array, e.g., relations involving the same actor. Existing estimators of standard errors that recognize such relational dependence rely on estimating extremely complex, heterogeneous structure across actors. This paper develops a new class of parsimonious coefficient and standard error estimators for regressions of relational arrays. Here we leverage an exchangeability assumption to derive standard error estimators that pool information across actors, and are substantially more accurate than existing estimators in a variety of settings. This exchangeability assumption is pervasive in network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression setting with relational data. We demonstrate improvements in inference theoretically, via a simulation study, and by analysis of a dataset involving international trade.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Measurement of the Largest-scale CMB E -mode Polarization with CLASS

We present measurements of large-scale cosmic microwave background E-mode polarization from the Cosmology Large Angular Scale Surveyor 90 GHz data. Using 115 det-yr of observations collected through 2024 with a variable-delay polarization modulator, we achieved a polarization sensitivity of 82 μK arcimin, comparable to Planck at similar frequencies (100 and 143 GHz ). The analysis demonstrates effective mitigation of systematic errors and addresses challenges to large-angular-scale power recovery posed by time-domain filtering in maximum-likelihood map-making. A novel implementation of the pixel-space transfer matrix is introduced, which enables efficient filtering simulations and bias correction in the power spectrum using the quadratic cross-spectrum estimator. Overall, we achieved an unbiased time-domain filtering correction to recover the largest angular scale polarization, with the only power deficit, arising from map-making nonlinearity, being characterized as <3%. Through cross-correlation with Planck, we detected the cosmic reionization at 99.4% significance and measured the reionization optical depth τ = $0.053^{+0.018}_{-0.019}$, marking the first ground-based attempt at such a measurement. At intermediate angular scales (ℓ > 30), our results, both independently and in cross-correlation with Planck, remain fully consistent with Planck’s measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1970

Analysis of remote sensing data for evaluation of vegetation resources

Research has centered around: (1) completion of a study on the use of remote sensing techniques as an aid to multiple use management; (2) determination of the information transfer at various image resolution levels for wildland areas; and (3) determination of the value of small scale multiband, multidate photography for the analysis of vegetation resources. In addition, a substantial effort was made to upgrade the automatic image classification and spectral signature acquisition capabilities of the laboratory. It was found that: (1) Remote sensing techniques should be useful in multiple use management to provide a first-cut analysis of an area. (2) Imagery with 400-500 feet ground resolvable distance (GRD), such as that expected from ERTS-1, should allow discriminations to be made between woody vegetation, grassland, and water bodies with approximately 80% accuracy. (3) Barley and wheat acreages in Maricopa County, Arizona could be estimated with acceptable accuracies using small scale multiband, multidate photography. Sampling errors for acreages of wheat, barley, small grains (wheat and barley combined), and all cropland were 13%, 11%, 8% and 3% respectively.

Source record↗
NASA NTRS1982

The inverse problem of constructing a gravimetric geoid

Computation of a single geoidal height from gravity acceleration data formally requires that the latter be known everywhere on the earth. A computational procedure based on linear inverse theory for estimating geoidal heights from incomplete sets of data is presented. The same scheme can be used to estimate gravity accelerations from altimetry-derived geoids. The systematic error owing to lack of data and the choice of a particular inverse operator is described by using resolution functions and their spherical harmonic expansions. An rms value of this error is also estimated by assuming a spectrum for the unknown geoid. The influence of the size of the data region, the spacing between data, the filtering applied to the data, and the model weighting function chosen are all quantified in a spherical geometry. The examples presented show that when low degree spherical harmonic coefficients are available - from satellite orbit analysis - a band-passed version of the geoid can be constructed from local gravity data, even with a relatively restricted data set.

Zlotnicki, V.↗
NASA NTRS1985

Future possibilities in objective analysis and data assimilation for atmospheric dynamics

The role that dynamics plays in estimating the state of the atmosphere from incomplete and noisy data is reviewed. Objective analysis represents an attempt at relying mostly on the data and minimizing the role of dynamics in the estimation. Data assimilation tries to balance properly the roles of dynamical and observational information. Sequential estimation is presented as the proper framework for understanding this balance, and the Kalman filter as the ideal, optimal procedure for data assimilation. The optimal filter computes forecast error covariances of a given atmospheric model exactly, and hence data assimilation should be closely connected with predictability studies. This connection is described, and consequences drawn for currently active areas of the atmospheric and related sciences, namely, mesoscale meteorology, long range forecasting, and upper ocean dynamics. Possibilities offered by judicious data assimilation in understanding barotropic adjustment, a phenomenon that appears to play a crucial role in atmospheric behavior on the scale of weeks to months, and hence in long range forecasting are addressed.

Ghil, M.↗
NASA NTRS1986

Color rendering of color camera data

Conditions under which a computational procedure can be applied to arbitrary camera sensors to permit estimation of the human photoreceptor response are considered. The adopted procedures recover the effective surface reflectance at the time of measurement, and the reflectance estimates depend not only on the surface, but upon the viewing geometry. The present method for color rendering assumes that the observer's state of adaptation at the time of viewing the original and the rendered images is the same. The analysis aids in specifying which classes of surfaces are required to be accurately rendered, and for which surfaces some error can be tolerated.

Wandell, Brian A.↗
NASA NTRS1989

Kalman estimation for SEDS measurements

The first on-orbit experiment of the Small Expendable Deployer System (SEDS) for tethered satellites will collect telemetry data for tethered length, rate of deployment, and tether tension. The post-flight analysis will use this data to reconstruct the deployment history and determine payload position and tether shape. Two Kalman estimator algorithms were written, and output using simulated measurement data was compared. Both estimators exhibited the same estimated state histories, indicating that numerical instability in the traditional algorithm was not the cause of filter divergence. Estimation of acceleration biases was added, which reduced the error but did not correct the divergence. An add-a-bead estimator that adds lumped masses as the tether is deployed was written, which provides a state model that matches the BEADSIM simulation providing the true measurements and states. This twenty-one bead estimator produced state histories similar to those of the two-bead estimator, indicating that the filter divergence was not caused by a reduced-order model. The noise models used to date are relatively simple and may be the source of estimator divergence. The investigation of colored noise models, cross-correlated measurement and process covariances, and noise-adaptive filter techniques is recommended.

Carrington, Connie K.↗
NASA NTRS1999

Elevation Change of the Southern Greenland Ice Sheet from Satellite Radar Altimeter Data

Long-term changes in the thickness of the polar ice sheets are important indicators of climate change. Understanding the contributions to the global water mass balance from the accumulation or ablation of grounded ice in Greenland and Antarctica is considered crucial for determining the source of the about 2 mm/yr sea-level rise in the last century. Though the Antarctic ice sheet is much larger than its northern counterpart, the Greenland ice sheet is more likely to undergo dramatic changes in response to a warming trend. This can be attributed to the warmer Greenland climate, as well as a potential for amplification of a global warming trend in the polar regions of the Northern Hemisphere. In collaboration with Drs. Curt Davis and Craig Kluever of the University of Missouri, we are using data from satellite radar altimeters to measure changes in the elevation of the Southern Greenland ice sheet from 1978 to the present. Difficulties with systematic altimeter measurement errors, particularly in intersatellite comparisons, beset earlier studies of the Greenland ice sheet thickness. We use altimeter data collected contemporaneously over the global ocean to establish a reference for correcting ice-sheet data. In addition, the waveform data from the ice-sheet radar returns are reprocessed to better determine the range from the satellite to the ice surface. At JPL, we are focusing our efforts principally on the reduction of orbit errors and range biases in the measurement systems on the various altimeter missions. Our approach emphasizes global characterization and reduction of the long-period orbit errors and range biases using altimeter data from NASA's Ocean Pathfinder program. Along-track sea-height residuals are sequentially filtered and backwards smoothed, and the radial orbit errors are modeled as sinusoids with a wavelength equal to one revolution of the satellite. The amplitudes of the sinusoids are treated as exponentially-correlated noise processes with a time-constant of six days. Measurement errors (e.g., altimeter range bias) are simultaneously recovered as constant parameters. The corrections derived from the global ocean analysis are then applied over the Greenland ice sheet. The orbit error and measurement bias corrections for different missions are developed in a single framework to enable robust linkage of ice-sheet measurements from 1978 to the present. In 1998, we completed our re-evaluation of the 1978 Seasat and 1985-1989 Geosat Exact Repeat Mission data. The estimates of ice thickness over Southern Greenland (south of 72N and above 2000 m) from 1978 to 1988 show large regional variations (+/-18 cm/yr), but yield an overall rate of +1.5 +/- 0.5 cm/yr (one standard error). Accounting for systematic errors, the estimate may not be significantly different from the null growth rate. The average elevation change from 1978 to 1988 is too small to assess whether the Greenland ice sheet is undergoing a long-term change.

Haines, Bruce J.↗
NASA NTRS1999

An Airborne Scanning Laser Altimetry Survey of Long Valley, California

Between 28 September and 7 October 1995, we conducted an airborne laser altimetry experiment over the Long Valley caldera, California, in which each of two scanning laser altimeters (dubbed SLICER and RASCAL) were flown in a NASA T-39 jet aircraft. Operating concurrently were a Global Positioning System (GPS) guidance system and dual frequency receivers for precise navigation and post-flight calculation or the airplane trajectory relative to a ground station, and an inertial navigation system (INS) for attitude determination. Reduction of raw laser ranges requires merging the differential kinematic GPS aircraft trajectory and the INS data with the laser data, and determination of the atmospheric delay. Data geolocation consists of obtaining the centre location and the mean elevation within each footprint in a geodetic coordinate system. The elevation of Crowley Lake is recovered to an accuracy of approximately 3 cm or better from 3 km above ground level and crossover analysis indicates that the elevation estimates are consistent from pass to pass. We test our geolocation procedures by comparing laser-derived elevations with those determined in situ for recognizable ground features. A comparison of laser and GPS-derived positions shows that the horizontal accuracy is better than the diameter of the footprint and vertical accuracy is within the error inherent in the range measurement. A comparison of SLICER elevation data with digital elevation models (DEMs) of the region shows that the DEM data provides surface topography to within stated accuracy limits. Although research continues to utilize the full potential of laser altimetry data, our results constitute a successful demonstration that the technique may be used to perform geodetic monitoring of surface topographic changes.

Hofton, M. A.↗
NASA NTRS1999

Precise Clock Solutions Using Carrier Phase from GPS Receivers in the International GPS Service

As one of its activities as an Analysis Center in the International GPS Service (IGS), the Jet Propulsion Laboratory (JPL) uses data from a globally distributed network of geodetic-quality GPS receivers to estimate precise clock solutions, relative to a chosen reference, for both the GPS satellites and GPS receiver internal clocks, every day. The GPS constellation and ground network provide geometrical strength resulting in formal errors of about 100 p sec for these estimates. Some of the receivers in the global IGS network contain high quality frequency references, such as hydrogen masers. The clock solutions for such receivers are smooth at the 20-p sec level on time scales of a few minutes. There are occasional (daily to weekly) shifts at the microsec level, symptomatic of receiver resets, and 200-p sec-level discontinuities at midnight due to 1-day processing boundaries. Relative clock solutions among 22 IGS sites proposed as "fiducial" in the IGS/BIPM pilot project have been examined over a recent 4-week period. This allows a quantitative measure of receiver reset frequency as a function of site. For days and-sites without resets, the Allan deviation of the relative clock solutions is also computed for subdaily values of tau..

Zumberge, J. F.↗
NASA NTRS2013

RFI-SIM: RFI Simulation Package

RFI-SIM simulates the RFI environment to estimate the interference from terrestrial emitters into spacecraft, or vice versa. A high-fidelity simulation of the RFI environment has been developed by employing all antenna- related and radar system-related parameters of multiple emitters, as well as that of the desired spacecraft. In the simulation, the real-time analysis of the interference and its effects on error budgets of a desired radar system is taken into account. This provides a reliable tool for radar system design to deal with RFI issues and to evaluate the sensitivity of various parts of a radar system including antenna pattern, RF front-end and digital processing to RFI signals.

Ghaemi, Hirad↗
NASA NTRS2010

Studies of the Effects of Actuator Errors on the HCIT/PIAA Contrast Performance

The High Contrast Imaging Testbed Phase Induced Amplitude Apodization (HCIT/PIAA) coronagraph system at JPL relies on an Electric-Field Conjugation (EFC) wavefront correction algorithm to obtain the required high contrast. This algorithm works with one deformable mirror (DM) to estimate the electric-field to be controlled, and with one or multiple DM's to create a "dark-hole" in the image plane. We have investigated the effects of DM actuator errors on the efficiency of the EFC algorithm. The structural design of the optical system as well as the parameters of various optical elements used in the analysis are drawn from those of the HCIT/PIAA system that have been and will be implemented with one or two DM's. The simulation takes into account the surface errors of various optical elements. In this paper, we report our findings in the case of narrowband wavelength light.

PIAA↗
NASA NTRS2019

Surrogate Modeling and Optimization of a Combustor with an Interdigitated Flushwall Injector

Design and Analysis of Computer Experiments (DACE) methods are applied and used to perform surrogate modeling and optimization of a simplified combustor flowpath with an interdigitated flushwall injector. The objectives of the optimization are the thrust potential and combustion efficiency, which are evaluated across a range of flight Mach numbers, duct heights, spanwise spacings, and injection angles. The focus of this work is to highlight the application of a sequential learning approach, in order to learn about the responses of the objective functions over the design space and to identify local regions of interest for further analysis. This approach is contrasted to a previous effort where only a single sampling set was used to fit surrogate models and perform optimization. The optimal solutions resulting from the previous and present approaches are different, due to surrogate model-guided local refinement of the design space allowed by the sequential learning method. The values of the global error estimates between the previous and present approaches are comparable, but the sequential method proved more computationally cost-effective. Further refinement in the optimal regions might be needed to improve predictive capability of surrogate models and to obtain the optimal solutions sets.

Rajiv R Shenoy↗
NASA NTRS1993

Investigation of spectral analysis techniques for randomly sampled velocimetry data

It is well known that velocimetry (LV) generates individual realization velocity data that are randomly or unevenly sampled in time. Spectral analysis of such data to obtain the turbulence spectra, and hence turbulence scales information, requires special techniques. The 'slotting' technique of Mayo et al, also described by Roberts and Ajmani, and the 'Direct Transform' method of Gaster and Roberts are well known in the LV community. The slotting technique is faster than the direct transform method in computation. There are practical limitations, however, as to how a high frequency and accurate estimate can be made for a given mean sampling rate. These high frequency estimates are important in obtaining the microscale information of turbulence structure. It was found from previous studies that reliable spectral estimates can be made up to about the mean sampling frequency (mean data rate) or less. If the data were evenly samples, the frequency range would be half the sampling frequency (i.e. up to Nyquist frequency); otherwise, aliasing problem would occur. The mean data rate and the sample size (total number of points) basically limit the frequency range. Also, there are large variabilities or errors associated with the high frequency estimates from randomly sampled signals. Roberts and Ajmani proposed certain pre-filtering techniques to reduce these variabilities, but at the cost of low frequency estimates. The prefiltering acts as a high-pass filter. Further, Shapiro and Silverman showed theoretically that, for Poisson sampled signals, it is possible to obtain alias-free spectral estimates far beyond the mean sampling frequency. But the question is, how far? During his tenure under 1993 NASA-ASEE Summer Faculty Fellowship Program, the author investigated from his studies on the spectral analysis techniques for randomly sampled signals that the spectral estimates can be enhanced or improved up to about 4-5 times the mean sampling frequency by using a suitable prefiltering technique. But, this increased bandwidth comes at the cost of the lower frequency estimates. The studies further showed that large data sets of the order of 100,000 points, or more, high data rates, and Poisson sampling are very crucial for obtaining reliable spectral estimates from randomly sampled data, such as LV data. Some of the results of the current study are presented.

Sree, Dave↗