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Results for “Bayesian inversion”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Modeling the Absorbing Aerosol Index

We propose a scheme to model the absorbing aerosol index and improve the biomass carbon inventories by optimizing the difference between TOMS aerosol index (AI) and modeled AI with an inverse model. Two absorbing aerosol types are considered, including biomass carbon and mineral dust. A priori biomass carbon source was generated by Liousse et al [1996]. Mineral dust emission is parameterized according to surface wind and soil moisture using the method developed by Ginoux [2000]. In this initial study, the coupled CCM1 and GRANTOUR model was used to determine the aerosol spatial and temporal distribution. With modeled aerosol concentrations and optical properties, we calculate the radiance at the top of the atmosphere at 340 nm and 380 nm with a radiative transfer model. The contrast of radiance at these two wavelengths will be used to calculate AI. Then we compare the modeled AI with TOMS AI. This paper reports our initial modeling for AI and its comparison with TOMS Nimbus 7 AI. For our follow-on project we will model the global AI with aerosol spatial and temporal distribution recomputed from the IMPACT model and DAO GEOS-1 meteorology fields. Then we will build an inverse model, which applies a Bayesian inverse technique to optimize the agreement of between model and observational data. The inverse model will tune the biomass burning source strength to reduce the difference between modelled AI and TOMS AI. Further simulations with a posteriori biomass carbon sources from the inverse model will be carried out. Results will be compared to available observations such as surface concentration and aerosol optical depth.

Penner, Joyce↗
NASA NTRS1985

Dislocation model for aseismic fault slip in the transverse ranges of Southern California

Geodetic data at a plate boundary can reveal the pattern of subsurface displacements that accompany plate motion. These displacements are modelled as the sum of rigid block motion and the elastic effects of frictional interaction between blocks. The frictional interactions are represented by uniform dislocation on each of several rectangular fault patches. The block velocities and fault parameters are then estimated from geodetic data. Bayesian inversion procedure employs prior estimates based on geological and seismological data. The method is applied to the Transverse Ranges, using prior geological and seismological data and geodetic data from the USGS trilateration networks. Geodetic data imply a displacement rate of about 20 mm/yr across the San Andreas Fault, while the geologic estimates exceed 30 mm/yr. The prior model and the final estimates both imply about 10 mm/yr crustal shortening normal to the trend of the San Andreas Fault. Aseismic fault motion is a major contributor to plate motion. The geodetic data can help to identify faults that are suffering rapid stress accumulation; in the Transverse Ranges those faults are the San Andreas and the Santa Susana.

Cheng, A.↗
NASA NTRS1986

Dislocation model for aseismic crustal deformation at Hollister, California

A model of crustal deformation during the interseismic phase is developed and applied (using the improved Bayesian inversion algorithm described by Jackson and Matsu'ura, 1985) to trilateration data for the USGS Hollister (CA) network. In the model, rigid blocks in motion relative to each other experience friction only in a brittle upper zone, while their ductile lower zones slide freely; the Hollister model comprises five blocks and nine rectangular fault patches. The data and results are presented in tables, graphs, and maps and characterized in detail. The model predicts steady block motion on time scales between 10 yr and 1 Myr, with net motion across the San Andreas/Calaveras fault system 38 + or - 3 mm/yr and brittle/ductile transition depths ranging from 0.4 to 11 km. Two San Andreas segments with higher probabilities of moderate-to-large earthquakes are identified.

Matsuura, Mitsuhiro↗
NASA NTRS1999

Measuring Greenland Ice Mass Variation With Gravity Recovery and the Climate Experiment Gravity and GPS

The response of the Greenland ice sheet to climate change could significantly alter sea level. The ice sheet was much thicker at the last glacial maximum. To gain insight into the global change process and the future trend, it is important to evaluate the ice mass variation as a function of time and space. The Gravity Recovery and Climate Experiment (GRACE) mission to fly in 2001 for 5 years will measure gravity changes associated with the current ice variation and the solid earth's response to past variations. Our objective is to assess the separability of different change sources, accuracy and resolution in the mass variation determination by the new gravity data and possible Global Positioning System (GPS) bedrock uplift measurements. We use a reference parameter state that follows a dynamic ice model for current mass variation and a variant of the Tushingham and Peltier ICE-3G deglaciation model for historical deglaciation. The current linear trend is also assumed to have started 5 kyr ago. The Earth model is fixed as preliminary reference Earth model (PREM) with four viscoelastic layers. A discrete Bayesian inverse algorithm is developed employing an isotropic Gaussian a priori covariance function over the ice sheet and time. We use data noise predicted by the University of Texas and JPL for major GRACE error sources. A 2 mm/yr uplift uncertainty is assumed for GPS occupation time of 5 years. We then carry out covariance analysis and inverse simulation using GRACE geoid coefficients up to degree 180 in conjunction with a number of GPS uplift rates. Present-day ice mass variation and historical deglaciation are solved simultaneously over 146 grids of roughly 110 km x 110 km and with 6 time increments of 3 kyr each, along with a common starting epoch of the current trend. For present-day ice thickness change, the covariance analysis using GRACE geoid data alone results in a root mean square (RMS) posterior root variance of 2.6 cm/yr, with fairly large a priori uncertainties in the parameters and a Gaussian correlation length of 350 km. Simulated inverse can successfully recover most features in the reference present-day change. The RMS difference between them over the grids is 2.8 cm/yr. The RMS difference becomes 1.1 cm/yr when both are averaged with a half Gaussian wavelength of 150 km. With a fixed Earth model, GRACE alone can separate the geoid signals due to past and current load fairly well. Shown are the reference geoid signatures of direct and elastic effects of the current trend, the viscoelastic effect of the same trend starting from 5 kyr ago, the Post Glacial Rebound (PGR), and the predicted GRACE geoid error. The difference between the reference and inverse modeled total viscoelastic signatures is also shown. Although past and current ice mass variations are allowed the same spatial scale, their geoid signals have different spatial patterns. GPS data can contribute to the ice mass determination as well. Additional information is contained in the original.

Wu, Xiao-Ping↗
NASA NTRS2010

A Ground Flash Fraction Retrieval Algorithm for GLM

A Bayesian inversion method is introduced for retrieving the fraction of ground flashes in a set of N lightning observed by a satellite lightning imager (such as the Geostationary Lightning Mapper, GLM). An exponential model is applied as a physically reasonable constraint to describe the measured lightning optical parameter distributions. Population statistics (i.e., the mean and variance) are invoked to add additional constraints to the retrieval process. The Maximum A Posteriori (MAP) solution is employed. The approach is tested by performing simulated retrievals, and retrieval error statistics are provided. The approach is feasible for N greater than 2000, and retrieval errors decrease as N is increased.

Koshak, William J.↗
NASA NTRS2011

Obtaining the Grobner Initialization for the Ground Flash Fraction Retrieval Algorithm

At optical wavelengths and from the vantage point of space, the multiple scattering cloud medium obscures one's view and prevents one from easily determining what flashes strike the ground. However, recent investigations have made some progress examining the (easier, but still difficult) problem of estimating the ground flash fraction in a set of N flashes observed from space In the study by Koshak, a Bayesian inversion method was introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function of three variables (one of which is the ground flash fraction) was minimized by a numerical method. This method has formed the basis of a Ground Flash Fraction Retrieval Algorithm (GoFFRA) that is being tested as part of GOES-R GLM risk reduction.

Solakiewicz, R.↗
NASA NTRS2011

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Solakiewicz, Richard↗
NASA NTRS2011

Tests of the Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

Satellite lightning imagers such as the NASA Tropical Rainfall Measuring Mission Lightning Imaging Sensor (TRMM/LIS) and the future GOES-R Geostationary Lightning Mapper (GLM) are designed to detect total lightning (ground flashes + cloud flashes). However, there is a desire to discriminate ground flashes from cloud flashes from the vantage point of space since this would enhance the overall information content of the satellite lightning data and likely improve its operational and scientific applications (e.g., in severe weather warning, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters (one of which is the ground flash fraction), a scalar function was minimized by a numerical method. In order to improve this optimization, a Grobner basis solution was introduced to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. In this study, we test the efficacy of the Grobner basis initialization using actual lightning imager measurements and ground flash truth derived from the national lightning network.

Koshak, William↗
NASA NTRS2012

The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.

Koshak, William↗
NASA NTRS2016

Probabilistic Prognosis of Non-Planar Fatigue Crack Growth

Quantifying the uncertainty in model parameters for the purpose of damage prognosis can be accomplished utilizing Bayesian inference and damage diagnosis data from sources such as non-destructive evaluation or structural health monitoring. The number of samples required to solve the Bayesian inverse problem through common sampling techniques (e.g., Markov chain Monte Carlo) renders high-fidelity finite element-based damage growth models unusable due to prohibitive computation times. However, these types of models are often the only option when attempting to model complex damage growth in real-world structures. Here, a recently developed high-fidelity crack growth model is used which, when compared to finite element-based modeling, has demonstrated reductions in computation times of three orders of magnitude through the use of surrogate models and machine learning. The model is flexible in that only the expensive computation of the crack driving forces is replaced by the surrogate models, leaving the remaining parameters accessible for uncertainty quantification. A probabilistic prognosis framework incorporating this model is developed and demonstrated for non-planar crack growth in a modified, edge-notched, aluminum tensile specimen. Predictions of remaining useful life are made over time for five updates of the damage diagnosis data, and prognostic metrics are utilized to evaluate the performance of the prognostic framework. Challenges specific to the probabilistic prognosis of non-planar fatigue crack growth are highlighted and discussed in the context of the experimental results.

Leser, Patrick E.↗
NASA NTRS2016

Constraining the Sulfur Dioxide Degassing Flux from Turrialba Volcano, Costa Rica Using Unmanned Aerial System Measurements

Observed sulfur dioxide (SO2)mixing ratios onboard unmanned aerial systems (UAS) duringMarch 11-13, 2013 are used to constrain the three-day averaged SO2 degassing flux fromTurrialba volcanowithin a Bayesian inverse modeling framework. A mesoscale model coupled with Lagrangian stochastic particle backward trajectories is used to quantify the source-receptor relationships at very high spatial resolutions (i.e., b1 km). The model shows better performance in reproducing the near-surface meteorological properties and observed SO2 variations when using a first-order closure non-local planetary boundary layer (PBL) scheme. The optimized SO2 degassing fluxes vary from 0.59 +/- 0.37 to 0.83 +/- 0.33 kt d−1 depending on the PBL scheme used. These fluxes are in good agreement with ground-based gas flux measurements, and correspond to corrective scale factors of 8-12 to the posteruptive SO2 degassing rate in the AeroCom emission inventory. The maximum a posteriori solution for the SO2 flux is highly sensitive to the specification of prior and observational errors, and relatively insensitive to the SO2 loss term and temporal averaging of observations. Our results indicate relatively low degassing activity but sustained sulfur emissions from Turrialba volcano to the troposphere during March 2013. This study demonstrates the utility of low-cost small UAS platforms for volcanic gas composition and flux analysis.

Xi, Xin↗
NASA NTRS2020

Constraining Fossil Fuel CO2 Emissions from Urban Area Using OCO-2 Observations of Total Column CO2

Satellite observations of the total column dry-air CO2(XCO2) are expected to support the quantification and monitoring of fossil fuel CO2 (ffCO2) emissions from urban areas. We evaluate the utility of the Orbiting Carbon Observatory 2 (OCO-2) XCO2 retrievals to optimize whole-city emissions, using a Bayesian inversion system and high-resolution transport modeling. The uncertainties of constrained emissions related to transport model, satellite measurements, and local biospheric fluxes are quantified. For the first two uncertainty sources, we examine cities of different landscapes: “plume city” located in relatively flat terrain, represented by Riyadh and Cairo; “basin city” located in basin terrain, represented by Los Angeles (LA). The retrieved scaling factors of emissions and their uncertainties show prominent variabilities from track to track, due to the varying meteorological conditions and relative locations of the tracks transecting plumes. To explore the performance of multiple tracks in retrieving emissions, pseudo data experiments are carried out. The estimated least number of tracks required to constrain the total emissions for Riyadh (<10% uncertainty), Cairo (<10%), and LA (<5%) are 5, 8, and 7, respectively. Additionally, to evaluate the impact of biospheric fluxes on derivation of the ffXCO2 enhancements, we conduct simulations for Pearl River Delta metropolitan area. Significant fractions of local XCO2 enhancements associated with local biospheric XCO2 variations are shown, which potentially lead to biased estimates of ffCO2 emissions. We demonstrate that satellite measurements can be used to improve urban ffCO2 emissions with a sufficient amount of measurements and appropriate representations of the uncertainty components.

Xinxin Ye↗
NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗
NASA NTRS2005

Bayesian Inference in Satellite Gravity Inversion

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

Kis, K. I.↗
NASA NTRS2014

A Regional CO2 Observing System Simulation Experiment for the ASCENDS Satellite Mission

Top-down estimates of the spatiotemporal variations in emissions and uptake of CO2 will benefit from the increasing measurement density brought by recent and future additions to the suite of in situ and remote CO2 measurement platforms. In particular, the planned NASA Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) satellite mission will provide greater coverage in cloudy regions, at high latitudes, and at night than passive satellite systems, as well as high precision and accuracy. In a novel approach to quantifying the ability of satellite column measurements to constrain CO2 fluxes, we use a portable library of footprints (surface influence functions) generated by the WRF-STILT Lagrangian transport model in a regional Bayesian synthesis inversion. The regional Lagrangian framework is well suited to make use of ASCENDS observations to constrain fluxes at high resolution, in this case at 1 degree latitude x 1 degree longitude and weekly for North America. We consider random measurement errors only, modeled as a function of mission and instrument design specifications along with realistic atmospheric and surface conditions. We find that the ASCENDS observations could potentially reduce flux uncertainties substantially at biome and finer scales. At the 1 degree x 1 degree, weekly scale, the largest uncertainty reductions, on the order of 50 percent, occur where and when there is good coverage by observations with low measurement errors and the a priori uncertainties are large. Uncertainty reductions are smaller for a 1.57 micron candidate wavelength than for a 2.05 micron wavelength, and are smaller for the higher of the two measurement error levels that we consider (1.0 ppm vs. 0.5 ppm clear-sky error at Railroad Valley, Nevada). Uncertainty reductions at the annual, biome scale range from 40 percent to 75 percent across our four instrument design cases, and from 65 percent to 85 percent for the continent as a whole. Our uncertainty reductions at various scales are substantially smaller than those from a global ASCENDS inversion on a coarser grid, demonstrating how quantitative results can depend on inversion methodology. The a posteriori flux uncertainties we obtain, ranging from 0.01 to 0.06 Pg C yr-1 across the biomes, would meet requirements for improved understanding of long-term carbon sinks suggested by a previous study.

remote sensing↗
NASA NTRS1985

A Bayesian approach to nonlinear inversion

Powerful methods are now available for solving linear parametric inverse problems. However, many inverse problems which arise in geohysics are nonlinear. Fortunately, it is possible to treat most of these with the air of linear perturbation theory and liner inversion. But a convenient method is needed for assessing the importance of nonlinearity in these quasi-linear problems. The present paper provides such a method. Matsu'ura and Jackson (1984) have presented a simple algorithm for evaluating the asymptotic covariance matrix fo estimation errors. In the present investigation, aspects of linear inversion are discussed, taking into account linear parametric inverse problems, nonuniqueness, prior information, confidence limits, conditional and marginal statistics, the relative importance of the prior and observational data, and standardized variables. Attention is also given to nonlinear inversion, and the application of the considered approaches to a number of examples.

Jackson, D. D.↗
NASA NTRS1987

Isotropic probability measures in infinite dimensional spaces: Inverse problems/prior information/stochastic inversion

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub n :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity)(P sub n to the -1(B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

Backus, George↗
NASA NTRS1987

Isotropic probability measures in infinite-dimensional spaces

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub in :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity) (P sub n to the -1 (B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

Backus, George↗