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At least 937 records · Page 52

Probabilistic inversion of circular phase spectra: application to two-station phase-velocity dispersion estimation in western Canada

SUMMARY Periodic directional and temporal measurements are common in seismology, and necessitate specific statistical analyses that are appropriate for circular quantities. In this work, we explore the use of a von Mises distribution as a representation of errors on circular seismological observations. Specifically, we automate the estimation of surface-wave phase-velocity dispersion for the teleseismic two-station method, which generally suffers from a 2π phase ambiguity. The use of Bayesian inverse techniques, which aim to rigorously quantify model parameter uncertainty, have become widespread throughout seismology over the last decade. Here, we apply Bayesian inversion to measurements of surface-wave phase spectra in order to estimate 1-D, path-averaged Earth structure between station pairs. The dispersion curve and associated uncertainties are additional results of the inversion, which can then be used as input for subsequent analyses (e.g. tomography). We demonstrate this technique through application to surface-wave recordings from long-running seismic stations throughout western Canada. Our results for over 10 000 station pairs reveal first-order tectonic features consistent with previous studies, which provides confidence in our approach as well as an initial step towards resolving a full 3-D seismic velocity model for the region. This work also presents a foundation for the inversion of surface-wave phase spectra to estimate 3-D Earth structure directly. Finally, the ideas presented in this work are not limited to the inversion of surface-wave phase spectra, but can also be considered for Bayesian geophysical inversion of any circular quantities.

Gosselin, Jeremy M. (ORCID:0000000203754102)↗

Probabilistic predictions and uncertainty estimation for radiological and nuclear effects modeling

Better characterization of meteorological uncertainty is needed to predict the effects of radiological and nuclear releases in the atmosphere. Multi-physics ensembles of atmospheric simulations can estimate uncertainty of physical processes, but they are often limited for computational reasons. Because weather uncertainty is important for emergency response applications, but the conventional way of running multi-physics ensembles is infeasible, we have developed new machine learning-based methods that quickly estimate and identify key sources of meteorological uncertainty. Machine learning accelerates the analysis of weather uncertainty by iteratively learning about model physics options that affect plume predictions. We have demonstrated the power of machine learning by creating a large multi-physics weather and dispersion ensemble dataset containing 1,200 simulations for two hypothetical radiological release scenarios. By training on less than 10% of the ensemble, we can quickly and accurately predict different outcomes, including the mass of radiological material deposited and spatial distribution and extent of contaminated areas.

54 ENVIRONMENTAL SCIENCES↗

Stochastic Simulation of Mudcrack Damage Formation in an Environmental Barrier Coating

The FEAMAC/CARES program, which integrates finite element analysis (FEA) with the MAC/GMC (Micromechanics Analysis Code with Generalized Method of Cells) and the CARES/Life (Ceramics Analysis and Reliability Evaluation of Structures / Life Prediction) programs, was used to simulate the formation of mudcracks during the cooling of a multilayered environmental barrier coating (EBC) deposited on a silicon carbide substrate. FEAMAC/CARES combines the MAC/GMC multiscale micromechanics analysis capability (primarily developed for composite materials) with the CARES/Life probabilistic multiaxial failure criteria (developed for brittle ceramic materials) and Abaqus (Dassault Systèmes) FEA. In this report, elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio elements enabled the formation of crack boundaries, leading to development of mudcrack-patterned damage. Finite element models of a disk-shaped three-dimensional specimen and a twodimensional model of a through-the-thickness cross section subjected to progressive cooling from 1,300 °C to an ambient temperature of 23 °C were made. Mudcrack damage in the coating resulted from the buildup of residual tensile stresses between the individual material constituents because of thermal expansion mismatches between coating layers and the substrate. A two-parameter Weibull distribution characterized the coating layer stochastic strength response and allowed the effect of the Weibull modulus on the formation of damage and crack segmentation lengths to be studied. The spontaneous initiation of cracking and crack coalescence resulted in progressively smaller mudcrack cells as cooling progressed, consistent with a fractal-behaved fracture pattern. Other failure modes such as delamination, and possibly spallation, could also be reproduced. The physical basis assumed and the heuristic approach employed, which involves a simple stochastic cellular automaton methodology to approximate the crack growth process, are described. The results ultimately show that a selforganizing mudcrack formation can derive from a Weibull distribution that is used to describe the stochastic strength response of the bulk brittle ceramic material layers of an EBC.

Nemeth, Noel N.↗

The WRF-Solar Ensemble Prediction System: Development, Test, and Validation

Providing reliable probabilistic solar radiation information is needed to improve management of the uncertainty and variability of solar generation. Thus, guidance on how to develop skillful and accurate ensemble forecasts is essential and it will ultimately contribute to integration of high amounts of solar energy on the grid. A team from the National Renewable Energy Laboratory and the National Center for Atmospheric Research had been collaborating to develop the WRF-Solar ensemble prediction system (WRF-Solar EPS) in the past three years to produce probabilistic solar irradiance forecasts and better predict solar energy by quantifying forecast uncertainty. The WRF-Solar EPS basically generates ensemble members for solar irradiance based on stochastic perturbations to provide intraday and day-ahead probabilistic forecasts. This study will present main research steps in developing the WRF-Solar EPS including: (a) tangent linear analysis for identifying key input variables of six WRF-Solar modules significantly related to predicting of cloud and solar irradiance, (b) combining stochastic perturbation technique with the WRF-Solar model, and (c) ensemble calibration method to decrease error and uncertainty of ensemble-based solar forecasts. The capability of WRF-Solar EPS is now updated to the most recent version of standard WRF model. This presentation will summarize comprehensive results from the evaluation of forecasts against the National Solar Radiation Data Base as well as ground-measured observations. Moreover, we will introduce the user's guide for WRF-Solar EPS (e.g., parameters to configure stochastic perturbations) and future extension of this research.

day-ahead forecast↗

Uncertainty Analysis of Slug Calorimeters in the HyMETS Arc-Jet Facility

The objective of this work is to perform an uncertainty analysis of the deduced stagnation heat flux environment on a slug calorimeter for conditions that span the performance envelope of the Hypersonic Materials Environmental Test System arc-jet facility located at NASA Langley Research Center. Analytical solutions are developed for boundary-value problems on the slug element accounting for non-ideal effects, including spatial variation in the slug heat flux, multi-dimensional thermal conduction, and back-face losses, which departs from the state-of-the-art method derived from the American Society of Testing and Materials. Boundary-value problem definitions are informed by preliminary finite element thermal analysis of the slug calorimeter assembly (including both slug and housing) and just the slug element. The analytical solutions are presented in a general sense and in a truncated form from error analysis. Results are shown in optimizing and validating the analytical models against available slug back-face thermal data. The optimization results indicate that the appropriate epistemic uncertainty of the deduced stagnation heat flux on the slug calorimeter is at most±2.5% for both a high-and low-enthalpy test condition. In addition, a numerical approach is used to determine the aleatory (probabilistic) uncertainty component in the slug stagnation heat flux by applying a marching least-squares slope routine through the steady-state portion of the slug back-face thermal response. Results indicate a compromise between the number of samples and the filter frequency of slug back-face thermal data points when evaluating the standard deviation of the deduced stagnation heat flux statistics. When combining the mixed uncertainty, both aleatory and epistemic, the interval of uncertainty in the deduced stagnation heat flux is determined to be up to ±4%, which is at least a 60% reduction from the standard uncertainty used in the state-of-the-art method.

uncertainty↗

Multi-Fidelity Gaussian Process for Distribution System Voltage Probabilistic Estimation with PVs

The increasing penetration of behind-the-meter PVs causes challenges to maintain voltage security due to the lack of distribution system visibility. This paper proposes a nonlinear autoregressive Gaussian process (NARGP) approach to fuse limited number of SCADA/AMI data together with historical pseudo measurements for distribution node voltage probabilistic estimation. The high-fidelity SCADA data are fused with the low-fidelity AMI and pseudo measurements by the autoregressive algorithm embedded in the Gaussian process. This allows us to use multi-fidelity data to achieve entire distribution system voltage visibility. Numerical results carried out on the IEEE 123node system demonstrate that the NARGP method is able to obtain high accuracy in estimating bus voltage and quantifying estimation uncertainties as compared to other approaches.

distribution system estimation↗

Enabling Dynamic Probabilistic Risk Assessment of Physical Security Using EMRALD and MAAP

The optimization of physical security in nuclear power plants requires sophisticated methodologies that integrate operator actions and plant behavior through advanced simulation tools. To address this, Idaho National Laboratory [JL2.1]has developed the Modeling and Analysis for Safety and Security using the Dynamic EMRALD Framework (MASS-DEF) methodology, an approach that integrates force-on-force simulations, dynamic probabilistic risk assessment, and thermal-hydraulics modeling [JL3.1]to enhance security planning while reducing costs. We developed a tool that produces reduced order models using thermal hydraulic simulations from the Modular Accident Analysis Program (MAAP) [1]. These models can quickly evaluate reactor core behavior during attack simulations, and in so doing, address two barriers of traditional methods: (1) MAAP simulations are computationally intensive, and (2) attack scenarios must be run in a secure environment, which complicates analysis and validation. By precomputing scenario outcomes for a small number of modified parameters, the reduced order model significantly decreases the computational cost and enables offsite review of the results.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Machine learning with knowledge constraints for process optimization of open-air perovskite solar cell manufacturing

Perovskite photovoltaics (PV) have achieved rapid development in the past decade in terms of power conversion efficiency of small-area lab-scale devices; however, successful commercialization still requires further development of low-cost, scalable, and high-throughput manufacturing techniques. One of the critical challenges of developing a new fabrication technique is the high-dimensional parameter space for optimization, but machine learning (ML) can readily be used to accelerate perovskite PV scaling. Herein, we present an ML-guided framework of sequential learning for manufacturing process optimization. We apply our methodology to the Rapid Spray Plasma Processing (RSPP) technique for perovskite thin films in ambient conditions. With a limited experimental budget of screening 100 process conditions, we demonstrated an efficiency improvement to 18.5% as the best-in-our-lab device fabricated by RSPP, and we also experimentally found 10 unique process conditions to produce the top-performing devices of more than 17% efficiency, which is 5 times higher rate of success than the control experiments with pseudo-random Latin hypercube sampling. Our model is enabled by three innovations: (a) flexible knowledge transfer between experimental processes by incorporating data from prior experimental data as a probabilistic constraint; (b) incorporation of both subjective human observations and ML insights when selecting next experiments; (c) adaptive strategy of locating the region of interest using Bayesian optimization first, and then conducting local exploration for high-efficiency devices. Furthermore, in virtual benchmarking, our framework achieves faster improvements with limited experimental budgets than traditional design-of-experiments methods (e.g., one-variable-at-a-time sampling). This framework shows the capability of incorporating researchers’ domain knowledge into the ML-guided optimization loop; therefore, it has the potential to facilitate the wider adoption of ML in scaling to perovskite PV manufacturing.

14 SOLAR ENERGY↗

Probabilistic Analysis of Aircraft Gas Turbine Disk Life and Reliability

Two series of low cycle fatigue (LCF) test data for two groups of different aircraft gas turbine engine compressor disk geometries were reanalyzed and compared using Weibull statistics. Both groups of disks were manufactured from titanium (Ti-6Al-4V) alloy. A NASA Glenn Research Center developed probabilistic computer code Probable Cause was used to predict disk life and reliability. A material-life factor A was determined for titanium (Ti-6Al-4V) alloy based upon fatigue disk data and successfully applied to predict the life of the disks as a function of speed. A comparison was made with the currently used life prediction method based upon crack growth rate. Applying an endurance limit to the computer code did not significantly affect the predicted lives under engine operating conditions. Failure location prediction correlates with those experimentally observed in the LCF tests. A reasonable correlation was obtained between the predicted disk lives using the Probable Cause code and a modified crack growth method for life prediction. Both methods slightly overpredict life for one disk group and significantly under predict it for the other.

Melis, Matthew E.↗

Propulsion System Modeling and Simulation

The Aerospace Systems Design Laboratory at the School of Aerospace Engineering in Georgia Institute of Technology has developed a core competency that enables propulsion technology managers to make technology investment decisions substantiated by propulsion and airframe technology system studies. This method assists the designer/manager in selecting appropriate technology concepts while accounting for the presence of risk and uncertainty as well as interactions between disciplines. This capability is incorporated into a single design simulation system that is described in this paper. This propulsion system design environment is created with a commercially available software called iSIGHT, which is a generic computational framework, and with analysis programs for engine cycle, engine flowpath, mission, and economic analyses. iSIGHT is used to integrate these analysis tools within a single computer platform and facilitate information transfer amongst the various codes. The resulting modeling and simulation (M&S) environment in conjunction with the response surface method provides the designer/decision-maker an analytical means to examine the entire design space from either a subsystem and/or system perspective. The results of this paper will enable managers to analytically play what-if games to gain insight in to the benefits (and/or degradation) of changing engine cycle design parameters. Furthermore, the propulsion design space will be explored probabilistically to show the feasibility and viability of the propulsion system integrated with a vehicle.

Tai, Jimmy C. M.↗

Probabilistic Modeling of the Renal Stone Formation Module

The Integrated Medical Model (IMM) is a probabilistic tool, used in mission planning decision making and medical systems risk assessments. The IMM project maintains a database of over 80 medical conditions that could occur during a spaceflight, documenting an incidence rate and end case scenarios for each. In some cases, where observational data are insufficient to adequately define the inflight medical risk, the IMM utilizes external probabilistic modules to model and estimate the event likelihoods. One such medical event of interest is an unpassed renal stone. Due to a high salt diet and high concentrations of calcium in the blood (due to bone depletion caused by unloading in the microgravity environment) astronauts are at a considerable elevated risk for developing renal calculi (nephrolithiasis) while in space. Lack of observed incidences of nephrolithiasis has led HRP to initiate the development of the Renal Stone Formation Module (RSFM) to create a probabilistic simulator capable of estimating the likelihood of symptomatic renal stone presentation in astronauts on exploration missions. The model consists of two major parts. The first is the probabilistic component, which utilizes probability distributions to assess the range of urine electrolyte parameters and a multivariate regression to transform estimated crystal density and size distributions to the likelihood of the presentation of nephrolithiasis symptoms. The second is a deterministic physical and chemical model of renal stone growth in the kidney developed by Kassemi et al. The probabilistic component of the renal stone model couples the input probability distributions describing the urine chemistry, astronaut physiology, and system parameters with the physical and chemical outputs and inputs to the deterministic stone growth model. These two parts of the model are necessary to capture the uncertainty in the likelihood estimate. The model will be driven by Monte Carlo simulations, continuously randomly sampling the probability distributions of the electrolyte concentrations and system parameters that are inputs into the deterministic model. The total urine chemistry concentrations are used to determine the urine chemistry activity using the Joint Expert Speciation System (JESS), a biochemistry model. Information used from JESS is then fed into the deterministic growth model. Outputs from JESS and the deterministic model are passed back to the probabilistic model where a multivariate regression is used to assess the likelihood of a stone forming and the likelihood of a stone requiring clinical intervention. The parameters used to determine to quantify these risks include: relative supersaturation (RS) of calcium oxalate, citrate/calcium ratio, crystal number density, total urine volume, pH, magnesium excretion, maximum stone width, and ureteral location. Methods and Validation: The RSFM is designed to perform a Monte Carlo simulation to generate probability distributions of clinically significant renal stones, as well as provide an associated uncertainty in the estimate. Initially, early versions will be used to test integration of the components and assess component validation and verification (V&V), with later versions used to address questions regarding design reference mission scenarios. Once integrated with the deterministic component, the credibility assessment of the integrated model will follow NASA STD 7009 requirements.

kidney stones↗

Validation methods for flight crucial systems

Research to develop techniques that can aid in determining the reliability and performance of digital electronic fault-tolerant systems, that have probability of catastrophic system failure on the order of 10 to the -9th at 10 hours, is reviewed. The computer-aided reliability estimation program (CARE III) provides general-purpose reliability analysis and a design tool for fault-tolerant systems; large reduction of state size; and a fault-handling model based on probabilistic description of detection, isolation, and recovery mechanisms. The application of design proof techniques as part of the design and development of the software implemented fault-tolerance computer is mentioned. Emulation techniques and experimental procedures are verified using specimens of fault-tolerant computers and the capabilities of the validation research laboratory, AIRLAB.

Holt, H. M.↗

Evaluating Probability of Containment Effectiveness at a GCS Sites using integrated assessment modeling approach with Bayesian decision Networks

Improved scientific and engineering understanding of the behavior of geologic CO2 storage together with established regulatory framework and incentive structures raise the prospects for accelerated, large-scale deployment of this greenhouse gas emissions reduction approach. Incentive structures call for the establishment of appropriate verification and accounting approaches to support claims of the integrity of a geologic storage complex and to justify taking credit for long-term storage. In this study, we present a framework for assessing the probability of containment effectiveness over the lifetime of a geologic carbon storage site (e.g., after 70 years of injection and post-injection site performance) using forward stochastic model realizations based on site characterization data and using a monitoring-informed Bayesian network based on hypothetical detectability from surface seismic surveys over the site injection and post-injection phases. The National Risk Assessment Partnership’s open-source Integrated Assessment Model (NRAP-Open-IAM) was utilized to develop an ensemble of 10,000 a priori stochastic forecasts of CO2 containment. Those simulations were used to train the Bayesian network model to estimate the prior probabilities of the CO2 leakage mass into overlying, monitorable aquifers considering the uncertainties in the reservoir properties, permeability of potentially leaky wells and the overlying aquifers. The conditional probabilities in the Bayesian network were either learned from the NRAP-Open-IAM simulations or derived from the predefined detection thresholds for the monitoring method. Observations obtained from monitoring, over time during the site operation phases were then used to generate updated posterior probabilities of containment (and any loss from containment) in the Bayesian network by propagating the prior probabilities through the conditional probabilities. We demonstrate how to construct and use the Bayesian network for verifying the long-term storage complex effectiveness informed by monitoring based on the NRAP-Open-IAM simulations previously developed for the FutureGen 2.0 site. This approach may have relevance for stake holders to demonstrate secure geologic storage, provide a defensible, probabilistic approach to claim credit for geologic storage, and to estimate the likelihood that any fraction of the claimed credit may need to be refunded to the creditor based on available monitoring information.

Bayesian network, Risk assessment, Monitoring, car↗

Extending Parsimonious Bayesian Inference

Parsimonious Bayesian inference is a theoretical framework for efficient data assimilation that seeks to balance increased consistency between predictions and training data against corresponding increases in model complexity. Within this framework, over-training is understood as optimization that encodes excessive information within model parameters while only achieving small improvements between predictions and training data. This project aims to develop practical methods of limiting excess model information during optimization. One key observation is that practical heuristics for parsimonious learning in high-dimensions must balance expressivity, i.e. the ability of the model to capture diverse predictions with only a few non-zero parameters, against discoverability, i.e. the ability to train the model with gradient-based optimization and drive parameters to low information states. As such, we developed logical activation functions that are able to adaptively approximate arbitrary truth tables that define Boolean logic operations within a probabilistic framework. These functions have demonstrated the ability to learn exclusive disjunction (XOR) and conditioned disjunction (if [condition] then [result_if_true] else [result_if_false]) within a single layer of a neural network. To efficiently exploit these activation functions to drive parsimonious learning required several other advances within the domain of variational inference. The most efficient form of complexity suppression is structured sparsification, driving most model parameters to zero while achieving the structural coherence among nonzeros needed for bandwidth reduction. Such models are not only far more efficient at suppressing information-theoretic complexity, they also reduce the other forms of complexity (computations, communication, storage, and the number of dependencies needed to evaluate predictions). Aiming to support enhanced sparsification, this project examined new approaches to high-dimensional variational inference that allow us to calibrate and control parameter uncertainty during optimization. By identifying which parameters can sustain sparsifying perturbations with little impact on prediction quality, we can develop better pruning strategies by framing them as approximate Bayesian inference. These advances also open paths to mitigate concerns with deploying advanced learning methods in resource-constrained environments, such as running models on power-limited or communication-limited devices.

97 MATHEMATICS AND COMPUTING↗

Risk-Informed Safety Analysis for Accident Tolerant Fuels

Accident Tolerant Fuels (ATF) are being tested by different nuclear vendors and research organizations and their introduction in the US light water reactors fleet is planned for the second half of the 2020`s. In the framework of the US-DOE Light-Water Reactor Sustainability program, Risk-Informed Systems Analysis pathway, researches are being conducted at the Idaho National Laboratory for developing tools and methods that can help the industry quantifying the benefits from the adoption of ATF technology. In this paper we describe the developed risk-informed methodology including the safety analysis codes improvements, and we present some results for selected accident scenarios. The developed methodology combines INL state-of-the-art deterministic Best Estimate code RELAP5-3D, and Probabilistic Risk Analysis tools RAVEN and SAPHIRE. The analyses are performed on a three-loops pressurized water reactor, simulating Station Blackout and LB-LOCA accidents and considering near-term ATFs, or FeCrAl and Chromium-coated clads. Finally, we show how, applying our methodology, the new Core Damage Frequency can be assessed. The results indicated that the main benefits in introducing near-term ATFs concern a significant reduction in the hydrogen production during accident conditions. No significant Core Damage Frequency reduction was found.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The CluMPR galaxy cluster-finding algorithm and DESI legacy survey galaxy cluster catalogue

ABSTRACT Galaxy clusters enable unique opportunities to study cosmology, dark matter, galaxy evolution, and strongly lensed transients. We here present a new cluster-finding algorithm, CluMPR (Clusters from Masses and Photometric Redshifts), that exploits photometric redshifts (photo-z’s) as well as photometric stellar mass measurements. CluMPR uses a 2D binary search tree to search for overdensities of massive galaxies with similar redshifts on the sky and then probabilistically assigns cluster membership by accounting for photo-z uncertainties. We leverage the deep DESI Legacy Survey grzW1W2 imaging over one-third of the sky to create a catalogue of $\sim 300\, 000$ galaxy cluster candidates out to z = 1, including tabulations of member galaxies and estimates of each cluster’s total stellar mass. Compared to other methods, CluMPR is particularly effective at identifying clusters at the high end of the redshift range considered (z = 0.75–1), with minimal contamination from low-mass groups. These characteristics make it ideal for identifying strongly lensed high-redshift supernovae and quasars that are powerful probes of cosmology, dark matter, and stellar astrophysics. As an example application of this cluster catalogue, we present a catalogue of candidate wide-angle strongly lensed quasars in Appendix C. The nine best candidates identified from this sample include two known lensed quasar systems and a possible changing-look lensed QSO with SDSS spectroscopy. All code and catalogues produced in this work are publicly available (see Data Availability).

79 ASTRONOMY AND ASTROPHYSICS↗

Computation-based reliability analysis

A reliability analysis method for computing systems is considered in which the underlying criteria for 'success' are based on the computations the system must perform in the use environment. Beginning with a general model of a 'computer with faults', intermediate concepts of a 'tolerance relation' and an 'environment space' are introduced which account for the computational needs of the user and the probabilistic nature of the use environment. These concepts are then incorporated to obtain a precisely defined class of computation-based reliability measures. Formulation of a particular measure is illustrated and results, applying this measure, are compared with those of a typical structure-based analysis.

Meyer, J. F.↗

A statistical inference approach for the retrieval of the atmospheric ozone profile from simulated satellite measurements of solar backscattered ultraviolet radiation

NASA's Mission to Planet Earth (MTPE) will address important interdisciplinary and environmental issues such as global warming, ozone depletion, deforestation, acid rain, and the like with its long term satellite observations of the Earth and with its comprehensive Data and Information System. Extensive sets of satellite observations supporting MTPE will be provided by the Earth Observing System (EOS), while more specific process related observations will be provided by smaller Earth Probes. MTPE will use data from ground and airborne scientific investigations to supplement and validate the global observations obtained from satellite imagery, while the EOS satellites will support interdisciplinary research and model development. This is important for understanding the processes that control the global environment and for improving the prediction of events. In this paper we illustrate the potential for powerful artificial intelligence (AI) techniques when used in the analysis of the formidable problems that exist in the NASA Earth Science programs and of those to be encountered in the future MTPE and EOS programs. These techniques, based on the logical and probabilistic reasoning aspects of plausible inference, strongly emphasize the synergetic relation between data and information. As such, they are ideally suited for the analysis of the massive data streams to be provided by both MTPE and EOS. To demonstrate this, we address both the satellite imagery and model enhancement issues for the problem of ozone profile retrieval through a method based on plausible scientific inferencing. Since in the retrieval problem, the atmospheric ozone profile that is consistent with a given set of measured radiances may not be unique, an optimum statistical method is used to estimate a 'best' profile solution from the radiances and from additional a priori information.

Bonavito, N. L.↗