Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Bayesian Robustness”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Measuring the robustness of predictive probability for early stopping in two-group comparisons

We report physical experiments are often expensive and time-consuming. Test engineers must certify the compatibility of aircraft and their weapon systems before they can be deployed in the field, but the testing required is time consuming, expensive, and resource limited. Adopting Bayesian adaptive designs is a promising way to borrow from the successes seen in the clinical trials domain. The use of predictive probability (PP) to stop testing early and make faster decisions is particularly appealing given the aforementioned constraints. Given the high-consequence nature of the tests performed in the national security space, a strong understanding of new methods is required before being deployed. Although PP has been thoroughly studied for binary data, there is less work with continuous data, where many reliability studies are interested in certifying the specification limits of components. A simulation study evaluating the robustness of this approach indicates early stopping based on PP is reasonably robust to minor assumption violations, especially when only a few interim analyses are conducted. The simulation study also compares PP to conditional power, showing its relative strengths and weaknesses. A post-hoc analysis exploring whether release requirements of a weapon system from an aircraft are within specification with desired reliability resulted in stopping the experiment early and saving 33% of the experimental runs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Designing the Protocols for Programmable Ammonia Catalysis

Programmable catalysis can provide a more energy-efficient and cost-effective route to enhancing commercial ammonia production, a key process in the advancement of renewable energy technologies and the manufacture of fertilizers and basic chemicals. This work explores the computational discovery of optimal forcing protocols to drive such dynamic catalysis models. By employing matrix-free time-stepper methods, coupled with an optimization approach, that integrates Bayesian optimization with a Bayesian continuation strategy to efficiently discover the periodic steady states of such periodically forced systems, we enable the discovery of complex optimal catalyst strain waveforms, while ensuring robust solver convergence. We demonstrate the flexibility of our approach to discover optimized forcing protocols under varying physical constraints on strain modulation or other catalyst operating parameters. We show that these can have a temporal structure more complex than simple step functions. In order to detect undesirable catalytic loops that may correlate with overall reduced performance, we perform a study using graph-theoretical analysis to investigate the dynamics of catalytic kinetic networks formed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2008

Sensor Selection and Data Validation for Reliable Integrated System Health Management

For new access to space systems with challenging mission requirements, effective implementation of integrated system health management (ISHM) must be available early in the program to support the design of systems that are safe, reliable, highly autonomous. Early ISHM availability is also needed to promote design for affordable operations; increased knowledge of functional health provided by ISHM supports construction of more efficient operations infrastructure. Lack of early ISHM inclusion in the system design process could result in retrofitting health management systems to augment and expand operational and safety requirements; thereby increasing program cost and risk due to increased instrumentation and computational complexity. Having the right sensors generating the required data to perform condition assessment, such as fault detection and isolation, with a high degree of confidence is critical to reliable operation of ISHM. Also, the data being generated by the sensors needs to be qualified to ensure that the assessments made by the ISHM is not based on faulty data. NASA Glenn Research Center has been developing technologies for sensor selection and data validation as part of the FDDR (Fault Detection, Diagnosis, and Response) element of the Upper Stage project of the Ares 1 launch vehicle development. This presentation will provide an overview of the GRC approach to sensor selection and data quality validation and will present recent results from applications that are representative of the complexity of propulsion systems for access to space vehicles. A brief overview of the sensor selection and data quality validation approaches is provided below. The NASA GRC developed Systematic Sensor Selection Strategy (S4) is a model-based procedure for systematically and quantitatively selecting an optimal sensor suite to provide overall health assessment of a host system. S4 can be logically partitioned into three major subdivisions: the knowledge base, the down-select iteration, and the final selection analysis. The knowledge base required for productive use of S4 consists of system design information and heritage experience together with a focus on components with health implications. The sensor suite down-selection is an iterative process for identifying a group of sensors that provide good fault detection and isolation for targeted fault scenarios. In the final selection analysis, a statistical evaluation algorithm provides the final robustness test for each down-selected sensor suite. NASA GRC has developed an approach to sensor data qualification that applies empirical relationships, threshold detection techniques, and Bayesian belief theory to a network of sensors related by physics (i.e., analytical redundancy) in order to identify the failure of a given sensor within the network. This data quality validation approach extends the state-of-the-art, from red-lines and reasonableness checks that flag a sensor after it fails, to include analytical redundancy-based methods that can identify a sensor in the process of failing. The focus of this effort is on understanding the proper application of analytical redundancy-based data qualification methods for onboard use in monitoring Upper Stage sensors.

Garg, Sanjay↗
DOE OSTI2022

Data augmentation for disruption prediction via robust surrogate models

The goal of this work is to generate large statistically representative data sets to train machine learning models for disruption prediction provided by data from few existing discharges. Such a comprehensive training database is important to achieve satisfying and reliable prediction results in artificial neural network classifiers. Here, we aim for a robust augmentation of the training database for multivariate time series data using Student t process regression. We apply Student t process regression in a state space formulation via Bayesian filtering to tackle challenges imposed by outliers and noise in the training data set and to reduce the computational complexity. Thus, the method can also be used if the time resolution is high. We use an uncorrelated model for each dimension and impose correlations afterwards via colouring transformations. We demonstrate the efficacy of our approach on plasma diagnostics data of three different disruption classes from the DIII-D tokamak. To evaluate if the distribution of the generated data is similar to the training data, we additionally perform statistical analyses using methods from time series analysis, descriptive statistics and classic machine learning clustering algorithms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Evolution of homologous recombination rates across bacteria

Bacteria are nonsexual organisms but are capable of exchanging DNA at diverse degrees through homologous recombination. Intriguingly, the rates of recombination vary immensely across lineages where some species have been described as purely clonal and others as “quasi-sexual.” However, estimating recombination rates has proven a difficult endeavor and estimates often vary substantially across studies. It is unclear whether these variations reflect natural variations across populations or are due to differences in methodologies. Consequently, the impact of recombination on bacterial evolution has not been extensively evaluated and the evolution of recombination rate—as a trait—remains to be accurately described. Here, we developed an approach based on Approximate Bayesian Computation that integrates multiple signals of recombination to estimate recombination rates. We inferred the rate of recombination of 162 bacterial species and one archaeon and tested the robustness of our approach. Our results confirm that recombination rates vary drastically across bacteria; however, we found that recombination rate—as a trait—is conserved in several lineages but evolves rapidly in others. Although some traits are thought to be associated with recombination rate (e.g., GC-content), we found no clear association between genomic or phenotypic traits and recombination rate. Overall, our results provide an overview of recombination rate, its evolution, and its impact on bacterial evolution.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Improved estimates of the Milky Way’s stellar mass and star formation rate from hierarchical Bayesian meta-analysis

We present improved estimates of several global properties of the Milky Way, including its current star formation rate (SFR), the stellar mass contained in its disk and bulge+bar components, as well as its total stellar mass. We do so by combining previous measurements from the literature using a hierarchical Bayesian (HB) statistical method that allows us to account for the possibility that any value may be incorrect or have underestimated errors. We show that this method is robust to a wide variety of assumptions about the nature of problems in individual measurements or error estimates. Ultimately, our analysis yields an SFR for the Galaxy of M-dot {sub ⋆}=1.65±0.19 M{sub ⊙} yr{sup −1}, assuming a Kroupa initial mass function (IMF). By combining HB methods with Monte Carlo simulations that incorporate the latest estimates of the Galactocentric radius of the Sun, R{sub 0}, the exponential scale length of the disk, L{sub d}, and the local surface density of stellar mass, Σ{sub ⋆}(R{sub 0}), we show that the mass of the Galactic bulge+bar is M{sub ⋆}{sup B}=0.91±0.07×10{sup 10} M{sub ⊙}, the disk mass is M{sub ⋆}{sup D}=5.17±1.11×10{sup 10} M{sub ⊙}, and their combination yields a total stellar mass of M{sub ⋆}=6.08±1.14×10{sup 10} M{sub ⊙} (assuming a Kroupa IMF and an exponential disk profile). This analysis is based upon a new compilation of literature bulge mass estimates, normalized to common assumptions about the stellar IMF and Galactic disk properties, presented herein. We additionally find a bulge-to-total mass ratio for the Milky Way of B/T=0.150{sub −0.019}{sup +0.028} and a specific SFR of M-dot {sub ⋆}/M{sub ⋆}=2.71±0.59×10{sup −11} yr{sup −1}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Copacabana: a probabilistic membership assignment method for galaxy clusters

Cosmological analyses using galaxy clusters in optical/near-infrared photometric surveys require robust characterization of their galaxy content. Precisely determining which galaxies belong to a cluster is crucial. In this paper, we present the COlor Probabilistic Assignment of Clusters And BAyesiaN Analysis (Copacabana) algorithm. Copacabana computes membership probabilities for all galaxies within an aperture centred on the cluster using photometric redshifts, colours, and projected radial probability density functions. We use simulations to validate Copacabana and we show that it achieves up to 89 per cent membership accuracy with a mild dependence on photometric redshift uncertainties and choice of aperture size. We find that the precision of the photometric redshifts has the largest impact on the determination of the membership probabilities followed by the choice of the cluster aperture size. We also quantify how much these uncertainties in the membership probabilities affect the stellar mass–cluster mass scaling relation, a relation that directly impacts cosmology. Using the sum of the stellar masses weighted by membership probabilities (⁠μ * ⁠) as the observable, we find that Copacabana can reach an accuracy of 0.06 dex in the measurement of the scaling relation at low redshift for a Legacy Survey of Space and Time type survey. These results indicate the potential of Copacabana and μ * to be used in cosmological analyses of optically selected clusters in the future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Estimation of k-ε parameters using surrogate models and jet-in-crossflow data

We demonstrate a Bayesian method that can be used to calibrate computationally expensive 3D RANS (Reynolds Av- eraged Navier Stokes) models with complex response surfaces. Such calibrations, conditioned on experimental data, can yield turbulence model parameters as probability density functions (PDF), concisely capturing the uncertainty in the parameter estimates. Methods such as Markov chain Monte Carlo (MCMC) estimate the PDF by sampling, with each sample requiring a run of the RANS model. Consequently a quick-running surrogate is used instead to the RANS simulator. The surrogate can be very difficult to design if the model's response i.e., the dependence of the calibration variable (the observable) on the parameter being estimated is complex. We show how the training data used to construct the surrogate can be employed to isolate a promising and physically realistic part of the parameter space, within which the response is well-behaved and easily modeled. We design a classifier, based on treed linear models, to model the "well-behaved region". This classifier serves as a prior in a Bayesian calibration study aimed at estimating 3 k - ε parameters ( C μ , C ε2 , C ε1 ) from experimental data of a transonic jet-in-crossflow interaction. The robustness of the calibration is investigated by checking its predictions of variables not included in the cal- ibration data. We also check the limit of applicability of the calibration by testing at off-calibration flow regimes. We find that calibration yield turbulence model parameters which predict the flowfield far better than when the nomi- nal values of the parameters are used. Substantial improvements are still obtained when we use the calibrated RANS model to predict jet-in-crossflow at Mach numbers and jet strengths quite different from those used to generate the ex- perimental (calibration) data. Thus the primary reason for poor predictive skill of RANS, when using nominal values of the turbulence model parameters, was parametric uncertainty, which was rectified by calibration. Post-calibration, the dominant contribution to model inaccuraries are due to the structural errors in RANS.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Cosmological constraints from a joint DESI DR1 Full-Shape and DR2 BAO

We present a cosmological analysis combining full-shape (FS) clustering measurements from the Dark Energy Spectroscopic Instrument (DESI) DR1 with baryon acoustic oscillation (BAO) measurements from DESI DR2. To achieve a robust combination that accounts for the correlation between the two data releases, we employ the ShapeFit compression method and estimate the joint covariance using EZmocks. This compressed approach inherently mitigates the prior volume effects that have previously dominated Bayesian constraints from DESI data with minimal external priors. Consequently, we obtain — for the first time within a Bayesian framework — reliable DESI-only constraints on extensions to ΛCDM using only a Big Bang Nucleosynthesis prior on the baryon density and a wide prior on the spectral index. In flat ΛCDM, we find Ω m = 0.3035 ± 0.0085, h = 0.6876 ± 0.0059, and σ 8 = 0.822 ± 0.034. For the w 0 w a CDM dynamical dark energy model, we measure w 0 = -0.49 ± 0.25 and w a = -1.52 ± 0.77, improving constraints by ∼ 30% relative to the analogous DR1 measurement and reducing the discrepancy with ΛCDM to 1.4σ when compared to BAO only analyses. We also report competitive limits on the sum of neutrino masses and spatial curvature. This work demonstrates that the ShapeFit compression provides a prior-robust and computationally efficient pathway to constrain beyond-ΛCDM physics with large-scale structure.

baryon acoustic oscillations↗
DOE OSTI2021

Statistical Uncertainty in Paleoclimate Proxy Reconstructions

A quantitative analysis of any environment older than the instrumental record relies on proxies. Uncertainties associated with proxy reconstructions are often underestimated, which can lead to artificial conflict between different proxies, and between data and models. In this paper, using ordinary least squares linear regression as a common example, we describe a simple, robust and generalizable method for quantifying uncertainty in proxy reconstructions. We highlight the primary controls on the magnitude of uncertainty, and compare this simple estimate to equivalent estimates from Bayesian, nonparametric and fiducial statistical frameworks. We discuss when it may be possible to reduce uncertainties, and conclude that the unexplained variance in the calibration must always feature in the uncertainty in the reconstruction. This directs future research toward explaining as much of the variance in the calibration data as possible. We also advocate for a “data-forward” approach, that clearly decouples the presentation of proxy data from plausible environmental inferences.

58 GEOSCIENCES↗
NASA NTRS2020

A Second Look at 12 Candidate Dual AGNs Using BAYMAX

We present an analysis of 12 optically selected dual active galactic nucleus (AGN) candidates at z < 0.34. Each candidate was originally identified via double-peaked [O III] λ5007 emission lines and received follow-up Chandra and Hubble Space Telescope (HST) observations. Because the X-ray data are low-count (<100 counts) with small separations (<1''), a robust analysis is necessary for classifying each source. Pairing long-slit [O III] observations with existing Chandra observations, we re-analyze the X-ray observations with Bayesian AnalYsis of AGNs in X-rays to determine whether the X-ray emission from each system is more likely a single or dual point source. We find that 4 of the 12 sources are likely dual X-ray point-source systems. We examine each point source's spectra via a Monte Carlo method that probabilistically identifies the likely origin of each photon. When doing so, we find that (i) the secondary X-ray point sources in two of the systems have L(X)< 10(exp 40) erg/s, such that we cannot rule out a non-AGN origin, (ii) one source has a secondary with L(X)> 10(exp 40) erg/s but a spectrum that is too soft to definitively preclude being X-ray emitting diffuse gas that was photoionized by the primary AGN, and (iii) one system (SDSS J1126+2944) is a dual AGN. Additionally, using complementary HST observations, we analyze a subsample of systems that are visually identified as merging. Our results suggest that dual AGNs may preferentially reside in mergers with small separations, consistent with both simulations and observations.

Adi Foord↗
DOE OSTI2021

Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes

Uncertainty propagation in complex engineering systems often poses significant computational challenges related to modeling and quantifying probability distributions of model outputs, as those emerge as the result of various sources of uncertainty that are inherent in the system under investigation. Gaussian Processes regression (GPs) is a robust meta-modeling technique that allows for fast model prediction and exploration of response surfaces. Multi-fidelity variations of GPs further leverage information from cheap and low fidelity model simulations in order to improve their predictive performance on the high fidelity model. In order to cope with the high volume of data required to train GPs in high dimensional design spaces, a common practice is to introduce latent design variables that are typically projections of the original input space to a lower dimensional subspace, and therefore substitute the problem of learning the initial high dimensional mapping, with that of training a GP on a low dimensional space. Here in this paper, we present a Bayesian approach to identify optimal transformations that map the input points to low dimensional latent variables. The \projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional shape parameterization of a three-dimensional airfoil on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction

42 ENGINEERING↗
DOE OSTI2021

Comparative Analysis of Machine Learning Models for Day-Ahead Photovoltaic Power Production Forecasting

A main challenge for integrating the intermittent photovoltaic (PV) power generation remains the accuracy of day-ahead forecasts and the establishment of robust performing methods. The purpose of this work is to address these technological challenges by evaluating the day-ahead PV production forecasting performance of different machine learning models under different supervised learning regimes and minimal input features. Specifically, the day-ahead forecasting capability of Bayesian neural network (BNN), support vector regression (SVR), and regression tree (RT) models was investigated by employing the same dataset for training and performance verification, thus enabling a valid comparison. The training regime analysis demonstrated that the performance of the investigated models was strongly dependent on the timeframe of the train set, training data sequence, and application of irradiance condition filters. Furthermore, accurate results were obtained utilizing only the measured power output and other calculated parameters for training. Consequently, useful information is provided for establishing a robust day-ahead forecasting methodology that utilizes calculated input parameters and an optimal supervised learning approach. Finally, the obtained results demonstrated that the optimally constructed BNN outperformed all other machine learning models achieving forecasting accuracies lower than 5%.

14 SOLAR ENERGY↗
NASA NTRS2024

Effective structural impact detection and localization using convolutional neural network and Bayesian information fusion with limited sensors

Due to their unpredictable nature, many impact events (e.g., overheight vehicles striking on bridges) go unnoticed or get reported many hours later. However, they can induce structural failures or hidden damage that accelerates the structure’s long-term degradation. Therefore, prompt impact detection and localization strategies are essential for early warning of impact events and rapid maintenance of structures. Most existing impact detection strategies are developed for aircraft composite panels utilizing high-rate synchronized measurement from densely deployed sensors. Limited efforts have been made for infrastructure or human habitats which generally require large-scale but low-rate measurement. In particular, due to harsh environments (e.g., deep space habitats under meteoroids), structural impact localization must be robust to limited sensors (e.g., sensor damage during impacts) and multi-source errors (e.g., measurement errors). In this study, an effective impact detection and localization strategy is proposed using a limited number of vibration measurements, especially in harsh environments (e.g. in deep space). Convolutional neural networks are trained for each sensor node and are fused using Bayesian theory to improve the accuracy of impact localization. Special considerations are paid to evaluate the effect of both measurement error and modeling error in the analysis. The proposed strategy is illustrated using 1D structure, and further validated in 3D geodesic dome structure numerically. The results demonstrate that it can detect and localize impact events accurately and robustly on structures.

Yuguang Fu↗
DOE OSTI2022

Global stochastic optimization of stellarator coil configurations

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project. Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than 0.1% of the cost of previous work, which considered solely local stochastic optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Transverse mode analysis for free-space laser beams using Bayesian analysis

Reliable and rapid assessment of the transverse mode quality of a free-space laser beam has a wide range of applications in laser development, research, and utilization. It has become even more important with recent advances in developing orbital angular momentum photon beams across a broad spectral region. In this work, a general modal analysis method for a free-space multimode laser beam has been developed based on Bayesian analysis. After transforming mode decomposition into a linear system problem, a Gaussian probabilistic model is used to find a closed-form solution. The method is found to be robust with the presence of Gaussian noise. Prior knowledge about the mode content can be incorporated into the method to improve the solution for situations when coherent disturbances or contamination are present in the laser beam. This method can be used to analyze the mode content for laser beams in different bases, such as Hermite–Gaussian (HG) modes and Laguerre–Gaussian (LG) modes. Three applications of this method are presented: a detailed modal analysis of the beam image from the incoherent intensity addition of HG modes and two examples of mode decomposition using the complex wavefront from the coherent superposition of HG and LG modes. The feasibility of this method is demonstrated using various simulation results. Based on digital images of a laser beam recorded without complex wavelength-limiting optics, in principle, this method can be used in a wide wavelength range from infrared to ultraviolet, and possibly x ray.

Liu, Peifan (ORCID:0000000273816153)↗
DOE OSTI2022

Data augmentation for disruption prediction via robust surrogate models

The goal of this work is to generate large statistically representative datasets to train machine learning models for disruption prediction provided by data from few existing discharges. Such a comprehensive training database is important to achieve satisfying and reliable prediction results in artificial neural network classifiers. Here, we aim for a robust augmentation of the training database for multivariate time series data using Student-t process regression. We apply Student-t process regression in a state space formulation via Bayesian filtering to tackle challenges imposed by outliers and noise in the training data set and to reduce the computational complexity. Thus, the method can also be used if the time resolution is high. We use an uncorrelated model for each dimension and impose correlations afterwards via coloring transformations. We demonstrate the efficacy of our approach on plasma diagnostics data of three different disruption classes from the DIII-D tokamak. To evaluate if the distribution of the generated data is similar to the training data, we additionally perform statistical analyses using methods from time series analysis, descriptive statistics, and classic machine learning clustering algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Radar-Based Bayesian Estimation of Ice Crystal Growth Parameters within a Microphysical Model

The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. Furthermore, the combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.

54 ENVIRONMENTAL SCIENCES↗