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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Markov Chain Monte Carlo Bayesian Learning for Neural Networks

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

Goodrich, Michael S.↗
NASA NTRSDate not supplied

Stochastic Reconstruction of Thermal Protection Material Properties from Arc-Jet Experiments

Material response models are used to assess reliability using variances in the bond-line temperature predictions based on uncertainties in trajectory, aerothermal environment, and material properties. A key deficiency in the current approach is that input uncertainties are too often subjective, empirical, or ad-hoc, and are not rigorously linked to the arc-jet test data used to develop the TPS material model. While materials such as PICA are well understood, future missions may require more novel materials such as HEEET where unknown uncertainties have real consequences on the ability to assess reliability. A quantifiable estimate of reliability requires an iterative methodology where the parameters driving the variance in bond-line temperature (for example) are systematically identified. A test campaign to collect data or develop new models can then be identified to reduce those input uncertainties. A Bayesian inference loop defines these connections mathematically, i.e., prior knowledge about uncertainty is updated based on observation. While these concepts are well known (and often applied intuitively in a non-rigorous approach), only recent advances in reduced-order modelling have made them computationally viable methods for engineering. By replacing deterministic inverse methods with stochastic approaches, the hope is new materials proposed for future missions can more rapidly be developed with a greater understanding of the TPS material reliability. Two additional steps for the analysis of arc jet test data are discussed. The first is ability to construct a reduced-order model using material response simulations (Icarus/US3D) of the arc-jet test articles, and the second is the inclusion of this surrogate model in the Bayesian inversion process. Both capabilities will be demonstrated using prior PICA arc-jet test data. The quality of a surrogate model will be investigated and the variances on the calibrated material properties will be compared to our current understanding of the PICA material model.

Material response↗
NASA NTRS1974

Reliability-based econometrics of aerospace structural systems: Design criteria and test options

The design criteria and test options for aerospace structural reliability were investigated. A decision methodology was developed for selecting a combination of structural tests and structural design factors. The decision method involves the use of Bayesian statistics and statistical decision theory. Procedures are discussed for obtaining and updating data-based probabilistic strength distributions for aerospace structures when test information is available and for obtaining subjective distributions when data are not available. The techniques used in developing the distributions are explained.

Thomas, J. M.↗
NASA NTRS1994

High Fidelity Modeling of Evolutionary Structures in IMOS

A methodology is proposed for testing, modal identification, and model correlation of structures which are assembled in an evolutionary manner. The methodology prescribes initial testing of a base structure without any attached components. The experimental modal properties are used to update the physical properties of the base structure finite element model using a Bayesian Estimation Technique (BET). The BET is implemented in METLAB using IMOS functions. As components are added to the base structure, additional tests are performed. Three testing options are proposed, all of which enable estimation of the physical parameters of the components alone. Furthermore, improvements to the original BET implementation have been made, which contribute to higher fidelity models and more efficient computational times.

structures testing assembling modeling BET Bayesia↗
NASA NTRS2016

Constructing the 'Best' Reliability Data for the Job - Developing Generic Reliability Data from Alternative Sources Early in a Product's Development Phase

Reliability practitioners advocate getting reliability involved early in a product development process. However, when assigned to estimate or assess the (potential) reliability of a product or system early in the design and development phase, they are faced with lack of reasonable models or methods for useful reliability estimation. Developing specific data is costly and time consuming. Instead, analysts rely on available data to assess reliability. Finding data relevant to the specific use and environment for any project is difficult, if not impossible. Instead, analysts attempt to develop the "best" or composite analog data to support the assessments. Industries, consortia and vendors across many areas have spent decades collecting, analyzing and tabulating fielded item and component reliability performance in terms of observed failures and operational use. This data resource provides a huge compendium of information for potential use, but can also be compartmented by industry, difficult to find out about, access, or manipulate. One method used incorporates processes for reviewing these existing data sources and identifying the available information based on similar equipment, then using that generic data to derive an analog composite. Dissimilarities in equipment descriptions, environment of intended use, quality and even failure modes impact the "best" data incorporated in an analog composite. Once developed, this composite analog data provides a "better" representation of the reliability of the equipment or component. It can be used to support early risk or reliability trade studies, or analytical models to establish the predicted reliability data points. It also establishes a baseline prior that may updated based on test data or observed operational constraints and failures, i.e., using Bayesian techniques. This tutorial presents a descriptive compilation of historical data sources across numerous industries and disciplines, along with examples of contents and data characteristics. It then presents methods for combining failure information from different sources and mathematical use of this data in early reliability estimation and analyses.

Kleinhammer, Roger K.↗
NASA NTRS2021

A Sub-Neptune and a Non-Transiting Neptune-Mass Companion Unveiled by ESPRESSO Around the Bright Late-F Dwarf HD 5278 (TOI-130)

Context. Transiting sub-Neptune-type planets, with radii approximately between 2 and 4R⊕, are of particular interest as their study allows us to gain insight into the formation and evolution of a class of planets that are not found in our Solar System. Aims. We exploit the extreme radial velocity (RV) precision of the ultra-stable echelle spectrograph ESPRESSO on the VLT to unveil the physical properties of the transiting sub-Neptune TOI-130 b, uncovered by the TESS mission orbiting the nearby, bright, late F-typestar HD 5278 (TOI-130) with a period of Pb=14.3 days. Methods. We used 43 ESPRESSO high-resolution spectra and broad-band photometry information to derive accurate stellar atmospheric and physical parameters of HD 5278. We exploited the TESS light curve and spectroscopic diagnostics to gauge the impact of stellar activity on the ESPRESSO RVs. We performed separate as well as joint analyses of the TESS photometry and the ESPRESSORVs using fully Bayesian frameworks to determine the system parameters. Results. Based on the ESPRESSO spectra, the updated stellar parameters of HD 5278 are Teff=6203±64K, logg=4.50±0.11dex, [Fe/H] =−0.12±0.04dex,M?=1.126+0.036−0.035M, and R?=1.194+0.017−0.016R. We determine HD 5278 b’s mass and radius to be Mb=7.8+1.5−1.4M⊕ and Rb=2.45±0.05R⊕. The derived mean density, %b=2.9+0.6−0.5g cm−3, is consistent with the bulk composition of a sub-Neptune with a substantial (∼30%) water mass fraction and with a gas envelope comprising ∼17% of the measured radius. Given the host brightness and irradiation levels, HD 5278 b is one of the best targets orbiting G-F primaries for follow-up atmospheric characterization measurements with HST and JWST. We discover a second, non-transiting companion in the system, with a period of Pc=40.87+0.18−0.17days and a minimum mass of Mcsinic=18.4+1.8−1.9M⊕. We study emerging trends in parameters space (e.g., mass, radius, stellar insolation, and mean density) of the growing population of transiting sub-Neptunes, and provide statistical evidence for a low occurrence of close-in,10−15M⊕companions around G-F primaries withTeff&5500K.

planetary systems↗
NASA NTRS2022

Advanced Statistical Methods in Spacecraft Flight Software Cost Estimation: Bayesian Regression and Nonlinear Principal Components Analysis to Support System Engineering in the Early Project Lifecycle

This paper provides an overview of the new features and model updates in the upcoming release of the NASA Analogy Software Cost Tool (ASCoT). ASCoT, hosted within the Online NASA Space Estimation Tools (ONSET) on the One NASA Cost Engineering (ONCE) Database, is a web-based tool that provides a suite of estimation tools to support early lifecycle NASA flight software cost analysis. In addition to the traditional parametric flight software costing method COCOMO II, ASCoT contains a Bayesian linear regression to predict total flight software development cost as a function of total spacecraft cost, as well as four analogic methods: k-Nearest Neighbors (kNN) and Clustering models to predict Effort (in work-months) and total source lines of code (SLOC). These methods are designed to work primarily with system-level inputs such as mission type (orbiter, lander, etc.), mission destination (Earth, Inner Planetary, etc.), and the number of instruments and deployables. Nonlinear principal components analysis (NLPCA) is performed to find the principal features of the data composed of both categorical and numerical variables and is necessary prior to defining our analogic methods. Sensitivity analyses and in- and out-of-sample model performance results are presented for the Bayesian CER and the analogic models.

Johnson, James K.↗
NASA NTRSDate not supplied

Countermeasures for Mitigation of Sensorimotor Decrements Following Head-Down Bed Rest

BACKGROUND Astronauts experience postflight disturbances in postural and locomotor control due to sensorimotor adaptations during spaceflight. These alterations may have adverse consequences if a rapid egress is required after landing. Although exercise is partially effective for mitigating cardiovascular and muscular deconditioning, additional countermeasures are needed to further preserve sensorimotor function for exploration missions. We have identified proprioceptive training and electrical muscle stimulation (EMS) as promising in-flight countermeasures. Since prolonged head down bed rest (HDBR) is a spaceflight analog for body unloading and causes postural and locomotor control decrements that parallel those observed after spaceflight, it can be used to accelerate the development of these countermeasures. METHODS This study will determine the effects of proprioceptive training and EMS on functional task performance and sensorimotor function following 60 days of 6° HDBR. Subjects will be randomly assigned to one of four groups: 1) an EMS arm, 2) a proprioceptive training arm, 3) an exercise plus proprioceptive training arm, and 4) a control arm. The EMS countermeasure will include daily bilateral stimulation of the quadriceps femoris muscle (30 minutes per session). Proprioceptive training will be performed three days per week (20 minutes per session) consisting of body-loaded postural tasks in the horizontal position on an air bearing sled. Exercise training will mimic current protocols used on the International Space Station, but treadmill aerobic exercise will be replaced with additional cycling aerobic exercise. Primary outcome measures will include pre and post HDBR functional tests that are representative of high priority exploration mission tasks and require high demand for dynamic control of postural stability. Additional measures will be used to identify the key physiological factors contributing to countermeasure benefits. Given the constrained samples size, a Bayesian modelling approach will be used to quantify the probability that there is an effect of a given magnitude. COUNTERMEASURE UPDATES Proprioceptive countermeasure design enhancements and human in the loop pilot testing continued through the Crew Health Countermeasures (CHC) Systems Capability Leadership Team (SCLT). The primary goals of this work were to enhance the visual feedback system’s capabilities and develop a proprioceptive training program for 60 days of HDBR. Six healthy non-astronaut volunteers participated in four pilot training sessions to systematically examine how each training variable (e.g., axial load, foot placement, and software profile) affects the overall proprioceptive challenge. The resulting training program will maintain an appropriate challenge during 60 days of HDBR by progressively decreasing the subject’s base of support, increasing tilt board target distances, and increasing axial loads using both subjective verbal feedback and objective performance data. RELEVANCE The deliverable from this project will be proof-of-concept sensorimotor countermeasure designs for functional task performance with full assessment of efficacy in a spaceflight analog. If the countermeasures are effective, they will be translated for validation with the suite of operationally implemented in-flight countermeasures.

T R Macaulay↗
NASA NTRS2012

A Bayesian Framework for Reliability Analysis of Spacecraft Deployments

Deployable subsystems are essential to mission success of most spacecraft. These subsystems enable critical functions including power, communications and thermal control. The loss of any of these functions will generally result in loss of the mission. These subsystems and their components often consist of unique designs and applications for which various standardized data sources are not applicable for estimating reliability and for assessing risks. In this study, a two stage sequential Bayesian framework for reliability estimation of spacecraft deployment was developed for this purpose. This process was then applied to the James Webb Space Telescope (JWST) Sunshield subsystem, a unique design intended for thermal control of the Optical Telescope Element. Initially, detailed studies of NASA deployment history, "heritage information", were conducted, extending over 45 years of spacecraft launches. This information was then coupled to a non-informative prior and a binomial likelihood function to create a posterior distribution for deployments of various subsystems uSing Monte Carlo Markov Chain sampling. Select distributions were then coupled to a subsequent analysis, using test data and anomaly occurrences on successive ground test deployments of scale model test articles of JWST hardware, to update the NASA heritage data. This allowed for a realistic prediction for the reliability of the complex Sunshield deployment, with credibility limits, within this two stage Bayesian framework.

Evans, John W.↗
NASA NTRS2020

In-Time UAV Flight-Trajectory Estimation and Tracking Using Bayesian Filters

Rapid increase of UAV operation in the next decade in areas of on-demand delivery, medical transportation services, law enforcement, traffic surveillance and several others pose potential risks to the low altitude airspace above densely populated areas. Safety assessment of airspace demands the need for a novel UAV traffic management (UTM) framework for regulation and tracking of the vehicles. Particularly for low-altitude UAV operations, quality of GPS measurements feeding into the UAV is often compromised by loss of communication link caused by presence of trees or tall buildings in proximity to the UAV flight path. Inaccurate GPS locations may yield to unreliable monitoring and inaccurate prognosis of remaining battery life and other safety metrics which rely on future expected trajectory of the UAV. This work therefore proposes a generalized monitoring and prediction methodology for autonomous UAVs using in-time GPS measurements. Firstly, a typical 4D smooth trajectory generation technique from a series of waypoint locations with associated expected times-of-arrival based on B-spline curves is presented. Initial uncertainty in the vehicle's expected cruise velocity is quantified to compute confidence intervals along the entire flight trajectory using error interval propagation approach. Further, the generated planned trajectory is considered as the prior knowledge which is updated during its flight with incoming GPS measurements in order to estimate its current location and corresponding kinematic profiles. Estimation of position is denoted in dicrete state-space representation such that position at a future time step is derived from position and velocity at current time step and expected velocity at the future time step. A linear Bayesian filtering algorithm is employed to efficiently refine position estimation from noisy GPS measurements and update the confidence intervals. Further, a dynamic re-planning strategy is implemented to incorporate unexpected detour or delay scenarios. Finally, critical challenges related to uncertainty quantification in trajectory prognosis for autonomous vehicles are identified, and potential solutions are discussed at the end of the paper. The entire monitoring framework is demonstrated on real UAV flight experiments conducted at the NASA Langley Research Center.

Banerjee, Portia↗
NASA NTRS2022

Updated Orbital Monitoring and Dynamical Masses for Nearby M-dwarf Binaries

Young M-type binaries are particularly useful for precise isochronal dating by taking advantage of their extended pre-main sequence evolution. Orbital monitoring of these low-mass objects becomes essential in constraining their fundamental properties, as dynamical masses can be extracted from their Keplerian motion. Here, we present the combined efforts of the AstraLux Large Multiplicity Survey, together with a filler sub-programme from the SpHere INfrared Exoplanet (SHINE) project and previously unpublished data from the FastCam lucky imaging camera at the Nordical Optical Telescope (NOT) and the NaCo instrument at the Very Large Telescope (VLT). Building on previous work, we use archival and new astrometric data to constrain orbital parameters for 20 M-type binaries. We identify that eight of the binaries have strong Bayesian probabilities and belong to known young moving groups (YMGs). We provide a first attempt at constraining orbital parameters for 14 of the binaries in our sample, with the remaining six having previously fitted orbits for which we provide additional astrometric data and updated Gaia parallaxes. The substantial orbital information built up here for four of the binaries allows for direct comparison between individual dynamical masses and theoretical masses from stellar evolutionary model isochrones, with an additional three binary systems with tentative individual dynamical mass estimates likely to be improved in the near future. We attained an overall agreement between the dynamical masses and the theoretical masses from the isochrones based on the assumed YMG age of the respective binary pair. The two systems with the best orbital constrains for which we obtained individual dynamical masses, J0728 and J2317, display higher dynamical masses than predicted by evolutionary models.

Astrometry / binaries↗
NASA NTRS2021

Upper Limits on the Isotropic Gravitational-Wave Background from Advanced LIGO and Advanced Virgo's Third Observing Run

We report results of a search for an isotropic gravitational-wave background (GWB) using data from Advanced LIGO's and Advanced Virgo's third observing run (O3) combined with upper limits from the earlier O1 and O2 runs. Unlike in previous observing runs in the advanced detector era, we include Virgo in the search for the GWB. The results of the search are consistent with uncorrelated noise, and therefore we place upper limits on the strength of the GWB. We find that the dimensionless energy density Ω(sub GW) ≤ 5.8 × 10(exp -9) at the 95% credible level for a at (frequency-independent) GWB, using a prior which is uniform in the log of the strength of the GWB, with 99% of the sensitivity coming from the band 20-76.6 Hz; Ω(sub GW)(f) ≤ 3.4 × 10(exp -9) at 25 Hz for a power-law GWB with a spectral index of 2/3 (consistent with expectations for compact binary coalescences), in the band 20-90.6 Hz; and Ω(sub GW)(f) ≤ 3.9 × 10(exp -10) at 25 Hz for a spectral index of 3, in the band 20-291.6 Hz. These upper limits improve over our previous results by a factor of 6.0 for a at GWB, 8.8 for a spectral index of 2/3, and 13.1 for a spectral index of 3. We also search for a GWB arising from scalar and vector modes, which are predicted by alternative theories of gravity; we do not find evidence of these, and place upper limits on the strength of GWBs with these polarizations. We demonstrate that there is no evidence of correlated noise of magnetic origin by performing a Bayesian analysis that allows for the presence of both a GWB and an effective magnetic background arising from geophysical Schumann resonances. We compare our upper limits to a fiducial model for the GWB from the merger of compact binaries, updating the model to use the most recent data-driven population inference from the systems detected during O3a. Finally, we combine our results with observations of individual mergers and show that, at design sensitivity, this joint approach may yield stronger constraints on the merger rate of binary black holes at z ≳ 2 than can be achieved with individually resolved mergers alone.

Ryan Abbott↗
NASA NTRS1991

Development of a Weibull posterior distribution by combining a Weibull prior with an actual failure distribution using Bayesian inference

A Bayesian inference process for system logistical planning is presented which provides a method for incorporating actual failures with prediction data for an ongoing and improving reliability estimates. The process uses the Weibull distribution, and provides a means for examining and updating logistical and maintenance support needs.

Giuntini, Michael E.↗
NASA NTRS1988

Probabilistic system identification in the time domain

The objective of system identification is to determine reliable dynamical models of a structure by systematically using its measured excitation and response. It brings together in an integrated fashion, experimental, analytical, and computational techniques in structural dynamics. Areas of application for system identification include the following: (1) Model Evaluation--assessing assumptions (linearity and equivalent viscous damping) and techniques (finite-element modeling) used to construct theoretical models of a structure; (2) Model Improvement--updating of a theoretical model to enable more accurate response predictions for possible future loads on the structure, or for control of the structure; (3) Empirical Modelling--developing empirical relationships (nonlinear models) or empirical parameter values (modal damping) because the present state of the art does not provide theoretical results; and (4) Damage Detection and Assessment--continual or episodic updating of a structural model through vibration monitoring to detect and locate any structural damage. It can be argued that since the construction or modification of models using test data is subject to inherent uncertainties, the above problems should be properly treated within a Bayesian probabilistic framework. Such a methodology is presented which allows the precision of the estimates of the model parameters to be computed. It also leads to a guiding principle in applications. Namely, when selecting a single model from a given class of models, one should take the most probable model in the class based on the experimental data. Practical applications of this principle are given which are based on the utilization of measured seismic motions in large civil structures. Examples include the application of a computer program MODE-ID to identify modal properties directly from seismic excitation and response time histories from a nine-story steel-frame building at JPL and from a freeway overpass bridge.

Beck, James L.↗
NASA NTRS2003

Automated Monitoring with a BCP Fault-Decision Test

The Bayesian conditional probability (BCP) technique is a statistical fault-decision technique that is suitable as the mathematical basis of the fault-manager module in the automated-monitoring system and method described in the immediately preceding article. Within the automated-monitoring system, the fault-manager module operates in conjunction with the fault-detector module, which can be based on any one of several fault-detection techniques; examples include a threshold-limit-comparison technique or the BSP or SPRT technique mentioned in the preceding article. The present BCP technique is used to evaluate a series of one or more fault-detection events for the purpose of filtering out occasional false alarms produced by many types of statistical fault-detection procedures. The BCP technique increases the probability that an automated monitoring system produces a correct decision regarding the presence or absence of a fault. Because occasional false alarms are an inevitable consequence of the SPRT, BSP, or any other statistically based fault-detection test, there is a need for a logical procedure to distinguish between true and false alarms. Heretofore, it has been common practice to make a fault decision on an ad hoc basis for example by following a multiple-observation voting strategy in which a signal is declared to be indicative of a fault if m of the last n observations produced a fault-detection alarm. The BCP technique was developed to obtain results more reliable than those afforded by a voting strategy. The BCP technique involves a test in which one applies Bayesian inference techniques to a series of one or more single-observation alarms produced by a fault-detection test. One considers the last n decisions generated by a fault-detection test in order to evaluate the conditional probability that a failure is indicated (see figure). Each new decision reached by a fault-detection test is treated as a new piece of evidence about the state of the monitored asset, and the conditional probability of failure for the system is updated on the basis of this new evidence. The conditional probability of failure is compared with a predefined limit. For a probability below the limit, the asset is declared to be healthy. For a probability above the limit, the asset is declared to be faulty.

Bickford, Randall L.↗
NASA NTRS2021

Computational Inference of Vibratory System with Incomplete Modal Information Using Parallel, Interactive and Adaptive Markov Chains

Inverse analysis of vibratory system is an important subject in fault identification, model updating, and robust design and control. It is challenging subject because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield results that are similar with respect to actual response measurements; and 3) uncertainties inevitably exist. The aim of this research is to leverage upon computational intelligence through statistical inference to facilitate an enhanced, probabilistic framework using incomplete modal response measurement. This new framework is built upon efficient inverse identification through optimization, whereas Bayesian inference is employed to account for the effect of uncertainties. To overcome the computational cost barrier, we adopt Markov chain Monte Carlo (MCMC) to characterize the target function/distribution. Instead of using single Markov chain in conventional Bayesian approach, we develop a new sampling theory with multiple parallel, interactive and adaptive Markov chains and incorporate it into Bayesian inference. This can harness the collective power of these Markov chains to realize the concurrent search of multiple local optima. The number of required Markov chains and their respective initial model parameters are automatically determined via Monte Carlo simulation-based sample pre-screening followed by K-means clustering analysis. These enhancements can effectively address the aforementioned challenges in finite element inverse analysis. The validity of this framework is systematically demonstrated through case studies.

K Zhou↗
NASA NTRS2005

Nonlinear Attitude Filtering Methods

This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST, the super-iterated extended Kalman filter, the interlaced extended Kalman filter, and the second-order Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A two-step approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, including particle filters and a Bayesian filter based on a non-Gaussian, finite-parameter probability density function on SO(3). Finally, the predictive filter, nonlinear observers and adaptive approaches are shown. The strengths and weaknesses of the various approaches are discussed.

F Landis Markley↗
NASA NTRS2017

A Method for Snow Reanalysis: The Sierra Nevada (USA) Example

This work presents a state-of-the art methodology for constructing snow water equivalent (SWE) reanalysis. The method is comprised of two main components: (1) a coupled land surface model and snow depletion curve model, which is used to generate an ensemble of predictions of SWE and snow cover area for a given set of (uncertain) inputs, and (2) a reanalysis step, which updates estimation variables to be consistent with the satellite observed depletion of the fractional snow cover time series. This method was applied over the Sierra Nevada (USA) based on the assimilation of remotely sensed fractional snow covered area data from the Landsat 5-8 record (1985-2016). The verified dataset (based on a comparison with over 9000 station years of in situ data) exhibited mean and root-mean-square errors less than 3 and 13 cm, respectively, and correlation greater than 0.95 compared with in situ SWE observations. The method (fully Bayesian), resolution (daily, 90-meter), temporal extent (31 years), and accuracy provide a unique dataset for investigating snow processes. This presentation illustrates how the reanalysis dataset was used to provide a basic accounting of the stored snowpack water in the Sierra Nevada over the last 31 years and ultimately improve real-time streamflow predictions.

Bayesian↗