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All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

A Particle Batch Smoother Approach to Snow Water Equivalent Estimation

This paper presents a newly proposed data assimilation method for historical snow water equivalent SWE estimation using remotely sensed fractional snow-covered area fSCA. The newly proposed approach consists of a particle batch smoother (PBS), which is compared to a previously applied Kalman-based ensemble batch smoother (EnBS) approach. The methods were applied over the 27-yr Landsat 5 record at snow pillow and snow course in situ verification sites in the American River basin in the Sierra Nevada (United States). This basin is more densely vegetated and thus more challenging for SWE estimation than the previous applications of the EnBS. Both data assimilation methods provided significant improvement over the prior (modeling only) estimates, with both able to significantly reduce prior SWE biases. The prior RMSE values at the snow pillow and snow course sites were reduced by 68%-82% and 60%-68%, respectively, when applying the data assimilation methods. This result is encouraging for a basin like the American where the moderate to high forest cover will necessarily obscure more of the snow-covered ground surface than in previously examined, less-vegetated basins. The PBS generally outperformed the EnBS: for snow pillows the PBSRMSE was approx.54%of that seen in the EnBS, while for snow courses the PBSRMSE was approx.79%of the EnBS. Sensitivity tests show relative insensitivity for both the PBS and EnBS results to ensemble size and fSCA measurement error, but a higher sensitivity for the EnBS to the mean prior precipitation input, especially in the case where significant prior biases exist.

EnBS↗
DOE OSTI2021

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

Ensemble Data Assimilation Without Ensembles: Methodology and Application to Ocean Data Assimilation

Two methods to estimate background error covariances for data assimilation are introduced. While both share properties with the ensemble Kalman filter (EnKF), they differ from it in that they do not require the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The first method is referred-to as SAFE (Space Adaptive Forecast error Estimation) because it estimates error covariances from the spatial distribution of model variables within a single state vector. It can thus be thought of as sampling an ensemble in space. The second method, named FAST (Flow Adaptive error Statistics from a Time series), constructs an ensemble sampled from a moving window along a model trajectory. The underlying assumption in these methods is that forecast errors in data assimilation are primarily phase errors in space and/or time.

Data Assimilation↗
DOE OSTI2024

Sequential Kalman tuning of the t -preconditioned Crank-Nicolson algorithm: efficient, adaptive and gradient-free inference for Bayesian inverse problems

Ensemble Kalman Inversion (EKI) has been proposed as an efficient method for the approximate solution of Bayesian inverse problems with expensive forward models. However, when applied to the Bayesian inverse problem EKI is only exact in the regime of Gaussian target measures and linear forward models. Here, in this work we propose embedding EKI and Flow Annealed Kalman Inversion, its normalizing flow (NF) preconditioned variant, within a Bayesian annealing scheme as part of an adaptive implementation of the t-preconditioned Crank-Nicolson (tpCN) sampler. The tpCN sampler differs from standard pCN in that its proposal is reversible with respect to the multivariate t-distribution. The more flexible tail behaviour allows for better adaptation to sampling from non-Gaussian targets. Within our Sequential Kalman Tuning (SKT) adaptation scheme, EKI is used to initialize and precondition the tpCN sampler for each annealed target. The subsequent tpCN iterations ensure particles are correctly distributed according to each annealed target, avoiding the accumulation of errors that would otherwise impact EKI. We demonstrate the performance of SKT for tpCN on three challenging numerical benchmarks, showing significant improvements in the rate of convergence compared to adaptation within standard SMC with importance weighted resampling at each temperature level, and compared to similar adaptive implementations of standard pCN. The SKT scheme applied to tpCN offers an efficient, practical solution for solving the Bayesian inverse problem when gradients of the forward model are not available. Code implementing the SKT schemes for tpCN is available at https://github.com/RichardGrumitt/KalmanMC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Joint state-parameter estimation for the reduced fracture model via the united filter

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

Bayesian inference↗
NASA NTRS2009

Advances in Land Data Assimilation at the NASA Goddard Space Flight Center

Research in land surface data assimilation has grown rapidly over the last decade. In this presentation we provide a brief overview of key research contributions by the NASA Goddard Space Flight Center (GSFC). The GSFC contributions to land assimilation primarily include the continued development and application of the Land Information System (US) and the ensemble Kalman filter (EnKF). In particular, we have developed a method to generate perturbation fields that are correlated in space, time, and across variables and that permit the flexible modeling of errors in land surface models and observations, along with an adaptive filtering approach that estimates observation and model error input parameters. A percentile-based scaling method that addresses soil moisture biases in model and observational estimates opened the path to the successful application of land data assimilation to satellite retrievals of surface soil moisture. Assimilation of AMSR-E surface soil moisture retrievals into the NASA Catchment model provided superior surface and root zone assimilation products (when validated against in situ measurements and compared to the model estimates or satellite observations alone). The multi-model capabilities of US were used to investigate the role of subsurface physics in the assimilation of surface soil moisture observations. Results indicate that the potential of surface soil moisture assimilation to improve root zone information is higher when the surface to root zone coupling is stronger. Building on this experience, GSFC leads the development of the Level 4 Surface and Root-Zone Soil Moisture (L4_SM) product for the planned NASA Soil-Moisture-Active-Passive (SMAP) mission. A key milestone was the design and execution of an Observing System Simulation Experiment that quantified the contribution of soil moisture retrievals to land data assimilation products as a function of retrieval and land model skill and yielded an estimate of the error budget for the SMAP L4_SM product. Terrestrial water storage observations from GRACE satellite system were also successfully assimilated into the NASA Catchment model and provided improved estimates of groundwater variability when compared to the model estimates alone. Moreover, satellite-based land surface temperature (LST) observations from the ISCCP archive were assimilated using a bias estimation module that was specifically designed for LST assimilation. As with soil moisture, LST assimilation provides modest yet statistically significant improvements when compared to the model or satellite observations alone. To achieve the improvement, however, the LST assimilation algorithm must be adapted to the specific formulation of LST in the land model. An improved method for the assimilation of snow cover observations was also developed. Finally, the coupling of LIS to the mesoscale Weather Research and Forecasting (WRF) model enabled investigations into how the sensitivity of land-atmosphere interactions to the specific choice of planetary boundary layer scheme and land surface model varies across surface moisture regimes, and how it can be quantified and evaluated against observations. The on-going development and integration of land assimilation modules into the Land Information System will enable the use of GSFC software with a variety of land models and make it accessible to the research community.

Reichle, Rolf↗
DOE OSTI2020

Calibration and Uncertainty Estimation Using the Ensemble Kalman Filter with a Large Subsurface Flow and Transport Model - 20321

At routinely monitored groundwater contamination sites, periodically measured environmental conditions such as groundwater levels and contaminant concentrations are used to inform and confirm a conceptual site model (CSM) and guide the development and calibration of a numerical groundwater flow and transport model. The calibration of groundwater flow and transport models after each measurement (sampling) event can illuminate deficiencies in a CSM, identify areas where additional monitoring is warranted, and predict the behavior of the system to guide decision making. However, manual and automated (e.g. PEST) model calibration tools can be time-consuming and computationally expensive to implement after each sampling event. Perhaps as a result, such calibration tools generally utilize all available monitoring data simultaneously rather than sequentially assimilating monitoring data one sampling event at a time as the results from sampling become available. A more real-time data assimilation approach may reduce parameter uncertainty, quantify the value of additional monitoring data, and produce a usable model more quickly and with less effort. To mitigate the potential time-consuming aspects of manual and widely applied automated calibration techniques, a data assimilation algorithm called the ensemble Kalman filter (EnKF) was evaluated as a relatively efficient method of model calibration and uncertainty assessment via the sequential integration of monitoring data into a model. The EnKF was able to successfully and efficiently assimilate monitoring and modeling data to calibrate a complex flow and transport model at a real-world site with significant subsurface heterogeneity, uncertainty, and 12 years of monitoring data (over 4,000 individual measurements of groundwater levels and over 2,500 measurements of contaminant concentrations). Starting with an uncalibrated model data from annual sampling events were sequentially assimilated, and the resultant predication errors and estimated parameter uncertainties were tracked. After all monitoring data were assimilated, both flow and transport residuals at the end of the EnKF process were comparable to those produced via a concurrent PEST calibration effort but required fewer model simulations. Both uncertainty and prediction errors decreased over time. In a real-time application, the adequacy of the model could be assessed after each sampling event. The benefits of such a real-time approach to utilizing monitoring data include reduced costs (in the form of model updates or site characterization efforts), early flagging of possible errors in the CSM, and a reduced risk of overfitting and corresponding increased confidence in model predictions. This tool may be particularly useful compared to other calibration techniques (e.g. manual, PEST) when model runtimes are long, calibration parameters are many, or parameter uncertainty is large. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2012

A Localized Ensemble Kalman Smoother

Numerous geophysical inverse problems prove difficult because the available measurements are indirectly related to the underlying unknown dynamic state and the physics governing the system may involve imperfect models or unobserved parameters. Data assimilation addresses these difficulties by combining the measurements and physical knowledge. The main challenge in such problems usually involves their high dimensionality and the standard statistical methods prove computationally intractable. This paper develops and addresses the theoretical convergence of a new high-dimensional Monte-Carlo approach called the localized ensemble Kalman smoother.

recursive estimation↗
NASA NTRS2013

Simultaneous Estimation of Model State Variables and Observation and Forecast Biases Using a Two-Stage Hybrid Kalman Filter

In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.

Data Assimilation↗
DOE OSTI2022

Autodifferentiable Ensemble Kalman Filters

Data assimilation is concerned with sequentially estimating a temporally evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and the state-space dynamics are unknown. This paper introduces a machine learning framework for learning dynamical systems in data assimilation. Here, our auto-differentiable ensemble Kalman filters (AD-EnKFs) blend ensemble Kalman filters for state recovery with machine learning tools for learning the dynamics. In doing so, AD-EnKFs leverage the ability of ensemble Kalman filters to scale to high-dimensional states and the power of automatic differentiation to train high-dimensional surrogate models for the dynamics. Numerical results using the Lorenz-96 model show that AD-EnKFs outperform existing methods that use expectation-maximization or particle filters to merge data assimilation and machine learning. In addition, AD-EnKFs are easy to implement and require minimal tuning.

autodifferentiation↗
DOE OSTI2026

Robustness of the Ensemble Score Filter to the Type of Assimilated Observation Networks

Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods depends on the observation network characteristics. In this study, we present initial experiments with the surface quasi‐geostrophic model, in which we compare a recently developed ensemble filter using score‐based diffusion models with the standard Local Ensemble Transform Kalman Filter (LETKF). Our results show that the analysis solutions respond differently to the number, spatial distribution, and nonlinear fraction of assimilated observations. We also find notable changes in the multiscale characteristics of the analysis errors. Given that standard DA techniques will eventually be replaced by more advanced methods, we hope this study sets the ground for future efforts to reassess the value of Earth observing systems in the context of newly emerging algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Advanced Multilevel Monte Carlo Methods

This article reviews the application of some advanced Monte Carlo techniques in the context of multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations, which can be biassed in some sense, for instance, by using the discretization of an associated probability law. The MLMC approach works with a hierarchy of biassed approximations, which become progressively more accurate and more expensive. Additionally, using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider some Markov chain Monte Carlo and sequential Monte Carlo methods, which have been introduced in the literature, and we describe different strategies that facilitate the application of MLMC within these methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2020

Underlying Fundamentals of Kalman Filtering for River Network Modeling

The grand challenge of producing hydrometeorological estimates every time and everywhere has motivated the fusion of sparse observations with dense numerical models, with a particular interest on discharge in river modeling. Ensemble methods are largely preferred as they enable the estimation of error properties, but at the expense of computational load and generally with underestimations. These imperfect stochastic estimates motivate the use of correction methods, that is, error localization and inflation, although the physical justifications for their optimality are limited. The purpose of this study is to use one of the simplest forms of data assimilation when applied to river modeling and reveal the underlying mechanisms impacting its performance. Our framework based on assimilating daily averaged in situ discharge measurements to correct daily averaged runoff was tested over a 4-yr case study of two rivers in Texas. Results show that under optimal conditions of inflation and localization, discharge simulations are consistently improved such that the mean values of Nash–Sutcliffe efficiency are enhanced from211.32 to 0.55 at observed gauges and from212.24 to21.10 at validation gauges. Yet, parameters controlling the inflation and the localization have a large impact on the performance. Further investigations of these sensitivities showed that optimal inflation occurs when compensating exactly for discrepancies in the magnitude of errors while optimal localization matches the distance traveled during one assimilation window. These results may be applicable to more advanced data assimilation methods as well as for larger applications motivated by upcoming river-observing satellite missions, such as NASA’s Surface Water and Ocean Topography mission.

Streamflow↗
NASA NTRS2008

NASA Tech Briefs, October 2008

Topics covered include: Control Architecture for Robotic Agent Command and Sensing; Algorithm for Wavefront Sensing Using an Extended Scene; CO2 Sensors Based on Nanocrystalline SnO2 Doped with CuO; Improved Airborne System for Sensing Wildfires; VHF Wide-Band, Dual-Polarization Microstrip-Patch Antenna; Onboard Data Processor for Change-Detection Radar Imaging; Using LDPC Code Constraints to Aid Recovery of Symbol Timing; System for Measuring Flexing of a Large Spaceborne Structure; Integrated Formation Optical Communication and Estimation System; Making Superconducting Welds between Superconducting Wires; Method for Thermal Spraying of Coatings Using Resonant-Pulsed Combustion; Coating Reduces Ice Adhesion; Hybrid Multifoil Aerogel Thermal Insulation; SHINE Virtual Machine Model for In-flight Updates of Critical Mission Software; Mars Image Collection Mosaic Builder; Providing Internet Access to High-Resolution Mars Images; Providing Internet Access to High-Resolution Lunar Images; Expressions Module for the Satellite Orbit Analysis Program Virtual Satellite; Small-Body Extensions for the Satellite Orbit Analysis Program (SOAP); Scripting Module for the Satellite Orbit Analysis Program (SOAP); XML-Based SHINE Knowledge Base Interchange Language; Core Technical Capability Laboratory Management System; MRO SOW Daily Script; Tool for Inspecting Alignment of Twinaxial Connectors; An ATP System for Deep-Space Optical Communication; Polar Traverse Rover Instrument; Expert System Control of Plant Growth in an Enclosed Space; Detecting Phycocyanin-Pigmented Microbes in Reflected Light; DMAC and NMP as Electrolyte Additives for Li-Ion Cells; Mass Spectrometer Containing Multiple Fixed Collectors; Waveguide Harmonic Generator for the SIM; Whispering Gallery Mode Resonator with Orthogonally Reconfigurable Filter Function; Stable Calibration of Raman Lidar Water-Vapor Measurements; Bimaterial Thermal Compensators for WGM Resonators; Root Source Analysis/ValuStream[Trade Mark] - A Methodology for Identifying and Managing Risks; Ensemble: an Architecture for Mission-Operations Software; Object Recognition Using Feature-and Color-Based Methods; On-Orbit Multi-Field Wavefront Control with a Kalman Filter; and The Interplanetary Overlay Networking Protocol Accelerator.

Source record↗
DOE OSTI2023

On unifying randomized methods for inverse problems

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a sample average approximation (SAA). More importantly, we are able to prove a single theoretical result that guarantees the asymptotic convergence for a variety of randomized methods. Additionally, viewing randomized methods as an SAA enables us to prove, for the first time, a single non-asymptotic error result that holds for randomized methods under consideration. Another important consequence of our unified framework is that it allows us to discover new randomization methods. Here, we present various numerical results for linear, nonlinear, algebraic, and PDE-constrained inverse problems that verify the theoretical convergence results and provide a discussion on the apparently different convergence rates and the behavior for various randomized methods.

42 ENGINEERING↗
DOE OSTI2023

A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering

The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it.

54 ENVIRONMENTAL SCIENCES↗