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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Improving Tropical Cyclogenesis Forecasts of Hurricane Irma (2017) through the Assimilation of All-Sky Infrared Brightness Temperatures

The assimilation of satellite all-sky infrared (IR) brightness temperatures (BTs) has been shown in previous studies to improve intensity forecasts of tropical cyclones. Here, in this study, we examine whether assimilating all-sky IR BTs can also potentially improve tropical cyclogenesis forecasts by improving the pregenesis cloud and moisture fields. By using an ensemble-based data assimilation system, we show that the assimilation of upper-tropospheric water vapor channel BTs observed by the Meteosat-10 SEVIRI instrument two days before the formation of a tropical depression improves the genesis forecast of Hurricane Irma (2017), a classic Cape Verde storm, by up to 24 h while also capturing its later rapid intensification in deterministic forecasts. In an experiment that withholds the assimilation of all-sky IR BTs, the assimilation of conventional observations from the Global Telecommunications System (GTS) leads to the premature genesis of Hurricane Irma by at least 24 h. This premature genesis is shown to result from an overestimation of the spatial coverage of deep convection within the African easterly wave (AEW) from which Irma eventually forms. The gross overestimation of deep convection without all-sky IR BTs is accompanied by higher column saturation fraction, stronger low-level convergence, and the earlier spinup of a low-level meso- β -scale vortex within the AEW that ultimately becomes Hurricane Irma. Through its adjustment to the initial moisture and cloud conditions, the assimilation of all-sky IR BTs leads to a more realistic convective evolution in forecasts and ultimately a more realistic timing of genesis.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Non-asymptotic analysis of ensemble Kalman updates: effective dimension and localization

Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in applications where generating each particle is costly. This paper develops a non-asymptotic analysis of ensemble Kalman updates, which rigorously explains why a small ensemble size suffices if the prior covariance has moderate effective dimension due to fast spectrum decay or approximate sparsity. Here, we present our theory in a unified framework, comparing everal implementations of ensemble Kalman updates that use perturbed observations, square root filtering and localization. As part of our analysis, we develop new dimension-free covariance estimation bounds for approximately sparse matrices that may be of independent interest.

Mathematics↗
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↗
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↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Predicting Thermal Performance of an Enhanced Geothermal System From Tracer Tests in a Data Assimilation Framework

Abstract Predicting the thermal performance of an enhanced geothermal system (EGS) requires a comprehensive characterization of the underlying fracture flow patterns from practically available data such as tracer data. However, due to the inherent complexities of subsurface fractures and the generally insufficient geological/geophysical data, interpreting tracer data for fracture flow characterization and thermal prediction remains a challenging task. The present study aims to tackle the challenge by leveraging a data assimilation method to maximize the utilization of information inherently contained in tracer data, and meanwhile maintain the flexibility to handle various uncertainties. A tracer data interpretation framework was proposed with the following three components integrated: (a) We use principal component analysis (PCA) to reduce the dimensionality of model parameter space. (b) We use ES‐MDA (ensemble smoother with multiple data assimilation) to invert for fracture aperture/flow fields and obtain posterior model ensembles for uncertainty quantification. Various data types are assimilated jointly to improve the predictive ability of the posterior ensemble. (c) The inverted fracture aperture fields are then incorporated into reservoir models to predict thermal performance. We developed a field‐scale EGS model to verify the ability of the framework to characterize highly heterogeneous fracture aperture/flow fields and predicting thermal performance. We also applied the framework to a mesoscale field experiment to demonstrate its potential application in real‐world geothermal reservoirs. The results indicate that the proposed framework can effectively retrieve fracture flow information from tracer data for thermal prediction and uncertainty quantification, and thus provide informative guidance for EGS optimization and risk management.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Penalized ensemble Kalman filters for high dimensional non-linear systems

The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when the ensemble size is smaller than the state space, as is often necessary for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, we propose a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF). Under certain conditions, it can be theoretically proven that the PEnKF will be accurate (the estimation error will converge to zero) despite having fewer ensemble members than state dimensions. Further, as contrasted to localization methods, the proposed approach learns the covariance structure associated with the dynamical system. These theoretical results are supported with simulations of several non-linear and high dimensional systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Development of an open-source regional data assimilation system in PEcAn v. 1.7.2: application to carbon cycle reanalysis across the contiguous US using SIPNET

Abstract. The ability to monitor, understand, and predict the dynamics of the terrestrial carbon cycle requires the capacity to robustly and coherently synthesize multiple streams of information that each provide partial information about different pools and fluxes. In this study, we introduce a new terrestrial carbon cycle data assimilation system, built on the PEcAn model–data eco-informatics system, and its application for the development of a proof-of-concept carbon “reanalysis” product that harmonizes carbon pools (leaf, wood, soil) and fluxes (GPP, Ra, Rh, NEE) across the contiguous United States from 1986–2019. We first calibrated this system against plant trait and flux tower net ecosystem exchange (NEE) using a novel emulated hierarchical Bayesian approach. Next, we extended the Tobit–Wishart ensemble filter (TWEnF) state data assimilation (SDA) framework, a generalization of the common ensemble Kalman filter which accounts for censored data and provides a fully Bayesian estimate of model process error, to a regional-scale system with a calibrated localization. Combined with additional workflows for propagating parameter, initial condition, and driver uncertainty, this represents the most complete and robust uncertainty accounting available for terrestrial carbon models. Our initial reanalysis was run on an irregular grid of ∼ 500 points selected using a stratified sampling method to efficiently capture environmental heterogeneity. Remotely sensed observations of aboveground biomass (Landsat LandTrendr) and leaf area index (LAI) (MODIS MOD15) were sequentially assimilated into the SIPNET model. Reanalysis soil carbon, which was indirectly constrained based on modeled covariances, showed general agreement with SoilGrids, an independent soil carbon data product. Reanalysis NEE, which was constrained based on posterior ensemble weights, also showed good agreement with eddy flux tower NEE and reduced root mean square error (RMSE) compared to the calibrated forecast. Ultimately, PEcAn's new open-source regional data assimilation framework provides a scalable workflow for harmonizing multiple data constraints and providing a uniform synthetic platform for carbon monitoring, reporting, and verification (MRV) as well as accelerating terrestrial carbon cycle research.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Deep learning-accelerated 3D carbon storage reservoir pressure forecasting based on data assimilation using surface displacement from InSAR

Fast forecasting of the reservoir pressure distribution during geologic carbon storage (GCS) by assimilating monitoring data is a challenging problem. Due to high drilling cost, GCS projects usually have spatially sparse measurements from few wells, leading to high uncertainties in reservoir pressure prediction. To address this challenge, we use low-cost Interferometric Synthetic-Aperture Radar (InSAR) data as monitoring data to infer reservoir pressure build up. We develop a deep learning-accelerated workflow to assimilate surface displacement maps interpreted from InSAR and to forecast dynamic reservoir pressure. Employing an Ensemble Smoother Multiple Data Assimilation (ES-MDA) framework, the workflow updates three-dimensional (3D) geologic properties and predicts reservoir pressure with quantified uncertainties. We use a synthetic commercial-scale GCS model with bimodally distributed permeability and porosity to demonstrate the efficacy of the workflow. A two-step CNN-PCA approach is employed to parameterize the bimodal fields. The computational efficiency of the workflow is boosted by two residual U-Net based surrogate models for surface displacement and reservoir pressure predictions, respectively. The workflow can complete data assimilation and reservoir pressure forecasting in half an hour on a personal computer.

25 ENERGY STORAGE↗
DOE OSTI2024

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates

This work develops a new multi delity ensemble Kalman lter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multi delity extensions of the EnKF, where the uncertainty in coarser delities in the hierarchy of models represent control variates for the uncertainty in ner delities. Small ensembles of high delity model runs are com- plemented by larger ensembles of cheaper, lower delity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse delity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman lters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two- delity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Rock Physics-Based Data Assimilation of Integrated Continuous Active-Source Seismic and Pressure Monitoring Data during Geological Carbon Storage

Summary There has been substantial controversy concerning the role of geological carbon storage (GCS) in sequestering anthropogenic carbon emissions to mitigate climate change and global warming. Arguments center on the inability to monitor a geological storage site precisely and continuously, especially highlighting the associated costs and spatiotemporal trade-offs when using conventional subsurface monitoring techniques (well logs, core samples, chemical tracers, and 4D seismics). Active surveillance of GCS sites is essential for managing and mitigating potential leaks but is also required by regulation. With the goal of enhancing the monitoring capability at GCS sites, we present a rock physics-based joint data assimilation model to study a popular GCS site at Cranfield, Mississippi, USA. Synthetic continuous active-source seismic monitoring (CASSM) data (in the form of Vp and Qp measurements) and wellbore pressure monitoring data are assimilated with an ensemble of reservoir realizations to monitor gas saturation and reservoir pressure changes over a period of 100 years. Synthetic seismic attributes are generated using rock physics models (RPMs) and wellbore pressure monitoring data are extracted from the ground truth. Two assimilation methods, ensemble Kalman filter (EnKF) and ensemble Kalman smoother (EnKS), are tested in an observation system simulation experiment (OSSE) environment to assess the prediction accuracy of the individual and composite observation systems. The joint monitoring system achieves more accurate estimates of gas saturation and pressure, across the time span from start of injection to end of forecast, as compared to a single type of monitoring tool and irrespective of data assimilation algorithm choice. These results indicate that jointly assimilated data from two types of sensors (in this case, crosswell seismic and downhole pressure) may lead to a more risk-reducing monitoring design. One would expect that more data, vis-à-vis inclusion of a new sensor type, will improve the accuracy of any GCS monitoring system. However, from a practical standpoint, one important question is whether such a gain in accuracy is worth the additional cost associated with the new sensor. This paper focuses on quantifying the gain in accuracy, such that a practitioner can answer this question.

Engineering↗
DOE OSTI2023

Matrix Approach to Accelerate Spin-Up of CLM5

Numerical models have been developed to investigate and understand responses of biogeochemical cycle to global changes. Steady state, when a system is in dynamic equilibrium, is generally required to initialize these model simulations. However, the spin-up process that is used to achieve steady state pose a great burden to computational resources, limiting the efficiency of global modeling analysis on biogeochemical cycles. This study introduces a new Semi-Analytical Spin-Up (SASU) to tackle this grand challenge. We applied SASU to Community Land Model version 5 and examined its computational efficiency and accuracy. At the Brazil site, SASU is computationally 7 times more efficient than (or saved up to 86% computational cost in comparison with) the traditional native dynamics (ND) spin-up to reach the same steady state. Globally, SASU is computationally 8 times more efficient than the accelerated decomposition spin-up and 50 times more efficient than ND. In summary, SASU achieves the highest computational efficiency for spin-up on site and globally in comparison with other spin-up methods. It is generalizable to wide biogeochemical models and thus makes computationally costly studies (e.g., parameter perturbation ensemble analysis and data assimilation) possible for a better understanding of biogeochemical cycle under climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Assimilation of X-band Phased-Array Radar Data with EnKF for the Analysis and Warning Forecast of a Tornadic storm

The impact of assimilating China's operational X-band Phased-Array radar's (X-PAR) data on the analysis and warning forecast of the vortex structure and intensity of the June 8, 2018 Foshan, Guangdong province, tornadic storm was investigated for the first time using an Ensemble Kalman Filter (EnKF) data assimilation system. Both radar radial velocity (Vr) and reflectivity (Z) from two S-band operational radars and one X-PAR were assimilated. Deterministic forecasts were launched every 6 min from 05:42 UTC (20 min before the tornado touched down) to 06:00 UTC from the EnKF mean analysis field. Five experiments were conducted to examine the added capability of Z assimilation of the EnKF system, and to investigate the impact of assimilating X-PAR data on the analysis and prediction of the tornadic storm. Compared to the experiment without Z assimilation, the assimilation of Z reduced the analysis error and greatly reduced the forecast error of Z. Furthermore, the assimilation of X-PAR data greatly improved the vortex structure of the tornadic storm at low levels, and improved the intensity of the rear inflow of the tornadic storm, especially with a higher assimilation frequency. Compared to the experiments without X-PAR data assimilation, assimilating X-PAR data improved the predictability of tornadic storm.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A Constrained Data Assimilation Algorithm Based on GSI Hybrid 3D-EnVar and Its Application

Abstract Data assimilation (DA) at mesoscales is important for severe weather forecasts, yet the techniques of data assimilation at this scale remain a challenge. This study introduces dynamical constraints in the Gridpoint Statistical Interpolation (GSI) three-dimensional ensemble variational (3D-EnVar) data assimilation algorithm to enable the use of high-resolution surface observations of precipitation to improve atmospheric analysis at mesoscales. The constraints use the conservations of mass and moisture. Mass constraint suppresses the unphysical high-frequency oscillation, while moisture conservation constrains the atmospheric states to conform with the observed high-resolution precipitation. We show that the constrained data assimilation (CDA) algorithm significantly reduced the spurious residuals of the mass and moisture budgets compared to the original data assimilation (ODA). A case study is presented for a squall line over the Southern Great Plains on 20 May 2011 during Midlatitude Continental Convective Clouds Experiment (MC3E) of the Atmospheric Radiation Measurement (ARM) program by using ODA or CDA analysis as initial condition of forecasts. The state variables, and the location and intensity of the squall line are better simulated in the CDA experiment. Results show how surface observation of precipitation can be used to improve atmospheric analysis through data assimilation by using the dynamical constraints of mass and moisture conservations.

Wang, Jia↗
DOE OSTI2021

Developing High-Resolution Constrained Variational Analysis of Vertical Velocity and Advective Tendencies within the Range of ARM Scanning Radars at the SGP

Research progress has been made in two areas. One is about the incorporation of the ARM variationally constrained objective analysis method into the WRF GSI data assimilation system. The other is the development of high resolution ARM data and its applications. Specially, we developed a new data assimilation algorithm by adding dynamical constraints to the WRF GSI data assimilation system using hybrid ensemble variational system to derive 3-D fields of atmospheric dynamics and thermodynamics over the ARM SGP sites. We also developed 4x4 km high-resolution constrained variational analysis data over the SGP during the PECAN and made them available to the community. Details are in the attached report.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING↗
DOE OSTI2022

Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties

Abstract Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We use a convolutional adversarial autoencoder (CAAE) to parameterize a heterogeneous non‐Gaussian conductivity field via a low‐dimensional latent representation. A three‐dimensional dense convolutional encoder‐decoder (DenseED) network serves as a forward surrogate of the flow and transport model. The CAAE‐DenseED surrogate is fed into the ensemble smoother with multiple data assimilation (ESMDA) algorithm to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE‐DenseED‐ESMDA inversion framework. The resulting CAAE‐DenseED‐ESMDA inversion strategy is used to identify a three‐dimensional contaminant source and conductivity field. A comparison of the inversion results from CAAE‐ESMDA with physical flow and transport simulator and from CAAE‐DenseED‐ESMDA shows that the latter yields accurate reconstruction results at the fraction of the computational cost of the former.

Zhou, Zitong↗