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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Effect of data assimilation in the Polar WRF with 3DVAR on the prediction of radiation, heat flux, cloud, and near surface atmospheric variables over Svalbard

Although the Polar Weather Research and Forecasting (PWRF) model has been developed for polar environments, simulations of atmospheric states in the polar region still have large uncertainties. Therefore, the effects of data assimilation (DA) to improve forecasts in the polar region were investigated for September 2017 using PWRF and the three-dimensional variational (3DVAR) DA method. The experiments without DA and those with DA assimilating only conventional observations and both conventional observations and satellite radiance data were performed. The forecasts from all experiments both without and with DA underestimated (overestimated) the downward longwave (shortwave) radiation flux due to the underestimation of the amount of Arctic clouds. When satellite radiance data (i.e., the Advanced Microwave Sounding Unit-A (AMSU-A) and Microwave Humidity Sounder (MHS)) were assimilated in addition to conventional observations in the PWRF, the distribution and amount of water vapor became closer to observations, which improves cloud liquid water forecasts. Therefore, when both conventional observations and radiance data were assimilated, the 25–30 h forecast errors of the downward longwave and shortwave radiation fluxes and sensible and latent heat fluxes decreased by 12.7%, 8.1%, 3.2%, and 7.8% with the WSM5 scheme and by 17.1%, 4.7%, 2.5%, and 3.1% with the 2-moment Morrison scheme, respectively, compared to those in the experiments without DA. The forecast errors of the 10 m wind and 2 m temperature with DA were smaller than those without DA at most observation stations. Therefore, the uncertainties of the Arctic forecasts in the PWRF decreased when using DA. To further improve Arctic forecasts, the assimilation of various additional satellite data is necessary.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Applications of Ensemble-based Data Assimilation Techniques for Aquifer Characterization using Tracer Data at Hanford 300 Area

Subsurface aquifer characterization often involves high parameter dimensionality and requires tremendous computational resources if employing a full Bayesian approach. Ensemble-based data assimilation techniques, including filtering and smoothing, are computationally efficient alternatives. Despite the increasing number of applications of ensemble-based methods in assimilating flow and transport related data for subsurface aquifer charaterization, most are limited to either synthetic studies or two-dimensional problems. In this study, we applied ensemble-based techniques for assimilating field tracer experimental data obtained from the Integrated Field Research Challenge (IFRC) site at the Hanford 300 Area. The forward problem was simulated using the massively-parallel three-dimensional flow and transport code PFLOTRAN to effectively deal with the highly transient flow boundary conditions at the site and to meet the computational demands of ensemble-based methods. This study demonstrates the effectiveness of ensemble-based methods for characterizing a heterogeneous aquifer by sequentially assimilating multiple types of data. The necessity of employing high performance computing is shown to enable increasingly mechanistic non-linear forward simulations to be performed within the data assimilation framework for a complex system with reasonable turnaround time.

data assimilation, ensemble kalman filter, inverse↗
DOE OSTI2020

New perspectives on butyrate assimilation in Rhodospirillum rubrum S1H under photoheterotrophic conditions

Background: The great metabolic versatility of the purple non-sulfur bacteria is of particular interest in green technology. Rhodospirillum rubrum S1H is an α-proteobacterium that is capable of photoheterotrophic assimilation of volatile fatty acids (VFAs). Butyrate is one of the most abundant VFAs produced during fermentative biodegradation of crude organic wastes in various applications. While there is a growing understanding of the photoassimilation of acetate, another abundantly produced VFA, the mechanisms involved in the photoheterotrophic metabolism of butyrate remain poorly studied. Results: In this work, we used proteomic and functional genomic analyses to determine potential metabolic pathways involved in the photoassimilation of butyrate. We propose that a fraction of butyrate is converted to acetyl-CoA, a reaction shared with polyhydroxybutyrate metabolism, while the other fraction supplies the ethylmalonyl-CoA (EMC) pathway used as an anaplerotic pathway to replenish the TCA cycle. Surprisingly, we also highlighted a potential assimilation pathway, through isoleucine synthesis and degradation, allowing the conversion of acetyl-CoA to propionyl-CoA. We tentatively named this pathway the methylbutanoyl-CoA pathway (MBC). An increase in isoleucine abundance was observed during the early growth phase under butyrate condition. Nevertheless, while the EMC and MBC pathways appeared to be concomitantly used, a genome-wide mutant fitness assay highlighted the EMC pathway as the only pathway strictly required for the assimilation of butyrate. Conclusion: Photoheterotrophic growth of Rs. rubrum with butyrate as sole carbon source requires a functional EMC pathway. In addition, a new assimilation pathway involving isoleucine synthesis and degradation, named the methylbutanoyl-CoA (MBC) pathway, could also be involved in the assimilation of this volatile fatty acid by Rs. rubrum.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order solution is that reduced order Karush–Kuhn–Tucker conditions accurately represent their full order counterparts. In particular, accurate reduced order approximations are needed for the forward and adjoint dynamical models, as well as for the reduced gradient. New strategies to construct reduced order based are developed for proper orthogonal decomposition (POD) ROM data assimilation using both Galerkin and Petrov–Galerkin projections. For the first time POD, tensorial POD, and discrete empirical interpolation method (DEIM) are employed to develop reduced data assimilation systems for a geophysical flow model, namely, the two dimensional shallow water equations. Numerical experiments confirm the theoretical framework for Galerkin projection. In the case of Petrov–Galerkin projection, stabilization strategies must be considered for the reduced order models. The new reduced order shallow water data assimilation system provides analyses similar to those produced by the full resolution data assimilation system in one tenth of the computational time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Ensemble‐Based Assimilation of Satellite All‐Sky Microwave Radiances Improves Intensity and Rainfall Predictions for Hurricane Harvey (2017)

Abstract Ensemble‐based data assimilation of radar observations across inner‐core regions of tropical cyclones (TCs) in tandem with satellite all‐sky infrared (IR) radiances across the TC domain improves TC track and intensity forecasts. This study further investigates potential enhancements in TC track, intensity, and rainfall forecasts via assimilation of all‐sky microwave (MW) radiances using Hurricane Harvey (2017) as an example. Assimilating Global Precipitation Measurement constellation all‐sky MW radiances in addition to GOES‐16 all‐sky IR radiances reduces the forecast errors in the TC track, rapid intensification (RI), and peak intensity compared to assimilating all‐sky IR radiances alone, including a 24‐hr increase in forecast lead‐time for RI. Assimilating all‐sky MW radiances also improves Harvey's hydrometeor fields, which leads to improved forecasts of rainfall after Harvey's landfall. This study indicates that avenues exist for producing more accurate forecasts for TCs using available yet underutilized data, leading to better warnings of and preparedness for TC‐associated hazards in the future.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows

In the past couple of years, there has been a proliferation in the use of machine learning approaches to represent subgrid-scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical simulations of these flows. Despite its success for different types of flow, the online deployment of a data-driven closure model can cause instabilities and biases in modeling the overall effect of subgrid-scale processes, which in turn leads to inaccurate prediction. To tackle this issue, we exploit the data assimilation technique to correct the physics-based model coupled with the neural network as a surrogate for unresolved flow dynamics in multiscale systems. In particular, we use a set of neural network architectures to learn the correlation between resolved flow variables and the parametrizations of unresolved flow dynamics and formulate a data assimilation approach to correct the hybrid model during their online deployment. We illustrate our framework in a set of applications of the multiscale Lorenz 96 system for which the parametrization model for unresolved scales is exactly known, and the two-dimensional Kraichnan turbulence system for which the parametrization model for unresolved scales is not known a priori. Our analysis, therefore, comprises a predictive dynamical core empowered by (i) a data-driven closure model for subgrid-scale processes, (ii) a data assimilation approach for forecast error correction, and (iii) both data-driven closure and data assimilation procedures. We show significant improvement in the long-term prediction of the underlying chaotic dynamics with our framework compared to using only neural network parametrizations for future prediction. Moreover, we demonstrate that these data-driven parametrization models can handle the non-Gaussian statistics of subgrid-scale processes, and effectively improve the accuracy of outer data assimilation workflow loops in a modular nonintrusive way.

42 ENGINEERING↗
DOE OSTI2022

Bacterial community dynamics explain carbon mineralization and assimilation in soils of different land-use history

Soil dwelling microorganisms are key players in the terrestrial carbon cycle, driving both the degradation and stabilization of soil organic matter. Bacterial community structure and function vary with respect to land use; yet the ecological drivers of this variation remain poorly described and difficult to predict. For this work, we conducted a multi-substrate DNA-stable isotope probing experiment across cropland, old-field, and forest habitats to link carbon mineralization dynamics with the dynamics of bacterial growth and carbon assimilation. We tracked the movement of 13 C derived from five distinct carbon sources as it was assimilated into bacterial DNA over time. We show that carbon mineralization, community composition, and carbon assimilation dynamics all differed with respect to land use. We also show that microbial community dynamics affect carbon assimilation dynamics and are associated with soil DNA content. Soil DNA yield is easy to measure and may be useful in predicting microbial community dynamics linked to soil carbon cycling. Soil dwelling microorganisms are key players in the terrestrial carbon cycle, driving both the degradation and stabilization of soil organic matter. Microbial communities vary with respect to land use, but we still have an incomplete understanding of how variation in community structure links to variation in community function. DNA stable isotope probing (DNA-SIP) is a high-resolution method that can identify specific microbial taxa that assimilate carbon in situ. We conducted a large-scale multi-substrate DNA-SIP experiment to explore differences in bacterial activity across land-use regimes. We show that microbial community dynamics vary with land use, that these dynamics are linked to soil carbon cycling, and that they are associated with easily measured soil properties.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Benefits and Cautions in Data Assimilation Strategies: An Example of Modeling Groundwater Recharge

Assimilating recent observations improves model outcomes for real-time assessments of groundwater processes. This is demonstrated in estimating time-varying recharge to a shallow fractured-rock aquifer in response to precipitation. Results from estimating the time-varying water-table altitude (h) and recharge, and their error covariances, are compared for forecasting, filtering, and fixed-lag smoothing (FLS), which are implemented using the Kalman Filter as applied to a data-driven, mechanistic model of recharge. Forecasting uses past observations to predict future states and is the current paradigm in most groundwater modeling investigations; filtering assimilates observations up to the current time to estimate current states; and FLS estimates states following a time lag over which additional observations are collected. Results for forecasting yield a large error covariance relative to the magnitude of the expected recharge. With assimilating recent observations of h, filtering and FLS produce estimates of recharge that better represent time-varying observations of h and reduce uncertainty in comparison to forecasting. Although model outcomes from applying data assimilation through filtering or FLS reduce model uncertainty, they are not necessarily mass conservative, whereas forecasting outcomes are mass conservative. Mass conservative outcomes from forecasting are not necessarily more accurate, because process errors are inherent in any model. Improvements in estimating real-time groundwater conditions that better represent observations need to be weighed for the model application against outcomes with inherent process deficiencies. In conclusion, results from data assimilation strategies discussed in this investigation are anticipated to be relevant to other groundwater processes models where system states are sensitive to system inputs.

aquifer recharge↗
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 OSTI2016

Sampling, feasibility, and priors in data assimilation

Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at relatively low cost, making the assimilation more efficient. A new analysis of the feasibility of data assimilation is presented, showing in detail why feasibility depends on the Frobenius norm of the covariance matrix of the noise and not on the number of variables. A discussion of the convergence of particular particle filters follows. A major open problem in numerical data assimilation is the determination of appropriate priors, a progress report on recent work on this problem is given. The analysis highlights the need for a careful attention both to the data and to the physics in data assimilation problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Data Assimilation in the ADAPT Photospheric Flux Transport Model

Global maps of the solar photospheric magnetic flux are fundamental drivers for simulations of the corona and solar wind and therefore are important predictors of geoeffective events. However, observations of the solar photosphere are only made intermittently over approximately half of the solar surface. The Air Force Data Assimilative Photospheric Flux Transport (ADAPT) model uses localized ensemble Kalman filtering techniques to adjust a set of photospheric simulations to agree with the available observations. At the same time, this information is propagated to areas of the simulation that have not been observed. ADAPT implements a local ensemble transform Kalman filter (LETKF) to accomplish data assimilation, allowing the covariance structure of the flux-transport model to influence assimilation of photosphere observations while eliminating spurious correlations between ensemble members arising from a limited ensemble size. We give a detailed account of the implementation of the LETKF into ADAPT. Advantages of the LETKF scheme over previously implemented assimilation methods are highlighted.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

On the feasibility of monitoring carbon monoxide in the lower troposphere from a constellation of northern hemisphere geostationary satellites: Global scale assimilation experiments (Part II)

In this paper, we describe the second phase of an Observing System Simulation Experiment (OSSE) that utilizes the synthetic measurements from a constellation of satellites measuring atmospheric composition from geostationary (GEO) Earth orbit presented in part I of the study. Our OSSE is focused on carbon monoxide observations over North America, East Asia and Europe where most of the anthropogenic sources are located. Here we assess the impact of a potential GEO constellation on constraining northern hemisphere (NH) carbon monoxide (CO) using data assimilation. We show how cloud cover affects the GEO constellation data density with the largest cloud cover (i.e., lowest data density) occurring during Asian summer. We compare the modeled state of the atmosphere (Control Run), before CO data assimilation, with the known “true” state of the atmosphere (Nature Run) and show that our setup provides realistic atmospheric CO fields and emission budgets. Overall, the Control Run underestimates CO concentrations in the northern hemisphere, especially in areas close to CO sources. Assimilation experiments show that constraining CO close to the main anthropogenic sources significantly reduces errors in NH CO compared to the Control Run. We assess the changes in error reduction when only single satellite instruments are available as compared to the full constellation. We find large differences in how measurements for each continental scale observation system affect the hemispherical improvement in long-range transport patterns, especially due to seasonal cloud cover. Finally, a GEO constellation will provide the most efficient constraint on NH CO during winter when CO lifetime is longer and increments from data assimilation associated with source regions are advected further around the globe.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

DART-PFLOTRAN: An ensemble-based data assimilation system for estimating subsurface flow and transport model parameters

Ensemble-based Data Assimilation (EDA), based on the Monte Carlo approach, has been effectively applied to estimate model parameters through inverse modeling in subsurface flow and transport problems. However, implementation of EDA approach involves a complicated workflow that include setting up and executing ensemble forward model simulations, processing observations and model simulation results for parameter updates, and repeat for sequential or iterative EDA. To facilitate the management of such workflow and lower the barriers for adopting EDA-based parameter estimation in subsurface science, we develop a generic software frame-work linking the Data Assimilation Research Testbed (DART) with a massively parallel subsurface FLOw and TRANsport code PFLOTRAN. The new DART-PFLOTRAN leverages both the core data assimilation engines in DART and the computational power afforded by PFLOTRAN. In addition to the standard smoother and filtering options, DART-PFLOTRAN enables an iterative EDA workflow based on the Ensemble Smoother for Multiple Data Assimilation method (ES-MDA) to improve estimation accuracy for nonlinear forward problems. Here, we verify the implementation of ES-MDA in DART-PFLOTRAN using two synthetic cases designed to estimate static permeability and dynamic exchange fluxes across the riverbed, respectively, from continuous temperature measurements made across a depth profile. One-dimensional hydro-thermal simulations are performed in both cases to relate temperature responses with the parameters of interest. In the case of estimating dynamic parameters, we demonstrate the flexibility of DART-PFLOTRAN in automating sequential ES-MDA workflow, which will significantly reduce the time researchers spend on managing complex workflows in similar applications. Both studies yield accurate estimations of the parameters compared to their synthetic truth, while ES-MDA leads to more accurate estimation when a high level of nonlinearity exist between observed responses and unknown parameters. With a code base in Python and Fortran, DART-PFLOTRAN paves the way for applications in large-scale subsurface inverse modeling by automating the complex workflow of sequential ES-MDA that can be executed on various computing platforms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A deep learning-accelerated data assimilation and forecasting workflow for commercial-scale geologic carbon storage

Fast assimilation of monitoring data to update forecasts of pressure buildup and carbon dioxide (CO 2 ) plume migration under geologic uncertainties is a challenging problem in geologic carbon storage. The high computational cost of data assimilation with a high-dimensional parameter space impedes fast decision-making for commercial-scale reservoir management. We propose to leverage physical understandings of porous medium flow behavior with deep learning techniques to develop a fast data assimilation-reservoir response forecasting workflow. Applying an Ensemble Smoother Multiple Data Assimilation (ES-MDA) framework, the workflow updates geologic properties and predicts reservoir performance with quantified uncertainty from pressure history and CO 2 plumes interpreted through seismic inversion. As the most computationally expensive component in such a workflow is reservoir simulation, we developed surrogate models to predict dynamic pressure and CO 2 plume extents under multi-well injection. The surrogate models employ deep convolutional neural networks, specifically, a wide residual network and a residual U-Net. The workflow is validated against a flat threedimensional reservoir model representative of a clastic shelf depositional environment. Intelligent treatments are applied to bridge between quantities in a true-3D reservoir model and those in a single-layer reservoir model. The workflow can complete history matching and reservoir forecasting with uncertainty quantification in less than one hour on a mainstream personal workstation.

25 ENERGY STORAGE↗
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 OSTI2022

The impact of multi-sensor land data assimilation on river discharge estimation

River discharge is one of the most critical renewable water resources. Accurately estimating river discharge with land surface models (LSMs) remains challenging due to the difficulty in estimating land water storages such as snow, soil moisture, and groundwater. While data assimilation (DA) ingesting optical, microwave, and gravity measurements from space can help constrain theses storage states, its impacts on runoff and eventually river discharge are not fully understood. In this study, by taking advantage of recently published land DA results that jointly assimilate eight different combinations of observations from the Moderate Resolution Imaging Spectroradiometer (MODIS), Gravity Recovery and Climate Experiment (GRACE), and Advanced Microwave Scanning Radiometer for EOS (AMSR-E), we quantify to what degree multi-sensor land DA improves the river discharge simulation skills over 40 global river basins, and investigate the complementary strengths of different satellite measurements on river discharge. To be more specific, river discharge is updated by feeding gridded runoff from the eight multi-sensor DA simulations into a vector-based river routing model named the Routing Application for Parallel computatIon of Discharge (RAPID). Our modeling results, including 7-year simulations at 177,458 river reaches globally, are used to study the seasonal to interannual variability of river discharge. It is found that assimilating GRACE has the greatest impact on global runoff patterns, leading to the most pronounced improvements in spatial river discharge in the middle and high latitudes with the R 2 increased by 0.16. The seasonal variation of spatial discharge is most skillful during the boreal summer. However, our evaluation also shows model and DA still struggle to generate reasonable variability and averaged discharge over permafrost regions. Finally, by assessing how different satellites add value to discharge forecasts, this study paves the way for more advanced multi-sensor satellite data assimilation to predict the terrestrial hydrological cycle.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Feature-based Data Assimilation in Geophysics

Many applications in science require that computational models and data be combined. In a Bayesian framework, this is usually done by denying likelihoods based on the mismatch of model outputs and data. However, matching model outputs and data in this way can be unnecessary or impossible. Using large amounts of steady state data is unnecessary because these data are redundant. It is impossible to assimilate data of complex systems into low-dimensional models, or to assimilate data, collected over long time scales, into chaotic models. One can address these issues by denying likelihoods based on suitable low-dimensional \features" of the data, rather than by the mismatch of model output and \raw" data. Our goal is to contribute to a more fundamental understanding of such a feature-based approach to data assimilation. We present noise models based on perturbed observations to de ne feature-based likelihood functions that lead to computationally efficient solutions. We also explain how a feature-based approach enables us to effectively assimilate selected aspects of data into models, and how this can be interpreted by a reduction in effective dimension. Numerical implementation of these ideas are illustrated in four examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Conditions for successful data assimilation

We show, using idealized models, that numerical data assimilation can be successful only if an effective dimension of the problem is not excessive. This effective dimension depends on the noise in the model and the data, and in physically reasonable problems, it can be moderate even when the number of variables is huge. We then analyze several data assimilation algorithms, including particle filters and variational methods. We show that well-designed particle filters can solve most of those data assimilation problems that can be solved in principle and compare the conditions under which variational methods can succeed to the conditions required of particle filters. We also discuss the limitations of our analysis. Key Points Data assimilation is feasible only if an effective dimension is moderate. The effective dimension is moderate, if the noise satisfies a balance condition. Particle filters can work, even if the dimension of the problem is large.

Chorin, Alexandre J.↗