scholarly journals Data assimilation for nonlinear systems with a hybrid nonlinear‐Kalman ensemble transform filter

2021 ◽  
Author(s):  
Lars Nerger
Keyword(s):  
Nonlinear Systems ◽  
Data Assimilation ◽  
Ensemble Transform

scholarly journals Gain Form of the Ensemble Transform Kalman Filter and Its Relevance to Satellite Data Assimilation with Model Space Ensemble Covariance Localization

2017 ◽  
Vol 145 (11) ◽  
pp. 4575-4592 ◽  
Author(s):  
Craig H. Bishop ◽  
Jeffrey S. Whitaker ◽  
Lili Lei
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Satellite Data ◽  
Localization Length ◽  
Model Space ◽  
Ensemble Size ◽  
Length Scales ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Expanded Ensemble

To ameliorate suboptimality in ensemble data assimilation, methods have been introduced that involve expanding the ensemble size. Such expansions can incorporate model space covariance localization and/or estimates of climatological or model error covariances. Model space covariance localization in the vertical overcomes problematic aspects of ensemble-based satellite data assimilation. In the case of the ensemble transform Kalman filter (ETKF), the expanded ensemble size associated with vertical covariance localization would also enable the simultaneous update of entire vertical columns of model variables from hyperspectral and multispectral satellite sounders. However, if the original formulation of the ETKF were applied to an expanded ensemble, it would produce an analysis ensemble that was the same size as the expanded forecast ensemble. This article describes a variation on the ETKF called the gain ETKF (GETKF) that takes advantage of covariances from the expanded ensemble, while producing an analysis ensemble that has the required size of the unexpanded forecast ensemble. The approach also yields an inflation factor that depends on the localization length scale that causes the GETKF to perform differently to an ensemble square root filter (EnSRF) using the same expanded ensemble. Experimentation described herein shows that the GETKF outperforms a range of alternative ETKF-based solutions to the aforementioned problems. In cycling data assimilation experiments with a newly developed storm-track version of the Lorenz-96 model, the GETKF analysis root-mean-square error (RMSE) matches the EnSRF RMSE at shorter than optimal localization length scales but is superior in that it yields smaller RMSEs for longer localization length scales.

scholarly journals Estimating Surface Carbon Fluxes Based on a Local Ensemble Transform Kalman Filter with a Short Assimilation Window and a Long Observation Window

2017 ◽  
Author(s):  
Yun Liu ◽  
Eugenia Kalnay ◽  
Ning Zeng ◽  
Ghassem Asrar ◽  
Zhaohui Chen ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Grid Point ◽  
Carbon Fluxes ◽  
Transfer Model ◽  
Observation Window ◽  
Surface Carbon ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Assimilation System

Abstract. We developed a Carbon data assimilation system to estimate the surface carbon fluxes using the Local Ensemble Transform Kalman Filter and atmospheric transfer model of GEOS-Chem driven by the MERRA-1 reanalysis of the meteorological fields based on the Goddard Earth Observing System Model, Version 5 (GEOS-5). This assimilation system is inspired by the method of Kang et al. [2011, 2012], who estimated the surface carbon fluxes in an Observing System Simulation Experiment (OSSE) mode, as evolving parameters in the assimilation of the atmospheric CO2, using a short assimilation window of 6 hours. They included the assimilation of the standard meteorological variables, so that the ensemble provided a measure of the uncertainty in the CO2 transport. After introducing new techniques such as variable localization, and increased observation weights near the surface, they obtained accurate carbon fluxes at grid point resolution. We developed a new version of the LETKF related to the Running-in-Place (RIP) method used to accelerate the spin-up of EnKF data assimilation [Kalnay and Yang, 2010; Wang et al., 2013, Yang et al., 2014]. Like RIP, the new assimilation system uses the no-cost smoothing algorithm for the LETKF [Kalnay et al., 2007b], which allows shifting at no cost the Kalman Filter solution forward or backward within an assimilation window. In the new scheme a long observation window (e.g., 7-days or longer) is used to create an LETKF ensemble at 7-days. Then, the RIP smoother is used to obtain an accurate final analysis at 1-day. This analysis has the advantage of being based on a short assimilation window, which makes it more accurate, and of having been exposed to the future 7-days observations, which accelerates the spin up. The assimilation and observation windows are then shifted forward by one day, and the process is repeated. This reduces significantly the analysis error, suggesting that this method could be used in other data assimilation problems.

scholarly journals Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling

2018 ◽  
Vol 25 (4) ◽  
pp. 731-746 ◽  
Author(s):  
Sangeetika Ruchi ◽  
Svetlana Dubinkina
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Particle Filter ◽  
Reservoir Modeling ◽  
Model Parameters ◽  
Uncertain Parameters ◽  
Initial Ensemble ◽  
Leading Mode ◽  
Ensemble Transform

Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable Markov chain Monte Carlo (MCMC) methods are computationally expensive. Sequential ensemble methods such as ensemble Kalman filters and particle filters provide a favorable alternative. However, ensemble Kalman filter has an assumption of Gaussianity. Ensemble transform particle filter does not have this assumption and has proven to be highly beneficial for an initial condition estimation and a small number of parameter estimations in chaotic dynamical systems with non-Gaussian distributions. In this paper we employ ensemble transform particle filter (ETPF) and ensemble transform Kalman filter (ETKF) for parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain parameters and compare them to importance sampling (IS). The large number of uncertain parameters is of particular interest for subsurface reservoir modeling as it allows us to parameterize permeability on the grid. We prove that the updated parameters obtained by ETPF lie within the range of an initial ensemble, which is not the case for ETKF. We examine the performance of ETPF and ETKF in a twin experiment setup, where observations of pressure are synthetically created based on the known values of parameters. For a small number of uncertain parameters (one and five) ETPF performs comparably to ETKF in terms of the mean estimation. For a large number of uncertain parameters (2500) ETKF is robust with respect to the initial ensemble, while ETPF is sensitive due to sampling error. Moreover, for the high-dimensional test problem ETPF gives an increase in the root mean square error after data assimilation is performed. This is resolved by applying distance-based localization, which however deteriorates a posterior estimation of the leading mode by largely increasing the variance due to a combination of less varying localized weights, not keeping the imposed bounds on the modes via the Karhunen–Loeve expansion, and the main variability explained by the leading mode. A possible remedy is instead of applying localization to use only leading modes that are well estimated by ETPF, which demands knowledge of which mode to truncate.

scholarly journals Volcanic ash forecast using ensemble-based data assimilation: the Ensemble Transform Kalman Filter coupled with FALL3D-7.2 model (ETKF-FALL3D, version 1.0)

2019 ◽  
Author(s):  
Soledad Osores ◽  
Juan Ruiz ◽  
Arnau Folch ◽  
Estela Collini
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Volcanic Ash ◽  
Source Parameters ◽  
Joint Estimation ◽  
Volcanic Ash Cloud ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Ash Cloud ◽  
Ash Dispersal

Abstract. Quantitative volcanic ash cloud forecasts are prone to uncertainties coming from the source term quantification (e.g. eruption strength or vertical distribution of the emitted particles), with consequent implications on operational ash impact assessment. We present an ensemble-based data assimilation and forecast system for volcanic ash dispersal and deposition aimed at reducing uncertainties related to eruption source parameters. The FALL3D atmospheric dispersal model is coupled with the Ensemble Transform Kalman Filter (ETKF) data assimilation technique by combining ash mass loading observations with ash dispersal simulations in order to obtain a better joint estimation of 3D ash concentration and source parameters. The ETKF-FALL3D data assimilation system is evaluated performing Observation System Simulation Experiments (OSSE) in which synthetic observations of fine ash mass loadings are assimilated. The evaluation of the ETKF-FALL3D system considering reference states of steady and time-varying eruption source parameters shows that the assimilation process gives both better estimations of ash concentration and time-dependent optimized values of eruption source parameters. The joint estimation of concentrations and source parameters leads to a better analysis and forecast of the 3D ash concentrations. Results show the potential of the methodology to improve volcanic ash cloud forecasts in operational contexts.

scholarly journals A Second-Order Exact Ensemble Square Root Filter for Nonlinear Data Assimilation

2015 ◽  
Vol 143 (4) ◽  
pp. 1347-1367 ◽  
Author(s):  
Julian Tödter ◽  
Bodo Ahrens
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Second Order ◽  
Square Root ◽  
Computationally Efficient ◽  
Research Activities ◽  
Wide Range ◽  
Matrix Square Root ◽  
Non Gaussian ◽  
Ensemble Transform

Abstract The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational data assimilation schemes and are applied in a wide range of operational and research activities. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the analysis mean and covariance are biased, and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) only relies on Bayes’s theorem, which guarantees an exact asymptotic behavior, but because of the so-called curse of dimensionality it is exposed to weight collapse. Here, it is shown how to obtain a new analysis ensemble whose mean and covariance exactly match the Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The properties and performance of the proposed algorithm are further investigated via a set of experiments. They indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. Localization enhances the potential applicability of this PF-inspired scheme in larger-dimensional systems. The proposed algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF).

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