scholarly journals Accounting for Skewness in Ensemble Data Assimilation

2012 ◽  
Vol 140 (7) ◽  
pp. 2346-2358 ◽  
Author(s):  
Daniel Hodyss
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Prior Distribution ◽  
State Of The Art ◽  
New Technique ◽  
Central Feature ◽  
Ensemble Size ◽  
Boussinesq Model ◽  
The Third

Abstract A practical data assimilation algorithm is presented that explicitly accounts for skewness in the prior distribution. The algorithm operates as a global solve (all observations are considered at once) using a minimization-based approach and Schur–Hadamard (elementwise) localization. The central feature of this technique is the squaring of the innovation and the ensemble perturbations so as to create an extended state space that accounts for the second, third, and fourth moments of the prior distribution. This new technique is illustrated in a simple scalar system as well as in a Boussinesq model configured to simulate nonlinearly evolving shear instabilities (Kelvin–Helmholtz waves). It is shown that an ensemble size of at least 100 members is needed to adequately resolve the third and fourth moments required for the algorithm. For ensembles of this size it is shown that this new technique is superior to a state-of-the-art ensemble Kalman filter in situations with significant skewness; otherwise, the new algorithm reduces to the performance of the ensemble Kalman filter.

scholarly journals Optimal ensemble size of ensemble Kalman filter in sequential soil moisture data assimilation

2015 ◽  
Vol 42 (16) ◽  
pp. 6710-6715 ◽  
Author(s):  
Jifu Yin ◽  
Xiwu Zhan ◽  
Youfei Zheng ◽  
Christopher R. Hain ◽  
Jicheng Liu ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Ensemble Size ◽  
Soil Moisture Data ◽  
Optimal Ensemble

Using the (3N)-dimensional generalized Lorenz systems as a testbed for data assimilation: The ensemble Kalman filter

2021 ◽  
Author(s):  
Sungju Moon ◽  
Jong-Jin Baik
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Lorenz System ◽  
Ensemble Size ◽  
Flexible Tool ◽  
Generalized System ◽  
Generalized Lorenz System ◽  
The Lorenz System ◽  
True System

AbstractThe feasibility of using a (3N)-dimensional generalization of the Lorenz system in testing a traditional implementation of the ensemble Kalman filter is explored through numerical experiments. The generalization extends the Lorenz system, known as the Lorenz ’63 model, into a (3N)-dimensional nonlinear system for any positive integer N. Because the extension involves inclusion of additional wavenumber modes, raising the dimension allows the system to resolve smaller-scale motions, a unique characteristic of the present generalization that can be relevant to real modeling scenarios. Model imperfections are simulated by assuming a high-dimensional generalized Lorenz system as the true system and a generalized system of dimension less than or equal to the dimension of the true system as the model system. Different scenarios relevant to data assimilation practices are simulated by varying the dimensional-differences between the model and true systems, ensemble size, and observation frequency and accuracy. It is suggested that the present generalization of the Lorenz system is an interesting and flexible tool for evaluating the effectiveness of data assimilation methods and a meaningful addition to the portfolio of testbed systems that includes the Lorenz ’63 and ’96 models, especially considering its relationship with the Lorenz ’63 model. The results presented in this study can serve as useful benchmarks for testing other data assimilation methods besides the ensemble Kalman filter.

scholarly journals Assessment of multilevel ensemble-based data assimilation for reservoir history matching

2019 ◽  
Vol 24 (1) ◽  
pp. 217-239
Author(s):  
Kristian Fossum ◽  
Trond Mannseth ◽  
Andreas S. Stordal
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Computational Cost ◽  
Ensemble Size ◽  
Matching Problems ◽  
Reservoir Models ◽  
Reservoir History Matching ◽  
Computational Resources

AbstractMultilevel ensemble-based data assimilation (DA) as an alternative to standard (single-level) ensemble-based DA for reservoir history matching problems is considered. Restricted computational resources currently limit the ensemble size to about 100 for field-scale cases, resulting in large sampling errors if no measures are taken to prevent it. With multilevel methods, the computational resources are spread over models with different accuracy and computational cost, enabling a substantially increased total ensemble size. Hence, reduced numerical accuracy is partially traded for increased statistical accuracy. A novel multilevel DA method, the multilevel hybrid ensemble Kalman filter (MLHEnKF) is proposed. Both the expected and the true efficiency of a previously published multilevel method, the multilevel ensemble Kalman filter (MLEnKF), and the MLHEnKF are assessed for a toy model and two reservoir models. A multilevel sequence of approximations is introduced for all models. This is achieved via spatial grid coarsening and simple upscaling for the reservoir models, and via a designed synthetic sequence for the toy model. For all models, the finest discretization level is assumed to correspond to the exact model. The results obtained show that, despite its good theoretical properties, MLEnKF does not perform well for the reservoir history matching problems considered. We also show that this is probably caused by the assumptions underlying its theoretical properties not being fulfilled for the multilevel reservoir models considered. The performance of MLHEnKF, which is designed to handle restricted computational resources well, is quite good. Furthermore, the toy model is utilized to set up a case where the assumptions underlying the theoretical properties of MLEnKF are fulfilled. On that case, MLEnKF performs very well and clearly better than MLHEnKF.

Data assimilation with the weighted ensemble Kalman filter

2010 ◽  
Author(s):  
Nicolas Papadakis ◽  
Etienne Mémin ◽  
Anne Cuzol ◽  
Nicolas Gengembre
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter

scholarly journals Parameters Estimation and Prediction of Water Movement and Solute Transport in Layered, Variably Saturated Soils Using the Ensemble Kalman Filter

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1520
Author(s):  
Zheng Jiang ◽  
Quanzhong Huang ◽  
Gendong Li ◽  
Guangyong Li
Keyword(s):  
Kalman Filter ◽  
Solute Transport ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Parameters Estimation ◽  
Saturated Soils ◽  
Hydrological Models ◽  
State Variables ◽  
Ensemble Size ◽  
Highly Nonlinear

The parameters of water movement and solute transport models are essential for the accurate simulation of soil moisture and salinity, particularly for layered soils in field conditions. Parameter estimation can be achieved using the inverse modeling method. However, this type of method cannot fully consider the uncertainties of measurements, boundary conditions, and parameters, resulting in inaccurate estimations of parameters and predictions of state variables. The ensemble Kalman filter (EnKF) is well-suited to data assimilation and parameter prediction in Situations with large numbers of variables and uncertainties. Thus, in this study, the EnKF was used to estimate the parameters of water movement and solute transport in layered, variably saturated soils. Our results indicate that when used in conjunction with the HYDRUS-1D software (University of California Riverside, California, CA, USA) the EnKF effectively estimates parameters and predicts state variables for layered, variably saturated soils. The assimilation of factors such as the initial perturbation and ensemble size significantly affected in the simulated results. A proposed ensemble size range of 50–100 was used when applying the EnKF to the highly nonlinear hydrological models of the present study. Although the simulation results for moisture did not exhibit substantial improvement with the assimilation, the simulation of the salinity was significantly improved through the assimilation of the salinity and relative solutetransport parameters. Reducing the uncertainties in measured data can improve the goodness-of-fit in the application of the EnKF method. Sparse field condition observation data also benefited from the accurate measurement of state variables in the case of EnKF assimilation. However, the application of the EnKF algorithm for layered, variably saturated soils with hydrological models requires further study, because it is a challenging and highly nonlinear problem.

Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea

2016 ◽  
Vol 66 (8) ◽  
pp. 955-971 ◽  
Author(s):  
Stéphanie Ponsar ◽  
Patrick Luyten ◽  
Valérie Dulière
Keyword(s):  
Kalman Filter ◽  
Numerical Model ◽  
Data Assimilation ◽  
North Sea ◽  
Ensemble Kalman Filter ◽  
The North ◽  
The North Sea

An ensemble Kalman filter data assimilation system for the martian atmosphere: Implementation and simulation experiments

Icarus ◽  
2010 ◽  
Vol 209 (2) ◽  
pp. 470-481 ◽  
Author(s):  
Matthew J. Hoffman ◽  
Steven J. Greybush ◽  
R. John Wilson ◽  
Gyorgyi Gyarmati ◽  
Ross N. Hoffman ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Martian Atmosphere ◽  
Simulation Experiments ◽  
Data Assimilation System ◽  
Assimilation System

scholarly journals Non-linear wave data assimilation with an ANN-type wind-wave model and Ensemble Kalman Filter (EnKF)

2010 ◽  
Vol 34 (8) ◽  
pp. 1984-1999 ◽  
Author(s):  
Ahmadreza Zamani ◽  
Ahmadreza Azimian ◽  
Arnold Heemink ◽  
Dimitri Solomatine
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Wind Wave ◽  
Wave Model ◽  
Linear Wave ◽  
Wave Data ◽  
Non Linear

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.

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