scholarly journals A localization technique for ensemble Kalman filters

2010 ◽  
pp. n/a-n/a ◽  
Author(s):  
Kay Bergemann ◽  
Sebastian Reich
Keyword(s):  
Kalman Filters ◽  
Ensemble Kalman Filters ◽  
Localization Technique

scholarly journals A Data-Driven Method for Improving the Correlation Estimation in Serial Ensemble Kalman Filters

2017 ◽  
Vol 145 (3) ◽  
pp. 985-1001 ◽  
Author(s):  
Michèle De La Chevrotière ◽  
John Harlim
Keyword(s):  
Kalman Filters ◽  
Data Driven ◽  
Training Procedure ◽  
Ensemble Kalman Filters ◽  
Regression Problem ◽  
Correlation Estimation ◽  
Sample Correlation ◽  
Correlation Statistics ◽  
Nonlinear Observation ◽  
Lorenz 96

A data-driven method for improving the correlation estimation in serial ensemble Kalman filters is introduced. The method finds a linear map that transforms, at each assimilation cycle, the poorly estimated sample correlation into an improved correlation. This map is obtained from an offline training procedure without any tuning as the solution of a linear regression problem that uses appropriate sample correlation statistics obtained from historical data assimilation outputs. In an idealized OSSE with the Lorenz-96 model and for a range of linear and nonlinear observation models, the proposed scheme improves the filter estimates, especially when the ensemble size is small relative to the dimension of the state space.

scholarly journals On Serial Observation Processing in Localized Ensemble Kalman Filters

2015 ◽  
Vol 143 (5) ◽  
pp. 1554-1567 ◽  
Author(s):  
Lars Nerger
Keyword(s):  
Ensemble Kalman Filter ◽  
Kalman Filters ◽  
Large Scale ◽  
The State ◽  
Ensemble Kalman Filters ◽  
Filter Performance ◽  
Error Covariance ◽  
Analysis Process ◽  
Scale Models ◽  
Serial Observation

Abstract Ensemble square root filters can either assimilate all observations that are available at a given time at once, or assimilate the observations in batches or one at a time. For large-scale models, the filters are typically applied with a localized analysis step. This study demonstrates that the interaction of serial observation processing and localization can destabilize the analysis process, and it examines under which conditions the instability becomes significant. The instability results from a repeated inconsistent update of the state error covariance matrix that is caused by the localization. The inconsistency is present in all ensemble Kalman filters, except for the classical ensemble Kalman filter with perturbed observations. With serial observation processing, its effect is small in cases when the assimilation changes the ensemble of model states only slightly. However, when the assimilation has a strong effect on the state estimates, the interaction of localization and serial observation processing can significantly deteriorate the filter performance. In realistic large-scale applications, when the assimilation changes the states only slightly and when the distribution of the observations is irregular and changing over time, the instability is likely not significant.

scholarly journals Ensemble clustering in deterministic ensemble Kalman filters

2012 ◽  
Vol 64 (1) ◽  
pp. 18039 ◽  
Author(s):  
Javier Amezcua ◽  
Kayo Ide ◽  
Craig H. Bishop ◽  
Eugenia Kalnay
Keyword(s):  
Kalman Filters ◽  
Ensemble Clustering ◽  
Ensemble Kalman Filters

scholarly journals Online learning of both state and dynamics using ensemble Kalman filters

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Marc Bocquet ◽  
◽  
Alban Farchi ◽  
Quentin Malartic
Keyword(s):  
Online Learning ◽  
Kalman Filters ◽  
Ensemble Kalman Filters

scholarly journals Comparisons of Empirical Localization Techniques for Serial Ensemble Kalman Filters in a Simple Atmospheric General Circulation Model

2014 ◽  
Vol 142 (2) ◽  
pp. 739-754 ◽  
Author(s):  
Lili Lei ◽  
Jeffrey L. Anderson
Keyword(s):  
Root Mean Square ◽  
General Circulation Model ◽  
Kalman Filters ◽  
General Circulation ◽  
Atmospheric General Circulation Model ◽  
Circulation Model ◽  
Mean Square ◽  
Ensemble Kalman Filters ◽  
Localization Function ◽  
Atmospheric General Circulation

Abstract Two techniques for estimating good localization functions for serial ensemble Kalman filters are compared in observing system simulation experiments (OSSEs) conducted with the dynamical core of an atmospheric general circulation model. The first technique, the global group filter (GGF), minimizes the root-mean-square (RMS) difference between the estimated regression coefficients using a hierarchical ensemble filter. The second, the empirical localization function (ELF), minimizes the RMS difference between the true values of the state variables and the posterior ensemble mean. Both techniques provide an estimate of the localization function for an observation’s impact on a state variable with few a priori assumptions about the localization function. The ELF localizations can have values larger than 1.0 at small distances, indicating that this technique addresses localization but also can correct the prior ensemble spread in the same way as a variance inflation when needed. OSSEs using ELF localizations generally have smaller root-mean-square error (RMSE) than the optimal Gaspari and Cohn (GC) localization function obtained by empirically tuning the GC width. The localization functions estimated by the GGF are broader than those from the ELF, and the OSSEs with the GGF localization generally have larger RMSE than the optimal GC localization function. The GGFs are too broad because of spurious correlation biases that occur in the OSSEs. These errors can be reduced by using a stochastic EnKF with perturbed observations instead of a deterministic EAKF.

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