An adaptive covariance inflation error correction algorithm for ensemble filters

By Jeffrey L. Anderson. 2007

497 citations recorded by the source corpus.

ABSTRACT Ensemble filter methods for combining model prior estimates with observations of a system to produce improved posterior estimates of the system state are nowbeing applied to a wide range of problems both in and out of the geophysics community. Basic implementations of ensemble filters are simple to develop even without any data assimilation expertise. However, obtaining good performance using small ensembles and/or models with significant amounts of error can be more challenging.Anumber of adjunct algorithms have been developed to ameliorate errors in ensemble filters. The most common are covariance inflation and localization which have been used in many applications of ensemble filters. Inflation algorithms modify the prior ensemble estimates of the state variance to reduce filter error and avoid filter divergence. These adjunct algorithms can require considerable tuning for good performance, which can entail significant expense. A hierarchical Bayesian approach is used to develop an adaptive covariance inflation algorithm for use with ensemble filters. This adaptive error correction algorithm uses the same observations that are used to adjust the ensemble filter estimate of the state to estimate appropriate values of covariance inflation. Results are shown for several low-order model examples and the algorithm produces results that are comparable with the best tuned inflation values, even for small ensembles in the presence of very large model error.

Subfields: Atmospheric Science, Geophysics, Oceanography

View Paper: https://www.semanticscholar.org/paper/857404f05c480ac0b24ee7112265b05606bb8e18

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Citations in the corpus

Spatially and temporally varying adaptive covariance inflation for ensemble filters (2009, methodology): “Recently, ensemble algorithms that adaptively determine appropriate values of inflation have been developed (Anderson, 2007a, hereafter A07).”
Ensemble Kalman filtering without the intrinsic need for inflation (2011, methodology): “…on the inflation issue, they are based on a specific maximum likelihood estimator of the inflation scaling, or of several scalars that parameterize the error covariance matrices (Mitchell and Houtekamer, 1999; Anderson, 2007b; Brankart et al., 2010) essentially following the ideas ofDee (1995).”
Using the ensemble Kalman filter to estimate multiplicative model parameters (2008, methodology): “The value of the covariance inflation factor is chosen using the adaptive covariance inflation algorithm proposed by Anderson (2007).”
The Gaussian Approach to Adaptive Covariance Inflation and Its Implementation with the Local Ensemble Transform Kalman Filter (2011, methodology): “To avoid manual optimization of localization functions, Anderson (2007a) and Bishop and Hodyss (2009a,b) proposed adaptive localization approaches.”
A Second-Order Exact Ensemble Square Root Filter for Nonlinear Data Assimilation (2015, methodology): “Following Anderson (2007), it should correspond to the actual innovation variance, (sinno) 2 5 dTd/k, in a wellcalibrated data assimilation system. c. Results and discussions 1) LORENZ 63 (L63) The first experiment concentrates on some basic properties of the NETF, using m5 100 ensemble members in…”
Data assimilation in the geosciences: An overview of methods, issues, and perspectives (2017, methodology): “Hence, adaptive schemes have been developed to make the task more automatic (Anderson, 2007; Bocquet, 2011; Bocquet, Raanes, & Hannart, 2015; Bocquet & Sakov, 2012; Brankart, Cosme, Testut, Brasseur, & Verron, 2010; Li, Kalnay, & Miyoshi, 2009; Liang et al., 2012; Miyoshi, 2011; Wang & Bishop,…”
The ensemble Kalman filter for combined state and parameter estimation (2009, methodology): “In [61] the covariance inflation is estimated based on the sequence of innovation statistics, while in [62] a method is presented that is based on augmenting the inflation parameter to the model state where it is updated as a parameter in the EnKF analysis computations.”
A Localized Particle Filter for High-Dimensional Nonlinear Systems (2016, methodology): “The EAKF uses the Anderson (2007) adaptive statespace inflation scheme with the prior standard deviation for the inflation coefficient g fixed at 0.1.”
Strongly Coupled Data Assimilation Using Leading Averaged Coupled Covariance (LACC). Part I: Simple Model Study* (2015, methodology): “The idea of adaptive inflation (Anderson 2007, 2009) could be useful to tune the weight factor and make it adaptive in time. For future research, one could continue to test the LACC method and related filtering techniques in simple conceptual models, preferably nonlinear or multidimensional like the”
Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter (2009, result): “These results are consistent with those of Anderson (2007) where an adaptive inflation from a hierarchical Bayesian method was compared to the best tuned time-constant inflation. With the suboptimal inflation from OMB(2) (actually under-estimating the best tuned inflation) it is not surprising that ”
A Review of Innovation-Based Methods to Jointly Estimate Model and Observation Error Covariance Matrices in Ensemble Data Assimilation (2018, methodology): “This feedback process leads to filter divergence, as was pointed331 out by Pham et al. (1998), Anderson and Anderson (1999) or Anderson (2007).”
Enhanced Adaptive Inflation Algorithm for Ensemble Filters (2018, background): “Multiplicative inflation (Anderson and Anderson 1999; Zheng 2009), on the other hand, increases the prior ensemble spread by a specific factor while pushing all members away from the mean.”