Ensemble Kalman filtering without the intrinsic need for inflation

By Marc Bocquet. 2011

104 citations recorded by the source corpus.

Abstract. The main intrinsic source of error in the ensemble Kalman filter (EnKF) is sampling error. External sources of error, such as model error or deviations from Gaussianity, depend on the dynamical properties of the model. Sampling errors can lead to instability of the filter which, as a consequence, often requires inflation and localization. The goal of this article is to derive an ensemble Kalman filter which is less sensitive to sampling errors. A prior probability density function conditional on the forecast ensemble is derived using Bayesian principles. Even though this prior is built upon the assumption that the ensemble is Gaussian-distributed, it is different from the Gaussian probability density function defined by the empirical mean and the empirical error covariance matrix of the ensemble, which is implicitly used in traditional EnKFs. This new prior generates a new class of ensemble Kalman filters, called finite-size ensemble Kalman filter (EnKF-N). One deterministic variant, the finite-size ensemble transform Kalman filter (ETKF-N), is derived. It is tested on the Lorenz '63 and Lorenz '95 models. In this context, ETKF-N is shown to be stable without inflation for ensemble size greater than the model unstable subspace dimension, at the same numerical cost as the ensemble transform Kalman filter (ETKF). One variant of ETKF-N seems to systematically outperform the ETKF with optimally tuned inflation. However it is shown that ETKF-N does not account for all sampling errors, and necessitates localization like any EnKF, whenever the ensemble size is too small. In order to explore the need for inflation in this small ensemble size regime, a local version of the new class of filters is defined (LETKF-N) and tested on the Lorenz '95 toy model. Whatever the size of the ensemble, the filter is stable. Its performance without inflation is slightly inferior to that of LETKF with optimally tuned inflation for small interval between updates, and superior to LETKF with optimally tuned inflation for large time interval between updates.

Subfields: Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/3c24ea331670efa17b3dade04110fc9e1b9066d0

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Citations in the corpus

Data assimilation in the geosciences: An overview of methods, issues, and perspectives (2017, background): “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,…”
Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation (2015, methodology): “Localization has to be superimposed onto the finite-size scheme to build a local EnKF-N without the intrinsic need for inflation (Bocquet, 2011).”
An iterative ensemble Kalman smoother (2014, methodology): “With a proper choice of G (Bocquet, 2011) and identifying x 0 = x0, one obtains J̃ (w) =(1) 2 [ y1 − H1 ◦ M1←0 ( x 0 + A0w )]T”
An Iterative EnKF for Strongly Nonlinear Systems (2012, unknown): “Bocquet (2011) introduced a new class of EnKF-like schemes derived from a new prior (background ) probability density function conditional on the forecast ensemble.”
A Review of Innovation-Based Methods to Jointly Estimate Model and Observation Error Covariance Matrices in Ensemble Data Assimilation (2018, methodology): “Building on Bocquet (2011); Bocquet et al. (2015); Ménétrier370 and Auligné (2015), this technique was extended in Satterfield et al. (2018) to adaptively tune a371 mixing ratio between the true and sample variances.372 Adaptive covariance inflations are estimation methods directly attached to a…”
Enhanced Adaptive Inflation Algorithm for Ensemble Filters (2018, background): “A separate issue is whether there are sufficientmembers to track all the directions of uncertainty growth (Bocquet and Carrassi 2017).”