Article Type:
Research Article

Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation

Marc Bocquet Université Paris-Est, CEREA Joint Laboratory École des Ponts ParisTech and EDF R&D, Champs-sur-Marne, and INRIA, Paris Rocquencourt Research Center, Paris, France

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Carlos A. Pires Universidade de Lisboa, and Instituto Dom Luiz (IDL), Centro de Geofísica da Universidade de Lisboa (CGUL), Lisbon, Portugal

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Lin Wu Université Paris-Est, CEREA Joint Laboratory École des Ponts ParisTech and EDF R&D, Champs-sur-Marne, and INRIA, Paris Rocquencourt Research Center, Paris, France

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Print Publication:
01 Aug 2010
Collections:
Intercomparisons of 4D-Variational Assimilation and the Ensemble Kalman Filter
DOI:
https://doi.org/10.1175/2010MWR3164.1
Page(s):
2997–3023
Restricted access

Abstract

This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized.

The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled.

The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are reviewed: maximum entropy filter, Gaussian anamorphosis, non-Gaussian priors, particle filter with an ensemble Kalman filter as a proposal distribution, maximum entropy on the mean, or strictly Bayesian inferences for large linear models, etc. Several ideas are illustrated with recent or original examples that possess some features of high-dimensional systems. Many of the new approaches are well understood only in special cases and have difficulties that remain to be circumvented. Some of the suggested approaches are quite promising, and sometimes already successful for moderately large though specific geophysical applications. Hints are given as to where progress might come from.

Corresponding author address: Marc Bocquet, École des Ponts ParisTech, CEREA, 6-8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne la Vallée, CEDEX 2, France. Email: bocquet@cerea.enpc.fr

This article included in the Intercomparisons of 4D-Variational Assimilation and the Ensemble Kalman Filter special collection.

Abstract

This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized.

The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled.

The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are reviewed: maximum entropy filter, Gaussian anamorphosis, non-Gaussian priors, particle filter with an ensemble Kalman filter as a proposal distribution, maximum entropy on the mean, or strictly Bayesian inferences for large linear models, etc. Several ideas are illustrated with recent or original examples that possess some features of high-dimensional systems. Many of the new approaches are well understood only in special cases and have difficulties that remain to be circumvented. Some of the suggested approaches are quite promising, and sometimes already successful for moderately large though specific geophysical applications. Hints are given as to where progress might come from.

Corresponding author address: Marc Bocquet, École des Ponts ParisTech, CEREA, 6-8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne la Vallée, CEDEX 2, France. Email: bocquet@cerea.enpc.fr

This article included in the Intercomparisons of 4D-Variational Assimilation and the Ensemble Kalman Filter special collection.

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