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Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach

Amezcua, J. and Van Leeuwen, P. (2014) Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach. Tellus A, 66. 23493. ISSN 1600-0870

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To link to this article DOI: 10.3402/tellusa.v66.23493

Abstract/Summary

The analysis step of the (ensemble) Kalman filter is optimal when (1) the distribution of the background is Gaussian, (2) state variables and observations are related via a linear operator, and (3) the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA) can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1)-(3) are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:37699
Uncontrolled Keywords:Gaussian anamorphosis, ensemble Kalman filter, nonlinearity, joint transformations, non-Gaussianity
Publisher:Co-Action Publishing

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