Measures of observation impact in non-Gaussian data assimilation

Fowler, A. ORCID: https://orcid.org/0000-0003-3650-3948 and Van Leeuwen, P. (2012) Measures of observation impact in non-Gaussian data assimilation. Tellus A, 64. 17192. ISSN 1600-0870 doi: 10.3402/tellusa.v64i0.17192

Abstract/Summary

ABSTRACT Non-Gaussian/non-linear data assimilation is becoming an increasingly important area of research in the Geosciences as the resolution and non-linearity of models are increased and more and more non-linear observation operators are being used. In this study, we look at the effect of relaxing the assumption of a Gaussian prior on the impact of observations within the data assimilation system. Three different measures of observation impact are studied: the sensitivity of the posterior mean to the observations, mutual information and relative entropy. The sensitivity of the posterior mean is derived analytically when the prior is modelled by a simplified Gaussian mixture and the observation errors are Gaussian. It is found that the sensitivity is a strong function of the value of the observation and proportional to the posterior variance. Similarly, relative entropy is found to be a strong function of the value of the observation. However, the errors in estimating these two measures using a Gaussian approximation to the prior can differ significantly. This hampers conclusions about the effect of the non-Gaussian prior on observation impact. Mutual information does not depend on the value of the observation and is seen to be close to its Gaussian approximation. These findings are illustrated with the particle filter applied to the Lorenz ’63 system. This article is concluded with a discussion of the appropriateness of these measures of observation impact for different situations.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/28160
Identification Number/DOI	10.3402/tellusa.v64i0.17192
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Co-Action Publishing
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