Title: Measures of observation impact in non-Gaussian data assimilation

Authors: Alison Fowler (Department of Meteorology, University of Reading, UK)
Peter Jan Van Leeuwen (Department of Meteorology, University of Reading, UK)

The impact of new observations in a data assimilation system is particularly important in the geosciences, where observations can be expensive and limited. Many measures of the impact of observations on both the analysis and the forecast currently exist. However, in applying these measures operationally assumptions about the linearity of the model and the observation operator are often necessary. These assumptions may have limited value with current and future highly non-linear models and non-linear data assimilation methods. Consequently our understanding of the potential of new observations may also be affected. The aim of this work is to highlight such cases when the non-Gaussianity of the prior becomes large enough such that impact measures based on linearizations are no longer useful. Four measures of the observations impact on the analysis will be studied; the sensitivity of the analysis to the observations, the degrees of freedom for signal, mutual information and relative entropy. In a Gaussian framework the first three of these measures can be shown to be calculable from the ratio of the background and observation error variances, for relative entropy the exact values of the background and observations and their error variances must also be known. Idealised experiments will show that representing the prior beyond the first and second moments can have a large impact on these measures, in some cases making them complicated functions of the characteristics of the prior and likelihood distributions. These results will then be put into context through the use of particle filter techniques.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: May 27 2011