**Nonlinear Data Assimilation for Satellite Retrievals**
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Van Leeuwen, Peter Jan
University of Reading, UNITED KINGDOM
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Satellite observations typically do not relate in a simple way to geophysical variables of interest. This means that so-called observation operators, that couple geophysical variables to the actual observations, are sometimes highly nonlinear. The standard procedure to obtain estimates of the geophysical variables from satellites is to try to invert this observation operator, subject to extra constraints to obtain a stable estimate. This process is called the retrieval process, and the product the retrieval. However, the constraints tend to be rather ad hoc. Furthermore, estimates of the errors on the retrieved geophysical variables is either too expensive, or highly simplified, e.g. as the inverse of the Hessian. Fully nonlinear data assimilation allow us to perform fully nonlinear retrievals that don't have the drawbacks mentioned above. They generate an estimate of the full probability density of the retrieval, so not only the mean and covariance are obtained, but also higher order moments and potentially multimodal behaviour. However, up to recently these methods have been prohibitively expensive for operational use. As part of the ESA Data Assimilation projects we have developed new fully nonlinear data-assimilation methods based on particle filters. The new ingredient is a careful choice of the proposal density for the particle filter, which allows us to generate samples from the high probability areas of the posterior probability density. These new methods allow us to generate extremely efficient fully nonlinear data-assimilation methods, even for high-dimensional retrieval problems. These new methods will be of great importance for proper retrieval of geophysical variables from complicated satellite missions like EarthCare.