Wavelet based representation of observation error covariance
Résumé
A common approximation in data assimilation is to assume observations to be uncorrelated (i.e. observation error covariance matrices are diagonal). This is obviously not true, in particular for satellite data. Due to the large amount of data to be considered storage, handling and inversion of non-diagonal observation error matrices is not feasible in practice, however if observations present some sort of spatial density (1D along track, or 2D area) one can adopt similar strategies as for background error observation matrices.
In this talk, after presenting possible solutions, we focus on a method based on the wavelet transform in order to represent (at a cheap cost) some of the observation error correlation in variational data assimilation context. We show that the diagonal of the covariance matrix in a wavelet space (if well chosen) is able to represent an important part of the error covariance (in the “physical” space). Specificity of the ocean, with complex boundaries and possibility of missing data (due to clouds for instance) can also be accounted for in this context. The benefit of this approach is demonstrated on twin experiments involving a 2D-shallow water model and synthetic observations.