A modified rrsqrt-filter for assimilating data in atmospheric chemistry models

The rrsqrt-filter is a special formulation of the Kalman filter for assimilation of data in large scale models. In this formulation, the covariance matrix of the model state is expressed in a limited number of modes. Two modifications have been made to the filter such that it is more robust when applied in combination with an atmospheric chemistry model; both act on the reduction of the covariance matrix into modes. The first modification proposes a transformation of the state, which makes the reduction invariant for a change in units and helps to collect the most important covariance structures in the first modes. The second modification extracts additional information from the reduction algorithm to limit the formation of unphysical states by the filter.