Dynamical effects of inflation in ensemble-based data assimilation under the presence of model error

Abstract

The role of multiplicative and additive covariance inflation on ensemble dynamics under the presence of model errors is examined. We show that multiplicative inflation significantly impacts the alignment of ensemble anomalies onto the backward Lyapunov vectors. Whereas the ensemble is expected to collapse onto the subspace corresponding to the unstable portions of the Lyapunov spectrum, the use of multiplicative inflation contributes to retain anomalies beyond that span. Given that model error implies that analysis error is not fully confined on the local unstable subspace, this uncovered feature of multiplicative inflation is of paramount importance for an optimal filtering. We propose hybrid schemes whereby additive perturbations complement multiplicative inflation by suitably increasing the dimension of the subspace spanned by the ensemble. The use of hybrid schemes improves analysis RMSE on the Lorenz-96 model compared to the use of multiplicative inflation alone, emphasizing the role of model dynamics when designing additive inflation schemes.