Abstract/Summary

Covariance inflation is one of the necessary tools enabling the success of ensemble Kalman filters (EnKFs) in high dimensional spaces and in the presence of model error. Inflation maintains the ensemble variance to a sufficiently large value, counteracting the variance damping at analysis times and its underestimate arising from model and sampling errors. In this work we investigate the effect of inflation on the dynamics of the EnKF ensemble. When the focus is on the recursive full cycle forecast-analysis-forecast, an apparently counter-intuitive effect of the multiplicative inflation appears in the span of the ensemble in the EnK. In particular, we demostrate that multiplicative inflation changes the alignment of ensemble anomalies onto the weakly-stable 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 subspace. Given that the presence of model error implies that the analysis error is no longer fully confined on the local unstable subspace, this 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.