Adaptive covariance relaxation methods for ensemble data assimilation based on innovation statistics
Covariance relaxation is a widely-used inflation technique, which plays an essential role in the ensemble Kalman filter because the ensemble-based error variance is usually underestimated mainly due to limited ensemble size and model imperfections. To avoid computationally-expensive manual tuning of the relaxation parameter, this study pioneers to propose adaptive covariance relaxation (ACR) approaches based on Desroziers’ innovation statistics (2005, QJRMS). Two ACR methods are implemented: relaxation to prior spread based on Ying and Zhang (2015, QJRMS), and relaxation to prior perturbations. We conduct a series of experiments in the real-world global atmosphere with both conventional observations and satellite radiances for the first time. The results demonstrate that the proposed ACR approaches provide nearly optimal relaxation parameter values and improve the analyses and forecasts compared to a baseline control experiment with an adaptive multiplicative inflation method. The adaptive relaxation methods are turned out to be robust to changes in the observing networks and observation error settings. We mathematically show that the innovation statistics for the analysis error covariance (a-minus-b o-minus-a statistics are more robust than those for the background error covariance (o-minus-b o-minus-b or a-minus-b o-minus-b statistics) if the observation and background error variances are imperfect.
Dr. Shunji Kotsuki RIKEN Center for Computational Science