Adaptive covariance relaxation methods for ensemble data assimilation: experiments in the real atmosphere

Covariance inflation plays an important role in the ensemble Kalman filter because the ensemble‐based error variance is usually underestimated due to various factors such as the limited ensemble size and model imperfections. Manual tuning of the inflation parameters by trial and error is computationally expensive; therefore, several studies have proposed approaches to adaptive estimation of the inflation parameters. Among others, this study focuses on the covariance relaxation method which realizes spatially dependent inflation with a spatially homogeneous relaxation parameter. This study performs a series of experiments with the non‐hydrostatic icosahedral atmospheric model (NICAM) and the local ensemble transform Kalman filter (LETKF) assimilating the real‐world conventional observations and satellite radiances. Two adaptive covariance relaxation methods are implemented: relaxation to prior spread based on Ying and Zhang (adaptive‐RTPS), and relaxation to prior perturbation (adaptive‐RTPP). Both adaptive‐RTPS and adaptive‐RTPP generally improve the analysis compared to a baseline control experiment with an adaptive multiplicative inflation method. However, the adaptive‐RTPS and adaptive‐RTPP methods lead to an over‐dispersive (under‐dispersive) ensemble in the sparsely (densely) observed regions compared with the adaptive multiplicative inflation method. We find that the adaptive‐RTPS and adaptive‐RTPP methods are robust to a sudden change in the observing networks and observation error settings. Covariance relaxation is a widely used inflation technique, which plays an essential role in the ensemble Kalman filter. To avoid computationally expensive manual tuning of the relaxation parameter, this study proposes adaptive covariance relaxation approaches and performs a series of experiments in the real‐world global atmosphere. The proposed approaches provide nearly optimal relaxation parameter values, are robust with observation error settings and inhomogeneous observing networks, and generally improve the analysis compared to an adaptive multiplicative inflation method.