On the Gaussian approach to adaptive covariance inflation

In ensemble Kalman filters, the error variance is usually underestimated due to limited ensemble size and other sources of imperfections, which is treated commonly by empirical covariance inflation. In order to avoid manual optimization of the multiplicative inflation parameters, previous studies proposed adaptive inflation approaches. Anderson applied the Bayesian estimation theory to the probability density function of the inflation parameters. Alternatively, Li et al. used the innovation statistics of Desroziers et al. and applied the Kalman filter analysis update based on the Gaussian assumption. In this study, Li et al.'s Gaussian approach is advanced to include the variance of the estimated inflation derived from the central limit theorem. It is shown that the Gaussian approach is an accurate approximation of Anderson's general Bayesian approach. Then, an advanced implementation of the Gaussian approach with the local ensemble transform Kalman filter is proposed, where the adaptive inflation parameters are computed simultaneously with the ensemble transform matrix at each grid point. The spatially and temporally adaptive inflation is implemented with the Lorenz 40-variable model and a low-resolution atmospheric general circulation model; perfect model experiments show promising results. The presentation will include recent developments of the Gaussian adaptive inflation method.