An Optimal Experimental Design Framework for Adaptive Inflation and Covariance Localization for Ensemble Filters.

Covariance inflation and localization are ubiquitously employed to counteract the effect of using ensembles of finite sizes in all practical data assimilation systems. The performance of the assimilation algorithm is critically influenced by the choice of the parameters of these techniques, that is, the inflation factor and the localization radius. These parameters are generally tuned by trial and error, rendering them expensive to optimize in practice. Spatially and temporally varying inflation parameter and localization radii have been recently proposed and have been empirically proven to enhance the performance of the employed assimilation filter. In this study, we present a variational framework for adaptive tuning of space-time inflation factors and localization radii. Each of these parameters is optimized independently and can be applied separately, with an objective to minimize the uncertainty in the posterior state. The proposed framework does not assume uncorrelated observation or prior errors and can in principle be applied without expert knowledge about the model and the observations. Thus, it is adequate for handling dense as well as sparse observational networks. We present the mathematical formulation, algorithmic description of the approach, and numerical experiments using the Lorenz-96 model and a deterministic implementation of the ensemble Kalman filter. The numerical results presented in this work provide compelling evidence of the merits of the approach.