Impact of data density in ensemble filters and smoothers

One of major practical obstacles in development of an operationally feasible ensemble assimilation/prediction methodology is the assimilation of dense observations, such as satellite measurements. Most of current ensemble Kalman filter (EnKF) algorithms assimilate observations sequentially, one by one, thus allowing for efficient parallel algorithms. When the number of observations is very large, however, the sequential observation approach breaks down, since the computational cost increases directly with the number of observations. In this work we explore alternative methods for assimilation of spatially and/or temporally dense observations, with direct implications on assimilation of polar-orbiting and geo-stationary satellite measurements. Using the Maximum Likelihood Ensemble Filter (MLEF) algorithm, the observation information matrix is exploited to efficiently utilize the information content of observations. The number of observations is effectively reduced to the size of independent information, possibly having significant impact when assimilating very dense observations. For spatially dense observations, we use an ensemble filter, while for the temporally dense observations an ensemble smoother is likely a better choice. Using the Colorado State University global shallow-water model, the impact of spatial and temporal density of observations on ensemble data assimilation is investigated in detail. A special attention is directed toward quantifying the practical benefit of reducing the number of observations to its information content.