Multiscale Data Assimilation for Very High Resolution Models

The commonly used data assimilation algorithms, including three-/four-dimensional variational and Kalman filter-based algorithm, are based on optimal estimation theory, in which both background state and observation error covariances are of fundamental importance. Using a variety of theoretical and numerical analyses, we show that those optimal estimation algorithms are inherently ineffective when they are applied to models at a horizontal resolution of the order of 1 km. The ineffectiveness arises from its filtering properties that are dictated by the error covariance. We suggest a multiscale data assimilation algorithm, in which the cost function is decomposed for a set of distinct spatial scales. Data assimilation is implemented sequentially from large to small scales. Results are presented to demonstrate the algorithm.