Exploiting Local Low Dimensionality of the Atmospheric Dynamics for Efficient Ensemble Kalman Filtering

Istvan Szunyogh, Edward Ott and Eugenia Kalnay

University of Maryland

It is shown that when the Earth's surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector. It is also shown how this finding can be exploited to formulate a potentially accurate and efficient data assimilation technique. The basic idea is that, since the expected forecast errors lie in a locally low dimensional subspace, the analysis resulting from the data assimilation should also lie in this subspace. This implies that operations only on relatively low dimensional matrices are required. The data assimilation analysis is done locally in a manner allowing massively parallel computation to be exploited. The local analyses are then used to construct global states and covariances for advancement to the next forecast time. Potential advantages of the method are discussed and some preliminary results for a quasi-geostrophic channel model are presented.