Exploiting Local Low Dimensionality of the Atmospheric Dynamics for Efficient Ensemble Kalman Filtering
Istvan Szunyogh, Edward Ott and Eugenia Kalnay
University of Maryland
Abstract:
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.