Publications 2008

‚ÄčA new approximate solution of the optimal nonlinear filter for data assimilation in meteorology and oceanography
I. Hoteit, D.T. Pham, G. Triantafyllou, and G. Korres
Monthly Weather Review, 136, 317-334, 2008
I. Hoteit, D.T. Pham, G. Triantafyllou, and G. Korres
Approximation theory; Covariance matrix; Kalman filters; Mathematical models; Mediterranean Sea
2008
‚ÄčThis paper introduces a new approximate solution of the optimal nonlinear filter suitable for nonlinear oceanic and atmospheric data assimilation problems. The method is based on a local linearization in a low-rank kernel representation of the state's probability density function. In the resulting low-rank kernel particle Kalman (LRKPK) filter, the standard (weight type) particle filter correction is complemented by a Kalman-type correction for each particle using the covariance matrix of the kernel mixture. The LRKPK filter's solution is then obtained as the weighted average of several low-rank square root Kalman filters operating in parallel. The Kalman-type correction reduces the risk of ensemble degeneracy, which enables the filter to efficiently operate with fewer particles than the particle filter. Combined with the low-rank approximation, it allows the implementation of the LRKPK filter with high-dimensional oceanic and atmospheric systems. The new filter is described and its relevance demonstrated through applications with the simple Lorenz model and a realistic configuration of the Princeton Ocean Model (POM) in the Mediterranean Sea.


 DOI: 10.1175/2007MWR1927.1