A new approximate solution of the optimal nonlinear filter for data assimilation in meteorology and oceanography

by I. Hoteit, D.T. Pham, G. Triantafyllou, G. Korres
Year: 2008

Bibliography

A 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

Abstract

​This 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

Keywords

Approximation Theory Covariance Matrix Kalman Filters Mathematical Models Mediterranean Sea