Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation

The Kuramoto–Sivashinsky equation plays an important role as a low-dimensional prototype for complicated fluid dynamics systems having been studied due to its chaotic pattern forming behavior. Up to now, efforts to carry out data assimilation with this 1-D model were restricted to variational adjoint methods domain and only Chorin and Krause (Proc. Natl. Acad. Sci. 2004; 101(42):15013–15017) tested it using a sequential Bayesian filter approach. In this work we compare three sequential data assimilation methods namely the Kalman filter approach, the sequential Monte Carlo particle filter approach and the maximum likelihood ensemble filter methods. This comparison is to the best of our knowledge novel. We compare in detail their relative performance for both linear and nonlinear observation operators. The results of these sequential data assimilation tests are discussed and conclusions are drawn as to the suitability of these data assimilation methods in the presence of linear and nonlinear observation operators. Copyright © 2009 John Wiley & Sons, Ltd.