Particle filter and EnKF as 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 quasi totally restricted to variational adjoint methods domain and only Chorin and Krause [26] tested it using a sequential Bayesian filter approach. In this work we compare the usual ensemble Kalman filter (EnKF) approach versus versions of the sequential Monte-Carlo particle filter approach and compare in detail their relative performance for both linear and nonlinear observation operators. Results of this sequential data assimilation tests are discussed using several versions of the particle filter addressing the important issue of resampling to avoid filter degeneracy.