Notes on data assimilation for nonlinear high-dimensional dynamics: stochastic approach

This manuscript is devoted to the attempts on the design of new nonlinear data assimilation schemes. The variational and sequential assimilation methods are reviewed with emphasis on their performances on dealing with nonlinearity and high dimension of the environmental dynamical systems. The nonlinear data assimilation is based on Bayesian formulation and its approximate solutions. Sequential Monte Carlo methods, especially particle filters, are discussed. Several issues, i.e. variational formulation in the information viewpoint in the context of nonlinear data assimilation, efficient sampling techniques, and parallel implementation of the filters, might bring new ideas for the design of new nonlinear data assimilation schemes. In the end we briefly summarize the applications of data assimilation for air pollution.