A Hybrid Monte-Carlo Sampling Smoother for Four Dimensional Data Assimilation

摘要

This paper constructs an ensemble-based sampling smoother forfour-dimensional data assimilation using a Hybrid/Hamiltonian Monte-Carloapproach. The smoother samples efficiently from the posterior probabilitydensity of the solution at the initial time. Unlike the well-known ensembleKalman smoother, which is optimal only in the linear Gaussian case, theproposed methodology naturally accommodates non-Gaussian errors and non-linearmodel dynamics and observation operators. Unlike the four-dimensionalvariational met\-hod, which only finds a mode of the posterior distribution,the smoother provides an estimate of the posterior uncertainty. One can use theensemble mean as the minimum variance estimate of the state, or can use theensemble in conjunction with the variational approach to estimate thebackground errors for subsequent assimilation windows. Numerical resultsdemonstrate the advantages of the proposed method compared to the traditionalvariational and ensemble-based smoothing methods.