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

TL;DR

This paper introduces a hybrid Monte Carlo sampling smoother for four-dimensional data assimilation that effectively handles non-Gaussian errors and non-linear dynamics, providing uncertainty estimates beyond traditional methods.

Contribution

It develops an ensemble-based Hamiltonian Monte Carlo smoother that improves sampling efficiency and captures posterior uncertainty in 4D data assimilation.

Findings

Outperforms traditional variational and ensemble smoothers in numerical tests.

Handles non-Gaussian errors and non-linear models effectively.

Provides posterior uncertainty estimates, unlike standard methods.

Abstract

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