A Hybrid Monte‐Carlo sampling smoother for four‐dimensional data assimilation

Abstract

Summary 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 nonlinear model dynamics and observation operators. Unlike the four‐dimensional variational method, 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. Copyright © 2016 John Wiley & Sons, Ltd.

The reduced‐order hybrid Monte Carlo sampling smoother

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“…Following , the mass matrix can be chosen as the diagonal matrix . Note that no further approximations are introduced to the numerical flow produced by the symplectic integrator because all calculations involving models states are calculated in the reduced space.…”

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