The Reduced-Order Hybrid Monte Carlo Sampling Smoother

TL;DR

This paper introduces reduced-order versions of the Hybrid Monte Carlo sampling smoother, significantly improving computational efficiency while accurately capturing the posterior distribution in data assimilation tasks.

Contribution

The paper presents novel reduced-order algorithms for the HMC sampling smoother, reducing computational cost without sacrificing accuracy in non-Gaussian data assimilation.

Findings

Reduced-order HMC smoother accurately captures posterior density

Significantly faster than full-order formulation

Validated on shallow-water equations model

Abstract

Hybrid Monte-Carlo (HMC) sampling smoother is a fully non-Gaussian four-dimensional data assimilation algorithm that works by directly sampling the posterior distribution formulated in the Bayesian framework. The smoother in its original formulation is computationally expensive due to the intrinsic requirement of running the forward and adjoint models repeatedly. Here we present computationally efficient versions of the HMC sampling smoother based on reduced-order approximations of the underlying model dynamics. The schemes developed herein are tested numerically using the shallow-water equations model on Cartesian coordinates. The results reveal that the reduced-order versions of the smoother are capable of accurately capturing the posterior probability density, while being significantly faster than the original full order formulation.