The reduced-order hybrid Monte Carlo sampling smoother

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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.

Technology, Computer Science, Interdisciplinary Applications, Mathematics, Interdisciplinary Applications, Mechanics, Physics, Fluids & Plasmas, Computer Science, Mathematics, Physics, data assimilation, Hamiltonian Monte Carlo, smoothing, reduced-order modeling, proper orthogonal decomposition, SHALLOW-WATER EQUATIONS, PROPER ORTHOGONAL DECOMPOSITION, VARIATIONAL DATA ASSIMILATION, PARTIAL-DIFFERENTIAL-EQUATIONS, DYNAMIC-MODE DECOMPOSITION, NONLINEAR MODEL, EMPIRICAL INTERPOLATION, COHERENT STRUCTURES, REDUCTION, POD