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A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Applications

Lolla, T. and P.F.J. Lermusiaux, 2017b. A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Applications. Monthly Weather Review. doi:10.1175/MWR-D-16-0065.1.

The Gaussian–Mixture–Model Dynamically–Orthogonal (GMM–DO) smoother is exemplified and contrasted with other smoothers by applications to three dynamical systems, all of which admit far–from–Gaussian statistics. A double–well–diffusion experiment is first used to examine the capabilities of the smoother and compare its performance to that of the Ensemble Kalman Smoother. A passive tracer advected by a reversible shear flow is then employed. The exact smoothed solution is obtained and utilized to validate the GMM–DO smoother and its results. Finally, the third example illustrates the applicability of the smoother in more complex ocean flows consisting of variable jets and eddies. To illustrate the non-Gaussian effects, comparisons are then made with the update of the Error Subspace Statistical Estimation smoother. In each application, the properties of the GMM–DO smoother and of its posterior probabilities are studied and quantified. Rigorous evaluation of Bayesian smoothers for nonlinear high-dimensional dynamical systems is challenging in itself. The present three dynamical system examples provide complementary and effective benchmarks for such evaluation.