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.