Real-time estimation of the relevant unresolved turbulent processes in the dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the unresolved processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and prediction based on discretized PDE models. This is particularly important when dealing with turbulent geophysical systems with rough energy spectra near the mesh scale of the numerical models. I will introduce and discuss a technique for Dynamic Stochastic Superresolution (DSS) of sparsely observed turbulent systems which is capable of `superresolving' the partially observed dynamics, including the detection of “black swans” which represent time-localized extreme events triggered by the unresolved dynamics. DSS operates in Fourier domain and exploits the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. This computationally cheap and robust approach has significant skill in the presence of model error which I will illustrate on a test bed of turbulent solutions from realistic nonlinear spatially extended systems. In the last part of the talk I will outline an information-theoretic framework for analyzing the error in DSS and other stochastic filtering algorithms of high-dimensional partially observed systems in the presence of model error.
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