Filtering Turbulent Systems with Stochastic Parameterized Extended Kalman Filter

John Harlim
North Carolina State University

The standard practice in filtering with model errors is to augment the dynamical equations for the physical process with ad-hocly chosen dynamical equations for the parameters (Friedland 1969, 1982). On the other hand, Fredericson and O'Kane (2009) showed high filtering skill of atmospheric blocking event with a more elaborate stochastic model; they parameterized damping and forcing with global nonlinear interaction across scales.

Motivated by these works, we (Gershgorin, Harlim, and Majda 2010a, b) introduced a novel strategy "Stochastic Parameterized Extended Kalman Filter" (SPEKF) as a simple nonlinear stochastic model with exactly solvable statistics that includes both the forcing and damping corrections ``on-the-fly". The exactly solvable feature is important because it suggests that no linear tangent approximation is required in SPEKF, as opposed to the standard Extended Kalman Filter. In this talk, I will briefly review the underlying theory and present numerical results with an SPDE that mimics the barotropic Rossby waves as well as recent results on the two-layer quasi-geostrophic model with baroclinic instabilities (Harlim and Majda 2010).

Presentation (PDF File)

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