Meeting Abstracts
Filtering Turbulent Sparsely Observed Geophysical Flows
John Harlim
North Carolina State University
(Abstract received 03/21/2012 for session C)
ABSTRACT
Filtering sparsely turbulent signals from nature is a central problem of contemporary data assimilation. In this talk, I will discuss filtering sparsely observed turbulent signals in which we simulate observations by adding white noise to solutions of the quasi-geostrophic (QG) model with turbulent cascades from baroclinic instability. In particular, we consider two separate regimes with varying Rossby radius mimicking the ``atmosphere'' and the ``ocean''. In the ``atmospheric'' case, large scale turbulent fluctuations are dominated by barotropic zonal jets with non-Gaussian statistics while the ``oceanic'' case has large scale blocking regime transitions with barotropic zonal jets and large scale Rossby waves.
I will discuss how to use tools from applied mathematics to develop cheap reduced stochastic filters, including the radical linear stochastic filters with model errors and the very recently developed exactly solvable Stochastic Parameterization Extended Kalman Filter (SPEKF) with additive and multiplicative bias corrections ``on the fly''. We will compare these cheap reduced filtering strategies with the state-of-the-art Local-Least-Squares Ensemble Adjustment Kalman Filter (LLS-EAKF) and we shall see that the cheap filters supersede the sophisticated LLS-EAKF in the numerically stiff ``oceanic" regime.