Stochastic subgrid tensor for geophysical flow modeling
Résumé
Stochastic models can be developed to perform ensemble forecasts of geophysical fluid dynamical systems and to betterhandle subgrid parametrizations. We propose to add to the smooth resolved velocity, an unresolved component, Gaussian, uncorrelated in time and inhomogeneous in space. This model changes the usual form of the material derivative of a tracer. This new form involves directly a multiplicative noise, an anisotropic and inhomogeneous diffusion, and a drift correction. As such, the rigorous derivation of this conservative model relates naturally the random forcing
to the subgrid parametrization. Stochastic versions of classical models can then be derived from conservation of mass, energy and momentum. Numerical simulations of our stochastic version of Surface Quasi-Geostrophic model improves both the accuracy of a single simulation.
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