Rotating shallow water flow under location uncertainty with a structure-preserving discretization
Résumé
We introduce a physically relevant stochastic representation of the rotating shallow water
equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the
fluid flow into a large-scale component and a noise term that models the unresolved flow components. As
for the classical (deterministic) system, this scheme, referred to as modeling under location uncertainty (LU),
conserves the global energy of any realization and provides the possibility to generate an ensemble of physically
relevant random simulations with a good trade-off between the model error representation and the ensemble's
spread. To maintain numerically the energy conservation feature, we combine an energy (in space) preserving
discretization of the underlying deterministic model with approximations of the stochastic terms that are based
on standard finite volume/difference operators. The LU derivation, built from the very same conservation
principles as the usual geophysical models, together with the numerical scheme proposed can be directly used
in existing dynamical cores of global numerical weather prediction models. The capabilities of the proposed
framework is demonstrated for an inviscid test case on the f-plane and for a barotropically unstable jet on the
sphere.
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