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Journal Articles Journal of Advances in Modeling Earth Systems Year : 2021

Rotating shallow water flow under location uncertainty with a structure-preserving discretization

Abstract

We introduce a physically relevant stochastic representation of the rotating shallow waterequations. The derivation relies mainly on a stochastic transport principle and on a decomposition of thefluid flow into a large-scale component and a noise term that models the unresolved flow components. Asfor 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 physicallyrelevant random simulations with a good trade-off between the model error representation and the ensemble'sspread. To maintain numerically the energy conservation feature, we combine an energy (in space) preservingdiscretization of the underlying deterministic model with approximations of the stochastic terms that are basedon standard finite volume/difference operators. The LU derivation, built from the very same conservationprinciples as the usual geophysical models, together with the numerical scheme proposed can be directly usedin existing dynamical cores of global numerical weather prediction models. The capabilities of the proposedframework is demonstrated for an inviscid test case on the f-plane and for a barotropically unstable jet on thesphere.
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Dates and versions

hal-03131680 , version 1 (04-02-2021)
hal-03131680 , version 2 (17-12-2021)
hal-03131680 , version 3 (28-06-2022)

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Rüdiger Brecht, Long Li, Werner Bauer, Etienne Mémin. Rotating shallow water flow under location uncertainty with a structure-preserving discretization. Journal of Advances in Modeling Earth Systems, 2021, 13 (12), pp.1-28. ⟨10.1029/2021MS002492⟩. ⟨hal-03131680v3⟩
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