EGU22-6267, updated on 28 Mar 2022
EGU General Assembly 2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Towards structure preserving discretizations of stochastic rotating shallow water equations on the sphere

Werner Bauer1, Rüdiger Brecht2, Long Li3, and Etienne Memin3
Werner Bauer et al.
  • 1Kingston University London, United Kingdom of Great Britain – England, Scotland, Wales (
  • 2Universität Bremen, Germany
  • 3Inria Rennes, France

We introduce a stochastic representation of the rotating shallow water equations and a corresponding structure preserving discretization. The stochastic flow model follows from using a stochastic transport principle and a decomposition of the fluid flow into a large-scale component and a noise term that models the unresolved flow components. Similarly to the deterministic case, this stochastic model (denoted as modeling under location uncertainty (LU)) conserves the global energy of any realization. Consequently, it permits us to generate an ensemble of physically relevant random simulations with a good trade-off between the representation of the model error and the ensemble's spread. Applying a structure-preserving discretization of the deterministic part of the equations and standard finite difference/volume approximations of the stochastic terms, the resulting stochastic scheme preserves (spatially) the total energy. To address the enstrophy accumulation at the grid scale, we augment the scheme with a scale selective (energy preserving) dissipation of enstrophy, usually required to stabilize such stochastic numerical models. We compare this setup with one that applies standard biharmonic dissipation for stabilization and we study its performance for test cases of geophysical relevance. 

How to cite: Bauer, W., Brecht, R., Li, L., and Memin, E.: Towards structure preserving discretizations of stochastic rotating shallow water equations on the sphere, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6267,, 2022.

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