Data-driven and data-agnostic stochastic parametrization of unresolved processes

Abstract

The simulation of planetary flows at all the scales that have a significant impact on the climate system is unachievable with nowadays computational resources. Large-scale simulations of the Ocean (as well as for Atmosphere) remains the primary tool of investigation while high resolution simulations can be obtained only for small geographical domains or short integration periods. The complex interdependence of mesoscale and sub-mesoscale dynamics, however, is lost in state-of-the-art simulations when performed at scales that are too large to capture these phenomena. Most of the modeling challenges arise from the representation of these effects in a parameterized manner. This work investigates the so called Location Uncertainty (LU) framework [1,2], that provides a solid theoretical background for the definition of a large-scale representation with an additional stochastic component representing the subgrid contribution, introducing new degrees of freedom to be exploited in the modeling of specific phenomena [2]. The model, that has been proven successful in several large-scale models for ocean dynamics [3,4,5,6], is implemented in the community ocean model NEMO (https://www.nemo-ocean.eu) in its hydrostatic primitive equation version, as outlined in [6] and already tested in [7]. An idealized double-gyre configuration is shown to be improved by the stochastic addition in both eddy permitting (~35km) and eddy resolving (~10km) regimes, under a variety of choices of the noise model including both data-driven and data-agnostic approaches.   [1] E. Mémin Fluid flow dynamics under location uncertainty,(2014), Geophysical & Astrophysical Fluid Dynamics, 108, 2, 119–146. [2] G. Tissot, E. Mémin, Q. Jamet, (2023), Stochastic compressible Navier-Stokes equations under Location uncertainty, Stochastic Transport in Upper Ocean Dynamics, Springer.  [3] W. Bauer, P. Chandramouli, L. Li, and E. Mémin. Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models. Ocean Modelling, 151:101646, 2020. [4] Rüdiger Brecht, Long Li, Werner Bauer and Etienne Mémin. Rotating Shallow Water Flow Under Location Uncertainty With a Structure-Preserving Discretization. Journal of Advances in Modeling Earth Systems, 13, 2021MS002492. [5] V. Resseguier, L. Li, G. Jouan, P. Dérian, E. Mémin, B. Chapron, (2021), New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamics, Archives of Computational Methods in Engineering. [6] F.L. Tucciarone, E. Mémin, L. Li, (2022), Primitive Equations Under Location Uncertainty: Analytical Description and Model Development, Stochastic Transport in Upper Ocean Dynamics, Springer. [7] F.L. Tucciarone, E. Mémin, L. Li, (2023), Data driven stochastic primitive equations with dynamic modes decomposition, Stochastic Transport in Upper Ocean Dynamics, Springer.