Stochastic parameterization of general non-hydrostatic processes with a focus on deep convection
Quentin
Jamet
Institut national de recherche en informatique et en automatique (INRIA)
Talk
(Virtual)
The aim of this work is to provide theoretical and numerical developments toward a stochastic parameterization of deep ocean convection for use in General Circulation Models (GCM). We first develop a stochastic version of the compressible Navier–Stokes equations in the framework of Location Uncertainty (Mémin, 2014), incorporating the effects of both smooth-in-time and stochastic source terms in the stochastic Reynolds transport theorem.
We derive stochastic transport equations for the primitive variables (i.e. density, velocity and temperature) by applying this conservation theorem to density, momentum and total energy. We demonstrate that previous results for incompressible stochastic Navier–Stokes equations and the stochastic Boussinesq equations can be recovered by applying low Mach and Boussinesq approximations, respectively, to this more general set of equations.
Based on these generalizations, we then conduct numerical analyses on Large Eddy Simulation (LES) of a free convection event with the aim of first identifying leading-order terms in the time evolution of the 1D vertical profile of temperature. Particularly, we illustrate that stochastic transport has a moderate impact, but its induced modified drift and associated diffusivity play a leading-order role in representing penetrative convection at the base of the mixed layer. Additionally, we show that when the horizontal homogeneity assumption is relaxed (i.e., moving from a 1D system to a 3D system), a direct quasi-nonhydrostatic pressure correction method (Klingbeil and Burchard, 2013) allows us to partially recover the kinetic energy spectral content of LES nonhydrostatic simulations without the need for a full non-hydrostatic model, thereby reducing numerical costs significantly. These preliminary results suggest that stochastic modeling, and the LU framework in particular, offer an attractive approach to representing the effects of coherent structures associated with deep ocean convection through stochastic parameterizations for use in GCMs and climate models.
We derive stochastic transport equations for the primitive variables (i.e. density, velocity and temperature) by applying this conservation theorem to density, momentum and total energy. We demonstrate that previous results for incompressible stochastic Navier–Stokes equations and the stochastic Boussinesq equations can be recovered by applying low Mach and Boussinesq approximations, respectively, to this more general set of equations.
Based on these generalizations, we then conduct numerical analyses on Large Eddy Simulation (LES) of a free convection event with the aim of first identifying leading-order terms in the time evolution of the 1D vertical profile of temperature. Particularly, we illustrate that stochastic transport has a moderate impact, but its induced modified drift and associated diffusivity play a leading-order role in representing penetrative convection at the base of the mixed layer. Additionally, we show that when the horizontal homogeneity assumption is relaxed (i.e., moving from a 1D system to a 3D system), a direct quasi-nonhydrostatic pressure correction method (Klingbeil and Burchard, 2013) allows us to partially recover the kinetic energy spectral content of LES nonhydrostatic simulations without the need for a full non-hydrostatic model, thereby reducing numerical costs significantly. These preliminary results suggest that stochastic modeling, and the LU framework in particular, offer an attractive approach to representing the effects of coherent structures associated with deep ocean convection through stochastic parameterizations for use in GCMs and climate models.
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jamet-quentin-oceanmodel-CP.pdf
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