27 Sep 2023
 | 27 Sep 2023

MQGeometry-1.0: a multi-layer quasi-geostrophic solver on non-rectangular geometries

Louis Thiry, Long Li, Guillaume Roullet, and Etienne Mémin

Abstract. This paper presents MQGeometry, a multi-layer quasi-geostrophic (QG) equations solver for non-rectangul ar geometries. We advect the potential voriticity (PV) with finite volumes to ensure global PV conservation thanks to a staggered discretization of the PV and stream-function (SF). Thanks to this staggering, the PV is defined inside the domain, removing the need for defining the PV on the domain's boundary. We compute PV fluxes with upwind-biased interpolations whose implicit dissipation replaces the usual explicit (hyper-)viscous dissipation. The presented discretization does not require the tuning of any additional parameter, e.g. additional eddy viscosity. We solve the QG elliptic equation with a fast discrete sine transform spectral solver on rectangular geometry. We extend this fast solver to non-rectangular geometries using the capacitance matrix method. We validate our solver on a vortex-shear instability test case in a circular domain, a vortex-wall interaction test-case, and on an idealized wind-driven double-gyre configuration in a octogonal domain at a eddy-permitting resolution. We release a concise, efficient, and auto-differentiable PyTorch implementation of our method to facilitate future developments upon this new discretization, e.g. machine learning parameterization or data-assimilation techniques.

Louis Thiry et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-1715', Anonymous Referee #1, 06 Oct 2023
    • AC1: 'Reply on RC1', Louis Thiry, 09 Nov 2023
  • RC2: 'Comment on egusphere-2023-1715', Anonymous Referee #2, 09 Oct 2023
    • AC2: 'Reply on RC2', Louis Thiry, 09 Nov 2023

Louis Thiry et al.

Louis Thiry et al.


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Short summary
We present a new way of solving the quasi-geostrophic (QG) equations, a simple set of equations describing ocean dynamics. Our method is solely based on the numerical methods used to solve the equations and requires no parameter tuning. Moreover, it can handle non-rectangular geometries, opening the study of QG equations on realistic domains. We release a Pytorch implementation to ease future machine-learning developments on top of the presented method.