Spurious Forces Can Dominate the Vorticity Budget of Ocean Gyres on the C‐Grid

Abstract

Accurately representing the sea floor has always been a challenge for the ocean modeling community. Quantifying the full influence of the sea floor on model circulations is important for both future model development and the interpretation of results from existing models. We present a diagnostic method that reveals how bottom topography influences the depth-integrated vorticity budget of general circulation models (GCMs) and we identify significant spurious forces that emerge from the discrete Coriolis force when calculated on a C-grid (Mesinger & Arakawa, 1976) using z-coordinates. The recent article by Stewart et al. (2021) also studied the impact of bottom topography on vorticity budgets. However, the model used by Stewart et al. ( 2021) is a two layer isopycnal model where the bottom topography is completely contained in the lower density layer. In this article we consider models that have a higher vertical resolution and a step-like bathymetry. It is in these more commonly used models that we identify a new category of spurious forces.The textbook theory of gyres relies on the idea of a depth-integrated vorticity budget and gyres can be classified by the leading order terms in the depth-integrated vorticity equation. For example, the Stommel (1948) gyre

Ocean Barotropic Vorticity Balances: Theory and Application to Numerical Models

“…With stronger boundary currents and rougher bathymetry, we expect at least as high numerical Coriolis torques at higher resolution, as confirmed by results from Styles et al. (2022) at the eddy‐permitting resolution.…”

“…From a model analysis perspective, the depth‐integrated vorticity Equation has the advantage of retaining most of the meridional flow and containing limited numerical torques, contrary to the BV Equation analyzed here and in Styles et al. (2022).…”

“…This package extends the work of Styles et al. (2022) who focused exclusively on the discretization of the BV Equation . The only required input parameters are: the terms of the zonal and meridional momentum equations, horizontal velocities, surface wind stress and the model mesh and mask parameters.…”

“…This issue has been thoroughly addressed for the BV equation by Styles et al. (2022) and we have extended the analysis to the alternatives vorticity equations for the depth‐integrated flow. First, we discuss the configuration dependence, given a C‐grid numerical platform with geopotential vertical coordinates.…”

“…A series of idealized configurations were proposed which addressed the effects of variable topography and baroclinicity on the depth‐integrated circulation (Borowski et al., 2002; Hendershott & Rizzoli, 1976; Jackson et al., 2006; Jagannathan et al., 2021; Jouanno & Capet, 2020; Olbers & Eden, 2003; Olbers & Lettmann, 2007; Stewart et al., 2021). In parallel, a limited number of studies have addressed the vorticity of the depth‐integrated circulation in three‐dimensional numerical simulations with realistic topography and external forcings (Bell, 1999; Ezer & Mellor, 1994; Gula et al., 2015; Hughes & de Cuevas, 2001; Le Bras et al., 2019; Le Corre et al., 2020; Myers et al., 1996; Schoonover et al., 2016; Sonnewald et al., 2019; Spence et al., 2012; Styles et al., 2022; Wang et al., 2017; Yeager, 2015). Overall, these studies highlight the limitations of the Sverdrup balance and the importance of the topographic, baroclinic and inertial torques.…”