A Kinematic Kinetic Energy Backscatter Parametrization: From Implementation to Global Ocean Simulations

Abstract

Ocean models at eddy-permitting resolution are generally overdissipative, damping the intensity of the mesoscale eddy field. To reduce overdissipation, we propose a simplified, kinematic energy backscatter parametrization built into the viscosity operator in conjunction with a new flow-dependent coefficient of viscosity based on nearest neighbor velocity differences. The new scheme mitigates excessive dissipation of energy and improves global ocean simulations at eddy-permitting resolution. We find that kinematic backscatter substantially raises simulated eddy kinetic energy, similar to an alternative, previously proposed dynamic backscatter parametrization. While dynamic backscatter is scale aware and energetically more consistent, its implementation is more complex. Furthermore, it turns out to be computationally more expensive, as it applies, among other things, an additional prognostic subgrid energy equation. The kinematic backscatter proposed here, by contrast, comes at no additional computational cost, following the principle of simplicity. Our primary focus is the discretization on triangular unstructured meshes with cell placement of velocities (an analog of B-grids), as employed by the Finite-volumE Sea ice-Ocean Model (FESOM2). The kinematic backscatter scheme with the new viscosity coefficient is implemented in FESOM2 and tested in the simplified geometry of a zonally reentrant channel as well as in a global ocean simulation on a 1/4°mesh. This first version of the new kinematic backscatter needs to be tuned to the specific resolution regime of the simulation. However, the tuning relies on a single parameter, emphasizing the overall practicality of the approach. Plain Language Summary At the currently affordable resolution, ocean models as part of climate models are facing the challenge of adequately representing mesoscale eddies, the weather systems of the oceans. The models tend to lose too much kinetic energy, which strongly reduces the strength of eddies in the simulations and causes large, systematic model errors. The so-called backscatter approach feeds energy back into the ocean to compensate for some of the lost energy. This leads to substantially better simulations of eddy variability as well as the oceanic mean currents and a reduction of systematic model errors in the distribution of salt and heat, as shown by comparison with observations. The key advantage of the scheme proposed here is that it can be implemented at no additional computational cost.

Geophysical fluid models with simple energy backscatter: explicit flows and unbounded exponential growth

“…[8]; we refer to [4] for a detailed discussion and relations to other approaches. Simulations with backscatter have been found to provide energy 'at the right place', matching the result more closely to observations and high resolutions comparisons [9].…”

“…Motivated by the numerical backscatter scheme [4,8,9], we have studied the impact of simplified backscatter via classes of explicit flows in the shallow water and rotating Boussinesq equations on the whole space. Here we have found that backscatter induces unbounded instability of the zero state in the sense of unboundedly and exponentially growing flows, also with vertical structure and also for stable stratification.…”

Sensitivity of a Coarse‐Resolution Global Ocean Model to a Spatially Variable Neutral Diffusivity

“…A range of theories have been developed, most of which focus primarily on the adiabatic eddy‐driven circulation represented by κ GM (e.g., Cessi, 2008; Eden et al., 2009; Eden & Greatbatch, 2008; Jansen & Held, 2014; Jansen et al., 2015, 2019; Mak et al., 2018; Marshall & Adcroft, 2010; Pearson et al., 2017; Smith & Vallis, 2002; Treguier et al., 1997; Visbeck et al., 1997). Some of these schemes are based on energy conservation and consider the effects of mesoscale eddies in the momentum budget (e.g., Bachman, 2019; Eden & Greatbatch, 2008; Jansen & Held, 2014; Jansen et al., 2019; Juricke et al., 2020). However, the independent choice of the neutral diffusivity κ n has received less attention.…”

Parameterizing the Impact of Unresolved Temperature Variability on the Large‐Scale Density Field: 2. Modeling

“…This is exacerbated by the fact that backscatter associated with Reynolds stresses (as studied by Grooms et al (2015)) occurs wherever the eddy kinetic energy is large, whereas the backscatter associated with density corrections is confined to a smaller subset of the domain where there are large resolved temperature gradients. Some combination of Reynolds-stress-driven backscatter (e.g., Bachman, 2019; Jansen et al, 2019; Juricke et al, 2020), backscatter associated with density corrections, and other forms of stochastic noise (e.g., Grooms, 2016;Grooms & Kleiber, 2019) may be necessary to achieve a large increase in low-resolution model variability.…”