Notes on Parameterized Energy Pathways in the Ocean: Insights From Stochastic and Deterministic Kinetic Energy Injection

Abstract

Accurately representing ocean dynamics across interacting scales remains a challenge in numerical modeling. This study examines mesoscale eddy parameterization in eddy-permitting ocean models by incorporating novel stochastic perturbations and comparing them with a well-tested dynamic kinetic energy backscatter scheme. Momentum dissipation through eddy viscosity, a key aspect at such model resolutions, causes excessive dissipation not only at the grid scale but across all scales, including energy-containing ones. This necessitates methods like dynamic backscatter to counteract energy loss and restore variability. Stochastic perturbations provide an alternative by reinjecting energy and capturing small-scale variability. Using a double-gyre FESOM2 configuration, we assess two stochastic forcing schemes, applied with and without dynamic backscatter. The stochastic perturbations are generated using linear inverse modeling based on a high-resolution reference simulation. Both stochastic methods improve simulated dynamics, particularly heat distribution and kinetic energy, though they are less effective at large scales than dynamic backscatter. Contrary to expectations, combining stochastic forcing with dynamic backscatter does not yield substantial improvements. Moreover, none of the schemes significantly enhances mean kinetic energy in the jet region, suggesting unresolved dynamics at this resolution despite increased eddy-kinetic energy (EKE). A comprehensive scale analysis, including kinetic energy production, transfer, dissipation, and spectra, highlights distinct energy pathways. Energy injection by dynamic backscatter directly increases kinetic energy, while stochastic perturbations enhance potential energy conversion and subsequent transfer to EKE. These findings emphasize the need for carefully designed energy injection patterns aligned with flow dynamics to improve parameterizations at eddy-permitting resolutions.