A document by Simone Silvestri. Click on the document to view its contents.

Current eddy-permitting and eddy-resolving ocean models require dissipation to prevent a spurious accumulation of enstrophy at the grid scale. We introduce a new numerical scheme for momentum advection in large-scale ocean models that involves upwinding through a weighted essentially non-oscillatory (WENO) reconstruction. The new scheme provides implicit dissipation and thereby avoids the need for an additional explicit dissipation that may require calibration of unknown parameters. This approach uses the rotational, "vector invariant" formulation of the momentum advection operator that is widely employed by global general circulation models. A novel formulation of the WENO "smoothness indicators" is key for avoiding excessive numerical dissipation of kinetic energy and enstrophy at grid-resolved scales. We test the new advection scheme against a standard approach that combines explicit dissipation with a dispersive discretization of the rotational advection operator in two scenarios: (i) two-dimensional turbulence and (ii) three-dimensional baroclinic equilibration. In both cases, the solutions are stable, free from dispersive artifacts, and achieve increased "effective" resolution compared to other approaches commonly used in ocean models.

We describe CATKE, a parameterization for ocean microturbulence with scales between 1 and 100 meters. CATKE is a one-equation model that predicts diffusive turbulent vertical fluxes a prognostic turbulent kinetic energy (TKE) and a diagnostic mixing length that features a dynamic model for convective adjustment (CA). With its convective mixing length, CATKE predicts not just the depth range where microturbulence acts but also the timescale over which mixing occurs, an important aspect of turbulent convection not captured by convective adjustment schemes. As a result, CATKE can describe the competition between convection and other processes such as baroclinic restractification or biogeochemical production-destruction. We estimate CATKE’s free parameters with a posteriori calibration to eighteen large eddy simulations of the ocean surface boundary layer, and validate CATKE against twelve additional large eddy simulations with stronger and weaker forcing than used during calibration. We find that a CATKE-parameterized single column model accurately predicts the depth structure of buoyancy and momentum at vertical resolutions between 2 and 16 meters and with time steps of 10-20 minutes. We propose directions for future model development, and future efforts to recalibrate CATKE’s parameters against more comprehensive and realistic datasets.

A data-driven emulator for the baroclinic double gyre ocean simulation is presented in this study. Traditional numerical simulations using partial differential equations (PDEs) often require substantial computational resources, hindering real-time applications and inhibiting model scalability. This study presents a novel approach employing neural operators to address these challenges in an idealized double-gyre ocean simulation. We propose a deep learning approach capable of learning the underlying dynamics of the ocean system, complementing the classical methods, and effectively replacing the need for explicit PDE solvers at inference time. By leveraging neural operators, we efficiently integrate the governing equations, providing a data-driven and computationally efficient framework for simulating the double-gyre ocean circulation. Our approach demonstrates promising results in terms of accuracy and computational efficiency, showcasing the potential for advancing ocean modeling through the fusion of neural operators and traditional oceanographic methodologies. In comparison to a dynamical numerical model, we obtain 600x speedups allowing us to create 2000-day ensembles in tens of seconds instead of hours.