Semi-Lagrangian advection in the NEMO ocean model

Abstract. As model resolutions increase, the Courant-Frederichs-Lewy (CFL) number based on advective motion becomes the limiting factor in setting the timestep of time-explicit circulation models. Some atmospheric models escape this limit by using an implicit or semi-implicit semi-Lagrangian formulation of advection. This formulation calculates fluid properties along parcel trajectories which follow the fluid motion and end, for each timestep, at prescribed grid-points. This work is the first application of the semi-Lagrangian method to an operational ocean model. In this context, we solve the difficulty posed by the ocean's irregular, interior boundaries by calculating parcel trajectories using a time-exponential formulation. This formulation ensures that all trajectories that are solutions to a fixed-point iteration have an origin point in the valid domain, and it does not require any prescribed extrapolation of the fluid velocities into the invalid (land) portion of the domain. We derive this method in a way that is compatible with the leapfrog timestepping scheme used in the NEMO-OPA (Nucleus for European Modelling of the Ocean, Océan Parallélisé) ocean model, and we present simulation results for a simplified test-case of flow past a model island and for 10-year free runs of the global ocean on the quarter-degree ORCA025 grid.