Development of a semi-Lagrangian advection scheme for the NEMO ocean model (3.1)

Abstract

As resolutions of ocean circulation models increase, the advective Courant number – the ratio between the distance travelled by a fluid parcel in one time step and the grid size – becomes the most stringent factor limiting model time steps. Some atmospheric models have escaped this limit by using an implicit or semi-implicit semi-Lagrangian formulation of advection, which calculates materially conserved fluid properties along trajectories which follow the fluid motion and end at prescribed grid points. Unfortunately, this formulation is not straightforward in ocean contexts, where the irregular, interior boundaries imposed by the shore and bottom orography are incompatible with traditional trajectory calculations. This work describes the adaptation of the semi-Lagrangian method as an advection module for an operational ocean model. We solve the difficulties of the ocean's internal boundaries by calculating parcel trajectories using a time-exponential formulation, which ensures that all parcel trajectories remain inside the ocean domain despite strong accelerations near the boundary. Additionally, we derive this method in a way that is compatible with the leapfrog time-stepping 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.