Long-wave explicit and Short-wave implicit (LESI) treatment of the barotropic mode to accurately calculate slow modes in ocean models

Many ocean models are primarily concerned with calculating currents of slowly propagating modes that are dynamically associated with buoyancy, Coriolis, field accelerations, and slowly-varying forcing. Calculating such slow modes involves adjustments by the very much faster barotropic mode. In order to minimize the computational cost, two approaches are commonly used. The split-explicit method solves for both fast and slow modes explicitly but with different time steps. The semi-implicit method uses the same time step for fast and slow modes but treats the fast barotropic waves implicitly and the slow modes explicitly. The present work demonstrates a refinement to the semi-implicit method. Weighted Jacobi iterations are used to low-pass filter the fast barotropic mode so that long wavelengths can be treated explicitly. The short-wave part of the fast barotopic mode is still treated implicitly. Damping of the fast barotropic modes is less severe than for the corresponding implicit calculation. Importantly, tests show that a slow internal wave is accurately modelled and the solution is stable, even with the addition of barotropic noise. The method is demonstrated using a three-dimensional model of a lagoon system.