Overview of evolution of ROMS computational kernel: How different things add up to make an ocean model.

Alexander Shchepetkin, I.G.P.P. UCLA

Starting with the analysis of time-stepping algorithms for a simple wave system of equations, we follow how bottom-up design of ROMS code
adds more and more features, and how several remotely-related contexts interact with each other to explain the choices we made. This involves weighted consideration of physical processes, mathematical algorithms, development of modern computer architecture. Due to mathematical feedback between the baroclinic momentum and tracer equations and, similarly, between the barotropic momentum and continuity equations, it is advantageous to treat both modes so that, after a time step for the momentum equation, the computed velocities participate immediately in the computation of tracers and continuity, and vice versa, rather than advancing all equations for one time step simultaneously. This leads to a new family of time-stepping algorithms that combine forward-backward feedback with the best known synchronous algorithms, allowing an increased time step due to the enhanced internal stability without sacrificing its accuracy. Based on these algorithms we design a split-explicit hydrodynamic kernel for a realistic oceanic model, which addresses multiple numerical issues associated with mode splitting. This kernel utilizes consistent temporal averaging of the barotropic mode via a specially designed filter function to guarantee both exact conservation and constancy preservation properties for tracers and yields more accurate (up to second-order), resolved barotropic processes, while preventing aliasing of unresolved barotropic signals into the slow baroclinic motions. It has a more accurate mode-splitting due to redefined barotropic pressure-gradient terms to account for the local variations in density field, while maintaining the computational efficiency of a split model. It is naturally compatible with a variety of centered and upstream-biased high-order advection algorithms, and helps to mitigate computational cost of expensive physical parameterization of mixing processes and submodels.