Influence of multi-step topography on barotropic waves and consequences for numerical modeling

Propagation of barotropic topographic Rossby waves (TRWs) and Kelvin type waves over topography consisting of multiple steps is investigated. The transformation of the wave solution from one limiting case with narrow and small steps most closely approximating a continuous slope to another limiting case with wide and high steps is analyzed. The analysis is based on the numerical simulation of the topographic waves by employing a model with σ-level (terrain following) vertical coordinates and several Z-level (geopotential following) vertical coordinate model configurations with a varying number of vertical levels. An analytical solution for frequencies of quasi-geostrophic waves over a multi-step topography is derived to examine how the wave solution transforms for different vertical resolution (yielding different step sizes). Analysis of the model and analytical results suggests criteria for the vertical resolution of a Z-level model with a given topography to support TRW-like solutions and to prevent the formation of artificial edge-trapped waves. When the model has a coarse vertical resolution yielding wide steps compared to the trapping scale of the wave the quasi-geostrophic waves convert to double Kelvin waves trapped along the step edges. In the model with fine vertical resolution there is a transition from the quasi-geostrophic wave to the TRW solution.