Internal Pressure Errors in Sigma-Coordinate Ocean Models

Abstract

Sigma-coordinate ocean models, or models based on more generalized topography following coordinate systems, are presently widely used in oceanographic studies. The controversy over internal pressure errors in sigma-coordinate ocean models is, however, still worrisome to at least some of the users. In the present study, experiments with the seamount case using both constant and large horizontal viscosities and a Smagorinsky-type viscosity are performed. For the constant viscosity (2000 m2 s?1) case, the errors do not grow prognostically. For the more realistic case with Smagorinsky viscosity and a value of the viscosity parameter in the range usually recommended, 0.2, the errors grow very strongly prognostically. Large vertical transports associated with the eight cyclones and anticyclones around the seamount create strong and real internal pressures that add on to the initial erroneous internal pressure. The growth may be balanced by multiplying the viscosity parameter by approximately a factor of 100. A more realistic experiment for the North Sea and the Skagerrak is also performed and model results and observations are compared. It is shown that conclusions from idealized experiments may not be valid in more realistic cases. Internal pressure errors may be very significant in areas where there is a combination of stratification and varying topography. When applying Smagorinsky-type viscosity, these errors may grow prognostically unless much larger values of the viscosity parameter than usually recommended are applied.