On Internal Pressure Errors in Sigma-Coordinate Ocean Models


Jarle Berntsen

Department of Mathematics, University of Bergen, Norway



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 worrying 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 m^2s^{-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 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. For instance the best algorithm for the seamount case produced artificial vertical excursions in the Skagerrak.

The main conclusion is that the internal pressure errors may still be very significant in areas where we have 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.

A new filtering technique that may reduce the pressure errors significantly will be presented.