On the pressure gradient error in sigma coordinate ocean models: A comparison with a laboratory experiment

Abstract

Boundary-fitted vertical coordinates are frequently used in three-dimensional primitive equation models. The sigma coordinate transformation, in which the water column is divided into a number of layers independently of the water depth, is commonly used. Unfortunately, it is well known that this transformation can produce an error in the calculation of the pressure gradient terms. The error can be significant in regions with steep topography and large density gradients. The importance of this error in simulations of coastal currents is difficult to test in reality. The competing effects of the models dynamics, its sensitivity, for example, to the chosen grid resolution or numerical techniques, are hard to separate. In the following we first identify the pressure gradient error and assess its magnitude in relation to two analytical reference solutions. A number of commonly used techniques to reduce the error are compared. Of these techniques, z-level based pressure gradient calculations are shown to improve the simulation results. We then take a step in the direction of a more realistic simulation and use a laboratory experiment as our reference solution. The results demonstrate that a sigma coordinate model can be used in a region such as the Skagerrak where steep topography and large density gradients are present. Errors do exist which need to be taken into account when interpreting the model results. This is important, as the Skagerrak dominates the North Sea and Baltic Sea system, and models that run with a coarse grid resolution may lead to artificial flows. Copyright 1999 by the American Geophysical Union.