Estimation of the internal pressure gradient in σ-coordinate ocean models: comparison of second-, fourth-, and sixth-order schemes

Sigma-coordinate ocean models are attractive because of their abilities to resolve bottom and surface boundary layers. However, these models can have large internal pressure gradient (IPG) errors. In this paper, two classes of methods for the estimation of the IPGs are assessed. The first is based on the integral approach used in the Princeton Ocean Model (POM). The second is suggested by Shchepetkin and McWilliams (2003) based on Green’s theorem; thus, area integrals of the pressure forces are transformed into line integrals. Numerical tests on the seamount problem, as well as on a northwestern Atlantic grid using both classes of methods, are presented. For each class, second-, fourth-, and sixth-order approximations are tested. Results produced with a fourth-order compact method and with cubic spline methods are also given. The results show that the methods based on the POM approach in general give smaller errors than the corresponding methods given in Shchepetkin and McWilliams (2003). The POM approach also is more robust when noise is added to the topography. In particular, the IPG errors may be substantially reduced by using the computationally simple fourth-order method from McCalpin (1994).