An operational comparative test of z-levels PGF schemes to reduce pressure gradient errors of the ocean model POM

Abstract

Numerical schemes for computing pressure gradient force (PGF) in sigma-coordinate ocean models are usually tested in absence of external forcing and with a horizontally uniform stratification, a condition where the ocean should be at rest. In this study PGF schemes based on z-coordinate levels are compared with the standard density scheme of Princeton Ocean Model (POM) in tests of this kind with different topographies and stratifications (including the idealized seamount problem and a realistic case in a basin-wide domain) to investigate if idealized results are verified in realistic cases. Results of the performed tests show that all the tested schemes produce stronger spurious currents in the realistic case respect to the seamount problem and the behavior of z-levels schemes, less robust than the standard POM scheme, is more stable over a realistic topography than in the seamount case. In the test realized with realistic topography and stratification spurious barotropic currents produced by z-levels schemes are strongly reduced respect to the POM standard scheme and the ‘spline interpolation’ scheme performs the best among the z-coordinate schemes, giving spurious barotropic currents of a few cm/s. Considering that pre-operational tests of this kind (unforced and with a flat stratification) can give useful indications on the effects of PGF errors in realistic cases (baroclinic, externally forced) on condition that bathymetry, stratification and distribution of grid cells is the same of the operational case, the reduced level of errors indicates the possibility to use z-levels PGF schemes in practical applications.