A comparison of second‐order and fourth‐order pressure gradient algorithms in a σ‐co‐ordinate ocean model

In stratified three‐dimensional models the use of a boundary‐fitted vertical co‐ordinate is known to produce errors in the horizontal pressure gradient calculation near steep topography. The error is due to the splitting of the horizontal pressure gradient term in each of the momentum equations into two parts and the subsequent incomplete cancellation of the truncation errors of those parts. In order to minimize these pressure gradient errors, a fourth‐order‐accurate pressure gradient calculation has been implemented and installed in SPEM, a three‐dimensional primitive equation ocean model. The stability and accuracy of the new scheme are compared with those of the original second‐order‐accurate model in a series of calculations of unforced flow in the vicinity of an isolated seamount. The new scheme is shown to have much smaller pressure gradient errors over a wide range of parameter space as well as a greater parametric domain of numerical stability.