Sea level variations induced by heating and cooling: An evaluation of the Boussinesq approximation in ocean models

In this paper a sigma coordinate ocean model is modified to remove the commonly used Boussinesq approximation so that the effect of thermal expansion is exactly included in the basic equations in order to cope with the seasonal heating cycle and the detection of climate change through variation in sea level height. Tests are performed to evaluate the differences between Boussinesq and non-Boussinesq calculations under different heating and cooling conditions and different model domains. For an idealized case of a flat bottom, shallow ocean basin without wind forcing, simulations of a warm eddy show that the non-Boussinesq dynamics have only a minor effect on the baroclinic current field. However, vertically averaged velocities, though small compared with the baroclinic velocities, are cyclonic for the Boussinesq calculation and anticyclonic for the non-Boussinesq calculation. The results indicate that global or closed basin Boussinesq models should be able to simulate most of the observed steric sea level changes on seasonal or climate timescales, when corrected by a spatially uniform, time-dependent factor calculated from the volume-averaged density change. The seasonal variation of the globally averaged sea level calculated from climatological data is small, about 1 cm. Variations in steric sea level in regional models, both Boussinesq and non-Boussinesq, may differ from those of global models owing to the unknown transport across their boundaries associated with the local heating and cooling. A spatially uniform, time-dependent correction, similar to that associated with thermal expansion, is proposed to account for transport across open boundaries of regional models. Variations of sea level obtained from a Boussinesq model of the Atlantic Ocean approximate the seasonal signal due to the heating/cooling cycle of each hemisphere as observed by satellite altimeter data.