Assessing the importance of non-Boussinesq effects in a coarse
resolution global ocean model.

M. Losch, A. Adcroft, and J.-M. Campin

The advent of the GRACE mission presents the opportunity to accurately
measure variations in bottom pressure. Such a data source will prove  
valuable in state estimation and constraining general circulation
models (GCMs) in general. However, conventional GCMs make the
Boussinesq approximation as a consequence of which mass is not
conserved. Thus Boussinesq models have an implicit drift in bottom
pressure. By use of the height-pressure coordinate isomorphism
implemented in the MIT GCM, we can evaluate the impact of
non-Boussinesq effects.  We find that although implementing a
non-Boussinesq model in pressure coordinates is relatively
straight-forward, making a direct comparison between height and
pressure coordinate (i.e., Boussinesq and non-Boussinesq) models is
not simple. Here we present a careful comparison of the Boussinesq and
non-Boussinesq solutions ensuring that only non-Boussinesq effects can
be responsible for the observed differences. As a yard-stick, we also 
compare differences between the Boussinesq hydrostatic and
non-hydrostatic models, another approximation commonly made in
GCMs. We find that model errors (differences) due to the Boussinesq
approximation are apparently smaller than the errors due to the
hydrostatic approximation. We also compare these model errors with
uncertainties associated with model parameterizations and find that
non-Boussinesq and non-hydrostatic effects are much smaller than these
uncertainties. We conclude that non-Boussinesq effects are negligible 
with respect to other model errors. However, since there is no
additional cost incurred in using a pressure coordinate model,
non-Boussinesq modeling is preferable simply for puristic reasons.