To what extent are sea level variations due to the expansion or contraction of the water column?

A simple model is used to study how does sea level change due to fresh water and heat fluxes through the ocean surface, as well as to wind forced and free waves. The first two contributions include dynamical effects related to the forced pressure gradients. These solutions (h_E & h_Q) are compared with the expected expansion of the water column (h_S & h_T) related to the salinity and temperature changes produced by the local fresh water and heat fluxes. These changes are restricted to a surface layer; deeper salinity and temperature variations are linked to vertical displacements of fluid elements, which are excluded from the definition of h_S and h_T.

Two conditions must be met in order to attribute sea level variations to the expansion or contraction of the water column. First, the sea level produced by the surface fluxes, h_E + h_Q, must be close to h_S + h_T. Second, this result is obtained with a mass-conserving model (i.e. one that allows for the thermohaline expansion of seawater) but not by the usual volume-conserving model (non-divergent three-dimensional velocity field).

It is found that the fresh water flux has a direct action on sea level, h_E, much larger than h_S. However, h_S is very similar to the part of h_E associated with baroclinic motions (essentially, the dynamic height) if and only if the horizontal scale is large enough. This result is the same with either volume or mass conserving models.

Surface heat flux, on the other hand, produces a sea level variation h_Q very similar to h_T if the horizontal scale is even larger. For the baroclinic part, this result is equally obtained with volume- or mass-conserving models, but a correct prediction of the barotropic part of h_Q at very large scales needs to be modeled in a mass-conserving model. In sum, the wavenumber and frequency of the heat flux must satisfy certain conditions in order for the inclusion of the thermal expansion to be crucial, and this is true only for the barotropic part of the response.