This paper develops an analysis framework to identify how physical processes, as represented in ocean climate models, impact the evolution of global mean sea level. The formulation utilizes the coarse grained equations appropriate for an ocean model, and starts from the vertically integrated mass conservation equation in its Lagrangian form. Global integration of this kinematic equation results in an evolution equation for global mean sea level that depends on two physical processes: boundary fluxes of mass and the non-Boussinesq steric effect. The non-Boussinesq steric effect itself contains contributions from boundary fluxes of buoyancy; interior buoyancy changes associated with parameterized subgrid scale processes; and motion across pressure surfaces. The non-Boussinesq steric effect can be diagnosed in either volume conserving Boussinesq or mass conserving non-Boussinesq ocean circulation models, with differences found to be negligible.
We find that surface heating is the dominant term affecting sea level arising from buoyancy fluxes, contributing to a net positive tendency to global mean sea level, largely due to low latitude heating and because the thermal expansion coefficient is much larger in the tropics than high latitudes. Subgrid scale effects from parameterized quasi-Stokes transport, vertical diffusion, cabbeling, and thermobaricity are also found to be significant, each resulting in a reduction of global mean sea level. Sea level rise through low latitude heating is largely compensated by a sea level drop from poleward eddy heat transport and ocean mixing. Spatial variations in the thermal expansion coefficient provide an essential modulation of how physical effects from mixing and eddy induced advective transport impact global mean sea level.
► Theoretical framework for how physical processes impact global mean sea level in ocean models. ► Mathematical and physical specification of the non-Boussinesq steric effect. ► How boundary buoyancy fluxes and interior processes impact global mean sea level. ► Global model examples of the non-Boussinesq steric effect with associated budget for global mean sea level.