Estimates of Cabbeling in the Global Ocean

Abstract

Owing to the larger thermal expansion coefficient at higher temperatures, more buoyancy is put into the ocean by heating than is removed by cooling at low temperatures. The authors show that, even with globally balanced thermal and haline surface forcing at the ocean surface, there is a negative density flux and hence a positive buoyancy flux. As shown by McDougall and Garrett, this must be compensated by interior densification on mixing due to the nonlinearity of the equation of state (cabbeling). Three issues that arise from this are addressed: the estimation of the annual input of density forcing, the effects of the seasonal cycle, and the total cabbeling potential of the ocean upon complete mixing. The annual expansion through surface density forcing in a steady-state ocean driven by balanced evaporation–precipitation–runoff (E–P–R) and net radiative budget at the surface Q[subscript net] is estimated as 74 000 m[superscript 3] s[superscript −1] (0.07 Sv; 1 Sv ≡ 10[superscript 6] m[superscript 3] s[superscript −1]), which would be equivalent to a sea level rise of 6.3 mm yr[superscript −1]. This is equivalent to approximately 3 times the estimated rate of sea level rise or 450% of the average Mississippi River discharge. When seasonal variations are included, this density forcing increases by 35% relative to the time-mean case to 101 000 m[super script 3] s[superscript −1] (0.1 Sv). Likely bounds are established on these numbers by using different Q[subscript net] and E–P–R datasets and the estimates are found to be robust to a factor of ~2. These values compare well with the cabbeling-induced contraction inferred from independent thermal dissipation rate estimates. The potential sea level decrease upon complete vertical mixing of the ocean is estimated as 230 mm. When horizontal mixing is included, the sea level drop is estimated as 300 mm.