To study the partition we express the ratio HA / HO as
HA / HO = PSIA/PSIO * (CA*DTA/CO*DTO) (1)
where PSIA, PSIO represent the strengths of the meridional mass transports in the respective fluids, CA, CO are their heat capacities, DTA is a typical vertical difference in moist potential temperature over the tropopause and DTO is a measure of the potential temperature change across the thermocline.
We argue that the observed partition of heat transport between atmosphere and ocean is a robust feature of the Earth climate and reflect two limits of Eq.(1):
(i) a dominance of atmospheric mass transport in mid-to-high latitudes, i.e. HA/ HO ~ PSIA / PSIO >> 1
(ii) a dominance of oceanic stratification in the Tropics, i.e. HA / HO ~ CA*DTA /CO*DTO << 1
Motivated by simple dynamical arguments, these ideas are tested against the NCEP-NCAR reanalysis, and a long simulation of a coupled atmosphere-ocean model of intermediate complexity.