The diapycnal diffusivity in the ocean is one of the least known parameters in current climate models. Measurements of this diffusivity are sparse and insufficient for compiling a global map. Inferences from inverse methods and energy budget calculations suggest as much as a factor of 5 difference in the global mean value of the diapycnal diffusivity. Yet, the climate is extremely sensitive to the diapycnal diffusivity. In this paper the sensitivity of the current climate to the diapycnal diffusivity is studied, focusing on the changes occurring in the ocean circulation. To this end, a coupled model with a three-dimensional ocean with idealized geometry is used.The results show that, at equilibrium, the strength of the thermohaline circulation in the North Atlantic scales with the 0.44 power of the diapycnal diffusivity, in contrast to the theoretical value based on scaling arguments for uncoupled models of 2/3. On the other hand, the strength of the circulation in the South Pacific scales with the 0.63 power of the diapycnal diffusivity in closer accordance with the theoretical value.The vertical heat balance in the global ocean is controlled by, in the downward direction, (i) advection and (ii) diapycnal diffusion; in the upward direction, (iii) isopycnal diffusion and (iv) parameterized mesoscale eddy [Gent-McWilliams (GM)] advection. The size of the latter three fluxes increases with diapycnal diffusivity, because the thickness of the thermocline also increases with diapycnal diffusivity leading to greater isopycnal slopes at high latitudes, and hence, enhanced isopycnal diffusion and GM advection. Thus larger diapycnal diffusion is compensated for by changes in isopycnal diffusion and GM advection. Little change is found for the advective flux because of compensation between downward and upward advection.Sensitivity results are presented for the hysteresis curve of the thermohaline circulation. The stability of the climate system to slow freshwater perturbations is reduced as a consequence of a smaller diapycnal diffusivity. This result is consistent with the findings of two-dimensional climate models. However, contrary to the results of these studies, a common threshold for the shutdown of the thermohaline circulation is not found in this model.
