Part I: 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 we study the sensitivity of the current climate to the diapycnal diffusivity using a coupled model with a 3-dimensional global ocean component with idealized geometry. In a subsequent paper we analyze the sensitivity of the climate change to the same parameter.
      Our 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 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. The implication is that the amount of water upwelling from the deep ocean may be regulated by the diapycnal diffusion in the Indo-Pacific Ocean.
     The vertical heat balance in the ocean is controlled by: in the downward direction, (i) advection and (ii) diapycnal diffusion; in the upward direction, (iii) isopycnal diffusion and (iv) bolus velocity (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.
     We present sensitivity results 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 confirms the findings of 2-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 our model.

Part II: The sensitivity of the transient climate to the diapycnal diffusivity in the ocean is studied for a global warming scenario in which CO2 increases by 1% per year for 75 years. The thermohaline circulation slows down for about 100 years and recovers afterward, for any value of the diapycnal diffusivity. The rates of slowdown and of recovery, as well as the percentage recovery of the circulation at the end of 1000-year integrations, are variable but a direct relation with the diapycnal diffusivity cannot be found. At year 70 (when CO2, has doubled) an increase of the diapycnal diffusivity from 0.1 cm²/s to 1.0 cm²/s leads to a decrease in surface air temperature of about 0.4 K and an increase in sea level rise of about 4 cm The steric height gradient is divided into thermal component and haline component. It appears that, in the first 60 years of simulated global warming, temperature variations dominate the salinity ones in weakly diffusive models, whereas the opposite occurs in strongly diffusive models.
      The analysis of the vertical heat balance reveals that deep ocean heat uptake is due to reduced upward isopycnal diffusive flux and Gent-McWilliams advective flux. Surface warming, induced by enhanced CO2 in the atmosphere, leads to a reduction of the isopycnal slope which translates into a reduction of the above fluxes. The amount of reduction is directly related to the magnitude of the isopycnal diffusive flux and GM advective flux at equilibrium. These latter fluxes depend on the thickness of the thermocline at equilibrium, hence on the diapycnal diffusion. Thus, the increase of deep-ocean heat uptake with diapycnal diffusivity is an indirect effect that the latter parameter has on the isopycnal diffusion and GM advection.

© 2005 American Meteorological Society