An adjoint analysis of the meridional overturning circulation in an ocean model

Using the adjoint of a fully three-dimensional primitive equation ocean model in an idealized geometry, spatial variations in the sensitivity to surface boundary forcing of the meridional overturning circulation's strength are studied. Steady-state sensitivities to diapycnal mixing, wind stress, freshwater, and heat forcing are examined. Three different, commonly used, boundary-forcing scenarios are studied, both with and without wind forcing. Almost identical circulation is achieved in each scenario, but the sensitivity patterns show major ( quantitative and qualitative) differences. Sensitivities to surface forcing and diapycnal mixing are substantially larger under mixed boundary conditions, in which fluxes of freshwater and heat are supplemented by a temperature relaxation term or under flux boundary conditions, in which climatological fluxes alone drive the circulation, than under restoring boundary conditions. The sensitivity pattern to diapycnal mixing, which peaks in the Tropics is similar both with and without wind forcing. Wind does, however, increase the sensitivity to diapycnal mixing in the regions of Ekman upwelling and decreases it in the regions of Ekman downwelling. Wind stress in the Southern Oceans plays a crucial role in restoring boundary conditions, but the effect is largely absent under mixed or flux boundary conditions. The results highlight how critical a careful formulation of the surface forcing terms is to ensuring a proper response to changes in forcing in ocean models.