The Equilibration of an Adjoint Model on Climatological Time Scales

Part I: Using the adjoint of a fully three-dimensional primitive equation model of the ocean general circulation, we study spatial variations in the sensitivity to surface boundary forcing of the meridional overturning circulation's strength. An idealized geometry, consisting of a single basin, closed in the northern hemisphere and with a periodic channel in southern hemisphere, is employed. Sensitivities to momentum, fresh water and heat forcing and examined on time scales of decades to centuries. Three different, commonly used, boundary forcing scenarios are studied. Almost identical circulation is achieved in each scenario, but the sensitivity patterns show major, quantitative and qualitative, differences. For relaxation boundary conditions, under which the surface hydrography of the ocean model is relaxed toward climatological values, the overturning is sensitive to changes in thermal forcing in high latitudes and to diapycnal mixing in the tropics. The sensitivities to surface forcing and diapycnal mixing are substantially larger under mixed boundary conditions, in which fluxes of fresh-water and heat are supplemented by a temperature relaxation term or under flux boundary conditions, in which climatological fluxes alone drive circulation. The sensitivities to buoyancy forcing also show substantial patterns away from the sites of convection and downwelling in models with less constraining surface boundary conditions. Winds in the southern hemisphere's open channel play an important role under restoring boundary conditions. The sensitivities are, however, dwarfed by a tropical - subtropical sensitivity pattern linked to Ekman processes under flux boundary conditions.

We examine the equilibrated and time evolving adjoint solutions to identify the principle "adjustment mechanisms" through which the overturning strength adapts to perturbations in surface forcing. The differences in sensitivities can be attributed to the different adjustment mechanisms being permitted, or suppressed, under different boundary conditions. The results indicate how feedbacks between the atmosphere and ocean in a coupled-climate simulation can be affected, and significantly altered, by boundary condition formulation. The results obtain using the simple geometry employed in this study carry over to a more realistic geometry study that is reported in a companion paper.

Part II: Multi-century sensitivities in a realistic geometry global ocean general circulation model are analyzed under different surface boundary conditions using an adjoint technique. The steady-state circulations of the different configurations are comparable and resemble the current planetary circulation well. This paper takes advantage of the adjoint model's ability to generate maps of sensitivity of a diagnostic, the meridional overturning's strength, to all model parameters. This property of adjoints is used to review several theories, which have been elaborated to explain the strength of the North Atlantic's meridional overturning. This paper demonstrates the profound impact of boundary conditions in permitting or suppressing mechanisms within a realistic model of the contemporary ocean circulation. For example, the so-called "Drake Passage Effect", in which wind stress in the Southern Ocean acts as the main driver of the overturning's strength, is shown to be an artifact of boundary conditions which restore the ocean's surface temperature and salinity towards prescribed climatologies. Advective transports from the Indian and Pacific basins play an important role in setting the strength of the overturning circulation under "mixed" boundary conditions, in which a flux of freshwater is specified at the ocean's surface.

The most "realistic" regime couples atmospheric energy and moisture balances to the ocean. In this configuration, inspection of the adjoint solutions' global maps of sensitivity to wind stress and diapycnal mixing suggests a significant role for near surface Ekman processes in the tropics. By increasing the ocean's stratification, Ekman pumping increases the efficiency of downward mixing of heat, which in turn can provide the requisite energy to upwell deep waters formed in the northern part of the basin. Buoyancy also plays an important role in setting the overturning's strength, through direct thermal forcing near the sites of convection, or through the advection of salinity anomalies in the Atlantic basin.