Tracer budgets in the warm water sphere

In global equilibrium numerical solutions for the oceanic general circulation, we examine the time-mean budgets for the tracers potential temperature and salinity integrated over volumes bounded by interior surfaces of constant tracer values and lying within the warm water sphere. In this domain, the budgets have surface fluxes primarily of one sign that must be balanced by mesoscale and microscale fluxes through its lower boundary, because advection makes a zero integral contribution. The mesoscale fluxes are represented by the isopycnally orientated, quasiadiabatic parameterization of Gent and McWilliams and contribute little to the integral budgets where isopycnals are nearly tangent to the volume boundary. The microscale fluxes occur with a small vertical diffusivity (K_v = O(10^-5) m² s^-1) in the predominantly stably stratified warm water sphere, yet they are shown to be sufficient to provide the primary balance against surface forcing in all ocean basins and over a wide range of tracer values. This is especially true for potential temperature because of the close alignment of isotherms and isopycnals. For salinity, however, the mesoscale isopycnal diffusion also contributes significantly to the budget. The budgets are dominated by the surface and interior fluxes from the time-mean circulation, although there are also modest contributions from the rectification of the seasonal cycle. These results are in contrast to previous analyses that concluded that much larger vertical diffusivities are required for budget balance. We do not attempt to fully resolve the relatively smaller role of vertical diffusion in other budget volumes outside the warm water sphere.