The sensitivity of a depth-coordinate model to diapycnal mixing induced by practical implementations of the isopycnal tracer diffusion scheme

The isopycnal tracer diffusion scheme is commonly used in a coarse-resolution global ocean model to parameterize the diffusive effect of mesoscale eddy stirring. This scheme implemented in a depth-coordinate model often accompanies a fail-safe system to prevent numerical instability caused by large isopycnal diffusion around steeply sloped isopycnal surfaces. Its practical implementation artificially induces spurious diapycnal mixing across an isopycnal surface whose slope exceeds a prescribed slope maximum. This slope maximum widely ranges from 1/1000 to 3/10 in a recent global ocean model intercomparison project of Coordinated Ocean-ice Reference Experiments phase II. This study quantitatively investigates the effects of isopycnal tracer diffusion on meridional overturning circulation by calculating water mass transformation rate due to isopycnal diffusion with the use of Walin's (1982) methodology. We focus on the following three effects of isopycnal diffusion in a depth-coordinate model: densification induced by nonlinearity of the equation of state, spurious diapycnal mixing in the interior ocean induced by practical implementation of the isopycnal diffusion scheme, and diapycnal mixing in the surface diabatic layer. It is revealed that a slope maximum that is too small (1/1000) leads to large spurious diapycnal mixing in the interior ocean. This diapycnal mixing supplies much buoyancy to the bottom water around Antarctica and makes it locally upwell within the Southern Ocean. It results in less northward export of bottom waters from the Southern Ocean into the Atlantic and the IndoPacific oceans and weakening of the bottom cell of meridional overturning circulation. This spurious diapycnal mixing is significantly suppressed if we use the slope maximum of more than 1/100 or tapering isopycnal diffusivity around steep isopycnal slopes. This study also shows that these changes in the implementation of the isopycnal diffusion scheme also affect the various aspects of the simulated Southern Ocean. The experiment tapering isopycnal diffusivity suppresses unrealistic open ocean deep convections and polynyas in the Weddell Sea by both diminishing spurious diapycnal mixing in the interior ocean and applying the strong diapycnal mixing in the surface boundary layer associated with the isopycnal diffusion scheme. It results in the smallest biases of the potential temperature distribution, the winter sea ice concentration and mixed layer depth in the Weddell Sea and the ACC transport in our coarse resolution model.