Impact of Isopycnal Diffusion on Heat Fluxes and the Transient Response of a Two-Dimensional Ocean Model

A two-dimensional (latitude–depth) ocean–climate model is used to assess the impact of calculating diffusive heat and salinity fluxes along and across isopycnal surfaces rather than in a vertical–horizontal coordinate system. Differences between the two model versions are small and are overwhelmed by uncertainties in the appropriate value of the diapycnal/vertical diffusion coefficient Kv. Isopycnal diffusion is important only if convection is not explicitly included and Kv is fixed rather than parameterized as N−1 (where N is the Brunt–Väisälä frequency). When convection is present, the switch to diffusion in isopycnal coordinates causes large changes in the convective heat flux that are largely offset by diffusion along isopycnal surfaces, with little change in the diapycnal heat flux. The effective vertical diffusion coefficient due to combined mixing across and along isopycnal surfaces is negative in some regions due to upward heat diffusion along sloping isopycnal surfaces combined with temperature decreasing downward. As Kv is varied, the model exhibits a range of qualitatively different behavior in response to heating due to a greenhouse gas increase. The qualitative behavior is unaffected by the use of isopycnal rather than vertical–horizontal diffusion. In some sensitivity tests the isopycnal diffusion coefficient is parameterized such that Ki∝N3/2/f. Since this causes Ki to decrease as isopycnal slope increases, its use further reduces the differences between isopycnal and nonisopycnal model versions. Differences in the transient surface temperature response of the two model versions to external forcing changes are small to negligible.