A DNS-based Turbulence Parametrization for Global Climate Models: Doubly Diffusive Convection

Global coupled climate modeling requires the representation of multiple widely separated scales in each model component. In the ocean component, the separation of scales is especially dramatic as small scale turbulence exerts significant control on the global scale overturning circulation.  The importance of this control is demonstrated in the context of analyses of the Dansgaard-Oeschger oscillation of Marine Isotope Stage 3 (MIS 3; see Peltier and Vettoretti, 2014)). In the University of Toronto version of CCSM4 water column diapycnal diffusivity is represented using the KPP parameterization of Large et al (1994). This includes explicit contributions due to double diffusion processes which demonstrably play an important role in determining the period of the D-O oscillation itself.

                                             

We have developed a DNS-based methodology to test the accuracy of the doubly diffusive contributions to KPP. High-resolution turbulence data sets have been produced based upon two different models: the “unbounded gradient model” and the “interface model” with depth-dependent temperature and salinity gradients. By fitting the vertical fluxes in the unbounded gradient model (for equilibrium states) as a function of density ratio (the governing non-dimensional parameter) we derive a functional form on the basis of which KPP can be revised.  By applying the revised scheme to the interface model we demonstrate that the local fluxes predicted agree well with those from the numerical simulations. The difference between this new parametrization scheme and KPP demonstrates that KPP may significantly overestimate the diffusivities for both heat and salt at low-density ratio.