A Fresh Look at the K-Profile Parameterization and Evaluating it Against Large Eddy Simulation Results
The K-Profile Parameterization (KPP; Large et al. 1994) is used by many ocean models to represent small scale exchanges of heat, salinity, momentum, and other important constituents (e.g. carbon) that cannot be directly resolved. Even though it has been used by many modeling centers for more than 20 years, it has not been subject to rigorous evaluation against LES. We conducted a significant number of large eddy simulations at very high resolution to assess the fidelity of a very prominent turbulence parameterization for ocean models. Through our evaluation, a new configuration of the KPP model is found that retains the same fidelity of the original model. Our results also point out a number of critical directions for future research of vertical mixing parameterizations.
Through this work, we have derived and presented a new configuration of KPP that is much simpler and not as prone to error in certain scenarios as the original KPP model. Our new presentation of KPP in a recent publication represents is clean and clear and our examination is now serving as a launching point for new and exciting veins of research into deficiencies we have noted in the KPP model. Finally, our LES test cases used to assess KPP are being used by other groups to assess different mixing models.
This study conducted a series of Large Eddy Simulations (LES) across a range of oceanographically important forcing regimes to examine the fidelity of the K-Profile Parameterization in a single column configuration. The simulations spanned across a range of stabilizing and destabilizing surface forcings, and thus highly turbulent, and more intermittent turbulent cases. Notably, KPP includes a representation of turbulent fluxes of temperature and salinity across regions without a local gradient. Physically this is a representation of large, ocean surface boundary layer filling eddies. Our simulations tested all of the physical and numerical assumptions of KPP. For example, KPP assumes that the diffusivity predicted by the scheme must match that predicted by mixing schemes for the ocean interior. We also tested the KPP representation of entrainment, a critical process to represent to accurately simulate the ocean carbon cycle. Numerically, we tested vertical grid spacings from 0.1m to 20m and timesteps from 30s to 1 hour. We found that KPP is very sensitive to resolution, but this sensitivity varied from test to test. In some circumstances, the resolution dependence could be reduced by altering the KPP entrainment rate equation. Positively, KPP is not sensitive to the chosen timestep, unlike other prominent models of vertical mixing. Physically, the non-gradient mixing parameterization is effective in strongly convective regimes but is incomplete. The KPP non-gradient term is dependent on the surface forcing alone. Our results suggest that this term must also depend on in-situ model fields. Finally, our testing has shown that matching diffusivities from KPP to other mixing schemes does not significantly improve model results and in some test cases degrades fidelity. To this end, we propose a new configuration of KPP that does not match diffusivities that performs as well, and in some cases better, than the original KPP. This configuration is being used for E3SMv1.