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While various parameterizations of vertical turbulent fluxes at differentlevels of complexity have been proposed, each has its own limitations. Forexample, simple first-order closure schemes such as the K-ProfileParameterization (KPP) lack energetic constraints; two-equation models like$k-\epsilon$ directly solve an equation for the turbulent kinetic energy but donot account for non-local fluxes, and high-order closures that include thenon-local transport terms are computationally expensive. To address these, herewe extend the Assumed-Distribution Higher-Order Closure (ADC) frameworkoriginally proposed for the atmospheric boundary layer and apply it to theocean surface boundary layer (OSBL). By assuming a probability distributionfunction relationship between the vertical velocity and tracers, allsecond-order and higher-order moments are exactly constructed and turbulenceclosure is achieved in the ADC scheme. In addition, the ADC parameterizationscheme has full energetic constraints. We have tested the ADC scheme against acombination of large eddy simulation (LES), KPP, and $k-\epsilon$ for surfacebuoyancy-driven convective mixing and found that the ADC scheme is robust withdifferent vertical resolutions and compares well to the LES results.

A new hybrid mass-flux/ high-order turbulence closure for ocean vertical mixing