Vertical mixing parameterization for the ocean surface boundary layer based on assumed distribution higher order closure

The vertical turbulent flux of heat, mass, and momentum is an important component in oceanic flows and is fundamental to understand the global heat budget of ocean and atmosphere. In the large-scale ocean and climate models, the small-scale turbulent fluxes are generally represented through an eddy diffusivity parameterization. Despite numerous studies, the current state of the science representations of vertical turbulent fluxes are subject to persistent biases stemming from missing physical processes (e.g., Langmuir turbulence, wave breaking) and poor inherent assumptions (e.g., lack of energetic constraints). Here we explore the mass flux approach for the first Assumed Distribution Higher Order Closure (ADC) in the ocean surface boundary layer. By assuming upward and downward moving plumes with associated probability distribution function relationships between different state variables, we can construct all higher-order moments, overcoming the classic turbulence closure problem. The ADC parameterization has full energetic constraints, includes non-local convective turbulence, and can easily integrate other physical phenomena like Langmuir turbulence (with appropriate modifications to the momentum equations and turbulent length scales). We have tested the ADC scheme in a single column framework across a range of oceanographically relevant forcing scenarios against horizontally averaged Large Eddy Simulations (LES). We find that the ADC scheme has little sensitivity to vertical resolution and timestep and compares well to the LES results.