An Integrated Energetics Approach to Modeling Oceanic Planetary Boundary Layer Mixing

The ocean’s surface boundary layer is critical for modeling the climate system, and can profoundly influence the overall stability and reliability of coupled climate models. One sophisticated approach to ocean turbulence modeling uses two prognostic equations: one for the turbulent kinetic energy (TKE) and another for a dissipation rate or turbulence length scale; this approach works best with finer spatial and temporal resolution than is ideal for ocean climate modeling. By contrast, the widely used K-profile parameterization (KPP) specifies a diffusivity profile based on a surface turbulent velocity and a boundary layer depth determined via a bulk Richardson number criterion, but lacks an explicit energy budget. Traditional bulk mixed layer models solve a TKE and potential energy balance equation implicitly for the consequences of mixing over a finite timestep, which is simplified by assuming that the water is perfectly homogenized within a surface mixed layer.

This talk presents a new approach to modeling mixing in the ocean’s surface boundary layer that combines strengths of all three of these traditional approaches to boundary layer mixing. The mixing is determined based on an integrated implicit energy balance equation (similar to a bulk mixed layer) but with finite diffusivities (similar to KPP or a two-equation closure). Central to this is new approach is the use of a TKE budget to balance the implicit potential energy changes throughout the water column due to the finite diffusivity at each point. The exact boundary layer depth is unimportant with this scheme, but the rates of mixing across model interfaces near the base of a mixed layer are carefully constrained by the energetics. The resulting scheme is remarkably insensitive to model resolution, gives a reasonable solution in a variety of idealized one-dimensional test cases, and works well in tests with NOAA/GFDL’s new CM4 coupled climate model. The robustness and generalizability of this integrated energetics approach to modeling mixing in the ocean’s surface boundary layer make it very promising for use in large-scale ocean modeling.