A Scale-Aware Three-Dimensional TKE Turbulent Mixing Parameterization for the Hurricane Analysis and Forecast System (HAFS)

One of the most challenging problems in numerical weather prediction is how to use a physically coherent parameterization scheme to represent the three-dimensional (3D) sub-grid scale (SGS) transport induced by the unresolved turbulence. In the state-of-the-art mesoscale and large-scale models, the coherent horizontal and vertical turbulent mixings induced by turbulent eddies are treated separately with the former being handled within a model’s dynamic solver and the latter being treated by a standalone module outside the dynamic solver often known as the planetary boundary layer (PBL) scheme. This separated parameterization strategy is based on two considerations. First, in fair-weather conditions the vertical turbulent mixing is much stronger than the horizontal mixing. Thus, it is appropriate to parameterize horizontal and vertical mixing separately. Second, most of model physics, such as microphysics and radiation, are parameterized in a one-dimensional (1D) vertical column framework, thus, it is natural to parameterize the vertical turbulent mixing in a 1D framework as well, so that different parameterizations can be bundled together known as the model physics package. However, in the inner core of a tropical cyclone (TC), turbulent eddies tend to generate inter-connected horizontal and vertical turbulent mixing with comparable magnitudes because of the large lateral contrasts across the eyewall and rainbands. This poses a challenge for the separated horizontal and vertical turbulent mixing schemes to realistically represent the 3D turbulent transport in the TC inner core. The problem becomes even more serious as model resolution increases to the gray zone where turbulent eddies possess both isotropic and anisotropic characteristics. To relax the problem, we have been developing a scale-aware (SC) 3D moist turbulent kinetic energy (TKE) turbulence scheme for treating the 3D turbulent mixing in the gray zone by transitioning a 3D TKE scheme used at the large eddy simulation (LES) limit to a 1D TKE scheme used at the mesoscale simulation limit. The new SA-3D TKE scheme considers full 3D TKE shear production tensor and 3D TKE turbulent transport and pressure correlation. It also parameterizes the horizontal and vertical turbulent mixing in a consistent way based on the prognostically predicted TKE. Numerical simulations by the Hurricane Analysis and Forecast System (HAFS) show that the implemented new SA-3D TKE scheme substantially improves HAFS’s skill in predicting intensities and structures of TCs.