Sensitivity of the Evolution and Structure of Simulated Tropical Cyclones to Turbulence Mixing Parameterizations

It is well recognized that the numerical forecasting of the intensity of tropical cyclones (TCs) is much more difficult than the forecasting of the TC tracks. The methods of parameterizing unresolved processes in numerical simulations have critical impacts on the evolution and intensity of the simulated TCs. Although at present the cumulus parameterization schemes are a critical issue in the numerical forecasting of TCs, the turbulence mixing parameterization will be more important in the TC forecasting at the resolution of O(1 km) or finer in the near future. Therefore, it is important to deepen the basic understandings of the evolution and structure of the simulated TCs at the O(1 km) resolution. This study investigates the sensitivity of the simulated TCs to turbulence (or subgrid-scale) mixing. The Weather Research and Forecasting (WRF) model is used to perform three-dimensional numerical simulations of TCs under an idealized environmental condition and with simplified model settings. The base-state environmental atmosphere is horizontally uniform with the vertical thermodynamic profiles being given by the Jordan (1958) sounding and with no initial winds. The model settings are determined basically by the Rotunno and Emanuel (1987) approach in their axisymmetric numerical simulations. The turbulence mixing is parameterized by the Smagorinsky-Lilly model (Lilly 1962) or by the formulation using the prognostic equation of turbulent kinetic energy (TKE) (Deardorff 1980). In the present numerical experiments, the model constant (so called the Smagorinsky constant, 0.25 as a standard value) is systematically changed in a wide range from the standard value. At the resolution of O(1 km) (and probably even O(100 m)), there is no theoretical background in choosing the value of the Smagorinsky constant. In addition, some of the boundary-layer schemes implemented in the WRF model are also examined. Thus, the examination of the sensitivity of the simulated TCs to the Smagorinsky constant should provide useful implications to the modeling of turbulence processes in numerical forecasting of TCs. From the comparison between the results with the different values of the Smagorinsky constant in terms of central pressure, the simulated TC shows an earlier development, more rapid rate of intensification, and deeper central pressure with a smaller value of the Smagorinsky constant. The radius of maximum wind evaluated at the 1-km height becomes smaller with a smaller value of the constant. With a smaller value of the constant, the secondary circulation, i.e., low-level inflow and upper level outflow, becomes more strengthened. An interesting feature is that with a smaller constant value, outward flow just above the low-level inflow becomes evident; this is considered to reflect the structural change of TC that has super-gradient flow at the low levels. As expected, a smaller value of the constant produces smaller values of turbulent diffusion coefficients, and the regions with non-zero turbulent diffusion is limited to the inflow layer. This feature indicates that turbulent diffusion, specifically in the horizontal directions, plays a significant role in controlling the structure and evolution of the simulated TCs and hence the steady-state intensity of the TCs.