The Tropical Cyclone Model-TCM3

     Tropical cyclone model (TCM3) was developed by Dr. Yuqing Wang between 1996-1999 when he worked at the Bureau of Meteorology Research Centre (BMRC) as a senior professional officer. TCM3 is hydrostatic primitive equation model formulated in Cartesian coordinates in the horizontal and F (pressure normalized by surface pressure) coordinate in the vertical with 21 vertical levels.  A two-way interactive, triply nested, movable mesh technique is used so that high resolution can be achieved in the cyclone core region so that the eyewall structure and evolution and the activity of the inner spiral rainbands can be captured by the model resolution (Fig. 1). 

    Fig. 2 gives the specified domain size, grid spacing for each mesh domain.  The outermost mesh A is fixed with open lateral boundary conditions in the north and south boundaries, and a cyclic boundary condition in the east-west direction.  The intermediate mesh B is used to capture the synoptic scale flow of the model tropical cyclone and moves following the model tropical cyclone during the course of time integration.  The innermost mesh C with a grid spacing of 5 km is designed to better resolve the central core and major spiral rainbands of a tropical cyclone and also moves with the model tropical cyclone.

    The two-way nesting is designed to minimize the effect of resolution jump between the coarse and fine mesh interface (Fig. 3). The time integration proceeds from the outermost domain to the innermost domain. Firstly, a large time step integration for the outmost domain then a intermediate time step for the intermediate domain, and finally three small-time steps for the innermost domain. Then another intermediate time step for the intermediate domain followed by three small steps for the innermost domain, and followed by the same one intermediate time step for the intermediate domain followed by three small time steps for the innermost domain. This complete one large time step integration of the all model domains. For each full time step of each domain, even smaller fractional time step is used to integrate the dynamical core, which is accomplished with the use of an Euler backward scheme followed by several steps with the leapfrog integration. The region between "I" and "M" in Fig. 3 belongs both the coarse and fine domains. When the fine mesh is integrated forward, the lateral boundary is shifted inward by one fine grid spacing therefore after 6 time steps, the actual lateral boundary of the fine mesh domain is located at "M", which is called mesh interface, while the "I" is called the input interface.

    The numerical accuracy of this nested algorithm was tested by integrating the dry version of the model initialized by a tropical cyclone-like vortex embedded in an easterly flow of 5 m/s. Figure 4 shows the surface pressure in the three model domains after 48 h (top), 96 h (middle), and 144 h (bottom) rows. The relative movement of mesh B can be seen from the mesh A (left column). It is obvious that the two-way nesting and mesh movement do not introduce any significant noise near the mesh interface.

    The model physics include an explicit cloud microphysics package to treat the grid scale moist processes (Wang 1999, 2001), which includes warm-rain and mixed-ice phase processes (Fig. 5), an E-, turbulence closure scheme for subgrid scale vertical turbulent mixing (Detering and Etling 1985); a modified Monin-Obukhov scheme for the surface flux calculation (Wang et al. 2001; Wang 2002). To conserve the internal energy, the dissipative heating due to molecular friction is considered in the model by adding the turbulent kinetic energy dissipation rate to the thermodynamic equation as a heat source. The massflux convective parameterization scheme originally developed by Tiedtke (1989) and later modified with convective available potential energy (CAPE) closure by Gregory et al. (2000) is used for the two outer meshes with grid spacing of 15 km and 45 km, respectively. The innermost mesh uses only the explicit cloud microphysics scheme to resolve the moist convection in the inner core region. A fourth-order horizontal diffusion is used for all three meshed with the horizontal diffusion coefficient depending on the horizontal deformation.

        Figure 6 shows the model simulated axisymmetric structure for a cyclone in the Southern Hemisphere (Wang 2001). what we see is that the model tropical cyclone structure looks quite realistic.

    The model simulated radar reflectivity at the surface is shown in Fig. 7a with a vertical cross-section across the storm center shown in Fig. 7b. The model simulated well the eyewall structure and both the inner and outer spiral rainbands.

    Figure 8 shows the time evolution of the model simulated radar reflectivity at the surface at every 6 hour intervals. Since the model was initialized with a symmetric vortex which had a maximum wind speed of 20 m/s at a radius of 100 km from the cyclone center, the initial development of deep convection thus was around the radius of maximum wind. The resulted in the local maximum of potential vorticity (PV) and thus the barotropic instability, eventually a breakdown of the original eyewall with outward propagating gravity waves. The new eyewall then formed after about 24 h with the development of both inner and outer spiral rainbands and asymmetric structure of the storm even within the inner core region.

    The asymmetric structure of the storm in the core region was dominated by the vortex Rossby waves (VRWs). Please see the details in Wang (2001, 2002a, 2002b). A more basic theoretical study of VRWs can be found from Montgomery and Kallenbach (1997). Figure 9 shows the wavenumber two VRWs simulated by TCM3. For explanation please refer to Tropical Cyclone Research.

    The above results illustrate that TCM3 can be a useful tool to investigate tropical cyclone motion, structure and intensity changes, in particular the scale interaction between the tropical cyclone and its large-scale environmental flow because of its use of triply nested movable mesh algorithm.

Some key references:

Detering, H.W., and D. Etling, 1985: Application of the E-, turbulence model to the atmospheric boundary layer.  Bound.-Layer Meteor., 33, 113-133.

Gregory, D., J.-J. Moncrette, C. Jakob, A.C.M. Beljaars, and T. Stockdale, 2000: Revision of the convection, radiation and cloud schemes in the ECMWF model. Quart. J. Roy. Meteor. Soc., 126, 2685-1710.

Montgomery, M.T., and R.J. Kallenbach, 1997: A theory for vortex Rossby-waves and its application to spiral bands and intensity changes in hurricanes.  Quart. J. Roy. Meteor. Soc., 123, 435-465.

Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models.  Mon. Wea. Rev., 117, 1779-1800.

Wang, Y., 1999: A triply nested movable mesh tropical cyclone model with explicit cloud microphysics-TCM3.  BMRC Research Report No. 74, 81pp, Bureau of Meteorology Research Centre, Australia.

Wang, Y., 2001: An explicit simulation of tropical cyclones with a triply nested movable mesh primitive equation model-TCM3. Part I: Model description and control experiment. Mon Wea. Rev., 129, 1370-1394.

Wang, Y., 2002: Vortex Rossby waves in a numerically simulated tropical cyclone. Part I: Overall structure, potential vorticity and kinetic energy budgets. J. Atmos. Sci. 59, 1213-1238.

Wang, Y., 2002: Vortex Rossby waves in a numerically simulated tropical cyclone. Part II: The role in tropical cyclone structure and intensity changes. J. Atmos. Sci. 59, 1239-1262.

Wang, Y., 2002: An explicit simulation of tropical cyclones with a triply nested movable mesh primitive equations model–TCM3. Part II: Model refinements and sensitivity to cloud microphysics parameterization. Mon. Wea. Rev., 130, 3022-3036.

Wang, Y., J.D. Kepert, and G.J. Holland, 2001: The effect of sea spray evaporation on tropical cyclone boundary layer structure and intensity.  Mon. Wea. Rev. 129, 2481-2500.