A Minimal Three-Dimensional Tropical Cyclone Model

Abstract

A minimal 3D numerical model designed for basic studies of tropical cyclone behavior is described. The model is formulated in coordinates on an f or ␤ plane and has three vertical levels, one characterizing a shallow boundary layer and the other two representing the upper and lower troposphere, respectively. It has three options for treating cumulus convection on the subgrid scale and a simple scheme for the explicit release of latent heat on the grid scale. The subgrid-scale schemes are based on the mass-flux models suggested by Arakawa and Ooyama in the late 1960s, but modified to include the effects of precipitation-cooled downdrafts. They differ from one another in the closure that determines the cloud-base mass flux. One closure is based on the assumption of boundary layer quasi-equilibrium proposed by Raymond and Emanuel.It is shown that a realistic hurricane-like vortex develops from a moderate strength initial vortex, even when the initial environment is slightly stable to deep convection. This is true for all three cumulus schemes as well as in the case where only the explicit release of latent heat is included. In all cases there is a period of gestation during which the boundary layer moisture in the inner core region increases on account of surface moisture fluxes, followed by a period of rapid deepening. Precipitation from the convection scheme dominates the explicit precipitation in the early stages of development, but this situation is reversed as the vortex matures. These findings are similar to those of Baik et al., who used the Betts-Miller parameterization scheme in an axisymmetric model with 11 levels in the vertical. The most striking difference between the model results using different convection schemes is the length of the gestation period, whereas the maximum intensity attained is similar for the three schemes. The calculations suggest the hypothesis that the period of rapid development in tropical cyclones is accompanied by a change in the character of deep convection in the inner core region from buoyantly driven, predominantly upright convection to slantwise forced moist ascent.

Paradigms for tropical cyclone intensification

“…Kurihara and Tuleya 1974); • those using minimal hydrostatic models, with or without cumulus parameterisation (e.g. Zhu et al 2001;Zhu and Smith 2002, Shin and Smith 2008 There have been investigations also of the analogous intensification problem on a β-plane, which is a prototype problem for tropical cyclone motion (e.g. Flatau et al 1994;Dengler and Reeder 1997;Holland 1996a, 1996b).…”

“…The feedback process appears to transcend the particular parameterisation of deep convection used by Ooyama. Although Ooyama took the cloud-base mass flux to be equal to the convergence of resolved-scale mass flux in the boundary layer, this restriction may be easily relaxed (Zhu et al 2001). …”

Tropical‐cyclone intensification and predictability in three dimensions

“…Ooyama, 1969;Emanuel, 1989Emanuel, , 1995Nguyen et al, 2002); those using hydrostatic three-dimensional models with cumulus parametrization (e.g. Zhu et al, 2001;Smith, 2002, 2003); those using hydrostatic three-dimensional models with explicit microphysics (e.g. Wang 2001Wang , 2002aWang , 2002b; and those using non-hydrostatic axisymmetric cloud models (e.g.…”

Evaluation of a reduced model for investigating hurricane formation from turbulence

“…The cumulus parametrizations involve prognostic equations for the EPTs of the boundary and middle layers, and a diagnostic equation for the saturation EPT of the upper layer. Readers interested in the historical use of similar three-layer models to elucidate the dynamics of hurricanes or midlatitude vortices may consult numerous references on the subject (O69; DeMaria and Schubert, 1984;DP88;Shapiro, 1992Shapiro, , 2000Dengler and Reeder, 1997;Zehnder, 2001;Zhu et al, 2001;Zhu and Smith, 2002;Arakawa, 2004;Lapeyre and Held, 2004;SD09). A complimentary body of literature demonstrates the use of reduced models to understand tropical waves and generic patterns of tropical convection Dunkerton, 1992,1993;Yano et al, 1995;Mapes, 2000;Frierson et al, 2004;Khouider and Majda, 2007;Bouchut et al, 2009).…”

“…While direct comparison of one reduced model to another has precedents (e.g. Zehnder, 2001;Zhu et al, 2001;Zhu and Smith, 2002), direct comparison to a CSR model has been largely neglected. Another distinguishing feature of the present comparison is the starting point -a disorganized state of rotational moistconvective turbulence, as opposed to a weak axisymmetric cyclone or a synoptic-scale dipole.…”