MODELING THE HURRICANE DYNAMICS WITH EXPLICIT MOIST CONVECTION

Principal Investigator: K. V. Ooyama
Objective: Comprehensive understanding of hurricane dynamics with a numerical model that explicitly includes the cloud-scale moist convection interacting with the hurricane environment.
Rationale: The power source of a tropical cyclone, such as a hurricane, is moist convection in the form of clouds. The cyclone's own circulation creates the mechanism for organizing and supporting the convection in the eye wall and outer rain bands. The large-scale environment also exerts controlling influences on the convection, especially in the initial stage of a cyclone and, often, at critical moments of intensification. Although operational hurricane models have significantly improved track forecasts, moist c onvection in those models is either parameterized or totally omitted. Hurricane models of the next generation may be well advised to include an explicit representation of moist convection under the controlling influences of the hurricane environment.
Method: A sequence of multiple nested domains will cover the necessary range of horizontal scales, from the cloud scale to the synoptic scale. The spectral representation of spatial fields by the SAFER method (see below) simplifies the nesting procedure. To prese rve both simplicity and generality in the design of a moist model, the role of thermodynamics in diagnosing the states of chemical constituents is cleanly separated from that of dynamics in predicting the spatial distributions of conservative properties. The microscale physics of precipitation and the eddy fluxes near the earth's surface have to be empirically formulated. The semi-implicit method of time integration is adopted to avoid excessively small time steps that acoustic waves would otherwise req uire for computational stability.
Accomplishment: An accurate and versatile numerical method, called Spectral Application of Finite-Element Representation (SAFER), was originally developed by Ooyama (1987), and is being utilized by several HRD projects that require data analysis, or modeling, in a limite d area (e.g., DeMaria et al. 1992). In application to a hyperbolic system of equations in a model on nested horizontal domains, the method allows the most accurate and noise-free interface condition, namely that the order of continuity of every field be the same across the interface as in the domain interior.

In application to the semi-implicit time integration of the atmospheric model, the equations for meteorological signals are essentially hyperbolic while those for stabilizing acoustic waves are elliptic. Until recently, there was a problem in handling th e mix of both types at interfaces of the nested domains. The problem is now solved by the discovery of a new algorithm for the acoustic adjustment over the nested domains, without sacrificing the best interface condition on meteorological fields.

The new method of semi-implicit interfacing has been tried in a multiple-nested version of a model for simulation of the squall-line generation. The model is in the two-dimensional vertical plane, and includes parameterized microphysics of precipitation w ithin the general formulation of thermodynamics as proposed by Ooyama (1990). In the earlier experiments with the single-domain model, a warm initial bubble (placed near the ground at x=0) generated long-lasting squall lines in the vertically sheared envi ronmental flow, when the wind aloft was about 10 m/s and the shear was confined to the lowest kilometer above the ground. In the current experiments, the same initial conditions are used in various geometrical arrangements of domain-nesting.

The results of the new, semi-implicit nesting procedure are demonstrated in Figure 1, in which the same stage of a convective cell of the squall line is compared for two different placements of the interface. The two cases w ill not produce exactly the same result, but their similarity is an encouraging sign of the technical success.

The spatial resolution affects numerical simulation even without nesting. The physical and dynamic nature of simulated phenomena must be considered in the selection of a geometrical configuration of nested domains. Such effects of the spatial resolution o n the squall-line simulation are demonstrated in Fig 2. In the experiment shown in the upper panel, the x-coordinate is moved at 10 m/s, and the squall line propagates at a slightly faster speed. Thus, the squall line is mai ntained by continual regeneration of small, but intense convective cells that are possible with the 1 km resolution. In the experiment shown in the lower panel, the x-coordinate is fixed, while the squall line propagates crossing the interfaces toward the successive domains of lesser resolution. The cells become broader and less intense in the 2-km domain, more so in the 4-km domain, and none occur in the 8-km domain.

More work remains to be done toward the eventual goal but, with the implementation of the semi-implicit nesting, the project has passed a major milestone.

Key references:
Ooyama, K. V., 1987: Scale-controlled objective analysis. Mon. Wea. Rev., 115, 2479-2506.

Ooyama, K. V., 1990: A thermodynamic foundation for modeling the moist atmosphere. J. Atmos. Sci., 47, 2580-2593.

DeMaria, M., S. D. Aberson, K. V. Ooyama, and S. J. Lord, 1992: A nested spectral model for hurricane track forecasting. Mon. Wea. Rev., 120, 1628-1643.

Last modified: 8/19/96