Principal Investigator: K. V. Ooyama
Collaborating scientist(s):

Objective: Comprehensive understanding of the hurricane dynamics with a numerical model that includes the cloud-scale moist convection explicitly interacting with the hurricane environment.
Rationale: The power source of the tropical cyclone, such as a hurricane, is the moist convection in the form of clouds. The cyclone's own circulations may create the mechanisms 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 recent advances in the operational hurricane models have significantly improved the track forecasts, the moist convection in those models is either parameterized or totally omitted. Hurricane models of the next generation may well be 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 preserve both the 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 surface have to be empirically formulated. The semi-implicit method of time integration is adopted to avoid excessively small time steps that the acoustic wave would otherwise require 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 limited area. In this method, a spatial field is represented by the amplitudes of cubic B-splines defined at equally spaced nodes. The bases being local, there is no restriction on the choice of boundary conditions, either homogeneous or inhomogeneous. The represented fields are continuously differentiable up to the second order, resulting in very accurate phase speeds of advected and propagating waves. This accuracy is critically important to noise-free nesting. In application to a model with a hyperbolic system of equations, the interface conditions are simply that all the fields are continuous across the interface up to the second order (DeMaria et al. 1992). The method is being extended for the current application. Under the semi-implicit method of time integration, certain aspects of the equations becomes elliptic in order to stabilize acoustic waves, and the best interface conditions on the acoustic components appear to be the radiation conditions.

The new formulation of the moist thermodynamics (Ooyama 1990) has been tested in a vertical two-dimensional model in a single periodic domain. The ice phase of water is included in the original theory, and the microphysics of precipitation is parameterized in the manner of Klemp and Wilhelmson (1978) with appropriate modifications for the ice phase precipitation. The spectral numerics by the SAFER method are used in all the spatial directions and the time integration is semi-implicit. Experiments for the generation of long-lasting squall lines have been conducted to examine how well the various components of the model perform together. Snap shots of a test run are shown in the figure for the initial growth of a cumulonimbus. After the time shown, new convective cells are continually generated and the squall line persists until the end of run at six hours. The ice phase, especially the reduced fall speed of ice/snow at higher levels, is found to be one of the important factors that promote vigorous regeneration of new cells.

Key reference:
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.

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