MODELING THE HURRICANE DYNAMICS WITH EXPLICIT MOIST CONVECTION
K. V. Ooyama
Comprehensive understanding of the hurricane dynamics with a numerical
model that includes the cloud-scale moist convection explicitly
interacting with the hurricane environment.
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.
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.
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.
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,
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