The
OWI Tropical Model, first developed as a practical
tool in the Ocean Data Gathering Program (ODGP) (Cardone
et al., 1976), can provide a fairly complete description
of time-space evolution of the surface winds in the boundary
layer of a tropical cyclone from the simple model parameters
available in historical storms. The model is an application
of a theoretical model of the horizontal airflow in the
boundary layer of a moving vortex. Numerical integration
allows the model to solve the vertically averaged equations
of motion that govern a boundary layer subject to horizontal
and vertical shear stresses. The equations are resolved
in a Cartesian coordinate system whose origin translates
at constant velocity, Vf, with the storm center of the pressure
field associated with the cyclone. Variations in storm intensity
and motion are represented by a series of quasi-steady state
solutions.
The original theoretical formulation of the model
is given by Chow (1971). A similar model was described
in the open literature by Shapiro (1983). The present
version of the model is the result of three major upgrades:
the first upgrade involved replacement of the empirical
scaling law by a similarity boundary layer formulation to
link the surface drag, surface wind and the model vertically
averaged velocity components (Cardone et al., 1992). The
second upgrade (Cardone et al., 1994) added spatial resolution
and generalized the pressure field specification. A more
complete description of the theoretical development of the
upgraded model is given by Thompson and Cardone (1996).
Last and most recently, modifications to the model PBL physics
allow the introduction a saturation roughness formulation
(a capped drag coefficient) consistent with that found by
Powell (2007) as part of the Modeling of Relevant Physics
of Sedimentation (MORPHOS) project (MORPHOS, 2009).
The
model pressure field is described as the sum of an axially
symmetric part and a large-scale pressure field of constant
gradient. The symmetric part is described in terms of an
exponential pressure profile, which has the following parameters:
Po minimum central pressure
dpi pressure deficit associated with up to two radii
Rpi scale radius of exponential pressure profile
Bi profile peakedness parameter
B is
an additional scaling parameter whose significance was discussed
by Holland (1980). This analytical form is also used to
explicitly model the storm pressure field for use in the
hydrodynamic model. The model may be prescribed with a single
profile (1 dp, B, Rp combination) for storm systems with
simple wind profiles. More complex wind profiles such as
those which display wind maxima at two radii or those with
a shelf-structure to the wind profile are described with
a double profile. Cox and Cardone (2007) describe the methodology
applied in the analysis of historical tropical cyclones,
while Cardone and Cox (2009) discusses the impact of complex
wind profiles on the ocean response.
The
model is driven from parameters that are derived from data
in historical meteorological records and the ambient pressure
field. The entire wind field history is computed from knowledge
of the variation of those parameters along the storm track
by computing solutions, or so-called "snapshots",
on the nested grid as often as is necessary to describe
different stages of intensity, and then interpolating the
entire time history from the snapshots.
As presently
formulated, the wind model is free of arbitrary calibration
constants, which might link the model to a particular storm
type or region. For example, differences in latitude are
handled properly in the primitive equation formulation through
the Coriolis parameter. The variations in structure between
tropical storm types manifest themselves basically in the
characteristics of the pressure field of the vortex itself
and of the surrounding region. The interaction of a tropical
cyclone and its environment can therefore be accounted
for by a proper specification of the input parameters. The
assignable parameters of the PBL formulation, namely PBL
depth and stability, and of the sea surface roughness formulation,
are taken from studies performed in the Gulf of Mexico.
The
model was validated originally against winds measured in
several ODGP storms. It has since been applied to nearly
every recent hurricane to affect the United States offshore
area, to all major storms to affect the South China Sea
since 1945, and to storms affecting many other foreign basins
including the Northwest Shelf of Australia, Tasman Sea of
New Zealand, Bay of Bengal, Arabian Sea and Caribbean Sea.
Many wind comparisons have been published (e.g., Ross and
Cardone, 1978; Cardone and Ross, 1979; Forristall et al.,
1977; 1978; 1980; Cardone et al., 1992; Cardone and Grant,
1994).
More
recent publications on the application of the
PBL model in driving the ADCIRC and coupled ADCIRC/SWAN
modeling system can be found in Hope et al., 2013 (Hurricane
Ike 2008), Dietrich et al., 2011 (Hurricane Gustav 2008),
Bacopoulos et al., 2012 (Hurricane Jeanne 2004), and Bunya
et al., 2010 (Hurricanes Katrina and Rita 2005). Application
in Hurricane Harvey (2017) is presented in Cox et al., 2017.
References
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