| dc.description.abstract | A linearized model in x,z and t coordinates,
a primitive equation barotropic model ana baroclinic
model based on the NCAR GCM are employed to examine
various aspects of the bounded derivative initialization
method proposed by Kreiss (1979, 1980).
Linearization is performed about a uniform
zonal basic current and the method of separation of
variables is applied to determine vertical and hori
zontal structures of the system. The investigation
is confined to the external vertical mode in x,t
coordinates. Harmonic dependency is assumed to solve
the horizontal structure problem. Solutions associated with the unbalanced inittal state are compared with
the case when the bounded derivative initialization
method is applied. The results show that the
unbalanced -initial state yields solutions dominated
by high frequency gravitational oscillations.
Application of the first order constraints of the
bounded derivative initialization method eliminates the
nondivergent wind component of the gravitational
motions, but the divergent component still remains.
The second order constraints eliminate virtually all
the high frequency oscillations in the vorticity.
divergence and the geopotential variables. First
order constraints arising from the bounded derivative
method are similar to geostrophjc balance while second
order constraints yield initial specification analogous
to quasi-geostrophic balancing of Philiips (1960) and,
normal mode initialization after Baer (1977) and
Uachenhauer (1977).
Concerning the primitive equation barotropic
model, we apply the bounded derivative method to design
and subsequently carry out successful test calculations
of an initialization scheme suitable for equatorial
regions in the presence of idealized orography which
depends on the zonal and meridional directions. To
implement the scheme, we specify a uniform zonal
current and then obtain the initial divergent component
of the motion and the geopotential through the application
of the bounded derivative method. For purposes
of comparison we also test unbalanced initial data.
In this case again we assume the same· initial uniform
zonal current but the geopotential height is obtained
by assuming steady-state conditions in absence of
orography. The computations indicate a stationary
orographic trough also reported by Semazzi (1980a,b),
with msximum intensity at the top of the mountain
both for easterly and westerly cases. The intensity
of the trough is greater in the easterly ease.We
observe divergence (of order 10-6 s-1 ) on the windward!ope and convergence on the lee slope irrespective
of the direction of the initial uniform zonal current.
The vorticity is of order 10-7s-1 thus one order
of magnitude weaker than the divergence. It retains
the same spatial distribution for easterly and westerly
cases.
The initialization scheme for the baroclinic
model which arise from the application of the bounded
derivative method comprises of two constraints. One is
the well known classical balance equation for calculating
the pressure and the other one is a three dimensional
elliptic equation for computing the initial
divergence. Suitable boundary conditions for the
.divergence equation are also determined as a result
of constraining the second order time derivatives of
the governine equations to be of order of synoptic
.meteorological motion. In order .to implem8nt the
proposed scheme, diabatic heating and the nondivergent
component ,of the wind field are assumed to be known
intially. | en |
