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into a severe cyclonic storm over southwest and adjoining southeast BoB at
0900 UTC of 28
th
Dec. near lat. 12.5°N and long. 85.0°E about 500 km east-
southeast of Chennai. It further moved west-southwestwards, intensified into
a very severe cyclonic storm and crossed north Tamil Nadu and Puducherry
coast, close to the south of Cuddalore (near lat. 11.6°N) between 0100 and
0200 UTC of 30
th
December, 2011 with an estimated wind speed of 120-140
kmph and estimated central pressure of 969 hPa. After the landfall, the system
moved westwards and weakened into a severe cyclonic storm at 0300 UTC of
30
th
December 2011 over north coastal Tamil Nadu. It further weakened into a
deep depression at 0600 UTC near lat. 11.6°N and long. 79.0°E and into a
depression at 1200 UTC of 30
th
December near Salem (Tamil Nadu). Figure
1(a-c) satellite imageries show the intensification and movement of the cyclone
Thane at different stages. Heavy to very rainfall (15-30 cm) occurred along the
costal regions.
3. Model Description
The WRF model is an outgrowth of a weather prediction system featuring
multiple dynamic cores designed to serve both operational and research needs.
It is based on a Eulerian solver for the fully compressible non-hydrostatic
prognostic equations, designed in conservation of mass, momentum, entropy
and scalars using flux form, with a mass (hydrostatic pressure) vertical
coordinate. The solver uses a third-order Runge-Kutta time integration scheme
coupled with a split-explicit second order time integration scheme for the
acoustic and gravity wave modes. Fifth-order upwind-biased advection
operations are used in the fully conservative flux divergence integration; second-
to sixth-order schemes are run-time selectable. A detailed description of the
model equations, physics and dynamics is available in Skamarock et al. (2005).
3DVAR Data Assimilation Technique
The formulation of 3DVAR is developed on the basis of Bayesian probabilities
and Gaussian error distributions. The basic target of WRF-3DVAR (hereafter
WRF-Var) data assimilation system is to produce an optimal estimate of the
true atmospheric state at analysis time through iterative solution of a prescribed
cost-function
J
(
x
).
J
(
x
) =
J
b
+
J
o
=
1
2
(
x
-
x
b
)
T
B
-1
(
x
-
x
b
) +
1
2
(
y
-
y
o
)
T
(
E
+
F
)
-1
(
y
-
y
o
)
( )
where
J
b
and
J
o
are the cost functions of background and observation
respectively;
x
is the state vector;
x
b
is the background or first guess;
B
is the
background error statistics covariances;
y
is the observation space (
y
=
Hx
);
H
is the forward (non-linear) operator;
y
o
is the observations;
E
is the observational
or instrumental error covariances matrix; and
F
is the representivity error
covariances matrix. Further, details about the components and real time
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