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where
is the total dry energy (the sum of kinetic energy and available
potential energy) of the CNOP or FSV at the grid point
E
d
.i;j;
z
/
.i;j;
z
/
.Thevalue
c
is
specified thus the sensitive areas have a proper size.
For the composite of the SVs (short for CSV or SVs), the sensitive areas
is defined as the horizontal grid points where the function
f
1
.i;j/
exceeds the
threshold value
c
. The function
f
1
.i;j/
is expressed as follows
Z
1
0
E
d
;
n
.i;j;
5
X
n
1
f
1
.i;j/
D
z
/
dz
(24.12)
n
D
1
where
.
n
is the singular value of the n th SV. In this study, the five leading SVs have been
composed.
The similarity between two vectors
X
Df
x
1
;x
2
;
x
m
g
E
d
;
n
.i;j;
z
/
is the total dry energy of the n th SV at the grid point
.i;j;
z
/
T
and
Y
Df
y
1
;y
2
;
y
m
g
T
is calculated according to the following formula:
P
i
D
1
x
i
y
i
s
P
i
D
1
x
i
<
X
;
Y
>
S
xy
D
p
p
D
s
P
i
D
1
y
i
:
(24.13)
<
>
<
>
X, X
Y, Y
24.3.2
Sensitivity of CNOP Sensitive Areas with Respect
to Horizontal Resolution
From Sect.
24.2.1
, it is known that the CNOPs depend on the nonlinear model
M
,so
different models due to different resolution may result in different CNOP sensitive
areas.
Zhou and Mu
(
2012a
) studied this issue. In their study, a set of experiments
are designed in which all the parameters are held constant except for the horizontal
resolution.
Three tropical cyclones, TC Matsa (2005), TC Meari (2004), and TC
Mindulle (2004), are investigated. A set of 24-h control forecasts, which served as
the basic state, are integrated from 0000 UTC 5 Aug 2005 to 0000 UTC 6 Aug 2005
(TC Matsa), from 0000 UTC 26 Sep 2004 to 0000 UTC 27 Sep 2004 (TC Meari),
and from 0000 UTC 28 Jun 2004 to 0000 UTC 29 Jun 2004 (TC Mindulle). For
each case, the forecasts are run at 120, 60, and 30-km horizontal resolutions with 11
vertical levels. For TC Matsa, the model domain covers
28
28;55
55;109
109
y
x
(
-direction) grids, respectively, for 120, 60, and 30-km horizontal
resolutions. For TC Meari, there are
-direction by
26
28;51
55
101
109
grids for each
horizontal resolution, and for TC Mindulle the domain sizes with respect to each
resolution are
,and
21
26;41
51
81
101
. For each case with the chosen grids,
the real physical domain is the same at all resolutions, thus the verification area can
be chosen the same.
,and
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