Geoscience Reference
In-Depth Information
radial velocity data. A simple one-dimensional method is used, namely, for each
radial, the adjacent velocity data pair is compared starting from near range to far
range of the radar. If the adjacent data pair is found to have large difference in the
velocity value, the velocity data at the further range would be de-aliased based on
the corresponding data at the nearer range. This method appears to be simple, but
it turns out to be quite effective in de-aliasing the radial velocity in most of the
situations.
After de-aliasing, the velocity data are medium-filtered to remove speckles and
large variations to help improve the quality of the radial velocity data. In the present
study, the template for medium-filtering has a grid size of 3 by 3, and the filtering
is performed for 3 times. The template dimensions and the number of filtering are
determined based on several trials. The radar data are interpolated into a 3D grid
with a size of 90 (in east-west direction)
90
(north-south) and 21 (vertical levels).
The corresponding resolution is
km. The 3D wind field is then obtained
by variational method. Details of this method could be found in
Shimizu et al.
(
2008
)
and a summary is described in the next paragraph. Using upper level winds collected
from wind profilers over Hong Kong, it was found that the 3D radar retrieval winds
are quite consistent with these observations and the root-mean-square errors of the
wind speed and wind direction are about 2 m/s and
1
1
0:5
20
ı
respectively.
The wind retrieval method aims at minimizing a cost function
J
defined as:
J
D
J
O
C
J
B
C
J
D
C
J
S
(22.2)
where:
1.
J
O
considers the difference between the measured radial velocity and the
retrieved radial velocity, namely,
X
m
P
2
J
O
D
1
2
rob
rm
V
rm
V
(22.3)
i;j;k
and,
V
rm
D
.x
x
m
/
u
C
.y
y
m
/
v
C
.
z
z
m
/.
w
C
w
T
/
P
q
(22.4)
.x
x
m
/
2
C
.y
y
m
/
2
C
.
z
z
m
/
2
is the projection of the retrieved 3D wind on the radial direction,
w
T
is the ter-
minal velocity of the rain drop that depends on the intensity of radar reflectivity,
V
rob
rm
is the observed radial velocity of the m-th radar (after interpolation) and
i;j;k
are the indices of the 3D grid.
2.
J
B
is the difference between the retrieved 3D wind field
.
u
;
v
;
w
/
and the
background 3D wind field
.
u
b
;
v
b
;
w
b
/
with the following equation:
2
4
X
i;j;k
3
u
u
b
/
2
C
X
i;j;k
v
v
b
/
2
C
X
i;j;k
J
B
D
1
2
w
w
b
/
2
5
(22.5)
u
b
.
v
b
.
w
b
.
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