Geoscience Reference
In-Depth Information
Figure A.1. Geometry relating the positions of two radars (0
;
0
;
0) and (x
1
;
0
;
0) and a point in
Cartesian space (x
;
y
;
z) to the distances from each radar to the target (R
1
and R
2
), the three
components of the wind (u
; v;
w), and the terminal fall velocity (W
t
).
spatial sampling rate and the scale of the phenomenon one is trying to resolve.
Multiple passes (successive corrections of the analysis interpolated to the data
points) of the objective analysis scheme steepens the spatial frequency response of
the spatial filter so that there is less damping at resolved spatial scales, but the
same amount of suppression of high-frequency noise. It is somewhat of an art to
determine precisely how to adapt an ''objective analysis'' technique to a given set
of radar data collected.
Horizontal velocity error variances in the x and y-directions
v
at low-
elevation angles are related to error variances of the mean Doppler velocity from
each radar
u
and
1
and
2
by the following:
2
u
þ
2
v
Þ=ð
2
1
þ
2
2
Þ¼
csc
2
ð
ð
A
:
4
Þ
where
is the between-beam angle and the Doppler velocities from each radar are
uncorrelated with each other. Based on experience, for dual-Doppler analyses of
acceptable quality, the between-beam angles from adjacent radars (
Figure A.2
)
should be at least 30
, but less than 150
, though studies have been conducted
with slightly narrower or wider between-beam angles, respectively, with some
success. It is apparent that if the between-beam angle is 180
, there is no informa-
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