Global Positioning System Reference
In-Depth Information
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[20
F
igure 6.10
Brightness temperature versus cloud liquid.
(Date source: Keihm, JPL.)
Lin
—
0.7
——
Nor
PgE
sh
ows
T
b
variations versus cloud liquid. Despite the large scatter (due to variable
P
WV), one can see that the slope of the
T
b
(
31
.
4
)
data is approximately twice as large
as
the slope of the
T
b
(
20
.
7
)
data.
Because of the relationships between ZWD, IWV, and PWV as seen by (6.32),
(6
.27), and (6.28), the strong correlation seen in Figure 6.9 between PWV and the
br
ightness temperature makes a simple statistical retrieval procedure for the ZWD
po
ssible. Assume a radiosonde reference station is available to determine ZWD and
th
at a WVR measures zenith
T
20
.
7
and
T
31
.
4
. Using the model
[20
ZWD
=
c
0
+
c
20
.
7
T
20
.
7
+
c
31
.
4
T
31
.
4
(6.53)
w
e can estimate accurate retrieval coefficients
c
31
.
4
. When users operate
a
WVR in the same climatological region, they can then readily compute the ZWD
at
their location from the observed brightness temperature and the estimated regres-
sio
n coefficients. This statistical retrieval procedure can be generalized by using an
ex
panded regression model in (6.53) and by incorporating brightness temperature
m
easurements from several radiosonde references distributed over a region.
The opacity may also be used in this regression. In fact, opacity varies more
lin
early with PWV than does the brightness temperature
T
b
. At high levels of water
va
por, or low elevation angles, the
T
b
measurements will eventually begin to saturate,
i.e
., the rate of the
T
b
increase with increasing vapor will start to fall off. This is not
tru
e for opacity, which essentially remains linear with the in-path vapor abundance.
O
pacity is available from (6.48) but also can be conveniently related to the brightness
te
mperature. Define mean radiation temperature
T
mr
as
c
0
,
ˆ
c
20
.
7
, and
ˆ
ˆ
0
(s) e
−τ
(s)
ds
T(s)
α
T
mr
≡
0
(6.54)
(s) e
−τ
(s)
ds
α
