Global Positioning System Reference
In-Depth Information
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
the radiative transfer equation to determine integrated water vapor and liquid water
as a function of the observed brightness temperatures. Westwater (1978) provides a
thorough error analysis for this standard dual-frequency case. The fact that at 23.8
GHz the absorption of water vapor is significantly higher than at 31.4 GHz (while
the absorption of liquid water changes monotonically over that region) can be used
to retrieve separately integrated water vapor and liquid water from the inversion of
the radiative transfer equation. With more channels distributed appropriately over the
frequency, one can roughly infer the water vapor profiles as well as integrated water
vapor and liquid water, or even temperature, vapor, and liquid profiles (Ware, 2002,
private communication).
6.
3.3 General Statistical Retrieval
[20
Consider the following experiment. Use a radiosonde to measure the temperature and
water vapor density profile along the vertical and use equations (6.27) and (6.28) to
compute IWV and PWV. Compute the brightness temperature
T
b
from the radiative
transfer equation (6.47) for each radiometer frequency using the frequency-dependent
absorption model for water vapor
Lin
—
0.0
——
No
PgE
α
wv
(f,T,p,p
w
)
and oxygen absorption.
Figure 6.9 shows the result of such an experiment. The plot shows the observed
T
b
for WVR channels at 20.7 and 31.4 GHz. The data refer to a Bermuda radiosonde
station and were collected over a three-year period. The Bermuda site experiences
nearly the full range of global humidity and cloud cover conditions. The scatter about
the heavily populated “clear” lines is due to the occurrence of cloudy cases. The
slopes of
T
b
(
20
.
7
)
are approximately 2.2 times the slopes of the
T
b
(
31
.
4
)
. The scatter
about the
T
b
(
31
.
4
)
“clear” line is approximately twice as large as the scatter about the
T
b
(
20
.
7
)
“clear” line. These results are indicative of the facts that (1) the sensitivity of
T
b
(
20
.
7
)
to PWV is approximately 2.2 times greater than that of
T
b
(
31
.
4
)
and (2) that
the sensitivity of
T
b
(
31
.
4
)
to liquid water is approximately 2 times greater than that
of
T
b
(
20
.
7
)
. The sensitivity to liquid water is also illustrated in Figure 6.10, which
[20
Figure 6.9
Brightness temperature versus precipitable water vapor.
(Date source: Keihm, JPL.)
