Global Positioning System Reference
In-Depth Information
10
−
6
N
wv
(w
∂
∂u
N
wv
du
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
ZWD
(
α
,
β
)
=
=
0
)
+
∂N
wv
∂n
∂N
wv
∂e
du
10
−
6
tan
+
cos
α
du
+
sin
α
β
1
tan
=
ZWD
+
(G
n
cos
α +
G
e
sin
a)
(6.26)
β
O
ne may attempt to estimate the model coefficients
G
n
and
G
e
from observations.
D
epending on the application and weather conditions, a possibly piecewise linear
m
odeling might be appropriate. Applications of the horizontal gradient method are
re
ported, e.g., by Bar-Sever et al. (1998) and Liu (1999).
[20
6.2.4 PrecipitableWater Vapor
Th
e GPS observables directly depend on the STD. This quantity, therefore, can be
es
timated from GPS observations. One might envision the scenario where widely
sp
aced receivers are located at known stations and that the precise ephemeris is also
av
ailable. If all other errors are taken into consideration, then the residual misclo-
su
res of the observations are the STD. We compute the ZHD from surface pressure
m
easurements and a hydrostatic delay model. Using appropriate mapping functions,
w
e could then compute ZWD from (6.21) using the estimated STD. Input to weather
m
odels typically requires that the ZWD be converted to precipitable water.
The integrated water vapor (IWV) along the vertical and the precipitable water
va
por (PWV) are defined as
Lin
—
0.4
——
Nor
*PgE
[20
IWV
≡
ρ
wv
dh
(6.27)
IWV
ρ
w
PWV
≡
(6.28)
where
ρ
w
is the density of liquid water. To relate the ZWD to these measures, it is
convenient to introduce the mean temperature
T
m
,
p
wv
T
Z
−
1
wv
dh
T
m
≡
(6.29)
p
wv
T
2
Z
−
1
wv
dh
The ZWD follows then from (6.16), using (6.14),
10
−
6
k
2
+
p
wv
T
k
3
T
m
Z
−
1
ZWD
=
wv
dh
(6.30)
To be precise let us recall that (6.30) represents the nonhydrostatic zenith delay. Using
the state equation of water vapor gas,
