Global Positioning System Reference
In-Depth Information
10
−
6
N
d
(h) dh
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
ZHD
=
(6.15)
10
−
6
N
wv
(h) dh
ZWD
=
(6.16)
Th
e hydrostatic refractivity
N
d
depends on total density
or the total pressure
p
.
W
hen integrating
N
d
along the ray path the hydrostatic equilibrium condition to ideal
ga
ses is applied. The integration of
N
wv
is complicated by the temporal and spatial
va
riation of the partial water vapor pressure
p
wv
along the path.
ρ
6.2.1 Model Zenith Delay Functions
Ev
en though the hydrostatic refractivity is based on the laws of ideal gases, the
in
tegration (6.15) still requires assumptions about the variation of temperature and
gr
avity along the path. Examples of solutions for the ZHD are Hopfield (1969) and
Sa
astamoinen (1972). Saastamoinen's solution is given in Davis et al. (1985) in the
form
[19
Lin
—
-
——
No
PgE
0
.
0022768
p
0[mbar]
ZHD
[m]
=
(6.17)
1
−
0
.
00266 cos 2
ϕ
−
0
.
00028
H
[km]
The symbol
p
0
denotes the total pressure at the site whose orthometric height is
H
and latitude is
ϕ
.
The model assumptions regarding the wet refractivity are more problematic be-
cause of temporal and spatial variability of water vapor. Mendes and Langley (1999)
analyzed radiosonde data and explored the correlation between the ZWD and the
surface partial water vapor pressure
p
wv,
0
. Their model is
[19
ZWD
[m]
=
0
.
0122
+
0
.
00943
p
wv,
0[mbar]
(6.18)
Surface meteorological data should be used with caution in the estimation of the
ZWD. Typical field observations can be influenced by “surface layer biases” intro-
duced by micro-meteorological effects. The measurements at the earth's surface are
not necessarily representative of adjacent layers along the line of sight to the satellites.
Temperature inversion can occur during nighttime when the air layers close to the
ground are cooler than the higher air layers, due to ground surface radiation loss. Con-
vection can occur during noontime when the sun heats the air layers near the ground.
Expressions exist that do not explicitly separate between ZHD and ZWD. In some
cases, the models are independent of direct meteorological measurements. The latter
typically derive their input from model atmospheres.
6.
2.2 Model Mapping Functions
Tropospheric delay is shortest in the zenith direction and increases with the zenith an-
gle
ϑ
as the air mass traversed by the signal increases. The exact functional relationship
