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 first integral refers to the curved propagation path. The path is curved due to
the decreasing index of refraction with height above the earth. The second integral
is the geometric straight-line distance the wave would take if the atmosphere were a
vacuum. The integration begins at the height of the receiver antenna.
Because the index of refraction
n(s)
is numerically close to unity, it is convenient
to introduce a separate symbol for the difference,
10
−
6
n(s)
−
1
=
N(s)
·
(6.5)
N
(s)
is called the refractivity. Great efforts have been made during the second part
of
the last century to determine the refractivity for microwaves. Examples of relevant
lit
erature are Thayer (1974) and Askne and Nordius (1987). The refractivity is usually
gi
ven in the form
k
1
p
d
T
k
2
p
wv
T
k
3
p
wv
[19
Z
−
1
d
Z
−
1
wv
T
2
Z
−
1
N
=
+
+
(6.6)
wv
Lin
—
1.0
——
Lon
PgE
p
d
Partial pressure of dry air (mbar). The dry gases of the atmosphere
are, in decreasing percentage of the total volume: N
2
,O
2
,Ar,CO
2
,
Ne, He, Kr, Xe, CH
4
,H
2
, and N
2
O. These gases represent 99.96% of
the volume.
p
wv
Partial pressure of water vapor (mbar). Water vapor is highly variable
but hardly exceeds 1% of the mass of the atmosphere. Most of the
water in the air is from water vapor. Even inside clouds, precipitation
and turbulence ensure that water droplet density remains low. This
variability presents a challenge to accurate GPS applications over long
distances on one hand, but on the other hand opens up a new field of
activity, i.e., remotely sensing the atmosphere for water vapor.
[19
T
Absolute temperature in degrees Kelvin [K].
Z
d,
Z
wv
Compressibility factors that take into account small departures in
behavior of moist atmosphere and ideal gas. Spilker (1996, p. 528)
lists the expressions. These factors are often set to unity.
k
1
,k
2
,k
3
Physical constants that are based in part on theory and in part on
experimental observations. Bevis et al. (1994) lists:
k
1
=
77
.
60
370100 K
2
/mbar.
K/mbar,
k
2
=
69
.
5 K/mbar,
k
3
=
The partial water vapor pressure and the relative humidity
R
h
are related by the well-
known expression, e.g., WMO (1961),
0
.
01
R
h
[%]
e
−
37
.
2465
+
0
.
213166
T
−
0
.
000256908
T
2
p
wv
[mbar]
=
(6.7)
The two partial pressures are related to the total pressure
p
, which is measured
directly, by
p
=
p
d
+
p
wv
(6.8)
