Geoscience Reference
In-Depth Information
=
(
.
9
h
0
+
)
±
,
h
eff
0
7300 m
400 m
(35)
which holds for all latitudes and all seasons.
3.1.1 Microwaves
With the pressure
p
0
at the site, it is now possible to determine the zenith hydrostatic
delay
Rp
0
M
d
g
eff
.
L
h
=
10
−
6
k
1
Δ
(36)
We follow Saastamoinen (
1972b
) and Davis et al. (
1985
) to find the appropriate coef-
ficients in Eq. (
36
). At first, the gravity
g
eff
at the effective height
h
eff
is determined
with
8062
1
10
−
6
h
eff
g
eff
=
9
.
−
0
.
00265 cos
(
2
θ)
−
0
.
31
·
,
(37)
which combined with Eq. (
35
) can be written as
g
eff
=
g
m
·
f
(θ,
h
0
),
(38)
with
g
m
=
9
.
7840 and
1
10
−
6
h
0
f
=
−
0
.
00266 cos
(
2
θ)
−
0
.
28
·
,
(39)
where
and
h
0
are latitude and orthometric (or ellipsoidal) height of the station.
Thus, the zenith hydrostatic delay is
θ
Rp
0
M
d
g
m
f
L
h
=
10
−
6
k
1
Δ
h
0
)
,
(40)
(θ,
and after substitution of all values we get for the zenith hydrostatic delay in meters
p
0
L
h
=
Δ
0
.
0022768
h
0
)
,
(41)
f
(θ,
where
p
0
is in hPa. The molar masses
M
d
and
M
w
stay constant up to heights of about
100 km (Davis
1986
), which is essential for all troposphere delay models. The errors
in the zenith hydrostatic delays are mainly caused by errors in
k
1
and in the surface
pressure measurements. At typical meteorological conditions the zenith hydrostatic
delays are about 2.3 m at sea level. An error in the surface pressure of 1 hPa causes
an error of about 2.3 mm. In order to reach an accuracy of 0.1 mm, the pressure
has to be measured with an accuracy of 0.05 hPa. The error due to the assumption
of hydrostatic equilibrium depends on the wind and is about 0.01 % (0.2 mm path
delay). Under severe weather conditions vertical accelerations can reach 1% of the
