Geoscience Reference
In-Depth Information
60
◦
latitude), which is
due to the larger pressure variations in these regions compared to equatorial regions
(Böhm et al.
2009a
).
±
towards higher latitudes (with maximum values at around
3.2 Wet Delay
3.2.1 Microwave Zenith Wet Delays
From Eq. (
30
) the zenith wet delay is
10
−
6
∞
h
0
∞
T
2
Z
−
w
d
z
k
2
Z
−
w
d
z
k
3
p
w
p
w
T
L
z
w
=
Δ
+
.
(46)
h
0
The first term in Eq. (
46
) is about 1.6 % of the second term.
The derivation of a model to account for the zenith wet delay (
L
z
w
)isbyfar
more challenging than the one for the hydrostatic delay. This is due to high spatial
and temporal variability and unpredictability of the amount of water vapor. Thus, the
temperature and the water vapor content at the Earth surface are not representative for
the air masses above. This is the reason why numerous models have been developed
over the past few decades for the wet delay, while preserving Saastamoinen's model
(with slight modifications) for determining the hydrostatic delay. The zenithwet delay
varies between a fewmmat the poles and about 40 cmabove the equatorial regions. In
order to keep millimeter accuracy in space geodetic techniques, the
Δ
L
z
w
is nowadays
estimated as an additional parameter within the data analysis. Nevertheless, some
models are listed below and can be used as an initial value in the data analysis or for
applications not requiring high accuracy.
Saastamoinen (
1972b
) proposes the calculation of the zenith wet delay
Δ
L
z
w
based
Δ
on ideal gas laws using a simple relation
p
w
0
T
0
,
L
z
w
=
Δ
0
.
0022768
(
1255
+
0
.
05
T
0
)
(47)
where
p
w
0
is the water vapor pressure and
T
0
is the temperature at the surface. Similar
to the hydrostatic delay, Hopfield (
1969
) proposes an expression for
L
z
w
as follows
Δ
10
−
6
5
L
z
w
=
Δ
N
w
(
h
0
)
h
w
,
(48)
with
N
w
(
the refractivity of wet air at the surface (located at height
h
0
) and a
mean value
h
w
=
h
0
)
11000 m for the height of the troposphere up to which water vapor
exists. Ifadis (
1986
) proposes to model the zenith wet delay as a function of surface
pressure, partial water vapor pressure and temperature. Mendes and Langley (
1998
)
derived a linear relation between
L
z
w
and partial water vapor pressure. Some other
Δ
