Geoscience Reference
In-Depth Information
To be able to calculate the mean temperature
T
m
the vertical profiles of the water
vapor and temperature have to be known. Such data can be obtained from radiosonde
measurements or calculated (and predicted) from operational meteorological models
(Wang et al.
2005
). In absence of this data, the empirically derived model by e.g.
Bevis et al. (
1992
) and Emardson and Derks (
2000
) can be used. The determination
of the mean temperature
T
m
from Eq. (
53
) is based on the weighting with water
vapor pressure in the atmosphere. Since water vapor is mainly located near the Earth
surface the mean temperature
T
m
will be highly correlated with the temperature at
the Earth surface
T
0
. Using 8718 profiles of radiosonde launches at 13 stations in the
United States between 27 and 65
◦
northern latitude, between 0 and 1600 m height,
and over a time span of 2 years Bevis et al. (
1992
) found
T
m
≈
70
.
2
+
0
.
72
T
0
,
(56)
L
z
w
and surface temperature are known
without error, the integrated water vapor can be computed with an average error of
less than 4 %.
It is clear from Eq. (
55
) that the wet delay is proportional to the integrated water
vapor content IWV (
IWV
with a standard deviation of
±
4.74 K. If
Δ
=
0
ρ
w
dz
). Since IWV is a variable that can be easily
obtained fromnumerical weather predictionmodels or measured by other techniques,
it is of great interest to have a simple expression for calculating the wet delay from
IWV, and vice versa. Thus we define the proportionality constant
Π
such that
L
z
w
,
=
ΠΔ
IWV
(57)
L
z
w
is the wet tropospheric delay in the zenith direction. By comparing Eqs.
(
55
) and (
57
), we find that
where
Δ
Π
can be related to
T
m
by
10
6
M
w
k
2
+
Π
=
T
m
R
,
(58)
k
3
The integrated water vapor in zenith direction can also be provided as precipitable
water (PW) which corresponds to the height of the equivalent water column above
the station
IWV
ρ
w
,
fl
,
PW
=
(59)
m
3
. With a dimensionless quantity
where
ρ
w
,
fl
is the density of liquid water in kg
/
L
z
w
and PW
κ
we can relate the
Δ
L
z
w
,
PW
=
κΔ
(60)
with
κ
defined as
