Geoscience Reference
In-Depth Information
413
0 g/m
3
0.05 g/m
3
1 g/m
3
412
411
410
409
408
407
0
20
40
60
80
100
Frequency [GHz]
Fig. 1
The total refractivity as function of frequency. The total pressure is 1013 hPa, the temperature
300 K, and the relative humidity is 100%. Three different cases are shown corresponding to different
concentrations of liquid water: 0, 0.05, and 1 g/m
3
at 100 GHz. This agrees with the published values for
k
4
in the microwave range,
which is generally about 1.45 (Liebe et al.
1993
; Solheim et al.
1999
).
By ignoring the liquid water term and assuming that the refractivity is frequency
independent, Eq. (
11
) becomes
p
d
T
p
w
T
p
w
Z
−
1
d
Z
−
1
w
T
2
Z
−
1
N
=
k
1
+
k
2
+
k
3
.
(15)
w
Several different laboratory measurements have been performed in order to deter-
mine the constants
k
1
,
k
2
, and
k
3
(e.g. Boudouris
1963
, Bevis et al.
1994
). Thayer
(
1974
) estimated these constants by extrapolating measurements made at optical
frequencies to the microwave region. The claimed accuracy was better than what is
obtained from other investigations due to more accurate refractivity measurements
being available for optical frequencies. However, as pointed out by e.g. Hill et al.
(
1982
) extrapolation of optical measurements is problematic due to several resonance
frequencies in the infrared region, thus the values published by Thayer (
1974
) should
not be used. Rüeger (
2002a
,
b
) summarized and discussed many of these investiga-
tions, and calculated the “best average” values for the constants. These values are
given in Table
1
. The accuracy of
k
1
is 0.015 % and the accuracy of the water vapor
part of the refractivity is 0.15 %.
Strictly speaking the constant
k
1
is dependent on the relative concentrations
of the different dry atmospheric gases, thus if these change
k
1
will also change.
Most dry atmospheric gases have stable concentrations. Of the major gases only the
concentration of carbon dioxide show a significant variation (it is increasing with
1.5-2 ppm/year). Rüeger (
2002a
) gives a formula for calculating
k
1
for different
carbon dioxide concentrations. In total the carbon dioxide makes
k
1
about 0.03 %
larger compared to a carbon dioxide free atmosphere. The
k
1
value given by Rüeger
