Geoscience Reference
In-Depth Information
Ta b l e 1
The “best average” values of the
k
1
,
k
2
,and
k
3
coefficients in Eq. (
15
), as presented by
Rüeger (
2002a
,
b
)
k
1
(K/hPa)
k
2
(K/hPa)
k
3
(K
2
/hPa)
375 ppm CO
2
77.6890 71.2952 375463
392 ppm CO
2
77.6900 71.2952 375463
For
k
1
two values are given corresponding to two different carbon dioxide concentrations: 375 ppm
(2004 level, used by Rüeger (
2002a
,
b
) and 392 ppm (2012 level)
(
2002a
,
b
) assumed a carbon dioxide concentration of 375 ppm (2004 level). Table
1
also shows
k
1
for a carbon dioxide concentration of 392 ppm (2012 level). The con-
centration of carbon dioxide also shows an annual variation of about 5 ppm, meaning
that
k
1
will have an annual variation of about 2
10
−
4
K/hPa. This variation is neg-
.
8
·
ligible for all practical purposes.
Using Eq. (
12
) it is possible to rewrite Eq. (
15
)as
R
M
d
ρ
+
p
w
T
k
3
p
w
k
2
Z
−
1
w
T
2
Z
−
1
N
=
k
1
+
=
N
h
+
N
w
,
(16)
w
where
k
2
=
k
1
M
M
d
k
2
−
and:
R
M
d
ρ,
N
h
=
k
1
(17)
p
w
T
k
3
p
w
k
2
Z
−
1
T
2
Z
−
1
N
w
=
+
.
(18)
w
w
N
h
is called the hydrostatic refractivity and
N
w
the wet (or non-hydrostatic) refrac-
tivity. The hydrostatic refractivity depends only on the total density of air, while the
wet part depends only on the partial pressure of water vapor and the temperature.
Figure
2
shows examples of vertical profiles of
N
h
and
N
w
. While the hydrostatic part
Fig. 2
Examples of vertical profiles of the hydrostatic andwet refractivity. The profiles are calulated
using radiosonde data from Vienna, Austria