Geoscience Reference
In-Depth Information
Using the homogeneous atmosphere we can easily determine the mass of the
atmosphere. It follows from the volume of a spherical shell with height H at constant
density.
r 3
4
3
3
r 2 H
m
=
V
· ρ =
(
r
+
H
)
ρ
4
π
ρ
(31)
10 18 kg, i.e.
about 1ppm of the Earth mass. More sophisticated calculations of the mass of the
atmosphere are shown by Karbon et al. ( 2013 ) in this topic.
The actual density of air at the Earth surface is larger close to the poles than at the
equator. The reason is the combination of lower temperature and the larger gravity at
the poles. The extension of the atmosphere is smaller at the poles than at the equator,
so the density gradient is larger in higher latitudes.
The decrease of temperature with height, known as its lapse rate, is nearly linear
and
m 3 , we get m
with r
=
6371km, H
=
8km,
ρ =
1
.
293 kg
/
=
5
.
27
·
65 C per 100m. Thus, we can set the temperature to t m which is the mean
temperature of the upper and lower limit of the layer. With Eq. 30 we get for Eq. 23 :
.
0
dp
p =−
dh
1
8 p
(32)
3 e
H 0 (
1
+ α ·
t m )
+
Integration between the heights h 1 and h 2 yields (in logarithmic form):
h 2
h 1
1
8 p
lnp 2 =
lnp 1
(33)
3 e
7979
(
1
+ α ·
t m )
+
This is the equation for barometric height measurements. For many practical
purposes this equation has to be inverted. We often need the pressure gradient dp
/
dh
or its inverse dh
dp and we express it in m/hPa (Table 2 ).
Although only a small fraction of the total volume of air, water vapor plays
important roles in the latent heat it holds, roles in energy releases during changes of
phase, roles in cloud formations and precipitation, as well as the radiative effects it
has in its interaction with electromagnetic waves. Its horizontal distribution relates
to the characteristics of the air masses in which it resides, but its vertical distribution
generally decreases with height. Although evaporation occurs at the Earth's surface,
air at higher altitudes with its lower temperatures cannot hold as much water vapor.
Whereas the total pressure decreases with height according to strict equations of
/
Ta b l e 2 Height difference
Δ
t B in C, p in hPa
20 C0 C20 C30 C
h in meter per 1hPa
(dry air)
1013
7.30
7.88
8.45
8.74
933
7.92
8.55
9.18
9.49
853
8.67
9.35
10.04
10.38
813
9.09
9.81
10.53
10.90
 
Search WWH ::




Custom Search