Geoscience Reference
In-Depth Information
hydrostatic balance, no such exact formulation holds for the water vapor pressure.
Its distribution is very variable temporally and spatially.
2.5 Increasing the Vertical Resolution of Meteorological Data
If not equipped with a GNSS receiver, radiosonde data do not include information
about the height, but the geopotential is determined by the equations shown in
value (
g
n
80665m/s
2
) to get the so-called geopotential heights
h
d
known in
geodesy as dynamic heights. These heights can be converted to geometric heights
h
(orthometric or sea level heights) if realistic gravity values are available which
depend mainly on height
h
and latitude
=
9
.
ϕ
.
g
h
C
g
n
=
1
g
n
·
1
g
n
·
h
2
h
d
=
g
(ϕ,
h
)
·
dh
≈
ϕ,
·
h
(34)
0
g
n
g
ϕ,
h
d
·
h
=
2
(35)
h
Applying the normal gravity in Eq.
36
suggested by Kraus (
2004
)
h
(36)
the geometric heights can be derived. Theoretically, this has to be done in an iterative
approach, but practically one application of Eq.
35
is sufficient. Note that the descrip-
tion of the height-dependence of
g
g
n
1
ϕ)
·
1
0000059 cos
2
10
−
7
g
(ϕ,
h
)
=
−
0
.
0026373 cos
(
2
ϕ)
+
0
.
(
2
−
3
.
14
·
·
which is given by
1
10
−
7
h
is an
(ϕ,
h
)
−
3
.
14
·
2
when
R
E
is the Earth
approximation to the more accurate expression 1
/(
1
+
h
/
R
E
)
radius.
Let's assume we have pressure values
p
in hPa, temperatures in Kelvin, and water
vapor pressure values
e
in hPa at a set of geometric heights
h
. Typically these data
are available up to 10hPa (30km) or 1hPa (50km), but to get highest accuracy for
some applications as described in the later parts of the topic, the meteorological data
have to be extended up to about 100km. Hobiger et al. (
2008
) use an upper limit of
86km, Rocken et al. (
2001
) use 136km. For example, the temperatures in Table
3
can be used, and the pressure can be extrapolated assuming an exponential decrease
from the uppermost level.
Additionally, the increments for the numerical integration of refractivity need to
be reduced. Following Rocken et al. (
2001
) height dependent increments can be
Ta b l e 3
Standard model for
the temperature at certain
heights up to 130km
height in km
25
50
80
100
130
temperature in K
220
268
200
210
533
