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θ
temperature
and the specific humidity
q
T
p
0
p
0
.
286
θ
=
,
(194)
p
w
q
=
62
p
,
(195)
1
.
1000 hPa. Thus
C
n
can be calculated as
where
p
0
=
∂
2
n
∂θ
∂θ
∂
z
+
∂
n
q
∂
q
a
2
L
4
/
3
0
C
n
=
,
(196)
∂
∂
z
where
a
2
is a constant (
a
2
2.8 (d'Auria et al.
1993
)). The vertical gradients should
not contain any variations due to turbulence, thus they should be evaluated over
height intervals larger than
L
0
.
Equation (
196
) is however only valid if there is turbulence present. When no
turbulence is present
C
n
should be (close to) zero. One way to determine if the air is
turbulent or not is to use the Richardson number
Ri
(Richardson
1920
)
≈
−
2
g
θ
∂θ
∂
∂
v
Ri
=
.
(197)
z
∂
z
The atmosphere is turbulent when
Ri
is larger than a critical Richardson number
Ri
c
,
typically
Ri
c
≈
0
.
25. Thus Eq. (
196
) modifies to
F
∂
2
n
∂θ
∂θ
∂
z
+
∂
n
q
∂
q
a
2
L
4
/
3
0
C
n
=
,
(198)
∂
∂
z
where
F
Ri
c
and zero otherwise. This is however still a bit too simplistic
since this assumes a very sharp transition between a turbulent and a non-turbulent
state. d'Auria et al. (
1993
) presented a model for
F
giving a more smooth transition
between 0 and 1 around
Ri
c
.
=
1if
Ri
<
6 Applications of Space Geodetic Techniques for Atmospheric
Studies
As discussed earlier, it is important to have a good model of the delay in the neutral
atmosphere in order to obtain the highest accuracy in the space geodetic results
(e.g. station positions). Since external estimates of the wet delay with high enough
accuracy are typically not available (at least for microwave techniques), the common
way of handling the wet delay in the data analysis is to estimate it, i.e. by modeling it
using mapping functions and gradients as described in Sect.
4.2
. Thus the results of
