Geoscience Reference
In-Depth Information
Fig. 14
The spatial structure function
D
L
(Eq.
186
) for the zenith wet delay
5
/
3
,for
H
We can here note three regions: for
ρ
H
we have
D
L
(ρ)
∝
ρ
ρ
L
C
n
H
2
L
2
/
3
(i.e. constant).
From he structure function
D
L
the covariance matrix for the turbulent fluctuations
in the tropospheric delay can be calculated. This can then be applied to weight the
observations in the estimation procedure. For more details, see e.g. Treuhaft and
Lanyi (
1987
). It is also possible to use
D
L
for simulating tropospheric delays, see
e.g. Nilsson and Haas (
2010
).
2
/
3
, and for
we have
D
L
(ρ)
∝
ρ
ρ
L
we
D
L
(ρ)
≈
5.2 Estimating C
n
In order to calculate the structure function
D
L
the profile of the structure constant
C
n
needs to be known. This parameter is highly variable, both in time and between
different locations. Several methods to determine
C
n
exist, see Nilsson and Haas
(
2010
) for a review of some of them.
One way to determine
C
n
is to use observations of variations in the tropospheric
delay. For example,
C
n
can be estimated from the observed variations of the tro-
pospheric delay between different directions (Nilsson et al.
2005
) or between differ-
ent locations (Treuhaft and Lanyi
1987
). Here we describe how to estimate
C
n
from
observations of the zenith delay variance over a time period
T
1
T
d
t
d
t
2
T
T
1
T
2
L
z
L
z
t
+
σ
L
(
T
)
=
Δ
(
t
+
t
0
)
−
(
t
0
)
.
(190)
0
0
