Geoscience Reference
In-Depth Information
Ta b l e 4
Parameters
c
0
,
c
10
,
c
11
,and
ψ
needed for computing the coefficient
c
of the hydrostatic
mapping function
Hemisphere
c
0
c
10
c
11
ψ
Northern
0.062
0.001
0.005
0
Southern
0.062
0.002
0.007
π
Mind that the
c
xx
coefficient is incorrect in the paper by Böhm et al. (
2006b
)
Ta b l e 5
Parameters
c
0
,
c
10
,
c
11
,and
Hemisphere
c
0
c
10
c
11
ψ
needed for
computing the coefficient
c
of
the total mapping function
ψ
Northern
0.063
0.000
0.004
0
Southern
0.063
0.001
0.006
π
cos
doy
1
c
10
−
28
c
11
2
+
c
h
=
c
0
+
25
·
2
π
+
ψ
+
·
·
(
1
−
cos
θ).
(122)
365
.
The VMF1 are valid (tuned) for elevation angles above 3
◦
, and the largest devi-
ations from ray-traces at other elevations show up at about 5
◦
elevation angle. The
ViennaMapping Function 1 is realized as discrete time series (resolution 6h) of coef-
ficients
a
, either on a global grid or at certain geodetic sites (see
http://ggosatm.hg.
tuwien.ac.at/
)
. Mind that with the gridded version of the VMF1, the height correction
of Niell (
1996
) has to be applied.
Instead of separating the delays into a hydrostatic and a wet part, an alternative
concept of total mapping functions has also been investigated for troposphere delay
modeling (Böhm et al.
2006b
), i.e. the use of a single total mapping function
mf
t
(Eq.
123
) both for mapping down the a priori zenith total delays
L
t
,
0
and as partial
Δ
L
t
,
res
(Eqs.
124
and
125
).
Table
5
summarizes the parameters for the
c
t
coefficient which have been determined
with the same approach as the
c
h
coefficients of the hydrotstatic VMF1. The
b
coefficient of the total VMF1 is also
b
t
= 0.0029.
derivative for the estimation of the residual total delays
Δ
)
=
Δ
L
h
(
e
)
+
Δ
L
w
(
e
)
+
Δ
L
bend
mf
t
(
e
,
(123)
L
h
+
Δ
L
z
w
Δ
L
t
L
h
+
Δ
L
z
w
=
Δ
L
t
,
0
+
Δ
L
t
,
res
,
Δ
=
Δ
(124)
L
t
,
0
·
L
t
,
res
·
Δ
L
(
e
)
=
Δ
mf
t
(
e
)
+
Δ
mf
t
(
e
).
(125)
Although a priori zenith total delays are required in the data analysis, a priori
zenith hydrostatic delays can also be applied because the mapping function for the a
priori zenith delays is the same as for the residual zenith delays (this only holds if there
are no constraints on the estimated zenith delays). With the classical separation into
a hydrostatic and a wet part, errors of the a priori zenith hydrostatic delays cannot be
fully compensated by the estimation of the remaining wet part since the hydrostatic
and wet mapping functions are not identical, especially at low elevation angles. The
advantage of the concept of total mapping functions is that the results are not affected
