Geoscience Reference
In-Depth Information
estimated wet delays, and
mf
h
(
)
and
mf
w
(
)
are the so-called mapping functions
which provide the ratio of the delay to the delay in zenith direction. The input to
both mapping functions is the vacuum elevation angle
e
, because the bending effect
is accounted for by the hydrostatic mapping function.
Errors in the zenith hydrostatic delays or the mapping functions have an influence
on station height errors as described with the rules of thumb by Niell et al. (
2001
)or
Böhm (
2004
) mentioned above. The following two examples illustrate this rule of
thumb, which—holding for both GPS and VLBI—depends on the actual distribution
of elevation angels and on whether elevation angle-dependent weighting is used:
The zenith hydrostatic and wet delays shall be 2000 and 200 mm, respectively, the
minimum elevation angle is 5
◦
, and the corresponding values for the true hydrostatic
and wet mapping functions are 10.15 (
mf
h
(
e
e
5
◦
)
5
◦
)
) and 10.75 (
mf
w
(
) (Böhm et al.
2006b
).
•
We assume an error in the total pressure at the station of +10 hPa, e.g. when
using the “mean” pressure from GPT during a time of low pressure. +10 hPa
correspond to
+20 mm zenith hydrostatic delay (Saastamoinen
1972b
), which
is then mapped down to 5
◦
elevation angle using the wrong mapping function
(wet instead of hydrostatic, factor
≈
0.6 = 10.15-10.75). At 5
◦
elevation angle
−
the mapping function error is
2.4 mm, would
be the resulting station height error. This results in a kind of atmosphere loading
correction (see Part 4, Wijaya et al. (
2013
)), because during a pressure low the
station heights go up (Tregoning and Herring
2006
; Steigenberger et al.
2009
).
−
12 mm, and one fifth of it, i.e.
−
5
◦
)
•
We consider an error in the wet mapping function of 0.1 (
mf
w
(
=10.85 instead
5
◦
)
of 10.75) or in the hydrostatic mapping function of 0.01 (
mf
h
(
=10.16 instead
of 10.15). The error at 5
◦
elevation angle is in both cases 20 mm, i.e. the resulting
error in the station height would be approximately +4 mm.
The scale height of the wet part in the troposphere is about 2 km, whereas the
scale height of the hydrostatic part is about 8 km (cf. Fig.
9
). The mapping func-
tions describe the ratio
(hydrostatic). Due to the
curvature of the Earth and the smaller scale height of the wet part, the hydrostatic
(
AB
)/(
B
0
B
)
(wet) and
(
AC
)/(
C
0
C
)
C
hydrostatic
B
A
wet
e
C
0
B
0
Earth
Fig. 9
The scale height of the wet part of the troposphere is about 2 km, the scale height of the
hydrostatic part is about 8 km. The mapping functions describe the ratio of the paths
(
AB
)/(
B
0
B
)
(wet) and
(
AC
)/(
C
0
C
)
(hydrostatic). The wet mapping function is larger than the hydrostatic map-
ping function
