Geoscience Reference
In-Depth Information
by poor a priori zenith hydrostatic delays (Böhm et al.
2006b
). On the other hand, the
value of total mapping function is close to that of the hydrostatic mapping function,
so it cannot account for the rapid variation of the wet zenith delays which occurs
even between the 6 hourly epochs of the total VMF1. Thus, it is preferable to keep
the separation into a hydrostatic and a wet mapping function, at least as long as the
time resolution is not 3h or better.
The goal of the Global Mapping Functions (GMF; Böhm et al.
2006a
)istomake
available mapping functions which can be used globally and implemented easily in
existing geodetic data analysis softwares and which are consistent with NWM-based
mapping functions, in particular with the VMF1 (Böhm et al.
2006b
). Compared
to the NMF (Niell
1996
), the parameterization of the coefficients in the three-term
continued fraction (Eq.
121
) has been refined to include also a longitude dependence.
Using global grids of monthly mean profiles for pressure, temperature, and humidity
from the ECMWF 40 years reanalysis data (ERA40), the coefficients
a
h
and
a
w
were
determined using data from the period September 1999 to August 2002 applying the
same strategy and the same
b
and
c
coefficients used for VMF1. Thus, at each of
the 312 grid points, 36 monthly
a
values were obtained for the hydrostatic and wet
mapping functions, respectively. The hydrostatic coefficients were reduced to mean
sea level by applying the height correction given by Niell (
1996
). The mean values,
a
0
, and the annual amplitudes,
A
, of the sinusoidal function (Eq.
126
) were fitted to
the
a
parameter time series of each grid point, with the phases referred to January 28,
corresponding to the NMF. The standard deviations of the monthly values at the
single grid points with respect to the values obtained from Eq. (
126
) increase from
the equator towards larger latitudes, with a maximum value of 8 mm (expressed
as equivalent station height error) in Siberia. For the wet component, the standard
deviations are generally smaller, with the maximum values being about 3 mm at the
equator Böhm et al. (
2006a
).
cos
doy
−
28
a
=
a
0
+
A
·
25
·
2
π
,
(126)
365
.
9
n
a
0
=
P
nm
(
sin
θ)(
A
nm
cos
(
m
λ)
+
B
nm
sin
(
m
λ)).
(127)
n
=
m
=
0
0
Then, the global grid of the mean values
a
0
and that of the amplitudes
A
for both
the hydrostatic and wet coefficients of the continued fraction form were expanded
into spatial spherical harmonic coefficients up to degree and order 9 (according to
Eq. (
127
)for
a
0
) in a least-squares adjustment. The residuals of the global grid of
a
0
and
A
values to the spherical harmonics are in the sub-millimeter range (in terms of
station height). The hydrostatic and wet coefficients
a
for any site coordinates and
day of year can then be determined using Eq. (
126
).
In Fig.
10
VMF1 and GMF hydrostatic mapping functions at 5
◦
elevation angle
are plotted for Fortaleza, Brazil. The GMF reflects a seasonal variability and, in
this respect, agrees well with the VMF1. However, a deficiency is evident in the
empirical mapping function compared to the VMF1 because GMF does not reveal
