Geoscience Reference
In-Depth Information
The factor in the denominator ensures that the mapping function is equal to one in
the zenith direction. The strong dependence of the MTT mapping function (Herring
1992
) on surface temperature induced Niell (
1996
) to develop the New Mapping
Functions (NMF, now often called Niell Mapping Functions). The NMF do not use
meteorological parameters at the sites, but only the day of the year (doy), station
latitude, and station height as input parameters. Thus, they can be easily applied at
stations without meteorological sensors, which often is the case for GNSS stations.
Niell (
1996
) used standard atmosphere data at various latitudes to determine hydro-
static and wet mapping functions down to 3
◦
elevation. Similar to Davis et al. (
1985
)
and Herring (
1992
), he used ray-tracing methods to determine the coefficients
a
,
b
,
and
c
of the continued fraction form in Eq. (
121
). NMF is based on sine functions to
describe the temporal variation of the coefficients. The period is 365.25 days and the
maximum/minimum is set to January 28 (doy 28). There is also a height correction
for the hydrostatic NMF (NMFh) which describes that mapping functions increase
with increasing height, i.e. the atmosphere above the site becomes flatter.
Niell (
2000
) was the first to determine mapping functions from numerical weather
models which are often available with a time resolution of 6 h. For the Isobaric
Mapping Functions (IMF), he used empirical functions for
b
and
c
, and he determined
the coefficients
a
of the continued fraction in Eq. (
121
) from re-analysis data of the
Goddard Space Flight Center Data Assimilation Office (DAO) (Schubert et al.
1993
).
For the hydrostatic IMF he used the height of the 200 hPa pressure level which is
readily available with most numerical weather models and which is describing the
thickness of the atmosphere well. For the wet IMF Niell suggested to use a coarse
ray-trace at 3
3
◦
initial elevation angle through numerical weather models. However,
some practical and conceptual limitations in the computation of the wet IMF induced
Böhm and Schuh (
2004
) to develop the Vienna Mapping Functions (VMF).
Thus, the VMF are characterized by the removal of some weaknesses of the
IMFw, e.g. the coarse vertical resolution of weather model data is improved by
vertical interpolation and the bending effect is taken into account rigorously. The
same approach is applied for the wet and the hydrostatic mapping function, i.e.
a ray-tracing is performed at an initial elevation angle of 3
.
3
◦
for the hydrostatic and
wet components yielding the hydrostatic delay, the wet delay, as well as the bending
effect and the outgoing (vacuum) elevation angle which is
.
3
◦
. (Please notice that
always the refractivity profile above the site vertical is used, which makes the 1D ray-
tracing simple and causes the delays to be symmetric with azimuth.) Together with
the zenith hydrostatic and wet delays which are also determined by ray-tracing, the
hydrostatic and wet mapping functions (Eq. (
121
)) at the outgoing elevation angle
are calculated. The geometric bending effect is added to the hydrostatic mapping
function. Similar to IMF, empirical functions are used for the
b
and
c
coefficients,
which allows the determination of
a
in Eq. (
121
) by simple inversion. Since the
coefficients
a
,
b
, and
c
are highly correlated, small errors in
b
and
c
can easily be
compensated with the
a
coefficients. However, Böhm et al. (
2006b
) improved the
b
and
c
coefficients, and consequently the
a
coefficients had to be re-calculated. The
coefficients of the so-called VMF1 are
b
h
= 0.0029,
b
w
= 0.00146,
c
w
= 0.04391,
and the coefficient
c
h
is provided with Eq. (
122
) and Table
4
≈
