Geoscience Reference
In-Depth Information
β
delay in zenith direction due to the tilting angle
, it is shown that the path delay at
(
)
(
)
the elevation angle
e
due to the gradients is cot
e
mf
e
G
, which is exactly what is
proposed by MacMillan (
1995
). Starting with
L
z
mf
)
+
∂
mf
∂
L
z
Δ
L
(
e
−
β)
=
Δ
·
mf
(
e
−
β)
≈
Δ
(
e
e
(
−
β)
,
(159)
and using 1
/
sin
(
e
)
as mapping function and with
L
z
β
=
G
/
,
(160)
we get
L
z
Δ
L
(
e
−
β)
=
Δ
·
mf
(
e
)
+
cot
(
e
)
mf
(
e
)
G
.
(161)
A gradient
G
of 1 mm corresponds to tilting angles of 1.5' (hydrostatic) and 17'
(wet). The effects on the zenith delays are 2
10
−
4
and 2
10
−
5
mm, respectively,
·
·
and can be neglected.
It is important to estimate gradients in the analysis of space geodetic observations,
in particular when observing at low elevation angles. On the other hand, there is no
need to apply a priori gradients if no constraints are applied on the estimation of
gradients.
4.3 Atmospheric Delays for SLR
4.3.1 Single-Color SLR Observations
The accuracy of the results obtained from Satellite Laser Ranging (SLR) measure-
ments is ultimately limited by the atmospheric propagation effects (as well as by by
the hardware system). In the 1970s, Marini and Murray (
1973
) developed a model to
correct the atmospheric delays in SLRmeasurements and their model became a stan-
dard correction model at that time. In the early 2000s, Mendes et al. (
2002
) pointed
out some limitation in that model, namely as regards the modeling of the elevation
dependency of the zenith atmospheric delays (the mapping function component of
the model). Thus, Mendes et al. (
2002
) developed their mapping functions (FCULa
and FCULb) that represents significant improvement over the mapping functions of
the Marini-Murray model. Of particular interest is the ability of the new mapping
functions to be used in combination with any zenith delay model, i.e. Mendes and
Pavlis (
2004
) model, used to predict the atmosphere delay in the zenith direction.
Similar to the microwave frequencies, the mapping functions are normally mod-
eled using Eq. (
121
). New mapping functions have been developed based on ray-
tracing through one full year (1999) of radiosonde data from 180 stations, globally
distributed, with a variable number of balloon launches per day. Two different para-
meterizationswere proposed byMendes et al. (
2002
) with the coefficients inEq. (
121
)
