Geoscience Reference
In-Depth Information
written as functions of the selected parameters. One parameterization of the mapping
function (FCULa) requires both site location and meteorological (surface tempera-
ture) data. The coefficients of the mapping function have the following mathematical
formulation
a
=
a
0
+
a
1
T
0
+
a
2
cos
θ
+
a
3
h
0
,
(162)
where
T
0
is the temperature at the station in degrees centigrade,
is the station
latitude, and
h
0
is the orthometric height of the station, in meters. The coefficients
b
and
c
are modeled similarly.
The second parameterization (FCULb) does not depend on any meteorological
data, i.e. similar to the model developed by Niell (
1996
) for radio wavelengths. For
this function, the coefficients have the following form
θ
cos
2
π
365
2
a
=
a
0
+
(
a
1
+
a
2
θ
d
)
25
(
doy
−
28
)
+
a
3
h
0
+
a
4
cos
θ,
(163)
.
where
θ
d
is the latitude of the station, in degrees, and doy is the decimal day of year
(UTC day since the beginning of the year). The coefficients in Eq. (
163
) are different
with those in Eq. (
122
) as the later one is derived based on microwave refractivity
index, which is independent on frequency.
These mapping functions along with the zenith delay model of Mendes and Pavlis
(
2004
) have become the standard model for correcting SLR measurements. Compar-
ing to the previously used mapping functions, the advantages of the new mapping
functions are obvious. They represent simpler expressions than those proposed by
the Marini and Murray (
1973
) model and allow the use of better zenith delay models.
The coefficients of the mapping functions are presented in Table
6
.
The latest progress in atmospheric corrections for single-color SLR is provided by
Hulley and Pavlis (
2007
) who applied a ray-tracing technique to calculate propagation
effects, including the effects of horizontal refractivity gradients. The use of ray-
tracing trough numerical weather models has been shown to improve the accuracy
of the SLR results.
4.3.2 Two-Color SLR Observations
The alternative to modeling is the application of two-color (i.e. two-frequency) SLR
measurements for the direct computation of the propagation delay by utilizing the
fact that the neutral atmosphere is dispersive for optical frequencies. The dispersion
causes the optical path lengths at two different frequencies to differ. This difference
depends on the two frequencies and is proportional to the path integrated atmospheric
density. Thus, the difference between the two optical paths can be used for calculating
the propagation delays (Wijaya and Brunner
2011
). This method has the potential to
improve the accuracy of SLR results (Abshire and Gardner
1985
).
Based on the previous works of Prilepin (
1957
) and Bender and Owens (
1965
),
Abshire and Gardner (
1985
) developed an atmospheric correction formula for the
