Geoscience Reference
In-Depth Information
Equation (
65
) is slightly different from the one developed by Mendes and Pavlis
(
2004
), which is expressed as
R
d
4
g
m
L
z
w
0
=
10
−
6
Δ
(
5
.
316
f
nh
(ν)
−
3
.
759
f
h
(ν))
p
w
0
.
(66)
Mendes and Pavlis (
2004
) derived their own dispersion factors
f
h
(λ)
and
f
nh
(λ)
based on the modified dispersion formula in Eq. (
24
) for the 0.532
m wavelength.
Equations (
65
) and (
66
) produce similar accuracy results if they are applied to real
SLR observations.
µ
4 Modeling Delays in the Neutral Atmosphere
There are basically two ways to handle the atmospheric delays when analyzing space
geodetic data; either external measurements of the atmospheric delays are used to cor-
rect the measurements, or the atmospheric delays are parameterized and estimated
in the data analysis. As seen in Sect.
3.1
the hydrostatic delay can be accurately
determined from surface pressure measurements. However, the wet delay cannot be
estimated that accurately frommeteorological measurements at the surface. Thus it is
common when analyzing space geodetic data to use surface pressure measurements
to model the hydrostatic delay, while the wet delay is estimated in the data analysis.
In the data analysis the tropospheric delays are modeled using mapping functions
and gradients (see Sect.
4.2
). An alternative strategy is to also use external estimates
of the hydrostatic and wet delays. Such estimates could for example be obtained from
ray-tracing though numerical weather models (Sect.
4.1
), a technique also commonly
applied for deriving expression for the tropospheric mapping functions. Another pos-
sibility is to infer the tropospheric delay frommeasurements by external instruments
such asWater Vapor Radiometers (WVR) (Sect.
4.4
). The numerical values etc. given
in these sections are for microwaves, although the general principles could of course
also be applied in the case of optical techniques. Tropospheric modeling for optical
frequencies (e.g. SLR) is discussed in Sect.
4.3
.
4.1 Ray-Tracing
From e.g. radiosonde data or numerical weather prediction models we can calculate
the refractivity field of the atmosphere. This could be used to estimate the atmospheric
delay simply by integrating the refractivity along the propagation path of the signal.
However, the problem is that we normally do not exactly know the propagation path.
To discover it we can apply the so-called ray-tracing technique. The ray-tracing
technique has been used in many fields of science where the propagation of an
electro-magnetic wave through a stratified medium has to be quantified. The ray-
tracing is based on the so-called Eikonal equation, which represents the solution of
