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Greene and Herring 1986 ). At optical frequencies, water vapor contributes only
about 1 % of the refractivity, however, since it is highly variable and it can introduce
substantial errors. By using ray-tracing through atmospheric profiles, Wijaya and
Brunner ( 2011 ) showed that the zenith wet delay can be several millimeters for SLR
measurements. Furthermore, the magnitude of the bending effects could reach a few
centimeters for measurements taken at an elevation angle of 10 .
The precision required for the range difference
measurements is very
stringent (fewmicrometers), which ismainly due to amplification of themeasurement
noise by the scaling factor
(R 1 R 2 )
(Abshire and Gardner 1985 ; Greene and Herring 1986 ).
This requirement cannot currently be achieved. However, if in the future the range
difference measurements could be improved to reach the required precision, the two-
color SLR system would be an interesting way of reduce atmospheric propagation
effects.
In order to anticipate possible future development of the two-color SLR systems,
Wijaya and Brunner ( 2011 ) have developed a new correction formula that can be
seen as an extension of the 2C-SLR formula
μ
σ = R 1 + μ(R 1 R 2 ) +
P 21 κ 1 ) +
H 21 ·
SIWV
.
(167)
The power of dispersion
μ
is given by
k d 1 )
k d 2 ) k d 1 )
μ =
,
(168)
and the water vapor factor is
10 6
k w 1
H 21 =
K
,
(169)
k w 2 )
. The slant integrated water vapor (SIWV) is
k d
)
k d 1 )
where K
=
k w 1 )
2
SIWV
=
ρ v (
r 1 )
d s 1 .
(170)
S 1
The formula in Eq. ( 167 ) eliminates the total atmospheric density effect including
its gradient and provides two terms to calculate the water vapor and the curvature
effects. The dispersion effect (contained in the second term in Eq. ( 167 )) can be
obtained from the observed optical path length difference
. The third term
represents the curvature effect of the ray path S 1 and the propagation corrections
from S 2 to S 1 . The last term represents the effects of the water vapor density. The
constant
(R 1 R 2 )
represent the power of the dispersion effects and the constant H 21 is the
scaling factor for the wet delays. Both of these coefficients only dependent on the
frequencies of the optical signals and can be calculated using Eqs. ( 168 ) and ( 169 ).
The new formula, Eq. ( 167 ), is a general expression for the atmospheric correction
μ
 
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