Geoscience Reference
In-Depth Information
Ta b l e 6
Coefficients (
a
i
,
b
i
,and
c
i
) for FCULa and FCULb mapping functions (Mendes et al.
2002
)
FCULa
FCULb
10
−
7
10
−
7
a
0
(
12100
.
8
±
1
.
9
)
×
(
11613
.
1
±
1
.
6
)
×
10
−
9
10
−
8
a
1
(
1729
.
5
.
8
±
4
.
3
)
×
(
−
933
.
8
±
9
.
7
)
×
10
−
7
10
−
11
a
2
(
319
.
1
±
3
.
1
)
×
(
−
595
.
8
±
4
.
1
)
×
10
−
11
10
−
11
a
3
(
−
1847
.
8
±
6
.
5
)
×
(
−
2462
.
7
±
6
.
8
)
×
10
−
7
a
4
−
(
1286
.
4
±
2
.
2
)
×
10
−
7
10
−
7
b
0
(
30496
.
5
±
6
.
6
)
×
(
29814
.
1
±
4
.
5
)
×
10
−
8
10
−
7
b
1
(
234
.
6
±
1
.
5
)
×
(
−
56
.
9
±
2
.
7
)
×
10
−
6
10
−
10
b
2
(
−
103
.
5
±
1
.
1
)
×
(
−
165
.
5
±
1
.
1
)
×
10
−
10
10
−
10
b
3
(
−
185
.
6
±
2
.
2
)
×
(
−
272
.
5
±
1
.
9
)
×
10
−
7
b
4
−
(
302
.
0
±
5
.
9
)
×
10
−
5
10
−
6
c
0
(
6877
.
7
±
1
.
2
)
×
(
68183
.
9
±
9
.
1
)
×
10
−
7
10
−
6
c
1
(
197
.
2
±
2
.
8
)
×
(
93
.
5
±
5
.
4
)
×
10
−
5
10
−
9
c
2
(
−
345
.
8
±
2
.
0
)
×
(
−
239
.
4
±
2
.
3
)
×
10
−
9
10
−
9
c
3
(
106
.
0
±
4
.
2
)
×
(
30
.
4
±
3
.
8
)
×
10
−
5
c
4
−
(
−
230
.
8
±
1
.
2
)
×
two-color SLR measurements (the 2C-SLR formula). This formula was later studied
by several investigators (Greene and Herring
1986
).
From the two-color SLR measurements theoretical path lengths
R
2
are
obtained (assume that the systemmeasures simultaneously individual optical paths).
With the 2C-SLR formula (Abshire and Gardner
1985
), the chord (straight line)
distance
R
1
and
σ
can be calculated by adding the term
μ(R
2
−
R
1
)
to
R
1
σ
=
R
1
+
μ(R
1
−
R
2
),
(164)
where
k
(ν
1
)
μ
=
(ν
1
)
,
(165)
k
(ν
2
)
−
k
with
k
being the dispersion factor. This factor depends on frequency and can be
calculated using (Edlén
1966
; Abshire and Gardner
1985
)
(ν
i
)
0
.
0164
λ
0
.
000228
λ
k
(ν
i
)
=
0
.
9650
+
+
,
(166)
2
i
2
i
where
λ
i
is the
i
:th wavelength in meters.
The 2C-SLR formula presented in Eq. (
164
) remove the largest part of the total
propagation delay, namely that associatedwith the dry atmospheric density. However,
the water vapor density and curvature effects still remain (Abshire and Gardner
1985
;
