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tion angle e , because close to the site this angle determines the refraction. It holds
that
e =
e
+ δ
e
(
e
),
(141)
where
δ
e can be described with (Davis et al. 1993 )
10 6 N S cot
δ
e
(
e
).
(142)
5 we get
2 .
N S is the refractivity at the Earth surface, and for N S =
300, e
=
δ
e
0
.
e )
Since
can be expanded into a series, and we get for the deviation
from the symmetric mapping function
δ
e is small, cot
(
10 6 N S csc 2
δ
mf
(
a
,
e
) =
mf 0 (
e
)
cot
(
e
)(
1
(
e
))(
Z n cos
(
a
) +
Z e sin
(
a
)).
(143)
With the delay gradients (or just gradients) G
L z
G
=
Z
· Δ
,
(144)
we get for the path delay
10 6 N S csc 2
)).
(145)
The equations above can be used to determine gradients by integrating over the
horizontal gradients of refractivity along the site vertical (see e.g. MacMillan and
Ma ( 1997 ), Böhm and Schuh ( 2007 ))
Δ
L
(
a
,
e
) = Δ
L 0 (
e
) +
mf 0 (
e
)
cot
(
e
)(
1
(
e
))(
G n cos
(
a
) +
G e sin
(
a
10 6
0
G a =
ξ a z d z
,
(146)
where a denotes the azimuth direction (e.g. e or n ). Figure 12 shows refractivity
gradients at the site vertical for the station Fortaleza.
Fig. 12 Weighted (with
height) refractivity gradients
( dN
30
hydrostatic
wet
z ) towards east at
Fortaleza (Brazil) on 21
November 2011 at 0:00 UT.
The black line shows the
hydrostatic, the red line the
wet gradients
(
z
) ·
25
20
15
10
5
0
−0.05
0
0.05
0.1
ppm
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