Geoscience Reference
In-Depth Information
Furthermore, it is shown that the concept of horizontal gradients corresponds to a
tilting of the mapping functions. This is used by Niell (
2001
) who uses the tilting of
the 200 hPa pressure level to get hydrostatic gradients. MacMillan (
1995
) proposes
to use the simple model
Δ
L
(
a
,
e
)
=
Δ
L
0
(
e
)
+
mf
h
(
e
)
cot
(
e
)(
G
n
cos
(
a
)
+
G
e
sin
(
a
)),
(154)
i.e. the difference between
e
and
e
is neglected. Chen and Herring (
1997
)usethe
gradient model
Δ
L
(
a
,
e
)
=
Δ
L
0
(
e
)
+
mf
g
(
e
)(
G
n
cos
(
a
)
+
G
e
sin
(
a
)),
(155)
1
mf
g
(
e
)
=
C
,
(156)
sin
(
e
)
tan
(
e
)
+
and
3
ξ
·
z
2
·
d
z
2
ξ
·
C
=
d
z
.
(157)
·
(
+
R
e
)
·
z
z
After integration they get for the coefficient
C
C
=
3
H
/
R
e
.
(158)
For scale heights of 6.5 km for the hydrostatic part and 1.5 km for the wet part of the
neutral atmosphere, they find the values 0.0031 and 0.0007 for the hydrostatic and
wet coefficients
C
, respectively. For the estimation of total gradients, Herring (
1992
)
suggests using 0.0032.
Gradients can also be interpreted by a tilting of the mapping function (Rothacher
et al.
1998
) see Fig.
13
. The basic relations are shown below assuming that the
atmosphere is flat (mapping function 1
) and that the path delay in zenith
direction is not changed by the tilting. If the gradient
G
is the deflection of the path
/
sin
(
e
)
G cot(e)
G
G
.
cot(e)
.
mf(e)
β
L
z
cot(e)
L
z
L
z
Atmosphere
β
e
Earth
Fig. 13
Tilting of themapping function by the angle
β
assuming a horizontally stratified atmosphere
