Geoscience Reference
In-Depth Information
In the following it is shown how gradients can be interpreted. Equation ( 128 ) can
be written in the form
N
(
x
,
z
) =
N 0 (
z
)(
1
+ α ·
x
),
(147)
α = ξ (
z
)/
N 0 (
z
),
(148)
with the constant vector
. This means that the relative gradient of refractivity is
constant, and we get for the gradient of the delay
α
10 6
=
α
zN 0 (
)
.
G
z
d z
(149)
0
Supposing that refractivity decreases exponentially with height, i.e.
N S e z / H
N 0 (
z
) =
,
(150)
and H is the scale height, we get for the integral in Eq. ( 149 ) the expression
10 6
H 2
G
=
α ·
N S ·
,
(151)
and for the gradient of refractivity
G
H 2 e z / H
10 6
ξ (
z
) =
.
(152)
The scale height H is the height of the neutral atmosphere (or of a part of it) if the
density is constant with height and the total mass is conserved. For the gradients of
refractivity at the Earth surface we get
G
H 2 .
10 6
ξ (
z
) =
(153)
This shows that for a given value of G the gradients of refractivity
are inversely
proportional to the squared scale heights H . A typical value for the gradients G is
1 mm. This corresponds to a path delay of
ξ
65 mm at 7 elevation. Assuming a
scale height H of 1 km the gradient of refractivity
is 1km 1 . With a scale height
ξ
= 0.015 km 1 . Hydrostatic atmospheric gradients which are caused by
pressure and temperature gradients, have a large spatial resolution of about 100 km
(Gardner 1976 ) and a temporal resolution of hours to days. Wet gradients have a
small spatial resolution (
of 8 km
| ξ |
<
10 km) and they can vary at hourly time scales or faster,
although longer time scales are also possible (e.g. at coastal regions). Wet gradients
are functions of water vapor pressure and temperature.
Presently, two models for the gradients are used in the analysis of space geodetic
techniques. These are the model byMacMillan ( 1995 ) that follows Davis et al. ( 1993 )
and the model by Chen and Herring ( 1997 ). Both concepts will be described below.
 
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