Global Positioning System Reference
In-Depth Information
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[19
Lin
—
3.0
——
No
PgE
Fi
gure 6.5 Comparison between occultation, radiosonde, and atmospheric model.
So
urce:
Kursinski et al., 1996. Permission by American Geophysical Union.
[19
The sections below provide details on the index of refraction and on absorption.
The general form of the index of refraction for electromagnetic wave can be written
as a complex number
n
¯
= µ −
i
χ
(6.1)
where
are related to refraction and absorption, respectively. Let
A
0
denote
the amplitude, we can write the equation of a wave as
µ
and
χ
A
0
e
i(
ω
t
−
n
ω
x/c)
A
0
e
i(
ω
t
−µω
x/c)
e
−χω
x/c
A
=
=
(6.2)
The wave propagates at speed
c/
, where
c
denotes the speed of light. The absorp-
tion in the medium is given by the exponential attenuation
e
−χω
x/c
. The absorption
coefficient is
µ
/c
. It is readily seen that the amplitude of the wave will reduce
by factor
e
at distance 1
/
κ = ωχ
.
For GPS frequencies and for frequencies in the microwave region, the index of
refraction can be written as
κ
n
(f )
in
(f )
n
¯
=
n
+
+
(6.3)