Geoscience Reference
In-Depth Information
N
e
ds
0
=
N
max
η
N
e
ds
0
.
(42)
The shape parameter
may be assumed with 0.66 as an appropriate value to account
for different electron density distributions.
N
max
represents the peak electron density
along the ray path. Substituting Eq.
42
into Eq.
41
, the third order ionospheric phase
delay can be written as:
η
812
.
4
ion
3
ph
Δρ
=−
N
max
η
N
e
ds
0
.
(43)
f
4
Integrated Electron Density
As already shown, the first, second and third order ionospheric delays require the
distribution of the electron density
N
e
along the ray path. If one is interested in
signal propagation in the ionosphere, however, the integral of the electron density
along the ray path becomes relevant (e.g. Schaer
1999
). This quantity is defined as
the Total Electron Content (TEC) and represents the total amount of free electrons
in a cylinder with a cross section of 1m
2
and a height equal to the slant signal path.
TEC is measured in Total Electron Content Unit (TECU), with 1 TECU equivalent
to 10
16
electrons/m
2
. For an arbitrary ray path the slant TEC (STEC) can be obtained
from
STEC
=
N
e
(
s
)
ds
,
(44)
where
N
e
is the electron density along the line of sight
ds
.
Using Eq.
44
the relation between the total electron content in TECU and
ionospheric delay in meters can be obtained. Taking Eq.
33
into account for the
carrier phase measurements we get
40
31
f
2
.
ion
ph
Δρ
=−
STEC
[
m
]
,
(45)
in the case of group delay measurements, the result is the same, but with opposite
sign
40
31
f
2
.
ion
gr
Δρ
=
STEC
[
m
]
.
(46)
can be defined as the
ionospheric path delay in meters per one TECU, related to a certain frequency
f
in Hz
Finally, using the constant derived from Eq.
22
the factor
ϑ
10
16
40
.
31
·
ϑ
=
[
m
/
TECU
]
.
(47)
f
2
