Geoscience Reference
In-Depth Information
Ta b l e 1
Relation between various GPS first-order measured parameters and TEC of Earth's
ionosphere extracted from Klobuchar (
1996
)
L
2
L
1
, differential group delay caused by the ionosphere
1ns of differential code delay
−
10
16
el/m
2
1.546ns of delay at
L
1
0.464m of range error at
L
1
2
.
852
×
10
16
el/m
2
0.300m of range error at
L
1
1ns of delay, measured at
L
1
1
.
8476
×
10
16
el/m
2
1m of range error
Measured at
L
1
=
6
.
15
×
10
16
el/m
2
Measured at
L
2
=
3
.
73
×
10
16
el/m
2
]
1 TEC units [1
×
0.351ns of differential delay
0.524ns of delay at
L
1
0.163m of range delay at
L
1
0.853 cycles of phase advance at
L
1
Table
1
shows some relations between the various GPS parameters and the TEC
extracted from Klobuchar (
1996
).
Single Layer Model and Mapping Function
For absolute TEC mapping using ground-based GNSS data, TEC along the verti-
cal should be taken into account. Since GPS basically provides measurements of
STEC, an elevation dependent mapping function is required which describes the
ratio between the STEC and the vertical TEC (VTEC):
STEC
VTEC
.
F
(
z
)
=
(48)
To get an approximation, a single-layer model (SLM) is usually adopted for the
ionosphere. In SLM it is assumed that all free electrons are concentrated in an infin-
itesimally thin layer above the Earth's surface (Schaer
1999
). The height
H
of that
shell is usually set between 350 and 500km, which is slightly above the height where
the highest electron density is expected (approximately above the height of the F2
layer peak). Figure
1
depicts the basic geometry of the SLM in the sun-fixed coor-
dinate system. The signal transmitted from the satellite to the receiver crosses the
ionospheric shell in the so-called ionospheric pierce point (IPP). The zenith angle at
the IPP is
z
and the signal arrives at the ground station with zenith angle
z
.From
Fig.
1
the relation between
z
and
z
could be derived:
R
sin
z
=
sin
z
.
(49)
R
+
H
≈
,
In Eq.
49
R
6
370 km is the mean Earth radius and
H
is the height of the single
layer in km.
