Geoscience Reference
In-Depth Information
solved for every two hour epoch and the unknowns which are the coefficients of the
spherical harmonics expansion (
a
nm
and
b
nm
in Eq.
92
) are estimated for every two
hours (1h or 15min solution is also possible) by a least-square adjustment.
The estimated unknown coefficients are then entered to calculate grid-wise VTEC
values over the globe using Eq.
92
. This results in thirteen two-hourly global maps
for one complete day. These maps are usually called Global Ionosphere Maps (GIM).
The IONospheric EXchange (IONEX) Format
The GIM are usually provided in the IONospheric EXchange (IONEX) format,
described in Schaer et al. (
1998
). The vertical TEC is represented as a function
of geocentric longitude and latitude (
), and time (
t
) in UT in the form of a raster
grid. At the time being, the spatial resolution of this grid is
λ
,
β
5
◦
in longitude and
Δλ
=
5
◦
Δβ
=
2
h
; although
the International GNSS Service (IGS) is considering going to higher time resolution
of 1h and finally 15min.
The interpolation of VTEC for a given epoch
T
i
with
i
2
.
in latitude, and the time resolution of the maps are
Δ
t
=
n
, was proposed
by Schaer et al. (
1998
), which is interpolating between consecutive rotatedTECmaps.
This can be formulated as follow:
=
1
,
2
, ...,
T
i
+
1
−
t
T
i
T
i
+
1
−
t
−
VTEC
i
(β, λ
i
)
+
VTEC
i
+
1
(β, λ
i
+
1
),
VTEC
(β, λ,
t
)
=
(97)
T
i
+
1
−
T
i
T
i
with
λ
i
T
i
≤
t
<
T
i
+
1
and
=
λ
+
(
t
−
T
i
).
T
i
around the Z-axis in order to compensate
the strong correlation between the ionosphere and the Sun's position. For the grid
interpolation, a bi-variate interpolation method can be applied, which uses a simple
four-point interpolation formula:
The TEC maps are rotated by
t
−
VTEC
(λ
0
+
p
Δλ, β
0
+
q
Δβ )
=
(
1
−
p
)(
1
−
q
)
VTEC
0
,
0
+
p
(
1
−
q
)
VTEC
1
,
0
+
(
1
−
p
)
qVTEC
0
,
1
+
pqVTEC
1
,
1
,
(98)
≤
<
≤
<
Δλ
Δβ
where 0
denote the grid widths in longitude
and latitude. Figure
3
depicts the interpolation concept.
p
1 and 0
q
1.
and
Ionosphere Working Group of the International GNSS Service
In 1998 a special Ionosphere Working Group (WG) of the IGS was initiated for
developing ionospheric products, as described by Schaer et al. (
1998
) andHernández-
Pajares (
2004
). The main products provided on a regular basis by the IGS Ionosphere
WG are the GIM, representing the VTEC over the entire Earth as a two-dimensional
raster in latitude and longitude in two-hourly snapshots, as well as the corresponding
