Journal of Global Positioning Systems (2006)
Vol. 5, No. 1-2:47-51
Ionospheric Tomography using A Regional GPS Network over South
Korea
Byung-Kyu Choi, Jong-Uk Park, Jong-Kyun Chung
Space Geodesy Division, Korea Astronomy & Space Science Institute, Daejeon, South Korea
e-mail: [e-mail] Tel: + 82-42-865-3237 ; Fax: [phone]
Abstract. The vertical profiles of electron distribution
near the low and mid-geomagnetic latitudes have been
investigated by the computerized tomography method
using Algebraic Reconstruction Technique (ART). The
slant total electron contents (STEC) data for ionospheric
tomography were measured at a regional GPS reference
network of nine stations that have been operated by
Korea Astronomy and Space Science Institute (KASI).
The results from tomographic reconstruction method are
in good agreement with profiles obtained by Ionosonde
near the KASI GPS stations. The electron density profiles
reconstructed by the tomographic method were compared
with the results from Ionosonde and IRI-2001 model.
GPS tomography reconstruction plays an important role
of complementary measurements of Ionosonde in
ionospheric structure.
Key words: ART, STEC, Ionosonde, IRI-2001
1 Introduction
Over the past decade, GPS has become a valuable tool for
determining total electron contents (TEC) of ionosphere
and so on. Nowdays, in order to study the characteristics
of ionosphere, the existing global and regional networks
of GPS stations have been commonly used. GPS-to-
ground signals trace out a network of measurements
through the ionosphere. However, the geometry does not
map easily into a plane for tomographic inversion and the
need to extend conventional imaging techniques to three
dimensional imaging has arisen (Bust et al., 2001);
Hernandez-Pajares et al., 2000).
Dual-frequency observations of GPS signals provide a
relative ionospheric delay of the two-frequency
electromagnetic waves traveling through a dispersive
medium. The relative total electron contents along the
line of sight can be derived from this delay (Lanyi and
Roth, 1998).
Since Austin et al.(1986) first proposed the possibility of
studying the ionosphere using satellite radio tomography,
tomographic reconstruction of the ionosphere and
plasmasphere electron density has become a popular and
successful means of studying the detailed features of the
ionosphere and plasmasphere. Generally, tomographic
technique is a mathematical method that is used to model
ionosphere. Tomographic ionosphere model is often
compared with the measurements of incoherent
backscatter radars and ionosondes(Hernandez-Pajares et
al., 2000).
An ionospheric tomography model can describe the
ionosphere field in a three-dimensional frame instead of a
two-dimensional frame as used by previous methods
(Gao and Liu, 2002).
This paper presents ionospheric tomography over South
Korea derived from KASI GPS network. The
independent verification of the reconstructed electron
density profile is also presented.
2 Background
2.1 Precise TEC Calculation
Basically, in order to estimate the electron density
distribution with height of ionosphere, the calculation for
slant TEC (STEC) or vertical TEC (VTEC) has to be
initially implemented (Hernandez et al., 1999). When
using the dual-frequency GPS data, it is available to
estimate precisely the TEC. Code measurements (P1, P2)
are expressed as follows (Gao and Liu, 2002).
1 2
1
40.3
1( )()( )
s
rtropmL
Pkc ttTECk
f
ρ
δδε εε =+−+++ + (1)
2 2
2
40.3
2( )()( )
s
rtropmL
Pkct tTECk
f
ρ
δδε εε =+−++++ (2)

48 Journal of Global Positioning Systems
where
ρ
is the true geometric range between receiver
and satellite (m), s t δ is the satellite clock error with
respect to GPS time (s), r t
δ
is the receiver clock error
with respect to GPS time (s), trop
ε
is the troposphere
delay error, m
ε
is the multi-path error and i
L
ε
(i = 1,2) is
the noise on L1/L2 GPS signals.
On the occasion of using carrier phase data, the following
linear combination equation is formed.
2
1
2
2
2
2
2
2
1
12
2
1
1)}(){( ff
f
N
f
f
N
f
f
I− ⋅−−−=
φφ
φ
(3)
where 1
f (1575.42 MHz) and 2 f(1227.60 MHz) are
frequencies on L1 and L2 respectively, 1
φ
and 2
φ
are
carrier phase measurements, 1 N and 2 Nare integer
ambiguities,
φ
I is the ionosphere delay on L1.
Due to the existence of ambiguities, the absolute
ionosphere delay on the carrier phase cannot be
determined. However, the differential ionospheric delay
over two consecutive epochs can be determined if there is
no cycle slip occurrence(Cannon, 1997).
2.2 Basic Function
Ionosphere can be divided into volumn pixels, voxels to
construct computer tomography. Voxel is the element in a
three-dimensional environment. Voxels in the Earth’s
ionosphere are indicated with latitude, longitude and
height. Assuming straight line approximation, those
voxels illuminated by the ray will be a basic function
equal to 1 and 0 otherwise, delta function. In case of
KASI network, two-dimensional voxels was considered
as follows.
⎩
⎨
⎧
=otherwise 0
rayby dilluminate cell if 1
),( hdij φ
(4)
As seen in Fig. 1, KASI network has consisted of nine
GPS reference stations and GPS reference stations of
KASI have been more widely distributed on the latitude
(Choi et al., 2005).
Fig. 2 shows the ray path of GPS signal observed by the
specific GPS reference station in KASI network. If GPS
signals pass voxels, as mentioned equation 4, basic
function should be 1; otherwise it should be 0 (zero).
Fig. 1 The Distribution of GPS reference stations in a regional KASI
network
Fig. 2 GPS signals passing voxels with two-dimensional frame
2.2 Basic Function
One of the most commonly used inversion techniques is
algebraic reconstruction technique (ART). The initial
guess with the experimental TEC data in an interactive is
required in the ART algorithm. ART algorithm can be
implemented as the following equation (5).
i
M
j
ijij
M
j
k
jiji
k
kk D
dd
ndSTEC
NN∑
∑
=
=
+
−
+=
1
1
1
λ
(5)
where i Dis the row of D, k is the iteration number,
and k
λ
is the relaxation parameter. The relaxation

Choi et al.: Ionospheric Tomography using A Regional GPS Network over South Korea 49
parameters,
λ
is usually confined to the interval 0 <
λ
<
2 and is the same for all iterations.
The ART algorithm, which can converge quickly in an
iterative fashion compared to other reconstruction
algorithms, is the preferable algorithm to use with
ionospheric reconstruction in a region like the GPS
network in South Korea.
Fig. 3 ART algorithm scheme
As mentioned above Fig. 3, the ART algorithm requires
some initial values of the quantity to be reconstructed.
For example, these initial values can be obtained from
models such as IRI-2001 (International Reference
Ionosphere), chapman profile models or Ionosonde based
on the measurement data. IRI-2001 model requires
further optional input parameters to get a true density
profile. Input parameters for IRI-2001 model can be
obtained from Ionosonde measurement data.
3 Data Processing
Tomography reconstructions based on KASI GPS
network data have been performed for the ionosphere
over narrowly limited South Korea.
The geographical region to be reconstructed is set by
geographic latitude and height. The full extent of latitude
is from 31° to 40° N on the geophysical coordinates and
that of the height is set within the limits of up to 1,000km
on Earth. The spatial resolution for the height is also set
in 10km. The elevation of the satellite at each GPS
reference station has been set greater than 15°.
If there are not enough GPS signals passing virtual voxels
over South Korea, the height precision of the electron
density profile is significantly affected by data gaps. In
case of that, it can be required sophisticated interpolation
method. We use IDW(Inverse Distance Weighted)
interpolation technique in model.
Fig. 4 The reconstructed electron density profile along the height over
South Korea at 1:00 UT(10:00 LT) on July 1, 2003
Fig. 5 The reconstructed electron density profile along the height over
South Korea at 4:00 UT(13:00 LT) on July 1, 2003
Fig. 4 obtained from data recorded at 1:00 UT (10:00 LT),
shows the high density distribution at 31°~32° N. Fig. 5
and 6 show examples of typical images of the dayside
ionosphere obtained during the quiet period on July 1,
2003. Above on images, the bar unit of the column
density is about 35 /100.1 cmelectron×.
The peak height of the electron density distribution in
Fig. 5 is about 300km and there is no a large difference of
the electron density distribution between 31° to 40 °N
because of a narrow region. But as seen in Fig. 5, at top-
side ionosphere over 500km, the electron density at 4:00
UT(13:00 LT) is higher than that of at 1:00UT in Fig. 4.
that is, the status of ionosphere depends on daily variation.

50 Journal of Global Positioning Systems
Fig. 6 The reconstructed electron density profile along the height over
South Korea at 7:00 UT (16:00 LT )on July 1, 2003
Fig. 7 The reconstructed Electron density profile along the height over
South Korea at 15:00 UT(24:00 LT) on July 1, 2003
Fig. 7 shows the electron density distribution obtained
from GPS data at 15:00 UT(24:00 LT). The important
thing is that the peak height of the electron density value,
calculated from GPS reconstruction, between the dayside
and the night-side is different. As mentioned above, the
peak height of the electron density value at the dayside is
about 300km in Fig. 6 whereas that at the night-side is
about 350km as seen in Fig. 7.
Fig. 8 shows that the electron density profiles (blue
circles) reconstructed by GPS are verified with the
corresponding density profile (red dots) measured by
Ionosonde at 37.5°N. The electron density profile by IRI-
2001 (green dots) is also presented.
Table 1 shows the RMSE between the reconstructed
tomography by GPS and results from IRI-2001 and
Ionosonde. It also shows that GPS reconstruction model
is well consistent with Ionosonde measurement, but is not
consistent with IRI-2001 empirical model.
Fig. 8 The electron density profiles plotted by GPS reconstruction, IRI-
2001 and Ionosonde
Tab. 1 Comparison of GPS reconstruction and IRI-2001 and Ionosond
Models RMSE(35 /10 cmel )
GPS Re. – Ionosonde 0.590
GPS Re. – IRI2001 1.850
4 Summary and Conclusions
The GPS reconstruction for ionospheric density profile
was performed by KASI GPS network. ART algorithm
was used to estimate the precise density profile over
South Korea. But ART algorithm has a disadvantage
requiring the initial values despite the fast convergence.
In order to estimate the electron density profile in
ionosphere, it is necessary to be considered the
determination of the precise STEC (Slant TEC) which is
calculated by a regional or global GPS network. In this
paper, there is good agreement at the bottom side
between the profile of GPS reconstruction and the profile
of Ionosonde, but less for the topside. We have shown
that the electron density in the height of the ionosphere is
changed with time.
In conclusion the electron density profile obtained by the
tomographic reconstruction method is in excellent
agreement with profile obtained by Ionosonde
measurement data. We have shown that high resolution
density profile can be also achieved when using GPS data
based on the network frame.

Choi et al.: Ionospheric Tomography using A Regional GPS Network over South Korea 51
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