Download Monitoring the 3 Dimensional Ionospheric Electron Distribution

Monitoring the 3 Dimensional Ionospheric
Electron Distribution based on GPS
Measurements
Stefan Schlüter1 , Claudia Stolle2 , Norbert Jakowski1 , and Christoph Jacobi2
1
2
DLR Institute of Communications and Navigation [email protected]
Institute for Meteorology University of Leipzig [email protected]
Summary. In the last decade GPS has become a valuable tool for determining various ionospheric and neutral atmospheric parameters. The presently existing global
and regional networks of GPS ground stations (e.g. regional surveying offices, International GPS service IGS) open the opportunity to establish monitoring systems to
estimate ionospheric and tropospheric/stratospheric key-parameters (e.g. electron
content, temperature, water vapour) on a regular base.
Here first results of a 3 dimensional ionospheric electron density monitoring system
applied for the European region are reported. The system is generally based on continuous GPS derived TEC measurements from the dense European IGS network
and uses model assisted (IRI, Gallagher model) iterative algebraic methods to solve
the inversion problem.
Nevertheless, even in dense GPS networks the available number of measurements
are inevitably sparse, and the combination of ground-based measurements gives not
fully satisfying vertical resolution. Therefore ionosonde and radio occultation data,
as those of CHAMP, have been used to improve the image reconstruction.
Key words: Ionosphere, 3D-Tomography, GPS, CHAMP, MART
1 Introduction
The already existing permanent operating GPS networks give the opportunity to install continuous ionospheric and tropospheric monitoring systems.
Succesful examples for such monitoring systems are, e.g., the estimation of
integrated water vapor in the atmosphere by the GFZ Potsdam, based on the
GPS reference stations of the SAPOS network [1] and the permanent estimation of the vertical total electron content of the ionosphere (TEC) on base of
the network of the International GPS Service (IGS) by the DLR Neustrelitz
[3], [5].
One step to extend the observation capability of these systems is the combination of the integrated measurements with a tomographic approach to
estimate 3 dimensional distributions of the selected parameter, here the ionospheric electron density applied for the European region.
The idea of this approach is to permanently operate a GPS ground-based
monitoring of the ionospheric electron density supported by ionosonde data
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Stefan Schlüter et al.
Fig. 1. Distribution of European IGS stations and ionosondes
and radio occultation measurements, which improve the vertical resolution
but are not permanently available for the selected region. A description of
the data processing and first results will be given in the following sections.
2 Data Processing
The monitored region selected for this approach extends from -20E to 40W
and from 32.5N to 70N. GPS data from 47 selected European IGS stations
as shown in Fig. 1 form the database for the tomographic reconstrution of
the ionosphere. In a first step the collected GPS code and carrier phase data
are preprocessed to estimate the TEC for every single ray path [6]. In order to remove the plasmaspheric contribution of the given GPS measured
TEC, a plasmaspheric correction factor is applied (In principle it possible to
include the plasmaspheric region in the tomography, but for this approach
we concentrate on the ionosphere). The factor describes the proportion of
the TEC fraction above and below 1000km altitude for each ray path. It is
computed using a combination of the ionospheric model IRI and the plasmaspheric Gallagher model [2]. As signal bending effects can be ignored in
ionospheric tomography, the ray paths are assumed as straight lines between
satellite and receiver.
For tomographic reconstruction the ionosphere in the selected region is
represented as a three-dimensional array of voxels. Here the voxels are defined
at a height range from 80 km up to 1000 km, with a resolution of 5◦ in
longitude, 2.5◦ in latitude and 10 km in height. The inversion problem can
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be expressed as a set of linear equations:
Ax = g,
(1)
where g represents the vector of the given TEC measurements, x the unknown
electron density in the voxels and A is a large sparse matrix containing the
voxel path lengths for each ray.
To solve this illposed problem (16560 unkowns and only about 400 measurements) mulitiplicative algebraic reconstruction technique (MART) is used.
In MART, each measurement is iteratively compared to a predicted (forward
projection) value computed from the current reconstructed data estimate.
A multiplicative correction factor is then applied to each voxel covered by
the measurement set. This causes the forward projection to approach the
measurement. The algorithm is given by
µ
¶λk aij /ai
gi
old
xnew
=
x
,
(2)
j
j
(xold , ai )
where aij are the elements of the matrix A and ai is the row vector of the
matrix A. As intitial guess for the iteration process the IRI model is used.
After all measured TEC values have been used during the iteration, NmF2
data from selected ionosonde measurements (here Rome and Juliusruh) are
compared with the tomographic result for these particular locations. The
iteration is repeated until no essential improvements are obtained by the
algorithm.
In order to fill the data gaps in the voxels which are not intersected by
rays and also to stabilize the solution a simple three-dimensional distance
weighted gaussian-like boxcar average of the specific width w is applied after
the iteration. Therefore we rewrite the vector x to a three-dimensional matrix
B with the dimension L, M, N and apply
 w−1 w−1 w−1
P P P


ωi,j,k Bl+i−w/2,m+i−w/2,n+i−w/2



i=0 j=0 k=0


w−1
P w−1
P w−1
P
ωi,j,k
Rl,m,n =
(3)

i=0 j=0 k=0






Bl,m,n , otherwise
where
l = w/2, · · · , L − w
m = w/2, · · · , M − w
n = w/2, · · · , N − w
(4)
and ω represents a weighting factor obtaind by
ωi,j,k = e
(i−w/2)2
c2
1
+
(j−w/2)2
c2
2
+
(k−w/2)2
c2
3
.
(5)
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120
samples: 1457
standard deviation:23.225
100
100
80
80
numbers
numbers
samples: 1457
standard deviation:26.960
60
60
40
40
20
20
0
−150
−100
−50
0
50
100
NmF2−residual between ionosonde and IRI data / e/(1010 m2)
150
0
−150
−100
−50
0
50
100
150
NmF2−residual between ionosonde and tomograpy data / e/(1010 m2)
Fig. 2. Residual between NmF2 data retrieved from selected ionosonde and the
IRI model(left panel) and tomography (right panel)
The values of the coefficients c1 , c2 , c3 and w, have been estimated by serveral
runs, cross-checking the tomographic result with ionosonde and TEC data
from the Neustrelitz maps. After the smoothing has been applied, B is rewritten to Ax and the iteration is restarted. The whole process is repeated until
no significant changes appear in the iteration process.
3 Evaluation
An important task in ionospheric tomography is the evaluation of the results.
In principle there are no sources of continuous data covering the whole European region and giving vertical information about the internal structure of
the ionosphere up to 1000 km. Therefore we have used NmF2 and hmF2, obtained by ionosonde measurements, as a key parameter for the evaluation of
vertical resolution of the tomographic reconstruction. In particular, 3-hourly
NmF2 and hmF2 estimates from April 1st to April 21th , 2000 of 11 European
ionosondes (see Fig. 1) were used for the comparison (the ionosonde stations
Juliusruh and Rome where not used in the comparison, because their data
have been taken for the tomogram). This period was chosen, because a geomagnetic storm event occured at April 6th , 2000. Such events, causing effects
which are not reproduced by the inital model, give good opportunity to prove
the potential of this very model dependent approach. The results for NmF2
and hmF2 residuals between the ionosonde data and the data obtained by tomography are given in Fig. 2 and 3. For comparison residuals under the same
conditions but using the initial model instead of tomography are computed
( see also 2 and 3).
The results show that the tomographic approach has led to an overall
improvement of the NmF2 model estimate of about 14% (comparing the
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70
samples: 1457
samples: 1457
standard deviation:35.134
60
50
50
40
40
numbers
numbers
standard deviation:35.539
60
30
30
20
20
10
10
0
−150
525
−100
−50
0
50
HmF2−residual between ionosonde and IRI data / km)
100
150
0
−150
−100
−50
0
50
100
150
HmF2−residual between ionosonde and tomography data / km)
Fig. 3. Residual between hmF2 data retrieved from selected ionosondes and the
IRI model (left panel) and tomography (right panel)
dispersion and the bias to the ionosondes in both statistics), whereas no
significant improvement can be found in the hmF2 data.
4 Including Radio Occultation Data
As shown, pure ground-based GPS measurements contain hardly any information on the vertical ionospheric profile. An opportunity to improve the
vertical resolution in tomography is the use of GPS radio-occultation data
as those obtained by the CHAMP satellite. To prove the potential improvement obtained by such data, a set of calibrated horizontal TEC data from
the CHAMP satellite [4] where included in the tomography and compared
with ionosonde data of the Juliusruh station, which was close to the ray path
of the occultation links. As an example Fig. 4 shows vertical profiles over
Juliusruh, obtained by the IRI model, ionosonde data (with a model extension above the electron density peak) and ground based GPS tomography.
Fig. 4 shows the corresponding results with CHAMP data included in the
tomographic algorithm. The improvement of the model estimate obtained by
the use of ground-based GPS data is shown in Fig. 4, as it has already been
indicated by the statistical investigations. Model correction by real data is
significantly better by combining ground-based GPS and radio occultation
data as demonstrated in Fig.4.
5 Conclusion
So far GPS based radio tomography is still in a developing state. However, it
was shown that the use of GPS networks as that of IGS can be the base for a
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Fig. 4. Height profile of electron density at Juliusruh (Germany), obtain by IRI,
ionosonde (the upper part is extended by a model) and GPS-tomography using IGS
data (left panel) and using combined IGS and CHAMP data (right panel).
continous three-dimensional ionospheric monitoring system. As exemplarily
shown, tomographic combination of ground-based GPS and radio-occultation
data can lead to promising results.
Regardless of the inversion method, to obtain tomographic results with a
resolution that allows the investigation of even smaller structures and phenomena in the ionosphere, more and especially horizontal measurements are
needed. Future navigation systems as the European Galileo and further radiooccultation missions may improve such data base.
Nevertheless, even under better data conditions, satellite radiotomography has to include additional information. In our case, using the recursive
MART algorithm, data of the IRI model were used as a priori information
and ionosonde data to obtain a stop criteria for the iteration process.
Acknowledgements
The authors are grateful to the CHAMP team, co-ordinated by the GFZ
Potsdam, for the given support and data. We also thank all members of the
IGS community for providing their data service. Ionosonde data have kindly
been provided by the IAP Kühlungsborn.
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