Annals 48, 2, 2005defdef


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ANNALS  OF  GEOPHYSICS, VOL.  48, N.  2, April  2005

Key  words ionospheric data ingestion – electron
density model – total electron content

1. Introduction

Like other empirical ionospheric models
(e.g., International Reference Ionosphere - IRI:
Bilitza, 2001) NeQuick has been conceived to
reproduce median values of the ionosphere
electron density. In order to improve its capa-
bilities to describe the ionosphere for actual
conditions, a technique based on experimental
Total Electron Content (TEC) data ingestion in-
to the model has been developed. The technique

considers global vertical TEC maps to deter-
mine the corresponding global grids of the
NeQuick driving parameter Az. When the Az
grid is computed, NeQuick model is able to cal-
culate the 3D electron density of the ionosphere
and therefore the total electron content value
for any given ray-path can be calculated by
means of numerical integration. The emphasis
has been put on TEC because it is directly re-
lated to the range delay in trans-ionospheric
propagation and therefore such kind of recon-
struction method could have an application re-
lated to satellite navigation systems.

It must be noted that other techniques to re-
construct the electron density of the ionosphere
have been developed. They are of different
complexity and can rely on several kinds of
models. The Global Assimilative Ionospheric
Model (Wang et al., 2004), for example, is
based on assimilation of data originating from
different sources and implies the use of first

A model assisted ionospheric electron
density reconstruction method 

based on vertical TEC data ingestion

Bruno Nava (1), Pierdavide Coïsson (1), Gloria Miró Amarante (1),
Francisco Azpilicueta (2) and Sandro M. Radicella (1)

(1) The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy
(2) Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Argentina

Abstract
A technique to reconstruct the electron density of the ionosphere starting from total electron content values has
been developed using the NeQuick ionospheric electron density model driven by its effective ionization param-
eter Az. The technique is based on the computation of Az values for a suitable worldwide grid of points. A sim-
ple way to obtain relevant Az grids is to use global vertical Total Electron Content (TEC) maps to define for each
grid point as Az value, the one that minimizes the difference between the experimental and the modeled vertical
TEC. Having a global grid of Az values it is possible to compute the electron density at any point in the iono-
sphere using NeQuick. As a consequence, slant TEC values for specific ground station to satellite links or ion-
osphere peak parameter values at any location can be calculated. The results of the comparisons between exper-
imental and reconstructed slant TEC as well as experimental and reconstructed peak parameters values indicate
that the proposed reconstruction method can be used to reproduce the observed ionosphere in a realistic way.

Mailing address: Dr. Bruno Nava, The Abdus Salam
International Centre for Theoretical Physics (ICTP), Strada
Costiera 11, 34014 Trieste, Italy; e-mail: bnava@ictp.it



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Bruno Nava, Pierdavide Coïsson, Gloria Miró Amarante, Francisco Azpilicueta and Sandro M. Radicella

principle models. On the contrary, the proposed
reconstruction method aims to be simpler, be-
ing based on the use of an empirical electron
density model and it foresees the ingestion of
only TEC data that, for instance, are the most
widely available ionospheric data.

2. NeQuick model

The NeQuick model is an ionospheric elec-
tron density model developed at the Aeronomy
and Radiopropagation Laboratory of The Ab-
dus Salam International Centre for Theoretical
Physics (ICTP), Trieste, Italy and at the Insti-
tute for Geophysics, Astrophysics and Meteo-
rology of the University of Graz, Austria, in the
framework of the European Commission
COST (Co-operation in the field of Scientific
and Technical Research) Action 251. It is based
on the original «profiler» proposed by Di Gio-
vanni and Radicella (DGR, Di Giovanni and
Radicella, 1990). NeQuick is able to give the
electron concentration distribution on both the
bottomside and topside of the ionosphere and it
is a quick-run model particularly tailored for
trans-ionospheric applications. The model has
been used by the European Space Agency EG-
NOS (European Geostationary Navigation
Overlay Service) Project for assessment analy-
sis and has been proposed for single-frequency
positioning operations in the framework of the
European Galileo Project. It has been adopted
by the International Telecommunication Union,
Radiocommunication sector (ITU-R) Recom-
mendation P.531-6 (now superseded by P.531-
7; ITU, 2001) as a suitable method for TEC
modeling. To describe the electron density of
the ionosphere above 100 km and up to the F2
layer peak this model uses a modified DGR
profile formulation (Radicella and Leitinger,
2001) which includes five semi-Epstein layers
with modeled thickness parameters and is
based on anchor points defined by foE, foF1,
foF2 and M(3000)F2 values (Hochegger et al.,
2000). These values can be modeled or experi-
mentally derived. The model topside is repre-
sented by a semi-Epstein layer with a height
dependent thickness parameter empirically de-
termined.

The basic inputs of NeQuick electron density
model are: position, time and solar flux (or sun-
spot number); the output is the electron concen-
tration at the given location and time. In addition
the NeQuick package includes specific routines to
evaluate the electron density along any ray-path
and the corresponding TEC by numerical integra-
tion. NeQuick (FORTRAN 77) source code is avail-
able at http://www.itu.int/ITU-R/software/study-
groups/rsg3/databanks/ionosph/

2.1. Reconstruction technique

For the purpose of the present work,
NeQuick has to be regarded as a «profiler»
driven by its local ionization level index that
plays the role of an effective 10.7 cm solar ra-
dio flux and determines the complete vertical
electron density profile at a given epoch and for
a given location. Being the vertical TEC calcu-
lated with NeQuick a monotonic function of
this index alone, it is possible to define as Az
the ionization level value that minimizes the
difference between an experimental vertical
TEC and the corresponding modeled vertical
TEC obtained by integration of the vertical
electron density profile.

Applying this concept to all vertical TEC val-
ues of a global experimental vertical TEC map, it
is possible to retrieve an Az grid that drives
NeQuick to generate a 3D representation of the
ionosphere over the globe and reproduces the
starting vertical TEC map with the requested ac-
curacy. The same approach was previously used
in Nava et al. (2003), while similar concepts
have been adopted in Komjathy et al. (1998).

In order to apply the described procedure,
NeQuick code has been adapted to use global
Az grids as input. The grid points are spaced
2.5° in latitude and 5° in longitude and are in-
terpolated to retrieve Az values at any wanted
geographic location. Under suitable conditions,
Az grids for different epochs can also be inter-
polated in time to obtain new grids for epochs
when experimental data are not available.

An operational application of this reconstruc-
tion method was implemented using available
experimental vertical TEC maps (Nava et al.,
2003). Several institutions around the world pro-



315

A model assisted ionospheric electron density reconstruction method based on vertical TEC data ingestion

duce such maps using Global Positioning Sys-
tem (GPS) derived slant TEC data: the network
of the International GPS Service (IGS) stations
in fact provides measurements that can be used
to obtain information on ionospheric electron
content along the ray-paths from satellites to
ground receivers. For example the Centre for Or-
bits DEterminations (CODE), University of
Berne, Switzerland, produces global bi-hourly
maps (Schaer et al., 1996) based on spherical
harmonics expansion of vertical TEC. These
maps are given on a daily basis and made avail-
able through the Internet (http://www.cx.uni-
be.ch/aiub/ionosphere.html).

For the purpose of the present study the ver-
tical TEC maps produced by the Satellite and
Geodesy Group of the National University of
La Plata, Argentina, have been used as refer-
ence for the minimization process. La Plata ver-
tical TEC maps are computed using GPS data
collected from an average of about 130 IGS sta-
tions distributed worldwide. La Plata maps are
based on a spherical harmonic expansion of de-
gree and order 15 for vertical TEC and the dai-
ly solution consists of 24 sets of coefficients
and one instrumental delay value for each sta-
tion and for each satellite included in the com-
putation (Brunini, 1998). La Plata maps have

been chosen because they are computed on
hourly basis and they are built using the sun
fixed/Modip reference frame, Modip µ being
defined by

tan
cos

=n
z

z

with φ the true magnetic dip in the ionosphere
(usually at 300 km) and φ the geographic lati-
tude (Rawer, 1963).

These features improve temporal and spatial
resolution of the vertical TEC maps and then
slightly better results are expected when
NeQuick is used together with the reconstruc-
tion technique to reproduce the electron density
of the ionosphere. An example of equivalent
vertical TEC for the day 27 March 2000 at
17:00 UT is shown in fig. 1.

2.2. Test of the technique

In order to evaluate the effectiveness of the
reconstruction technique, slant TEC and verti-
cal incidence experimental data have been used
for comparison with the corresponding recon-
structed quantities.

Fig. 1. Example of global vertical TEC map produced with La Plata technique for the day 27 March 2000,
17:00 UT.



316

Bruno Nava, Pierdavide Coïsson, Gloria Miró Amarante, Francisco Azpilicueta and Sandro M. Radicella

The day 27 March 2000 (a quiet day in a pe-
riod of high solar activity) was chosen as refer-
ence day for the test and hourly La Plata maps
were used to generate the set of 24 Az grids
needed to drive the NeQuick model.

2.3. Slant TEC

For consistency reasons, the slant TEC data
used to validate the reconstruction technique
were computed from RINEX files recorded at

Fig. 2. Cumulative distributions of the absolute values of the differences between experimental and recon-
structed slant TEC data for stations lying in different Modip intervals. The statistics are computed using slant
TEC data at 5 min time intervals for the day 27 March 2000.



317

A model assisted ionospheric electron density reconstruction method based on vertical TEC data ingestion

the same IGS stations used to obtain the vertical
TEC maps. An elevation mask of 10° to all avail-
able satellites was applied and for practical pur-
poses slant TEC data every 5 min were used. The
experimental slant TEC data were compared
with the corresponding slant TEC values com-

puted with NeQuick driven by Az grids derived
from La Plata vertical TEC maps. Therefore Az
values at 5 min time interval were calculated by
interpolation of consecutive hourly Az values.

Defining as error the difference between a
reconstructed and the corresponding experimen-
tal slant TEC, for each IGS station the data
analysis was based on the computation of cumu-
lative distributions of the absolute values of the
errors obtained with 24 h of data. In order to
have a global view of the reconstruction tech-
nique capabilities, cumulative distributions of
the absolute values of the errors were computed
taking into account data for stations lying in spe-
cific Modip intervals. These results are shown in
fig. 2, where the cumulative distributions of the
absolute values of the errors are plotted together
with the lines corresponding to 50 and 95 per-
centiles. The statistics are summarized in table I,
where the number of stations considered and the
value in TECU (1 TECU = 1016m−2) correspon-
ding to the 95 percentile for each Modip interval
are indicated.

The analyzed data show a general asymme-
try of errors behavior in the two hemispheres of

Table I. Statistical analysis summary for the day 27
March 2000: the first and second columns indicate
the Modip interval with the corresponding number of
IGS stations whose data were used to compute the
cumulative distribution of the absolute value of the
errors; the third column indicates the 95 percentile of
the distribution of the absolute value of the errors.

Modip interval Number of stations 95 percentile

(−90°, −60°) 2 31.6 TECU
(−60°, −30°) 25 27.0 TECU

(−30°, 0°) 5 37.4 TECU
(0°, 30°) 4 37.4 TECU
(30°, 60°) 72 19.6 TECU
(60°, 90°) 24 17.9 TECU

Fig. 3. Location of the IGS stations homogeneously distributed used to perform a concise analysis of the re-
construction technique performances for the day 27 March 2000. Modip isolines at −60°, −30°, 0°, 30°, 60° are
indicated.



Fig. 4. Cumulative distributions of the absolute values of the differences between experimental and recon-
structed slant TEC data corresponding to 27 IGS stations homogeneously distributed in Modip, for the day 27
March 2000. In the first case (left panel) the modeled slant TEC were reconstructed using NeQuick driven by Az
grids derived from La Plata vertical TEC maps. In the second case (right panel) the modeled slant TEC data were
calculated using NeQuick driven by the solar flux of the day.

318

Bruno Nava, Pierdavide Coïsson, Gloria Miró Amarante, Francisco Azpilicueta and Sandro M. Radicella

the Earth, whereas in the same hemisphere a lat-
itudinal dependence of the errors magnitude can
be observed: the agreement between experimen-
tal and reconstructed slant TEC is worse for sta-
tions with low Modip than for the other regions.
This would indicate a lower effectiveness of the
reconstruction method at low latitudes, as could
be expected because of the complexity and high
variability of the ionosphere at low latitudes.
Nevertheless it must be noted that a part of this
performance reduction could be related to a
poor data coverage and lower experimental data
quality for low-latitude regions.

As a final step, in order to have a concise in-
dication of the reconstruction technique per-
formances at global level, 27 IGS stations ho-
mogeneously distributed in Modip (see fig. 3)
were selected and the corresponding experi-
mental and reconstructed slant TEC data (using
NeQuick driven by Az grids derived from La
Plata vertical TEC maps) were used to compute
the cumulative distribution of the absolute val-
ue of the errors for the reference day. The re-
sults are shown in the left panel of fig. 4, where
the cumulative distribution of the absolute val-
ue of the errors is plotted together with the lines
corresponding to 50 and 95 percentiles. In this
case the 95 percentile of 28.6 TECU represents
the global performances of the reconstruction
technique for the reference day.

The same experimental data set was used
with modeled slant TEC obtained using
NeQuick driven by the 10.7 cm solar radio
flux corresponding to the day 27 March 2000
as given by the Space Environment Center
(http://www.sec.noaa.gov). The corresponding
cumulative distribution of the absolute value
of the errors was computed and is shown in the
right panel of fig. 4. In this case, the 95 per-
centile is 56.1 TECU and represents the glob-
al performances of NeQuick model for the ref-
erence day, without any adaptations derived
from TEC data ingestion. Therefore the com-
parison of the cumulative distributions in fig. 4
gives an indication of the potentiality of the re-
construction technique based on model adap-
tation through actual data. For the reference
day, the slant TEC errors at 95 percent level
are reduced to a half of those obtained with the
standard use of the Nequick model.

2.4. Vertical incidence parameters

Experimental peak parameters obtained
from worldwide distributed ionosondes were
used to test the capability of reconstruction
method to reproduce peak parameters values on
the basis of Az grid calculation. An exhaustive
analysis is given in (Miró Amarante et al.,



319

A model assisted ionospheric electron density reconstruction method based on vertical TEC data ingestion

2003) and, as a further example, the compari-
son between hourly foF2 measured at the loca-
tions indicated in table II on 27 March 2000 and
the same values reconstructed with NeQuick
model driven by Az grids derived from La Plata
maps is presented in fig. 5. As can be seen from
the linear fit shown in the plot, there is a good
agreement between experimental and recon-

Fig. 5. Measured and reconstructed foF2 using
NeQuick model driven by Az grids derived from La
Plata vertical TEC maps for the day 27 March 2000.
The best fit-line is also indicated.

Fig. 6. Example of global foF2 map reconstructed using NeQuick model driven by Az grids derived from La
Plata vertical TEC maps for the day 27 March 2000, 17:00 UT.

Table II. Ionosondes used to validate the electron
density reconstruction technique based on NeQuick
model driven by Az grids derived from La Plata ver-
tical TEC maps for the day 27 March 2000.

Ionosonde Ionosonde Ionosonde
Lat N (°) Long E (°)

Bermuda 32.4 – 64.7
Dyess 32.5 – 99.7

Millstone Hill 42.6 – 71.5
Puerto Rico (Ramey) 18.5 – 67.1

Wallops Island 37.9 – 75.5
Fairford 51.7 – 1.5

Goose Bay 53.3 – 60.3
Narssarssuaq 61.2 – 45.4
Sondrestrom 67.0 – 51.0

Qaanaaq 77.5 – 69.4

structed foF2. Therefore, even if the same de-
gree of accuracy cannot be expected at all geo-
graphical locations, an attempt to reconstruct
global foF2 maps using only GPS derived TEC



320

Bruno Nava, Pierdavide Coïsson, Gloria Miró Amarante, Francisco Azpilicueta and Sandro M. Radicella

data has been made. As an example, fig. 6 illus-
trates a reconstructed worldwide foF2 map for
the day 27 March 2000, 17:00 UT.

3. Conclusions

A model assisted reconstruction technique,
able to provide a realistic 3D representation of
the electron density of the ionosphere under
given conditions, has been developed. It is
based on experimental vertical TEC data inges-
tion into the NeQuick model: vertical TEC
maps are used to retrieve worldwide grids for
the model driving parameter Az. These Az grids
are computed at any epoch for which a vertical
TEC map is available and, under particular con-
ditions, the Az grids can be interpolated in time
to provide new grids for epochs when vertical
TEC maps are not available. The computation
of an Az grid allows to calculate the electron
density of the ionosphere all over the world
with the NeQuick model. As a consequence it is
possible to calculate the TEC along any
ground-to-satellite ray-path or to reconstruct
global foF2 maps. The reconstruction technique
itself improves the model performances at glob-
al level when NeQuick is used to reconstruct
experimental slant TEC values as it is demon-
strated by the reduction to a half of the slant
TEC errors at 95 percent level. The tests per-
formed and the results obtained encourage fur-
ther developments of the technique.

4. Future developments

At present the described reconstruction
method is based on pre-calculated vertical TEC
maps used to retrieve the Az grid values that can
drive NeQuick. It is important to observe that
Az grids can be calculated in several ways. A
possible method to construct Az grids, starting
from experimental data, could be based on di-
rect ingestion of slant TEC data. In this case a
new approach should be followed in order to
derive global Az grid, starting from scattered
slant TEC measurements. In addition, due to
the flexibility of the NeQuick model, a recon-
struction method based on a combined use of

Az grids and experimental peak parameters val-
ues could be implemented.

REFERENCES

BILITZA, D. (2001): International Reference Ionosphere
2000, Radio Sci., 36 (2), 261-275.

BRUNINI, C. A. (1998): Global Ionospheric model from GPS
measurements, Ph.D. Thesis (Facultad de Ciencias As-
tronómicas y Geofísicas, La Plata National University).

DI GIOVANNI, G. and S.M. RADICELLA (1990): An analytical
model of the electron density profile in the ionosphere,
Adv. Space Res., 10 (11), 27-30.

HOCHEGGER, G., B. NAVA, S.M. RADICELLA and R.
LEITINGER (2000): A family of ionospheric models for
different uses, Phys. Chem. Earth, 25 (4), 307-310.

ITU (2001): Ionospheric propagation data and prediction
methods required for the design of satellite services
and systems ionosphere characteristics, Recommenda-
tion P.531-6, approved in 2001-02, managed by ITU-R
Study Group SG3 (version 6 superseded in 2004 by
version 7).

KOMJATHY, A., R.B. LANGLEY and D. BILITZA (1998): In-
gesting GPS-derived TEC data into the International
Reference Ionosphere for single frequency radar al-
timeter ionospheric delay corrections, Adv. Space Res.,
22 (6), 793-801.

MIRÓ AMARANTE, G., S.M. RADICELLA, B. NAVA and P.
COÏSSON (2003): Validation of a new method for ionos-
pheric electron density reconstruction by means of ver-
tical incidence data, in Proceedings of ‘Atmospheric
Remote Sensing using Satellite navigation Systems’,
Special Symposium of the URSI Joint Working Group,
Matera (FG), Italy, 335-342.

NAVA, B., P. COÏSSON, G. MIRÓ AMARANTE and S.M. RADI-
CELLA (2003): A new model assisted method for iono-
sphere electron density reconstruction, in Proceedings
of ‘Atmospheric Remote Sensing using Satellite navi-
gation Systems’, Special Symposium of the URSI Joint
Working Group, Matera (FG), Italy, 343-348.

RADICELLA, S.M. and R. LEITINGER (2001): The evolution
of the DGR approach to model electron density pro-
files, Adv. Space Res., 27, 35-40.

RAWER, K. (1963): Propagation of decameter waves (HF-
band), in Meteorological and Astronomical Influences
on Radio Wave Propagation, edited by B. LANDMARK
(Pergamon Press, New York), 221-250.

SCHAER, S., G. BEUTLER, M. ROTHACHER and T.A. SPRINGER
(1996): Daily Global Ionosphere Maps based on GPS
carrier phase data routinely produced by the CODE
analysis center, in Proceedings of the IGS AC Work-
shop, Silver Spring MD, U.S.A.

WANG, C., G. HAJJ, X. PI, I.G. ROSEN and B. WILSON
(2004): Development of the Global Assimilative Ionos-
pheric Model, Radio Sci., 39, RS1S06, doi: 10.1029/
2002RS002854.

(received October 15, 2004;
accepted March 09, 2005)