In order to provide a scientific base to the NeQuick characterisation under
disturbed conditions, the comparison of its performance for quiet and storm
days is investigated in the southern mid-latitude. This investigation was
realised using the two versions of the NeQuick model which were adapted to
local and storm-specific response by using the critical frequency of the F2
layer (foF2) and the propagation factor (M(3000)F2) derived from
three South African ionosonde measurements, Hermanus (34.40∘ S,
19.20∘ E), Grahamstown (33.30∘ S, 26.50∘ E) and
Louisvale (28.50∘ S, 21.20∘ E). The number of free
electrons contained within a 1 m squared column section known as total
electron content (TEC) is a
widely used ionospheric parameter to estimate its impact on the radio signal
passing through. In this study, the TEC derived from the adapted NeQuick
version is compared with observed TEC derived from Global Navigation
Satellite System (GNSS) data from co-located or nearby GNSS dual-frequency
receivers. The Hermanus K-index is used to select all the disturbed days
(K-index ≥ 5) upon moving from low to high solar activity (from 2009
to 2012). For each disturbed day, a quiet reference day of the same month was
chosen for the investigation. The study reveals that the NeQuick model shows
similar reliability for both magnetic quiet and disturbed conditions, but its
accuracy is affected by the solar activity. The model is much better for
moderate solar activity epochs (2009 and 2010), while it exhibits a
discrepancy with observations during high solar activity epochs. For instance
in Hermanus, the difference between GPS TEC and NeQuick TEC (ΔTEC) is
generally lower than 10 TECu in 2009, and it sometimes reaches 20 TECu in
2011 and 2012. It is also noticed that NeQuick 2 is more accurate than
NeQuick 1, with an improvement in TEC estimation more significant for the
high solar activity epochs. The improvement realised in the latest version of
NeQuick is more than 15 % and sometimes reaches 50 %.
Ionosphere (mid-latitude ionosphere; modelling and forecasting)Introduction
The accuracy of the Global Positioning System (GPS) in particular and the
GNSS in general is affected by several factors such as the troposphere,
multipath and the ionosphere. The ionosphere is the cause of the largest
errors in an open-sky scenario and can cause an error in the positioning of
about 100 m . Indeed, the ionosphere induces a group time delay
and phase advance of GNSS signals . It is shown
() that the delay is proportional to the total electron
content (TEC) and the inverse of the square of the carrier frequency defined
as follows:
dt=α⋅TECcf2,
where dt is the time delay expressed in seconds, c the speed of
light in the vacuum (c=3×108 m s-1),
f the signal frequency in Hz, α=40.3×1016 and TEC in TECu
(1 TECu =1016 electrons m-2).
Knowing the TEC permits one to estimate the impact of the ionospheric error
on GNSS position estimation. Taking advantage of the dispersive property of
the ionosphere, the use of dual-frequency signals (L1 at 1575.42 MHz and L2
at 1227.60 MHz) allows estimation to first order of the ionospheric delay.
The ionospheric error in GNSS position estimation can be mitigated by the use
of augmentation systems like the Ground Based Augmentation System (GBAS) and
the Space Based Augmentation System (SBAS). These systems broadcast
ionospheric correction messages to the GNSS receiver according to its
localisation. This technique, which can be used by both single- and
dual-frequency receivers, requires more complex and expensive receivers
. The easiest way for single-frequency (SF) receivers to
compensate for the ionospheric error is to rely on an ionospheric correction
algorithm based on existing models such as the Klobuchar and NeQuick models
(). These models are used to provide the TEC corrections
for SF GNSS receivers. Like any ionospheric model, NeQuick is regularly
evaluated regarding its dependence on different parameters which affect the
ionosphere such as the geographic (or geomagnetic) coordinates, the solar
activity, the season and the time of day. In the preliminary study of NeQuick
as a model for ionospheric effect mitigation, adapted the model
to a daily feature by using the effective ionisation level Az computed from
GNSS data from selected IGS monitor stations. They revealed that the model
was affected by the geographical distribution of the monitor stations. Later,
, constraining the model to a daily behaviour by means of
ionosonde-derived foF2 and M(3000), at the northern mid-latitude,
reported that both versions of NeQuick were providing the TEC with a root
mean square (rms) error higher than 5 TECu during the year of high solar
activity and lower than 4 TECu for the year of solar minimum. They also
revealed that the use of NeQuick provided a significant improvement on the
accuracy of the TEC estimates during the solar maximum. However, in their
study, these authors have selected only data from days that were considered
to be geomagnetically quiet since they did not expect the model to perform
well during disturbed days. Using 10 international geomagnetic quiet days,
evaluated three topside options of the IRI-2012 model topside
at five stations situated around the same longitude from low to mid
latitudes. During this study, which covered different solar activity (from
minimum to maximum), it was revealed that the IRI with the NeQuick topside
option shown good agreement with GPS TEC in 2009, in all seasons. For years
of maximum solar activity (2012–2013), the IRI using NeQuick as the topside
option has a performance depending on the season. In the African equatorial
sector, noticed that NeQuick 2 was more accurate during epochs
with moderate solar activity than during epochs characterised by low solar
activity. investigated the performance of NeQuick 1 (NeQuick
ITU-R) in modelling the daily TEC over the South African region, taking into
account both solar and magnetic conditions. It was reported that NeQuick 1
did not perform well during the epochs of maximum solar activity. However,
the study was limited to only one location (Hermanus; 34.40∘ S,
19.20∘ E), and only 3 disturbed days were evaluated. The present
work investigates the accuracy of NeQuick over a wider geographic latitude
range than and over a larger number of disturbed days. To
extend the verification of NeQuick over a larger geographic range the data
from two other ionosonde stations in South Africa are considered. To select
the disturbed days, the Hermanus K-index was used instead of the Dst index
as done by . The improvements in TEC estimation over the region
of interest which is afforded by the NeQuick 2 model are evaluated by
comparison with the corresponding predictions of the NeQuick 1 model.
Summary of NeQuick basic parameters.
Anchor pointEF1 (if it exists)F2Height (km) HmE = 120HmF1HmF2Electron density NmE (0.124 foE2)NmF1 (0.124 foF12)NmF2 (0.124 foF22)Thickness parameterTopsideBEtopBF1topBF2top(km)BottomBEbotBF1botBF2bot
Coordinates of the selected stations.
Ionosonde stationGeographic coordinates(geomagnetic coordinates)Distance to nearest used GPSreference stationHermanus34.40∘ S; 19.20∘ E(42.33∘ S; 82.13∘ E)co-locatedGrahamstown33.30∘ S; 26.50∘ E(41.95∘ S; 90.17∘ E)co-locatedLouisvale28.50∘ S; 21.20∘ E(38.31∘ S; 86.87∘ E)<12 kmNeQuick model
The NeQuick and Klobuchar models are the bases of algorithms used for
mitigating the ionospheric effects on GNSS signals
(). These models are incorporated into SF
receivers in order to estimate the TEC along the ray path of the signal from
the satellite to the receiver. It has been revealed that the Klobuchar model,
the one currently used by GPS SF receivers, is able to reduce the
ionospheric-induced error to about 50 % . The NeQuick model,
which is presented as being more efficient than the Klobuchar model
, is used by the Galileo SF receivers for mitigating
ionospheric-induced error. In contrast to the Klobuchar model, which
simplifies the ionosphere as being a thin single layer localised at the
ionospheric pierce point (IPP) at 350 km in altitude , NeQuick
is a three-dimensional model. It provides the electron density profile along
the ray path and calculates the TEC by numerical integration.
Developed at the Telecommunication and Information & Communication
Technology for Development (T/ICT4D) laboratory of the Abdus Salam
International Centre for Theoretical Physics (ICTP) in cooperation with the
Institute for Geophysics, Astrophysics and Meteorology (IGAM) of the
University of Graz, Austria, NeQuick is fully described in many articles
(). This quick-run model, presented as
suitable for trans-ionospheric applications (), is
widely used internationally for scientific purposes as well as for the
determination of ionospheric effects on satellite navigation and positioning
systems. In the framework of navigation system assessment by the European
Space Agency, NeQuick was used to model a realistic ionosphere. The model
relies on anchor points and thickness parameters to establish the ionospheric
vertical density profile. Table gives the list of the anchor points
and thickness parameters used by the NeQuick model. These parameters are
defined by providing to the model the following ionospheric parameters
recorded by an ionosonde: the critical frequency of the E, F1 and F2 layers
(foE, foF1 and foF2 respectively) and M(3000)F2.
The original or default NeQuick model is a climatological model. It uses
empirical ionospheric parameters and provides monthly median output
. As emphasised by , an ionospheric correction
model has to have a daily output. For Galileo SF, NeQuick G (Galileo), the
adaptation of the NeQuick model to real time, is governed by the effective
ionisation level parameter called Az (Eq. ) ().
Az(μ)=a0+a1μ+a2μ2μ is the modip and a0, a1, and a2 are coefficients
broadcast to Galileo single-frequency receivers through the navigation
message.
The Az coefficients contain
information on the daily solar activity and the local condition
(). In this present assessment, by means of the data
ingestion technique , the daily and local modifications of the
model are acquired by the use of locally recorded ionosonde and geomagnetic
data.
NeQuick being an empirical model, the growing inventory of topside and in
situ ionospheric data (ISIS2, IK19 and Cosmos 1809 satellites) was applied to
facilitate some significant changes () which led to the
release of NeQuick 2. The model is written in the Fortran 77 language. The
source code of NeQuick 2 is available at
https://www.itu.int/dms_pubrec/itu-r/rec/p/R-REC-P.531-12-201309-S!!ZIP-E.zip
(last access: 18 August 2018). An online option
of NeQuick 2 is also accessible at
http://t-ict4d.ictp.it/nequick2/nequick-2-web-model (last access:
18 August 2018).
Data and processing
The ionosonde data used in this present study have been collected from three
South African digisonde stations. There are GPS dual-frequency reference
stations which are close by or co-located with each of the ionosonde stations
(see Table ).
Only foF2 and M(3000)F2 ionosonde values have been used to run the
NeQuick model, thus ingesting these experimental parameters into the model.
The other model parameters (foE and foF1) are calculated by
the NeQuick program using its empirical relations since they do not appear
most of the time in the ionograms . The ionosonde parameters
obtained after a manual scaling are used as input parameters for the NeQuick
model to provide TEC, called NeQ1 TEC and NeQ2 TEC respectively for NeQuick 1
and NeQuick 2. In order to take into account the solar activity, the daily
solar flux F10.7 is used to feed the NeQuick model. The modelled TEC was
compared to the TEC derived from the data of co-located or nearby GPS
receivers. The GPS data are stored in Receiver Independent Exchange format
(RINEX) and the TEC (GPS TEC) values are determined using the program
developed at Boston College . The retrieval of TEC from GPS
measurements is subject to biases due to the transmitter (satellite) and
receiver hardware. These biases are estimated and eliminated during the
processing by the software. This software has been used in many studies to
compute the observed TEC from dual-frequency GPS receiver observations
(). The output allows the user
to obtain detailed data such as elevation angles and the vertical TEC of each
satellite as seen from the GPS receiver. The vertical TEC (VTEC) computed
exclusively from satellites with elevation angles above 50∘ is
selected. This selection excludes ionospheric pierce points (IPPs) too far
from the vertical at the ionosonde location. This reduces the impact of the
mapping function from the measured slant TEC to the estimated vertical TEC
(Fig. ).
Distribution of GPS IPPs over Hermanus ionosonde station for all the
selected days in 2012. The IPPs presented are those of each
hour.
Comparison between GPS TEC, NeQuick 1 TEC (NeQ1 TEC) and NeQuick 2
TEC (NeQ2 TEC) for 2010. The geomagnetic condition is represented by the
K-index indicated by the black line (left: K<4, right: K≥5). The
rms calculated as defined in Eq. () is also indicated.
The difference between GPS TEC and NeQuick 1 TEC (ΔTEC1) and
between GPS TEC and NeQuick 2 TEC (ΔTEC2). The dotted marks represent
the ΔTEC of each selected day, while the solid line represents the
average of all those ΔTEC.
In order to examine the model under different ionospheric conditions and
according to the availability of ionosonde data, the analysis was limited to
the period from 2009 to 2012. Within this period the solar activity recorded
includes a minimum, moderate and maximum level. These solar activity levels
were classified according to the solar flux F10.7 which varies from 68 to
153 sfu. The Hermanus K-index was used to select the geomagnetic
condition. The days with a K-index ≥5 were considered disturbed
. For each disturbed day found, a quiet day based on data
availability in the same month was selected for the comparative study
according to the geomagnetic state (Table ). For the statistical
analysis the following formulas were used.
The TEC difference (ΔTEC) is calculated as follows:
ΔTECi=TECGPS-TECNeQi,i=1;2.
The daily root mean square (RMSiD) is inferred using the following equation:
RMSiD=1n∑h=024(ΔTECih)2,
where n is the number of available hours and the subscript i indicates
the NeQuick model used.
The RMSY inferred from each hour of the selected days of the
concerned year.
The improvement of NeQuick 2 as compared to NeQuick 1 averaged over
all selected days for each year considered.
To infer the yearly root mean square (RMSiY), representing the
overall rms of the selected days of the concerned year, the following
equation is used:
RMSiY=1n×N∑d=1N∑h=024(ΔTECi)d2,
where N is the number of selected days.
The improvement P obtained by using NeQuick 2 relative to NeQuick 1 is
P=RMS1-RMS2RMS1×100.
Results
Figure presents the results of the assessment above Hermanus,
Grahamstown and Louisvale stations for 2010. In these figures, the plots
related to days within the same column share the same geomagnetic condition,
while the plots in every row represent the hourly TEC of 2 days of the same
month. In most of the cases regardless of the magnetic condition, the adapted
NeQuick and the GPS TEC show peaks at the same time. The daily rms values
indicated in each plot show that the models have a similar performance during
quiet (left) and disturbed (right) days. For example, for Louisvale in 2010
NeQuick 1 is more accurate on disturbed days 2 May and
3 August 2010
(rms = 3.40 and 2.55 TECu respectively) than on quiet days 5 May and
5 August 2010 (rms = 4.29 and 4.11 TECu respectively). The opposite is
observed in other cases; for instance, the model is less accurate on
disturbed day 4 August 2010 (rms = 4.11 TECu) than on quiet day
8 August 2010 (rms = 3.24 TECu). Equally with NeQuick 2 the same trend as
for the geomagnetic state is observed. Similar observations are noticed for
the other locations considered. The daily rms values also reveal that the TEC
delivered using NeQuick 2 is closer to GPS TEC than NeQuick 1 TEC since for
each day in 2010, RMS2 is smaller than RMS1. Figure
shows the difference between the NeQuick TEC and the GPS TEC for each of the
selected days of the analysed years (2009, 2010, 2011 and 2012). These plots
revealed that the discrepancy between the GPS TEC and the NeQuick TEC is
higher during the period from 08:00 to 14:00 UT (10:00 to 16:00 LT). We
stress that it is within this time period situated around the local noon that
the TEC has its highest values. It can be noted that there is a better match
between the model and observations in 2009 and 2010 (years of solar minimum)
than in 2011 and 2012 (years of solar maximum). It is important to point out
that only 1 disturbed day was recorded in 2009; therefore, the results of
this year have a very low statistical significance. The extent of the models
in overestimating/underestimating is better appreciated by focusing on the
averaged TEC difference depicted in Fig. . Considering the time of
day, it can be observed that the models show overestimations and
underestimations of the TEC without any consistent trend, except from 08:00
to 14:00 UT in 2010, where the TEC is generally overestimated
(ΔTEC<0). From one year to another, we observe this same
trend, except in 2009, for which the models generally underestimate the TEC
(ΔTEC>0).
Focusing on the dependence of ΔTEC on solar activity, the performance
of NeQuick 1 is generally better for days of solar minimum (2009) and solar
moderate activity (2010) years than for days of solar maximum (2011 and 2012)
during which a prominent discrepancy stands out clearly. Indeed, while for
2009 and 2010 ΔTEC is lower than 10 TECu except from
18:00 to 22:00 UT in 2009 in Hermanus (Fig. ), higher values of
ΔTEC (sometimes reaching 20 TECu) are present
for 2011 and 2012. For NeQuick 2, though the same tendency is generally
observed, a reduction of the gap between the performance of the model during
the solar maximum and the two lower solar activity epochs is noticed.
For a more thorough analysis, the rms errors inferred from each hour of the
selected days of the concerned year are presented in Fig. . This
latter figure confirms the previous raw observations. Thus, it reveals that
the accuracy of both NeQuick models in following the TEC trend is similar for
quiet (blue) and disturbed (red) geomagnetic states. Except in Hermanus, it
is noticed that there are 2 years in which the model is better during quiet
days (2010 and 2011) and 2 years where the opposite is observed (2009 and
2012). It is clearly observed that NeQuick 1 offers high rms values during
solar maximum years (2011 and 2012), while the rms inferred during these
solar maximum years using NeQuick 2 undergoes a decrease. The last figure
(Fig. ) allows us to estimate the improvement realised while
updating NeQuick 1 to NeQuick 2. It is noticed that NeQuick 2 is more
accurate than NeQuick 1. In almost all years a positive improvement is
recorded. This improvement realised can be more than 30 % (Hermanus,
2011: 55 %; Grahamstown, 2010: 33 % and Louisvale, 2012: 42 %).
Discussion and conclusion
The accuracy of the NeQuick model in estimating TEC over the southern African
region was assessed in this study. In order to carry out this investigation,
the TEC modelled was compared by means of the two versions of NeQuick with
the TEC derived from the GPS observations from the same location under
different geomagnetic and solar conditions. Focusing on the first version of
the NeQuick model (NeQuick 1), it has been noticed that the model has
encountered some deficiency during the years of solar maximum. This report
confirms the results of the earlier study performed by in the
European sector. With more selected quiet days, found rms
errors of NeQuick 1 higher in a high solar activity year (7.7 TECu) than in
low solar activity (3.8 TECu). In our case the same tendency was observed.
While rms values are higher than 5 TECu during the high solar activity years
(2011 and 2012), they are lower than 4.6 TECu during low solar activity years
(2009 and 2010) for all the selected locations. Including the latest version
(NeQuick 2), also found that both versions have better
performance during the low solar activity period (RMS<3.5 TECu)
than during the high solar activity period (RMS>5.1 TECu). This
present study confirms this result (except for the year 2009). While for 2010
(solar moderate year) the rms is always smaller than 4 TECu, it can reach
6 TECu in 2011 and 2012 (solar maximum years). Knowing that the highest TEC
values are recorded during high solar activity, it can be stated that the
accuracy of NeQuick decreases with the increase in TEC value. Also, it is
observed that the discrepancy between the NeQuick TEC (both versions) and GPS
TEC was higher around the local noon, which is the period when the TEC
reaches its highest values. Those two observations led us to conclude that
the accuracy of the NeQuick model was proportional to the TEC value. In a
comparative study of both versions, it is observed that NeQuick 2 is
generally more accurate than NeQuick 1. The improvement realised in the
latest version of NeQuick can reach 50 %. This improvement is more
pronounced during years with a high solar activity (above 15 % in 2011
and 2012 for all stations). Those results are in agreement with the
investigation carried out by for the northern mid-latitude
during quiet days. They showed that NeQuick 2 is more accurate than
NeQuick 1, with a more significant improvement in solar maximum (67.3 %)
than in solar minimum (56.2 %). For the obtained results it can be
observed that on disturbed days NeQuick 2 is better than NeQuick 1, except in
2009 (probably for the reason mentioned above). For this assessment realised
within the southern African region, it is noticed that the models have
similar performances for the three selected locations. We found that the
model, after being adjusted by foF2 and M(3000)F2 inferred from
ionosonde electron density profiles, gives a similar correlation with GPS TEC
during quiet and disturbed conditions. The NeQuick model, which has been
chosen for the correction of ionospheric errors in position estimation by
means of Galileo SF receivers, appears to be sufficiently accurate for
operations which do not involve human safety. For the improvement of the
model the algorithm for the calculation of TEC values, particularly around
local noon, should be improved.
We acknowledge the National Geo-spatial Information, South
Africa, for operating and maintaining the TrigNet receiver network and making
GPS observational data freely available via ftp access at
ftp://ftp.trignet.co.za (last access: 18 August 2018). Data from the
South African Ionosonde network are made available through the South African
National Space Agency (SANSA), who are acknowledged for facilitating and
coordinating the continued availability of data. South African Ionosonde data
can also be freely accessible to the public from the Digital Ionogram
DataBase through http://ulcar.uml.edu/DIDBase (last access:
18 August 2018).
SMA modified the NeQuick model code (data ingestion
technique) and performed the simulations. JBH provided the software to
extract the GPS TEC and explained its use. He proposed the study. OKO
proposed the model of the study (NeQuick model) and the method of
investigation (ionospheric data ingestion). PJC proposed the purpose of the
investigation (investigate the NeQuick model under different geomagnetic
conditions). ZKZ proposed the figure comments. SMA prepared the manuscript
with contributions from all co-authors.
The authors declare that they have no conflict of
interest.
Acknowledgements
Sylvain M. Ahoua is very grateful to the South African National Space Agency
(SANSA) Space Science Directorate for their financial support and hospitality
through the visiting graduate research programme. The authors also express
their acknowledgements to the T/ICT4D Laboratory of the ICTP, Trieste, Italy,
for providing the source codes of NeQuick 1 and NeQuick 2. Finally, the
authors would like to extend their gratitude to the South African TrigNet
network and to Boston College for providing respectively GPS data and GPS TEC
software. The topical editor, Dalia
Buresova, thanks Pierdavide Coïsson and one anonymous referee for help in
evaluating this paper.
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