Choice of the Definition Method for the Total Electron Content to

Describe the Conditions in the Ionosphere

Olga Maltseva

Institute of Physics Southern Federal University, Stachki, 194, Rostov-on-Don, Russia

mal@ip.rsu.ru

Keywords: GPS. Total electron content TEC. Ionospheric models. Radio wave propagation. Geomagnetic disturbances.

Abstract: Conditions of radio-wave propagation in the ionosphere, influencing functioning of the modern navigation

and communication systems, are defined by the critical frequency foF2 and an electron density distribution

termed the N(h)- profile. In the given paper, the experimental values of the total electron content TEC(obs)

are used for their determination. It is shown that the median of the equivalent slab thickness of the

ionosphere is the good calibration factor, allowing to obtain values of foF2 from TEC(obs) of any global

map though in most cases values of foF2, the closest to foF2(obs), are provided with the JPL map. For

coordination of the N(h)-profile with values of TEC(obs), coefficient K(PL), modifying a plasmaspheric

part of a profile, is entered (up to heights of navigation and geostationary satellites). In this case, the CODE

map is the best one. It is necessary to have models of the ТЕС parameter to support navigation system

operation. It is shown that the big progress in modeling of this parameter is reached during the last years:

appearance of various models allows us to compare and use them at forecast ТЕС for any level of solar

activity. It is especially important, because values of solar spots and the F10.7 parameter and also

geomagnetic indexes of Kp, Dst, АЕ are well enough predicted.

1 INTRODUCTION

The ionosphere plays an important role in the life of

mankind: it mitigates the blows of solar wind and

provides wave propagation of various frequency

bands. The systems connected to the ionosphere are

most full presented in Tab. 1 from the paper

(Goodman, 2005).

Category 1 involves those systems that depend

upon the ionosphere (i.e., involve the ionosphere as

part of the system), and category 2 involves those

systems for which the ionosphere is simply a

nuisance. The special role for description of the

ionospheric conditions is played by models, and the

model, capable to provide high accuracy of

description of ionospheric characteristic distribution,

should be adapted for the experimental information

in a real time mode.

Table 1: Categories of radio systems in terms of

ionospheric dependence

Category 1: systems

that depend upon the

ionosphere

Category 2: systems for

which the ionosphere is

simply a nuisance

VLF–LF

communication and

navigation

Satellite

communication

MF communication

Satellite navigation

(e.g., GPS&GLONASS)

HF communication

Space-based radar and

imaging

HF broadcasting

(‘‘short-wave’’ listening)

Terrestrial radar

surveillance and tracking

OTH radar

surveillance

Meteor-burst

communication

HFDF and

HF SIGINT

Any other system for

which the ionosphere is not

necessary for conveyance

Olga M.

Choice of the Deﬁnition Method for the Total Electron Content to Describe the Conditions in the Ionosphere.

DOI: 10.5220/0005421200510061

In Proceedings of the Third International Conference on Telecommunications and Remote Sensing (ICTRS 2014), pages 51-61

ISBN: 978-989-758-033-8

The data which can be used in such an approach

should be available and operatively updated.

Traditional parameters meeting such

requirements are the critical frequency foF2 and

maximum height hmF2. Because the total electron

content TEC is the most important parameter of the

ionosphere for the operation of technological

systems, in the given paper it is used for this

purpose. TEC data are available and is updated in

several Internet archives. From huge number of

possible applications of ТЕС, in the present paper

the preference is given for an estimation of

possibility of determination of propagation

conditions. It means usage of ТЕС for determination

of foF2 (or too NmF2) and N(h)- profiles. The huge

need exists in the forecast of these parameters, and,

hence, of ТЕС. It is possible to select three methods

of the TEC determination: (1) measurements, (2)

empirical modeling, (3) integration of theoretical or

empirical N(h)-profiles. Information and results are

given for each of these methods.

2 MEASUREMENT METHODS

The most widespread are global maps JPL, CODE,

UPC, ESA, created by Jet Propulsion Laboratory of

California Institute of Technology (Pasadena, USA),

the Center for Orbit Determination in Europe

(CODE) of the International GPS Service for

Geodynamics (Switzerland), Astronomy and

Geomatics of the Polytechnical University of

Catalonia, Barcelona, Spain (UPC), European Space

Agency (Germany) respectively as TEC

experimental data (e.g. Schaer et al., 1995;

Mannucci et al., 1998; Hernandez-Pajares et al.,

1997; Sardon et al., 1994; Jakowski et al., 1996). For

specific coordinates and time, the maps can be

derived from the IONEX (IONosphere map

Exchange) files (ftp://cddis.gsfc.nasa.gov/pub/

gps/products/ionex/). Owing to the big differences of

methods (on determination of biases, approximating

functions, etc.), values of ТЕС for various maps and

other methods of determination ТЕС are strongly

differed. Traditional examples of such differences

are Figures from the paper (Arikan et al., 2003).

Now, the GPS community selected the average

IGS values as the standard (Hernandez et al., 2009),

therefore in the given paper all maps, including IGS,

are used. These maps are given on the same site and

already start to be used, e.g. (Lean et al., 2011). We

use all maps for comparison. However, under the

valid remark of (Lastovicka, 2013), such selection

does not remove the restrictions inherent in each

method. JPL is used in paper (Gulyaeva and

Stanislawska, 2008), CODE is used in paper

(Jakowski et al, 2006). Other methods also yield

comparable results.

Figure 1: Comparison of the estimated TEC values from

the algorithm with other models of TEC for Kiruna,

estimated VTEC from the developed algorithm (solid

line), RCRU (dashed line), IRI model (pluses),

gAGE/UPC (triangles and a solid line), JPL-GNISD

(diamonds and a solid line), ESA/ESOC (circles and a

solid line), NRCan (stars and a solid line), CODE (squares

and a solid line). (a) 25 April 2001 and (b) 28 April 2001.

3 METHODS OF EMPIRICAL

MODELING

Empirical modeling plays an important role both for

the forecast of ionospheric parameters, and for

validation of models. For modeling of ТЕС,

basically, the method of orthogonal components is

used (Zhang et al., 2012; Ivanov et al., 2011),

however authors do not give appropriate coefficients

and functions. Besides, there is a difficulty of the

forecast at an output for temporal boundaries of the

used data, therefore the main attention is given for

avaiable and new models. Many long years, the most

simple model of Klobuchar (Klobuchar, 1987) was

unique for adjustment of delay of signals in the

ionosphere and till now is widely used for systems

with single-frequency receivers though the authors

using it note a row of shortcomings, for example

(Chen and Gao, 2005). The model (Kakinami, 2009)

is an example of models for specific station which

should possess the high accuracy. The model is

based on values of the instrumental biases given by

the JPL laboratory. Results of the test of this model

Third International Conference on Telecommunications and Remote Sensing

in the form of correspondence between model and

experimental values are given on Fig. 2.

Figure 2: Comparison of model and observational ТЕС for

the Taiwan model near to a maximum of solar activity.

Seasonal course of ТЕС at the given latitude and

the full conformity of model and observational ТЕС

for autumn and winter months is perfectly seen. In

the spring and in the summer, the model

underestimates values. Range of the root mean

square (RMS) deviation makes 4-14 TECU, the

relative RMSD makes 6-18 %. On Fig. 3, results for

a minimum of solar activity are yielded.

Additionaly, values of IGS are shown by asterisks.

Figure 3: Comparison of model and observational ТЕС for

the Taiwan model near to a minimum of solar activity.

It is seen that values of ТЕС can be in 2-3 times

less, than in a maximum of solar activity. The model

can both to underestimate and to overestimate the

observational values. The range of absolute

deviations has made 1-10 TECU. Absolute (σ,

TECU) and relative (σ, %) RMSD are presented to

Tab. 2 for four months of three years.

Table 2: Absolute and relative RMS deviations for the

model (Kakinami, 2009).

σ,

TECU

Mar

Jun

Sep

Dec

2002

13.5

8.0

3.5

4.0

2006

3.0

1.7

2.6

2.2

2010

5.6

2.8

5.9

5.6

σ, %

Mar

Jun

Sep

Dec

2002

15.8

17.2

6.0

8.9

2006

14.7

9.5

14.6

16.2

2010

24.3

16.3

26.2

24.3

If to compare these results with 50 % -

estimation for the model (Klobuchar, 1987) then

improving in 2-5 times may be got. Important

property of the model is dependence of ТЕС on a

daily index. The previous Figures 2 and 3 showed

results for medians. The following Fig. 4 gives

comparison of daily model and experimental values

for August 2002.

Good correspondence of dynamics of TEC

variations is seen. That proves to be true by

quantitative estimations of absolute deviations 6.4

TECU, absolute RMS deviations 8.3 TECU and

relative RMSD 16.4 %. These results show high

efficiency of the model and a way of its

construction. It can be used for validation of other

models.

One more aspect of use of models is connected

with reconstruction of ТЕС values for those periods

when there were no regular measurements of ТЕС

(before 1998). The possibility of such reconstruction

is illustrated on Fig. 5 according to GPS

measurements at the Taiwan station in the morning

since September 1996 till August 1997 (Wu et al.,

2004). Icon ТЕС represents measurements, TW -

values of the Taiwan model.

It is seen that results are satisfactory as a first

approximation. They give representation also about

possibilities of forecast forward.

Choice of the Definition Method for the Total Electron Content to Describe the Conditions in the Ionosphere

Figure 4: Comparison of daily model and experimental ТЕС for August 2002.

Figure 5: Comparison of model and observational ТЕС in

years 1996-1997.

The Neustrelitz Global Model (NGM) unlike the

Taiwan model is global one (Jakowski et al., 2011).

Except the ТЕС model, it includes models of other

parameters (NmF2, hmF2) (Hoque and Jakowski,

2011, 2012). Authors of this model have fulfilled

own validation however it is not enough for certain

conclusions about efficiency of their model. Results

of more extensive validation are given in (Maltseva

et al., 2013c) for a middle-latitude region and in

(Maltseva et al., 2013b) for low-latitude area in

which the greatest advantages were expected.

Results of additional validation for low-latitude

stations Niue and Sao Luis are given on Fig. 6, for

high-altitude stations are given on Fig. 7.

Figure 6: Cases of the NGM model advantage at definition

of foF2 (two low-latitude stations, 2010, 2004, 2002).

Third International Conference on Telecommunications and Remote Sensing

Figure 7: Cases of the NGM model advantage at definition

of foF2 (three high-altitude stations, 2010, 2007).

In these cases, periods of the NGM model

advantages are seen, however the major statistics on

all regions shows that the NGM model not always

yields the best results, than the IRI model.

Discrepancy between radio occultation and

ionosonde values of NmF2 may be one of the

reasons why insert of great number of radio

occultation measurements has not led to

improvement of the NGM model, e.g. (Hajj and

Romans, 1998; Tsai and Tsai, 2004). Nevertheless, it

can be recommended for use in low- and high-

latitude areas.

Process of model development continues

constantly that is additional confirmation of an

urgency of this process. The latest model is the

model of authors (Mukhtarov et al., 2013a, b). It, on

the one hand, is the most physically proved, on the

other hand, according to estimates of authors, their

model is two times more exact, than the NGM

model. In papers (Mukhtarov et al., 2013a, b), not

only the ТЕС model is developed, but also model of

its error (Mukhtarov et al., 2013b). Difference from

the NGM model is the consideration not only

components, caused by sunlight, but also the regular

wave structure of the tidal nature influencing from

the lower atmosphere. The model is constructed

according to the CODE map for 1999-2011. As the

starting parameter, not only coefficient F10.7 is

chosen, but also its linear velocity of change K

It is

one more difference of this model from all previous

options. For all array of the used data, the following

estimates are obtained: mean (systematic) error

МЕ=0.003TECU, at such МЕ, root of mean square

error (RMSE) and an error of a standard deviation

(STDE) were equal and have made

RMSE=STDE=3.387TECU. These estimates are

compared to estimates for the TEC(NGM) model

(Jakowski et al., 2011): ME =-0.3TECU,

RMSE=7.5TECU. Thus, the Bulgarian model has a

smaller error in two times. However it is worth to

note that both models are climatological, i.e. they

describe a mean state in quiet geomagnetic

conditions, and the difference in number of

coefficients (12 against 4374) is underlined. Authors

of (Mukhtarov et al., 2013a) absolutely validly do

not consider a great number of coefficients as a

model deficiency because these coefficients are

calculated once, however they are inaccessible.

Coefficients of the TEC(NGM) model are published

and may be used by any user. In turn, we can note

that there are "tails" in an error distribution of any

model. It is important to determine, what latitudinal

areas and to what conditions of solar activity they

concern. As any model cannot work equally well in

all latitudinal areas and meet the possible

requirements, validation of models does not cease to

be an actual problem. These requirements are

connected with limitation of approaches, the used

data, distinction of physical processes.

Thus, it is possible to specify major progress in

modeling of parameter ТЕС: occurrence of various

models allows us to compare and use them at

forecast of ТЕС for any level of solar activity. It is

especially important because values of solar spots

and parameter F10.7, and also geomagnetic

coefficients of Kp, Dst, АЕ are well enough

predicted (e.g. Pesnell, 2012; Tobiska et al., 2013).

4 DEFINITION OF FoF2 ON

CURRENT VALUES OF ТЕС

Definition of foF2 on current values of ТЕС in the

this paper is based on use of median of the

equivalent slab thickness of the ionosphere τ.

Empirical models of τ have appeared earlier, than

empirical models of ТЕС. Definition of ТЕС under

formula TEC=τ*NmF2, where the independent

empirical model of τ should be used, was one of

Choice of the Definition Method for the Total Electron Content to Describe the Conditions in the Ionosphere

main applications of the τ model. NmF2 is possible

to take from the IRI model or any another. The

simple relation for τ =ТЕС/NmF2 shows that τ is

width of a slab in the form of a rectangle with

constant concentration NmF2. For definition of ТЕС

and NmF2, the τ(IRI) model was traditionally used

(e.g. Houminer and Soicher, 1996; Gulyaeva, 2003)

though it also is not empirical in the same sense in

what the ТЕС(IRI) model is not empirical model of

ТЕС. On the basis of expression foF2=foF2(IRI)*

SQRT(TEC(obs)/TEC(IRI)), GIM-TEC adaptive

ionospheric weather assessment and forecast system

was constructed (Gulyaeva et al., 2013). It is easy to

show that value which can be designated τ(obs,IRI)

is used in this case. It means that model values of

NmF2 and the observational values of ТЕС are used

at definition of τ(obs,IRI). It differs as from τ(IRI,

IRI), and from τ(obs, obs) which are designated

τ(IRI) and τ(obs) for brevity of records. Papers

(Maltseva et al., 2012a, b) are devoted results of use

of median τ(med) from values τ(obs). Empirical

models of ionospheric parameters are known to

include median or mean values hence they

characterize a mean state, close to the quiet.

Advantage of median τ(med) is that it allows to

determine foF2 on current values of ТЕС. These

foF2 values differ from averages and are closer to

the real. In paper (Maltseva et al., 2012a), it is

shown that the median τ(med) allows to determine

foF2 during disturbances or to fill gaps of the foF2

data. The estimate of efficiency of use of values τ is

done by means of calculation of deviations |ΔfoF2|

of calculated foF2 from the observational ones. The

observational values of ТЕС form the whole array:

JPL, CODE, UPC, ESA, La Plata, IONOLab TEC,

RAL and others. To each of these values, the various

values of τ correspond. The example of τ behavior

for the JPL map is shown on Fig. 8 for the Juliusruh

station for April 2000 (near to a maximum of solar

activity) and April 2009 (near to a minimum of solar

activity).

Figure 8: An example of comparison of τ for various

options of ТЕС and NmF2.

Example of the foF2 definition by means of

various τ is given on Fig. 9 together with

experimental values of ТЕС for the JPL map. These

values are shown together with medians. This

picture specifies presence of disturbance.

Tab. 3 shows results of |ΔfoF2| calculation for

four global maps JPL, CODE, UPC, ESA. These are

monthly average values of deviations for the

instantaneous quantities foF2(ins). Values of |ΔfoF2|

for τ(IRI) are given for comparison.

The table illustrates the most general regularities:

the greatest deviations are proper τ(IRI) in the initial

model, the little smaller deviations correspond to

τ(obs, IRI). The best conformity is given by median

of τ(obs). From four maps, the best conformity

concerns the JPL map in this case. And though it

gives the best conformity in most cases, there are

conditions and regions in which the best conformity

can be given and by other maps. More often it is

CODE, sometimes - UPC. And even there was a

station (Sao Luis) for which the best conformity is

given by the ESA map in certain cases. The huge

statistics of calculations for more, than 30 stations

and 10 years, shows that deviations of the calculated

frequencies from the observational values have the

greatest quantity for τ(IRI), the least - for τ(obs), i.e.

τ(med). Deviations for τ(obs, IRI) lie between them,

closer to |ΔfoF2| for τ(IRI) more often. New results,

including the data for values IGS, are given in Tab.

4 for high- and low-latitude stations which

determine boundaries of values |ΔfoF2|, because

values for middle-latitude stations are always less.

Values, averaging for 2013, are given.

Figure 9: An example of use of median of τ for definition

of foF2.

Third International Conference on Telecommunications and Remote Sensing

Table 3: Deviations |ΔfoF2| for various options of τ definition.

|∆foF2|,

April

2000

April

2009

MHz

τ(IRI)→

1.034

τ(IRI)→

0.554

(obs,IRI)

τ(obs)

(obs,IRI)

τ(obs)

JPL

0.660

0.452

0.497

0.205

CODE

0.677

0.484

0.501

0.222

UPC

0.731

0.544

0.472

0.237

ESA

1.013

0.907

0.496

0.242

Table 4: Correspondence between experimental and calculated foF2 according to three stations.

|ΔfoF2ǀ

τ(IRI)

τ(obs, IRI)

τ(obs)

station

IRI

JPL

CODE

UPC

ESA

IGS

JPL

CODE

UPC

ESA

IGS

Thule

0.82

0.71

0.75

0.71

0.75

0.71

0.41

0.45

0.41

0.45

0.41

Longyear

0.69

0.61

0.67

0.59

0.63

0.62

0.40

0.49

0.38

0.43

0.41

Niue

2.19

2.09

2.16

2.15

2.13

1.01

1.10

1.09

1.06

1.04

Value for IGS is inscribed in the general

statistics and more often there is a little above, than a

value for the best map. It is worth to note that the

proximity of values |ΔfoF2| for various maps

testifies that τ is good calibration coefficient for

ТЕС.

Figure 10: Comparison of results of foF2 definition with

use of various τ.

In connection with such results, there is a

question on empirical model of τ. One of

possibilities is to pay attention to the NGM model

which allows to calculate NmF2(NGM) and

TEC(NGM). Having values NmF2(NGM) and

TEC(NGM), it is possible to calculate values of the

equivalent slab thickness of the ionosphere τ(NGM)

=TEC(NGM)/NmF2(NGM). The purpose is to

estimate, how much the model τ(NGM) is closer to

τ(obs) than τ(IRI). Such estimate is done by

comparison of instantaneous values |ΔfoF2(ins)|. For

the NGM model, values of foF2(ins) are obtained

from values ТЕС(CODE) with use of τ(NGM). On

Fig. 10, examples of comparison of critical

frequencies for two global maps are given ("best"

and "worst" from the point of view of definition of

foF2 in each specific case) and two models (IRI and

NGM) for middle-latitude and two high-altitude

stations in the conditions of various solar activity.

It is seen that near to a maximum of activity

(2001) the NGM model yields the best results than

the IRI model and the ESA map. In the conditions of

low activity (2006) at middle-latitude station, it

yields results, close to IRI. At high latitudes, the

NGM model gives major deviations in winter and

autumn, and it is seen that the CODE map yields the

worst results in these cases. At an increase of solar

activity in 2011 and the corresponding increase of

the ТЕС, the NGM model again starts to yield

results, the best than the IRI model. Thus, in most

cases τ(NGM) provides results, the best than τ(IRI),

however its deviations do not come nearer anywhere

to the values given by τ(JPL). In the conditions of a

minimum of activity, the NGM model has no

advantages to low-latitude stations.

Choice of the Definition Method for the Total Electron Content to Describe the Conditions in the Ionosphere

As a whole, it is possible to tell that τ(NGM)

may carry out a role of the empirical model of τ. At

use of other map instead of the CODE map,

probably, results would be better.

4 N(h)-PROFILE S OF THE

IONOSPHERE AND VALUES

OF ТЕС

As it is known, conditions in the ionosphere are

determined by distribution of concentration, or N(h)-

profile. N(h)-profile can be divided into three parts:

bottom side, topside and plasmaspheric. The bottom

side is determined by the experimental critical

frequency foF2. The topside is improved by means

of the plasma frequencies measured on satellites, but

there is a residual of ТЕС. It is possible to use

coefficient K(PL) which is selected for the full

conformity with the observational ТЕС. However

there is no data for development and validation of

the K(PL) model yet. Having such model, it will be

possible even to improve determination of foF2.

Details of use of ТЕС for determination of N(h)-

profile to heights of navigation satellites are the

following. In paper (Maltseva et al., 2013c), it has

been shown that use of the plasma frequencies

measured on satellites allows to improve the shape

of the topside side. As a result, values of ТЕС for the

several N(h)-profiles transiting through the critical

frequency foF2 and a various combination of plasma

frequencies are obtained: (1) satellite s1, (2) satellite

s2, (3) both satellites s1 and s2. Two first options are

realized in most cases. The third option is realized in

case of simultaneous passage of two satellites over

the given point. The illustration of obtained values

of ТЕС is given for the Juliusruh station on Fig. 11.

Simultaneous passages took place for 6 days

specified in Tab. 5 in UT=13 and UT=23. Values for

the initial IRI model are shown by black circles. Red

circles show the observational values. Green

triangles show values for the first option, by violet

crosses - for the second one, blue asterisks – for the

third case. Orange circles show ТЕС for the N(h)-

profiles transiting through both plasma frequencies

and adapting by coefficient K(PL). All values are

given for four maps in decreasing order of values.

This order is specified in Tab. 5.

Figure 11: TEC, calculated for N(h)-profiles, transiting

through the critical frequency foF2 and a various

combination of plasma frequencies.

Table 5: Days, hours and names of maps in decreasing

order of ТЕС for simultaneous passages of satellites over

the Juliusruh station in April 2001.

day

hour

map

ESA

JPL

UPC

CODE

JPL

UPC

CODE

ESA

JPL

CODE

UPC

ESA

JPL

UPC

CODE

ESA

UPC

JPL

ESA

CODE

JPL

UPC

CODE

ESA

Big difference between ТЕС for the corrected

N(h)-profiles and ТЕС for the initial model,

corresponding to quiet conditions, speaks about

influence of disturbances. N(h)-profiles transiting

through frequency of one of satellites, are close each

other. That can testify both to "interchangeability" of

profiles, and about their ambiguity. In most cases,

orange circles coincide with red points. It testifies

that the N(h)-profile, transiting through plasma

frequencies of both satellites, provides the

observational value of ТЕС. It is reached by

selection of coefficient K(PL) shown on Fig. 12 also

for four maps.

Figure 12: Behavior of coefficient K(PL) for four global

maps of ТЕС in cases of simultaneous passages of

satellites.

Third International Conference on Telecommunications and Remote Sensing

It is seen that values of K(PL) decrease with

decreasing TEC(obs). Relation K(PL) =1 specifies

the full conformity of model ТЕС and TEC(obs). It

is obvious that it is possible to select the ТЕС value

to which relation K(PL) =1 corresponds. There are

some cases with the negative value K(PL) =-0.001.

They can be identified by misfit of orange and red

circles on Fig. 13. It means that the N(h)-profile,

providing TEC(obs), is not found. It occurs when

ТЕС for N(h)-profiles s1 exceed TEC(obs).

The N(h)-profiles corresponding to these ТЕС

are given on Fig. 13.

Figure 13: Topside and plasmaspheric parts of N(h)-

profiles corresponding various global maps of TEC.

4 CONCLUSIONS

In recent years, the TEC has become an important

parameter to describe the state of the propagation

medium. However, its use encounters certain

difficulties associated with a variety of values. This

diversity leads to ambiguity of parameters

determined through TEC and models. This paper

makes the following recommendations. 1. The best

method of TEC modeling is the EOC. 2. To

determine foF2, it is possible to use τ, which is a

good calibration factor, including τ(NGM). 3. Using

plasma frequencies measured on satellites allows us

to construct N(h)-profiles, closer to the real part in

the topside part. 4. For full proximity of N (h)-

profiles with experimental TEC(obs), we must enter

the factor K(PL), modifying plasmaspheric part of

profile. Its value depends on the choice of TEC(obs).

In this regard, we can focus on IGS.

Choice of the Definition Method for the Total Electron Content to Describe the Conditions in the Ionosphere

ACKNOWLEDGEMENTS

Author thanks organizations and scientists who are

developing the IRI model, providing data of SPIDR,

JPL, CODE, UPC, ESA, and Dr M. Hoque for

detailed comments on the NGM model.

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Choice of the Definition Method for the Total Electron Content to Describe the Conditions in the Ionosphere