Available online at www.sciencedirect.com

www.elsevier.com/locate/asr

Advances in Space Research 52 (2013) 801–809

Time series modeling and analysis of trends of dailyaveraged ionospheric total electron content

Shuhui Li ⇑, Junhuan Peng 1, Weichao Xu 2, Kun Qin 3

School of Land Science and Technology, China University of Geosciences (Beijing), 29 Xueyuan Road, Haidian District, Beijing 100083, China

Received 27 March 2013; received in revised form 21 May 2013; accepted 22 May 2013Available online 5 June 2013

Abstract

A 10.7 cm solar radio flux F10.7, geomagnetic planetary equivalent amplitude (Ap index), and period variations were considered inthis paper to construct a linear model for daily averaged ionospheric total electron content (TEC). The correlation coefficient of the mod-eled results and International GNSS Service (IGS) observables was approximately 0.97, which implied that the model could accuratelyreflect the realistic variation characteristics of the daily averaged TEC. The influences of the different factors on TEC and its character-istics at different latitudes were examined with this model. Results show that solar activity, annual and semiannual cycles are the threemost important factors that affect daily averaged TEC. Solar activity is the primary determinant of TEC during periods with high solaractivity, whereas periodic factors primarily contribute to TEC during periods with minimum solar activity. The extent of the influences ofthe different factors on TEC exhibits obvious differences at varying latitudes. The magnitude of the semiannual variation becomes lesssignificant with the increase in latitude. Furthermore, a geomagnetic storm causes an increase in TEC at low latitudes and a decrease athigh latitudes.� 2013 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Time series; Ionosphere; TEC; Solar F10.7 index; Geomagnetic Ap index

1. Introduction

The ionosphere is an important part of near-Earthspace. The ionosphere is affected by solar activity, theSun–Earth relative position, and the interaction amongthe ionosphere, magnetosphere and thermosphere. Acous-tic-gravity waves, geomagnetic storms, solar eclipses, andsolar radio bursts also cause disturbances to the iono-sphere. Therefore, both long-term climatological variationsand short-term diurnal changes occur in the ionosphere.The investigation of the inherent characteristics and rules

0273-1177/$36.00 � 2013 COSPAR. Published by Elsevier Ltd. All rights rese

http://dx.doi.org/10.1016/j.asr.2013.05.032

⇑ Corresponding author. Tel./fax: +86 10 823 218 07.E-mail addresses: li.shuhui@163.com (S. Li), pengjunhuan@163.com

(J. Peng), xuweichao928@163.com (W. Xu), sdau_qinkun@163.com(K. Qin).

1 Tel.: +86 10 823 223 71; fax: +86 10 823 218 07.2 Tel.: +86 10 823 236 34; fax: +86 10 823 218 07.3 Tel.: +86 10 823 240 28; tel./fax: +86 10 823 218 07.

of variations in ionospheric TEC is important to the fieldof ionospheric physics and the correction of electromag-netic wave refraction.

The ionosphere has been investigated by many research-ers with the purpose of analyzing its short and long-termcharacteristics to establish an empirical model (Klobuchar,1987; Daniell et al., 1995; Minow, 2004; Strangeways et al.,2009; Chauhan and Singh, 2010). Many researchers havealso investigated the factors that influence TEC to developan ionospheric model based on data gathered in the past.For example, Gulyaeva (1999) utilized a triangle functionmethod that considered three factors, namely, local time,month and geomagnetic latitude, to construct a regionalempirical analysis model. Stankov and Jakowski (2006)analyzed long-term data series to establish the averageresponse of TEC to geomagnetic activity conditions overEurope and proposed a model to describe the TEC relativedeviations from the corresponding monthly medians. Iva-nov et al. (2011) utilized a natural orthogonal function that

rved.

802 S. Li et al. / Advances in Space Research 52 (2013) 801–809

considered several factors, including day of the year,month, geographic coordinate and the solar F10.7 index,to establish a global TEC empirical model. Combiningtrend, periodical and stochastic components, Erdoganand Arslan (2009) modeled the vertical TEC (VTEC) datafor different station satellite pairs, and the fitted modelswere used for the 5 min ahead prediction of the VTECobservations. Chen et al. (2011) constructed a time seriesmodel for ionosphere data released by IGS, in which thetime series of TEC was decomposed to trend, periodicaland random terms. The aforementioned models canaddress the variations in the ionospheric parameters; how-ever, the dependence of the ionospheric characteristics onspecific factors remains a subject for investigation.

Numerous researchers have utilized linear time seriesmodels to quantitatively determine the impact of differentfactors on ionospheric TEC climatological variations. For-bes et al. (2000) adopted multiple linear regression analysisand considered annual and semiannual terms as well as thesolar F10.7 index and its 81-day mean value as influencingfactors to construct an empirical model. The constructedmodel is useful in studying the effects of solar activityand season variability on F-region peak plasma density.Afraimovich et al. (2006) introduced a new parameternamed global electron content (GEC) and constructed asimple linear regression model between GEC and solarF10.7 index. She et al. (2008) adopted the solar F10.7 indexand periodic oscillation of TEC to establish a linear modelfor GEC. The resulting model had a correlation coefficientof 0.965 with the observations. Afraimovich et al. (2008)have found that the GEC is characterized by strong sea-sonal variations with maximum relative amplitude of about10% during the rising and falling parts of the solar activityand up to 30% during the period of maximum. Yu et al.(2009) studied the linear model of global ionosphericTEC standard deviation covariance with the F10.7 index,geomagnetic Ap index, and periodic change. Yu et al.’sresults proved that solar activity and season variationsare dominant factors. Lean et al. (2011) constructed a lin-ear model to study global ionospheric TEC by consideringfour factors, namely, solar extreme ultraviolet (EUV)(0 nm–103 nm) flux, the geomagnetic Ap index, periodoscillations, and a secular trend. The model yielded a cor-relation coefficient of 0.993 with the observations. Theimpact of different factors on daily averaged TEC orGEC has also been studied in detail with these linear mod-els. However, minimal attention has been provided to thecharacteristics of the different factors at various latitudes.

Data from Global Ionospheric Maps (GIMs) providedby IGS were utilized in this study to calculate daily aver-aged TEC at specific grid points. A linear empirical modelwas constructed. The model is a function of several vari-ables such as solar activity, geomagnetic activity, periodicvariation and secular trend. The influences of thesedifferent variables on daily averaged TEC at different lati-tudes were successfully investigated with the constructedmodel.

2. Method

Based on the method utilized by Lean et al. (2011), thetime series of daily averaged TEC at a certain grid pointwas decomposed into four parts, namely, solar activitycomponent, magnetic activity component, periodic compo-nent, and secular trend. The main factors considered in themodel are solar F10.7 index F 10:7 and its 81-day smoothedvalue F 10:7 81, geomagnetic Ap index Ap, and period T . Theionospheric daily averaged TEC time series model isexpressed as

TECðdÞ ¼ TECperiodðdÞ þ TECsolarðdÞþ TECgeomagnaticðdÞ þ TECtrendðdÞ þ TEC0 ð1Þ

where TECðdÞ is the ionospheric daily averaged TEC valueand d specifies its number; TECperoidðdÞ is the periodic com-ponent; TECsolarðdÞ is the solar activity component;TECtrendðdÞ is the secular trend; and TEC0 is a constant.

The annual cycle (365.25 days) was selected as the fun-damental period to accurately represent the impact of var-iation cycles on ionospheric TEC. Multiples and fractionsof the annual cycle, such as annual, biennial, triennial,semiannual, 1/3, 1/4, and 1/5 year cycles, were utilized ascandidates. The 27-day periodicity caused by solar rotationwas also considered to be a candidate cycle. Given that theith cycle is T i, the influence of the cycle (P i) can beexpressed as a harmonic expansion.

P iðdÞ ¼ ai � sinð2pd=T iÞ þ bi � cosð2pd=T iÞ ð2Þ

where ai and bi are coefficients.The comprehensive influ-ence of periodic variation and solar activity was also con-sidered in the model because the amplitudes of periodicvariation at different solar activities are different. If M maincycles exist in daily averaged TEC, the periodic componentcan be written as

TECperoidðdÞ ¼XM

i¼1

½ai � sinð2pd=T iÞ þ bi � cosð2pd=T iÞ�

þXM

i¼1

½ci � inð2pd=T iÞ þ di

� cosð2pd=T iÞ� � F 10:7 81ðdÞ ð3Þ

where ai, bi, ci, and di are all coefficients. The number of thecoefficients of the periodic component is 4M . With the pre-vious day’s solar F10.7 index and its 81-day smoothed va-lue F 10:7 81, the solar activity component is defined as

TECsolarðdÞ ¼ f1 � F 10:7ðd � 1Þ þ f2 � F 10:7 81ðd � 1Þ ð4Þ

where f1 and f2 are coefficients. The geomagnetic activitycomponent of the daily averaged TEC time series is definedas

TECgeomaneticðdÞ ¼ f3 � Apðd � 1Þ þ f4 � Apðd � 2Þ þ f5

� Apðd � 3Þ ð5Þ

S. Li et al. / Advances in Space Research 52 (2013) 801–809 803

where Apðd � 1Þ, Apðd � 2Þ, and Apðd � 3Þ are the geomag-netic Ap indices a day, two days and three days before,respectively, and f3, f4, and f5 are coefficients. The seculartrend part of the model is defined as

TECtrendðdÞ ¼ f6 � d ð6Þwhere f6 is the coefficient of the linear trend. In summary, atotal of 4M þ 7 model coefficients exist when the constantTEC0 is considered. Based on the daily averaged TEC val-ues at a certain grid point from the IGS GIMs, the modelparameters can be calculated by least squares method.

The significance test for the explaining variables was uti-lized to select the main cycles of the time series. The statis-tics is presented as follows:

T ¼ b̂i � bi

Sb̂i

� tðn� k � 1Þ ð7Þ

where b̂i is the estimated value of coefficient bi, which is theexplaining variable in the linear model, and Sb̂i

is the stan-dard deviation of b̂i. Given the significant level a, the crit-ical value is then expressed as ta=2ðn� k � 1Þ. Therefore, ifjT j > ta=2ðn� k � 1Þ, the corresponding explaining variablecan be included in the model.

3. Result and discussion

3.1. Modeled results at 40�N, 115�E

The data at the grid point with the geographic coordi-nate 40�N, 115�E were analyzed as an example. A totalof 5274 daily averaged TEC values were obtained for thegrid point based on two-hour resolution TEC data pro-vided by IGS from day 087 of the year 1998 to day 247of the year 2012. The initial main cycles were selected byperforming a significance test for the explaining variablesat 95% confidence level. The final main cycles that wereincluded in the model are annual, semiannual, 1/3 years,and 1/4 years. The significance test statistics T of eachexplaining variable and the critical value are shown in

0

10

20

30

40

50

60

70

T

f1 f2 f3 f4 f5 f6 b1c1 d1a1 a1

Fig. 1. Significance test statistics T of each explaining variable in the model.component, and suffixes 1, 1/2, 1/3, and 1/4 represent annual, semiannual, 1/3 ycomponent coefficients; f3, f4, and f5 are the geomagnetic activity component

Fig. 1. The figure indicates that the most significant factorsare solar activity and the cosine coefficients of the annualand semiannual cycles.

Each of the components was removed one by one tocompare the influences of the different factors in a detailedmanner. The root-mean-square (RMS) of the fitted modelwith varying factors are shown in Fig. 2. The RMS of themodel, which includes all the factors mentioned above, is2.3928 TECU (1 TECU = 1016 electrons/m2). When the1/4 years cycle is removed, RMS becomes 2.4273 TECU.RMS becomes 2.4969 TECU when the 1/3 years cycle isalso removed. RMS then becomes 3.5842 TECU whensemiannual period is removed. When the solar activitycomponent is removed, RMS becomes 8.1512 TECU.Analysis of the data in Fig. 2 indicates that the fitting errorincreases when the model excludes some or all the factors.

The least squares method was adopted to construct thedaily averaged TEC time series model based on the 5274data at 40�N, 115�E during the study period. The compar-ison between the modeled value and observables is shownin Fig. 3. The modeled result matches the observables verywell, acquiring a correlation coefficient of 0.97. Fig. 3 alsoshows the post-fit residuals in the time series model. Theresiduals are obviously different in years with high andlow solar activity. The residuals evidently exhibit a largefluctuation at high solar activities, reaching �16.44 TECUduring maximum solar activity. Fig. 4 shows the histogramof the residuals. The statistical error clearly exhibits a nor-mal distribution. By defining the observables and modeledresults as the X and Y axis, respectively, a scatter diagramcan demonstrate how they correlate (Fig. 5). We thereforeconclude that the time series model can accurately repre-sent the daily averaged TEC.

According to Eq. (3), every component of the time seriescan be calculated and then utilized to represent the influ-ences of cycle variations, solar activity, geomagnetic activ-ity and secular trend. The components of the time series at40�N, 115�E are shown in Fig. 6. The figure presents thecontributions of the different factors to ionospheric daily

/2b1/2 c1/2 d1/2 a1/3 b1/3

c1/3d1/3 a1/4 b1/4 c1/4

d1/4

The critical value is 1.9604. a, b, c, and d are coefficients of the periodicears, and 1/4 years periodicity, respectively. f1, and f2 are the solar activity

coefficients; and f6 is the coefficient of the linear trend.

all 1/4 years removed semiannual removed0

2

4

6

8

10

TEC

U

magnetic effectremoved

annualremoved

solar activityremoved

1/3 yearsremoved

Fig. 2. Comparison of the RMS of the models with different factors.

0 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012-20

-10

0

10

20

30

40

50

60

70

Time (Years)

TEC

dai

ly m

ean

valu

es /T

ECU

post fit residuesIGS observablessresults of the model

Fig. 3. Daily averaged TEC and the fitted results from time series model.

-20 -10 0 10 200

100

200

300

400

500

600

700

Post fit residues /TECU

Cou

nts

Fig. 4. Histogram of the post-fit residuals of daily averaged TEC.0 10 20 30 40 50 60

0

10

20

30

40

50

60

Res

ults

of m

odel

/TEC

U

Daily averaged TEC /TECU

Fig. 5. Scatter diagram of the observed and modeled daily averaged TEC.

804 S. Li et al. / Advances in Space Research 52 (2013) 801–809

averaged TEC. The constant value of 6.55 TECU in themodeled results increases by 1.51 TECU during the 14-yearperiod. The time series are mainly determined by solaractivity and are proportional to the F10.7 index. The solaractivity component reflects the primary climatological

variation characteristic of daily averaged TEC becausethe existence of the ionosphere depends on ultraviolet

0 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012-20

-10

0

10

20

30

40

Time (Years)

TEC

Uperiod conponentsgeomagnetic activity componenttrend and constant solar activity component

Fig. 6. Components of the daily averaged TEC time series model.

S. Li et al. / Advances in Space Research 52 (2013) 801–809 805

radiation from the sun. The solar component reached 38.45TECU in 2002. However, in 2009 when solar activity wasquite low, the minimum value was reached (0 TECU).The most prominent factor of daily averaged TEC at thistime was periodic variation.

The influence of periodic variation is a combination ofthe simultaneous impact of four types of cycles, namely,annual, semiannual, 1/3 years, and 1/4 years. The ampli-tude of periodic variation varies remarkably at differentlevels of solar activity. Fig. 7 indicates that annual andsemiannual cycles are the main factors of periodic variationin daily averaged TEC.

0 1999 2000 2001 2002 2003 2004 2005-15

-10

-5

0

5

10

15

Time

TEC

U

Fig. 7. Different parts of the perio

Fig. 6 shows that the influence of the geomagnetic Ap

index on TEC is mostly close to 0 TECU and becomes neg-ative at 40�N, 115�E. However, highly significant values ofgeomagnetic activity component appear sporadically. Dur-ing a strong magnetic storm in October 2003, the value ofthe geomagnetic activity component reached its maximumat �10.88 TECU. In a relatively detailed manner, Fig. 8shows the modeled results during geomagnetic storm inApril, 2002 and October, 2003. The time series modelincluding magnetic activity component can reflect thechange with the time point and variation characteristic spe-cifically and clearly, although the amplitudes are not the

2006 2007 2008 2009 2010 2011 2012

(Years)

all periodic componentsannual and semiannual periodic componentselse periodic components

dic components of the model.

4.1 4.6 4.11 4.16 4.21 4.26 4.300

200

400

4.1 4.6 4.11 4.16 4.21 4.26 4.3030

40

50

60

TEC

U

4.1 4.6 4.11 4.16 4.21 4.26 4.30-10

-5

0

Date in 2002

TEC

U

10.15 10.20 10.25 10.30 11.4 11.9 11.130

200

400

10.15 10.20 10.25 10.30 11.4 11.9 11.1310

20

30

40

TEC

U

10.15 10.20 10.25 10.30 11.4 11.9 11.13-15

-10

-5

0

Date in 2003

TEC

U

geomagnetic activity component geomagnetic activity component

27 days smoothed observed modeled27 days smoothed observed modeled

solar F10.7 index geomagnetic Ap index solar F10.7 index geomagnetic Ap index

(e)

(f)(c)

(d)(a)

(b)

Fig. 8. The impact on modeled daily TEC average value at 40�N, 115�E during the storms in April, 2002 and October, 2003. (a) Solar F10.7 index andgeomagnetic Ap index; (b) 27 days smoothed, observed and modeled TEC daily averaged value; (c) Geomagnetic activity component estimated by themodel in April, 2002 and (d)–(f) are the data from October 15th–November 13th, 2003.

806 S. Li et al. / Advances in Space Research 52 (2013) 801–809

same. The RMS between observed and modeled daily aver-aged TEC for the two geomagnetic storms are 3.1157 and4.4770 TECU respectively.

Researchers consider solar EUV irradiance the decidingfactor for the ionization degree of the ionosphere. Leanet al. (2011) revealed that the correlation coefficient of solarEUV (0 nm–103 nm) radiation flux and global averagedTEC is 0.90. The modeled results yield a correlation coeffi-cient of 0.99 with the observables when EUV radiation fluxand its 81-day smoothed value w utilized. However, EUVobservations are not consecutive and should be analyzedfurther. Therefore, we adopted the solar F10.7 index andits 81-day smoothed value with a correlation coefficientof 0.86 at 40�N, 115�E. The modeled results yielded a cor-relation coefficient of 0.97 with the observables.

3.2. Variation in the characteristics of daily averaged TEC atdifferent latitudes

We selected several grid points in meridian 115�E. Thelatitudes of the grid points vary from 80�S to 80�N. Thedifference in latitude between two adjacent grid points is20�. The data of years 2002 and 2009 were analyzed. Thetwo years exhibit different levels of solar activity.

Fig. 9 shows the influence of solar activity on daily aver-aged TEC at different latitudes. The amplitude in 2002 ismuch larger than that in 2009 because of the significant dif-ference in solar activity. However, the characteristics of thetwo years at different latitudes are similar. Fig. 9 showsthat the maximum influence of solar activity occurs at thegrid point with the latitude of 20�N. The daily averagedvalue of TEC is greater at the aforementioned grid pointthan at the other grid points because the former is in theequatorial anomaly area, resulting in the fluctuation. Theinfluence of solar activity decreases as latitude increases.

The component related to the solar F10.7 index and its81-day smoothed value declines rapidly with the increasein latitude, the variation characteristics exhibited in 2002and 2009 are consistent. The Sun-Earth relative positionchanges at different latitudes. When a grid pointapproaches a high latitude, the variations in TEC becomeinactive. The variation in daily average TEC is even at lat-itude 80�N. We therefore conclude that TEC variation isless sensitive to daily solar activity changes in polarregions.

Fig. 10 shows the impact of annual variation on dailyaveraged TEC at different latitudes. The annual periodcomponents in 2002 are rather small compared with thesolar activity components shown in Fig. 9(a), particularlyat grid points with latitudes of 20�N and 0� where the solaractivity components are higher than 50 TECU. However,the influence of annual variation in 2009 is comparablygreater than that of solar activity. The phases of annualvariation in both years at grid points in the same hemi-sphere are much closer to each other. Slight differencescan be observed in the amplitudes at different latitudes;however, these differences are negligible.

Fig. 11 shows that the difference of the semiannual per-iod component at different latitudes is remarkable. Theamplitudes of semiannual variations at 20�N and 0� arealmost equal and are evidently greater than those at highlatitudes. Semiannual variation declines with the increasein latitude. The main reason for this is the passing of thesun through the equator twice a year, which produces aremarkable semiannual variation in the equatorial iono-sphere, causing an obvious annual change in the iono-sphere at mid and high latitudes.

Figs. 9–11 indicate that the different components exhibitconsistent characteristics in both years. Only the compo-nent related to solar activity cannot coincide with the

0 100 200 3000

10

20

30

40

50

60

70

80

Days of year in 2002

TEC

U

0 100 200 3000

1

2

3

4

5

6

7

Days of year in 2009

TEC

U

(80S,115E) (60S 115E) (40S,115E) (20S,115E) (0,115E) (20N,115E) (40N,115E) (60N,115E) (80N,115E)

(a) 2002, high activity year (b) 2009, low activity year

Fig. 9. Influences of solar activity at different latitudes. (a) Year of high solar activity (2002) and (b) year of low solar activity (2009).

0 100 200 300-10

-5

0

5

10

15

Days of year in 2002

TEC

U

0 100 200 300-5

-4

-3

-2

-1

0

1

2

3

4

5

Days of year in 2009

TEC

U

(80S,115E) (60S (40S,115E) (20S,115E) (0,115E) (20N,115E) (40N,115E) (60N,115E) (80N,115E)

(b) 2009, low activity year(a) 2002, high activity year

Fig. 10. Impact of annual variation on daily averaged TEC at different latitudes. (a) Year of high solar activity (2002) and (b) year of low solar activity(2009).

S. Li et al. / Advances in Space Research 52 (2013) 801–809 807

morphology of the variation in daily averaged TEC. There-fore, the period variations are essential. The differences indaily averaged TEC for the grid points at the polar areaare mainly caused by the solar activity component. The dif-ferences in daily averaged TEC for the grid points at midand high latitudes are primarily caused by periodicvariations.

Fig. 12 shows the influence of geomagnetic activity. Thefigure indicates that magnetic activity has different effectson ionospheric TEC at different latitudes. The values at20�N and at the equator are positive and almost equal,whereas the values at other latitudes are almost negative.Previous research results have indicated that the influence

of a magnetic storm on the ionosphere depends on geo-graphic location, local time, and season and that iono-spheric TEC above low-latitude areas usually increasessubstantially during the initial phase followed by adecrease depending on latitude and season (Araujo-Pra-dere et al., 2006; Stankov et al., 2010). The strongestchanges in the ionospheric electron concentration areobserved during geomagnetic storm-time periods. Also,ionospheric perturbations due to geomagnetic storms arecharacterized by strong horizontal gradients and rapidchanges of the ionization that can induce spatial gradientsof TEC substantially larger than during “quiet” times(Jakowski et al., 2008). The results of our linear model,

0 100 200 300-20

-15

-10

-5

0

5

10

15

20

Days of year in 2002

TEC

U

0 100 200 300-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

Days of year in 2009

TEC

U(80S,115E) (60S (40S,115E) (20S,115E) (0,115E) (20N,115E) (40N,115E) (60N,115E) (80N,115E)

(b) 2009, low activity year(a) 2002, high activity year

Fig. 11. Impact of semiannual variation on daily averaged TEC at different latitudes. (a) Year of high solar activity (2002) and (b) year of low solaractivity (2009).

0 100 200 300-10

-5

0

5

Day of year in 2002

TEC

U

0 50 100 150 200 250 300 350-2

-1

0

1

Day of year in 2009

TEC

U

0 50 100 150 200 250 300 350-6

-4

-2

0

2

Day of year in 2002

TEC

U

0 100 200 300-2

-1.5

-1

-0.5

0

0.5

Day of year in 2009

TEC

U

(0,115E)(20N,115E)(40N,115E)(60N,115E)(80N,115E)

(80S,115E)(60S,115E)(40S,115E)(20S,115E)

(a) 2002, high activity year,0~80N

(b) 2002, high activity year,20S~80S

(c) 2009, low activity year,0~80N

(d) 2009, low activity year,20S~80S

Fig. 12. Components of geomagnetic activity at different latitudes. (a) Year of high solar activity (2002), form 0 to 80�N. (b) Year of high solar activity(2002), form 20�S to 80�S. (c) Year of low solar activity (2009), form 0 to 80�N. (d) Year of low solar activity (2009), form 20�S to 80�S.

808 S. Li et al. / Advances in Space Research 52 (2013) 801–809

which indicate that the geomagnetic activity component ismostly close to 0, are consistent with the results of previousresearch. During a magnetic storm, observables changeobviously but recover afterward. The same occurrencewas observed in the modeled result. In Lean et al.’s study(2011), global daily averaged TEC was considered todecline during a magnetic storm. Although the geomag-netic activity component of the model in the present studyis positive at low latitudes, the increase is rather small.However, the decreases at mid and high latitudes areremarkably large. Therefore, our result matches the resultobtained by Lean et al. (2011).

4. Conclusion

The study of the rules and characteristics of temporaland spatial variation in ionospheric TEC is important tothe field of ionospheric physics and its application to com-munication and navigation. A linear model for IGS dailyaveraged TEC time series at grid points with different lati-tudes was analyzed in this study for approximately14 years. The variations in daily averaged TEC are repre-sented by secular trend, periodic variation, and the influ-ences of both solar and geomagnetic activity. Thefollowing conclusions can be drawn from the present study.

S. Li et al. / Advances in Space Research 52 (2013) 801–809 809

(i) Analysis of the different components shows that themain factors that influence ionospheric daily aver-aged TEC are solar activity, annual cycle, and semi-annual cycle.

(ii) The three components above contribute differently toTEC value in years with different solar activity levels.At high solar activity, the solar activity itself is theprimary determinant of TEC. The periodic factorscontribute primarily to the changes in TEC at mini-mum solar activity.

(iii) The characteristics of annual variation at grid pointsin the same hemisphere are similar.

(iv) The amplitudes of semiannual variations at 20�N andat the equator are obviously higher than those at highlatitudes.

(v) The effects of magnetic activity at 20�N and at theequator are positive, whereas the values at other lat-itudes are almost negative.

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (Grant Numbers 41104025 and41074009), and the Fundamental Research Funds for theCentral Universities (Grant Numbers 2652012116 and2652012119). The authors are also grateful for the com-ments by the editor and two reviewers, which helped usto improve our manuscript significantly.

References

Afraimovich, E.L., Astafyeva, E.I., Zhivetiev, I.V. Solar activity andglobal electron content. Dokl. Earth Sci. 409A (6), 921–924, 2006.

Afraimovich, E.L., Astafyeva, E.I., Zhivetiev, I.V., et al. Global electroncontent: a new conception to track solar activity. Ann. Geophys. 26,335–344, 2008.

Araujo-Pradere, E.A., Fuller-Rowell, T.J., Spencer, P.S.J. Consistentfeatures of TEC changes during ionospheric storms. J. Atmos. Sol.Terr. Phys. 68, 1834–1842, 2006.

Chauhan, V., Singh, O.P. A morphological study of GPS-TEC data atAgra and their comparison with the IRI model. Adv. Space Res. 46,280–290, 2010.

Chen, P., Yao, Y., Wu, H. TEC prediction of ionosphere based on timeseries analysis. Geom. Inf. Sci. Wuhan Univ. 36 (3), 267–270 (inChinese), 2011.

Daniell Jr., R.E., Brown, L.D., Anderson, D.N., et al. Parameterizedionospheric model: a global ionospheric parameterization based onfirst principles modes. Radio Sci. 30 (5), 1499–1510, 1995.

Erdogan, H., Arslan, N. Identifcation of vertical total electron content bytime series analysis. Digital Signal Process. 19, 740–749, 2009.

Forbes, J.M., Palo, S.E., Zhang, X. Variability of the ionosphere. J.Atmos. Sol. Terr. Phys. 62, 685–693, 2000.

Gulyaeva, T.L. Regional analytical model of ionospheric total electroncontent: monthly mean and standard deviation. Radio Sci. 34 (6),1507–1512, 1999.

Ivanov, V.B., Gefan, G.D., Gorbachev, O.A. Global empirical modelingof the total electron content of the ionosphere for satellite radionavigation systems. J. Atmos. Sol. Terr. Phys. 73, 1703–1707, 2011.

Jakowski, N., Mielich, J., Borries, C., et al. Large scale ionosphericgradients over Europe observed in October 2003. J. Atmos. Sol. Terr.Phys. 70 (15), 1894–1903, 2008.

Klobuchar, J.A. Ionospheric time delay algorithm for single frequencyGPS users. IEEE Trans. Aerosp. Electron. Syst. 23, 325–331, 1987.

Lean, J.L., Meier, R.R., Picone, J.M., et al. Ionospheric total electroncontent: global and hemispheric climatology. J. Geophys. Res. 116,A10318, http://dx.doi.org/10.1029/2011JA016567, 2011.

Minow, J.I. Development and implementation of an empirical ionospherevariability model. Adv. Space Res. 33, 887–892, 2004.

She, C., Wan, W., Xu, G. Climatological analysis and modeling of theionospheric global electron content. Chin. Sci. Bull. 53 (2), 282–288,2008.

Stankov, S.M., Jakowski, N. Indexing the local ionospheric response tomagnetic activity by using total electron content measurements. ActaGeod. Geophys. Hung. 41 (1), 1–15, 2006.

Stankov, S.M., Stegen, K., Warnant, R. Seasonal variations of storm-timeTEC at European middle latitudes. Adv. Space Res. 46 (10), 1318–1325, 2010.

Strangeways, H.J., Kutiev, I., Cander, L.R., et al. Near-Earth spaceplasma modelling and forecasting. Ann. Geophys. 52 (3–4), 255–271,2009.

Yu, Y., Wan, W., Liu, L., et al. A global ionospheric TEC perturbationindex. Chin. J. Geophys. 52 (9), 2189–2194 (in Chinese), 2009.