Performance evaluation of linear time-series ionospheric Total Electron Content model over low latitude Indian GPS stations

Accepted Manuscript Performance evaluation of Linear Time-Series Ionospheric Total Electron Content Model over Low latitude Indian GPS Stations J.R.K. Kumar Dabbakuti, D. Venkata Ratnam PII: DOI: Reference:

S0273-1177(17)30453-2 http://dx.doi.org/10.1016/j.asr.2017.06.027 JASR 13281

To appear in:

Advances in Space Research

Received Date: Revised Date: Accepted Date:

20 March 2017 7 June 2017 13 June 2017

Please cite this article as: Kumar Dabbakuti, J.R.K., Venkata Ratnam, D., Performance evaluation of Linear TimeSeries Ionospheric Total Electron Content Model over Low latitude Indian GPS Stations, Advances in Space Research (2017), doi: http://dx.doi.org/10.1016/j.asr.2017.06.027

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Performance evaluation of Linear Time-Series Ionospheric Total Electron Content Model over Low latitude Indian GPS Stations J R K Kumar Dabbakuti and D. Venkata Ratnam* Department of ECE, KLEF, K L University, Vaddeswaram, Guntur, 522502, Andhra Pradesh, India

Abstract Precise modeling of the ionospheric Total Electron Content (TEC) is a critical aspect of Positioning, Navigation, and Timing (PNT) services intended for the Global Navigation Satellite Systems (GNSS) applications as well as Earth Observation System (EOS), satellite communication, and space weather forecasting applications. In this paper, linear time series modeling has been carried out on ionospheric TEC at two different locations at Koneru Lakshmaiah University (KLU), Guntur (geographic 16.44° N, 80.62° E; geomagnetic 7.55° N) and Bangalore (geographic 12.97° N, 77.59° E; geomagnetic 4.53° N) at the northern lowlatitude region, for the year 2013 in the 24th solar cycle. The impact of the solar and geomagnetic activity on periodic oscillations of TEC has been investigated. Results confirm that the correlation coefficient of the estimated TEC from the linear model TEC and the observed GPS-TEC is around 93%. Solar activity is the key component that influences ionospheric daily averaged TEC while periodic component reveals the seasonal dependency of TEC. Furthermore, it is observed that the influence of geomagnetic activity component on TEC is different at both the latitudes. The accuracy of the model has been assessed by comparing the International Reference Ionosphere (IRI) 2012 model TEC and TEC measurements. Moreover, the absence of winter anomaly is remarkable, as determined by the Root Mean Square Error (RMSE) between the linear model TEC and GPS-TEC. On the contrary, the IRI2012 model TEC evidently failed to predict the absence of winter anomaly in the Equatorial Ionization Anomaly (EIA) crest region. The outcome of this work will be useful for improving the ionospheric now-casting models under various geophysical conditions.

Keywords: GNSS, TEC, Modeling, IRI, India *

Corresponding author

E-mail addresses [email protected]; *[email protected]

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1. Introduction Investigation of the intrinsic characteristics of ionospheric perturbations is important for understanding ionospheric variability. Numerous researchers have proposed ionospheric models with respect to solar, geomagnetic and periodic components that influence ionospheric TEC climatological variations(Forbes et al., 2000; Afraimovich et al., 2006; She et al., 2008; Yu et al., 2009; Lean et al., 2011; Li et al., 2013). Forbes et al. (2000) constructed an empirical ionospheric model by considering the solar F10.7 index and its 81day running average F10.7 index value apart from periodic components. It was demonstrated that solar activity and seasonal component are prime contributors to F-region ionospheric variability. Afraimovich et al. (2006) proposed a new global TEC model based on linear regression method and demonstrated the relation between global TEC and solar activity component F10.7 index. It was reported that Global Electron Content (GEC) and F10.7 series regression are well approximated by linear dependence. Global TEC models do not consider local characteristics and seasonal variation. She et al. (2008) appended the periodic oscillation component to the linear GTEC global model to describe seasonal dependence. The resultant model has ensured better performance than the model proposed by Afraimovich et al. (2006). In this work, the geomagnetic component has not been considered in the Linear TEC model. In recent years, Araujo-Pradere et al. (2005) have reported that ionospheric variability increases with geomagnetic activity at all latitudes. Yu et al. (2009) have studied the ionospheric TEC climatological variations with a new perturbation index (σDGE) by considering the solar F10.7 index and geomagnetic Ap index. It was confirmed that the global perturbation index (σDGE) correlated well with F10.7 and Ap indices. Lean et al. (2011) proposed a linear time series TEC model using the Global Ionospheric Maps (GIM) data. Li et al. (2013) have also investigated the different factors that influence TEC climatological variations at different latitudes using GIM data. The reported linear TEC models were not evaluated with the standard ionospheric model International Reference Ionosphere (IRI).The described methods represent ionospheric TEC responses by considering the GIM –TEC. The GIM model TEC may not be adequate for characterizing low-latitude ionospheric variations (Jee et al., 2010). In the last two decades, several researchers have investigated GPS-based ionospheric TEC variations and compared with the IRI model estimations over equatorial and low latitude region across the Indian (Bagiya et al., 2009; Kumar et al., 2012; Sharma et al., 2012; Dashora and Suresh, 2015). These studies complement climatological improvements in the global 2

empirical International Reference Ionosphere (IRI) model. Further, numerous researchers have

been investigated GPS-based ionospheric TEC variations and compared with the IRI model estimations over equatorial and low latitude region across African as well as American longitudes (Akala et al., 2013; Adeniyi., 2014; Okoh et al., 2014; Akala et al., 2015; Tariku et al., 2015). The authors have addressed the limitations of IRI model predictions during the early morning and post-sunset hours during low solar activity (LSA) and high solar activity (HSA). Most of these papers describe that TEC analysis is carried out either with Global ionospheric TEC models or by ground-based Global Navigation Satellite Systems (GNSS) TEC observations. Modeling of TEC response over low-latitude regions is necessary. In this paper, an attempt has been made to represent climatological variations over low-latitude regions based on the linear time series TEC model, considering low northern geographic latitudes (< 23 degrees). The aim of this paper is to investigate low-latitude ionospheric TEC variations with GPS-TEC observations by considering three factors, namely, solar activity(F10.7p), geomagnetic activity (Ap), and periodic components at three different frequencies semiannual oscillation (SAO), annual oscillation (AO) and terannual oscillation (TO) during the HSA period for the year 2013.

2. Methodology Modeling and Analysis of Ionospheric GPS-TEC characteristics for the year 2013 was considered at two low-latitude GNSS stations in India, located at KLU-Guntur (geographic 16.44° N, 80.62° E; geomagnetic 7.55° N) and Bangalore (geographic 12.97° N, 77.59° E; geomagnetic 4.53° N), respectively. Novatel GNSS receiver at KLU-Guntur with a sampling rate of 1 sec. GPS data was converted into GPS-TEC and scintillation data observations with l minute sampling interval acquired GPS-TEC data. IGS stations (Bangalore) recorded the observations for every 30 s (http://sopac.ucsd.edu). The slant TEC data was converted into vertical TEC (vTEC) using GPS satellite elevation and azimuthal angles and receiver coordinates. The mean of vTEC values of all visible satellites of every epoch (5 minutes interval) was calculated. The hourly mean vTEC values were derived for each day. The daily averaged vTEC values were calculated by considering the hourly mean vTEC observations. Linear TEC time series model studied in this work has still used the same concept of Lean et al. (2011) so as to analyze the daily averaged vTEC. The major factors, namely, solar EUV irradiance ( F10.7 p ), geomagnetic activity (Ap), and periodic oscillations (annual, semiannual

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and terannual oscillations) are considered in the model. Since the units of solar activity index and geomagnetic index differ from the unit of vTEC values, therefore, the coefficients of each parameter in the proposed linear model are normalized as unitless values (Yenen et al., 2015). The daily averaged vTEC values, solar activity index (F10.7) and geomagnetic index (Ap) were normalized as follows. NvTEC(d )  vTEC(d ) max(vTEC(d ))

(1)

F10.7a  F10.7(d ) max( F10.7(d ))

(2)

Apa  Ap(d ) max( Ap(d ))

(3)

where, NvTEC(d ) is the normalized vertical TEC values, F10.7a is the normalized solar proxy, Apa is the normalized geomagnetic proxy and d indicates the day. The ionospheric linear TEC model can be decomposed into different ionospheric parameters based on their relative contributions and is expressed as, NvTEC (d )  TECo (d )  TECsol (d )  TECosc (d )  TECgeo (d )

(4)

where, TECo (d ) is a constant of 0.05 which represents additional variations arising from solar activity, TECsol (d ) is the solar activity component, TECosc (d ) is the periodic component at three different frequencies, and TECgeo (d ) is the geomagnetic component. Here, since the solar activity F10.7 differs greatly in the aspects of day-to-day and monthly variations (Liu et al., 2004), therefore, F10.7p was considered in the proposed linear model to represent the solar activity influence on TEC. The F10.7 p  (F10.7a  F10.7a A) 2 , could be determined on the basis of daily averaged solar activity index F10.7a and its 81-day running average F10.7a A . The F10.7 p index represents fairly well the intensity of solar EUV flux (Liu et al., 2006, 2011). Solar irradiance empirical models have used the F10.7 p index as a solar EUV proxy (Richards et al., 1994). TECsol (d )  c1 F10.7 p(d  1)  c2 F10.7 p_ 81 (d 1)

(5)

where, (d  1) the lag of one day and c1 , c2 are the unknown coefficients to be estimated. The influences of periodic oscillations at different periods (182.6, 365.25, and 121.7 days) are expressed as a combination of solar modulated terms as follows.

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TECosc (t )  c3 .sin(2 d / 182.6)  c4 .cos(2 d / 182.6)  c5 .sin(2 d / 365.25)  c6 .cos(2 d / 365.25)  c7 .sin(2 d / 121.7)  c8 .cos(2 d / 121.7)  [c9 .sin(2 d / 182.6)  c10 .cos(2 d / 182.6) 

(6)

c11.sin(2 d / 365.25)  c12 .cos(2 d / 365.25)  c13 .sin(2 d / 121.7)  c14 .cos(2 d / 121.7)].F10.7 p_ 81 ( d )

where the periodic component is a function sine and cosine terms to resolve the phase and amplitude of each oscillation and their modulation is given as a linear function of

81-day

running average of solar EUV proxy ( F10.7 p ). The periods of 182.6, 365.25, and 121.7 days represent the semiannual oscillation (SAO), annual oscillation (AO) and terannual oscillation (TO), respectively, c3 to c14 are the unknown coefficients to be estimated. The daily mean TEC values derived from the geomagnetic activity component (Ap index) are given by, TECgeo (d )  c15 . Ap(d  1)  c16 . Ap(d  2)  c17 . Ap(d  3)

(7)

where, (d  2),(d  3) are the lag 2 days and 3 days of Ap indices, respectively, and c15 , c16 , c17 are the unknown coefficients to be obtained.

The seventeen unknown coefficients c1, c2c17 were determined by the Weighted Least Square (WLS) method (Menke, 1984). Model TEC values were estimated by using model coefficients for two GNSS stations. The Linear TEC model was considered to investigate ionospheric TEC variability and its characteristics. For every season, the error between the observed GPS-TEC values and the model TEC values was calculated using em 

NvTEC  NvTEC 2

NvTEC

100

(8)

2

where, NvTEC is the normalized model TEC values and . 2 denotes the metric distance between two vectors. The deviations between the observed GPS-TEC values and the model TEC values are also be studied by root mean square error (RMSE) and is given by:

 i 1 ( X i  Yi )2 n

RMSE 

(9)

n

where Xi represents the observed GPS-TEC data, Yi can be the TEC data of either the proposed linear model or the IRI2012 model,

5

3 Results The observed GPS-TEC and the IRI2012 model TEC data were considered to investigate the influences on ionospheric TEC and its characteristics during the year-2013 at two geographic locations (KLU-Guntur and Bangalore). The daily averaged GPS-TEC at KLUGuntur and Bangalore stations was considered for analysis. While the KLU-Guntur station is located at the inner edge of the EIA crest region, the Bangalore station is closer to the geomagnetic equator region. The observed GPS-TEC and the model TEC values are shown in Fig. 1(a) and (b), respectively. It was noticed that the double peak structures in GPS-TEC and model TEC values were similar to the semiannual variation. The semiannual variation of the EIA could also be due to the combined effect of the solar zenith angle and magnetic field geometry (Wu et al., 2004).

Fig. 1. Normalized variation of observed TEC and model TEC values during the year 2013 at KLU -Guntur (a) and Bangalore (b). Lower panel (c) and (d) represents the respective scatter diagrams between observed and model TEC at both stations.

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Fig. 1(c) and (d) represent the scatter plots between observed and model TEC values. The correlation was computed based on the normalized TEC values. The correlation coefficient was more than 0.93, indicating that the linear model TEC effectively represents the ionospheric variations based on their corresponding contributions with the ionospheric influencing parameters. In addition, the influence of individual components on ionospheric climatology was determined by removing the model TEC error of each component from the model. The model error obtained from Eq. (8) was 6.0% and 4.8% at KLU-Guntur and Bangalore stations, respectively. The error became 6.8% and 5.4% when the terannual component was removed; it became 9.4% and 6.1% when the annual part was removed and 16.1% and 9.1% when the semiannual component was removed. Subsequently, the model error became 16.7% and 11.8% when the geomagnetic component was removed. The model error became 93.4% and 87.8% when solar activity component was removed. Hence, it was confirmed that the solar activity was the key component that influenced ionospheric daily averaged TEC. Fig 2. shows the influence of different components such as solar activity, periodic variations and geomagnetic activity at the two GNSS stations.

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Fig. 2. Influence of different components obtained from the TEC time series model at (KLU-Guntur) and Bangalore It is evident from Fig. 2(a) that the influence of solar activity was moderate for the two locations and its influence increased at the station away from the equator. This is due to the characteristic EIA involving EEJ and the fountain effect over Indian region (Madhav Haridas and Manju, 2012). The correlation coefficient (r) between solar activity component and GPS-TEC was observed to be higher over the Bangalore station (0.58) than the KLU-Guntur station (0.53). The quantitative analysis revealed that the influence of the solar activity was more at equatorial regions, and the impact decreases with increasing latitudes. It was also confirmed from Fig. 2(a) that the influence of solar activity (F10.7p) index on TEC was more than 0.7 during the winter months. The daily averaged F10.7p index during the winter months was more than 160 sfu. Planetary geomagnetic disturbance Ap (index) has been used to define the influence of geomagnetic activity and their impact on ionospheric TEC. Fig. 2(b) shows the influence of geomagnetic activity. From Fig. 2(b), it was noted that the influence of geomagnetic component (Ap index) was 0.1 and 0.2 at two stations during March 17 th in 2013. The daily averaged Ap index during March 17 th was 72 nT. It was also noted that the influence of geomagnetic activity on TEC was different at different latitudes. The influence of geomagnetic activity values was positive for both GNSS stations Fig. (2b). Araujo-Pradere et al.(2006) and Stankov et al.(2010) reported that the influence of geomagnetic activity on the ionosphere depends on geographic location, local time, and season. The same occurrence was observed by (Lean et al., 2011; Li et al., 2013). They reported that the influence of geomagnetic activity values at 20°N and the equator were positive and almost equal, whereas the values at other latitudes were almost negative. The characterization of the solar cycle modulation of the periodic component in Fig. 2(c) was obtained by complex demodulation of the observed GPS-TEC at annual, semiannual and terannual periods. It can be observed that for the three parameters, there are two peaks at the equinoxes. The amplitudes were higher, and the double peak structure was similar to the seasonal variation of the maximum electron density (Liu et al., 2009; Wu et al., 2012). The seasonal variations of electron density for a location at a fixed local time can be considered to be a superposition of the annual and semiannual components. The enhancement of the peak with solar activity maybe associated with the semiannual variations of the equatorial E × B drift (Chen et al., 2009).

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Fig. 3. Influence of annual (a), semiannual (b) and terannual (c) components obtained from the TEC time series model. Fig. 3(a) shows the impact of the annual oscillations for the year 2013( KLU-Guntur and Bangalore GPS Stations) It can be observed that ionospheric TEC values reach a maximum peak during the summer months( June and July) at KLU-Guntur and Bangalore GPS TEC stations, respectively. Fig. 3(b) shows the impact of the semiannual oscillations, which is characterized by two maxima in March/April and September/October and minima in summer solstice. Fig. 3(c) shows the influence of terannual variations that reflect the changes in ionospheric TEC. The patterns of terannual variations have shown in two regions with small differences in the amplitudes. It confirmed that the impact of terannual variations is small over the two GNSS stations during the high solar activity year 2013. Lean et al. (2011) have also reported that the terannual variations contribute a few TECU during high solar activity in 2003. The periodic(annual/semiannual/terannual) oscillation results correlate well with previous studies (Lean et al., 2011; Li et al., 2013). Table 1 depicts the model TEC errors ( em ) between the observed GPS-TEC values and the model TEC values for all seasons using 17 linear TEC model coefficients. It is evident from the results that the model error was less for the autumn and spring seasons for both the stations and larger for the summer and winter months (Table 1). Table 1 Error analysis at KLU-Guntur and Bangalore stations for all the seasons Seasonal variations for the year 2013

KLU (Guntur)

Bangalore

(16.44° N,

(12.97° N, 77.59°

80.62° E)

E)

em (%)

em (%)

Spring

5.0

4.2

Summer

7.0

5.4

9

Autumn

5.5

4.7

Winter

5.7

4.6

4 Discussion on Data-Model TEC validation observations The accuracy of the model TEC can be validated by the model TEC residuals, which are estimated by the discrepancies between the observed and the model TEC measurements (Jakowski et al., 2011). The discrepancies were assessed by Root Mean Square Error (RMSE). The daily averaged observed GPS-TEC was considered to validate the linear model TEC as well as the IRI2012 model TEC over KLU-Guntur and Bangalore GNSS stations. Upper panels of Fig. 4(a) and (b) illustrate the variations of GPS-TEC with the linear model TEC and IRI2012 model TEC values at KLU-Guntur and Bangalore while the lower panels of Fig. 4( c) and (d) show the deviations of observed GPS-TEC with the linear model TEC and IRI2012 model. The linear correlation coefficients of the model and observed TEC values were found to be 0.94 and 0.93 at KLU-Guntur and Bangalore, respectively. RMSE of observed GPS-TEC and linear model TEC was between 0.04 and 0.03. In contrast, the IRI2012 model TEC has a lesser accuracy with respective RMS error values of 0.10 and 0.08.

Fig. 4. Upper panel of (a) at KLU-Guntur and (b) Bangalore illustrates the variations of observed GPS-TEC with the linear model TEC and IRI2012 model. Lower panels (c) and (d) show the errors. 10

The model error obtained from Eq. (8) was 6.0% and 4.8% at KLU-Guntur and Bangalore stations, respectively. Fig. 5 shows the actual GPS-TEC (before normalized) with the linear model TEC and IRI2012 model TEC, it is noticed that the influences on the actual TEC values show the similar trends as the normalized TEC values.

Fig. 5. Upper panel of (a) at KLU-Guntur and (b) Bangalore illustrates the variations of actual GPS-TEC with the linear model TEC and IRI2012 model TEC during the year 2013. Lower panels (c) and (d) show the errors. The model error between actual TEC and linear model TEC values was 6.10 % and 4.85 % at KLU-Guntur and Bangalore stations, respectively (Eq. 8). The maximum discrepancies between actual TEC and Normalized TEC values found to be 0.1% for KLU-Guntur and Bangalore stations (Figs. 4-5). Further, seasonal variations were compared with similar locations with linear and IRI2012 models. The seasonal variations were categorized into four seasons: spring equinox (March and April), autumn equinox (September and October), winter solstice (November, December, January and February), summer solstice (May, June, July and August). Table 2 shows seasonal RMSE between the linear TEC model values and IRI-2012 model values with observed GPS-TEC values in the year 2013. Table 2 illustrates the seasonal RMS errors between the linear and IRI2012 model data with observed GPS-TEC measurements for all seasons. 11

Seasonal Variations for the year 2013 Spring Summer Autumn Winter

KLU-Guntur

Bangalore

(16.44° N, 80.62° E) RMSE

(12.97° N, 77.59° E) RMSE

0.04 0.08 0.05 0.06 0.05 0.13 0.04 0.12

0.03 0.04 0.04 0.08 0.04 0.12 0.03 0.06

Linear TEC model IRI2012 model model Linear TEC model IRI2012 model model Linear TEC model IRI2012 model modelmodel Linear TEC model IRI2012 model

Seasonal RMSE between the linear model values and IRI2012 model values with observed GPS-TEC were computed (Eq. 9). The RMSE was 0.05 and 0.04 for the autumn and spring equinox and 0.05 and 0.04 during summer and winter solstices, respectively. However, the RMSE between IRI2012 model during autumn and spring equinox seasons were 0.13 and 0.08 and the RMSE during summer and winter seasons were 0.06 and 0.12 at KLU-Guntur, respectively. The RMSE of linear TEC model was 0.04 and 0.03 for the autumn and spring equinoxes and the RMSE during summer and winter seasons was of 0.04 and 0.03 at Bangalore station. However, the RMSE of IRI 2012 model was 0.12 and 0.04 during autumn and spring equinox seasons and 0.08 and 0.06 during summer and winter seasons respectively. It is evident that RMSE values were less in winter as compared to summer, indicating the absence of winter anomaly for two stations (Table 2). Fig. 6 depicts seasonal variation of the observed GPS-TEC with model TEC and IRI2012 values at KLU-Guntur.

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Fig. 6. Seasonal variation of the observed GPS-TEC with Linear model TEC and IRI2012 values at KLU-Guntur during the year 2013. It observed that the linear model values agree more closely with the observed GPS-TEC than with that of IRI 2012 model values during all four seasons. The IRI2012 model TEC tends to overestimate GPS-TEC during the autumn and winter seasons and slightly follow the trends during spring and summer seasons. GPS-TEC and linear model TEC recorded maximum values during summer seasons of June, July and around June, while winter seasons recorded the lowest values in January, February and around December (Fig. 6). It is evident that recorded values are less in winter as compared to summer, indicating the absence of winter anomaly at KLU-Guntur. The IRI2012 model values have failed to predict the absence of winter anomaly at the EIA crest region (KLU-Guntur), showing higher values in winter than in summer (Fig. 6) and (Table 2).

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Fig. 7. Seasonal variation of the observed GPS-TEC with Linear model TEC and IRI2012 values at Bangalore during the year 2013. Fig. 7 depicts the seasonal variation of the observed GPS-TEC values with model TEC and IRI2012 values at Bangalore. It observed that the linear model values agree more closely with the observed GPS-TEC than with that of IRI 2012 model values during all four seasons. The IRI2012 model TEC tends to overestimate GPS-TEC during the autumn season and underestimates during spring, summer and winter seasons. GPS-TEC and linear model TEC recorded maximum values during summer seasons of June, July and around June, while winter seasons recorded the lowest values in January, February and around December (Fig. 7). It is evident that recorded values are less in winter as compared to summer, indicating the absence of winter anomaly at Bangalore. The IRI2012 model values predict the absence of winter anomaly at the Bangalore showing higher values in summer than in winter (Fig. 7) and (Table 2). The seasonal climatological TEC variation in equatorial and low-latitude regions may vary with different factors such as solar zenith angle, changes in thermospheric concentration of O/N2 ratio, direction of neutral wind flow and EEJ (Wu et al., 2008; Bagiya et al., 2009; Kumar et al., 2012). However, RMSE of IRI2012 model TEC values failed to predict the absence of winter anomaly at the EIA crest region (KLU-Guntur);in fact, it showed higher values in winter than in summer. Further, it was observed that the linear model values agreed

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better with the observed GPS-TEC than with that of IRI2012 model TEC values, as evidenced by low RMSE error values for all seasons. Winter anomaly was described with regards to the variation of solstice months, having higher TEC values in winter than in summer (Rishbeth et al., 2000). TEC winter anomaly varied for different regions and was dominated by various factors, such as meridional neutral wind and O/N2 ratio. While neutral composition has a significant impact on electron density, production and loss rates of electrons depend on the O/N2 ratio (Aggarwal et al., 2012).The production ratio depends upon the atomic oxygen concentration, and the loss rate is balanced by the molecular concentration. Thus, the O/N2 ratio is linearly proportional to the equilibrium electron density. Therefore, the O/N2 ratio data of two GNSS stations was obtained by the MSISE90 atmospheric model. The absence of winter anomaly at the two GNSS stations may be related to the latitudinal difference in solar activity effects on O/N2 concentration. However, the RMSE values of the IRI2012 model TEC did show the difference in winter anomaly for the KLU-Guntur station; it did not function well in the EIA transition region. The IRI2012 model TEC performance was better at the low latitude region (Bangalore) during the solar maximum (2013); Kumar and Singh (2016) have also confirmed these findings. From these results, the linear model TEC performed well in representing the ionospheric TEC climatology variations and seasonal anomaly for both winter and summer solstice conditions at solar maximum (2013). The linear model TEC attributes the relative deviation from the IRI2012 model. IRI model TEC is based on monthly-hourly medians. It is an empirical and deterministic model and computes TEC up to 2000 km (Bilitza, 2001). IRI model fails to provide reliable results over the low-latitude region because most of the data used in this empirical model were collected from mid and high latitudes; very limited ionospheric data sources from low latitudes were considered in the IRI2012 model. IRI model discrepancies were due to height limitation and inaccurate predictions of the bottom side and topside electron density profiles. There is a necessity to improve the IRI2012 model to characterize the low-latitude ionospheric conditions. The IRI-Plas model is an extension of the IRI model by adding the plasmaspheric characteristics of higher altitudes. IRI-Plas computes TEC up to GPS orbital height of 20,000 km so that it also has the plasmaspheric content similar to GPSTEC (Gulyaeva, 2011; Sezen et al., 2013; Arikan et al., 2015). In future, the linear TEC model will be evaluated with IRI-Plas model TEC to understand the low-latitude ionospheric variability under various geophysical conditions.

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5 Conclusion The GPS-derived ionospheric TEC variation was analyzed based on the linear model TEC at KLU-Guntur and Bangalore GNSS stations lying in the northern low-latitudes. The variations in daily averaged TEC were represented by the impact of solar activity, geomagnetic activity, and periodic oscillations at three frequencies. The key observations and conclusions are as follows: 1) The linear time series model TEC can effectively replicate the influences of solar activity, geomagnetic and periodic variations. Analysis of the different components showed that the main factor that influenced ionospheric daily averaged TEC was solar activity, and it was moderate for two locations. The influence of geomagnetic-activity-component-values is positive, and is different at different latitudes. The characteristics of periodic variation at two locations were similar and its influence increased with latitudes. 2) The influence of each component can be obtained by removing the model TEC error of each component from the model TEC. The model error was 6.0% and 4.8% at KLU-Guntur and Bangalore stations, which became 6.8% and 5.4% when the terannual component was removed; it became 9.4% and 6.1% when the annual was removed. The model error became 16.1% and 9.1% when semiannual was removed. Subsequently, the model error became 16.7% and 11.8% when the geomagnetic component was removed. The model error became 93.4% and 87.8% when solar activity component was removed. 3) The linear correlation between the linear model TEC and the observed GPS-TEC dataset at KLU-Guntur and Bangalore were observed to be 94% and 93%, respectively. 4) The results were compared with the observed GPS-TEC and IRI2012 model TEC estimation; the model TEC residuals confirmed that the linear model TEC better represented the ionospheric variation in GPS-TEC data than the IRI2012 model. 5) The seasonal variations residual error between the linear model TEC and the IRI2012 model TEC with GPS-TEC values revealed the presence of a seasonal anomaly. Also, model TEC showed the absence of winter anomaly in the year 2013, but the IRI2012 model TEC failed to point out the above abnormality. 6 Acknowledgments The above work is a part of the project titled “Development of Ionospheric TEC Data Assimilation Model based on Kalman Filter using Ground and Space based GNSS and Ionosonde observations” sponsored by the Science and Engineering Research Board(SERB), New Delhi, India, vide sanction letter No: ECR/2015/000410. The contribution is also 16

supported by Department of Science and Technology (DST), New Delhi, India, SR/FST/ESI130/2013(C) under DST-FIST Program. The authors thank the reviewers for their helpful comments.

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