Investigation of space weather effects on GPS satellite navigation systems is very crucial in high-precision positional applications such as aircraft landings and missile guidance, etc. The geomagnetic storms can drastically affect the total electron content (TEC) of the ionosphere even in low latitudes, especially for Indian region as it comes under low-latitude region. Hence, the performance of three prominent ionospheric models is investigated for adverse ionospheric conditions using 17 GPS TEC stations data. The models characterized the ionospheric disturbances due to two magnetic storms well.
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 Adverse conditions due to the space weather can cause disruption in satellite operations, communication, and navigation systems [Harra and Mason, 2004; Tsurutani et al., 2005]. Investigation of space weather effects especially on Satellite Based Augmentation Systems (SBAS) is very crucial to meet the Category I Precision Approach (CAT-1 PA) requirements of aircraft landings.
 The Indian SBAS system is known as GPS Aided Geo Augmented Navigation (GAGAN). GAGAN is a joint project between the Indian Space Research Organization (ISRO) and Airports Authority of India (AAI) to acquire and document data over India to cater the needs of Indian civil aviation [Suryanarayana Rao, 2007]. The geomagnetic storm time effects at low latitudes are especially important because the equatorial plasma fountain is highly responsive to such disturbance electric fields. The solar wind, which is a continuous stream of solar plasma and magnetic field, is responsible for events like coronal mass ejections (CME). The geomagnetic storms can cause rapid changes in total electron content (TEC) of Global Positioning System (GPS) signals [Forster and Jakowski, 2000]. There is a necessity to incorporate a provision in the models for detecting this kind of ionosphere anomalies.
 Several ionospheric models namely planar fit, Inverse Distance Weight (IDW), Minimum Mean Square Estimator (MMSE), Kriging, Junkins and Bi-linear models are investigated over the Indian region [Sarma et al., 2006]. Another two models namely Modified Planar Fit Method (MPFM) and Spherical Harmonics Functions (SHF) model are investigated under geomagnetic storm conditions [Sarma et al., 2009; Venkata Ratnam et al., 2009]. It was proved that decorrelation over Indian region is not constant rather it is variable with respect to region and time. Therefore, MPFM model can be implemented with adaptable decorrelation parameter based on the limiting cases of typical ionospheric disturbance. It is found that, for low-latitude region, the decorrelation is varied up to 2.0 m. This model is also supplemented with ionospheric irregularity detector and adaptable decorrelation. In this paper, to check the suitability of functional based models over the low-latitude region, SHF model is investigated along with MPFM and MMSE models.
 The Ionospheric Grid Point (IGP) delays due to these models are estimated. Grid Ionospheric Vertical Error (GIVE) values due to the MPFM and MMSE models are calculated. The estimation of ionospheric delays due to the adverse space weather conditions using near real time models is very important for improving the positional accuracy applications of GPS augmentation systems.
2. Adverse Space Weather Conditions
 One of the features of a magnetic storm is a decrease in horizontal magnetic field intensity during the main phase followed by a subsequent recovery [Harra and Mason, 2004; Tsurutani et al., 2005; Zhao et al., 2005]. Generally to measure the intensity of magnetic storms Dst index is used. Apart from the Dst index, Kp and Ap indices are also available to identify the quiet and disturbed days. Details on Kp and Ap indices are given elsewhere [Perrone, 1998]. Super storms have Dst ≤ −350 nT, while major storms have Dst ≤ −100 nT. Generally geomagnetic storms have three phases namely (1) initial phase, (2) main phase and (3) recovery phase. In the initial phase, the magnetic field increases up to 10–50 nT. In main phase, the magnetic field decreases by ≥−100 nT whereas for recovery phase, the magnetic field returns to its prestorm ambient value [Harra and Mason, 2004]. Two prominent geomagnetic storms are considered in our analysis.
2.1. Geomagnetic Storm of 22–27 July 2004
 The storm started around midnight of 22–23 July 2004. The Dst index reached a minimum value of −100, −130 and −200 nT for 23, 25 and 27 July, respectively. The maximum sum of Kp index of the whole day reached 38, 58 and 61 for 23, 25 and 27 July, respectively. The negative variations in the Dst index are indicated due to the ring current which flows around the Earth from east to west in the equatorial plane during storm time [Mursula et al., 2008].
2.2. Geomagnetic Storm of 7–11 November 2004
 The minimum Dst value of −373 nT occurred on 8 November 2004 with a maximum Kp index of 9. On 10 November 2004, the minimum Dst value was −119 nT. The 8 and 10 November 2004 storms are ranked as third and eighth biggest storms in the solar cycle number 23. In the initial phase of storm, sudden commencements of three pulses are observed in morning hours of 8 November 2004. To investigate the impact of these storms on the performance of satellite based communication and navigation systems, the GAGAN data is used for the analysis.
3. Ionospheric Delay Models
 Ionospheric delay models are essential in SBAS for improving near real time positional accuracy. Ionosphere in the form of a thin shell is assumed at a height of 350 km from the Earth's surface [Wide Area Augmentation System Minimum Operational Performance Standard (WAAS MOPS), 1998]. To characterize the ionosphere over Indian region, approximately 64 IGPs are to be defined with their Grid Ionospheric Vertical Delays (GIVDs) and corresponding error bounds, GIVEs. Using the IGP information and their approximated position, a single frequency GPS user can estimate the ionospheric corrections. The considered three prominent ionospheric models have some specific advantages such as spatial correlation between IPP measurements and fast and easy computation, ability to define ionospheric delay in a few coefficients.
3.1. MMSE Model
 MMSE technique proposed by Lejeune and El-Arini  is based on the principle of postestimation of the expectation of the square of the error between the measured and estimated vertical ionospheric delays. In this model, the expected vertical ionospheric delay at each IGP (IIGP) is given as,
where Cxy is cross covariance matrix of IPP and IGP delays. Cyy is covariance matrix of IPP delays. IIPP is measured IPP delays. μs is mean of IPP delays.
 The corresponding vector of error variances (Ev2) is estimated as [WAAS MOPS, 1998],
where Cxx is initial covariance matrix. These error variances are used to estimate error bounds i.e., GIVE values at each IGP.
With a constant of 3.29, GIVE yields 99.9th percentile of the postcorrection ionospheric delay errors. d is the distance in kilometers between the IGP and the IPP closest to it and DGIVE is a constant decorrelation parameter equal to 800 km.
3.2. MPFM Model
 The “decorrelation function parameter” in the Planar fit method proposed by Walter et al.  is assumed as constant. This model is supplemented with ionospheric irregularity detector which uses chi-square test and adaptable decorrelation method to estimate IGP delays [Sparks et al., 2004]. Chi-square test is also used to test the correctness in delay estimations made by the model. IGP delays are estimated using ionospheric irregularity detector and adaptable decorrelation values. GIVE can be computed as [Walter et al., 2000],
where σGIVE2 is the variance of the vertical delays at the four corners. The formal error variance on the ionospheric delay estimates at the IGP using planar fit method is given by [Walter et al., 2000],
where G is the observation matrix and W is the weight matrix.
3.3. SHF Model
 The SHF model is a two-dimensional Fourier series and can be used for estimating ionospheric delays [Zhao et al., 2005; Perrone, 1998]. The mathematical expression of vertical TEC using spherical harmonics is given as [Schaer et al., 1995].
where θ is the geographic latitude of an IPP, λ is the geographic longitude of an IPP, n, m are integer degree and order of Legendre function, respectively, Cnm, Snm are unknown spherical harmonic coefficients, [cos(θ)] are normalized associated Legendre functions.
4. Results and Discussion
 A low-latitude crest region IGP location (25°N, 75°E) is considered for investigating the ionospheric effects due to the magnetic storms. The GPS data obtained from SAC, Ahmedabad, India consists of 23 parameters. Out of these, only 7 parameters namely SV number, week number, seconds of the week, elevation, azimuth, TEC and DTEC are considered. In this paper, 17 GPS stations data over the Indian region is considered for the analysis. More details of GPS stations and TEC data are reported elsewhere [Sarma et al., 2009; Venkata Ratnam and Sarma, 2006]. For simple and compact characterization of TEC along a signal path length, TEC along the path has to be converted to vertical TEC using a standard mapping function, which is a function of elevation angle of the satellite from the receiver [Langley et al., 2002]. There is no provision for detection of ionospheric irregularities in the MMSE model. Most of the times, the MPFM model is able to characterize the disturbed ionospheric conditions. For both storm days, IGP (25°N, 75°E) delays and Dst Index with respect to time are presented in Figures 1 and 2.
4.1. Estimation of IGP Delays Due to MPFM, MMSE, and SHF Models (July 2004)
 On prestorm day (22 July 2004), all the models show diurnal ionospheric variations. Even though the maximum peak of IGP delays due to MPFM, MMSE and SHF models are 5.98 m (13.33 h), 7.15 m (12.59 h) and 6.58 m (12.33 h) and occurred at different times, they have shown the same trend (Figure 1).
 On first storm day (23 July 2004), a severe storm with a minimum Dst index value of −100 nT occurred. In MPFM model, the maximum IGP delay is 8.75 m (15.58 h). The corresponding peak values for MMSE and SHF models are 8.20 m (13.58 h) and 8.67 m (16.83 h), respectively. Compared to prestorm day data, it can be seen that the maximum IGP delays of the models are larger. It is found that IGP delays are increased during the main phase of storm (Figure 1). The enhancement of the IGP delays is due to prompt penetration of electric field. The prompt penetration of electric field is eastward during the day. Therefore, it enhances daytime eastward dynamo field at equatorial region. This enhanced eastward field causes increased plasma flow upward to heights where recombination is low and hence TEC increases [Maruyama et al., 2004; Tsurutani et al., 2004]. MMSE model estimates ionospheric delays based on correlations properties of measured IPP delays and locations. The MMSE model is not able to estimate properly during storm period as compared to the other models. The MMSE algorithm implicitly assumes that the ionospheric conditions remain constant over the grid [Lejeune and El-Arini, 1999]. The observed secondary peak could be due to the local ionospheric delays are more as compared to the mean value of delays.
 On poststorm day (24 July 2004), maximum peak IGP delays due to MPFM, MMSE and SHF models are 6.42 m (14.00 h), 7.41 m (13.16 h) and 6.24 m (15.16 h), respectively. It is evident that the maximum IGP delays of all the models are less compared to the maximum delays on the storm day. It can be seen from the results that the IGP delays due to all the models are depleted during the recovery phase of the storm (Figure 1). The depletions of the IGP delays during the poststorm day due to the redistribution of ionization associated with the storm induced effects. And also, it may be due to the enhancement of EIA [Tsurutani et al., 2004].
 On second storm day (25 July 2004), a minimum Dst index of −150 nT is noted. The maximum peak of IGP delays of MPFM, MMSE and SHF models are 7.75 m (16.75 h), 7.71 m (17.33 h) and 7.72 m (16.75 h), respectively. It can be observed that IGP delays are larger as compared to the previous day.
 On poststorm day (26 July 2004), maximum peak of IGP delays of MPFM, MMSE and SHF models are 4.12 m (14.58 h), 5.17 m (16.67 h) and 4.55 m (15.08 h), respectively. It is observed that IGP delay variations are depleted during this day (Figure 1).
 On third storm day (27 July 2004), a minimum Dst index of −200 nT is noted. The maximum peak of IGP delays of MPFM, MMSE and SHF models are 5.86 m (14.67 h), 6.19 m (18.67 h) and 6.27 m (15.41 h), respectively.
 On poststorm day (28 July 2004), maximum peak of IGP delays of MPFM, MMSE and SHF models are 7.7 m (13.00 h), 7.65 m (12.25 h) and 5.62 m (14.41 h), respectively, reaching almost prestorm delay values (Figure 1). Compared to SHF model, the GIVD due to MPMF and MMSE are higher. The reason is that SHF model produces smoother values. It is observed that the standard deviation of MPFM model is less as compared to other models [Sarma et al., 2010].
4.2. Estimation of IGP Delays Due to Modified MPFM, MMSE, and SHF Models (November 2004)
 On prestorm day (7 November 2004), all the models show diurnal ionospheric variations. Even though the maximum peak of IGP delays due to MPFM, MMSE and SHF models are 9.02 m (14.58 h), 8.73 m (16.50 h) and 9.51 m (15.42 h) and occurred at different times, they have shown the same trend (Figure 2).
 On first storm day (8 November 2004), a severe storm with a minimum Dst index value of −373 nT at 12.16 h was occurred. In MPFM model, the maximum IGP delay is 7.06 m (14.91 h). The corresponding peak values of MMSE and SHF models are 7.61 m (16.41 h) and 7.77 m (13.67 h). Compared to prestorm day data, it can be seen that the maximum IGP delays of the models are less. It is found that IGP delays are depleted during the main phase of storm around 12.16 h (Figure 2). The disturbance dynamo electric field as against the prompt penetration field is westward whereas daytime ionospheric dynamo electric field is in eastward direction. This causes suppression of EIA and the consequent TEC depletion [Tsurutani et al., 2004].
 On poststorm day (9 November 2004), maximum peak IGP delays due to MPFM, MMSE and SHF models are 11.15 m (15.00 h), 10.9 m (12.83 h) and 11.68 m (13.58 h), respectively. It is evident that, the maximum IGP delays of all the models are higher compared to the maximum delays on the storm day. It can be seen from the results that the maximum IGP delays due to all the models increased during the recovery phase of the storm to its near-to-quiet conditions (Figure 2). Enhancements and decrease of the GIVD values occurred mainly due to either E × B drifts at equatorial region or equator ward meridional winds [Lakshmi et al., 1997].
 On second storm day (10 November 2004), a minimum Dst index of −119 nT is noted. The maximum peak of IGP delays of MPFM, MMSE and SHF models are 9.1 m (17.25 h), 9.79 m (16.75 h) and 8.04 m (16.75 h), respectively.
 On poststorm day (11 November 2004), maximum peak of IGP delays of MPFM, MMSE and SHF models are 10.82 m (15.75 h), 9.24 m (16.16 h) and 9.77 m (14.08 h), respectively (Figure 2).
Dabas et al.  reported the results of the foF2 data of New Delhi station corresponding to this storm. It is observed that a substantial decrease occurred in foF2 values from ionosonde on 8 and 10 November 2004. Similar observations are reported elsewhere using GPS data [Pandey and Dashora, 2005]. In this analysis, the features such as sudden changes in ionospheric delays due to adverse conditions are very well characterized using these experimental models, which are essential for performance evaluation of GAGAN system.
4.3. Estimation of GIVE Values Due to MPFM and MMSE Models
 The response of ionosphere delay models for geomagnetic storm conditions is primarily investigated. The considered IGP (75°E, 25°N) location comes near the northern equatorial anomaly crest region. The GIVE values provide the error bounds only. This particular IGP is expected to give large GIVE values. However, the obtained GIVE values are safe within a maximum limit of 45 m [WAAS MOPS, 1998]. GIVE results are shown in Figures 3 and 4 for two storm periods. During summer storm period, the maximum GIVE value is 4.57 m for MPFM model and 2.64 m for MMSE model (Figure 3). During winter storm period, the maximum GIVE value is 6.1 m for MPFM model and 3.5 m for MMSE model (Figure 4). From Figures 3 and 4 it can be seen that GIVE values due to MPFM model are higher than MMSE model. SHF model estimates GIVDs. But, it cannot estimate GIVE values. The MMSE model estimates GIVE values based on the error variances of IGP delays. In MPFM model, adaptable decorrelation function is used to model the ionospheric time delays. Due to the adaptable decorrelation values, GIVE values are increased to protect the user. The MPFM model is able to detect and mitigate the ionospheric irregularities. The GIVE estimation would be useful for providing differential ionospheric corrections with better error bounds to GPS/GNSS augmentation system users.
 Space weather effects on SBAS systems are one of the major concerns especially over the low-latitude region. In this paper, MPFM, MMSE and SHF models are investigated for both adverse and quiet conditions. The results indicate that all the three models follow the standard half cosine pattern showing diurnal variations of ionospheric delays. During storm days, large scale time dependent enhancements and decrease of the vertical delays are observed. It is confirmed from the results that IGP delays provided by the three analyzed models are enhanced during the summer storm in contrast to depletion during winter storm. The GIVE values for MPFM and MMSE models are estimated. It is found that the MPFM model provides better ionospheric delay estimation under severe ionospheric conditions. However, MMSE model provides better availability of SBAS systems even under severe conditions as MMSE GIVE algorithm is not dependent on the number and locations of neighboring IPPs. SHF model estimates IGP delays only. This model represents ionospheric behavior with less number of coefficients. These investigations would be useful for identification of a suitable ionospheric model for GAGAN over low-latitude regions.
 The above work has been carried out under the project entitled “Coherent Radio Beacon Experiment (CRABEX)” sponsored by SPL, VSSC, Trivandrum, India, vide sanction letter SPL/CRABEX/BUDTR/2010, dated: 31 May 2010.