Using the GPS data from as many as 114 GPS stations of the International GPS Service for Geodynamics (IGS), the morphological features of the ionospheric total electron content (TEC) variations on the sunlit hemisphere during the 4B solar flare on 28 October 2003 is studied. It is found that the strongest sudden increase of TEC (SITEC) happened during the flare, and the magnitudes of SITEC vary at regions with different local solar zenith angle (SZA). In the northern hemisphere, the TEC enhancement is approximately symmetrical to the local noon, and its value is usually greater than 14 TECU (1 TECU = 1016/m2) if the SZA is less than 60°. On the whole, as the SZA increases, the value of TEC enhancement in the northern hemisphere decreases. It is worth mentioning that even in the regions of SZA between 90° and 100°, the SITEC was still seen from the temporal TEC curves. Using a photochemical model, the electron production rate over the sunlit boundary region is calculated and some obvious features of SITEC over this region are analyzed. In the polar region, the effect of this flare on the ionosphere exceeds the effect of the ionospheric scintillations and it seems that the ionosphere in the northern polar region responses more sensitively to this flare. In the end, superimposed on the curves of the rate of TEC change, there are some small disturbances (spikes) synchronously appearing on all curves and thus indicating an existence of similar structures in the EUV band of the flare.
 As one of the fastest and most severe solar events, solar flares affect the Earth's upper atmosphere seriously. During a flare, the extreme ultraviolet (EUV) and X rays emitted from the solar active region ionize the Earth's neutral compositions in the altitudes of ionosphere so to make the extra ionospheric ionization, known as sudden ionospheric disturbances (SIDs). Since 1960s, the solar flare effects on the ionosphere have been comprehensively studied with various methods and this has been well reviewed by Mitra  and more recently by Davies . It is generally accepted that different behaviors of SIDs are manifestations of increases of electron density at different altitudes [Liu et al., 1996]. Although the increase of electron density during a flare appears in all ionospheric subregions, the increase of electron density in the F region due to the extra ionization of EUV radiation is thought to be responsible for a large fraction of the SITEC so that SITEC can be used as an index to represent the response of the ionospheric F region to solar flares [Mendillo, 1974]. With the advent of satellite beacon methods for measuring the ionospheric TEC, it has become one of the chief means for studying the F region flare effects. In this subject, the spatial behavior of TEC and the change of electron density at different heights are two noticeable and interesting issues [Thome and Wagner, 1971; Mendillo et al., 1974]. Up to now, it is generally accepted that the increase of electron density during the flare occurs mainly in the F region due to the extra ionization of EUV radiation. Mendillo  analyzed the ionospheric disturbance during a large flare with the TEC data by means of Faraday rotation measurements made at 17 stations located in the northern hemisphere and showed a synoptic picture of the ionospheric TEC enhancement for the first time. However, owing to the limitation of the satellite beacon method in terms of lack of spatial coverage of the stations, some problems could not be thoroughly analyzed in their study.
 During the period 28 October to 4 November 2003, a large number of outstanding solar events occurred. Six large solar flares of X class occurred that triggered a nearly continuous series of geophysical disturbances. One of the largest flares occurred at 0951 UT, 28 October 2003, the class of which is X 17/4B, which was produced in the solar active region of 486 classified by NOAA. The location of the flare is at 16°S 08°E, which is nearly at Sun's central meridian and it is the first 4B level flare occurring in the 23rd solar cycle. Such seldom-seen conditions together with wide spatial coverage of GPS stations of IGS network provide a very good chance to study the global ionospheric response to solar flares. In this paper the morphological features of the global sunlit ionosphere during this flare are analyzed in detail.
2. Data and Methods
 The start, maximum, and end times of the flare were 0951 UT, 1110 UT, and 1124 UT, respectively. In order to reveal the morphological features of the sunlit ionosphere, the GPS data in standard RINEX format observed by the GPS receivers of the IGS network located in the dayside region were downloaded through the internet on the SOPAC server (available at http://sopac.ucsd.edu). Considering the data quality, the observations of 114 GPS stations were chosen to derive ionospheric TEC. In order to study the spatial boundary effect of the ionosphere, some GPS stations located in the night region are also selected.
 The temporal resolution of the GPS data is usually 30 s (very few are 15 s). All stations use high-precision, dual-frequency GPS receivers, which can provide carrier phase and pseudo-range measurements in two L-band frequencies (f1 = 1575.42 MHz, f2 = 1227.60 MHz). Using these four measurements, combining the geometrical relation of the satellite, ionosphere, and receiver, a precision vertical TEC can be derived at every observational epoch according to formula (1) [Lanyi and Roth, 1988]
where dtri and dtpi are the time delays calculated from the measurements of two-frequency pseudo-ranges and carrier phases and dts and dtr are the instrumental biases of the satellite and the receiver. Brs is the offset between the relative TEC and the absolute TEC. Here χi is the satellite zenith angle at the ionospheric penetration point (IPP), which is the point of intersection of the line of sight and the ionospheric shell, and hion is the height of the ionospheric shell, which is taken to be 400 km in this study. Here eli is the elevation of the satellite calculated from the satellite broadcast ephemeris. R is the Earth radius. N is the number of measurements (one per 30 s) in a continuous phase track.
 For each GPS station, at least four vertical TEC values with different IPP can be derived for an interval of 30 s. Since the timescale of a sudden increase of TEC during a flare is usually short, the TEC enhancement obtained from the temporal TEC variation curve can be considered to be at the same IPP. By the way, this study is focused on ionospheric disturbances caused by flare radiation and only the relative change of the TEC during the flare is important; therefore the instrumental biases are not removed during TEC calculation.
 In order to analyze the TEC change caused only by the solar flare, the changes due to other nonflare factors, such as background changes, should be eliminated from the temporal TEC curves. To ensure resolution, the temporal TEC curves that show obvious disturbances before sudden increase of TEC would not be used to derive TEC enhancements. The following expression is used to derive TEC enhancement from the qualified temporal TEC curves:
where ti is the start time of TEC increase in the TEC curves due to flare radiation, ti+n is the time when TEC increases to its maximum and ti−m is the time properly chosen as a reference time before the flare starts. Here n is the number of observational records during the time period from ti to ti+n, and m is the number of records from ti−m to ti. So after this correction by subtraction of the second term on the right-hand side of the expression (2), DTEC can be regarded as the TEC change caused by the flare extra radiation. The detail description of the method to derive absolute TEC and DTEC used in this paper can refer to Zhang and Xiao .
3. Results and Analysis
3.1. TEC Curves
Figures 1a–1f show the results of TEC temporal variations derived from measurements observed at six different GPS stations. The curves are obtained from the same one GPS receiver, while each curve is derived from measurements of a given satellite-receiver pair. Figure 1 can be divided into three groups corresponding to different local SZA. The first group (Figures 1a and 1b) reveals the ionospheric TEC in the regions with smaller SZA and it can be seen that a very strong SITEC event occurred during this flare. From 1101:30 UT to 1110:30 UT the TEC increased as much as 17 TECU, which is almost one third of the average background ionospheric TEC of the local noon, and this is the largest TEC enhancement ever reported so far; as an example for comparison, the largest TEC enhancement caused by the well-studied flare occurred on 14 July 2000 is only about 5 TECU [Zhang et al., 2002a]. The second group (Figures 1c and 1d) is the TEC curves for two receivers located in the regions of local sunset and sunrise. The SITEC is still obvious although the SZA in this region is very large. It is up to about 7 TECU that is even much larger than the largest TEC enhancements for other flares recently reported [Zhang et al., 2002a; Zhang and Xiao, 2003]. The last group (Figures 1e and 1f) shows the temporal TEC variation curves during this flare derived from the measurements of two GPS receivers located in the polar region. The obvious TEC enhancement can be seen in this figure although there are fluctuations in the temporal TEC curves due to the ionospheric scintillations. On the whole, the TEC enhancement observed at Trol (located in North Pole region) is about 8 TECU, and the TEC enhancement observed at Dav1 (located in the Antarctic) is about 5 TECU.
 It should be noted that in general, the TEC enhancements at polar region during solar flares are difficult to distinguish from the temporal TEC curves because it is masked by the background ionospheric scintillation. For example, this is shown in a study of flare effects on 15 April 2001 [Zhang and Xiao, 2003].
 Another point to be discussed is the reason for such a strong response of the ionosphere to this solar flare. Actually, in a recent study of the ionospheric response to a solar flare with the level of X14.4/2B that occurred on the solar disc of 20°S 85°W [Zhang and Xiao, 2003], it was shown that the largest TEC enhancement is only about 2.6 TECU which is much smaller than that for the time reported in this work. Notice that the levels of the soft X-ray fluxes for these two flares are similar. It is reasonably to think that the large difference of the TEC enhancements is due to the difference of EUV fluxes reaching to the Earth during the two flares. Now, it is generally accepted that the main part of the TEC enhancement is attributed to the extra EUV radiation and that it appears mainly in the F region [Donnelly, 1969, 1976; Taylor and Watkins, 1970; Mendillo et al., 1974; Matsoukas et al., 1972]. So, it can be estimated that during this flare, most part of the 17 TECU is caused by the solar extra EUV and lays mainly in the F region. That the flare is very close to the solar central meridian (16°S 08°E) and its active region is very large (4B) may be the main factors to cause such a strong ionospheric response; thereafter, such response indicates the intense increase of the EUV flux in the terrestrial space related somehow with these two factors.
3.2. Morphology of the Ionospheric TEC Enhancement
 There are as many as 602 temporal TEC curves derived from all qualified GPS observations. The magnitudes of TEC enhancement can be derived from these curves. During this process, the curves accompanied by TID or phase unlock are removed in order to ensure the resolution of TEC enhancement. In the end the TEC enhancement classified according to their values at as many as 585 different IPP are obtained and plotted represented by five different colors in Figure 2. In order to show the relationship of TEC enhancement with SZA, the contour line of SZA at 1110 UT is plotted in this figure, and the locations of the GPS stations used in the solution are also denoted by open triangle. On the whole sunlit hemisphere the magnitudes of SITEC vary clearly at different regions. In the northern hemisphere (winter hemisphere) the TEC enhancement is approximately symmetrical to the local noon, and the value of the enhancement is usually greater than 14 TECU for the area with SZA less than 60°; in fact, the largest TEC enhancement is as great as 17.6 TECU. As the SZA increases, the values of TEC enhancement in the northern hemisphere decrease. For instance, in the region of SZA between 60° and 75° the TEC enhancement varies from 11 to 14 TECU, in the region of SZA between 75° and 85° it varies from 7 to 11 TECU, and in the region of SZA between the region of 85° and 95° it varies from 4 to 7 TECU.
 In the southern hemisphere the general trend of enhancement decreasing with increasing SZA is the same, although this conclusion is not as sure as for that in the northern hemisphere due to the lack of stations in the southern hemisphere.
 The red dashed line in Figure 2 is a contour where SZA is equal to 90°. It is seen from this figure that the SITEC still exists outside the sunlit region. The TEC enhancements vary from 0.6 to 7 TECU in the region of the SZA between 90° and 100°. In order to reveal this phenomenon in detail, Figure 3 gives the relationship between the values of TEC enhancement and the value of local SZA of corresponding IPPs near the shadow boundary region. From this figure we can see that the TEC enhancements decrease while the local SZA increases in the boundary region. In the region where the local SZA is equal to 90°, the value of TEC enhancement is about 7 TECU. At the region with SZA of 95° the TEC enhancements decrease to about 4 TECU, and at the region with SZA of 100° the TEC enhancements are about 1–2 TECU. As a comparison, the globally largest TEC enhancement caused by the flare occurred on 14 July 2000 was less than 5 TECU; therefore the flare that occurred on 28 October 2003 was a very intense one.
 Because of the absorption along the ray path of radiation by denser neutral atmosphere, the EUV and X ray could not penetrate deep enough to reach the region with very large solar zenith angle, and the obvious increase of electron density at lower height of ionosphere in this region does therefore not exist. Nevertheless, in this region, the extra flare radiation can ionize neutral species in the higher ionosphere due to the limited absorption of EUV along the thinner atmospheric path. Therefore the TEC enhancements in this region mainly come from the higher ionosphere. Figure 4 is a schematic illustration for the sunlit region of the atmosphere to show the interactions between solar radiation and the atmosphere in this region. The distribution of the neutral components in the atmosphere is assumed to be spherically symmetric as indicated in the figure. O represents the center of the Earth, and r is Earth radius. The axis X is directed to the Sun and the axis Z is directed to the Zenith (the solar irradiation is assumed to be plane wave). Solar radiation enters the upper atmosphere horizontally, making a zenith angle of 90°. To calculate the ionization of neutral components, the atmosphere of this part is horizontally stratified into layers, as shown in the figure. The vertical line in each layer represents the furthest position that the radiation can reach. It should be noted that the neutral air in the same layer is inhomogeneous. This figure helps to understand how the observed SITEC is produced in this boundary region.
 Assuming a notional solar flux model during the flare, the electron production rate over the boundary region as showed in Figure 4 can be calculated [Rithbeth and Garriot, 1969]. The number densities of neutral components along the ray path are obtained from the modified MSIS-90 model. The solar flux from EUV to X ray during the flare is assumed to increase by a multiplication factor relative to the background solar flux; for example, the factor between 1025 Å and 103 Å is 10, between 103 Å and 15 Å is 200, and between 15 Å and 1 Å is 10,000. The background solar flux and cross sections for different neutral particles used in photochemical calculations are based on Torr et al. . Figure 5 shows the profile of the electron production rate at different solar zenith angle near this region calculated using above method. From this figure, we can summarize some obvious features about particle ionization over this boundary region. As the zenith angle increasing, the peak height of ionization increases, and the percentage of electron production rate with altitude is larger at larger zenith region. For example, the electron production rate occurs mainly above 200 km over the region of 90° SZA; however, over the region of 95° SZA it becomes mainly above 250 km. Considering the ions-electron recombination process at different altitude, the SITEC over this boundary region should occur in the higher F region.
 In fact, using the observations from GPS stations near the boundary of the shadow on the ground in the night hemisphere, Leononvich et al.  proposed a method for estimating the contribution from different ionospheric regions to the response of TEC variations to the flare occurred on 14 July 2000, and it was found that about 25% of the TEC increase corresponds to the ionospheric region lying above 300 km. In their study, the absolute radiation absorption by neutral atmosphere in the lower height over the shadow region is not considered effectively, so the 25% of the TEC increase should occur higher than the height of 300 km.
 Besides the above-mentioned features, the dependence of TEC enhancement on northern and southern hemisphere occurrence can also be seen in Figure 2. For example, the values of TEC enhancement vary generally from 7 to 11 TECU between the latitude belt of 60°N and 75°N. Then, the values vary only from 4 to 7 TECU between the latitude belt between 60°S and 75°S, although the SZA in the southern hemisphere is about 65° and the SZA in the northern hemisphere is about 80°. This clearly shows that the response of ionosphere to the flare in northern and southern hemisphere is different. The different distribution of the neutral components in northern and southern hemisphere should be responsible for this dependence of TEC enhancement on these two hemispheres.
3.3. TEC Rate Change Curves
 The rate change of TEC obtained from the differential temporal TEC curves has relationship with the evolution of EUV and hard X-ray flux during the solar flare. Therefore the evolution process of the flare can be partly deduced from the change of the ionospheric TEC. Figure 6 shows the rate of TEC derived from GPS measurements (the sample rate at Ramo and Drag stations is 15 s) observed at several GPS stations. Some small but synchronous disturbances on these TEC rate curves are revealed. In detail, there are as many as six of this kind of the synchronous spikes during the TEC increase. Among them, two a bit larger disturbances occurred at about 1102:30 UT and 1105 UT, and the rate of them is about 3 TECU/min and 2 TECU/min respectively. Because these disturbances are synchronous for all curves, it can be concluded that they are caused by the solar flare radiation and the flare demonstrates some sub-burst process; actually, these small ionospheric disturbances show the complicated impulsive phase of the flare. The flux of the soft X ray observed by GOES is also plotted in this figure; small disturbances do not exist in the soft X-ray observation that is coincident with the previous study [Zhang et al., 2002a; Zhang and Xiao, 2003]. The ionization source producing these TEC disturbances includes soft X ray, hard X ray, and EUV. Because the soft X ray observed in GOES has no such kind of synchronous disturbances and the flux of the hard X ray cannot produce the ionization as high as 1016 m−2, we can conclude that the EUV flux must have such kind of disturbance, which is responsible for the synchronous TEC disturbances.
4. Brief Summary
 Using the ionospheric TEC derived from the GPS data observed at 114 GPS stations of the IGS network, the sunlit ionospheric response to the flare occurred on 28 October 2003 is analyzed. It is found that the flare caused a very large SITEC, and the largest TEC enhancement is 17.6 TECU, which is the largest one ever reported so far. The TEC enhancement in the region of local sunrise or sunset is usually larger than 4 TECU. It is worth mentioning that even in the region with the SZA larger than 90°, the SITEC effect is still obvious. Using a photochemical model, the ion production rate over the sunlit boundary region is calculated and some obvious features of SITEC over this region are analyzed. In the polar region, the TEC enhancements caused by the flare are larger than 4 TECU, indicating that the effect of the solar flare on the ionosphere is more obvious than the effect of the ionospheric scintillation over this region. Therefore it is easy to distinguish the flare's effect from the temporal TEC variation curves.
 For the morphological features of the global ionospheric TEC enhancements, it is found that the strength of SITEC varies at different regions. In the northern hemisphere the TEC enhancement is approximately symmetrical to the local noon. When the SZA increases, the TEC enhancement in the northern hemisphere decreases. On the other hand, the response of the ionosphere to the flare in the northern and southern hemispheres is different. It seems that the northern hemisphere (winter hemisphere) responses more sensitively to this flare, especially at high latitudes
 There are small disturbances of the TEC rate that are synchronous for different stations. Since soft X-ray fluxes measured by GOES showed no signs of such spike-like events, this may indicate that these small disturbances are caused by the similar structure of EUV band of this flare.
 Authors would like to thank Asgeir Brekke for constructive discussions and suggestions. We wish to thank referees for so many valuable suggestions that greatly improved the presentation of this paper. We also thank IGS for providing highly accurate GPS data. The NSFC (grants 40274053 and 40134020) and PBEC (grant XK100010404) jointly supported this work.
 Arthur Richmond thanks E. L. Afraimovich and W. Kent Tobiska for their assistance in evaluating this paper.