The characteristics of the ionospheric response to the solar flare on Apr. 15, 2001 were studied using the total electron content (TEC) obtained at GPS observational stations in the whole sunlit hemisphere under International GPS Service for Geodynamics. It was found that the largest enhancement of the sudden increase of total electron content during this flare is ∼2.6 TECU (1 TECU = 1016 m−2). The effects of solar flare radiation on the ionosphere can be recognized even in the region at 0600 or 1800 LT. Owing to ionospheric scintillation, the TEC enhancement could not be derived from temporal TEC variation curves in high latitudes. On the other hand, the synoptic picture of the sunlit ionospheric response to the flare was obtained, and the results showed the relationship of TEC enhancements with solar zenith angles. The larger the solar zenith angle, the smaller the TEC enhancement. Even minor fast changes in TEC during this flare are revealed in the changing rate of temporal TEC variations in midlatitudes and low latitudes. These small globally synchronous disturbances of TEC were compared with the solar X-ray fluxes of this flare observed by satellites, and a close correlation between those small ionospheric disturbances and the hard X-ray flux fluctuations was found.
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 The extreme ultraviolet (EUV) and X rays emitted during solar flares ionize the neutral components in the ionosphere and increase the ionospheric electron density. This causes many kinds of sudden ionospheric disturbances (SIDs), such as sudden frequency deviation (SFD) [Donnelly, 1967], sudden phase anomaly (SPA) [Jones, 1971; Ohshio, 1971], short wave fadeout (SWF) [Stonehocker, 1970], geomagnetic solar flare effect (GSFE) [Richmond and Venkateswaran, 1971], and sudden increase of total electron content (SITEC) [Garriott et al., 1967]. Since the 1960s, the solar flare effects on the ionosphere have been extensively studied with different observation methods. These studies were well reviewed by Mitra  and more recently by Davies . It is generally accepted that different kinds of SIDs are manifestations of an increase of electron density at different heights [Liu et al., 1996]. For example, SWF and SPA are caused by the increase of electron density in the D and E regions. Although the increase of electron density during a solar flare occurs in every ionospheric region, the increase of electron density in the F region is thought to be responsible for a large fraction of the SITEC, so SITEC can be used as an index to represent the ionospheric response of the F region to solar flares [Mendillo, 1974]. With the advent of satellite beacon methods for observing the ionospheric total electronic content (TEC), it has become one of the chief means for routinely monitoring the F region flare effects. In the study of the ionospheric TEC response to the solar flare, the change of electron density at different height is a noticeable and interesting issue [Thome and Wagner, 1971; Mendillo et al., 1974]. Another interesting problem involves the temporal and spatial behavior of TEC in the sunlit hemisphere. Mendillo et al.  reported contrasting study of TEC and electron density observed by incoherent scatter radar during a flare. They concluded that the electron density increase during the flare occurs mainly in the F region due to the extra ionization of EUV radiation. Mendillo  also 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. Because of the limitation of spatial coverage of the stations, some problems could not be thoroughly analyzed in their study; for example, the relations of TEC enhancement with solar zenith angle were not obvious in their results. Recently, the studies of the ionospheric response to solar flares using the TEC derived from GPS data obtained from the International GPS Service for Geodynamics (IGS) network were reported, which showed the advantages of this method to study this kind of ionospheric disturbance using global GPS network. Using this method, some more detailed correlations were studied and discussed, such as the correlation between the ionospheric disturbances and hard X ray, the ionospheric response to solar flares with different class of X ray, the diurnal variation of TEC enhancement, and the asymmetric response of the ionosphere in the Northern and Southern hemispheres to flares [Afraimovich, 2000; Afraimovich et al., 2000, 2001a, 2001b, 2001c, 2002; Leonovich et al., 2002; Zhang and Xiao, 2000a, Zhang et al., 2002a, 2002b].
 Two-frequency observations of GPS signals provide a relative ionospheric delay of the two-frequency electromagnetic waves traveling through a dispersive medium. The TEC along the line of sight is derived from this delay [Lanyi and Roth, 1988]. The ionospheric study in this way has the advantages of higher precision, higher spatial and temporal resolution, much wider spatial coverage, and ease of data availability [Moore, 2001]. Since the advent of GPS, the study of the ionospheric disturbances using GPS data has been reported frequently. Besides of the study of ionospheric response to solar flare, Ho et al. [1996, 1998] studied the evolutions of the global ionospheric TEC using GPS measurements from the IGS network for two magnetically disturbed periods. Saito et al.  mapped the two-dimensional TEC disturbances and observed a large traveling ionospheric disturbance over Japan with the local GPS network, i.e., GPS Earth Observatory Network (GEONET), the densest local GPS network in the world. Some other authors reported the study of the ionospheric response to large earthquakes [Calais and Minster, 1995; Afraimovich et al., 2001d], rocket launches [Calais and Minster, 1996; Afraimovich et al., 2000], and industrial surface explosions [Fitzgerald, 1997].
 A remarkable problem put forward in our former study is that the morphological characteristics of the sunlit ionospheric response to flares were quite different [Zhang and Xiao, 2000a, Zhang et al., 2002a]. Therefore more case studies of the ionospheric response to flares are necessary, especially the response of sunlit ionosphere covering as vast an area as possible. The period of 1–15 April 2001 was a solar active interval during which a number of large solar flares occurred. Considering the most favorable locations of GPS stations in the sunlit hemisphere during flare burst, we have chosen to study in this paper, using GPS data obtained in the IGS network, the ionospheric response to the flare that occurred at 1336 UT on 15 April 2001.
2. Observations and Methods
 The maximum X-ray flux of the flare observed by Geosynchronous Operational Environmental Satellites (GOES) is X14.4/2B, and it occurred in solar active region 9415 classified by the National Oceanic and Atmospheric Administration. The location of the flare on the solar disk was 20°S, 85°W, which was near the west limb of the Sun. The start, maximum, and end times of the flare were 1336, 1349, and 1535 UT, respectively. Its time evolution showed that this flare was a kind of impulsive flare. In order to reveal the whole sunlit ionospheric response to the flare, as many observations as possible from the GPS receivers in the IGS network located in the sunlit hemisphere were collected. Table 1 is a list of these GPS stations' geographic parameters and their local time when the flare occurred.
Table 1. The Names and Their Geographical Locations of GPS Stations Used in the Study
 The GPS data as standard Receiver Independent Exchange (RINEX) format can be downloaded from Internet site on the Srripps Orbit and Permanent Array Center (SOPAC) server (available at ftp://lox.ucsd.edu). The temporal resolution of the data is usually 30 s. All stations use high precision, dual-frequency GPS receivers, which can provide carrier phase and pseudo-range measurements in two L-band frequency (f1 = 1575.42 MHz, f2 = 1227.60 MHz) simultaneously every 30 s. Using these four measurements, combining the geometrical relation of the satellite, ionosphere, and receiver, a precision TEC can be derived at every observational epoch according to equation (1). [Lanyi and Roth, 1988; Hofmann-Wellenhof et al., 1992; Mannucci et al., 1998; Zhang and Xiao, 2000b]. For each GPS station of IGS, at least four TEC values with different ionospheric penetration points (IPPs), which is the point of intersection of the line of sight and the ionospheric shell, can be derived for an interval of 30 s. In order to compare the TEC values obtained from different satellite-receiver pairs, the TEC along each line of sight should be converted to the vertical TEC at every IPP. Since the timescale of a sudden increase of TEC during a flare is usually short, the TEC enhancement caused by the extra radiation of the flare can be considered to be at the same IPP. During the TEC calculation the satellites' instrumental bias is removed, but the receivers' instrumental bias is not removed. Since this study is focused on ionospheric disturbances caused by flare radiation, only relative TEC changes or TEC enhancements during the flare are useful, and it is reasonable to ignore the receiver's biases.
where dtri and dtpi are the time delays calculated from the measurements of two-frequency pseudoranges 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. The variable χi is the satellite zenith angle at the IPP at the height of the ionospheric shell hion, which is taken to be 400 km in this study. The variable 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.
 The height of the ionospheric shell is a parameter that affects the precision of the TEC calculation. Nevertheless, it is impossible to obtain the real value of the height on the whole sunlit hemisphere. The values of the height calculated from the profiles of the electron density at different latitudes obtained in IRI model varies from 300 to 500 km or so [Zhang and Xiao, 2000b]. So in this study we set this height to be 400 km that is more reasonable in the region of lower and middle latitude. Actually, if the elevation is large, the influence of its value on the TEC calculating is very small. According to the calculating results, the relative error of the TEC calculated using above formulas is larger than the relative error of the TEC calculated from GPS dual carrier phase measurements that does not exceed 1014 m−2 [Hofmann-Wellenhof et al., 1992] but is still sufficient for the study of this kind of ionospheric disturbance.
 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 exist 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 expression (2), DTEC can be regarded as the TEC change caused mainly by the flare extra radiation. Actually, the second term on the right-hand side of expression (2) is the TEC change of the background ionosphere during this period.
3. Results and Analysis
3.1. Temporal Total Electron Content (TEC) Variation Curve
Figures 1a–1d show some temporal TEC variation curves derived from observations from four GPS receivers located in the region of lower solar zenith angles during the flare period. It can be seen that the phenomenon of the SITEC appears during the flare and the recovery time of ionosphere lasts more than 1 hour. At ∼1344:30 UT the TEC suddenly increases and lasts until 1352:30 UT. During this period the largest TEC increases as high as 2.6 TECU or so. Using TEC derived from GPS data of the IGS network, Zhang and Xiao [2000a]; Zhang et al. [2002a] studied ionospheric response to two large flares that one occurred on 6 November 1997 (flare's class is X9.4/2B; its location on solar disc is 18°S, 63°W), the other occurred on 14 July 2000 (flare's class is X5.7/3B; its location on solar disc is 22°N, 07°W), and results showed that the largest TEC increase on 6 November 1997 is ∼2.8 TECU [Zhang and Xiao, 2000a], and the largest TEC increase on 14 July 2000 is ∼5.6 TECU [Zhang et al., 2002a]. Compared with the values of TEC enhancement during the flare on 6 November 1997 and on 14 July 2000, the ionospheric TEC response to this flare is weaker, although its maximum X-ray flux is much larger than that of the other two flares. In the past decades many authors focused on the relationship between the ionospheric response to solar flare intensity and the location of the flares on the solar disc. By analyzing the numerous data obtained from frequency Doppler shift of the ionospheric-reflected short-wave radio signal in detecting the ionospheric effect to solar flares, Donnelly [1969, 1971, 1976] carried some pioneering works about the relationship between the ionospheric response to flares and their locations on the Sun, it was found that the amplitude of the ionospheric response decreased with the angular distance of the flare from the central meridian of the Sun. By analyzing the correlation of solar radio bursts and SITEC of the ionosphere, Matsoukas et al.  obtained similar results. More recently, using TEC derived from IGS network during the flares of the different X-ray classes, Afraimovich et al. [2001c, 2002] and Zhang et al. [2002b] also studied the relationship between the TEC increases and the flares' parameters, and similar results were obtained. The parameters of this flare indicate that the angular distance of the flare is 85°W and is larger than the angular distances of the other two flares that occurred on 6 November 1997 and on 14 July 2000. So this result is in agreement with the conclusions made previously [Donnelly, 1969, 1971, 1976; Matsoukas et al., 1972; Afraimovich et al., 2001c, 2002; Zhang et al., 2002b].
 On the other hand, since the TEC increase is produced mainly by the additional ionization of the extra radiation of EUV, the dependence of TEC enhancement on the angular distance of the flare implies that the EUV radiation flux near the Earth also depends on the location of the flare on the solar disc. It is thus further concluded that the X-ray flux in the band of GOES observation does not correlate with EUV flux in geospace during the solar flare. It is generally believed that the regions of soft X-ray radiation and EUV radiation in the solar atmosphere during the flare are different. The soft X-ray region is generally thought to have thermal origin and is much higher than the region of the EUV and, hard X ray is thought to be thick target bremsstrahlung by energetic electrons [Adriana et al., 2000]. We guess that the dependence of EUV radiation flux on the flare location on solar disc could be explained if the solar atmospheric absorption to EUV radiation is taken into account. To verify this hypothesis, more statistical and theoretical study is needed.
Figures 1e–1f show several temporal TEC variation curves derived from the GPS measurements made at two stations located in the sunrise and sunset regions, respectively. It can be seen that the SITEC still occurs even at such large solar zenith angle, and the value of the TEC enhancement varies from ∼0.5 to 1 TECU.
Figures 1g–1h plots the temporal TEC variation curves derived from the GPS measurements made at two high-latitude GPS stations. Because strong GPS signal fluctuations in amplitude and phase occurred (due to the existence of high-latitude irregularities), the quality of the GPS data was degraded [Thomas et al., 2001]. From Figure 1 we can see that the TEC fluctuation is so severe that the TEC change caused by flare radiation could not be distinguished from the temporal TEC variation curves. Figure 2 shows the temporal rate of TEC variations, which can be as high as 0.5 TECU every 30 s. The flare's effect cannot be distinguished from these curves either, so the value of the TEC enhancement cannot be derived from these curves. This implies that the effect of scintillations on the GPS system is more severe than the effect of the solar flares in high-latitude regions.
3.2. The Distribution of TEC Enhancement in the Sunlit Hemisphere
 The TEC enhancement at each IPP can be derived from the temporal TEC variation using expression (2). Figure 3 shows the synoptic picture of the ionospheric TEC enhancement over the sunlit hemisphere. The open triangles in Figure 3 represent the positions of the GPS stations, and the dashed contour lines in Figure 3 represent the solar zenith angle of sunlit hemisphere at 1348 UT. The locations of circles in Figure 3 represent every IPP, and their darkness level represents the value of TEC enhancement. The spatial characteristic of the sunlit ionospheric response to the flare is shown in Figure 3. On the whole, the flare radiation affects entire sunlit ionosphere and the smaller the solar zenith angle, the larger the TEC enhancement. In the areas near sunrise and sunset, the influence of the flare on the ionosphere still can be distinguished. In fact, using the observations from GPS stations near the boundary of the shadow on the ground in the night hemisphere, Leonovich et al.  proposed a new method for estimating the contribution from different ionospheric regions to the response of TEC variations to the flare that occurred on 14 July 2000, and it was found that ∼25% of the TEC increase corresponds to the ionospheric region lying above 300 km. By the way, there are six GPS stations in the region of high latitudes (>60°S or >65°N); the TEC enhancements could not be derived from the temporal TEC variations due to the GPS signal fluctuation even if the flare effects on the ionosphere exist.
Figure 4 shows the relationship of TEC enhancement with the solar zenith angle at corresponding IPP; their correlation can be clearly seen and is in accord with Chapman ionospheric theory [Rithbeth and Garriot, 1969]. Because of the larger number of ionospheric observatories and their better spatial distribution, the correlation of TEC enhancement with solar zenith angle shown in Figure 4 is clearer than that obtained by Mendillo et al. . Actually, the similar correlation was also obtained in our previous study about the ionospheric response to the flare on 14 July 2000 using TEC derived from the IGS network [Zhang et al., 2002a].
 The diurnal dependence and Southern and Northern hemisphere difference of the ionospheric response to flare are two interesting issues. Using the solar radio bursts flux and the simultaneous ionospheric TEC records from August 1968 to August 1970, Matsoukas et al.  studied the diurnal variations of the SITEC and found that radio bursts are likely to be less associated with SITEC during the early morning. For example, among the 12 solar radio bursts occurring in the morning and afternoon, respectively, only three SITEC events happened during the morning, but seven SITEC events happened during the afternoon. By means of the values of SITEC derived from the observations of GPS receivers of IGS located between the latitude belt of 30° and 45°N, Zhang and Xiao [2000a]; Zhang et al. [2002a] studied the diurnal variation of SITEC during the two flares mentioned above and found an obviously asymmetrical feature to the local noon during the flare on 6 November 1997 and a weaker asymmetrical feature to the local noon during the flare on 14 July 2000. However, the ionospheric response of the region in the local morning to the flare on 6 November 1997 is stronger than the response in the afternoon, which was very different to the result Matsoukas et al.  obtained. Besides the diurnal variations of SITEC, the dependence of the hemisphere about the ionospheric response to solar flare was also analyzed in the study of the ionospheric response to the flare on 14 July 2000; it was found that the TEC increases in the Southern Hemisphere was larger than that in the Northern Hemisphere for the same solar zenith angle. Figure 5 shows the diurnal variation of TEC enhancement between the latitude belt of 30° and 45°N. The distribution of the TEC enhancement along the longitude belt corresponding to 0800 and 0900 LT is plotted in Figure 6. In comparison with the ionospheric response to the other two flares on 6 November 1997 and 14 July 2001, the asymmetrical response to the flare in the region of local morning and local afternoon, and the different response in the Northern and Southern Hemispheres are weaker also. As Matsoukas et al. mentioned, besides the solar zenith angle, other factors, such as the absolute value of TEC and the neutral and the electron density profiles, also play important roles in the global ionospheric response on the radiation of solar flare. We think that further case studies and analysis will be helpful for the understanding of the characteristics of the global ionospheric response to solar flare. In order to explain these differences, the global distribution of the atmospheric neutral compositions during these flares is needed.
3.3. The Temporal Rate of TEC Variation
 The temporal rate of TEC variation, which can be derived from the temporal TEC variation curves, is useful in understanding the fine structure of the ionospheric disturbances and in revealing the flare evolution. Afraimovich et al.  suggested the concept of a new technology for global detection of atmospheric disturbances of natural and technogenic origin by means of GPS observations. Then, the temporal rate of TEC and its corresponding with hard X ray during some flares were studied according to this concept [Afraimovich et al., 2001a, 2001b]. In the study of the ionospheric response to the solar flare on 14 July 2000, the global correlative minor disturbances were shown in the temporal rate of TEC variation [Zhang et al., 2002a].
Figure 7 shows the temporal rate of TEC curves obtained at several GPS stations at the beginning of the flare. The rate of TEC (ROT) increases quickly; it reaches its maximum at ∼1346 UT and lasts ∼4 min, then the ROT begins to decrease until 1356 UT. It is noticeable that some minor synchronous disturbances exist in these ROT curves, which occur at ∼1347, 1348, 1349, and 1354 UT. The last minor disturbance lasts ∼2 min, and the others last ∼1 min. The level of this kind of disturbances is above 0.1 TECU. Actually, these minor synchronous disturbances exist in the entire sunlit hemisphere, indicating that they are not caused by any dynamic process in the ionosphere; the variations of this flare radiation must correspond to these small disturbances. According to the ionospheric continuity equation, the rate of electron density variation with time is proportional to the electron production rate, which is directly related to solar radiation if the electron loss process is ignored [Rithbeth and Garriot, 1969]. By integrating the production rate of the electron density along altitude we can see that the rate of TEC is also proportional to the integrated rate of electron production rate. Therefore these minor synchronous disturbances must be produced by the solar radiation that has similar minor disturbances. The solar radiations that can ionize the neutral atmosphere at ionosphere heights include X rays and EUV. It is usually believed that the correlation among EUV, hard X ray, and solar radio bursts in centimeters is good during the flare [Vanderveen et al., 1988]. Mendillo  compared the rate of change of TEC with the solar radio flux at 35 GHz and found a good correlation between them. Matsoukas et al.  studied the correlation of solar radio burst and sudden increases of the TEC. These studies were useful for us to understand the ionospheric changes during the flare. But because the solar radio flux is not the source of ionization for the ionosphere, more direct observations between X ray, EUV, and ionospheric changes during the flare are needed. In recent years, observations of solar X rays and UV from space became available. Using these data, some new results were obtained [Kosugi et al., 1991; Warren, 2000]. Similar to the works that Afraimovich  and Afraimovich et al. [2001a, 2001b] published, Figure 8 shows the correlation between the rate of TEC and X-ray flux observed by the GOES and Yohkoh satellites during this flare. It can be seen from Figure 8 that the correlation between the rate of TEC and the soft X ray (wavelength = 1–8 Å) is not good, but the correlation with hard X ray (in the band of 53–93 KeV) observed by Yohkoh is so obvious that some minor disturbances also appear in the hard X-ray flux. On the other hand, as pointed out by Afraimovich et al. [2001b], GPS data with a time resolution of 30 s is insufficient for a detailed analysis of the fine structure of the SID time dependence. In Figure 8d the sample rate of the GPS observation is 15 s, and more fine structure of the synchronous disturbances can be seen. It is found that there are two peaks in the first disturbance of the ROT curves that is completely correlated with the profile of hard X ray. Although there are no observations on hard X rays after 1352 UT, from the last disturbance in the ROT curves that appears at ∼1354 UT we can guess that similar disturbances would exist in the hard X-ray flux around this time. So if the time resolution of GPS data is high enough, the rate of the change of ionospheric TEC should be one feasible method to deduce some features of the flare evolution during the impulsive phase of solar flare.
 The ionospheric response to the flare which occurred at 1336 UT on 15 April 2001 was analyzed throughout the sunlit ionosphere. TEC curves and TEC enhancements were derived from the measurements of as many as 54 GPS stations during the flare. The results demonstrate that SITECs occur in the whole sunlit ionosphere due to solar flare radiation. The largest value of TEC enhancement in the sunlit ionosphere is ∼2.6 TECU. The influences of the flare radiation even reach the region 0600 and 1800 LT where the solar zenith angle is as high as 85° and the values of TEC enhancement are only ∼0.5 TECU. Because of the background ionospheric scintillation, the SITEC could not be revealed, and the TEC enhancements could not be derived from the temporal TEC variations at high latitudes. From the synoptic picture of the sunlit ionospheric response to the flare, we see the diurnal dependence of the ionospheric response to the flare, but no obvious asymmetrical feature of the ionospheric response to the flare appeared during the flare on 6 November 1997. The feature of the hemisphere dependence of the ionospheric response observed during the flare on 14 July 2000 is also unobvious in this flare. In order to explain these differences, the global distribution of the atmospheric neutral compositions during these flares is needed. On the other hand, the dependence of TEC increases on solar zenith angle at each IPP is observed again; the smaller the solar zenith angle, the larger the TEC enhancement.
 Some minor synchronous disturbances appear in the curves of the rate of TEC. Each minor disturbance lasts ∼1 min, and the amplitude of this kind of disturbance is above 0.1 TECU. These synchronous disturbances of this kind exist in the whole sunlit ionosphere. The disturbances are directly related to the process of the flare evolution. By comparing this kind of disturbance with the X-ray flux, the similar disturbances also appear in the hard X ray flux observed by the Yohkoh satellite, but no similar disturbances appear in the soft X-ray flux (wavelength = 1–8 Å) observed by GOES satellite. The ROT variations derived from GPS data with temporal resolution of 15 s observed at one GPS station are also obtained, and more fine structure of the ionospheric disturbances is revealed in these ROT curves. Therefore if the temporal resolution of the raw GPS data from IGS is high enough, more fine structure of ionospheric disturbances can be revealed, from which the process of flare evolution in hard X ray or EUV can be partly deduced also.
 The authors are grateful to Amy Knack for his assistance in combining the suggestions of referees to one marked copy. We wish to thank the referees and their colleagues for so many valuable suggestions that greatly improved the presentation of this paper. We also thank IGS for providing highly accurate GPS data. The National Natural Science Foundation of China (grants 40274053 and 40134020) and the Chinese Basic Key Research Program (grant G2000078408) jointly supported this work.
 Arthur Richmond thanks E. L. Afraimovich and Kenneth Davies for their assistance in evaluating this manuscript.