A Study of Solar Flare Effects on the Geomagnetic Field Components during Solar Cycles 23 and 24

: In this paper, we investigated the impact of solar ﬂares on the horizontal (H), eastward (Y) and vertical (Z) components of the geomagnetic ﬁeld during solar cycles 23 and 24 (SC23/24) using data of magnetometer measurements on the sunlit side of the Earth. We examined the relation between sunspot number and solar ﬂare occurrence of various classes during both cycles. During SC23/24, we obtained correlation coefﬁcient of 0.93/0.97, 0.96/0.96 and 0.60/0.56 for C-class, M-class and X-class ﬂare, respectively. The three components of the geomagnetic ﬁeld reached a peak a few minutes after the solar ﬂare occurrence. Generally, the magnetic crochet of the H component was negative between the mid-latitudes and Low-latitudes in both hemispheres and positive at low latitudes. By contrast, the analysis of the latitudinal variation of the Y and Z components showed that unlike the H component, their patterns of variations were not coherent in latitude. The peak amplitude of solar ﬂare effect (sfe) on the various geomagnetic components depended on many factors including the local time at the observing station, the solar zenith angle, the position of the station with respect to the magnetic equator, the position of solar ﬂare on the sun and the intensity of the ﬂare. Thus, these peaks were stronger for the stations around the magnetic equator and very low when the geomagnetic ﬁeld components were close to their nighttime values. Both cycles presented similar monthly variations with the highest sfe value ( ∆ H sfe = 48.82 nT for cycle 23 and ∆ H sfe = 24.68 nT for cycle 24) registered in September and lowest in June for cycle 23 ( ∆ H sfe = 8.69 nT) and July for cycle 24 ( ∆ H sfe = 10.69 nT). Furthermore, the sfe was generally higher in cycle 23 than in cycle 24.


Introduction
The sun is a powerful star and the primary source of energy on the Earth. The dynamics of the sun's magnetic field is primarily governed by internal dynamo processes which can be quite sporadic in nature. Activities on the sun can significantly affect the environment of all planets in the solar system, particularly Earth's atmosphere. These include solar flares, coronal mass ejections, solar wind, proton events and the emission of gamma rays which can substantially change the magnetic, chemical and electrical status of the geospace environment, thus affecting the Global Navigation Satellite System (GNSS) which has now found diverse applications in various fields. This study focused on the electromagnetic interactions and the related changes in the geomagnetic field during solar flares.

GOES Satellite Data
Between 1996 and 2018, a large number of solar flares (SFs) were produced on the sun, and their effects were felt in all longitudinal sectors on the Earth. The SFs were selected from GOES archives available at www.spaceweatherlive.com/fr/archive.html, accessed on 1 November 2021. The selection was based on the geographical position of the active region (AR) from which the flare was emitted with respect to the Earth. We equally obtained X-ray flux data in the wavelength band of 0.1-0.8 Â from GOES8 (https: //www.ngdc.noaa.gov/stp/satellite/goes/dataaccess.html, accessed on 1 November 2021). Among the 6200 SFs observed, we selected only 289 that presented favorable characteristics for our study. A large part of these flares corresponded with those of published by the service of rapid Magnetic Variation (SRMV) (http://www.obsebre.es/en/rapid, accessed on 1 November 2021).

Magnetometer Data
The magnetic response to the flares was observed at magnetometer stations distributed over three longitudinal sectors: South and North America, Europe-Africa and Asian-Australia longitudes. The horizontal (H), east (Y) and vertical (Z) components of the geomagnetic field were obtained from the magnetometers belonging to INTERMAGNET (https://www.intermagnet.org/data-donnee/, accessed on 1 November 2021). Figure 1 shows the geographical locations of the magnetic observatories while Table 1 presents their geomagnetic and geographic coordinates. In this study, we selected solar flares which occurred during quiet days provided by the World Data Centre for Geomagnetism, Kyoto, Japan. We computed the magnitude of geomagnetic field (∆H) using the ∆X and ∆Y magnetic components as ∆H = (∆X 2 + ∆Y 2 ) 1/2 . In this study, we computed ∆Y and ∆Z following the method in [21]. Then, we estimated ∆H using the method proposed in [22]. The amplitude variations in H, Y and Z components before and after the solar flare were estimated.  The respective amplitude variations X, Y, and Z were computed using Equations (1)-(3).
where X 1 , Y 1 and Z 1 are the values of the geomagnetic field components recorded by magnetometers, and X 00 , Y 00 and Z 00 are the mean values of X 1 , Y 1 and Z 1 between 23:00 LT to 02:00 LT. We finally computed the enhancements due to solar flare on the ∆H s f e , ∆Y s f e and ∆Z s f e using Equations (4)- (6): where H max, Y max , and Z max are the amplitude of geomagnetic components at the peak time of the flare, and X min , Y min and Z min are the values of the field components recorded just before the start time of the flare. We obtained a total of 1025 sunspot numbers in SC23 and 541 in SC24. From SC23 to SC24, we observed a decreasing trend of the sunspot numbers and a corresponding decrease in magnetic activity. This reduction in magnetic activity accounts for the small number of the SFs classes M and X records in SC24.
Atmosphere 2022, 12, x FOR PEER REVIEW 6 of 27 M-class and 144 X-class flares. We obtained a total of 1025 sunspot numbers in SC23 and 541 in SC24. From SC23 to SC24, we observed a decreasing trend of the sunspot numbers and a corresponding decrease in magnetic activity. This reduction in magnetic activity accounts for the small number of the SFs classes M and X records in SC24.  Figure 3 presents the relation between the occurrence of SF of various classes and sunspot number. We took the yearly mean occurrence of flare and sunspot number and computed the correlation coefficient between both quantities. Generally, there was a positive linear relation between solar flare and sunspot number for all flare classes expect A and B class flares. The correlation coefficients were stronger for C-class (0.93/0.97) and M-class (0.96/0.96) and moderate (0.60/0.56) for X-class during SC23/24, respectively. There was no significant difference in the correlation coefficient between SC23 and SC24 despite the obvious difference in the number of sunspots registered during both solar  and B class flares. The correlation coefficients were stronger for C-class (0.93/0.97) and Mclass (0.96/0.96) and moderate (0.60/0.56) for X-class during SC23/24, respectively. There was no significant difference in the correlation coefficient between SC23 and SC24 despite the obvious difference in the number of sunspots registered during both solar cycles.

Variation of Sfe during Selected Solar Flare Events
We are analyzed a total 289 sfes, 73 sfes associate from X-class and 216 sfes associate from M-class. We noted that from 1996 to 2000, the AR of about 23 flares whose effects could still be felt on the geomagnetic field components, had no information about their location on the solar disc. Oppositely, from 2001 to 2018, the AR of 266 flares, had information about their location. Therefore, it was found that 61 of them occurred at the center of the solar disc, 150 on the limb and 55 between the center and the limb otherwise referred to as the "Intermediate Zone" in this work. Table 2 presents the distribution of the flare according to their location on the solar disc. Based on the flare location on the solar disc, we have distinguished relevant categories of sfe on the geomagnetic field components. An example of each flare class has been analyzed as case study. These include the X2.6 solar flare of 27 November 1997, X9.4 solar

Variation of Sfe during Selected Solar Flare Events
We are analyzed a total 289 sfes, 73 sfes associate from X-class and 216 sfes associate from M-class. We noted that from 1996 to 2000, the AR of about 23 flares whose effects could still be felt on the geomagnetic field components, had no information about their location on the solar disc. Oppositely, from 2001 to 2018, the AR of 266 flares, had information about their location. Therefore, it was found that 61 of them occurred at the center of the solar disc, 150 on the limb and 55 between the center and the limb otherwise referred to as the "Intermediate Zone" in this work. Table 2 presents the distribution of the flare according to their location on the solar disc. Based on the flare location on the solar disc, we have distinguished relevant categories of sfe on the geomagnetic field components. An example of each flare class has been analyzed as case study. These include the X2. 6    The latitudinal variation of the magnetic response to the X2.6 solar flare is shown in Figure 5. This figure deals with the diurnal variation of the horizontal (H), eastward (Y) and vertical (Z) components of the Earth's geomagnetic field on 27 November 1997, at stations located in the Europe-Africa longitude. At the MBO station, H suddenly increased and reached a maximum at approximately 13:19 LT. It then dropped and returned to its normal variation at approximately 13:23 LT. The sudden increase in H was observed simultaneously at all stations, but its amplitude differed from one station to the other. For example, it decreased from the stations located close to the magnetic equator to those at the boundaries of the northern and southern hemispheres. The magnetic signature of the flare (ΔHsfe) otherwise known as the magnetic crochet was positive at low latitudes and negative at mid-latitudes. For the X2.6 solar flare, the maximum value of the magnetic crochet was recorded at MBO (ΔHsfe = 24.21 nT) rather than BNG (ΔHsfe = 9.64 nT) which is closer to the magnetic equator. The corresponding local time of occurrence The illuminated part of the Earth during this flare of 27 November 1997, is shown in Figure 4 (left below), with noon in UT closer to Europe-Africa longitude sector. Table 3 presents data obtained from the magnetic stations located on the illuminated part of the Earth during this event. This table contains the IAGA codes of observatories, the solar zenith angle (SZA) calculated from the website http://www.solartopo.com/orbite-solaire.htm, accessed on 1 November 2021, the magnetic crochet value and the universal time of occurrence of the maximum sfe at each station. From this Table 3, it can be seen that the strongest magnetic responses associated with the X2.6 was observed mainly at stations with a low solar zenith angle and which were close to the magnetic equator during the local noon. This was the case of GUI, TAM, STJ, HER and MBO. We also noted that the sfe was not observed simultaneously at all observatories. The time interval varied by few seconds from one station to another. It was observed from Figure 4 (right-below) dealing with the sfe in the South and North America, Europe-Africa and Asia-Australia longitudes during the X2.6 flare event of 27 November 1997, the mean magnetic amplitude of sfe was stronger in the Europe-Africa sector. The latitudinal variation of the magnetic response to the X2.6 solar flare is shown in Figure 5. This figure deals with the diurnal variation of the horizontal (H), eastward (Y) and vertical (Z) components of the Earth's geomagnetic field on 27 November 1997, at stations located in the Europe-Africa longitude. At the MBO station, H suddenly increased and reached a maximum at approximately 13:19 LT. It then dropped and returned to its normal variation at approximately 13:23 LT. The sudden increase in H was observed simultaneously at all stations, but its amplitude differed from one station to the other. For example, it decreased from the stations located close to the magnetic equator to those at the boundaries of the northern and southern hemispheres. The magnetic signature of the flare (∆H sfe ) otherwise known as the magnetic crochet was positive at low latitudes and negative at mid-latitudes. For the X2.6 solar flare, the maximum value of the magnetic crochet was recorded at MBO (∆H sfe = 24.21 nT) rather than BNG (∆H sfe = 9.64 nT) which is closer to the magnetic equator. The corresponding local time of occurrence of the peak solar flare effect was 14:01 LT at the BNG station. For the Eastward component (Y), the magnetic response associated with the November 27, 1997, flare manifested in the form of a negative crochet in the Northern Hemisphere and positive crochet in the Southern Hemisphere. The amplitude reversal occurred between the equatorial stations MBO and BNG. The maximum values of sfe were observed at MBO, were ∆Y sfe = 13.5 nT at 13:19 LT and ∆Y sfe = −6.3 nT at BNG.
The magnetic crochet for the vertical component (Z) had strong amplitudes around the magnetic equator. The maximum value was also observed at MBO, with ∆Z sfe = −7.1 nT at 13:19 LT. We also noticed a reversal of the signs in the amplitude of the magnetic crochet between the GUI, MBO and BNG stations. This value is ∆Z sfe = −0.6 nT at BNG.  UT, reached its peak at 11:55 UT and ended at 12:09 UT. The flare, therefore, lasted for approximately 20 min. The magnetic response associated with this flare is presented in Table 4. The peak amplitudes of the crochets at the magnetometer stations during the solar flare X9.4 are shown in Table 4. This solar flare had a greater magnetic effect at the respective stations. From Figure 6b, the Europe-Africa longitude registered the highest amplitude of the mean magnetic crochet. We therefore limited the analysis of the sfe associated related to this flare to this longitude. In line with this, variations of the geomagnetic components are presented in Figure 7. Despite the strong variation of the geomagnetic components on this day, the magnetic signature of the X9.4 solar flare could still be clearly distinguished at about 12:00 LT. The magnetic crochets were negative at mid-latitudes and positive around the magnetic equator. The fluctuations in the H, Y and Z components from 15:00 UT could have been due to the weak increase in polar cap potential as Dst decreased slightly to reach a minimum of −34 nT at 17:30 UT (not shown). Stations located close to the magnetic equator recorded the highest values of the amplitude of the crochet at about 11:55 LT with MBO recorded a peak ∆H sfe of 56.44 nT at 12:00 LT. show respectively X-ray flux and mean Hsfe for X6.4.      Table 5. Observatories around the magnetic equator with a low SZA had the highest magnetic peaks. The sfe was pronounced in the Europe-Africa sector as seen in Figure 6d. Also, from Figure 8 showing the variation of the sfe with latitude during the M1.4 and M4.2 flares, the magnetic crochets had similar variations on the H, Y and Z components. In addition, the variations in the peak H were not different from the previous cases examined. The peak magnetic crochets associated with the M1.4 class flare amplitude was smaller than the one associated with the M4.  It therefore lasted~5 min. The geographic position of the sunspot from which this flare emanated was S18W51. Table 6 presents the characteristics of stations located at the mid and low-latitudes as well as their corresponding sfes on 3 July 2002 at 02:08 UT. From this table, most magnetic stations with high crochet were characterized by low SZA and were close to the magnetic equator during the local noon. These stations were located in the Asia-Australia longitude. The time of occurrence of the peak crocket in the different stations differed from one place to another with a time difference of just few seconds. Figure 6f shows the mean distribution of sfe in the different longitude sectors. The magnetic crochet over the Europe-Africa longitude was almost zero at 02:13 UT on 3 July 2002 given that stations over this sector were still in the early morning period. The Asia-Australia longitude sector on the other hand, recorded the highest crochet value. The magnetic crochet of the H component in this sector was stronger than in the American sector. The perturbation on the geomagnetic components associated with the X1.5-class solar flare of 3 July 2002 is shown in Figure 9 Table 7. Despite a high SZA certain stations in America recorded sometimes a high peak of sfe than those in the Africa-Europe sector. The histograms in Figure 6e confirm that the sfe was pronounced in the American longitude during this event.  Figure 10a,b shows the sfe on the geomagnetic H, Y and Z components recorded in the South America and Europe-Africa longitudes. The magnetic equator in the South America sector was located around the SJG and KOU, while it was located between MBO and BNG for the African longitude. The sfe on the H component was always reversed between the mid and low-latitudes in both sectors, with a difference in the magnitude of the magnetic crochets. The amplitudes of the Magnetic crochets were greater in the America than Europe-Africa sector. At VSS, the peak ∆H sfe was 66. In Figure 11, we presented two examples of solar flares which occurred successively in the same AR 1882 on 25 October 2013. The X1.7 class flare started at 07:53 LT, reached its peak at 08:01 LT and ended at 08:09 LT, while the X2.1 one that started at 14:51 LT reached its peak at 15:03 LT and ended at 15:12 LT (Figure 11a). The effect of both flares was observed in the Europe-Africa longitude. Their magnetic effects on the H component are shown in Figure 11b. It was observed that irrespective of the flare class, the sfe on H was pronounced when the flare occurred around the local noon at a particular station. For example, the X1.7 resulted in a greater magnetic crochet on H in AAE which was in the local noon. The AAE and SPT stations, recorded the respective peak sfe values of 40.60 nT and 6.53 nT for Class X1.7 flare, and 0.70 nT and 5.2 nT for Class X2.1 flare. For the ASC, DBV and GUI stations, the magnetic effects of the X2.1 class solar flare on H were stronger than those of Class X1.7. The summary synthesis of all class study is presented in the Table 8.     We observe that, the solar flares effects are stronger during March equinox (Febru-ary-March-April) and September equinox (August-September-October), and weak during June solstice (May-June-July) and December Solstice (November-December-January). On the average, the sfes were stronger in the cycle 23 than the cycle 24. The highest sfe value was recorded in September during both cycles with ΔHsfe = 48.82 nT for cycle 23 and ΔHsfe = 24.68 nT for cycle 24. Conversely, the lowest values of the sfe were registered in June for cycle 23 (ΔHsfe = 8.69 nT) and July for cycle 24 (ΔHsfe = 10.69 nT).

Discussion
Since the 19th century, meticulous observations of the sun have made it possible to highlight the regularity in the evolution of sunspots. These sunspots are places where formation of the active regions (ARs) responsible for certain solar events such as solar

Discussion
Since the 19th century, meticulous observations of the sun have made it possible to highlight the regularity in the evolution of sunspots. These sunspots are places where formation of the active regions (ARs) responsible for certain solar events such as solar flares (SFs) form. Past studies have shown that there are several ways of classifying solar flares [23]. During periods of strong magnetic activity, a large number of ARs are visible on the sun. The authors of [24] showed that the cyclic variation of sunspots is essentially identical to that of SFs. However, their study did not highlight the variation of sunspots with different classes of SF. In this paper, we made a correlation study between sunspots and each class of SFs. Our results showed that during solar cycles 23 and 24, the number of C and M-class flares were strongly correlated (0.93/0.97 and 0.96/0.96 during SC 23/24 for the respective flare) with sunspot number, while A and B-class correlated negatively with sunspot numbers. This negative correlation between sunspots and classes A and B is due to the fact that both classes of flare are lagged respect the solar cycle. The X-class flares which has a significant impact on the Earth's atmosphere occurred less and correlated moderately with sunspot number (0.60/0.56 during SC23/24). Previous studies have found that more energetic solar flares do not occur frequently on the sun. For example, it has been shown that approximately less than 100 X class solar flares occur every 125,000 years on the surface of the sun [25,26]. However, the authors of [27] revealed that the largest flares (X45 or X50 class) that occur on the visible hemisphere part of the sun can occur at least once per century. We observed that most of the flares that occurred on the surface of the sun did not have a visible magnetic signature on magnetometer recordings at various ground stations. The reasons for this include the fact that these flares occurred during strong magnetic disturbance when the irregular variation of the geomagnetic field components masked the magnetic crochet. The works in [28,29] revealed that other factors, such as poor distribution of observatories around the globe, lack of stations in ocean regions and natural noise, may prevent the observation of magnetic crochets on geomagnetic field component.
Among the 6200 solar flares observed, we studied only 289 most of which corresponded with the solar flares provided by SRMV (http://www.obsebre.es/en/rapid, accessed on 1 November 2021).
The 289 SFs were studied taking into consideration their position on the solar disc (center, transition zone and limb). We notice that the maximum peak of sfe does not always occur simultaneously at different observatories, and it is more delayed with increasing solar zenith angle in the sunlit hemisphere for some weak sfe. The same results were observed in [9]. It was observed that the sfe produced by the X9.4-class (limb) was smaller than the sfe produce by X6.2-class (center) at the equator. The statistical analysis of the solar flare carried out by [30] showed that a limb flare has a smaller effect than a central flare on the ionosphere. This is due to the EUV absorption in the solar atmosphere. Another factor is the ability of an active region to produce several solar flares as was the case during the two flares of class M1.4 and M4.2, on 30 November 1997. Interestingly, during the successive solar flares of 25 October 2013, some stations experienced stronger sfe during the class X1.7 that occurred at 7:53 UT than the X2.1 one that took place at 14:51 UT. The analysis showed that this case was observed when the effects of the lower-class solar flare were recorded around the local noon time when the H-component usually reached its peak variation. A similar result was obtained at the Millstone Hill station (42.6 • N, 71.5 • W) by [31]. They studied two solar flares the X8.3-class flare and the X9.3-class flare which occurred at 11:00 LT and 7:00 LT, respectively, from the same active region. They showed that the response of the ionosphere to the solar flare X8.3 was more important than the X9.3-class. The analysis of horizontal component H of the geomagnetic field revealed some important characteristics of solar flares. Thus, we note that the stations around magnetic equator during a flare recorded the highest peak of the magnetic crochet. This is due to the high conductivity of this region due to the equatorial electrojet [32]. Furthermore, we observed an inversion of the magnetic crochets on the H component between midlatitudes and low latitudes. Generally, the amplitude of the H component was negative in mid-latitudes in both hemispheres and positive in low latitudes. The authors of [20] showed that the reversed sfe appears as a physical consequence of the ionospheric current system geometry and is due to the displacement that the sfe system undergoes in longitude and/or latitude with respect to the sq system. In addition, note that in most of our cases, the amplitude of the magnetic crocket on the H component was inversely proportional to the solar zenith angle. The authors of [31] showed that the position of the solar flare relative to the solar zenith angle and the power of luminance are determining factors in the ionosphere's response to the solar flare. Furthermore, magnetic crochets are not observed synchronously (a few seconds), in stations separated by a short time.
The analysis of the latitudinal variation of the eastward Y and vertical Z components showed that unlike the horizontal H component their patterns of variations were not coherent in latitude. However, the maximum amplitudes of the sfe on the two components (∆Y sfe and ∆Z sfe ) were observed in the same stations around the magnetic equator, while lower values were obtained over the northern and southern hemispheric limits. Previous studies in [32] have shown that the variations in ∆Y sfe and ∆Z sfe were strongly influenced by the presence of equatorial electrojet and counter electrojet currents around magnetic equator. Similar studies are presented in [33].
In general, the analysis of the variation in latitude of the three components showed a magnetic disturbance appearing as a temporary increase in the diurnal variation of the geomagnetic filed components. The magnetic crochets decreased in amplitude closer to the limits of both sunlit hemisphere and were not observed at night. These peaks were generally stronger for the stations around the magnetic equator and were very low when the geomagnetic field components were close to their night values. Furthermore, it is noted that when a solar flare occurs at a local time close to noon, where the zenith angle is small, the magnetic response was very strong on all geomagnetic components. Such condition favors a strong reaction of the ionosphere to the solar flare and thus, a strong magnetic crochet in stations close to the equator. Studies of the impact of solar zenith angle on SF responses have been conducted in [7,34]. The authors of [7] focused of the sfes on ionospheric absorption with the systematic analysis of ionograms measured at mid-latitude and low-latitude ionosonde stations under different solar zenith angles. [29] analyzed the effect of intense solar flare on TEC variation at low-latitude with and without geomagnetic disturbances, local times effects (solar zenith angle effects) and changing the location of the solar active region. Both studies showed that the solar zenith angle affects the ionospheric response to solar flare.
Finally, the results of the analysis of the monthly variation of SC 23 and 24 sfe revealed that sfe varied from season to season and from cycle to cycle. The average values obtained from a reduced sample of data show that the ∆H sfe is generally higher in cycle 23 than in cycle 24, which could be justified by the higher level of solar activity characteristic of the last solar cycle. In addition, the average sfe values were higher in the equinoctial month in both solar cycles. In summary, the position of the active region on the sun, the local time, the SZA and the seasonal variations (equinox and solstice seasons), are determining factors in the magnetic response of the components, following a solar flare.

Conclusions
In this work we have investigated the effect of SFs on the horizontal (H), eastward (Y) and vertical (Z) components of the earth magnetic field using ground-based magnetometers data during solar cycles 23 and 24 (SC23/24). The relation between sunspot number and solar flare occurrence has also been examined for different flare classes. Our results show that: Funding: This research received no external funding.