Temporal and seasonal variability of low-latitude D-region ionospheric response to solar flares using VLF observations

Temporal and seasonal variability of low-latitude D-region ionospheric response to solar flares using VLF observations | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Temporal and seasonal variability of low-latitude D-region ionospheric response to solar flares using VLF observations Shivani Chandra, Rajat Tripathi, Mahesh N. Shrivastava, Abhirup Datta, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8615895/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The present work investigates the impact of solar flares on the D-region ionosphere using Very Low Frequency (VLF) signals transmitted from NWC (21.81°S, 114.16°E; 19.8 kHz) and recorded at a low-latitude receiving station in Dehradun, India (30.31°N, 78.03°E). The analysis covers the period from July 2022 to June 2023 and includes a total of 234 solar flare events, comprising 153 C-class and 81 M-class flares. Variations in VLF signal amplitude were examined in conjunction with solar X-ray flux data obtained from the GOES satellite. The amplitude difference (ΔA) between flare and non-flare days, as well as the time delay (Δt) between the GOES X-ray flux peak and the corresponding VLF response, were analyzed as functions of local time and season. The results reveal a pronounced local time dependence of both amplitude enhancements and response delays, with maximum perturbations observed during the morning hours for both flare classes. Seasonal analysis indicates stronger ionospheric responses during winter compared to summer and equinox periods, likely due to reduced background electron densities in the D-region. Several anomalous amplitude variations that could not be explained solely by local time or seasonal effects were attributed to factors such as the location of the flare on the solar disk and prevailing geomagnetic conditions. These findings suggest complex interdependencies among solar, ionospheric, and geomagnetic parameters. This study extends previous investigations by providing a comprehensive temporal and seasonal characterization of the low-latitude D-region ionospheric response to solar flare activity, emphasizing the roles of solar zenith angle, flare intensity, and ionospheric relaxation processes. Solar Flare D-region Ionosphere VLF Signal Temporal Variation Seasonal Variation Solar X-ray Flux Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Key points 1. VLF signal amplitude shows local time and seasonal dependence, peaking in the morning and winter. 2. Time delay between X-ray peak and VLF response varies with flare intensity, local time, and season. 3. A nonlinear relationship exists between flare intensity and VLF amplitude change, influenced by flare location and geomagnetic factors. 1. Introduction Solar flares are sudden and intense releases of electromagnetic energy from the Sun, resulting from the rapid reconfiguration of stressed solar magnetic fields. These events emit radiation across a broad range of the electromagnetic spectrum, including Extreme Ultraviolet (EUV), X-rays, and radio waves. Enhanced solar radiation during flare events significantly affects Earth’s ionosphere, particularly the D-region, by increasing ionization levels (Mitra, 1974). The D-region, located between approximately 60 and 90 km altitude in the upper mesosphere and lower thermosphere, is the lowest ionospheric layer and plays a critical role in radio wave propagation. Under quiet solar conditions, ionization in the D-region is primarily maintained by solar Lyman-α radiation (121.6 nm), which ionizes nitric oxide (NO) molecules (Hargreaves, 2003). During solar flares, however, enhanced soft X-ray radiation in the 0.1–0.8 nm wavelength range leads to additional ionization of neutral atmospheric constituents, particularly molecular nitrogen (N₂) and oxygen (O₂), resulting in a rapid increase in electron density (Nicolet and Aikin, 1960). These changes strongly influence the propagation characteristics of Very Low Frequency (VLF; 3–30 kHz) radio signals within the Earth–ionosphere waveguide (EIWG). Consequently, VLF observations have been widely used as a sensitive diagnostic tool for monitoring D-region ionospheric variability (Grubor et al., 2005 ; Maurya et al., 2010 , 2018 ; Phanikumar et al., 2014 ; Singh et al., 2011 , 2012 ; Kumar et al., 2023 ). The response of the D-region ionosphere to solar flares has often been characterized using the waveguide parameters reference height (H′) and sharpness factor (β), which describe the effective reflection height and electron density gradient, respectively. These parameters are commonly estimated using the Long Wave Propagation Capability (LWPC) model (Wait and Spies, 1964 ). For example, Singh et al. ( 2014 ) analyzed solar flare events during the rising phase of Solar Cycle 24 using VLF signals from the NWC transmitter recorded at a low-latitude station in India, reporting a reduction in H′ by 5–6 km during an X-class flare and an increase in β to ~ 0.48 km⁻¹. McRae and Thomson (2004) investigated flare-induced ionospheric perturbations using multiple VLF transmitter–receiver paths and observed amplitude enhancements of up to ~ 10 dB and significant phase delay reductions during strong flares. Their results indicated a decrease in H′ from ~ 71 km to ~ 58 km and an increase in β to saturation values near 0.52 km⁻¹, with VLF amplitude enhancements scaling logarithmically with X-ray flux. Most previous studies have primarily focused on flare-induced changes in VLF signal amplitude and phase associated with enhanced solar X-ray flux (Grubor et al., 2005 ; Zigman et al., 2007; Kumar and Kumar, 2014 , 2018 ; Kolarski and Grubor, 2014 ; Hayes et al., 2017 ). However, relatively fewer investigations have addressed the temporal response of the D-region ionosphere, often referred to as ionospheric “sluggishness” (Appleton, 1953 ) or “relaxation time” (Mitra, 1974). This time delay between the peak of the solar X-ray flux and the corresponding VLF signal response arises from the balance between electron production and loss processes in the D-region and provides valuable insight into ionospheric chemistry and recombination mechanisms (Basak and Chakrabarti, 2013 ; Hayes et al., 2017 , 2021 ; Žigman et al., 2007 ). Additionally, the dependence of this response on local time, season, and geomagnetic conditions remains insufficiently explored, particularly at low latitudes. Selvakumaran et al. ( 2015 ) examined 41 solar flare events using VLF observations from the NWC transmitter recorded at Allahabad, India, and demonstrated that the ionospheric response time varies with flare class, local time, and geomagnetic activity. While their study provided important insights, it was limited in terms of event statistics and seasonal coverage. In this context, the present study aims to investigate the effects of solar flares on the low-latitude D-region ionosphere using VLF observations from the NWC transmitter (19.8 kHz) recorded by an UltraMSK receiver at Dehradun, India (30.3165°N, 78.0322°E), covering the period from July 2022 to June 2023. A total of 66 solar flare events, including 40 C-class and 26 M-class flares, are analyzed. The study focuses on (i) flare-induced changes in VLF signal amplitude difference (ΔA), (ii) the temporal delay between GOES X-ray flux peaks and VLF responses, and (iii) the dependence of these parameters on local time and seasonal variability. By providing a detailed temporal and seasonal characterization of flare-induced D-region perturbations at low latitudes, this work contributes to a more comprehensive understanding of ionospheric response processes and extends earlier studies based on shorter datasets and limited seasonal coverage. 2. Data and Methodology VLF signal data were recorded using the Ultra MSK recording setup at a receiver located in Dehradun, India (30.3° N, 78.1° E). This setup monitors VLF transmissions from the NWC transmitter (21.8° S, 114.2° E) from Australia operating at 19.8 kHz. A total of 234 solar flares—comprising 153 C-class and 81 M-class events—were selected for analysis, based on the availability of VLF data from the Dehradun receiver, during the period from Nov 2020 to Jan 2025. Only flares occurring between 00:00 UT and 12:00 UT were included in the study. Information on flare intensity, start time, peak time, and end time was obtained from https://spaceweatherlive.com . X-ray flux data in the 0.1–0.8 nm wavelength range were sourced from the Geostationary Operational Environmental Satellite (GOES) operated by the National Oceanic and Atmospheric Administration (NOAA), USA ( http://www.sec.noaa.gov ). In the present study, the amplitude difference (ΔA) was computed using the equation: $$\:\varvec{\Delta\:}\mathbf{A}=\:{\text{A}}_{\mathbf{f}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{e}\:\mathbf{d}\mathbf{a}\mathbf{y}}\:-\:{\text{A}}_{\mathbf{n}\mathbf{o}\mathbf{n}\:\mathbf{f}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{e}\:\mathbf{d}\mathbf{a}\mathbf{y}}$$ where \(\:{\text{A}}_{\mathbf{f}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{e}\:\mathbf{d}\mathbf{a}\mathbf{y}}\) denotes the peak amplitude of the VLF signal on the day of a flare, and \(\:{\text{A}}_{\mathbf{n}\mathbf{o}\mathbf{n}\:\mathbf{f}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{e}\:\mathbf{d}\mathbf{a}\mathbf{y}}\) corresponds to the peak amplitude on a quiet day with no solar activity (Selvakumaran, 2015). The time delay between the VLF signal response and the X-ray flare was calculated for the start, peak, and end times using: $$\:\varDelta\:\mathbf{t}={\mathbf{t}}_{\mathbf{V}\mathbf{L}\mathbf{F}\:}-\:{\:\mathbf{t}}_{\mathbf{X}-\mathbf{r}\mathbf{a}\mathbf{y}\:\mathbf{f}\mathbf{l}\mathbf{u}\mathbf{x}}\:,$$ where \(\:{\mathbf{t}}_{\mathbf{V}\mathbf{L}\mathbf{F}}\) represents the corresponding start, peak, or end time observed in the VLF data, and \(\:{\mathbf{t}}_{\mathbf{X}-\mathbf{r}\mathbf{a}\mathbf{y}\:\mathbf{f}\mathbf{l}\mathbf{u}\mathbf{x}}\) is the respective time obtained from GOES observations. Local Time (LT) was calculated using the relation: LT = Universal Time UT + 05:30hours. Two case studies of M-class and C-class flares are illustrated in Figs. 1 and 2 . On 18 January 2023, an M1.7-class flare detected by GOES began at 10:21 UT, peaked at 10:35 UT (16:05 LT), and ended at 10:52 UT. The corresponding VLF signal perturbation began at 10:29 UT, peaked at 10:39 UT (16:09 LT), and concluded at 11:01 UT. Similarly, on 25 February 2023, a C8-class flare commenced at 04:12 UT, peaked at 04:22 UT (09:52 LT), and ended at 04:32 UT. The associated VLF signal response began at 04:21 UT, reached its peak at 04:28 UT (09:58 LT), and ended at 04:42 UT. In both cases, the VLF amplitude response exhibited a delay relative to the GOES X-ray flux peak. This time lag is consistent with previous studies (Kumar and Kumar, 2014 ; Selvakumaran, 2015; Grubor et al., 2005 ; Zigman et al., 2007), which attribute such delays to the ionization and relaxation dynamics of the D-region of the ionosphere. The variation in the amplitude of the NWC transmitter signal (19.8 kHz) in response to GOES X-ray flux for solar flares occurring in different months is presented in Figs. 1 and 2 . The VLF signal amplitude difference (ΔA) is directly influenced by enhanced solar X-ray flux and can be effectively used to infer changes in electron density in the lower ionosphere associated with solar flare activity. Previous studies, such as Selvakumaran (2015), examined the impact of solar flares on VLF signal amplitude and reported that ΔA generally increases with flare intensity; however, the relationship is nonlinear. In several cases, weaker flares were found to produce larger amplitude perturbations than stronger flares. This behaviour was attributed to factors including the local time of flare occurrence, pre-flare ionospheric conditions, and flare class (C, M, or X). That study also reported a time delay (Δt) between the peak of the solar X-ray flux and the corresponding peak in the VLF signal response, which varied with both flare intensity and local time (morning, noon, and evening). The characteristics of all solar flare events analyzed in the present study are compiled and provided in Supplementary Table S1 . The selected events include both C- and M-class flares, covering a wide range of X-ray flux intensities. In the present analysis, ΔA for C-class flares ranges from 0.18 to 2.65 dB, while for M-class flares it ranges from 0.39 to 5.41 dB. The intensities of the analyzed flares span from C1.9 to C9.9 for C-class and from M1.0 to M8.77 for M-class events. Thus, the analyzed flares differ significantly in X-ray flux intensity, leading to varying degrees of ionospheric response. A third-degree polynomial fit is applied to represent the relationship between flare intensity and amplitude perturbation, as this provides the best fit to the observed data. This approach is consistent with earlier findings by McRae and Thomson (2004) and Selvakumaran et al. ( 2015 ). As noted in these studies and confirmed here, the nonlinear behavior of ΔA with flare intensity is likely influenced by pre-flare ionospheric conditions and local time effects. To minimize pre-flare contamination, a minimum time separation of approximately two hours was maintained between consecutive flares; events occurring closer in time were excluded from the analysis. In general, ΔA increases with increasing flare intensity, although the variation is not linear. For example, two C-class flares (C5.8 and C3.7) occurring on 18 August 2022 produced ΔA values of 1.14 dB and 0.31 dB, respectively. However, inconsistencies are also observed for flares of similar class occurring on different days. For instance, a C9.9 flare on 25 September 2023 (13:45 LT) produced a ΔA of 1.49 dB, which is lower than the ΔA of 1.98 dB observed for a C9.0 flare on 9 April 2023 (11:40 LT). Such discrepancies are attributed primarily to local time dependence of the solar flare–ionosphere interaction. Similar behavior is observed for M-class flares. For example, an M5.41 flare on 30 March 2023 (13:09 LT) produced a ΔA of 3.48 dB, which is lower than the ΔA of 4.10 dB observed for an M5.08 flare on 16 August 2023 (13:31 LT). These anomalies further support the conclusion that local time plays a critical role in modulating the VLF amplitude response to solar flares. To investigate the dependence of ΔA on local time, flare occurrences were categorized into three local time intervals: morning (06:00–10:00 LT), noon (10:00–15:00 LT), and evening (15:00–18:00 LT). This classification enables a systematic examination of diurnal effects on ionospheric response. Table 1 , summarizes the average values of ΔA, Δt, H′, and β for C- and M-class flares within these time intervals. The analysis reveals that both C-class and M-class flares exhibit maximum amplitude differences during the morning hours, followed by reduced responses around noon and evening. Although ΔA generally decreases from morning to noon and shows a slight increase toward evening, the overall trend is not strictly linear, reflecting the combined influence of solar zenith angle, background electron density, and flare intensity on the D-region ionosphere. 3. Results and Discussion In this section, we investigate the impact of solar flares on the D-region of the ionosphere by analyzing amplitude variations in VLF signal propagation. Specifically, we examine the variation in amplitude difference with respect to local time and seasonal dependence to better understand the diurnal and seasonal behaviour of the D-region ionospheric response to solar flares. 3.1 Local time variation The response of the D-region ionosphere to solar flare activity exhibits a clear dependence on local time. Figures 4 (a) and 4(b) show the variation of the VLF signal amplitude difference (ΔA, in dB) as a function of local time for C-class and M-class solar flares, respectively. The analysis is restricted to daytime events occurring between 00:00 and 12:00 UT. Figure 4 (a) demonstrates a systematic variation in ΔA associated with C-class solar flares. The average amplitude difference is found to be highest during the morning hours (≈ 1.02 dB), followed by a gradual decrease toward local noon (≈ 0.95 dB) and evening (≈ 0.92 dB). This trend indicates that VLF signal perturbations induced by C-class flares are more pronounced during the morning and weaken as the day progresses. A similar local time dependence is observed for M-class solar flares, as shown in Fig. 4 (b). The average ΔA during the morning (≈ 2.94 dB) and noon (≈ 2.94 dB) periods is higher than that observed during the evening (≈ 2.56 dB). The enhanced amplitude response during the morning and noon intervals is partly influenced by the occurrence of higher-intensity M-class flares during these periods, including an M8.77 flare at 07:54 LT and an M6.0 flare at 14:09 LT, which produced peak amplitude enhancements of approximately 5.11 dB and 4.14 dB, respectively. Previous studies have shown that the VLF amplitude response to solar flares is sensitive to the transmitter–receiver path length. Thomson and Clilverd (2001) reported relatively weaker amplitude variations for long propagation paths (~ 10,000 km). In contrast, the present study, based on a medium path length of approximately 6,000 km, exhibits more pronounced amplitude changes, suggesting that propagation geometry plays a significant role in determining the observed VLF response. Selvakumaran et al. ( 2015 ) reported differing local time trends for C- and M-class flares during daytime conditions. However, the present results indicate a broadly similar pattern of local time dependence for both flare classes. As also noted by Selvakumaran et al. ( 2015 ), higher-intensity M-class flares tend to occur preferentially during the morning and noon periods, contributing to the enhanced amplitude responses observed during these intervals. The larger amplitude perturbations observed during the morning hours for both C- and M-class flares can be attributed to diurnal variations in the solar zenith angle. During the morning, the relatively larger zenith angle increases the effective path length of solar radiation through the atmosphere, enhancing ionization in the D-region (Grubor et al., 2005 ; Selvakumaran et al., 2015 ). In addition, the background electron density in the D-region is lower during the morning compared to local noon (Ohya et al., 2006; Maurya et al., 2012b), making flare-induced ionization enhancements more prominent. Around noon, when background ionization levels are already high due to maximum solar illumination, the incremental effect of solar flares becomes less distinguishable. Consequently, the D-region exhibits a stronger relative response to solar flare activity during morning hours than during other parts of the day. Table 1 Average value of \(\:\varDelta\:\text{A}\) , \(\:\varDelta\:\text{t}\) , \(\:{H}^{{\prime\:}}\) and \(\:{{\beta\:}}^{{\prime\:}}\) different time period (morning, noon and evening period) for C and M class flares. Time Period Amplitude difference \(\:\varDelta\:\text{A}\) (dB) Peak Time delay \(\:\varDelta\:\text{t}\) (min) Reflection height \(\:{\text{H}}^{{\prime\:}}\) (km) \(\:\text{S}\text{h}\text{a}\text{r}\text{p}\text{n}\text{e}\text{s}\text{s}\:\text{f}\text{a}\text{c}\text{t}\text{o}\text{r}\:{{\beta\:}}^{{\prime\:}}\:({\text{k}\text{m}}^{-1}\) C-Class Morning (05–10 LT) 1.02 3.80 73.16 0.34 Noon (10–15 LT) 0.95 3.23 73.44 0.33 Evening (15–18 LT) 0.92 4.33 73.00 0.34 M-Class Morning (05–10 LT) 2.94 3.77 70.81 0.40 Noon (10–15 LT) 2.85 2.56 80.00 0.37 Evening (15–18 LT) 2.56 3.00 70.87 0.40 3.2 Seasonal Variation Seasonal dependence of the D-region ionospheric response to solar flares is examined using the VLF signal amplitude difference (ΔA). Figure 5 (a) shows the seasonal variation of ΔA for C-class solar flares, with the data grouped into three seasons: summer (May–August), winter (November–February), and equinox (March–April and September–October). As shown in Fig. 5 (a), the amplitude difference associated with C-class flares exhibits a clear seasonal trend, with the highest average ΔA observed during the winter season (~ 2.65 dB). This is followed by the equinox period (~ 2.56 dB), while the lowest ΔA is recorded during summer (~ 2.44 dB). The reduced amplitude response during summer suggests a weaker relative ionospheric perturbation under higher background ionization conditions. A similar seasonal behavior is observed for M-class solar flares, as illustrated in Fig. 5 (b). The average amplitude difference is again maximized during winter (~ 5.41 dB), slightly lower during equinox (~ 5.34 dB), and reaches a minimum during summer (~ 5.11 dB). The consistent seasonal pattern for both C- and M-class flares indicates that the D-region response is governed not only by flare intensity but also by seasonal variations in background ionospheric conditions. The enhanced amplitude differences observed during winter can be attributed to lower background electron densities in the D-region. During summer, increased solar illumination and smaller solar zenith angles lead to higher electron densities, which reduce the relative impact of additional ionization caused by solar flares. In contrast, during winter, the larger solar zenith angle results in reduced background ionization, allowing flare-induced electron density enhancements to produce more pronounced perturbations in VLF signal amplitudes (Gupta, 1998 ; Tang et al., 2023 ). These results emphasize the importance of seasonal variability in modulating the D-region ionospheric response to solar flare activity. The stronger wintertime response highlights the role of background ionospheric conditions, particularly electron density and solar zenith angle, in controlling the magnitude of VLF signal perturbations. 3.3 Time delay characteristic of D-region ionosphere response for C-Class and M-Class flare Several studies have reported a measurable time delay between the peak of solar X-ray flux during a flare and the corresponding peak in VLF signal amplitude perturbation (Mitra, 1974; Grubor et al., 2005 ; Zigman et al., 2007; Kumar and Kumar, 2014 ). This delay has been referred to as the relaxation time (Mitra, 1974) or ionospheric sluggishness (Valnicek and Ranzinger, 1972 ), and represents the time required for the D-region ionosphere to adjust to enhanced ionization and subsequently recover through recombination processes following flare-induced X-ray irradiation (Mitra, 1974; Selvakumaran et al., 2015 ). In addition to the delay between flare and VLF peak times, the overall relaxation behavior is influenced by the temporal offset between the start, peak, and end times of the solar flare and the corresponding VLF response. However, a systematic investigation of the dependence of these delays on local time and seasonal variability remains limited. Figure 6 (a) shows the local time dependence of the time delay (Δt, in minutes) between the solar flare and the VLF signal response for C-class flares. The delays are grouped into start-time (red), peak-time (green), and end-time (blue) differences. The results indicate that Δt varies between approximately 1 and 9 minutes for the start and peak responses, while the end-time delays are significantly larger and exhibit strong local time dependence. For C-class flares, the mean start-time delays are 4.19, 4.95, and 6.40 minutes during the morning, noon, and evening periods, respectively. The corresponding peak-time delays are 3.72, 3.23, and 4.33 minutes. End-time delays are substantially higher, with mean values of 17.5 minutes in the morning, 19.91 minutes at noon, and a maximum of 36.16 minutes during the evening. The enhanced end-time delays observed near evening hours suggest a slower ionospheric recovery following flare termination. This behavior can be attributed to local time–dependent changes in background electron density and recombination rates. Toward evening, reduced solar illumination and decreasing ion production can lead to slower relaxation of flare-induced ionization, resulting in prolonged recovery times. Figure 6 (b) presents the corresponding results for M-class solar flares. The start- and peak-time delays for M-class flares range from ~ 0 to 8 minutes and are generally smaller than those observed for C-class flares. The mean start-time delays are 5.48, 4.84, and 7.50 minutes for morning, noon, and evening periods, respectively, while the peak-time delays are 3.77, 2.56, and 3.00 minutes. As in the case of C-class flares, the end-time delays are markedly larger, with average values of 27.54 minutes in the morning, 24.33 minutes at noon, and a maximum of 35.40 minutes in the evening. Overall, the results demonstrate that end-time delays are significantly greater than start- and peak-time delays for both flare classes, indicating a prolonged ionospheric recovery phase after flare cessation. The largest average end-time delays are consistently observed during evening hours, particularly for M-class flares, suggesting that stronger perturbations combined with reduced ion production contribute to slower recombination in the D-region. Compared to C-class flares, M-class flares generally exhibit shorter start- and peak-time delays. According to Mitra (1974), the relaxation time is inversely related to the electron density in the D-region, with higher electron densities leading to faster ionospheric response. Since M-class flares produce stronger ionization enhancements than C-class flares, the observed shorter delays are consistent with theoretical expectations. Similar class-dependent behavior of Δt has been reported by Selvakumaran et al. ( 2015 ), although their study did not separately analyze start-time and end-time delays. It is important to note that although C-class flares exhibit longer response delays, this does not imply a stronger ionospheric perturbation than that caused by M-class flares. Instead, the longer delays associated with weaker flares reflect slower ionization–recombination dynamics under lower electron density conditions. These findings highlight the combined influence of flare intensity, background ionospheric state, and local time on the temporal response of the D-region ionosphere to solar flare activity. 3.4 Seasonal variation of start, peak and end time delay for both C and M class flares Seasonal variability in the temporal response of the D-region ionosphere to solar flare activity is examined using normalized start-, peak-, and end-time delays. Figure 7 (a) shows the seasonal variation of these delays for C-class solar flares, with the data grouped into summer, winter, and equinox seasons. For C-class flares (Fig. 7 (a)), the maximum start-time delays reach 14 minutes during summer, 16 minutes during winter, and 17 minutes during the equinox season. The corresponding maximum peak-time delays are 6, 9, and 9 minutes, respectively. End-time delays are significantly larger than both start- and peak-time delays in all seasons, with maximum values of 56 minutes in summer, 75 minutes in winter, and 85 minutes during equinox conditions. These results indicate that ionospheric recovery following C-class flares is slowest during equinox and winter seasons, while substantially shorter recovery times are observed during summer. Figure 7 (b) presents the seasonal variation of time delays for M-class solar flares. The maximum start-time delays are 23 minutes in both summer and winter, decreasing to 10 minutes during the equinox season. Peak-time delays remain relatively consistent across seasons, reaching maximum values of approximately 8 minutes in summer, winter, and equinox periods. The end-time delays again dominate the response, with maximum values of 40 minutes in summer, 45 minutes in winter, and 76 minutes during the equinox season. For M-class flares, the equinox season exhibits the longest recovery times compared to winter and summer. Overall, both flare classes exhibit a consistent seasonal pattern, with end-time delays significantly exceeding start- and peak-time delays, highlighting the prolonged ionospheric relaxation phase following flare cessation. Although C-class flares generally show larger overall time delays than M-class flares, the start-time delays are, on average, higher for M-class flares. This behavior reflects the competing roles of flare intensity and background ionospheric conditions in controlling D-region response times. The observed seasonal dependence of time delays can be attributed to variations in background electron density and solar zenith angle. During summer, higher background ionization levels facilitate faster recombination and recovery, resulting in shorter delays. In contrast, during winter and equinox seasons, reduced background electron densities and larger solar zenith angles lead to slower ionospheric relaxation processes and prolonged recovery times. Among the 234 solar flare events analyzed, a small number of exceptional cases exhibited negative time delays, indicating that the VLF signal amplitude reached its peak before the corresponding peak in soft X-ray flux measured by GOES. Specifically, three C-class flares and three M-class flares showed negative peak-time delays, as summarized in supplementary Table S1 and illustrated in Fig. 8 . Previous studies have reported that early enhancements in hard X-ray emissions (25–50 keV) and non-thermal energetic electrons during the impulsive phase of solar flares can dominate D-region ionization before the soft X-ray maximum is reached (Hayes et al., 2021 ; Chakraborty, 2022; Liu and Füllekrug, 2025 ). For example, a C6.9 flare on 22 January 2025 exhibited a soft X-ray peak at 06:22 UT, while the corresponding VLF amplitude peaked at 06:21 UT, resulting in a − 1 minute time delay. Similarly, an M3.3 flare on 02 September 2023 showed a soft X-ray peak at 07:13 UT, whereas the VLF response peaked at 07:07 UT, yielding a − 5 minute delay. As shown in Fig. 8 , the maximum negative time delay observed in this study is − 5 minutes, indicating that the VLF signal enhancement can precede the soft X-ray maximum by several minutes. This behavior suggests that D-region ionization during these events is initially driven by harder X-rays or energetic particles that penetrate deeper into the lower ionosphere earlier than soft X-rays. These anomalous cases highlight the complexity of ionospheric response mechanisms during solar flares and underscore the need for further investigations incorporating multi-wavelength solar observations and detailed ionospheric modeling. 3.5 Variation in wait D-region parameters due to C and M classes of solar flare Enhanced ionization during solar flare events causes the effective upper boundary of the Earth–ionosphere waveguide (EIWG) to descend. This behavior is typically manifested as a reduction in the effective reflection height (H′) accompanied by an increase in the sharpness factor (β), reflecting a steeper electron density gradient in the D-region (Grubor et al., 2008). In the present study, the D-region parameters H′ and β were estimated using the Long Wave Propagation Capability (LWPC) model for both C- and M-class solar flares. The local time dependence of H′ and β, which is closely related to variations in solar zenith angle, is shown in Figs. 9 and 10 for C- and M-class flares, respectively. The corresponding average values are summarized in Table 2. For C-class solar flares (Fig. 9 ), the average value of H′ is found to be highest during the noon period (73.4 km), slightly lower during the morning (73.1 km), and lowest during the evening (72.9 km). In contrast, the sharpness factor β exhibits an opposite trend. The values of β range between 0.29 and 0.42 km⁻¹, with the highest average values occurring during the morning and evening periods (≈ 0.34 km⁻¹), while a marginally lower average value (≈ 0.33 km⁻¹) is observed during local noon. This inverse relationship between H′ and β is consistent with enhanced ionization leading to a lowered reflection height and a steeper electron density gradient. For M-class solar flares (Fig. 10 ), the reflection height H′ shows a wider range of variation, extending from approximately 67 km to 74 km. As indicated in Table 2, the average H′ reaches its maximum during the noon period (70.0 km), followed by the evening (70.87 km), and exhibits the minimum value during the morning (70.81 km). The sharpness factor β for M-class flares varies from 0.30 to 0.53 km⁻¹. The average β values are highest during the morning and evening periods (≈ 0.40 km⁻¹) and decrease slightly during the noon period (≈ 0.37 km⁻¹). Overall, both C- and M-class flares exhibit a consistent inverse relationship between H′ and β, confirming that enhanced solar flare–induced ionization lowers the effective reflection height while increasing the sharpness of the D-region electron density profile. The more pronounced variations observed for M-class flares reflect their higher ionizing efficiency compared to C-class flares. The observed local time dependence of H′ and β highlights the combined influence of solar zenith angle, background ionospheric conditions, and flare intensity on the D-region response. 3.6 VLF Amplitude Anomalies The impact of solar flares on VLF signal amplitude was investigated by examining the variation of amplitude difference (ΔA) across a range of flare intensities. In general, an increase in solar flare intensity leads to enhanced D-region ionization and, consequently, an increase in ΔA. However, the relationship between flare class and ΔA is clearly nonlinear, indicating that flare intensity alone is insufficient to fully describe the observed VLF response. For C-class flares, several examples illustrate this nonlinearity. The C6.6 flare on 08 October 2022 (06:15 LT) produced a ΔA of 1.27 dB, which is lower than the ΔA of 1.41 dB observed for the slightly weaker C6.5 flare on 22 October 2022 (11:13 LT). This discrepancy can be attributed primarily to local time effects, as ionospheric background conditions vary significantly between morning and late-morning periods. Similarly, the C9.6 flare on 14 February 2023 (11:58 LT) yielded a relatively small ΔA of 0.70 dB, whereas a weaker C5.0 flare on 05 August 2022 (12:17 LT) produced a higher ΔA of 0.83 dB. Such cases highlight the influence of seasonal variations in background electron density, which modulate the relative ionospheric response to flare-induced ionization. Additional anomalies are observed that cannot be explained solely by local time or seasonal effects. For example, the C3.7 flare on 02 December 2022 (07:41 LT) produced a ΔA of 1.14 dB, exceeding the ΔA of 0.53 dB associated with the stronger C4.6 flare on 12 November 2022 (07:57 LT). Likewise, the C6.2 flare on 11 April 2023 (08:39 LT) exhibited a ΔA of only 0.54 dB, which is considerably lower than the ΔA of 1.49 dB observed for the weaker C2.5 flare on 11 November 2022 (08:54 LT). These inconsistencies indicate the presence of additional controlling factors beyond flare magnitude, local time, and season. For M-class flares, similar nonlinear behavior is evident. The M8.77 flare on 02 October 2022 (07:54 LT) resulted in a ΔA of 2.35 dB, which is lower than the ΔA of 2.52 dB produced by the weaker M5.08 flare on 16 August 2022 (13:31 LT). This difference can again be explained by local time–dependent ionospheric conditions. Seasonal influences are also apparent; for example, the M2.5 flare on 19 May 2023 (10:31 LT) generated a ΔA of 3.68 dB, exceeding the ΔA of 2.88 dB observed for the slightly stronger M2.83 flare on 10 April 2023 (10:51 LT). Some anomalies persist even after accounting for local time and seasonal effects. In such cases, the location of the flare on the solar disk plays an important role. For C-class flares, the C6.2 event on 11 April 2023 (S21E11) produced a smaller ΔA than the weaker C2.5 flare on 11 November 2022 (N13W14), which occurred closer to the solar disk center. Similarly, the C3.3 flare on 13 August 2022 (S11W26) resulted in a higher ΔA (0.57 dB) than the stronger C4.8 flare on 26 August 2022 (S27W58), which occurred closer to the solar limb. These observations are consistent with reduced effective ionizing flux reaching Earth for flares occurring near the solar limb due to projection effects and increased absorption. For M-class flares, geomagnetic activity is found to play an additional role in certain anomalous cases. The M1.3 flare on 18 June 2023 (06:09 LT) produced an exceptionally large ΔA of 10.1 dB, despite being weaker than the M5.3 flare on 19 May 2023 (06:21 LT), which showed a ΔA of only 2.09 dB. The corresponding Dst index values indicate moderate geomagnetic storm conditions (Dst = − 33 nT) during the M1.3 flare, compared to quiet geomagnetic conditions (Dst = + 8 nT) during the M5.3 event. Enhanced geomagnetic activity likely modified the background ionospheric state, amplifying the VLF response during the weaker flare. In other cases where geomagnetic effects are negligible, solar disk location again provides a plausible explanation. For instance, the M1.5 flare on 15 December 2022 (S19W69) produced a ΔA of 6.38 dB, exceeding the ΔA of 3.78 dB observed for the stronger M3.3 flare on 03 March 2023 (N23W75). The relatively closer proximity of the M1.5 flare to the solar disk center likely resulted in a higher effective ionizing flux incident on the Earth’s atmosphere. Overall, these results demonstrate that while flare intensity is an important driver of VLF amplitude perturbations, the ionospheric response is strongly modulated by local time, seasonal background conditions, solar disk location, and geomagnetic activity. The interplay among these factors leads to the observed nonlinear and event-specific variations in ΔA, underscoring the complexity of D-region ionospheric response mechanisms during solar flare events. Conclusion This study investigates the response of the D-region ionosphere to solar flare activity using VLF signal amplitude perturbations from the NWC transmitter, recorded over the period November 2020 to January 2025. The analysis focuses on C- and M-class solar flares and examines how local time, seasonal variability, flare location on the solar disk, and geomagnetic activity collectively modulate ionospheric disturbances. A pronounced local time dependence is observed in the VLF amplitude difference (ΔA) for both C- and M-class flares. For both flare classes, ΔA is largest during morning hours, decreases toward local noon, and is weakest during the evening. This behavior is primarily governed by variations in solar zenith angle and background D-region electron density. During the morning, larger zenith angles and lower ambient electron densities enhance the relative impact of flare-induced ionization, resulting in stronger VLF perturbations. LWPC-derived parameters support this interpretation, showing reduced reflection heights (H′) and enhanced sharpness factors (β) during periods of stronger ionospheric response. Clear seasonal dependence is also evident. Both C- and M-class flares produce the strongest amplitude perturbations during winter, followed by equinox periods, with the weakest responses occurring in summer. This seasonal pattern reflects variations in background electron density, which is lowest during winter, allowing flare-induced ionization to produce a larger relative enhancement. Seasonal variability is further supported by the behavior of ionospheric relaxation times, with longer recovery (end-time) delays observed during winter and equinox seasons, indicating slower recombination under reduced background ionization conditions. The analysis of time delay characteristics reveals three distinct components—start, peak, and end-time delays—for both flare classes. End-time delays are consistently the largest, reflecting the prolonged recovery of the disturbed D-region after flare cessation. M-class flares generally exhibit shorter delays than C-class flares, consistent with theoretical expectations that higher electron densities produced by stronger flares lead to faster ionospheric response. A small number of exceptional events show negative time delays, where VLF amplitude peaks precede the soft X-ray maximum. These cases are likely associated with early ionization driven by hard X-rays or energetic electrons during the impulsive phase of the flare. LWPC modeling of Wait parameters (H′ and β) confirms that enhanced flare-induced ionization lowers the effective reflection height and increases the sharpness of the D-region electron density profile. For both flare classes, H′ reaches maximum values near local noon and decreases toward morning and evening, while β exhibits the opposite trend. M-class flares produce larger overall reductions in H′ and higher β values than C-class flares, consistent with their greater ionizing efficiency and in agreement with earlier studies. Finally, the relationship between flare intensity and ΔA is found to be nonlinear. In several cases, weaker flares produce larger amplitude perturbations than stronger flares. These anomalies are influenced by a combination of factors, including local time, seasonal background conditions, solar disk location (central meridian distance), and geomagnetic activity. While many anomalous responses can be explained by these parameters, a few events remain unresolved, highlighting the complexity of D-region response mechanisms and the need for further investigations incorporating multi-wavelength solar observations and detailed ionospheric modeling. Overall, this study provides a comprehensive characterization of the low-latitude D-region ionospheric response to solar flares, emphasizing the combined roles of flare intensity, background ionospheric state, solar geometry, and geomagnetic conditions. The results contribute to a better understanding of flare-induced ionospheric dynamics and demonstrate the continued value of VLF observations for monitoring the lower ionosphere. Declarations Author statement All the authors declare no conflict of interest Ethics declaration not applicable. Funding statement: Ajeet Kumar Maurya received project funding from the Anusandhan National Research Foundation (ANRF), New Delhi, India, under the CORE research grant (CRG/2021/001322). Author Contribution Conceptualization, S.C., R.T., A.K.M. and S.S; methodology, S.C., A.D., R. S. and M.N.S.; formal analysis, S.C., R.T., S.S. and A.K.M.; data curation, A.K.M. writing—original draft preparation, S.C. and A.K.M; writing—review and editing, M.N.S., A.K.M., R.T., S.S., A.D. and R.S.; supervision, S.S., A.K.M., A.D. and R.S; project administration A.K.M. All authors have read and agreed to the published version of the manuscript Acknowledgements Author Ajeet Kumar Maurya thanks to the Anusandhan National Research Foundation (ANRF), New Delhi, India, for the CORE research grant (CRG/2021/001322) which supported this work. Shivani Chandra thanks CORE grant (CRG/2021/001322) for junior research fellowship. Data Availability The details of the data used in this work are provided here. The X-ray flux (0.1-0.8 nm) with a one-minute resolution was obtained from GOES ( [https://data.darts.isas.jaxa.jp/pub/solar/mirror/sswdb/goes/xray/](https:/data.darts.isas.jaxa.jp/pub/solar/mirror/sswdb/goes/xray) ). The solar flare location on the solar disc was provided from [www.solarmonitor.org](file:/D:/Paper/Suniti_work/Publication/www.solarmonitor.org) . The solar flare intensity, start time, peak time and end time is obtained from the [https://spaceweatherlive.com](https:/spaceweatherlive.com) . References Appleton, E.V., 1953. A note on the “sluggishness” of the ionosphere. J. Atmos. Terr. Phys. 3, 282–284. https://doi.org/10.1016/0021-9169(53)90129-9 Basak, T., Chakrabarti, S.K., 2013. 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Supplementary Files ShivanifalretimeandSeasonsSupplementaryinformation.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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16:59:15","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":137992,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eVariation in amplitude of the NWC signal and corresponding GOES X-ray flux during the C8-class flare event on 25 February 2023.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8615895/v1/c83bef440998a70f5b3676a4.jpeg"},{"id":101297293,"identity":"eedb997e-0d78-4b22-ba84-bd43e1cb6c2d","added_by":"auto","created_at":"2026-01-28 09:26:26","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":684705,"visible":true,"origin":"","legend":"\u003cp\u003eLegend not included with this 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16:59:15","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":135378,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eSeasonal variation of amplitude difference (ΔA, dB) for C-class solar flares.\u003cstrong\u003e (b) \u003c/strong\u003eSame as\u003cstrong\u003e (a), \u003c/strong\u003ebut for M-class solar flares.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8615895/v1/7823a8801242c6a7c9ed6faf.jpeg"},{"id":101248012,"identity":"f1f48d00-f129-47ab-9b11-1062d9bdf0bd","added_by":"auto","created_at":"2026-01-27 16:59:15","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":196085,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eLocal time variation of start, peak, and end time delays (Δt, minutes) for C-class solar flares.\u003cstrong\u003e (b) \u003c/strong\u003eSame as (a), but for M-class solar flares.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8615895/v1/054307c2d3e224a7f95dce26.jpeg"},{"id":101248018,"identity":"6a4c4bd6-1cdb-454d-87e9-488da7ceeec7","added_by":"auto","created_at":"2026-01-27 16:59:15","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":196464,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eSeasonal variation of start-, peak-, and end-time delays (Δt, minutes) for C-class solar flares.\u003cstrong\u003e (b) \u003c/strong\u003eSame as (a), but for M-class solar flares.\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8615895/v1/ff3045a57dcc429599527cd8.jpeg"},{"id":101248009,"identity":"e2b24a61-0881-40b8-881e-4eda1dace631","added_by":"auto","created_at":"2026-01-27 16:59:15","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":117357,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between time delay and peak GOES 1–8 Å soft X-ray flux for C- and M-class solar flares. The horizontal black line denotes zero time delay, while the red and blue dashed lines indicate the mean values of the respective distributions.\u003c/p\u003e","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8615895/v1/0633974d9965721ca5d06f73.jpeg"},{"id":101296862,"identity":"4ffd381d-dba2-4cd9-8526-617b394ae874","added_by":"auto","created_at":"2026-01-28 09:22:11","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":184906,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eLocal time variation of reflection height H′ for C-class solar flares. \u003cstrong\u003e(b)\u003c/strong\u003eLocal time variation of sharpness factor β for C-class solar flares.\u003c/p\u003e","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8615895/v1/4e86112eb6fc4b3809702ac7.jpeg"},{"id":101248010,"identity":"bccea564-673d-441f-aee0-d30f7096c4e2","added_by":"auto","created_at":"2026-01-27 16:59:15","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":174622,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) \u003c/strong\u003eLocal time variation of reflection height H′ for M-class solar flares.\u003cstrong\u003e (b) \u003c/strong\u003eLocal time variation of sharpness factor β for M-class solar flares.\u003c/p\u003e","description":"","filename":"floatimage10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8615895/v1/899133ef0bbf874cfe7a9a89.jpeg"},{"id":104779448,"identity":"29068626-118c-44c8-a75c-31feede4ac14","added_by":"auto","created_at":"2026-03-17 07:40:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3025261,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8615895/v1/cb1a24f6-48a6-443b-9812-9f08d4873ee0.pdf"},{"id":101248008,"identity":"0a5dd24c-179f-4150-b463-a2f8d4a9df2b","added_by":"auto","created_at":"2026-01-27 16:59:15","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":80496,"visible":true,"origin":"","legend":"","description":"","filename":"ShivanifalretimeandSeasonsSupplementaryinformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-8615895/v1/e697fa76bb91ae586d6c6815.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Temporal and seasonal variability of low-latitude D-region ionospheric response to solar flares using VLF observations","fulltext":[{"header":"Key points","content":"\u003cp\u003e1. VLF signal amplitude shows local time and seasonal dependence, peaking in the morning and winter.\u003c/p\u003e\u003cp\u003e2. Time delay between X-ray peak and VLF response varies with flare intensity, local time, and season.\u003c/p\u003e\u003cp\u003e3. A nonlinear relationship exists between flare intensity and VLF amplitude change, influenced by flare location and geomagnetic factors.\u003c/p\u003e"},{"header":"1. Introduction","content":"\u003cp\u003eSolar flares are sudden and intense releases of electromagnetic energy from the Sun, resulting from the rapid reconfiguration of stressed solar magnetic fields. These events emit radiation across a broad range of the electromagnetic spectrum, including Extreme Ultraviolet (EUV), X-rays, and radio waves. Enhanced solar radiation during flare events significantly affects Earth\u0026rsquo;s ionosphere, particularly the D-region, by increasing ionization levels (Mitra, 1974). The D-region, located between approximately 60 and 90 km altitude in the upper mesosphere and lower thermosphere, is the lowest ionospheric layer and plays a critical role in radio wave propagation.\u003c/p\u003e \u003cp\u003eUnder quiet solar conditions, ionization in the D-region is primarily maintained by solar Lyman-α radiation (121.6 nm), which ionizes nitric oxide (NO) molecules (Hargreaves, 2003). During solar flares, however, enhanced soft X-ray radiation in the 0.1\u0026ndash;0.8 nm wavelength range leads to additional ionization of neutral atmospheric constituents, particularly molecular nitrogen (N₂) and oxygen (O₂), resulting in a rapid increase in electron density (Nicolet and Aikin, 1960). These changes strongly influence the propagation characteristics of Very Low Frequency (VLF; 3\u0026ndash;30 kHz) radio signals within the Earth\u0026ndash;ionosphere waveguide (EIWG). Consequently, VLF observations have been widely used as a sensitive diagnostic tool for monitoring D-region ionospheric variability (Grubor et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Maurya et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2010\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Phanikumar et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Singh et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2011\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Kumar et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe response of the D-region ionosphere to solar flares has often been characterized using the waveguide parameters reference height (H\u0026prime;) and sharpness factor (β), which describe the effective reflection height and electron density gradient, respectively. These parameters are commonly estimated using the Long Wave Propagation Capability (LWPC) model (Wait and Spies, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1964\u003c/span\u003e). For example, Singh et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) analyzed solar flare events during the rising phase of Solar Cycle 24 using VLF signals from the NWC transmitter recorded at a low-latitude station in India, reporting a reduction in H\u0026prime; by 5\u0026ndash;6 km during an X-class flare and an increase in β to ~\u0026thinsp;0.48 km⁻\u0026sup1;. McRae and Thomson (2004) investigated flare-induced ionospheric perturbations using multiple VLF transmitter\u0026ndash;receiver paths and observed amplitude enhancements of up to ~\u0026thinsp;10 dB and significant phase delay reductions during strong flares. Their results indicated a decrease in H\u0026prime; from ~\u0026thinsp;71 km to ~\u0026thinsp;58 km and an increase in β to saturation values near 0.52 km⁻\u0026sup1;, with VLF amplitude enhancements scaling logarithmically with X-ray flux.\u003c/p\u003e \u003cp\u003eMost previous studies have primarily focused on flare-induced changes in VLF signal amplitude and phase associated with enhanced solar X-ray flux (Grubor et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Zigman et al., 2007; Kumar and Kumar, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2014\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Kolarski and Grubor, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Hayes et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). However, relatively fewer investigations have addressed the temporal response of the D-region ionosphere, often referred to as ionospheric \u0026ldquo;sluggishness\u0026rdquo; (Appleton, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1953\u003c/span\u003e) or \u0026ldquo;relaxation time\u0026rdquo; (Mitra, 1974). This time delay between the peak of the solar X-ray flux and the corresponding VLF signal response arises from the balance between electron production and loss processes in the D-region and provides valuable insight into ionospheric chemistry and recombination mechanisms (Basak and Chakrabarti, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Hayes et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2017\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Žigman et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Additionally, the dependence of this response on local time, season, and geomagnetic conditions remains insufficiently explored, particularly at low latitudes.\u003c/p\u003e \u003cp\u003eSelvakumaran et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) examined 41 solar flare events using VLF observations from the NWC transmitter recorded at Allahabad, India, and demonstrated that the ionospheric response time varies with flare class, local time, and geomagnetic activity. While their study provided important insights, it was limited in terms of event statistics and seasonal coverage.\u003c/p\u003e \u003cp\u003eIn this context, the present study aims to investigate the effects of solar flares on the low-latitude D-region ionosphere using VLF observations from the NWC transmitter (19.8 kHz) recorded by an UltraMSK receiver at Dehradun, India (30.3165\u0026deg;N, 78.0322\u0026deg;E), covering the period from July 2022 to June 2023. A total of 66 solar flare events, including 40 C-class and 26 M-class flares, are analyzed. The study focuses on (i) flare-induced changes in VLF signal amplitude difference (ΔA), (ii) the temporal delay between GOES X-ray flux peaks and VLF responses, and (iii) the dependence of these parameters on local time and seasonal variability. By providing a detailed temporal and seasonal characterization of flare-induced D-region perturbations at low latitudes, this work contributes to a more comprehensive understanding of ionospheric response processes and extends earlier studies based on shorter datasets and limited seasonal coverage.\u003c/p\u003e"},{"header":"2. Data and Methodology","content":"\u003cp\u003eVLF signal data were recorded using the Ultra MSK recording setup at a receiver located in Dehradun, India (30.3\u0026deg; N, 78.1\u0026deg; E). This setup monitors VLF transmissions from the NWC transmitter (21.8\u0026deg; S, 114.2\u0026deg; E) from Australia operating at 19.8 kHz.\u003c/p\u003e \u003cp\u003eA total of 234 solar flares\u0026mdash;comprising 153 C-class and 81 M-class events\u0026mdash;were selected for analysis, based on the availability of VLF data from the Dehradun receiver, during the period from Nov 2020 to Jan 2025. Only flares occurring between 00:00 UT and 12:00 UT were included in the study. Information on flare intensity, start time, peak time, and end time was obtained from \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://spaceweatherlive.com\u003c/span\u003e\u003cspan address=\"https://spaceweatherlive.com\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. X-ray flux data in the 0.1\u0026ndash;0.8 nm wavelength range were sourced from the Geostationary Operational Environmental Satellite (GOES) operated by the National Oceanic and Atmospheric Administration (NOAA), USA (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://www.sec.noaa.gov\u003c/span\u003e\u003cspan address=\"http://www.sec.noaa.gov\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn the present study, the amplitude difference (ΔA) was computed using the equation:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\varvec{\\Delta\\:}\\mathbf{A}=\\:{\\text{A}}_{\\mathbf{f}\\mathbf{l}\\mathbf{a}\\mathbf{r}\\mathbf{e}\\:\\mathbf{d}\\mathbf{a}\\mathbf{y}}\\:-\\:{\\text{A}}_{\\mathbf{n}\\mathbf{o}\\mathbf{n}\\:\\mathbf{f}\\mathbf{l}\\mathbf{a}\\mathbf{r}\\mathbf{e}\\:\\mathbf{d}\\mathbf{a}\\mathbf{y}}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{A}}_{\\mathbf{f}\\mathbf{l}\\mathbf{a}\\mathbf{r}\\mathbf{e}\\:\\mathbf{d}\\mathbf{a}\\mathbf{y}}\\)\u003c/span\u003e\u003c/span\u003e denotes the peak amplitude of the VLF signal on the day of a flare, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{A}}_{\\mathbf{n}\\mathbf{o}\\mathbf{n}\\:\\mathbf{f}\\mathbf{l}\\mathbf{a}\\mathbf{r}\\mathbf{e}\\:\\mathbf{d}\\mathbf{a}\\mathbf{y}}\\)\u003c/span\u003e\u003c/span\u003e corresponds to the peak amplitude on a quiet day with no solar activity (Selvakumaran, 2015). The time delay between the VLF signal response and the X-ray flare was calculated for the start, peak, and end times using:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:\\mathbf{t}={\\mathbf{t}}_{\\mathbf{V}\\mathbf{L}\\mathbf{F}\\:}-\\:{\\:\\mathbf{t}}_{\\mathbf{X}-\\mathbf{r}\\mathbf{a}\\mathbf{y}\\:\\mathbf{f}\\mathbf{l}\\mathbf{u}\\mathbf{x}}\\:,$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mathbf{t}}_{\\mathbf{V}\\mathbf{L}\\mathbf{F}}\\)\u003c/span\u003e\u003c/span\u003e represents the corresponding start, peak, or end time observed in the VLF data, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mathbf{t}}_{\\mathbf{X}-\\mathbf{r}\\mathbf{a}\\mathbf{y}\\:\\mathbf{f}\\mathbf{l}\\mathbf{u}\\mathbf{x}}\\)\u003c/span\u003e\u003c/span\u003e is the respective time obtained from GOES observations. Local Time (LT) was calculated using the relation:\u003c/p\u003e \u003cp\u003e \u003cb\u003eLT\u0026thinsp;=\u0026thinsp;Universal Time UT\u0026thinsp;+\u0026thinsp;05:30hours.\u003c/b\u003e \u003c/p\u003e \u003cp\u003eTwo case studies of M-class and C-class flares are illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. On 18 January 2023, an M1.7-class flare detected by GOES began at 10:21 UT, peaked at 10:35 UT (16:05 LT), and ended at 10:52 UT. The corresponding VLF signal perturbation began at 10:29 UT, peaked at 10:39 UT (16:09 LT), and concluded at 11:01 UT.\u003c/p\u003e \u003cp\u003eSimilarly, on 25 February 2023, a C8-class flare commenced at 04:12 UT, peaked at 04:22 UT (09:52 LT), and ended at 04:32 UT. The associated VLF signal response began at 04:21 UT, reached its peak at 04:28 UT (09:58 LT), and ended at 04:42 UT.\u003c/p\u003e \u003cp\u003eIn both cases, the VLF amplitude response exhibited a delay relative to the GOES X-ray flux peak. This time lag is consistent with previous studies (Kumar and Kumar, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Selvakumaran, 2015; Grubor et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Zigman et al., 2007), which attribute such delays to the ionization and relaxation dynamics of the D-region of the ionosphere.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe variation in the amplitude of the NWC transmitter signal (19.8 kHz) in response to GOES X-ray flux for solar flares occurring in different months is presented in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The VLF signal amplitude difference (ΔA) is directly influenced by enhanced solar X-ray flux and can be effectively used to infer changes in electron density in the lower ionosphere associated with solar flare activity.\u003c/p\u003e \u003cp\u003ePrevious studies, such as Selvakumaran (2015), examined the impact of solar flares on VLF signal amplitude and reported that ΔA generally increases with flare intensity; however, the relationship is nonlinear. In several cases, weaker flares were found to produce larger amplitude perturbations than stronger flares. This behaviour was attributed to factors including the local time of flare occurrence, pre-flare ionospheric conditions, and flare class (C, M, or X). That study also reported a time delay (Δt) between the peak of the solar X-ray flux and the corresponding peak in the VLF signal response, which varied with both flare intensity and local time (morning, noon, and evening).\u003c/p\u003e \u003cp\u003eThe characteristics of all solar flare events analyzed in the present study are compiled and provided in Supplementary Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e. The selected events include both C- and M-class flares, covering a wide range of X-ray flux intensities. In the present analysis, ΔA for C-class flares ranges from 0.18 to 2.65 dB, while for M-class flares it ranges from 0.39 to 5.41 dB. The intensities of the analyzed flares span from C1.9 to C9.9 for C-class and from M1.0 to M8.77 for M-class events. Thus, the analyzed flares differ significantly in X-ray flux intensity, leading to varying degrees of ionospheric response.\u003c/p\u003e \u003cp\u003eA third-degree polynomial fit is applied to represent the relationship between flare intensity and amplitude perturbation, as this provides the best fit to the observed data. This approach is consistent with earlier findings by McRae and Thomson (2004) and Selvakumaran et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). As noted in these studies and confirmed here, the nonlinear behavior of ΔA with flare intensity is likely influenced by pre-flare ionospheric conditions and local time effects. To minimize pre-flare contamination, a minimum time separation of approximately two hours was maintained between consecutive flares; events occurring closer in time were excluded from the analysis.\u003c/p\u003e \u003cp\u003eIn general, ΔA increases with increasing flare intensity, although the variation is not linear. For example, two C-class flares (C5.8 and C3.7) occurring on 18 August 2022 produced ΔA values of 1.14 dB and 0.31 dB, respectively. However, inconsistencies are also observed for flares of similar class occurring on different days. For instance, a C9.9 flare on 25 September 2023 (13:45 LT) produced a ΔA of 1.49 dB, which is lower than the ΔA of 1.98 dB observed for a C9.0 flare on 9 April 2023 (11:40 LT). Such discrepancies are attributed primarily to local time dependence of the solar flare\u0026ndash;ionosphere interaction.\u003c/p\u003e \u003cp\u003eSimilar behavior is observed for M-class flares. For example, an M5.41 flare on 30 March 2023 (13:09 LT) produced a ΔA of 3.48 dB, which is lower than the ΔA of 4.10 dB observed for an M5.08 flare on 16 August 2023 (13:31 LT). These anomalies further support the conclusion that local time plays a critical role in modulating the VLF amplitude response to solar flares.\u003c/p\u003e \u003cp\u003eTo investigate the dependence of ΔA on local time, flare occurrences were categorized into three local time intervals: morning (06:00\u0026ndash;10:00 LT), noon (10:00\u0026ndash;15:00 LT), and evening (15:00\u0026ndash;18:00 LT). This classification enables a systematic examination of diurnal effects on ionospheric response. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, summarizes the average values of ΔA, Δt, H\u0026prime;, and β for C- and M-class flares within these time intervals.\u003c/p\u003e \u003cp\u003eThe analysis reveals that both C-class and M-class flares exhibit maximum amplitude differences during the morning hours, followed by reduced responses around noon and evening. Although ΔA generally decreases from morning to noon and shows a slight increase toward evening, the overall trend is not strictly linear, reflecting the combined influence of solar zenith angle, background electron density, and flare intensity on the D-region ionosphere.\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eIn this section, we investigate the impact of solar flares on the D-region of the ionosphere by analyzing amplitude variations in VLF signal propagation. Specifically, we examine the variation in amplitude difference with respect to local time and seasonal dependence to better understand the diurnal and seasonal behaviour of the D-region ionospheric response to solar flares.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Local time variation\u003c/h2\u003e \u003cp\u003eThe response of the D-region ionosphere to solar flare activity exhibits a clear dependence on local time. Figures\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a) and 4(b) show the variation of the VLF signal amplitude difference (ΔA, in dB) as a function of local time for C-class and M-class solar flares, respectively. The analysis is restricted to daytime events occurring between 00:00 and 12:00 UT.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a) demonstrates a systematic variation in ΔA associated with C-class solar flares. The average amplitude difference is found to be highest during the morning hours (\u0026asymp;\u0026thinsp;1.02 dB), followed by a gradual decrease toward local noon (\u0026asymp;\u0026thinsp;0.95 dB) and evening (\u0026asymp;\u0026thinsp;0.92 dB). This trend indicates that VLF signal perturbations induced by C-class flares are more pronounced during the morning and weaken as the day progresses.\u003c/p\u003e \u003cp\u003eA similar local time dependence is observed for M-class solar flares, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b). The average ΔA during the morning (\u0026asymp;\u0026thinsp;2.94 dB) and noon (\u0026asymp;\u0026thinsp;2.94 dB) periods is higher than that observed during the evening (\u0026asymp;\u0026thinsp;2.56 dB). The enhanced amplitude response during the morning and noon intervals is partly influenced by the occurrence of higher-intensity M-class flares during these periods, including an M8.77 flare at 07:54 LT and an M6.0 flare at 14:09 LT, which produced peak amplitude enhancements of approximately 5.11 dB and 4.14 dB, respectively.\u003c/p\u003e \u003cp\u003ePrevious studies have shown that the VLF amplitude response to solar flares is sensitive to the transmitter\u0026ndash;receiver path length. Thomson and Clilverd (2001) reported relatively weaker amplitude variations for long propagation paths (~\u0026thinsp;10,000 km). In contrast, the present study, based on a medium path length of approximately 6,000 km, exhibits more pronounced amplitude changes, suggesting that propagation geometry plays a significant role in determining the observed VLF response.\u003c/p\u003e \u003cp\u003eSelvakumaran et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) reported differing local time trends for C- and M-class flares during daytime conditions. However, the present results indicate a broadly similar pattern of local time dependence for both flare classes. As also noted by Selvakumaran et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), higher-intensity M-class flares tend to occur preferentially during the morning and noon periods, contributing to the enhanced amplitude responses observed during these intervals.\u003c/p\u003e \u003cp\u003eThe larger amplitude perturbations observed during the morning hours for both C- and M-class flares can be attributed to diurnal variations in the solar zenith angle. During the morning, the relatively larger zenith angle increases the effective path length of solar radiation through the atmosphere, enhancing ionization in the D-region (Grubor et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Selvakumaran et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). In addition, the background electron density in the D-region is lower during the morning compared to local noon (Ohya et al., 2006; Maurya et al., 2012b), making flare-induced ionization enhancements more prominent. Around noon, when background ionization levels are already high due to maximum solar illumination, the incremental effect of solar flares becomes less distinguishable. Consequently, the D-region exhibits a stronger relative response to solar flare activity during morning hours than during other parts of the day.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{A}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{t}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}^{{\\prime\\:}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\beta\\:}}^{{\\prime\\:}}\\)\u003c/span\u003e\u003c/span\u003e different time period (morning, noon and evening period) for C and M class flares.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime Period\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAmplitude difference \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{A}\\)\u003c/span\u003e\u003c/span\u003e (dB)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePeak Time delay \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e(min)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReflection height \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{H}}^{{\\prime\\:}}\\)\u003c/span\u003e\u003c/span\u003e (km)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{S}\\text{h}\\text{a}\\text{r}\\text{p}\\text{n}\\text{e}\\text{s}\\text{s}\\:\\text{f}\\text{a}\\text{c}\\text{t}\\text{o}\\text{r}\\:{{\\beta\\:}}^{{\\prime\\:}}\\:({\\text{k}\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eC-Class\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMorning (05\u0026ndash;10 LT)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e73.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNoon (10\u0026ndash;15 LT)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e73.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEvening (15\u0026ndash;18 LT)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e73.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eM-Class\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMorning (05\u0026ndash;10 LT)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNoon (10\u0026ndash;15 LT)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e80.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEvening (15\u0026ndash;18 LT)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Seasonal Variation\u003c/h2\u003e \u003cp\u003eSeasonal dependence of the D-region ionospheric response to solar flares is examined using the VLF signal amplitude difference (ΔA). Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a) shows the seasonal variation of ΔA for C-class solar flares, with the data grouped into three seasons: summer (May\u0026ndash;August), winter (November\u0026ndash;February), and equinox (March\u0026ndash;April and September\u0026ndash;October).\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a), the amplitude difference associated with C-class flares exhibits a clear seasonal trend, with the highest average ΔA observed during the winter season (~\u0026thinsp;2.65 dB). This is followed by the equinox period (~\u0026thinsp;2.56 dB), while the lowest ΔA is recorded during summer (~\u0026thinsp;2.44 dB). The reduced amplitude response during summer suggests a weaker relative ionospheric perturbation under higher background ionization conditions.\u003c/p\u003e \u003cp\u003eA similar seasonal behavior is observed for M-class solar flares, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b). The average amplitude difference is again maximized during winter (~\u0026thinsp;5.41 dB), slightly lower during equinox (~\u0026thinsp;5.34 dB), and reaches a minimum during summer (~\u0026thinsp;5.11 dB). The consistent seasonal pattern for both C- and M-class flares indicates that the D-region response is governed not only by flare intensity but also by seasonal variations in background ionospheric conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe enhanced amplitude differences observed during winter can be attributed to lower background electron densities in the D-region. During summer, increased solar illumination and smaller solar zenith angles lead to higher electron densities, which reduce the relative impact of additional ionization caused by solar flares. In contrast, during winter, the larger solar zenith angle results in reduced background ionization, allowing flare-induced electron density enhancements to produce more pronounced perturbations in VLF signal amplitudes (Gupta, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Tang et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThese results emphasize the importance of seasonal variability in modulating the D-region ionospheric response to solar flare activity. The stronger wintertime response highlights the role of background ionospheric conditions, particularly electron density and solar zenith angle, in controlling the magnitude of VLF signal perturbations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Time delay characteristic of D-region ionosphere response for C-Class and M-Class flare\u003c/h2\u003e \u003cp\u003eSeveral studies have reported a measurable time delay between the peak of solar X-ray flux during a flare and the corresponding peak in VLF signal amplitude perturbation (Mitra, 1974; Grubor et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Zigman et al., 2007; Kumar and Kumar, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). This delay has been referred to as the relaxation time (Mitra, 1974) or ionospheric sluggishness (Valnicek and Ranzinger, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1972\u003c/span\u003e), and represents the time required for the D-region ionosphere to adjust to enhanced ionization and subsequently recover through recombination processes following flare-induced X-ray irradiation (Mitra, 1974; Selvakumaran et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). In addition to the delay between flare and VLF peak times, the overall relaxation behavior is influenced by the temporal offset between the start, peak, and end times of the solar flare and the corresponding VLF response. However, a systematic investigation of the dependence of these delays on local time and seasonal variability remains limited.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) shows the local time dependence of the time delay (Δt, in minutes) between the solar flare and the VLF signal response for C-class flares. The delays are grouped into start-time (red), peak-time (green), and end-time (blue) differences. The results indicate that Δt varies between approximately 1 and 9 minutes for the start and peak responses, while the end-time delays are significantly larger and exhibit strong local time dependence. For C-class flares, the mean start-time delays are 4.19, 4.95, and 6.40 minutes during the morning, noon, and evening periods, respectively. The corresponding peak-time delays are 3.72, 3.23, and 4.33 minutes. End-time delays are substantially higher, with mean values of 17.5 minutes in the morning, 19.91 minutes at noon, and a maximum of 36.16 minutes during the evening.\u003c/p\u003e \u003cp\u003eThe enhanced end-time delays observed near evening hours suggest a slower ionospheric recovery following flare termination. This behavior can be attributed to local time\u0026ndash;dependent changes in background electron density and recombination rates. Toward evening, reduced solar illumination and decreasing ion production can lead to slower relaxation of flare-induced ionization, resulting in prolonged recovery times.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b) presents the corresponding results for M-class solar flares. The start- and peak-time delays for M-class flares range from ~\u0026thinsp;0 to 8 minutes and are generally smaller than those observed for C-class flares. The mean start-time delays are 5.48, 4.84, and 7.50 minutes for morning, noon, and evening periods, respectively, while the peak-time delays are 3.77, 2.56, and 3.00 minutes. As in the case of C-class flares, the end-time delays are markedly larger, with average values of 27.54 minutes in the morning, 24.33 minutes at noon, and a maximum of 35.40 minutes in the evening.\u003c/p\u003e \u003cp\u003eOverall, the results demonstrate that end-time delays are significantly greater than start- and peak-time delays for both flare classes, indicating a prolonged ionospheric recovery phase after flare cessation. The largest average end-time delays are consistently observed during evening hours, particularly for M-class flares, suggesting that stronger perturbations combined with reduced ion production contribute to slower recombination in the D-region.\u003c/p\u003e \u003cp\u003eCompared to C-class flares, M-class flares generally exhibit shorter start- and peak-time delays. According to Mitra (1974), the relaxation time is inversely related to the electron density in the D-region, with higher electron densities leading to faster ionospheric response. Since M-class flares produce stronger ionization enhancements than C-class flares, the observed shorter delays are consistent with theoretical expectations. Similar class-dependent behavior of Δt has been reported by Selvakumaran et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), although their study did not separately analyze start-time and end-time delays.\u003c/p\u003e \u003cp\u003eIt is important to note that although C-class flares exhibit longer response delays, this does not imply a stronger ionospheric perturbation than that caused by M-class flares. Instead, the longer delays associated with weaker flares reflect slower ionization\u0026ndash;recombination dynamics under lower electron density conditions. These findings highlight the combined influence of flare intensity, background ionospheric state, and local time on the temporal response of the D-region ionosphere to solar flare activity.\u003c/p\u003e \u003cp\u003e \u003cb\u003e3.4 Seasonal variation of start, peak and end time delay for both C and M class flares\u003c/b\u003e \u003c/p\u003e \u003cp\u003eSeasonal variability in the temporal response of the D-region ionosphere to solar flare activity is examined using normalized start-, peak-, and end-time delays. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) shows the seasonal variation of these delays for C-class solar flares, with the data grouped into summer, winter, and equinox seasons.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor C-class flares (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a)), the maximum start-time delays reach 14 minutes during summer, 16 minutes during winter, and 17 minutes during the equinox season. The corresponding maximum peak-time delays are 6, 9, and 9 minutes, respectively. End-time delays are significantly larger than both start- and peak-time delays in all seasons, with maximum values of 56 minutes in summer, 75 minutes in winter, and 85 minutes during equinox conditions. These results indicate that ionospheric recovery following C-class flares is slowest during equinox and winter seasons, while substantially shorter recovery times are observed during summer.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b) presents the seasonal variation of time delays for M-class solar flares. The maximum start-time delays are 23 minutes in both summer and winter, decreasing to 10 minutes during the equinox season. Peak-time delays remain relatively consistent across seasons, reaching maximum values of approximately 8 minutes in summer, winter, and equinox periods. The end-time delays again dominate the response, with maximum values of 40 minutes in summer, 45 minutes in winter, and 76 minutes during the equinox season. For M-class flares, the equinox season exhibits the longest recovery times compared to winter and summer.\u003c/p\u003e \u003cp\u003eOverall, both flare classes exhibit a consistent seasonal pattern, with end-time delays significantly exceeding start- and peak-time delays, highlighting the prolonged ionospheric relaxation phase following flare cessation. Although C-class flares generally show larger overall time delays than M-class flares, the start-time delays are, on average, higher for M-class flares. This behavior reflects the competing roles of flare intensity and background ionospheric conditions in controlling D-region response times.\u003c/p\u003e \u003cp\u003eThe observed seasonal dependence of time delays can be attributed to variations in background electron density and solar zenith angle. During summer, higher background ionization levels facilitate faster recombination and recovery, resulting in shorter delays. In contrast, during winter and equinox seasons, reduced background electron densities and larger solar zenith angles lead to slower ionospheric relaxation processes and prolonged recovery times.\u003c/p\u003e \u003cp\u003eAmong the 234 solar flare events analyzed, a small number of exceptional cases exhibited negative time delays, indicating that the VLF signal amplitude reached its peak before the corresponding peak in soft X-ray flux measured by GOES. Specifically, three C-class flares and three M-class flares showed negative peak-time delays, as summarized in supplementary Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e and illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePrevious studies have reported that early enhancements in hard X-ray emissions (25\u0026ndash;50 keV) and non-thermal energetic electrons during the impulsive phase of solar flares can dominate D-region ionization before the soft X-ray maximum is reached (Hayes et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Chakraborty, 2022; Liu and F\u0026uuml;llekrug, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). For example, a C6.9 flare on 22 January 2025 exhibited a soft X-ray peak at 06:22 UT, while the corresponding VLF amplitude peaked at 06:21 UT, resulting in a \u0026minus;\u0026thinsp;1 minute time delay. Similarly, an M3.3 flare on 02 September 2023 showed a soft X-ray peak at 07:13 UT, whereas the VLF response peaked at 07:07 UT, yielding a \u0026minus;\u0026thinsp;5 minute delay.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e, the maximum negative time delay observed in this study is \u0026minus;\u0026thinsp;5 minutes, indicating that the VLF signal enhancement can precede the soft X-ray maximum by several minutes. This behavior suggests that D-region ionization during these events is initially driven by harder X-rays or energetic particles that penetrate deeper into the lower ionosphere earlier than soft X-rays. These anomalous cases highlight the complexity of ionospheric response mechanisms during solar flares and underscore the need for further investigations incorporating multi-wavelength solar observations and detailed ionospheric modeling.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e\u003cb\u003e3.5 Variation in wait D-region parameters due to C and M classes of solar flare\u003c/b\u003e\u003c/h2\u003e \u003cp\u003eEnhanced ionization during solar flare events causes the effective upper boundary of the Earth\u0026ndash;ionosphere waveguide (EIWG) to descend. This behavior is typically manifested as a reduction in the effective reflection height (H\u0026prime;) accompanied by an increase in the sharpness factor (β), reflecting a steeper electron density gradient in the D-region (Grubor et al., 2008). In the present study, the D-region parameters H\u0026prime; and β were estimated using the Long Wave Propagation Capability (LWPC) model for both C- and M-class solar flares.\u003c/p\u003e \u003cp\u003eThe local time dependence of H\u0026prime; and β, which is closely related to variations in solar zenith angle, is shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e and \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e for C- and M-class flares, respectively. The corresponding average values are summarized in Table\u0026nbsp;2.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor C-class solar flares (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e), the average value of H\u0026prime; is found to be highest during the noon period (73.4 km), slightly lower during the morning (73.1 km), and lowest during the evening (72.9 km). In contrast, the sharpness factor β exhibits an opposite trend. The values of β range between 0.29 and 0.42 km⁻\u0026sup1;, with the highest average values occurring during the morning and evening periods (\u0026asymp;\u0026thinsp;0.34 km⁻\u0026sup1;), while a marginally lower average value (\u0026asymp;\u0026thinsp;0.33 km⁻\u0026sup1;) is observed during local noon. This inverse relationship between H\u0026prime; and β is consistent with enhanced ionization leading to a lowered reflection height and a steeper electron density gradient.\u003c/p\u003e \u003cp\u003eFor M-class solar flares (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e), the reflection height H\u0026prime; shows a wider range of variation, extending from approximately 67 km to 74 km. As indicated in Table\u0026nbsp;2, the average H\u0026prime; reaches its maximum during the noon period (70.0 km), followed by the evening (70.87 km), and exhibits the minimum value during the morning (70.81 km). The sharpness factor β for M-class flares varies from 0.30 to 0.53 km⁻\u0026sup1;. The average β values are highest during the morning and evening periods (\u0026asymp;\u0026thinsp;0.40 km⁻\u0026sup1;) and decrease slightly during the noon period (\u0026asymp;\u0026thinsp;0.37 km⁻\u0026sup1;).\u003c/p\u003e \u003cp\u003eOverall, both C- and M-class flares exhibit a consistent inverse relationship between H\u0026prime; and β, confirming that enhanced solar flare\u0026ndash;induced ionization lowers the effective reflection height while increasing the sharpness of the D-region electron density profile. The more pronounced variations observed for M-class flares reflect their higher ionizing efficiency compared to C-class flares. The observed local time dependence of H\u0026prime; and β highlights the combined influence of solar zenith angle, background ionospheric conditions, and flare intensity on the D-region response.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.6 VLF Amplitude Anomalies\u003c/h2\u003e \u003cp\u003eThe impact of solar flares on VLF signal amplitude was investigated by examining the variation of amplitude difference (ΔA) across a range of flare intensities. In general, an increase in solar flare intensity leads to enhanced D-region ionization and, consequently, an increase in ΔA. However, the relationship between flare class and ΔA is clearly nonlinear, indicating that flare intensity alone is insufficient to fully describe the observed VLF response.\u003c/p\u003e \u003cp\u003eFor C-class flares, several examples illustrate this nonlinearity. The C6.6 flare on 08 October 2022 (06:15 LT) produced a ΔA of 1.27 dB, which is lower than the ΔA of 1.41 dB observed for the slightly weaker C6.5 flare on 22 October 2022 (11:13 LT). This discrepancy can be attributed primarily to local time effects, as ionospheric background conditions vary significantly between morning and late-morning periods. Similarly, the C9.6 flare on 14 February 2023 (11:58 LT) yielded a relatively small ΔA of 0.70 dB, whereas a weaker C5.0 flare on 05 August 2022 (12:17 LT) produced a higher ΔA of 0.83 dB. Such cases highlight the influence of seasonal variations in background electron density, which modulate the relative ionospheric response to flare-induced ionization.\u003c/p\u003e \u003cp\u003eAdditional anomalies are observed that cannot be explained solely by local time or seasonal effects. For example, the C3.7 flare on 02 December 2022 (07:41 LT) produced a ΔA of 1.14 dB, exceeding the ΔA of 0.53 dB associated with the stronger C4.6 flare on 12 November 2022 (07:57 LT). Likewise, the C6.2 flare on 11 April 2023 (08:39 LT) exhibited a ΔA of only 0.54 dB, which is considerably lower than the ΔA of 1.49 dB observed for the weaker C2.5 flare on 11 November 2022 (08:54 LT). These inconsistencies indicate the presence of additional controlling factors beyond flare magnitude, local time, and season.\u003c/p\u003e \u003cp\u003eFor M-class flares, similar nonlinear behavior is evident. The M8.77 flare on 02 October 2022 (07:54 LT) resulted in a ΔA of 2.35 dB, which is lower than the ΔA of 2.52 dB produced by the weaker M5.08 flare on 16 August 2022 (13:31 LT). This difference can again be explained by local time\u0026ndash;dependent ionospheric conditions. Seasonal influences are also apparent; for example, the M2.5 flare on 19 May 2023 (10:31 LT) generated a ΔA of 3.68 dB, exceeding the ΔA of 2.88 dB observed for the slightly stronger M2.83 flare on 10 April 2023 (10:51 LT).\u003c/p\u003e \u003cp\u003eSome anomalies persist even after accounting for local time and seasonal effects. In such cases, the location of the flare on the solar disk plays an important role. For C-class flares, the C6.2 event on 11 April 2023 (S21E11) produced a smaller ΔA than the weaker C2.5 flare on 11 November 2022 (N13W14), which occurred closer to the solar disk center. Similarly, the C3.3 flare on 13 August 2022 (S11W26) resulted in a higher ΔA (0.57 dB) than the stronger C4.8 flare on 26 August 2022 (S27W58), which occurred closer to the solar limb. These observations are consistent with reduced effective ionizing flux reaching Earth for flares occurring near the solar limb due to projection effects and increased absorption.\u003c/p\u003e \u003cp\u003eFor M-class flares, geomagnetic activity is found to play an additional role in certain anomalous cases. The M1.3 flare on 18 June 2023 (06:09 LT) produced an exceptionally large ΔA of 10.1 dB, despite being weaker than the M5.3 flare on 19 May 2023 (06:21 LT), which showed a ΔA of only 2.09 dB. The corresponding Dst index values indicate moderate geomagnetic storm conditions (Dst\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;33 nT) during the M1.3 flare, compared to quiet geomagnetic conditions (Dst\u0026thinsp;=\u0026thinsp;+\u0026thinsp;8 nT) during the M5.3 event. Enhanced geomagnetic activity likely modified the background ionospheric state, amplifying the VLF response during the weaker flare.\u003c/p\u003e \u003cp\u003eIn other cases where geomagnetic effects are negligible, solar disk location again provides a plausible explanation. For instance, the M1.5 flare on 15 December 2022 (S19W69) produced a ΔA of 6.38 dB, exceeding the ΔA of 3.78 dB observed for the stronger M3.3 flare on 03 March 2023 (N23W75). The relatively closer proximity of the M1.5 flare to the solar disk center likely resulted in a higher effective ionizing flux incident on the Earth\u0026rsquo;s atmosphere.\u003c/p\u003e \u003cp\u003eOverall, these results demonstrate that while flare intensity is an important driver of VLF amplitude perturbations, the ionospheric response is strongly modulated by local time, seasonal background conditions, solar disk location, and geomagnetic activity. The interplay among these factors leads to the observed nonlinear and event-specific variations in ΔA, underscoring the complexity of D-region ionospheric response mechanisms during solar flare events.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study investigates the response of the D-region ionosphere to solar flare activity using VLF signal amplitude perturbations from the NWC transmitter, recorded over the period November 2020 to January 2025. The analysis focuses on C- and M-class solar flares and examines how local time, seasonal variability, flare location on the solar disk, and geomagnetic activity collectively modulate ionospheric disturbances.\u003c/p\u003e \u003cp\u003eA pronounced local time dependence is observed in the VLF amplitude difference (ΔA) for both C- and M-class flares. For both flare classes, ΔA is largest during morning hours, decreases toward local noon, and is weakest during the evening. This behavior is primarily governed by variations in solar zenith angle and background D-region electron density. During the morning, larger zenith angles and lower ambient electron densities enhance the relative impact of flare-induced ionization, resulting in stronger VLF perturbations. LWPC-derived parameters support this interpretation, showing reduced reflection heights (H\u0026prime;) and enhanced sharpness factors (β) during periods of stronger ionospheric response.\u003c/p\u003e \u003cp\u003eClear seasonal dependence is also evident. Both C- and M-class flares produce the strongest amplitude perturbations during winter, followed by equinox periods, with the weakest responses occurring in summer. This seasonal pattern reflects variations in background electron density, which is lowest during winter, allowing flare-induced ionization to produce a larger relative enhancement. Seasonal variability is further supported by the behavior of ionospheric relaxation times, with longer recovery (end-time) delays observed during winter and equinox seasons, indicating slower recombination under reduced background ionization conditions.\u003c/p\u003e \u003cp\u003eThe analysis of time delay characteristics reveals three distinct components\u0026mdash;start, peak, and end-time delays\u0026mdash;for both flare classes. End-time delays are consistently the largest, reflecting the prolonged recovery of the disturbed D-region after flare cessation. M-class flares generally exhibit shorter delays than C-class flares, consistent with theoretical expectations that higher electron densities produced by stronger flares lead to faster ionospheric response. A small number of exceptional events show negative time delays, where VLF amplitude peaks precede the soft X-ray maximum. These cases are likely associated with early ionization driven by hard X-rays or energetic electrons during the impulsive phase of the flare.\u003c/p\u003e \u003cp\u003eLWPC modeling of Wait parameters (H\u0026prime; and β) confirms that enhanced flare-induced ionization lowers the effective reflection height and increases the sharpness of the D-region electron density profile. For both flare classes, H\u0026prime; reaches maximum values near local noon and decreases toward morning and evening, while β exhibits the opposite trend. M-class flares produce larger overall reductions in H\u0026prime; and higher β values than C-class flares, consistent with their greater ionizing efficiency and in agreement with earlier studies.\u003c/p\u003e \u003cp\u003eFinally, the relationship between flare intensity and ΔA is found to be nonlinear. In several cases, weaker flares produce larger amplitude perturbations than stronger flares. These anomalies are influenced by a combination of factors, including local time, seasonal background conditions, solar disk location (central meridian distance), and geomagnetic activity. While many anomalous responses can be explained by these parameters, a few events remain unresolved, highlighting the complexity of D-region response mechanisms and the need for further investigations incorporating multi-wavelength solar observations and detailed ionospheric modeling.\u003c/p\u003e \u003cp\u003eOverall, this study provides a comprehensive characterization of the low-latitude D-region ionospheric response to solar flares, emphasizing the combined roles of flare intensity, background ionospheric state, solar geometry, and geomagnetic conditions. The results contribute to a better understanding of flare-induced ionospheric dynamics and demonstrate the continued value of VLF observations for monitoring the lower ionosphere.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eAuthor statement\u003c/h2\u003e \u003cp\u003eAll the authors declare no conflict of interest\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eEthics declaration\u003c/h2\u003e \u003cp\u003enot applicable.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding statement:\u003c/h2\u003e \u003cp\u003eAjeet Kumar Maurya received project funding from the Anusandhan National Research Foundation (ANRF), New Delhi, India, under the CORE research grant (CRG/2021/001322).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization, S.C., R.T., A.K.M. and S.S; methodology, S.C., A.D., R. S. and M.N.S.; formal analysis, S.C., R.T., S.S. and A.K.M.; data curation, A.K.M. writing\u0026mdash;original draft preparation, S.C. and A.K.M; writing\u0026mdash;review and editing, M.N.S., A.K.M., R.T., S.S., A.D. and R.S.; supervision, S.S., A.K.M., A.D. and R.S; project administration A.K.M. All authors have read and agreed to the published version of the manuscript\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eAuthor Ajeet Kumar Maurya thanks to the Anusandhan National Research Foundation (ANRF), New Delhi, India, for the CORE research grant (CRG/2021/001322) which supported this work. Shivani Chandra thanks CORE grant (CRG/2021/001322) for junior research fellowship.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe details of the data used in this work are provided here. The X-ray flux (0.1-0.8 nm) with a one-minute resolution was obtained from GOES ( [https://data.darts.isas.jaxa.jp/pub/solar/mirror/sswdb/goes/xray/](https:/data.darts.isas.jaxa.jp/pub/solar/mirror/sswdb/goes/xray) ). The solar flare location on the solar disc was provided from [www.solarmonitor.org](file:/D:/Paper/Suniti_work/Publication/www.solarmonitor.org) . The solar flare intensity, start time, peak time and end time is obtained from the [https://spaceweatherlive.com](https:/spaceweatherlive.com) .\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003eAppleton, E.V., 1953. A note on the “sluggishness” of the ionosphere. J. Atmos. Terr. Phys. 3, 282–284. https://doi.org/10.1016/0021-9169(53)90129-9\u003c/p\u003e\n\u003cp\u003eBasak, T., Chakrabarti, S.K., 2013. Effective recombination coefficient and solar zenith angle effects on low-latitude D-region ionosphere evaluated from VLF signal amplitude and its time delay during X-ray solar flares. Astrophys. 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Ionosphere gives size of greatest solar flare. Geophys. Res. Lett. 31, L06803. https://doi.org/10.1029/2003GL019345\u003c/p\u003e\n\u003cp\u003eValnicek, B., Ranzinger, P., 1972. X-ray emission and D-region ‘sluggishness’. Bull. Astron. Inst. Czechoslovakia 23, 318–322.\u003c/p\u003e\n\u003cp\u003eWait, J.R., Spies, K.P., 1964. Characteristics of the earth-ionosphere waveguide for VLF radio waves. Natl. Bur. Stand. Tech. Note No. 300. https://doi.org/10.6028/NBS.TN.300NIST\u003c/p\u003e\n\u003cp\u003eŽigman, V., Grubor, D., Šulić, D., 2007. D-region electron density evaluated from VLF amplitude time delay during X-ray solar flares. J. Atmos. Sol. Terr. Phys. 69(7), 775–792. https://doi.org/10.1016/j.jastp.2007.01.012\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Solar Flare, D-region Ionosphere, VLF Signal, Temporal Variation, Seasonal Variation, Solar X-ray Flux","lastPublishedDoi":"10.21203/rs.3.rs-8615895/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8615895/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe present work investigates the impact of solar flares on the D-region ionosphere using Very Low Frequency (VLF) signals transmitted from NWC (21.81°S, 114.16°E; 19.8 kHz) and recorded at a low-latitude receiving station in Dehradun, India (30.31°N, 78.03°E). The analysis covers the period from July 2022 to June 2023 and includes a total of 234 solar flare events, comprising 153 C-class and 81 M-class flares. Variations in VLF signal amplitude were examined in conjunction with solar X-ray flux data obtained from the GOES satellite. The amplitude difference (ΔA) between flare and non-flare days, as well as the time delay (Δt) between the GOES X-ray flux peak and the corresponding VLF response, were analyzed as functions of local time and season. The results reveal a pronounced local time dependence of both amplitude enhancements and response delays, with maximum perturbations observed during the morning hours for both flare classes. Seasonal analysis indicates stronger ionospheric responses during winter compared to summer and equinox periods, likely due to reduced background electron densities in the D-region. Several anomalous amplitude variations that could not be explained solely by local time or seasonal effects were attributed to factors such as the location of the flare on the solar disk and prevailing geomagnetic conditions. These findings suggest complex interdependencies among solar, ionospheric, and geomagnetic parameters. This study extends previous investigations by providing a comprehensive temporal and seasonal characterization of the low-latitude D-region ionospheric response to solar flare activity, emphasizing the roles of solar zenith angle, flare intensity, and ionospheric relaxation processes.\u003c/p\u003e","manuscriptTitle":"Temporal and seasonal variability of low-latitude D-region ionospheric response to solar flares using VLF observations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-27 16:59:04","doi":"10.21203/rs.3.rs-8615895/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"2c719044-c1cf-4941-919d-e5617d9410ce","owner":[],"postedDate":"January 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-09T21:54:03+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-27 16:59:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8615895","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8615895","identity":"rs-8615895","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}