{"paper_id":"187cd513-a34b-4d63-b2d1-07f46803375e","body_text":"On the variation of solar terminator for long and short VLF transmitter receiver great circle path over low and equatorial region | 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 On the variation of solar terminator for long and short VLF transmitter receiver great circle path over low and equatorial region Suniti Saharan, Shreyam Jana, Rajat Tripathi, Sudipta Sasmal, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5882821/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Sep, 2025 Read the published version in Acta Geophysica → Version 1 posted 6 You are reading this latest preprint version Abstract The present study investigates the effect of the solar terminator time (TT) on the low- and equatorial-latitude transmitter-receiver great circle path (TRGCP). Very Low Frequency (VLF) signals from the VTX (18.6 kHz) and NWC (19.8 kHz) transmitters, recorded at the low-latitude Indian station, Dehradun, are utilized. The TRGCP distance from NWC to Dehradun is ~6,962 km (long path), and from VTX to Dehradun is ~2,455 km (short path). The observations suggest that morning terminator time (TTM) forms due to mode transitions at both the receiver and transmitter for the short path. Monthly variations in TT show transitions in TTM and Terminator Time Evening (TTE), dominating during the equinoxes. The TTM for the NWC and VTX paths demonstrates a dependency on the transmitter during summer and the receiver during winter. A correlation between local time and TTM and TTE is estimated for both the NWC and VTX transmitter-receiver paths. Specifically, for the NWC path, the correlation with the receiver's local time during TTM and TTE is 0.5 and 0.7, respectively, while the correlation with the local time of NWC during TTM and TTE is 0.5 and 0.7, respectively, for morning and evening. A similar correlation pattern was observed for the VTX path at the receiver location (TTM: r = 0.8, TTE: r = 0.7) and at the transmitter location (TTM: r = 0.8, TTE: r = 0.7), respectively, during morning and evening. To simulate the signal amplitude and the variation of the TTM and TTE, the Long Wavelength Propagation Capability (LWPC) program was employed. A significant correlation was observed between the observed and simulated signals, indicating a strong agreement between the model and the observed data. VLF waves Ionosphere Solar Terminator D-region LWPC Wave Propagation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Key Points VLF amplitude at TT for the short path (VTX-Dehradun) shows good correlations with local sunrise and sunset compared to the long path (NWC-Dehradun). Modal interference is significant for the short path compared to the long path, resulting in fluctuations in the VTX signal during sunrise and sunset. The simulated signal amplitude has been found to provide more accurate results for non-uniform path characteristics, as observed from LWPC. 1. Introduction The solar terminator is a moving line that divides any planetary body into its day side and night side. It passes any point on Earth twice a day, once at sunrise and once at sunset, except in polar regions. This process gives rise to acoustic gravity waves (AGW) (Galushko et al., 1998; Hines, 1960), fluctuations, and scintillation (Mersha et al., 2021) in the ionospheric plasma at varying altitudes. The D-region of the ionosphere (altitude range 60–90 km) is significantly affected by changes in the solar terminator. The D-region, situated between the neutral and ionized parts of the atmosphere, plays a pivotal role in sun-Earth interactions (Hargreaves, 1992). Conventional methods for accessing this region, such as ionosondes, balloons, and satellites, face challenges due to its low altitude and electron density. Nevertheless, transmitting Very Low Frequency (VLF) radio waves through the waveguide formed by the Earth and the lower ionosphere ensures unrivalled accessibility for studying the D-region (Crombie, 1964). At sunrise and sunset, the height discontinuity leads to modal interference in the VLF signals, with an increase in the number of modes along the night side of the VLF path and a decrease when the VLF signal enters the day side (Lynn, 2010). This modal interference results in minima in the amplitude and phase of VLF signals when they reflect off the D region during sunrise and sunset. The time at which amplitude minima are observed in VLF signals is referred to as the terminator time (TT), which is typically observed during sunrise and sunset (Maekawa and Hayakawa, 2006). Prior studies have examined the diurnal variation in VLF signal minima in relation to sunrise and sunset time ( Crombie, 1965; Lynn, 1967) and the direction of the VLF propagation path (Araki, 1972; Lynn, 1976). Chand and Kumar (2017) investigated west-east and east-west VLF propagation paths to Fiji, focusing on nighttime D-region and modal interference. Their finding revealed significant daily and seasonal variability in D-region reflection heights, with maximum variations of roughly 10 km for NWC signals and 23 km for NLK signals. Clilverd et al. (1999) employed long wave propagation capability (LWPC) modeling to examine the effects of sunrise on signals along extended north-south VLF pathways. Their findings indicated that sunrise minima remained consistent on an annual basis. The majority of these studies have focused on estimating the extent of model interference and the anomalous effects of sunrise and sunset on the extended VLF path. In addition to diurnal and seasonal changes, solar terminator variations are affected by geophysical events such as geomagnetic storms, earthquakes, and cyclones (Yoshida et al., 2008; Choudhury et al., 2015; Maurya et al., 2013, 2016, 2018; NaitAmor et al., 2018; Phanikumar et al., 2018; Ray et al., 2011). Choudhury et al. (2015) examined the effects of geomagnetic storms on VLF signals in the lower ionosphere. Their findings indicated that as geomagnetic storms intensified, there was an increase in the electron density in the ionosphere's D layer, leading to a decrease in the D-layer Preparation Time (DLPT) depth. Ray et al. (2011) examined nighttime fluctuations in VLF signals due to seismic activity. They proposed that these variations could serve as indicators of impending seismic events. Furthermore, Yoshida et al. (2008) observed that the VLF terminator time exhibited significant variations during seismic events, emphasizing the dependence on factors such as VLF path length and orientation. Maurya et al. (2016) investigated the Nepal earthquake that occurred on April 25, 2015, utilizing VLF signals. They reported substantial alterations in the evening TT following the occurrence of the EQ event. Das et al. (2021) utilized VLF data from three transmitters to study tropical cyclone Fani and found that it caused disturbances across the atmosphere, from the troposphere to the ionosphere, which impacted VLF signal conductivity in the lower ionosphere. It is imperative to comprehend the trends of TT before and during solar and geophysical events to ascertain the precise impact of any geophysical occurrence Chand and Kumar (2017) examined west-east and east-west VLF propagation pathways to Fiji, with a particular emphasis on nighttime D-region and modal interference. Their findings revealed substantial daily and seasonal variability in D-region reflection heights, with maximum variations approximating 10 km for NWC signals and 23 km for NLK signals. Sasmal et al. (2014) investigated VLF signals during the 2011 Japan earthquake, discovering a maximum shift on the earthquake day and a significant sunrise TT shift before the earthquake. While the VLF terminator has been utilized to examine the impacts of geophysical events on the lower ionosphere, there is a paucity of research that has focused on the local sunrise/sunset effect on the short and medium VLF path, which covers the low and equatorial latitude region. The present study aims to elucidate the quiet time variation of the VLF terminator over the low and equatorial regions, as received at Doon station (DDN). The study's primary focus is on two distinct path lengths: the VTX-DDN path, which measures less than 3,000 kilometers, and the NWC-DDN path, which is characterized by a longer distance. The objective is to ascertain the extent to which local sunrise and sunset affect quiet time TT over the selected paths. Additionally, the study examines seasonal effects and the local time of both the transmitter and receiver. Numerical simulations are employed to study the diurnal variation of the VLF signal received at the Doon receiving station to facilitate a comprehensive analysis. The structure of the paper is as follows: Section 2 presents the data and analysis method, Sections 3 and 4 present Results and Discussion, respectively, and Section 5 concludes the paper. 2. Data and method of analysis The current study presents data from the UltraMSK VLF receiver of Doon University (DDN), which is located in Dehradun, India, at geographic coordinates 30.32°N, 78.03°E. For further details regarding UltraMSK, please visit the website ( https://www.ultramsk.com ). For the present study, two VLF transmitters VTX and NWC were selected for analysis. The transmitter VTX is from India and is located in Vijayanarayanam, India, at geographic coordinates (8.38°N, 77.75°E), and transmits a signal at frequency of 18.2 kHz. The second VLF transmitter, NWC is located in Perth, Australia, at geographic coordinates (21.81°S, 114.16°E) and transmit a signal at a frequency of 19.8 kHz. As illustrated in Fig. 1 , the receiver DDN, transmitters VTX and transmitter receiver great circle path (TRGCP) are shown with sunrise and sunset on 31st January 2021 with respect to DDN and VTX. The TRGCP from the VTX to DDN traverse a distance of 2455 km and is oriented in the south-north direction. Figure 1 also displays the sunrise and sunset on January 31, 2021, observed at both the transmitter and receiver locations. However, the VLF signal from NWC traverses a significantly longer distance of 6962 km, travelling from south to northwest to reach the Doon receiver. Further, Fig. 2 illustrates the solar terminator position at sunrise and sunset on January 31, 2021, concerning DDN and NWC. Here, the VLF signal from NWC traverses a significantly longer distance of 6962 km, traveling from south to northwest to reach the DDN receiver. The miller projection Python code was used to show day and night over the globe. This analysis encompasses geomagnetic quiet days of each month for the entire year of 2021. The information about quiet days is obtained from the website https://isgi.unistra.fr/index.php . The whole year is divided into different seasons: summer (May, June, July, and August), winter (November, December, January, and February), and equinox (March, April, September, and October). The maximum monthly mean sunspot number in 2021 is recorded as 67.5, which is also notably very low. The local sunrise and sunset times of the transmitters and receivers are calculated at the D region of the ionosphere (at an altitude of 70km). These calculations consider the solar declination angle and hour angle, as well as the effects of altitude and atmospheric refraction from the Earth. As illustrated in Fig. 3 the amplitude changes recorded at DDN via VTX and NWC transmitters are presented as function of time in UTC. It is noteworthy that the VTX amplitude signal exhibits four minima, as reported by several researchers (Chand and Kumar, 2017; Šulić et al., 2016). Two minima are observed in the morning, designated as SR1 and SR2, while the remaining two minima are observed in the evening, labelled as SS1 and SS2. The current study's morning and evening terminators for the VTX signal are SR2 and SS2, respectively. The transmitter NWC amplitude signal exhibits a modal transition with two minima: the first at sunrise time, represented by SR or TTM (Terminator Time Morning), marking the modal transition from night to daytime; the second at sunset time, represented by SS or TTE (Terminator Time Evening), occurring during the modal transition from daytime to nighttime. These transitions are illustrated in Fig. 3 . 3. Results and Discussion 3.1 Diurnal variation of VLF signal amplitude In this study, we examine the quiet days of 2021, with Figure 4 illustrating the amplitude variation of the VTX and NWC signal for a single day from each month. We endeavour to maintain a consistent date across all months; however, due to the exclusive consideration of quiet days, this was not feasible. Nevertheless, we have endeavoured to approximate this as closely as possible. The amplitude minima, attributed to the modal transition at sunrise and sunset due to discontinuity in reflection height (as elucidated by Clilverd et al., 1999), are represented by vertical lines in both transmitted VLF signals. The month of January is regarded as the reference month for TT. Šulić et al. (2016) conducted an investigation into various transmitters recorded at Belgrade. They have observed four amplitude minima in the received DHO VLF signal and classified them into two categories. The first category is caused by the transition from night to day and vice versa. In contrast, the second category occurs in all short pathways that are symmetrically arranged following the local noon. However, the amplitude VLF signal from VTX also exhibited two pairs of amplitude minima. Specifically, SR1 and SR2 exhibited amplitude minima during sunrise, while SS1 and SS2 displayed amplitude minima during sunset (refer to Figures 3). As the study progresses into the subsequent months, a notable shift in the SR1 and SR2 signals is observed, with a gradual migration toward the night side (left) up until April. However, in May, no SR1 observations were recorded, and SR2 also underwent a decline, a trend that persisted until July. Subsequently, in August, SR1 resumed its role in the plot, reaching its full manifestation in September. The remaining months of October, November, and December witnessed a gradual return of SR1 and SR2 to their original locations. Concurrently, TT's SS1 and SS2 gradually migrate to the night side (right) until April. The most pronounced shift occurs in May, and in June and July, TT in the evenings gradually approaches the reference time. TT subsequently attains proximity to the reference TT in the ensuing months. During summer, TTM and TTE exhibit maximum separation, while during winter, they demonstrate proximity. A similar shifting tendency in the amplitude minima of the NWC signal during morning and evening hours has been observed, paralleling the shifting tendency in the VTX signal. In the TTM, a leftward movement is evident, while the TTE exhibits a rightward shift. A noteworthy observation is the presence of two amplitude minima in the TTE during the period spanning from April to September. Upon closer examination of the amplitude plot, it is evident that SR returns in October, SS (consisting of two minima) disappears, and a single amplitude minimum emerges in the subsequent months. The transition (disappearing or fading) in TTM and TTE is observed in March and April, while TT reappears in the amplitude signal in September and October. A monthly examination of TTM and TTE reveals transitions in both transmitters. The months in which TT disappears (both morning and evening) are observed in March and April, and in September and October, TT reappears in the amplitude signal. The current study observes that day lengths are longer during summer and winter. According to Lynn et al. (1967), sunrise fading is dependent on the angle formed by the propagation path with the terminator. It was also determined that the observed anomalies in the fading spacing could be attributed to anomalously high mode conversion occurring along the path proximate to the geomagnetic equator. Walker (1964) and Ries (1967) both demonstrated that the fluctuations in the occurrence of TT throughout the year could be effectively explained by examining the seasonal shifts in sunrise times at lower ionospheric altitudes within the range of 60-90 km for a fixed location. Šulić et al., (2016) investigated the low solar activity VLF signal, leading to the understanding of a gradual change in amplitude variation between winter and summer. This finding was further compounded by the observation that the sun's illumination varies with the seasons, thereby impacting amplitude minima. Notably, steep amplitude minima were observed during the summer season. Building upon these findings Crombie (1964) undertook a comprehensive investigation into the VLF signal's amplitude minima over long paths at dawn and dusk. This investigation yielded the remarkable conclusion that sunrise fades more quickly than sunset. Consequently, observing these amplitude minima during summer can be challenging though the NWC transmitter can also suffer from this problem. The SR2 and SS2 were observed in the VTX transmitter throughout the year. In the present study, we observed sharp TT (amplitude minima) during winter via both VLF signal paths. 3.2 Seasonal variation of sunrise and sunset terminator time Figure 5 displays different months on the X-axis and TTM and TTE on the Y-axis. Vertical dashed lines distinguish between summer, winter, and equinox. Figure 5 green lines depict the TT as it was recorded at Doon station, the receiver; the red line displays the local sunrise time of the transmitter (VTX), whereas the blue line shows the local sunrise time of the receiver (Dehradun). Furthermore, the D region sunrise and sunset are considered as the local sunrise and sunset of the receiver and transmitter. As illustrated in Figure 6, the TTM (upper plot) and TTE (lower plot) are represented on the Y-axis and the X-axis, respectively, for several months. The various seasons, including summer, winters, and equinox, are demarcated by vertical dashed lines. The green line in Figure 6 displays the TTM & TTE recorded at the receiver (Dehradun), the red line, shows the transmitter's local sunrise and sunset time of NWC, and the blue line indicates, the receiver's local sunrise and sunset time (Dehradun). As illustrated in Figure 5, the transmitter time exhibited a parallel alignment with the TTM during the summer months and a divergent trajectory during the winter season. Conversely, the receiver exhibited a shift closer to TTM during winter months and a deviation during summer months. However, it is important to note that the terminator time difference exhibits distinct behavior during evening hours. No discernible TT trend was identified in the VTX transmitter, either from the transmitter or the receiver. As illustrated in Figure 6, the receiver time exhibits a parallel alignment with TTM during summer months, while a disparity is observed during winter. Conversely, the transmitter demonstrates a larger gap during the summer months, with a crossing occurring during the equinox season, and a smaller gap during the winter months. Conversely, the TTE difference with the receiver displays an alternate seasonal trend in the NWC transmitter, characterized by lower differences during winter and higher differences during summer. This discrepancy is likely attributable to the distinct local times observed in Dehradun and NWC. In the present study, the transmitter VTX VLF signal was observed to travel from south to north, traversing a short path of 2,455 kilometers. The TTM dependence exhibited a seasonality, with a reliance on transmitters during summer months and on receivers during winter. When considering TTE, the VTX signal demonstrated no clear trend, suggesting that TT dependence varies according to the season. In contrast, Maekawa and Hayakawa (2006) observed an antithetical dependence over a short path (north-south), finding that TTM exhibited a dependence on the receiver during summer and the transmitter during winter. However, in the present study, an opposite dependence was observed, which may be attributed to the disparate propagation directions of the VLF signal. The TTM of the NWC transmitter (long path, 6962 km, South to North West) exhibits greater dependence on the receiver during summer months and on the transmitter during winter months. The TTE of the NWC transmitter demonstrates seasonality, with a dependence on the receiver during summer months and on the transmitter during winter months (see Figure 6). This finding aligns with the observations reported by Maekawa and Hayakawa (2006), who noted complex alterations in the long south-to-north path (6921 km) during TTM and TTE. They concluded that the winter anomaly was attributable to a parallel VLF path coinciding with the transition of sunrise and sunset. They deduced from the long path that TTM occurs at the receiver's sunrise time in the summer and the transmitter's sunrise time in the winter, and that TTE depends more on the receiver during winters and summers than on the transmitter. They stated that the changeover period for TT is the autumn. In conclusion, the seasonal dependence is reliant upon the path length between the receiver and transmitter and also on the direction of propagation. 3.3 Dependence of terminator time on the receiver and transmitter’s local dawn and dusk times. A review of the literature reveals that TT has been identified as a precursor to geophysical events. The present study explores the influence of the receiver and transmitter's local dawn and dusk times on TT. Figure 7 presents a scatter plot of TTM and TTE along the Y-axis and the local time of dawn and dusk at the receiver and transmitter on the X-axis. The Figure 7 (a) and 7(b) reveals a strong correlation between TTM and local dawn and dusk times, with correlation coefficients of 0.8 and 0.8, respectively. Furthermore, the association between TTE and the local sunset time at the receiver and transmitter is demonstrated in Figures 7(c) and 7(d), with correlation coefficients of 0.7 and 0.7, respectively. As illustrated in Figure 8, the local times of dawn and dusk at the receiver and NWC transmitter are shown on the X-axis, along with a scatter plot of TTM and TTE along the Y-axis. Figures 8(a) and (b) display the TTM with the local times of the receiver and transmitter, respectively, with correlations of 0.5 and 0.5. Figures 8(c) and (d) illustrate the relationship between TTE and the local sunset time at the receiver and transmitter, respectively. The receiver and transmitter employing TTE have correlation values of 0.7 and 0.7, respectively. As illustrated in Figures 7 and 8, the time-varying nature of the TTM and TTE is contingent on the temporal settings of the transmitter and receiver, respectively. Figure 7 reveals a correlation between TT and local time receivers via VTX of 0.8 (TTM) and 0.7 (TTE). Similarly, a 0.8 and 0.7 correlation is observed between the transmitter's local time and TT. Sasmal and Chakrabarti (2009) examined the VLF signal transmitted received in Kolkata. They have used four-year data to create an SCC (standardized calibration curve) for the 1941 km transmitter-receiver signal path. They observed that TTM and TTE occur between the transmitter and receiver's sunrise and sunset. They concluded that a single hop dominates the terminator and that the reflection occurs halfway between the transmitter and receiver. Maekawa and Hayakawa (2006) also observed that the TT lies between the sunrise and sunset times of the receiver and transmitters, but they did not report the correlation values. For NWC (see Figure 8), the correlation with receiver local time during the morning and evening terminator is 0.5 and 0.7, respectively. The correlation with the local time of the transmitter (NWC) is 0.5 in the TTM and 0.7 in the TTE. The receiver is in the dark when sunrise occurs in the transmitter, NWC (see Figure 2). When a VLF signal propagates from the day side to the night side or vice versa, it encounters a discontinuity in the height of the waveguide. This is attributable to the disparity in electron density of the D layer of the ionosphere. 3.4 Numerical Simulation 3.4.1. Signal Amplitude Simulation To analyze the sunrise and sunset terminator features discussed in sections 3.1–3.3, we employed the Long Wavelength Propagation Capability (LWPC) code (Ferguson and Snyder, 1998), a widely used numerical model for studying lower ionospheric characteristics via VLF radio wave propagation. The LWPC treats the Earth’s surface and the lower ionosphere as conducting waveguide boundaries, with increasing ionospheric conductivity at higher altitudes. The LWPC model includes sub-programs such as HOMOGENEOUS, RANGE, GRID, and CHI, each simulating VLF signal characteristics under different ionospheric conditions. For example, HOMOGENEOUS assumes uniform conditions along the propagation path, while RANGE accounts for varying conditions based on solar illumination. The GRID model employs geographical grids, and CHI incorporates solar zenith angle effects. Input parameters, including transmitter and receiver locations, frequency, date, time, electron density, and reflection height, allow these sub-programs to simulate VLF signal amplitude and phase. LWPC relies on Wait’s two-component model (Wait and Spies, 1964), characterized by the sharpness parameter (β) and effective reflection height (h′). The BEARING sub-program calculates signal amplitude and phase across the propagation path under uniform ionospheric conditions. In contrast, the RTBL (Range Table) sub-program enables a more realistic representation by dividing the propagation path into segments and incorporating electron density profiles from the International Reference Ionosphere model. This study uses BEARING and RTBL to compute and compare signal amplitude profiles at terminator times for two propagation paths: the short VTX-Dehradun and the long NWC-Dehradun. The LWPC, based on waveguide mode theory, calculates total field strength as the summation of individual wave modes. While the default LWPC assumes uniform ionospheric conditions during daytime, RTBL provides a more accurate simulation by addressing non-uniformities. By leveraging both sub-programs, we compare the terminator time profiles and signal amplitudes for the two paths, highlighting differences in modal interference and attenuation due to their distinct propagation lengths. This approach enables a more nuanced understanding of sunrise and sunset terminator dynamics. In this simulation process, we use two different observation times: 00:00:00 UTC and 12:00:00 UTC. Figures 9 show the morning and evening terminator times taken from the observation data for (a) VTX and (b) NWC transmitters, respectively. The red and blue lines are for TTM and TTE, and the black dashed line is a running mean of the same. These times are the primary inputs of the LWPC codes for which we run the two simulations for the entire year. Figure 10 illustrates the observed (black line) and simulated (red line) amplitude profiles at the terminator time for both (a) VTX and (b) NWC paths. The observed amplitudes are normalized using LWPC-simulated values at local mid-noon. The top panels show the amplitudes at the terminator time, while the bottom panels represent TTE values. The observed and simulated amplitudes for VTX show similar patterns throughout the year, although the observed TTE exhibits more fluctuations than the simulated results (Figure 10). Minor mismatches in amplitude values are attributed to over-approximations in LWPC. However, the day and nighttime attenuation profiles align well, validating the diurnal signal patterns. For the NWC-Doon path, the observed and simulated amplitudes also follow similar trends but with larger mismatches. These discrepancies arise due to the longer path length, reducing waveguide-mode conversions, and the trans-equatorial nature of the path, which involves differing local sunrise and sunset times at the transmitter and receiver ends. To address these mismatches, the RANGE TABULAR sub-program was used with non-uniform electron density. The VTX-Doon path (2439 km) was divided into eight 305-km segments, while the NWC-Doon path (6962 km) was divided into 16 435-km segments. Electron density profiles were collected for altitudes between 64 and 84 km at 2-km intervals. Simulations for both uniform and non-uniform conditions were performed. Figure 11 shows the uniform ionospheric condition's simulated signal amplitude profiles for (a) VTX and (b) NWC at 00:00:00 UTC (black) and 12:00:00 UTC (red). Vertical dashed lines indicate segment divisions and the receiver location. The signal amplitudes and daily profiles for both paths closely align with observed profiles, as shown in Figure 3. A similar exercise with a non-uniform ionospheric condition is presented in Figure 12 Which show that the spatial amplitude profiles for VTX and NWC differ significantly under uniform and non-uniform ionospheric conditions. The differences are smaller for VTX than NWC, attributed to the longer path of NWC, which undergoes more waveguide mode conversions. The non-uniform condition effectively captures daytime and nighttime signal amplitude levels. The simulated daily profiles for VTX and NWC under non-uniform conditions align well with observed data (Figure 3). Notably, nighttime signals remain unaffected by solar zenith angle, consistent with the default LWPC prescription. These results highlight the importance of incorporating realistic ionospheric non-uniformity into the LWPC model for improved accuracy. 3.4.2. Modal Attenuation and Modal Conversion The most interesting observation in the current work is the presence of double terminator time for VTX-Doon paths during the winter; however, these double peaks disappear in the summer. Interestingly, no such effect has been observed in the NWC-Doon case. To interpret this effect, we examine the modal attenuation for both the path from the outcomes of LWPC. Diurnal variation of VLF signal shows (Figure 3), four amplitude minima in the VTX VLF signal. Šulić et al., (2016) observed four minima from the VLF signal from DHO, which travels across the land path similar to the current study VTX path. They discovered that an amplitude minimum shows the transition along the VLF path at sunrise and sunset. They also stated that the SR1 was well correlated with changes in illumination at the middle path. This is also observed by Maekawa and Hayakawa, (2006) over the North-south short propagation path (JJY-HOK); they also found unstable TTE. In Figure 1(a), sunrise first occurs at Doon, then at VTX; in Figure 1(c). The sunset first observed at Doon (Figure 1(b)) then, at VTX, (Figure 1(d)). Mode conversion and modal attenuation are critical processes in the sub-ionospheric propagation of VLF waves, influencing their behaviour and reception. Mode conversion occurs when VLF waves, propagating within the Earth-ionosphere waveguide, interact with irregularities or boundaries such as the day-night terminator or ionospheric disturbances. These interactions lead to the exchange of energy between different propagation modes. Modal attenuation, on the other hand, describes the gradual weakening of these modes as they travel, driven by factors such as the conductivity of the Earth’s surface, ionospheric electron density, and waveguide geometry. These effects are particularly significant at the day-night transition (the terminator), where rapid changes in ionospheric conditions lead to dynamic shifts in propagation characteristics. Understanding these phenomena is crucial for optimizing VLF applications, including long-distance communication, navigation, and monitoring of earth’s ionosphere. The VLF double terminator effect is prominently observed during sunrise and sunset, where the transition between night and day causes oscillatory patterns or a double peak in VLF signal strength. This phenomenon arises due to the complex interaction of electromagnetic waves with the ionosphere's changing conditions, particularly the D-layer's conductivity. During these terminator times, the rapid shift in ionization levels leads to the coexistence of day-mode and night-mode propagation paths. These distinct paths produce modal interference, creating characteristic peaks and dips in the signal amplitude. Figure 13 shows the spatial profile of the modal attenuation for the VTX-Doon path on January 21 during the sunrise (a) and sunset (b) terminator. The different modes during sunrise and sunset terminator times show a gradual increase in the attenuation, resulting in damping in the signal from the transmitter to the receiver. However, near the receiving end, the attenuations are different. In the morning, the attenuation for modes 1, 3, 5, and 6 shows depletion followed by an enhancement, although the attenuation for modes 2 and 4 remains constant. This nature of modes enables the possibility of modal interference at the receiver end. At sunset, the interference patterns are more prominent, where the same number of modes shows sudden attenuation inversion. In addition, a new mode (mode 7) appears around a distance of 1900 km, showing a steep decrease of modal attenuation. It is needless to say all fluctuations occur at the receiver's end, creating the double minim effect in the VLF signal amplitude. Figure 13 (c) and (d) shows the modal attenuation for the VTX-Doon path for the summer (June 4). In contrast to the winter season, the signal amplitude for summer contains more modes with a sharp modal conversion. Significantly, all the major modal attenuations occur much before the receiving location. Near the vicinity of the receiving location, the modes are quite steady, with almost average linear attenuation. For the sunrise part, the less dominating modes (8 and 10) disappear well before the receiving location, which causes maximum fluctuations. Thus, these two modes are not contributing to the resultant signal amplitude. For sunset time, a similar scenario happens for modes 8 and 10. In parallel, Mode 7 shows a sharp increase in attenuation but exhibits similar characteristics to other steady modes near the receiver. Thus, the summer signal shows lesser modal interference and fluctuations in the receiver side for the VTX-Doon path compared to the winter. This causes the double minima structure for the VTX-Doon path for the winter. Furthermore, Figure 2, the depiction shows the occurrence of both sunrise and sunset at the Doon receiver and NWC transmitter. Initially, sunrise happens at NWC, followed by Doon experiencing its sunrise. Likewise, the first sunset is observed at NWC, and then Doon follows with its sunset. It is clearly visible in Figure 14, the modal attenuation profile for the NWC-Doon winter (January 21) and summer (June 01) signal that the profile exhibits a similar nature to that of the VTX-Doon summer profiles where at the receiving end the modes are stable even though there are fluctuation over the middle of this long path. In contrast to the VTX-Doon winter path, no new modes are generated at the receiver end due to the mode conversion mechanism. Thus, it can be concluded that the summer signal of VTX-Doon and the winter and summer signals of NWC-doon do not show any double minima nature due to mode conversion process at the receiver’s end. 4. Conclusions The present study investigates the solar minimum year 2021 by observing Very Low Frequency (VLF) signal paths over two distinct transmitter-receiver configurations: NWC-Dehradun and VTX-Dehradun. The analysis focuses on the seasonal variations in signal amplitude, seasonal shifts in terminator times, and their dependencies on local sunrise and sunset times. The primary conclusions drawn from this study are as follows: • Both the TTM and TTE variations show a significant corroboration with the observed local sunrise and sunset time’s profiles. This implies that the local lower ionosphere plays a vital role in the signal attenuation characteristics due to the formation and decomposition of the ionospheric D-layer. This is being replicated through the Terminator Times. The current study shows a higher correlation between TTs and local sunrise/sunset times. • The TTM and TTE for VTX show much correlated results with the local sunrise and sunset time due to the shorter path. This also follows the actual day-night terminator shadow over the path for which the transmitter and receiver are in the same solar illumination condition at the observable time (00:00:00 UTC and 12:00:00 UTC), showing a finite state of modal conversion. However, for the NWC, the path is more extended and trans-equatorial. As a result, the transmitter and receiver are not in the same solar illuminating stage, and the signal may experience multiple day and night conditions during its propagation. Thus, the TTM and TTE do not corroborate similarly with the VTX path’s local sunrise and sunset times. • As the modal transformation is entirely different for short and long paths, it is evident from the observation that the VTX shows multiple minima during the sunrise and sunset. In contrast, for NWC, the minima are quite flat and single. This is also reflected in the TTM and TTE profiles for VTX and NWC, where the fluctuation in the termination times is larger in VTX. • It is also evident that we found a significant difference in the seasonal effect for short and long propagation paths. The direction of the propagation also plays a key role in the difference in the daily signal profiles. • The observed and simulated signal profiles at TTE and TTM are well correlated. However, the correlation is larger in the VTX signal in comparison to the NWC signal. • The simulated signal profile in both uniform and non-uniform ionospheric conditions shows significant differences in both spatial and temporal signal amplitude profiles. The effect of the solar zenith angle on the daytime signal amplitude due to the difference in production and recombination of the electron and ions is visible in the diurnal simulated amplitude profiles. This work provides a good comparison between the signal characteristics, particularly at the sunrise and sunset terminator times for a short and long path, and it also satisfactorily validates the previous results. There are some mismatches in the observed and simulated signal amplitudes. To overcome this mismatch, incorporating non-uniformity through actual electron density profiles must be fed with smaller spatial intervals over the propagation path. To get more accurate results, an amalgamation of the effect of the solar zenith angle on the Wait’s exponential parameters can be done. In a more extensive study, an ion chemistry model can be applied to get a true knowledge of the production and recombination characteristics of the lower ionosphere, which can improve the results significantly. Also, a comparative study with more propagation paths is required to get more explicit knowledge of the dependency and variation of terminator times. This will be done in the near future. Declarations The authors have no relevant financial or non-financial interests to disclose. Author contributions All authors contributed to this article. Suniti Saharan performed the data analysis and drafted the paper. Shreyam Jana and Rajat Tripathi also contributed in data analysis. Ajeet K Maurya and Sudipta Sasmal contributed to conceptualization, resource gathering and drafting review and editing. Abhirup Datta and Himani Sharma contributed in reviewing and editing. Acknowledgements AKM thanks the University Grant Commission (UGC), New Delhi, India, for start-up-grant No.F.4–5(42-FRP)(lV-cycle)/201 7(BSR) and to the Anusandhan National Research Foundation (ANRF) New Delhi, India for the CORE research grant (CRG/2021/001322). References Araki T (1973) Anomalous diurnal changes of transequatorial VLF radio waves. 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Natural Hazards and Earth System Sciences, 13, 2331–2336. https://doi.org/10.5194/nhess-13-2331-2013 Maurya AK, Venkatesham K, Kumar S, Singh R, Tiwari P, & Singh A K (2018) Effects of St. Patrick’s Day geomagnetic storm of March 2015 and of June 2015 on low-equatorial D region ionosphere. Journal of Geophysical Research: Space Physics, 123. https://doi.org/10.1029/2018JA025536 Mersha MW, Lewi E, Jakowski N, Wilken V, Berdermann J, & Kriegel M (2021) On the relationship between low latitude scintillation onset and sunset terminator over Africa. Remote Sensing, 13, 2087. https://doi.org/10.3390/rs13112087 NaitAmor S, Cohen M B, Kumar S, Chanrion O, & Neubert T (2018) VLF signal anomalies during cyclone activity in the Atlantic Ocean. Geophysical Research Letters, 45(19), 10-185. https://doi.org/10.1029/2018GL078988 Phanikumar D V, Maurya A K, Kumar K N, Venkatesham K, Singh R, Sharma S, & Naja M (2018) Anomalous variations of VLF sub-ionospheric signal and mesospheric ozone prior to the 2015 Gorkha Nepal earthquake. Scientific Reports, 8(1), 9381. https://doi.org/10.1038/s41598-018-27559-3 Ray S, Chakrabarti S K, Mondal S K, & Sasmal S (2011) Ionospheric anomaly due to seismic activities-III: Correlation between nighttime VLF amplitude fluctuations and effective magnitudes of earthquakes in the Indian subcontinent. Natural Hazards and Earth System Sciences, 11(10), 2699-2704. https://doi.org/10.5194/nhess-11-2699-2011 Ries G (1967) Results concerning the sunrise effect of VLF signals propagated over long paths. 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US Department of Commerce, National Bureau of Standards. Walker D (1964) Phase steps and amplitude fading of VLF signals at dawn and dusk. TIL. Yoshida M, Yamauchi T, Horie T, & Hayakawa M (2008) On the generation mechanism of terminator times in subionospheric VLF/LF propagation and its possible application to seismogenic effects. Natural Hazards and Earth System Sciences, 8(1), 129-134. https://doi.org/10.5194/nhess-8-129-2008 Cite Share Download PDF Status: Published Journal Publication published 13 Sep, 2025 Read the published version in Acta Geophysica → Version 1 posted Editorial decision: Major revisions 21 Apr, 2025 Reviewers agreed at journal 28 Feb, 2025 Reviewers invited by journal 24 Feb, 2025 Editor invited by journal 09 Feb, 2025 Editor assigned by journal 03 Feb, 2025 First submitted to journal 30 Jan, 2025 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. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-5882821\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":420295818,\"identity\":\"96eb6c6b-6bfe-4490-a8f8-5ddb4f8488c8\",\"order_by\":0,\"name\":\"Suniti Saharan\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Doon University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Suniti\",\"middleName\":\"\",\"lastName\":\"Saharan\",\"suffix\":\"\"},{\"id\":420295819,\"identity\":\"6b141f65-7761-4a5f-94ec-61e9258013ac\",\"order_by\":1,\"name\":\"Shreyam Jana\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Institute of Astronomy Space and Earth Sciences\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Shreyam\",\"middleName\":\"\",\"lastName\":\"Jana\",\"suffix\":\"\"},{\"id\":420295820,\"identity\":\"bfd9d49f-4308-491b-956d-2ab6d1b9ac92\",\"order_by\":2,\"name\":\"Rajat Tripathi\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Babasaheb Bhimrao Ambedkar University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Rajat\",\"middleName\":\"\",\"lastName\":\"Tripathi\",\"suffix\":\"\"},{\"id\":420295821,\"identity\":\"9a0e9598-581a-4c36-9207-3cf1f8d0cb74\",\"order_by\":3,\"name\":\"Sudipta Sasmal\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Insitute of Astronomy Space and Earth Sciences\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Sudipta\",\"middleName\":\"\",\"lastName\":\"Sasmal\",\"suffix\":\"\"},{\"id\":420295822,\"identity\":\"3e7c25e9-8c55-4009-aa9c-f52b2316b9f4\",\"order_by\":4,\"name\":\"Ajeet Kumar Maurya\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYFCCAyBCgoeBvQFIG1gQqeUASAsPSK+BBEkWJYBJwqr5Gw8ffPyBwUJGPvL51Q0/CiQY+Nu7E/BqkThwLNkA5DDD2zllN3uADpM4c3YDAUedMZMAa5mdk3aDB6jFQCIXvxb5A+e//wBrmXkm7eYfYrQYHDjDBg4xeQn2Y7eJssXwwDFjiTMGEjwGPDlst2WADIJ+kbtx+OGHioo6e/n2489uvvljI8ff3kvA+0C/A50HciGPAYjPg185CPA3QGj5BvYHhFWPglEwCkbBiAQA9OdIgNkz5UAAAAAASUVORK5CYII=\",\"orcid\":\"https://orcid.org/0000-0003-0310-9899\",\"institution\":\"Babasaheb Bhimrao Ambedkar University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Ajeet\",\"middleName\":\"Kumar\",\"lastName\":\"Maurya\",\"suffix\":\"\"},{\"id\":420295823,\"identity\":\"8efefefb-22d4-4f14-9492-f89acd781430\",\"order_by\":5,\"name\":\"Abhirup Datta\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Indian Institute of Technology Indore\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Abhirup\",\"middleName\":\"\",\"lastName\":\"Datta\",\"suffix\":\"\"},{\"id\":420295824,\"identity\":\"f8d8a824-607e-4812-a207-aa6abb15ee60\",\"order_by\":6,\"name\":\"Himani Sharma\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Doon University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Himani\",\"middleName\":\"\",\"lastName\":\"Sharma\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2025-01-22 17:34:30\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-5882821/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-5882821/v1\",\"draftVersion\":[],\"editorialEvents\":[{\"content\":\"https://doi.org/10.1007/s11600-025-01686-3\",\"type\":\"published\",\"date\":\"2025-09-13T15:57:03+00:00\"}],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":77211031,\"identity\":\"21a81c84-fa3d-447a-a196-7a402fc6e83d\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:54:42\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":6612430,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eDisplays the sunrise and sunset times for Doon and VTX using a Miller projection. Part (a) illustrates the sunrise at the Doon receiver, while part (b) demonstrates the sunset at the Doon receiver. Part (c) displays the sunrise at the VTX transmitter, and part (d) presents the sunset at VTX.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/71dce56b6c35ffd9a883f277.png\"},{\"id\":77209170,\"identity\":\"74be6c23-8c43-4ca3-8714-41190f75fcd0\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:46:45\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":8397064,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eDisplay the sunrise and sunset times for Doon and NWC using a Miller projection. Part (a) illustrates the sunrise at Doon receiver, while part (b) demonstrates the sunset at Doon. Part (c) displays the sunrise at the NWC, and part (d) presents the sunset at the NWC.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/45b8df389e2cee8d0f9906b9.png\"},{\"id\":77209105,\"identity\":\"0fca7a83-efa9-45ef-a9be-66e03b24ae48\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:46:42\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":105059,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eDisplay the diurnal amplitude variation of 2 January 2021 from the NWC and VTX transmitters recorded at Doon receiver.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/c75016107e7124108605e614.png\"},{\"id\":77211669,\"identity\":\"1979d6aa-dade-4944-8534-ca300e42ba72\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 09:02:44\",\"extension\":\"png\",\"order_by\":4,\"title\":\"Figure 4\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":1018376,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eDisplay the diurnal amplitude variation with time, of the different months of year 2021 from the (a) VTX and (b) NWC transmitters. Vertical black lines show the TTM and TTE.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure4.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/eeada50db3b43f6a6f68421d.png\"},{\"id\":77213312,\"identity\":\"63ed638a-b803-4174-9303-b685755940aa\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 09:10:44\",\"extension\":\"png\",\"order_by\":5,\"title\":\"Figure 5\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":539515,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003ePlots depicting seasonal variations in TTM (first plot) and TTE (second plot) for 2021 from VTX transmitter. The green line depicts the TT, the blue line represents the local receiver’s time, and the red line displays the local transmitter’s time. Vertical dash lines distinguish different seasons.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure5.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/d6cf8aa00901637c66808b91.png\"},{\"id\":77209102,\"identity\":\"9a99ef97-ca43-4177-a0ad-7da5f82fb33b\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:46:42\",\"extension\":\"png\",\"order_by\":6,\"title\":\"Figure 6\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":505224,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eIllustrate seasonal variations in TTM (first plot) and TTE (second plot) for 2021, as measured by the NWC transmitter. The green line signifies the TT, the blue line denotes the local receiver's time, and the red line illustrates the local transmitter's time. The vertical dash lines denote the distinction between the various seasons.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure6.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/8b60372ee0d227f9afd53984.png\"},{\"id\":77211665,\"identity\":\"0a7a3df3-7d08-4bd4-b350-3d25f21d8f37\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 09:02:42\",\"extension\":\"png\",\"order_by\":7,\"title\":\"Figure 7\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":296120,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eThe dependence of TT, (a) and (c) show the plot of TT and receiver local time, (b) and (d) show the plot of TT and VTX transmitter local time. All the time are calculated at D-region altitude of 70km.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure7.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/eca969d4a89bb5aaf9ac103f.png\"},{\"id\":77209104,\"identity\":\"a808b280-d053-4d3f-ad7f-7d31ffb75974\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:46:42\",\"extension\":\"png\",\"order_by\":8,\"title\":\"Figure 8\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":309054,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eThe dependence of TT, (a) and (c) show the plot of TT and receiver local time, (b) and (d) show the plot of TT and NWC transmitter local time. All the time are calculated at D-region altitude of 70km.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure8.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/07bba36ee72e460d786bfe3e.png\"},{\"id\":77209118,\"identity\":\"fb86a521-bcc2-4d4c-8e24-341a1464f074\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:46:43\",\"extension\":\"png\",\"order_by\":9,\"title\":\"Figure 9\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":270781,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eThe variation of terminator time as a function of day number for (a) VTX and (b) NWC. The red and green lines represent the morning and evening terminator times, respectively. The black dashed line indicates the best-fitted curve.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure9.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/dc87757447725335ddce74b0.png\"},{\"id\":77209114,\"identity\":\"f60e5f5e-3fbc-417c-98e1-34d821aeebc9\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:46:42\",\"extension\":\"png\",\"order_by\":10,\"title\":\"Figure 10\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":385295,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eComparison of observed and simulated signal amplitude for the (a) VTX-Doon path, the panel shows the amplitude variation as a function of day number for the TTM, whereas (b) the lower panel illustrates the same for TTE. (c) NWC-Doon path shows the amplitude variation as a function of day number for the TTM, (d) the lower panel illustrates the same for TTE. The black and red curves represent the observed and simulated signal.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure10.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/ef77c3d21ca8ad29ad2cf1dc.png\"},{\"id\":77211667,\"identity\":\"be8fc3a2-e053-4d9f-97e1-982c6e8708f9\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 09:02:42\",\"extension\":\"png\",\"order_by\":11,\"title\":\"Figure 11\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":474971,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eVariation of simulated signal amplitude for (a) VTX and (b) NWC as a function of the distance between the transmitter and receiver under uniform ionospheric conditions. The black curve represents the amplitude at 00:00:00 UTC, while the red curve represents the signal at 12:00:00 UTC. The dashed vertical lines indicate the locations of the eight segments along the entire path, with the receiver’s position marked by a red vertical dashed line.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure11.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/694fb795737a06844c9a91d3.png\"},{\"id\":77211040,\"identity\":\"e5ade8f5-7eba-4437-a67d-f1d5f456065e\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:54:43\",\"extension\":\"png\",\"order_by\":12,\"title\":\"Figure 12\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":514546,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eVariation of simulated signal amplitude for (a) VTX and (b) NWC as a function of the distance between the transmitter and receiver in non-uniform ionospheric conditions. The color codes of the curves are the same as in Figure 11.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure12.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/798556d38ff3c92d28461df0.png\"},{\"id\":77211060,\"identity\":\"3a497ba2-e8f1-47e9-b6c3-0726d6168572\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:54:45\",\"extension\":\"png\",\"order_by\":13,\"title\":\"Figure 13\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":739235,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eModal attenuation as a distance function for the VTX-Doon path on January 21 during the sunrise (a) and sunset (b), terminator times. Modal attenuation on June 04 during the sunrise (c) and sunset (d), terminator times.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure13.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/2683417ad4342c539b6b75c1.png\"},{\"id\":77211029,\"identity\":\"8c601e33-cdc6-4daf-be6b-a5087c6c72db\",\"added_by\":\"auto\",\"created_at\":\"2025-02-26 08:54:42\",\"extension\":\"png\",\"order_by\":14,\"title\":\"Figure 14\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":834616,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eModal attenuation as a distance function for the NWC-Doon path on January 21 during the sunrise (a) and sunset (b), terminator times. Modal attenuation on June 01 during the sunrise (c) and sunset (d), terminator times.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure14.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/4856482cfc47bc36511462f8.png\"},{\"id\":91817664,\"identity\":\"7da22eaa-012b-4edc-95eb-b1bb941b04d9\",\"added_by\":\"auto\",\"created_at\":\"2025-09-22 07:00:23\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":20942216,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5882821/v1/734aca0f-f3e7-451a-8fe1-0ba89c5ba319.pdf\"}],\"financialInterests\":\"\",\"formattedTitle\":\"On the variation of solar terminator for long and short VLF transmitter receiver great circle path over low and equatorial region\",\"fulltext\":[{\"header\":\"Key Points\",\"content\":\"\\u003cul type=\\\"disc\\\"\\u003e\\n \\u003cli\\u003eVLF amplitude at TT for the short path (VTX-Dehradun) shows good correlations with local sunrise and sunset compared to the long path (NWC-Dehradun).\\u003c/li\\u003e\\n \\u003cli\\u003eModal interference is significant for the short path compared to the long path, resulting in fluctuations in the VTX signal during sunrise and sunset.\\u003c/li\\u003e\\n \\u003cli\\u003eThe simulated signal amplitude has been found to provide more accurate results for non-uniform path characteristics, as observed from LWPC.\\u003c/li\\u003e\\n\\u003c/ul\\u003e\"},{\"header\":\"1. Introduction\",\"content\":\"\\u003cp\\u003e \\u003cdiv class=\\\"BlockQuote\\\"\\u003e \\u003cp\\u003eThe solar terminator is a moving line that divides any planetary body into its day side and night side. It passes any point on Earth twice a day, once at sunrise and once at sunset, except in polar regions. This process gives rise to acoustic gravity waves (AGW) (Galushko et al., 1998; Hines, 1960), fluctuations, and scintillation (Mersha et al., 2021) in the ionospheric plasma at varying altitudes. The D-region of the ionosphere (altitude range 60\\u0026ndash;90 km) is significantly affected by changes in the solar terminator. The D-region, situated between the neutral and ionized parts of the atmosphere, plays a pivotal role in sun-Earth interactions (Hargreaves, 1992). Conventional methods for accessing this region, such as ionosondes, balloons, and satellites, face challenges due to its low altitude and electron density. Nevertheless, transmitting Very Low Frequency (VLF) radio waves through the waveguide formed by the Earth and the lower ionosphere ensures unrivalled accessibility for studying the D-region (Crombie, 1964).\\u003c/p\\u003e \\u003cp\\u003eAt sunrise and sunset, the height discontinuity leads to modal interference in the VLF signals, with an increase in the number of modes along the night side of the VLF path and a decrease when the VLF signal enters the day side (Lynn, 2010). This modal interference results in minima in the amplitude and phase of VLF signals when they reflect off the D region during sunrise and sunset. The time at which amplitude minima are observed in VLF signals is referred to as the terminator time (TT), which is typically observed during sunrise and sunset (Maekawa and Hayakawa, 2006).\\u003c/p\\u003e \\u003cp\\u003ePrior studies have examined the diurnal variation in VLF signal minima in relation to sunrise and sunset time \\u003cb\\u003e(\\u003c/b\\u003eCrombie, 1965; Lynn, 1967) and the direction of the VLF propagation path (Araki, 1972; Lynn, 1976). Chand and Kumar (2017) investigated west-east and east-west VLF propagation paths to Fiji, focusing on nighttime D-region and modal interference. Their finding revealed significant daily and seasonal variability in D-region reflection heights, with maximum variations of roughly 10 km for NWC signals and 23 km for NLK signals. Clilverd et al. (1999) employed long wave propagation capability (LWPC) modeling to examine the effects of sunrise on signals along extended north-south VLF pathways. Their findings indicated that sunrise minima remained consistent on an annual basis. The majority of these studies have focused on estimating the extent of model interference and the anomalous effects of sunrise and sunset on the extended VLF path. In addition to diurnal and seasonal changes, solar terminator variations are affected by geophysical events such as geomagnetic storms, earthquakes, and cyclones (Yoshida et al., 2008; Choudhury et al., 2015; Maurya et al., 2013, 2016, 2018; NaitAmor et al., 2018; Phanikumar et al., 2018; Ray et al., 2011). Choudhury et al. (2015) examined the effects of geomagnetic storms on VLF signals in the lower ionosphere. Their findings indicated that as geomagnetic storms intensified, there was an increase in the electron density in the ionosphere's D layer, leading to a decrease in the D-layer Preparation Time (DLPT) depth. Ray et al. (2011) examined nighttime fluctuations in VLF signals due to seismic activity. They proposed that these variations could serve as indicators of impending seismic events. Furthermore, Yoshida et al. (2008) observed that the VLF terminator time exhibited significant variations during seismic events, emphasizing the dependence on factors such as VLF path length and orientation. Maurya et al. (2016) investigated the Nepal earthquake that occurred on April 25, 2015, utilizing VLF signals. They reported substantial alterations in the evening TT following the occurrence of the EQ event. Das et al. (2021) utilized VLF data from three transmitters to study tropical cyclone Fani and found that it caused disturbances across the atmosphere, from the troposphere to the ionosphere, which impacted VLF signal conductivity in the lower ionosphere.\\u003c/p\\u003e \\u003cp\\u003eIt is imperative to comprehend the trends of TT before and during solar and geophysical events to ascertain the precise impact of any geophysical occurrence Chand and Kumar (2017) examined west-east and east-west VLF propagation pathways to Fiji, with a particular emphasis on nighttime D-region and modal interference. Their findings revealed substantial daily and seasonal variability in D-region reflection heights, with maximum variations approximating 10 km for NWC signals and 23 km for NLK signals. Sasmal et al. (2014) investigated VLF signals during the 2011 Japan earthquake, discovering a maximum shift on the earthquake day and a significant sunrise TT shift before the earthquake.\\u003c/p\\u003e \\u003cp\\u003eWhile the VLF terminator has been utilized to examine the impacts of geophysical events on the lower ionosphere, there is a paucity of research that has focused on the local sunrise/sunset effect on the short and medium VLF path, which covers the low and equatorial latitude region. The present study aims to elucidate the quiet time variation of the VLF terminator over the low and equatorial regions, as received at Doon station (DDN). The study's primary focus is on two distinct path lengths: the VTX-DDN path, which measures less than 3,000 kilometers, and the NWC-DDN path, which is characterized by a longer distance. The objective is to ascertain the extent to which local sunrise and sunset affect quiet time TT over the selected paths. Additionally, the study examines seasonal effects and the local time of both the transmitter and receiver. Numerical simulations are employed to study the diurnal variation of the VLF signal received at the Doon receiving station to facilitate a comprehensive analysis. The structure of the paper is as follows: Section 2 presents the data and analysis method, Sections 3 and \\u003cspan refid=\\\"Sec10\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e present Results and Discussion, respectively, and Section 5 concludes the paper.\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/p\\u003e\"},{\"header\":\"2. Data and method of analysis\",\"content\":\"\\u003cp\\u003e \\u003cdiv class=\\\"BlockQuote\\\"\\u003e \\u003cp\\u003eThe current study presents data from the UltraMSK VLF receiver of Doon University (DDN), which is located in Dehradun, India, at geographic coordinates 30.32\\u0026deg;N, 78.03\\u0026deg;E. For further details regarding UltraMSK, please visit the website (\\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ehttps://www.ultramsk.com\\u003c/span\\u003e\\u003cspan address=\\\"https://www.ultramsk.com\\\" targettype=\\\"URL\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e\\u003cb\\u003e).\\u003c/b\\u003e For the present study, two VLF transmitters VTX and NWC were selected for analysis. The transmitter VTX is from India and is located in Vijayanarayanam, India, at geographic coordinates (8.38\\u0026deg;N, 77.75\\u0026deg;E), and transmits a signal at frequency of 18.2 kHz. The second VLF transmitter, NWC is located in Perth, Australia, at geographic coordinates (21.81\\u0026deg;S, 114.16\\u0026deg;E) and transmit a signal at a frequency of 19.8 kHz. As illustrated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e, the receiver DDN, transmitters VTX and transmitter receiver great circle path (TRGCP) are shown with sunrise and sunset on 31st January 2021 with respect to DDN and VTX. The TRGCP from the VTX to DDN traverse a distance of 2455 km and is oriented in the south-north direction. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e also displays the sunrise and sunset on January 31, 2021, observed at both the transmitter and receiver locations. However, the VLF signal from NWC traverses a significantly longer distance of 6962 km, travelling from south to northwest to reach the Doon receiver. Further, Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e illustrates the solar terminator position at sunrise and sunset on January 31, 2021, concerning DDN and NWC. Here, the VLF signal from NWC traverses a significantly longer distance of 6962 km, traveling from south to northwest to reach the DDN receiver. The miller projection Python code was used to show day and night over the globe.\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eThis analysis encompasses geomagnetic quiet days of each month for the entire year of 2021. The information about quiet days is obtained from the website \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ehttps://isgi.unistra.fr/index.php\\u003c/span\\u003e\\u003cspan address=\\\"https://isgi.unistra.fr/index.php\\\" targettype=\\\"URL\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e. The whole year is divided into different seasons: summer (May, June, July, and August), winter (November, December, January, and February), and equinox (March, April, September, and October). The maximum monthly mean sunspot number in 2021 is recorded as 67.5, which is also notably very low. The local sunrise and sunset times of the transmitters and receivers are calculated at the D region of the ionosphere (at an altitude of 70km). These calculations consider the solar declination angle and hour angle, as well as the effects of altitude and atmospheric refraction from the Earth.\\u003c/p\\u003e \\u003cp\\u003eAs illustrated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e the amplitude changes recorded at DDN via VTX and NWC transmitters are presented as function of time in UTC. It is noteworthy that the VTX amplitude signal exhibits four minima, as reported by several researchers (Chand and Kumar, 2017; Šulić et al., 2016). Two minima are observed in the morning, designated as SR1 and SR2, while the remaining two minima are observed in the evening, labelled as SS1 and SS2. The current study's morning and evening terminators for the VTX signal are SR2 and SS2, respectively. The transmitter NWC amplitude signal exhibits a modal transition with two minima: the first at sunrise time, represented by SR or TTM (Terminator Time Morning), marking the modal transition from night to daytime; the second at sunset time, represented by SS or TTE (Terminator Time Evening), occurring during the modal transition from daytime to nighttime. These transitions are illustrated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e\"},{\"header\":\"3. Results and Discussion\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003e3.1 Diurnal variation of VLF signal amplitude\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eIn this study, we examine the quiet days of 2021, with Figure 4 illustrating the amplitude variation of the VTX and NWC signal for a single day from each month. We endeavour to maintain a consistent date across all months; however, due to the exclusive consideration of quiet days, this was not feasible. Nevertheless, we have endeavoured to approximate this as closely as possible. The amplitude minima, attributed to the modal transition at sunrise and sunset due to discontinuity in reflection height (as elucidated by Clilverd et al., 1999), are represented by vertical lines in both transmitted VLF signals. The month of January is regarded as the reference month for TT. \\u0026Scaron;ulić et al. (2016) conducted an investigation into various transmitters recorded at Belgrade. They have observed four amplitude minima in the received DHO VLF signal and classified them into two categories. The first category is caused by the transition from night to day and vice versa. In contrast, the second category occurs in all short pathways that are symmetrically arranged following the local noon. However, the amplitude VLF signal from VTX also exhibited two pairs of amplitude minima. Specifically, SR1 and SR2 exhibited amplitude minima during sunrise, while SS1 and SS2 displayed amplitude minima during sunset (refer to Figures 3).\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eAs the study progresses into the subsequent months, a notable shift in the SR1 and SR2 signals is observed, with a gradual migration toward the night side (left) up until April. However, in May, no SR1 observations were recorded, and SR2 also underwent a decline, a trend that persisted until July. Subsequently, in August, SR1 resumed its role in the plot, reaching its full manifestation in September. The remaining months of October, November, and December witnessed a gradual return of SR1 and SR2 to their original locations. Concurrently, TT\\u0026apos;s SS1 and SS2 gradually migrate to the night side (right) until April. The most pronounced shift occurs in May, and in June and July, TT in the evenings gradually approaches the reference time. TT subsequently attains proximity to the reference TT in the ensuing months. During summer, TTM and TTE exhibit maximum separation, while during winter, they demonstrate proximity.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eA similar shifting tendency in the amplitude minima of the NWC signal during morning and evening hours has been observed, paralleling the shifting tendency in the VTX signal. In the TTM, a leftward movement is evident, while the TTE exhibits a rightward shift. A noteworthy observation is the presence of two amplitude minima in the TTE during the period spanning from April to September. Upon closer examination of the amplitude plot, it is evident that SR returns in October, SS (consisting of two minima) disappears, and a single amplitude minimum emerges in the subsequent months. The transition (disappearing or fading) in TTM and TTE is observed in March and April, while TT reappears in the amplitude signal in September and October.\\u003c/p\\u003e\\n\\u003cp\\u003eA monthly examination of TTM and TTE reveals transitions in both transmitters. The months in which TT disappears (both morning and evening) are observed in March and April, and in September and October, TT reappears in the amplitude signal. The current study observes that day lengths are longer during summer and winter. According to Lynn et al. (1967), sunrise fading is dependent on the angle formed by the propagation path with the terminator. It was also determined that the observed anomalies in the fading spacing could be attributed to anomalously high mode conversion occurring along the path proximate to the geomagnetic equator. Walker (1964) and Ries (1967) both demonstrated that the fluctuations in the occurrence of TT throughout the year could be effectively explained by examining the seasonal shifts in sunrise times at lower ionospheric altitudes within the range of 60-90 km for a fixed location.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026Scaron;ulić et al., (2016)\\u0026nbsp;investigated the low solar activity VLF signal, leading to the understanding of a gradual change in amplitude variation between winter and summer. This finding was further compounded by the observation that the sun\\u0026apos;s illumination varies with the seasons, thereby impacting amplitude minima. Notably, steep amplitude minima were observed during the summer season. Building upon these findings Crombie (1964) undertook a comprehensive investigation into the VLF signal\\u0026apos;s amplitude minima over long paths at dawn and dusk. This investigation yielded the remarkable conclusion that sunrise fades more quickly than sunset. Consequently, observing these amplitude minima during summer can be challenging though the NWC transmitter can also suffer from this problem. The SR2 and SS2 were observed in the VTX transmitter throughout the year. In the present study, we observed sharp TT (amplitude minima) during winter via both VLF signal paths.\\u003cstrong\\u003e\\u0026nbsp;\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003e3.2 Seasonal variation of sunrise and sunset terminator time\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eFigure 5 displays different months on the X-axis and TTM and TTE on the Y-axis. Vertical dashed lines distinguish between summer, winter, and equinox. Figure 5 green lines depict the TT as it was recorded at Doon station, the receiver; the red line displays the local sunrise time of the transmitter (VTX), whereas the blue line shows the local sunrise time of the receiver (Dehradun). Furthermore, the D region sunrise and sunset are considered as the local sunrise and sunset of the receiver and transmitter. \\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eAs illustrated in Figure 6, the TTM (upper plot) and TTE (lower plot) are represented on the Y-axis and the X-axis, respectively, for several months. The various seasons, including summer, winters, and equinox, are demarcated by vertical dashed lines. The green line in Figure 6 displays the TTM \\u0026amp; TTE recorded at the receiver (Dehradun), the red line, shows the transmitter\\u0026apos;s local sunrise and sunset time of NWC, and the blue line indicates, the receiver\\u0026apos;s local sunrise and sunset time (Dehradun).\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eAs illustrated in Figure 5, the transmitter time exhibited a parallel alignment with the TTM during the summer months and a divergent trajectory during the winter season. Conversely, the receiver exhibited a shift closer to TTM during winter months and a deviation during summer months. However, it is important to note that the terminator time difference exhibits distinct behavior during evening hours. No discernible TT trend was identified in the VTX transmitter, either from the transmitter or the receiver.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eAs illustrated in Figure 6, the receiver time exhibits a parallel alignment with TTM during summer months, while a disparity is observed during winter. Conversely, the transmitter demonstrates a larger gap during the summer months, with a crossing occurring during the equinox season, and a smaller gap during the winter months. Conversely, the TTE difference with the receiver displays an alternate seasonal trend in the NWC transmitter, characterized by lower differences during winter and higher\\u0026nbsp;differences during summer. This discrepancy is likely attributable to the distinct local times observed in Dehradun and NWC.\\u003c/p\\u003e\\n\\u003cp\\u003eIn the present study, the transmitter VTX VLF signal was observed to travel from south to north, traversing a short path of 2,455 kilometers. The TTM dependence exhibited a seasonality, with a reliance on transmitters during summer months and on receivers during winter. When considering TTE, the VTX signal demonstrated no clear trend, suggesting that TT dependence varies according to the season. In contrast, Maekawa and Hayakawa (2006) observed an antithetical dependence over a short path (north-south), finding that TTM exhibited a dependence on the receiver during summer and the transmitter during winter. However, in the present study, an opposite dependence was observed, which may be attributed to the disparate propagation directions of the VLF signal.\\u003c/p\\u003e\\n\\u003cp\\u003eThe TTM of the NWC transmitter (long path, 6962 km, South to North West) exhibits greater dependence on the receiver during summer months and on the transmitter during winter months. The TTE of the NWC transmitter demonstrates seasonality, with a dependence on the receiver during summer months and on the transmitter during winter months (see Figure 6). This finding aligns with the observations reported by Maekawa and Hayakawa (2006), who noted complex alterations in the long south-to-north path (6921 km) during TTM and TTE. They concluded that the winter anomaly was attributable to a parallel VLF path coinciding with the transition of sunrise and sunset. They deduced from the long path that TTM occurs at the receiver\\u0026apos;s sunrise time in the summer and the transmitter\\u0026apos;s sunrise time in the winter, and that TTE depends more on the receiver during winters and summers than on the transmitter. They stated that the changeover period for TT is the autumn. In conclusion, the seasonal dependence is reliant upon the path length between the receiver and transmitter and also on the direction of propagation.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003e3.3 Dependence of terminator time on\\u0026nbsp;\\u003c/strong\\u003e\\u003cstrong\\u003ethe receiver and transmitter\\u0026rsquo;s local dawn and dusk times.\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eA review of the literature reveals that TT has been identified as a precursor to geophysical events. The present study explores the influence of the receiver and transmitter\\u0026apos;s local dawn and dusk times on TT.\\u003c/p\\u003e\\n\\u003cp\\u003eFigure 7 presents a scatter plot of TTM and TTE along the Y-axis and the local time of dawn and dusk at the receiver and transmitter on the X-axis. The Figure 7 (a) and 7(b) reveals a strong correlation between TTM and local dawn and dusk times, with correlation coefficients of 0.8 and 0.8, respectively. Furthermore, the association between TTE and the local sunset time at the receiver and transmitter is demonstrated in Figures 7(c) and 7(d), with correlation coefficients of 0.7 and 0.7, respectively.\\u003c/p\\u003e\\n\\u003cp\\u003eAs illustrated in Figure 8, the local times of dawn and dusk at the receiver and NWC transmitter are shown on the X-axis, along with a scatter plot of TTM and TTE along the Y-axis. Figures 8(a) and (b) display the TTM with the local times of the receiver and transmitter, respectively, with correlations of 0.5 and 0.5. Figures 8(c) and (d) illustrate the relationship between TTE and the local sunset time at the receiver and transmitter, respectively. The receiver and transmitter employing TTE have correlation values of 0.7 and 0.7, respectively.\\u003c/p\\u003e\\n\\u003cp\\u003eAs illustrated in Figures 7 and 8, the time-varying nature of the TTM and TTE is contingent on the temporal settings of the transmitter and receiver, respectively. Figure 7 reveals a correlation between TT and local time receivers via VTX of 0.8 (TTM) and 0.7 (TTE). Similarly, a 0.8 and 0.7 correlation is observed between the transmitter\\u0026apos;s local time and TT. Sasmal and Chakrabarti (2009) examined the VLF signal transmitted received in Kolkata. They have used \\u0026nbsp;four-year data to create an SCC (standardized calibration curve) for the 1941 km transmitter-receiver signal path. They observed that TTM and TTE occur between the transmitter and receiver\\u0026apos;s sunrise and sunset. They concluded that a single hop dominates the terminator and that the reflection occurs halfway between the transmitter and receiver. Maekawa and Hayakawa (2006) also observed that the TT lies between the sunrise and sunset times of the receiver and transmitters, but they did not report the correlation values. For NWC (see Figure 8), the correlation with receiver local time during the morning and evening terminator is 0.5 and 0.7, respectively. The correlation with the local time of the transmitter (NWC) is 0.5 in the TTM and 0.7 in the TTE. The receiver is in the dark when sunrise occurs in the transmitter, NWC (see Figure 2). When a VLF signal propagates from the day side to the night side or vice versa, it encounters a discontinuity in the height of the waveguide. This is attributable to the disparity in electron density of the D layer of the ionosphere.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003e3.4 Numerical Simulation\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003e3.4.1. Signal Amplitude Simulation\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eTo analyze the sunrise and sunset terminator features discussed in sections 3.1\\u0026ndash;3.3, we employed the Long Wavelength Propagation Capability (LWPC) code (Ferguson and Snyder, 1998), a widely used numerical model for studying lower ionospheric characteristics via VLF radio wave propagation. The LWPC treats the Earth\\u0026rsquo;s surface and the lower ionosphere as conducting waveguide boundaries, with increasing ionospheric conductivity at higher altitudes.\\u003c/p\\u003e\\n\\u003cp\\u003eThe LWPC model includes sub-programs such as HOMOGENEOUS, RANGE, GRID, and CHI, each simulating VLF signal characteristics under different ionospheric conditions. For example, HOMOGENEOUS assumes uniform conditions along the propagation path, while RANGE accounts for varying conditions based on solar illumination. The GRID model employs geographical grids, and CHI incorporates solar zenith angle effects.\\u003c/p\\u003e\\n\\u003cp\\u003eInput parameters, including transmitter and receiver locations, frequency, date, time, electron density, and reflection height, allow these sub-programs to simulate VLF signal amplitude and phase. LWPC relies on Wait\\u0026rsquo;s two-component model (Wait and Spies, 1964), characterized by the sharpness parameter (\\u0026beta;) and effective reflection height (h\\u0026prime;). The BEARING sub-program calculates signal amplitude and phase across the propagation path under uniform ionospheric conditions. In contrast, the RTBL (Range Table) sub-program enables a more realistic representation by dividing the propagation path into segments and incorporating electron density profiles from the International Reference Ionosphere model.\\u003c/p\\u003e\\n\\u003cp\\u003eThis study uses BEARING and RTBL to compute and compare signal amplitude profiles at terminator times for two propagation paths: the short VTX-Dehradun and the long NWC-Dehradun. The LWPC, based on waveguide mode theory, calculates total field strength as the summation of individual wave modes. While the default LWPC assumes uniform ionospheric conditions during daytime, RTBL provides a more accurate simulation by addressing non-uniformities. By leveraging both sub-programs, we compare the terminator time profiles and signal amplitudes for the two paths, highlighting differences in modal interference and attenuation due to their distinct propagation lengths. This approach enables a more nuanced understanding of sunrise and sunset terminator dynamics.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eIn this simulation process, we use two different observation times: 00:00:00 UTC and 12:00:00 UTC. Figures 9 show the morning and evening terminator times taken from the observation data for (a) VTX and (b) NWC transmitters, respectively. The red and blue lines are for TTM and TTE, and the black dashed line is a running mean of the same. These times are the primary inputs of the LWPC codes for which we run the two simulations for the entire year.\\u003c/p\\u003e\\n\\u003cp\\u003eFigure 10 illustrates the observed (black line) and simulated (red line) amplitude profiles at the terminator time for both (a) VTX and (b) NWC paths. The observed amplitudes are normalized using LWPC-simulated values at local mid-noon. The top panels show the amplitudes at the terminator time, while the bottom panels represent TTE values.\\u003c/p\\u003e\\n\\u003cp\\u003eThe observed and simulated amplitudes for VTX show similar patterns throughout the year, although the observed TTE exhibits more fluctuations than the simulated results (Figure 10). Minor mismatches in amplitude values are attributed to over-approximations in LWPC. However, the day and nighttime attenuation profiles align well, validating the diurnal signal patterns. For the NWC-Doon path, the observed and simulated amplitudes also follow similar trends but with larger mismatches. These discrepancies arise due to the longer path length, reducing waveguide-mode conversions, and the trans-equatorial nature of the path, which involves differing local sunrise and sunset times at the transmitter and receiver ends.\\u003c/p\\u003e\\n\\u003cp\\u003eTo address these mismatches, the RANGE TABULAR sub-program was used with non-uniform electron density. The VTX-Doon path (2439 km) was divided into eight 305-km segments, while the NWC-Doon path (6962 km) was divided into 16 435-km segments. Electron density profiles were collected for altitudes between 64 and 84 km at 2-km intervals. Simulations for both uniform and non-uniform conditions were performed.\\u003c/p\\u003e\\n\\u003cp\\u003eFigure 11 shows the uniform ionospheric condition\\u0026apos;s simulated signal amplitude profiles for (a) VTX and (b) NWC at 00:00:00 UTC (black) and 12:00:00 UTC (red). Vertical dashed lines indicate segment divisions and the receiver location. The signal amplitudes and daily profiles for both paths closely align with observed profiles, as shown in Figure 3.\\u003c/p\\u003e\\n\\u003cp\\u003eA similar exercise with a non-uniform ionospheric condition is presented in Figure 12 Which show that the spatial amplitude profiles for VTX and NWC differ significantly under uniform and non-uniform ionospheric conditions. The differences are smaller for VTX than NWC, attributed to the longer path of NWC, which undergoes more waveguide mode conversions. The non-uniform condition effectively captures daytime and nighttime signal amplitude levels. The simulated daily profiles for VTX and NWC under non-uniform conditions align well with observed data (Figure 3). Notably, nighttime signals remain unaffected by solar zenith angle, consistent with the default LWPC prescription. These results highlight the importance of incorporating realistic ionospheric non-uniformity into the LWPC model for improved accuracy.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003e3.4.2. Modal Attenuation and Modal Conversion\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe most interesting observation in the current work is the presence of double terminator time for VTX-Doon paths during the winter; however, these double peaks disappear in the summer. Interestingly, no such effect has been observed in the NWC-Doon case. To interpret this effect, we examine the modal attenuation for both the path from the outcomes of LWPC. Diurnal variation of VLF signal shows (Figure 3), four amplitude minima in the VTX VLF signal. \\u0026Scaron;ulić et al., (2016) observed four minima from the VLF signal from DHO, which travels across the land path similar to the current study VTX path. They discovered that an amplitude minimum shows the transition along the VLF path at\\u0026nbsp;sunrise and sunset. They also stated that the SR1 was well correlated with changes in illumination at the middle path. This is also observed by Maekawa and Hayakawa, (2006)\\u003cstrong\\u003e\\u0026nbsp;\\u003c/strong\\u003eover the North-south short propagation path (JJY-HOK); they also found unstable TTE. In Figure 1(a), sunrise first occurs at Doon, then at VTX; in Figure 1(c). The sunset first observed at Doon (Figure 1(b)) then, at VTX, (Figure 1(d)).\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eMode conversion and modal attenuation are critical processes in the sub-ionospheric propagation of VLF waves, influencing their behaviour and reception. Mode conversion occurs when VLF waves, propagating within the Earth-ionosphere waveguide, interact with irregularities or boundaries such as the day-night terminator or ionospheric disturbances. These interactions lead to the exchange of energy between different propagation modes. Modal attenuation, on the other hand, describes the gradual weakening of these modes as they travel, driven by factors such as the conductivity of the Earth\\u0026rsquo;s surface, ionospheric electron density, and waveguide geometry. These effects are particularly significant at the day-night transition (the terminator), where rapid changes in ionospheric conditions lead to dynamic shifts in propagation characteristics. Understanding these phenomena is crucial for optimizing VLF applications, including long-distance communication, navigation, and monitoring of earth\\u0026rsquo;s ionosphere. The VLF double terminator effect is prominently observed during sunrise and sunset, where the transition between night and day causes oscillatory patterns or a double peak in VLF signal strength. This phenomenon arises due to the complex interaction of electromagnetic waves with the ionosphere\\u0026apos;s changing conditions, particularly the D-layer\\u0026apos;s conductivity. During these terminator times, the rapid shift in ionization levels leads to the coexistence of day-mode and night-mode propagation paths. These distinct paths produce modal interference, creating characteristic peaks and dips in the signal amplitude.\\u003c/p\\u003e\\n\\u003cp\\u003eFigure 13 shows the spatial profile of the modal attenuation for the VTX-Doon path on January 21 during the sunrise (a) and sunset (b) terminator. The different modes during sunrise and sunset terminator times show a gradual increase in the attenuation, resulting in damping in the signal from the transmitter to the receiver. However, near the receiving end, the attenuations are different. In the morning, the attenuation for modes 1, 3, 5, and 6 shows depletion followed by an enhancement, although the attenuation for modes 2 and 4 remains constant. This nature of modes enables the possibility of modal interference at the receiver end. At sunset, the interference patterns are more prominent, where the same number of modes shows sudden attenuation inversion. In addition, a new mode (mode 7) appears around a distance of 1900 km, showing a steep decrease of modal attenuation. It is needless to say all fluctuations occur at the receiver\\u0026apos;s end, creating the double minim effect in the VLF signal amplitude.\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eFigure 13 (c) and (d) shows the modal attenuation for the VTX-Doon path for the summer (June 4). In contrast to the winter season, the signal amplitude for summer contains more modes with a sharp modal conversion. Significantly, all the major modal attenuations occur much before the receiving location. Near the vicinity of the receiving location, the modes are quite steady, with almost average linear attenuation. For the sunrise part, the less dominating modes (8 and 10) disappear well before the receiving location, which causes maximum fluctuations. Thus, these two modes are not contributing to the resultant signal amplitude. For sunset time, a similar scenario happens for modes 8 and 10. In parallel, Mode 7 shows a sharp increase in attenuation but exhibits similar characteristics to other steady modes near the receiver. Thus, the summer signal shows lesser modal interference and fluctuations in the receiver side for the VTX-Doon path compared to the winter. This causes the double minima structure for the VTX-Doon path for the winter.\\u003c/p\\u003e\\n\\u003cp\\u003eFurthermore, Figure 2, the depiction shows the occurrence of both sunrise and sunset at the Doon receiver and NWC transmitter. Initially, sunrise happens at NWC, followed by Doon experiencing its sunrise. Likewise, the first sunset is observed at NWC, and then Doon follows with its sunset.\\u003c/p\\u003e\\n\\u003cp\\u003eIt is clearly visible in Figure 14, the modal attenuation profile for the NWC-Doon winter (January 21) and summer (June 01) signal that the profile exhibits a similar nature to that of the VTX-Doon summer profiles where at the receiving end the modes are stable even though there are fluctuation over the middle of this long path. In contrast to the VTX-Doon winter path, no new modes are generated at the receiver end due to the mode conversion mechanism. Thus, it can be concluded that the summer signal of VTX-Doon and the winter and summer signals of NWC-doon do not show any double minima nature due to mode conversion process at the receiver\\u0026rsquo;s end.\\u003c/p\\u003e\"},{\"header\":\"4. Conclusions\",\"content\":\"\\u003cp\\u003eThe present study investigates the solar minimum year 2021 by observing Very Low Frequency (VLF) signal paths over two distinct transmitter-receiver configurations: NWC-Dehradun and VTX-Dehradun. The analysis focuses on the seasonal variations in signal amplitude, seasonal shifts in terminator times, and their dependencies on local sunrise and sunset times. The primary conclusions drawn from this study are as follows:\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026bull; Both the TTM and TTE variations show a significant corroboration with the observed local sunrise and sunset time\\u0026rsquo;s profiles. This implies that the local lower ionosphere plays a vital role in the signal attenuation characteristics due to the formation and decomposition of the ionospheric D-layer. This is being replicated through the Terminator Times. The current study shows a higher correlation between TTs and local sunrise/sunset times. \\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026bull; The TTM and TTE for VTX show much correlated results with the local sunrise and sunset time due to the shorter path. This also follows the actual day-night terminator shadow over the path for which the transmitter and receiver are in the same solar illumination condition at the observable time (00:00:00 UTC and 12:00:00 UTC), showing a finite state of modal conversion. However, for the NWC, the path is more extended and trans-equatorial. As a result, the transmitter and receiver are not in the same solar illuminating stage, and the signal may experience multiple day and night conditions during its propagation. Thus, the TTM and TTE do not corroborate similarly with the VTX path\\u0026rsquo;s local sunrise and sunset times. \\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026bull; As the modal transformation is entirely different for short and long paths, it is evident from the observation that the VTX shows multiple minima during the sunrise and sunset. In contrast, for NWC, the minima are quite flat and single. This is also reflected in the TTM and TTE profiles for VTX and NWC, where the fluctuation in the termination times is larger in VTX. \\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026bull; It is also evident that we found a significant difference in the seasonal effect for short and long propagation paths. The direction of the propagation also plays a key role in the difference in the daily signal profiles. \\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026bull; The observed and simulated signal profiles at TTE and TTM are well correlated. However, the correlation is larger in the VTX signal in comparison to the NWC signal. \\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026bull; The simulated signal profile in both uniform and non-uniform ionospheric conditions shows significant differences in both spatial and temporal signal amplitude profiles. The effect of the solar zenith angle on the daytime signal amplitude due to the difference in production and recombination of the electron and ions is visible in the diurnal simulated amplitude profiles. \\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003eThis work provides a good comparison between the signal characteristics, particularly at the sunrise and sunset terminator times for a short and long path, and it also satisfactorily validates the previous results. There are some mismatches in the observed and simulated signal amplitudes. To overcome this mismatch, incorporating non-uniformity through actual electron density profiles must be fed with smaller spatial intervals over the propagation path. To get more accurate results, an amalgamation of the effect of the solar zenith angle on the Wait\\u0026rsquo;s exponential parameters can be done. In a more extensive study, an ion chemistry model can be applied to get a true knowledge of the production and recombination characteristics of the lower ionosphere, which can improve the results significantly. Also, a comparative study with more propagation paths is required to get more explicit knowledge of the dependency and variation of terminator times. This will be done in the near future.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003eThe authors have no relevant financial or non-financial interests to disclose.\\u003c/p\\u003e\\n\\u003ch2\\u003eAuthor contributions\\u003c/h2\\u003e\\n\\u003cp\\u003eAll authors contributed to this article. Suniti Saharan performed the data analysis and drafted the paper. Shreyam Jana and Rajat Tripathi also contributed in data analysis. Ajeet K Maurya and Sudipta Sasmal contributed to conceptualization, resource gathering and drafting review and editing. Abhirup Datta and Himani Sharma contributed in reviewing and editing.\\u003c/p\\u003e\\n\\u003ch2\\u003eAcknowledgements\\u003c/h2\\u003e\\n\\u003cp\\u003eAKM thanks the University Grant Commission (UGC), New Delhi, India, for start-up-grant No.F.4\\u0026ndash;5(42-FRP)(lV-cycle)/201 7(BSR) and to the Anusandhan National Research Foundation (ANRF) New Delhi, India for the CORE research grant (CRG/2021/001322).\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\n\\u003cli\\u003eAraki T (1973) Anomalous diurnal changes of transequatorial VLF radio waves. Journal of Atmospheric and Terrestrial Physics, 35(4), 693-703. https://doi.org/10.1016/0021-9169(73)90200-6\\u003c/li\\u003e\\n\\u003cli\\u003eChand AE, \\u0026amp; Kumar S (2017) VLF modal interference distance and nighttime D region VLF reflection height for west-east and east-west propagation paths to Fiji. Radio Science, 52(8), 1004-1015. https://doi.org/10.1002/2016RS006221\\u003c/li\\u003e\\n\\u003cli\\u003eChoudhury A, De BK, Guha A, \\u0026amp; Roy R (2015) Long-duration geomagnetic storm effects on the D region of the ionosphere: Some case studies using VLF signal. Journal of Geophysical Research: Space Physics, 120(1), 778-787. \\u003cu\\u003ehttps://doi.org/10.1002/2014JA020738\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eClilverd MA, Thomson NR, \\u0026amp; Rodger CJ (1999) Sunrise effects on VLF signals propagating over a long north-south path. Radio Science, 34(4), 939-948. https://doi.org/10.1029/1999RS900052\\u003c/li\\u003e\\n\\u003cli\\u003eCrombie DD (1964) Periodic fading of VLF signals received over long paths during sunrise and sunset. Journal of Research National Bureau of Standards, Radio Science D, 68(1), 27-35.\\u003c/li\\u003e\\n\\u003cli\\u003eCrombie DD (1966) Further observations of sunrise and sunset fading of very‐low‐frequency signals. Radio Science, 1(1), 47-51.\\u003c/li\\u003e\\n\\u003cli\\u003eDas B, Sarkar S, Haldar PK, Midya SK, \\u0026amp; Pal S (2021) D-region ionospheric disturbances associated with the Extremely Severe Cyclone Fani over North Indian Ocean as observed from two tropical VLF stations. Advances in Space Research, 67(1), 75-86. \\u003cu\\u003ehttps://doi.org/10.1016/j.asr.2020.09.018\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eFerguson JA, \\u0026amp; Snyder FP (1998) Computer programs for assessment of long-wavelength radio communications, Version 2.0. Users Guide and Source Files. Space and Naval Warfare Systems Center Technical Document 3030.\\u003c/li\\u003e\\n\\u003cli\\u003eGalushko VG, Paznukhov VV, Yampolski YM, \\u0026amp; Foster JC (1998, July) Incoherent scatter radar observations of AGW/TID events generated by the moving solar terminator. In Annales Geophysicae (Vol. 16, No. 7, pp. 821-827). G\\u0026ouml;ttingen, Germany: Springer Verlag. \\u003cu\\u003ehttps://doi.org/10.1007/s00585-998-0821-3\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eHargreaves JK (1992) The solar-terrestrial environment: an introduction to geospace\\u0026mdash;the science of the terrestrial upper atmosphere, ionosphere, and magnetosphere. Cambridge University Press.\\u003c/li\\u003e\\n\\u003cli\\u003eHines CO (1960) Internal atmospheric gravity waves at ionospheric heights. Canadian Journal of Physics, 38(11), 1441-1481. \\u003cu\\u003ehttps://doi.org/10.1139/p60-150\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eLynn KJ (2010, October) VLF waveguide propagation: The basics. In AIP Conference Proceedings (Vol. 1286, No. 1, pp. 3-41). American Institute of Physics. \\u003cu\\u003ehttps://doi.org/10.1063/1.3512893\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eLynn KJW (1967) Anomalous sunrise effects observed on a long transequatorial VLF propagation path. Journal of Geophysical Research: Space Physics, 72(14), 3575\\u0026ndash;3582.\\u003cu\\u003e \\u003c/u\\u003ehttps://doi.org/10.1002/rds196726521\\u003c/li\\u003e\\n\\u003cli\\u003eLynn KJW (1977) VLF modal interference over west-east paths. Journal of Atmospheric and Terrestrial Physics, 39(3), 347-357. https://doi.org/10.1016/S0021-9169(77)90149-0\\u003c/li\\u003e\\n\\u003cli\\u003eMaekawa S, \\u0026amp; Hayakawa M (2006) A statistical study on the dependence of characteristics of VLF/LF terminator times on the propagation direction. IEEJ Transactions on Fundamentals and Materials, 126(4), 220-226. \\u003cu\\u003ehttps://doi.org/10.1541/ieejfms.126.220\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eMaurya AK, Venkatesham K, Tiwari P, Vijaykumar K, Singh R, Singh AK, \\u0026amp; Ramesh DS (2016) The 25 April 2015 Nepal Earthquake: Investigation of precursor in VLF subionospheric signal. Journal of Geophysical Research: Space Physics, 121(10), 10-403. \\u003cu\\u003ehttps://doi.org/10.1002/2016JA022721\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eMaurya A K, Singh, R., Veenadhari, B., Kumar, S., \\u0026amp; Singh A K (2013) Sub-ionospheric VLF perturbations associated with the 12 May 2008 M7.9 Sichuan earthquake. Natural Hazards and Earth System Sciences, 13, 2331\\u0026ndash;2336. \\u003cu\\u003ehttps://doi.org/10.5194/nhess-13-2331-2013\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eMaurya AK, Venkatesham K, Kumar S, Singh R, Tiwari P, \\u0026amp; Singh A K (2018) Effects of St. Patrick\\u0026rsquo;s Day geomagnetic storm of March 2015 and of June 2015 on low-equatorial D region ionosphere. Journal of Geophysical Research: Space Physics, 123. \\u003cu\\u003ehttps://doi.org/10.1029/2018JA025536\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eMersha MW, Lewi E, Jakowski N, Wilken V, Berdermann J, \\u0026amp; Kriegel M (2021) On the relationship between low latitude scintillation onset and sunset terminator over Africa. Remote Sensing, 13, 2087. \\u003cu\\u003ehttps://doi.org/10.3390/rs13112087\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eNaitAmor S, Cohen M B, Kumar S, Chanrion O, \\u0026amp; Neubert T (2018) VLF signal anomalies during cyclone activity in the Atlantic Ocean. Geophysical Research Letters, 45(19), 10-185. \\u003cu\\u003ehttps://doi.org/10.1029/2018GL078988\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003ePhanikumar D V, Maurya A K, Kumar K N, Venkatesham K, Singh R, Sharma S, \\u0026amp; Naja M (2018) Anomalous variations of VLF sub-ionospheric signal and mesospheric ozone prior to the 2015 Gorkha Nepal earthquake. Scientific Reports, 8(1), 9381. \\u003cu\\u003ehttps://doi.org/10.1038/s41598-018-27559-3\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eRay S, Chakrabarti S K, Mondal S K, \\u0026amp; Sasmal S (2011) Ionospheric anomaly due to seismic activities-III: Correlation between nighttime VLF amplitude fluctuations and effective magnitudes of earthquakes in the Indian subcontinent. Natural Hazards and Earth System Sciences, 11(10), 2699-2704. \\u003cu\\u003ehttps://doi.org/10.5194/nhess-11-2699-2011\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eRies G (1967) Results concerning the sunrise effect of VLF signals propagated over long paths. Radio Science, 2(6), 531-538. https://doi.org/10.1002/rds196726531\\u003c/li\\u003e\\n\\u003cli\\u003eSasmal S, \\u0026amp; Chakrabarti S K (2009) Ionospheric anomaly due to seismic activities\\u0026ndash;Part 1: Calibration of the VLF signal of VTX 18.2 KHz station from Kolkata and deviation during seismic events. Natural Hazards and Earth System Sciences, 9(4), 1403-1408. \\u003cu\\u003ehttps://doi.org/10.5194/nhess-9-1403-2009\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003cli\\u003eSasmal S, Pal S, \\u0026amp; Chakrabarti S K (2014) Study of long path VLF signal propagation characteristics as observed from Indian Antarctic station, Maitri. Advances in Space Research, 54(8), 1619-1628. https://doi.org/10.1016/j.asr.2014.06.002\\u003c/li\\u003e\\n\\u003cli\\u003eSˇuli\\u0026acute;c D M, Sre\\u0026acute;ckovi\\u0026acute;c V A, \\u0026amp; Mihajlov A A (2016) A study of VLF signals variations associated with the changes of ionization level in the D-region in consequence of solar conditions. Advances in Space Research, 57(4), 1029-1043. https://doi.org/10.1016/j.asr.2015.12.025 \\u003c/li\\u003e\\n\\u003cli\\u003eWait J R, \\u0026amp; Spies K P (1964) Characteristics of the Earth-ionosphere waveguide for VLF radio waves. US Department of Commerce, National Bureau of Standards.\\u003c/li\\u003e\\n\\u003cli\\u003eWalker D (1964) Phase steps and amplitude fading of VLF signals at dawn and dusk. TIL.\\u003c/li\\u003e\\n\\u003cli\\u003eYoshida M, Yamauchi T, Horie T, \\u0026amp; Hayakawa M (2008) On the generation mechanism of terminator times in subionospheric VLF/LF propagation and its possible application to seismogenic effects. Natural Hazards and Earth System Sciences, 8(1), 129-134. \\u003cu\\u003ehttps://doi.org/10.5194/nhess-8-129-2008\\u003c/u\\u003e\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":true,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"acta-geophysica\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"agph\",\"sideBox\":\"Learn more about [Acta Geophysica](http://link.springer.com/journal/11600)\",\"snPcode\":\"11600\",\"submissionUrl\":\"https://www.editorialmanager.com/agph/default2.aspx\",\"title\":\"Acta Geophysica\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false},\"keywords\":\"VLF waves, Ionosphere, Solar Terminator, D-region, LWPC, Wave Propagation\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-5882821/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-5882821/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThe present study investigates the effect of the solar terminator time (TT) on the low- and equatorial-latitude transmitter-receiver great circle path (TRGCP). Very Low Frequency (VLF) signals from the VTX (18.6 kHz) and NWC (19.8 kHz) transmitters, recorded at the low-latitude Indian station, Dehradun, are utilized. The TRGCP distance from NWC to Dehradun is ~6,962 km (long path), and from VTX to Dehradun is ~2,455 km (short path). The observations suggest that morning terminator time (TTM) forms due to mode transitions at both the receiver and transmitter for the short path. Monthly variations in TT show transitions in TTM and Terminator Time Evening (TTE), dominating during the equinoxes. The TTM for the NWC and VTX paths demonstrates a dependency on the transmitter during summer and the receiver during winter. A correlation between local time and TTM and TTE is estimated for both the NWC and VTX transmitter-receiver paths. Specifically, for the NWC path, the correlation with the receiver's local time during TTM and TTE is 0.5 and 0.7, respectively, while the correlation with the local time of NWC during TTM and TTE is 0.5 and 0.7, respectively, for morning and evening. A similar correlation pattern was observed for the VTX path at the receiver location (TTM: r = 0.8, TTE: r = 0.7) and at the transmitter location (TTM: r = 0.8, TTE: r = 0.7), respectively, during morning and evening. To simulate the signal amplitude and the variation of the TTM and TTE, the Long Wavelength Propagation Capability (LWPC) program was employed. A significant correlation was observed between the observed and simulated signals, indicating a strong agreement between the model and the observed data.\\u003c/p\\u003e\",\"manuscriptTitle\":\"On the variation of solar terminator for long and short VLF transmitter receiver great circle path over low and equatorial region\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2025-02-26 08:46:36\",\"doi\":\"10.21203/rs.3.rs-5882821/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Major revisions\",\"date\":\"2025-04-21T06:04:56+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"\",\"date\":\"2025-02-28T15:14:12+00:00\",\"index\":0,\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2025-02-24T17:17:29+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvited\",\"content\":\"Acta Geophysica\",\"date\":\"2025-02-09T12:23:58+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2025-02-03T18:41:45+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Acta Geophysica\",\"date\":\"2025-01-30T12:23:22+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"acta-geophysica\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"agph\",\"sideBox\":\"Learn more about [Acta Geophysica](http://link.springer.com/journal/11600)\",\"snPcode\":\"11600\",\"submissionUrl\":\"https://www.editorialmanager.com/agph/default2.aspx\",\"title\":\"Acta Geophysica\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false}}],\"origin\":\"\",\"ownerIdentity\":\"2c719044-c1cf-4941-919d-e5617d9410ce\",\"owner\":[],\"postedDate\":\"February 26th, 2025\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"published-in-journal\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2025-09-22T06:51:12+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-5882821\",\"link\":\"https://doi.org/10.1007/s11600-025-01686-3\",\"journal\":{\"identity\":\"acta-geophysica\",\"isVorOnly\":false,\"title\":\"Acta Geophysica\"},\"publishedOn\":\"2025-09-13 15:57:03\",\"publishedOnDateReadable\":\"September 13th, 2025\"},\"versionCreatedAt\":\"2025-02-26 08:46:36\",\"video\":\"\",\"vorDoi\":\"10.1007/s11600-025-01686-3\",\"vorDoiUrl\":\"https://doi.org/10.1007/s11600-025-01686-3\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-5882821\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-5882821\",\"identity\":\"rs-5882821\",\"version\":[\"v1\"]},\"buildId\":\"8U1c8b4HqxoKbykW_rLl7\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}