Investigation of the October effect in very low-frequency (VLF) signals

Subionospheric very low-frequency (VLF) radio signals are reflected by free electrons in the ionospheric D-region at about 60–90 km altitude and can propagate over long distances, which makes them useful for monitoring the state of the D-region or perturbations due to solar flares. At the D-region height, the ionosphere is mainly ionized by solar Lyman-α radiation. The reflection characteristics of VLF signals depend on the state and dynamics of the D-region, which is highly influenced by Lyman-α radiation. Although the amplitude of the received terrestrial VLF signal changes as a function of solar zenith angle over the course of the year, the VLF amplitude shows a distinctive sharp decrease around October, which is hence called the “October effect”. This study investigates the occurrence of the October effect and its dependencies on latitude and longitude. We developed a method to detect the occurrence of the October effect in the long-term VLF data and derive key parameters characterizing (start and end date, intensity) the sudden decrease in the signal amplitude. This investigation using a network of VLF stations distributed over low-, middle-, and high-latitude regions shows that the occurrence of the October effect has a clear latitudinal dependency, occurring earlier in high-latitude regions than at midlatitudes. No low-latitude signature is found.

1 Introduction

The ionosphere consists of several regions, of which the so-called D-region is the least ionized but the most complex in terms of composition and a very dynamic layer. The D-region forms due to ionization by solar radiation (Nicolet and Aikin, 1960) at heights from about 60–90 km. The Lyman-α radiation photo-ionizes nitric oxide, and galactic cosmic rays ionize all the other the neutral constituents. As a result, during the day the D-region is at a height of about 70 km and during the night at 85 km (Thomson, et al., 2017). This dependency on the Lyman-α radiation is also visible in the comparison between times of high and low solar activity, as a reduction in the solar activity leads to a decreased electron density and therefore a weaker noon very low-frequency (VLF) amplitude (Thomson and Clilverd, 2000; Correia et al., 2011). In turn, an increase in solar activity leads to an increase in electron density (Singer et al., 2011). However, at higher latitudes galactic cosmic rays become more significant for the ionization as the solar zenith angle (SZA) increases (Thomson. et al., 2017).

Subionospheric VLF signals propagate through the Earth–ionosphere waveguide (Barr, 1971; Davies, 1990), with its upper boundary given by the D-region. The wave propagation is controlled by the index of refraction of the ionospheric medium and thus controlled by the D-region electron density and the collision frequency of the electrons with the predominant neutral constituents (i.e., N₂ and O₂; Hartree, 1931).

The annual variation of the noontime D-region electron density shows a gradual increase in the first half of the year until it reaches a plateau in summer. In October a strong decrease is observed and the electron density reaches a low level in winter (Renkwitz et al., 2023). These changes in the D-region electron number density also affect VLF propagation. During solar flare events (McRae and Thomson, 2004) and geomagnetic storms (Nwankwo et al., 2022) rapid temporal changes may occur in the D-region electron density and vertical structure (and thus collision frequency with neutral constituents), which influences VLF propagation.

Seen approximately from the middle of the year, the SZA at noon shows a symmetrical course over the year, and therefore the seasonal VLF signal amplitude behavior at noon would also be expected to be symmetrical. Recently, Macotela et al. (2021) found an asymmetry in the VLF signal amplitude noon curve, which is referred to as the fall effect. The VLF signal amplitude does not mirror the variation of the SZA and tends to remain at midsummer levels or increase somewhat before experiencing a strong and sudden decrease around October. This decrease in October has also been reported by Banyś (2017). We investigate the strong and sudden decrease at the beginning of October, which we refer to as the October effect. The term “October effect” was first used by Pancheva and Mukhtarov (1996) for the sharp transition of the electron density profile in the lower D-region in autumn, which in turn affects VLF propagation. In addition to that, recently Wendt et al. (2024) found that there is no October effect at night.

The October effect is shown in Fig. 1 for three propagation paths at different latitudes together with the solar elevation angle (SEA) observed at the mid-reflection point (MRP). The SEA is the opposite angle of the SZA. Figure 1a shows the location of the propagation paths and their corresponding transmitter (Tx), receiver (Rx), and MRP (black dot). Figure 1b shows the VLF composite signal amplitude at noon for the propagation path NAA–SOD (MRP at 64° N), with an early and strong October effect (marked by vertical broken lines), and Fig. 1c shows NAA–ESK (MRP at 54° N) with a later October effect. Additionally, Fig. 1b shows a decrease in VLF amplitude prior to the October effect. Finally, Fig. 1d shows the VLF amplitude for the propagation path from NAU–STJ (MRP at 33° N), and it shows no October effect. The VLF amplitude follows the overall trend of the SEA.

The investigation of the October effect's dependencies will help to better understand the course of the VLF signal amplitude fluctuations. As pointed out in Banyś (2017), considering the background VLF signal amplitude is crucial to correlate the VLF signal response to the strength of a solar flare. In order to identify the physical origin of the October effect, we attempt to quantify its characteristics and determine its variation with geographic latitude and longitude. The paper is structured as follows: first, the data sources and propagation paths used are presented in Sect. 2. Then, the method for determining the parameters of the October effect is introduced in Sect. 3. With that, we obtain clear results in Sect. 4 for determining the dependency of the October effect on latitude on longitude. The results are then discussed in Sect. 5, and our conclusions are summarized in Sect. 6.

2 Data

The data used in this study are made available by the Antarctic–Arctic Radiation-Belt (Dynamic) Deposition – VLF Atmospheric Research Konsortia (AARDDVARK) (Clilverd et al., 2009) network by the British Antarctic Survey (BAS) and the DLR's Global Ionospheric Flare Detection System (GIFDS) (Wenzel et al., 2016) network. The available datasets include either 1 or 10 Hz relative measurements of the signal amplitude and phase, depending on the receivable transmitters and receiver types used. The receiver stations of the AARDVARK network are mainly located at high latitudes, while GIFDS receiver stations are located at midlatitudes. For a detailed description of the technical background of GIFDS we refer to Banyś (2017). This work focuses on the analysis of the amplitude data. The transmitter (Tx)–receiver (Rx) combinations used and their corresponding frequencies, locations of Tx–Rx, and MRP are shown in Table 1.

Figure 1 Map of great circle propagation paths used in (a). Tx (triangle up), MRP (dot), Rx (triangle down). A_day (black) ±σ (gray) with the SEA (red) for three exemplary VLF links: (b) NAA–SOD, (c) NAA–ESK, and (d) NAU–STJ. A_day represents composites of different years due to different data availability: for NAU–STJ in 2014, 2016, and 2019; for NAA–ESK in 2016–2019, and for NAA–SOD in 2013, 2015–2016, and 2021. The relevant time period for the October effect is in light gray. The determined t_start and t_end of A_day are shown as dashed vertical black lines in (b) and (c). A_day in (d) shows no October effect.

The propagation paths used are illustrated on their corresponding maps. The following VLF receiver station data are used in the analysis, and their abbreviations are given in parentheses: Eskdalemuir (ESK), Neustrelitz (NTZ), St. Johns (STJ), Kilpisjärvi (KIL), Sodankylä (SOD), and Ny-Ålesund (NYÅ). The transmitters are represented by their call signs. The propagation paths used are mainly over North America and the Atlantic. The signals originate mainly from US transmitter stations and are received in Europe. The Tx–Rx combinations used are chosen due to their comparability in latitude and longitude and availability of continuous measurements over a long time period. Furthermore, only years of propagation paths without huge data gaps or jumps in the amplitude signal level are considered, as these jumps could indicate a change of receiver hardware.

Table 1 Overview of all transmitter–receiver combinations used.

3 Methods

Data processing is crucial to derive meaningful conclusions. Since the measurements are relative and each receiver station is unique, it is challenging to formulate a general approach to the data and to make comparisons between the propagation paths. Therefore, we propose a detection method based on the derivatives, and therefore the data do not require further preprocessing. If comparable composites of data are required, a recent work by Schneider et al. (2024) provides a clear overview. In Fig. 2, we have considered the propagation path of NAA–NYÅ in 2021 and we describe the process of obtaining the key parameters of the October effect: the start date t_start, the end date t_end, the date of maximum amplitude decrease t_max, and the intensity m_Oct of the October effect. First, we computed the median of VLF amplitude A for every 10 min interval for 1 entire year separately for each propagation path from the raw VLF amplitude measurements (see Fig. 2a). In the next step we define the local noontime as the time of the maximum SZA at the MRP of the propagation path. At this local noontime we set a time window of ±1 h to derive the median VLF amplitude noon curve A_day(t) from A(t) as a rolling median of 21 d. Palit et al. (2018) showed that short X-ray bursts also have just a very short effect on VLF modulation. Furthermore, Palit et al. (2018) also noted that during local noon the VLF modulation (due to a change in electron density as a result of X-ray burst) is small because the relative change is smaller. As we observe the October effect only during noon, the influences of such VLF modulations are further minimized. Other short-timed events like lightning or early/fast VLF events are very rapid events with short signal recovery times from 10 to 100 s (Haldoupis et al., 2006). Longer-lived events like solar flares also have a longer impact on VLF propagation (Banyś, 2017), which could significantly change A_day(t) on one day. During geomagnetic storms the VLF amplitude may be decreased for a couple of days (Nwankwo et al., 2022), which would also significantly change A_day(t) for these days. All these influences should be mitigated by the long 21 d rolling median to derive the overall noon curve. Altogether, the method ensures that effects of ionospheric perturbations on the VLF amplitude are minimized and can be considered negligible in our analysis.

From A_day(t) the first derivative $\mathrm{d}{A}_{\mathrm{day}}/\mathrm{d}t$ and the second derivative $\mathrm{d}{A}_{\mathrm{day}}^{\mathrm{2}}/\mathrm{d}{t}^{\mathrm{2}}$ are calculated (see Fig. 2c and d). We use the minimum and maximum in $\mathrm{d}{A}_{\mathrm{day}}^{\mathrm{2}}/\mathrm{d}{t}^{\mathrm{2}}$ to define the start t_start and the end t_end of the October effect (see the red points in Fig. 2b). Additionally, the time of the maximum decrease in the October effect t_max is found by getting the zero crossing $\mathrm{d}{A}_{\mathrm{day}}^{\mathrm{2}}/\mathrm{d}{t}^{\mathrm{2}}=\mathrm{0}$. t_max also marks the point of the lowest gradient in A_day and is the local minimum in $\mathrm{d}{A}_{\mathrm{day}}/\mathrm{d}t$. From t_start and t_end the duration of the October effect is easily computed by $\mathrm{\Delta }t=t_{\mathrm{end}}-t_{\mathrm{start}}$. To obtain a quantity of the intensity of the October effect the slope of A_day is used. The most northern propagation paths may not be completely in daylight during the winter, which leads to an uncertainty in finding t_end. Therefore, the slope is calculated from t_start to t_max, and thus the intensity of the October effect is derived by $m_{\mathrm{Oct}}=\left(A_{\max }-A_{\mathrm{start}}\right)/\left(t_{\max }-t_{\mathrm{start}}\right)$.

Missing data and data within noise level may lead to false interpretation; for example, the regular vertical dark blue stripes in the daytime are from maintenance downtimes of the NAA transmitter. Therefore, $\mathrm{d}{A}_{\mathrm{day}}/\mathrm{d}t$ is smoothed by a Gaussian filter. The method we use to calculate A and A_day considers NaNs in the data to be missing data and the median then gets calculated from fewer data points or is considered a NaN when there are no data points. Adding to that, we formulate certain criteria for the determination of the October effect.

t_start and t_end need to lie in the same minimum in $\mathrm{d}{A}_{\mathrm{day}}/\mathrm{d}t$ (see Fig. 2c). If this is not the case, the algorithm searches for the next set of t_start and t_end by limiting the time window of the search.

No huge spikes ($\mathrm{d}{A}_{\mathrm{day}}/\mathrm{d}t)\mathit{>}\mathrm{2.5}$ dB d⁻¹ avoid receiver stations where a hardware change has occurred. This would be visible due to a change in the overall level of A_noon.

$\mathrm{d}{A}_{\mathrm{day}}^{\mathrm{2}}/\mathrm{d}{t}^{\mathrm{2}}$ at t_start and t_end needs to be bigger than 0.005 dB d⁻², as seen as a dotted horizontal line in Fig. 2d. This is to ensure that a significant decrease happens around October, and thus the October effect occurs.

Δt must be longer than 7 d to consider outages in the transmitter, which could be identified as sharp decreases.

Between t_start and t_end there need to be more days with data points than $\mathrm{\Delta }t/\mathrm{2}$.

The algorithm searches in a time window from 5 September to 15 November. t_start and t_end should differ from these limits.

Figure 2 Steps for deriving t_start, t_max, and t_end of the October effect: (a) smoothed VLF amplitude over the year for each day with a time window (shaded) at local noon. (b) Deduced noon curve A_day (solid) with t_start, t_max, and t_end (dashed) and associated values A_start, A_max, and A_end (dotted). (c) First derivative $\mathrm{d}{A}_{\mathrm{day}}/\mathrm{d}t$ and (d) second derivative $\mathrm{d}{A}_{\mathrm{day}}^{\mathrm{2}}/\mathrm{d}{t}^{\mathrm{2}}$ defining t_start, t_max, and t_end if the threshold (dotted) is exceeded.

4 Results

Next, we investigate how the October effect varies from year to year and with longitude and latitude. For this purpose, a careful selection of Tx–Rx pairs is necessary. For studying the variation of the October effect with longitude, propagation paths with the same latitude related to their MRP are selected. Likewise, propagation paths with the same longitude related to their MRP are selected for investigating the latitudinal dependency.

4.1 Year-to-year variability

First, the year-to-year variation is investigated and the results are shown in Fig. 3. To distinguish the different propagation paths, they are color-coded according to the latitude or longitude of the mid-reflection point. This is shown in Fig. 3a and e. The variation of t_start is shown in Fig. 4b and f, t_end is shown in Fig. 3c and g, and the intensity m_Oct is shown in Fig. 3d and h. Comparing the different propagation paths over time, a clear trend in t_start, t_end, or m_Oct of the October effect is not visible, but there is a significant variation over the years. This points to a highly variable D-region, which is driven by both variations in ionization and dynamics of the neutral atmosphere. From the color-coded t_start in Fig. 3b and f and t_end in Fig. 3c and g of the October effect, a possible latitudinal and longitudinal dependency is visible, as the October effect occurs earlier at higher latitudes and more easterly longitudes – over the limited longitudinal range studied. This is investigated further in the next subsection.

4.2 Latitudinal dependency

To investigate the latitudinal dependence of the October effect, eight propagation paths (NAA–SOD/KIL/ESK/NTZ, NRK–STJ/ NYÅ, NDK–SOD/KIL) are used, as their MRPs are around 40° W. From t_start in Fig. 4b it is evident that the October effect occurs earlier at higher latitudes. Likewise, from the variation of t_end in Fig. 4b we see that the October effect also ends earlier with increasing latitude. Interestingly, the duration Δt stays constant. The intensity m_Oct in Fig. 4c shows a wider spread at higher latitudes, which could point to less solar forcing of the October effect and therefore its dependency on the dynamics of the atmosphere.

It is important to point out that in Fig. 4a to c two additional propagation paths (NDK–SOD/KIL) are shown. For these paths the October effect occurs even earlier in the year, which suggests that not only the higher latitude but also being in the American sector could be relevant. This is further supported by the additionally shown propagation path NRK–NYÅ. The MRP for this propagation path has about the same latitude (∼70° N) as NDK–SOD/KIL, but the October effect occurs later. This could be attributed to the more eastern longitude.

Considering the geomagnetic latitude, which is shown in Fig. 5b, a linear trend in the latitudinal dependency is visible. Also, t_start and t_end of NRK–NYÅ now align with the overall trend. The geomagnetic latitude of its MRP is about 71.6° N, while NDK–SOD/KIL is about 77.6° N in geomagnetic latitude.

Figure 3 Yearly variations of the October effect: panels (a) and (e) show maps with the propagation paths used. On the left (a–d) is the yearly variation of the latitudinal dependency investigation color-coded in latitude, and on the right (e–h) are the propagation paths for the longitudinal dependency investigation color-coded in longitude. Panels (b) and (f) show t_start, panels (c) and (g) t_end, and panels (d) and (h) the intensity m_Oct of the October effect.

4.3 Longitudinal dependency

To investigate the longitudinal dependency 10 propagation paths (NLK–SOD/KIL/NYÅ, NDK–SOD/KIL/NYÅ, NAA–SOD/KIL/NYÅ, and NRK–NYÅ) are selected. While their MRPs are all at comparable latitudes of about 65 to 75° N, they differ greatly in longitude from 110 to 10° W. Figure 4d shows the great circle paths and their corresponding MRPs, marked with dots in the same line color. It should also be noted that although these propagation paths have different ranges, we considered them all to be long propagation paths.

In Fig. 4e and f the results for t_start, t_end, and m_Oct are shown. In the American sector the October effect occurs earlier and also ends earlier. Again, the duration Δt stays about the same. Also, the intensity m_Oct does not vary with longitude; rather, it is scattered over a wide range of values. This is in contrast to the latitudinal dependency of m_Oct.

It is important to point out that the latitude, which also has an effect on t_start and t_end, is slightly different for these propagation paths, but these are the best paths to compare in longitude, as the possibilities are very limited. Adding to this point, it should be considered that these propagation paths span a wide range of longitudes and therefore the longitudinal dependency might be smeared out over these long paths. Unfortunately, there are no paths that run meridional at different longitudes, as these would possibly be best for such a comparison. This is in contrast to the investigation of the latitudinal dependency, as the propagation paths used there have a more zonal propagation direction.

Another point is that the most eastern propagation path from NRK–NYÅ differs from the general trend of t_start and t_end. One reason for this might be that the propagation path is much shorter and that the transmitter NRK has a higher frequency of 37.5 kHz, thus being in the low frequency (LF), because the VLF range is defined as the frequency range of 3–30 kHz. But as NRK–NYÅ aligns well in linear trend the geomagnetic latitudinal dependency (see Fig. 5d), the higher frequency, and the shorter propagation path do not seem to be a main influence here.

It should be noted that the most westward propagation path NLK–NYÅ also does not follow the general trend and the October effect occurs later in the year. This “S-shaped” behavior of the longitudinal dependency of the October effect suggests a connection to the distance from the auroral oval, as the shape and extension of the auroral oval differ at different longitudes. Here the direct comparison to the geomagnetic longitude shows no significant change in the overall trend and the S-shaped behavior is still visible, as can be seen in Fig. 5d.

5 Discussion

VLF signal amplitude measurements conducted by the AARDDVARK and GIFDS networks from the years 2006 to 2022 for different propagation paths (see Table 1) show a distinct sudden sharp decrease in the VLF noon amplitude A_day (see Fig. 1) around October. This sudden decrease is called the October effect and does not have a satisfactory explanation yet. The variation of A_day in Fig. 1 would be expected to follow the overall symmetrical course of the SZA over the year, as the F10.7 irradiance from the Sun is the main driver of the electron density in the ionospheric D-region.

Figure 4 Latitudinal and longitudinal dependency of the October effect: panels (a) and (d) show maps with the propagation paths used. On the left (a–c) is the latitudinal dependency color-coded in longitude and on the right (d–f) the longitudinal dependency color-coded in latitude. Panels (b) and (e) show the t_start (triangle up) and t_end (triangle down) of the October effect. The triangles are at the median and the lines show the spread of the values. Panels (c) and (f) show the intensity m_Oct of the October effect.

Figure 5 Dependency of the October effect on geomagnetic latitude and longitude: panels (a) and (c) show maps with the propagation paths used. On the left (a–b) is the geomagnetic latitudinal dependency color-coded in geomagnetic longitude and on the right (c–d) the geomagnetic longitudinal dependency color-coded in geomagnetic latitude. Panels (b) and (d) show the t_start (triangle up) and t_end (triangle down) of the October effect. The triangles are at the median and the lines show the spread of the values.

In this study we presented a method (Sect. 3, Fig. 2) to detect the October effect in the seasonal variation of the VLF amplitude A_day. With this method we quantified the start t_start, the end t_end, the intensity m_Oct, and the duration Δt of the October effect. A strong yearly variation in t_start and t_end is visible in Fig. 3b, c, f, and g. This yearly variation shows a latitudinal and longitudinal dependency of t_start and t_end. The results presented here suggest two cases for further investigation: one with propagation paths, where the MRP is at a similar longitude range to isolate the latitudinal dependency, and another case where the MRP is at a similar latitudinal range to investigate the longitudinal dependency.

A challenge in detecting the October effect is the determination of t_end, as the VLF amplitude in winter begins to rise again and also shows a stronger variation in some propagation paths. Therefore, the end point is not always clearly determined, especially a high latitudes where parts of the propagation paths do not lie in daylight during winter. This also has an effect on the determination of the duration Δt of the October effect. For the future we also plan to investigate the October effect in the Southern Hemisphere, although even fewer data are available for this.

We also investigated the dependency of the October effect on the solar activity, but we did not identify conclusive results. As we hypothesize that the October effect is connected to the dynamics of the neutral atmosphere, more solar forcing of the D-region should result in a weaker October effect. As an example of this solar forcing Clilverd et al. (2006) showed that the ionospheric effective height is lowered during solar proton events (SPEs), which occur when the Sun is active. The weaker October effect is sometimes visible in A_day, where the sudden decrease in A_day is more gradual than usual. Also, a wider spread of m_Oct was observed during times with lower solar activity for some propagation paths than at times with high solar activity. Additionally, Wendt et al. (2024) found an increase in neutral atmospheric temperature during the October effect, which supports the connection between the October effect and the dynamics of the neutral atmosphere. This will be a topic for our ongoing work.

6 Conclusions

From the results in Figs. 4 and 5, it can be concluded that the October effect is dependent on the latitude and also shows systematic variations over a limited range of longitude. It occurs earlier at higher latitudes and the spread of the intensity of the October effect (m_Oct) is also larger in that region. Additionally, it occurs earlier in the American sector than the European sector. The longitudinal dependency of t_start and t_end of the October effect shows a distinct “S-shaped” behavior. This S-shaped behavior points strongly to an association with the distance from the auroral oval. When t_start and t_end are considered in the terms of the magnetic latitude and longitude, a clear linear dependency on geomagnetic latitude is visible, while the S-shaped behavior of the longitudinal dependency continues to be visible in the geomagnetic longitude. Adding to that, as the spread of the intensity m_Oct is larger at higher latitudes, where less solar forcing occurs, the neutral atmosphere and its dynamic nature appear to be the main driver of the October effect. Summarizing our conclusion, the October effect is dependent on latitude, as the October effect occurs earlier at higher latitudes, and the spread of the intensity of the October effect (m_Oct) is also larger, and longitude, as the October effect occurs earlier in the American sector than in the European sector.

These behaviors are even clearer if t_start and t_end are compared in terms of geomagnetic latitude and longitude instead of geographic latitude and longitude.