1 Introduction

The ionized meteor trails generated during the entry of meteors to the Earth’s atmosphere at a high velocity is considered as an indirect source of information on the mesospheric conditions. The durations of the overdense meteor echoes scattered from the high density meteor trails is directly impacted by the removal rate of the ionized species. Previously, the diffusion of the free electrons was suggested to be the dominant cause behind the removal of the trails and consequently the reduction of the echo durations (e.g. Kaiser 1953). Subsequent studies speculated the major cause of the removal of the trails to the free electrons attachment to neutral atmospheric molecules (e.g. Davis et al. 1959). Thereafter, the role of the secondary ozone layer in oxidizing the ionized trails was proposed to be the primary cause of the removal below the 95 km height (Baggaley and Cummack 1974). The relationship between the ozone deionization process and the overdense meteor echo durations was elaborated by Baggaley (1979). This relationship was further developed to ozone concentration observation method by Jones et al. (1990). The method uses the knee-shaped curve of the statistical cumulative logarithmic plot of the meteor echo counts versus echo durations during a certain period. The knee point on this curve where the meteor echo counts dramatically drops down is determined as the transition from the diffusion-limited regime to the chemistry-limited regime. As the mesospheric ozone is inversely related to the solar activity (e.g. Merkel et al. 2011), the varying position of the knee during the daytime and night time, seasonally or annually can be an indirect observation unit for the mesospheric ozone concentration and the solar activity level.

Having the advantage of longer meteor echo durations, meteor observation by radio forward scattering would normally be a preferred option for this method with respect to the backscattering systems. The basic parameters of meteor echo counts and durations are obtainable by the basic setup receiver configuration of the forward scattering meteor radars (Fig. 1), where a single antenna and a single receiver are used. This configuration is spread not only among professionals but also among amateur radio observers worldwide. In Japan there exist more than 100 receiving sites with similar setups. It could be beneficial for this type of observers to add an educational scientific usage to their systems through meteor echo duration analyses. However, the automation of observing and recording the meteor parameters would be required in order to perform a statistical analysis over large amounts of data accurately.

Fig. 1
figure 1

Basic system setup for meteors observation (http://www.imo.net/radio/practical/setups)

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The purpose of this paper is to present a trial to extend the usage of the most basic meteor radar system setup to observe the mesospheric ozone concentration variations. The methodology and the tools used are explained in addition to statistical results during 2 distinct meteor showers; the Perseids and the Geminids. The detailed chemical explanation of the meteor ions reactions with the mesospheric ozone is beyond the scope of this paper.

2 Observation method

The Kochi University of Technology (KUT) meteor observation system utilizes the forward scattering of the continuous 50 W, 53.75 MHz radio signal transmitted from the Sabae station at Fukui National College of Technology (FNCT) in Japan at a distance of 340 km from KUT. The operation of the KUT meteor observation system is detailed in Madkour et al. (2016). The KUT system constitutes multiple interferometric receivers setup, only one receiver was used for the duration distribution analysis and a second receiver was used for duration accuracy check. The interferometric setup was used to estimate height trends as a preliminary step towards a complete vertical ozone concentration measurements.

2.1 Duration measurement

The developed software Meteor Echo Counter (MEC) uses image processing algorithm to automate counting of meteor echoes and their durations (Noguchi and Yamamoto 2008). The input to the MEC is the HROFFT (Ham-band Radio meteor Observation Fast Fourier Transform) spectrum images generated every 10 minutes. The output of MEC is the same input HROFFT images during the period selected for analysis but with duration measurements marked with superimposed hatches above each overdense meteor echo detected (e.g. Fig. 2), in addition to a daily text file summarizing all meteor echo records. The text files are then combined and filtered for the required meteor echo duration conditions. For the KUT forward scattering system, the persistent observation of the signal power profiles showed that the overdense type meteor echoes are usually longer than 1.5 ∼ 2 seconds. Therefore, for the scope of the chemistry-limited analysis, the records were filtered for only echoes with durations more than 2 seconds.

Fig. 2
figure 2

Output images of MEC showing the duration above the overdense meteor echoes detected

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The accuracy of the duration measurements within the KUT system is checked by comparing two receivers measurements by using the HROFFT in the 2-channels mode. For the Perseids meteor shower with many long duration echoes the average accuracy was determined to be within \({\pm}2\sim 3\) seconds range by comparing 2 channels, while for the Geminids meteor shower it was within a range of ±1 second.

As the duration of meteor echoes is dependent on many factors such as the transmitter-receiver distance and the transmitting power level, other systems may have different duration thresholds for overdense meteor echoes. Moreover, other systems may have different duration measurements for the same meteor trails observed. The performed duration distribution analysis is then not targeting to compare with other systems rather than to compare two distinct meteor shower events using the same tools and derive the relative differences.

2.2 Ozone concentration observation

With a daily detection average of around 50 overdense meteor echoes (during meteor showers for the KUT system), it is possible to plot the cumulative duration distribution against the corresponding overdense meteor echo counts and obtain the knee-shaped curve. The chemical process and radio derivations of this method are detailed in the previous works listed in the introduction section and here we simplify the relevant conclusions used in the analysis. The simplified reaction of the secondary ozone layer with the meteor ionized trails occurs in two consecutive steps. Firstly, the meteor ions are oxidized by the ozone:

$$M^{+} + O_{3} \rightarrow MO^{+} + O_{2}, $$

where \(M^{+}\) is the meteor ions. The oxidized ions are then combined with the meteor trails free electrons,

$$MO^{+} + e^{-} \rightarrow M+O. $$

The gradual loss of the meteor trail plasma occurs with time constant \(T= ( \alpha [O_{3} ])^{-1}\). Where \(\alpha \) is the oxidization rate of free electrons with ozone (\(\approx 2\times 10^{-16}\mbox{ m}^{3}\,\mbox{s}^{-1}\)).

The ozone concentration at the knee point “\(T_{c}\)” in the duration distribution curve can then be obtained by the relation:

$$ [O_{3} ]= ( \alpha T_{c} )^{-1}. $$
(1)

This relation should generate one ozone concentration value for each duration distribution curve. Therefore, a large number of overdense meteor echoes is required at different height levels to observe the secondary ozone concentration profile vertically. Hence, it becomes necessary to determine the heights of the meteor trails corresponding to the knee position. Despite that it is not possible to determine the meteor height using the basic receiver setup configuration applied here, the relative comparison of the knee position of meteor groups arriving at different times such as day and night or during different meteor showers could be indicative about the mesospheric ozone concentration level.

2.3 Height estimation

The geometry of the forward scattering observation systems introduces many complexities to calculate the meteor trail heights. It is not possible to estimate the meteor trail heights from the basic setup configuration only. However, the agreed suggestion of the presence of a meteor hot spot near the midpoint path between the transmitter and receiver (e.g. Forsyth and Vogan 1955; McKinley 1961; Carbognani et al. 2001) could allow height estimation through multiple receivers interferometric setup for direction finding. In Fig. 3, the point ‘F’ represents the originating signal source from FNCT station and the point ‘K’ represents the receiver at KUT. The projection from the reflecting point on the meteor trail ‘M’ to the ground plane ‘P’ represents the required height ‘h’. The elevation angle ‘\(\beta \)’ and the azimuthal angle ‘\(\alpha \)’ are calculated by interferometric analysis (Madkour et al. 2016). The meteor echoes with ‘\(\alpha \)’ more than ±90° (behind the KUT radar) were not considered in this analysis. The remaining parameter required to calculate the height will then be the receiver range KM or the projected distance along the transmission path ‘L’. Neglecting the Earth curvature, It can be possible to estimate the meteor trail heights from the equation:

$$ h=L\cdot \tan \beta \mbox{ sec}\, \alpha. $$
(2)
Fig. 3
figure 3

Meteor trail height estimation by direction finding

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3 Results and discussion

The two meteor showers Perseids and Geminids were selected for this analysis firstly because the availability of data records in the KUT system since 2005 during the both shower periods can be sufficient for statistical analysis. Secondly, because these two showers represent two streams of distinct characteristics such as occurrence time, velocity and height. For the Perseids meteor shower the selected period for analysis was from August 8th to August 15th, while for the Geminids meteor shower the selected period was from December 10th to 17th. All the overdense meteor echoes during the selected periods were included in the analysis, given that the sporadic overdense meteor echoes normally have very low rates in the KUT system (less than 2 % of rates during showers peak time) and can be neglected. Overall, more than 12,000 HROFFT images were analyzed by MEC software during the selected periods. After filtering the results by duration to only overdense echoes, a total of 2779 overdense meteor echoes for Perseids and 2431 for Geminids were resulted. Although MEC software includes different level settings for noise elimination, meteor echoes longer than the knee durations were manually verified again on the original HROFFT image spectra. This was specifically necessary for the cases of Perseids long duration echoes of more than 40 seconds which is the typical duration range of electromagnetic noise-source interference sometimes seen in the KUT system.

The cumulative duration distribution in logarithmic scale for Perseids and Geminids is shown in Figs. 4 and 5, respectively. The Perseids are counted in duration bins of 5 seconds while the Geminids are counted in duration bins of 2 seconds. The knee position for the Perseids was determined in the duration range of \(45\sim 50\) seconds and for the Geminids in the range of \(12\sim 13\) seconds. The discrepancy in the knee position agrees with the impact of the aforementioned distinct characteristics of the two showers. The velocity and height range of the Geminids was agreed by both optical and radio observations to have lower levels than that of the Perseids (e.g. Jacchia et al. 1967; Baggaley 1979). Therefore, meteor ionized trails of the Geminids could be more affected by the secondary ozone layer maxima below 95 km. Also, the depletion of the ionized trails of the slower Geminids meteors in the atmosphere is higher than that of the faster Perseids meteors and therefore the loss of the electrons is higher, thus moving the knee position of the Geminids to an earlier stage.

Fig. 4
figure 4

The duration distribution of the Perseids overdense meteor echoes from 2005 to 2015

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Fig. 5
figure 5

The duration distribution of the Geminids overdense meteor echoes from 2005 to 2015

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In order to estimate the heights of the meteor trails corresponding to the knee, we attempted to use the method in Sect. 2.3 to analyze the elevation and azimuth angles of a sample of meteor echoes at the knee during the peak period of the two showers. The height trend as a function of the unknown transmission path distance ‘L’ from KUT is shown in Fig. 6. This height trend is although logic from the perspective of lower height levels of Geminids than that of the Perseids, it contradicts the existence of a hot spot in the forward scattering systems around the mid point of the transmission path. Following this trend, at the midpoint distance of 170 km the Perseids heights would measure ∼200 km and the Geminids ∼170 km. This is impractical not only because it is uncommon height for meteors but also due to the echo ceiling effect for the frequency used of 53.75 MHz (Ceplecha et al. 1998). The uncertain height trend has been included in this analysis to point out the possibility of reaching a vertical ozone concentration measurement method by estimating the meteor positions. The positioning can be achievable in the basic radar setups by the addition of two remote receiving stations.

Fig. 6
figure 6

Heights of Perseids and Geminids meteor echo samples at the knee in vertical axis versus the propagation path distance ‘L’ in the horizontal axis. The horizontal dashed lines represent the average meteor height region (80–110 km). The vertical dashed lines represent the used range in the height estimation example

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To illustrate an example showing the calculation method of the vertical ozone concentration, a range for the distance ‘L’ from 75 km to 80 km was assumed (Fig. 6). By using Eq. (1) for an average ‘\(T_{c}\)’ of 47.5 s for the Perseids and 12.5 s for the Geminids to calculate the ozone concentration, the results in Fig. 7 were obtained. The obtained values although do not coincide with the satellite measured values but the difference between the Geminids and the Perseids agrees with the decreasing trend. This preliminary figure is only for the sake of showing a practical example and the complete figure could be reached with more meteor showers analysis associated with the specific heights of each.

Fig. 7
figure 7

Vertical ozone concentration profile (in cm−3) calculated using the knee curves of Perseids (in blue) and Geminids (in green) using (1) compared to the SABER satellite measurements averaged over all seasons from January 2002–July 2012 (after Smith et al. 2013). The height ranges corresponds to the selected range of ‘L’ from 75 km to 80 km

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The observation of the mesospheric ozone concentration variations could allow indirect observation of the 11-years solar cycle activity. The annual data records however were not complete for all years and for some years were totally missing. To observe the 11-years solar cycle activity, two years were selected that has full uninterrupted data records with 5 or 6 years separation. The knee positions of the Geminids 2006 and Geminids 2011 representing low and high sunspot number progression levels (Fig. 8) are compared in Fig. 9. The knee position for Geminids 2006 is observed at duration range of \(8\sim 9\) seconds which is less than the average Geminids knee durations. This although agrees with the impact of lower solar activity and the increase in the ozone concentration level in 2006, there can be other factors impacting the radio detection rates for the 2 single years such as the varying flux nature of the Geminids shower itself (Neslusan 2015). The continuous annual analysis of the Geminids duration distribution for the whole 11-years solar cycle becomes essential to confirm the solar cycle activity observation by this method.

Fig. 8
figure 8

Solar sunspot progression of the current solar cycle activity since 2000 (NOAA/SWPC). Marks with red show the points of comparison

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Fig. 9
figure 9

The duration distributions of the Geminids 2006 (minimum solar activity) and Geminids 2011 (maximum solar activity)

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4 Conclusion

A trial to use a low cost meteor radar basic setup in observing the mesospheric ozone concentration and the solar cycle activity was performed. Although exploratory, this analysis might provide some insight into the role of the secondary ozone layer in the removal of the meteor ionized trails. The obtained knee positions are generally in agreement with the expected mesospheric ozone conditions in the selected cases. Up to this system setup level, the knee duration can be the observation unit for ozone concentration variations. The method can be enhanced further to measure the vertical ozone concentration profile by introducing two remote receivers to determine the meteor trail positions and hence estimate meteor heights. Also, the comparison of 2 single years at the solar cycle halfway can be considered as a partial solar activity observation and it can be ideally confirmed by tracking the annual duration distribution for a whole 11-years solar cycle.

The used method should be applicable in observing the relative duration differences within the same meteor radar system. To standardize the method and compare results of different systems, it might be mandatory to reach a common agreement on the minimum number of overdense meteor echoes required to recognize the knee curve. It is also important to consider the impact of using different frequency, power, transmitter-receiver distance and method of duration measurement on the resulted durations. Similar meteor radar setups as well as amateur observers are encouraged to perform similar analysis and share the duration distribution curves resulted from different meteor shower events. Observers using the HROFFT software could benefit from the developed MEC software that was made free for use in world wide.