A performance appraisal of the global survey and the fully automated methods of Forbush event identification and timing using small-amplitude Forbush decreases

ABSTRACT

Forbush decrease (FD), commonly defined as an abrupt reduction in the time-intensity flux of cosmic rays (CRs), is one of the long-investigated astrophysical phenomena. Though the subject has received considerable attention, the peculiarities of each event and different varieties of FDs still present them as the most spectacular and intractable CR intensity variations. Their unpredictable forms and diversities make accurate identification and precise timing of the events difficult. Event selection has remained predominantly manual up to the present era of high-speed and sophisticated computer software. Several catalogues appear in the literature. But no two event lists are comparable. The significant disparities among FD catalogues have led to many conflicting and controversial submissions. A comprehensive validation study of FD lists and their methods of selection are some of the important steps to settle or minimize the age-long disputes in the strongly disputed CR influence on space weather. Such a study will guarantee result reproducibility. Two comprehensive FD catalogues, prepared by the global survey method (GSM) and the recently developed fully automated method (FAM), are well suited for such a test. Our results show that the FAM is more efficient and accurate than the GSM. The presence of many other CR phenomena that constitute noise when timing/calculating the magnitude of small FDs requires both numerical filtering and harmonic analysis to handle. FAM is equipped with various subroutines that perform such analytical transformations and other rigorous analyses.

1 INTRODUCTION

Alhassan, Okike & Chukwude (2022, Al2022, hereafter) opined that accurate detection and precise timing of astrophysical transients like X-ray photons, coronal mass ejection (CME), |$\gamma$|-burst, ground-level enhancements (GLEs), big and small Forbush decreases (FDs) are among the unsolved problems in astrophysics. This is particularly applicable to weak cosmic ray (CR) signals such as small amplitude FDs (Menteso et al. 2023) and small (‘hidden’) or sub-GLEs (Miroshnichenko, Vashenyk & Perez-Peraze 2013). Al2022 blamed the observed stagnant progress in signal detection on the predominant but inefficient manual event detection and timing techniques (see also Okike 2019a, b, 2020a, b; Okike & Nwuzor 2020; Okike & Umahi 2019a, b). For example, the investigation of CMEs started as early as the 1970s (e.g. Yashiro, Michalek & Gopalswamy 2008; Gopalswamy 2016). However, detection of the event has only been recently automated (Pant et al. 2016; Lamy et al. 2019; Williams & Morgan 2022). Some reported significant progress in both manual and automatic detection of CMEs has drawn the attention of researchers to compare manual and automated CME lists (see Yashiro et al. 2008; Hess & Colaninno 2017; Lamy et al. 2019). While CR astrophysicists are still hedged in by the cumbersome and age-old manual/semi-automated selection techniques, Hess & Colaninno (2017) report that others have created numerous automatic detection algorithms for the identification of CMEs. Some of the automated catalogues like Solar Eruption Event Detection System (SEEDS), Computer Aided CME Tracking (CACTus), and Coronal Image Processing (CORIMP) allow for consistency/validation tests. In the light of the indicated progress in CME research, a serious question mark hangs on the poor technological advancement recorded by CRs/FDs physicists.

Some authors (Pittocks 1978; Marcz 1997; Laken et al. 2012; Okike 2021) speculate that unvalidated FD lists might be the reasons for the conflicting and misleading conclusions in some past articles investigating CR–climate connection. Among all the researchers that attempt to create a large list of FDs (see Lockwood 1990; Tinsley & Deen 1991; Cane, Richardson & von Rosenvinge 1996, for example), the effort of the IZMIRAN¹ remains the most outstanding. Their FD catalogue is the most comprehensive. The catalogue is presented at their website http://spaceweather.izmiran.ru/eng/dbs.html, the FEID.² The FD catalogue on the website is selected using a special technique referred to as the global survey method (GSM). Belov (2008) and the references within report that the GSM was employed by the group over 60 yr ago (see also Belov et al. 2018a). FDs and CR anisotropy calculated using the GSM are available at the FEID. The GSM is an analysis technique that attempts to unite/assimilate and analyse CR data from different neutron monitors (NMs) at different locations at the Earth’s surface (Krymsky et al. 1969; Belov et al. 2018a).

Though there are many publications (see http://spaceweather.izmiran.ru/eng/papers.html) utilizing data from the FEID, a review of the available literature shows that a comprehensive comparison of the IZMIRAN FD list with those developed by external researchers is yet open. As a result of the absence of such validation studies and by extension, lack of result reproducibility (Atmanspacher et al. 2014; Plesser 2018), publications based on the data in the FEID may attract the attention of some critical voices (e.g Pittocks 1978), especially because of the inherent bias in other existing subjective FD catalogues.

Some of the most interesting events in the IZMIRAN FD catalogue are the small amplitude FDs (⁠|$\lt 3$| per cent) (Menteso et al. 2023). These events belong to the class of weak and elusive signals in astrophysics. Identification as well as timing of small FDs is a daunting task. This could explain why there is a paucity of catalogues of small FDs in the literature. Except for the lists of small FDs created by Menteso et al. (2023) from four NMs [(Apatity (APTY), Moscow (MOSC), Newark (NWRK), and Oulu (OULU)] for Solar Cycle 23 and the IZMIRAN FD lists, we are not aware of other catalogues containing a significant number of small FDs. For example, out of the 250 FDs in the list of Lockwood (1990), only two events have a magnitude of |$\lt 3$| per cent. Out of the 65 events selected by Pudovkin & Veretenenko (1995), 14 have their magnitude in the range of |$\lt 3$| per cent whereas, there are only 2 small FDs in the list of Kane (2010). Following a thorough review of the literature, we can infer that almost 99 per cent of the existing FD event lists contain only high-magnitude FDs (⁠|$\gt $|3 per cent) (see also Cane, Richardson & von Rosenvinge 1993, 1996; Oh, Yi & Kim 2008; Svensmark, Bondo & Svensmark 2009; Calogovic et al. 2010; Svensmark, Enghoff & Svensmark 2012; Kedula 2015; Svensmark et al. 2016).

After many years of FD-based space weather research, progress in the field requires validation studies of the existing FD catalogues. Such investigations are important for both the big and small FD event lists. They will, for example, increase the public acceptance of the widely acclaimed but strongly debated influence of CRs on terrestrial weather. While high-magnitude FDs have received some attention in this regard (Cane et al. 1996; Okike 2019b, 2021; Okike et al. 2021a, 2021b), a detailed comparison of catalogues of small amplitude FDs have yet to be published. The significant number of small FDs detectable by the GSM and the recently developed FAM of Forbush event selection provides a good testbed for a comparative investigation of the detection accuracy and efficiency of the GSM and the FAM. Thus, a comprehensive comparison of small FDs detected using the GSM and the FAM is the focus of this work. It is important to define the scope of this article at this stage. A detailed description of the two techniques will not be given here. Only a brief description is presented (see Section 4). There are several publications dedicated to the detailed explanations of the two methods and their functionalities (e.g. Belov et al. 2018a, b; Okike & Nwuzor 2020; Okike 2021; Okike et al. 2021b, Al2022). Details of the technical advancements required by the two algorithms will not be discussed. It suffices to mention that both codes are not able to simultaneously time the onset and time of FD minimum. While Oh et al. (2008) decide event simultaneity by the overlap of FD event main phase regardless of the locations of the NMs, Okike & Collier (2011) considers an event as globally simultaneous if the complete FD profiles overlap irrespective of the location of the NMs. Neither the GSM nor FAM event timing follows such overlap.

The remaining sections of this article are structured as follows: Section 2 delves into the subject of small FDs, Section 3 tells about the motivation, Section 4 is on the source of data and the method of analysis, Section 5 presents the results and discussion, Sections 6 and 7, respectively, summarize and conclude the findings of the work.

2 SMALL FDS

While the literature in the field is dominated by high-amplitude FDs or a mixture of low- and high-amplitude events, publications that conduct a comprehensive investigation of small FDs are rare. This research gap immediately suggests that many aspects and properties of small FDs, including their definition, have yet to receive adequate attention. While large FDs (magnitude |$\gt 3$| per cent) may generally be defined as abrupt decreases in CR intensity with slow recovery lasting several days (e.g. Cane et al. 1993; Laken et al. 2012; Sarbdeep 2017), small FDs (⁠|$\lt 3$| per cent) are of slower development (Kryakunova et al. 2015). Thus, the sudden/sharp reduction that characterizes the onset of the big events may not apply to the small FDs. The symmetry (V- or U-shapes) frequently observed in the time profile of large FDs (Badruddin & Singh 2006) may be lacking in small events. The time-intensity of small FDs may rather appear asymmetric, looking like wavy depressions. The theoretical definition of small FDs based on the event amplitude started appearing in the literature in the 1970s (see Kontor, Lyubimov & Pereslegina 1977). Events of the amplitude of |$\approx$| 1 per cent are taken as small FDs. Nevertheless, the threshold chosen to define small FDs depends on the data resolution. Smaller baselines [CR (per cent) |$\le$| 1] are used for daily averaged (e.g. Lockwood 1990; Tinsley & Deen 1991; Pudovkin & Veretenenko 1995; Dumbovic et al. 2011, 2012; Okike & Umahi 2019b) whereas larger baseline [CR (per cent) |$\ge$| 3] is employed for hourly averaged (Cane et al. 1993, 1996; Oh et al. 2008; Oh & Yi 2009; Lee et al. 2015; Okike 2021) data. However, the magnitude of small FDs on the IZMIRAN website is as small as 0.3–0.5 per cent. Since the GSM employs hourly averaged data, this implies that they use a very small threshold [CR (per cent) |$\le$| 1] to identify small FDs. In view of the large detection baselines generally employed by other researchers analysing hourly data, an event magnitude of |$\lt 1$| per cent in the FEID should be, admittedly, taken as a groundbreaking achievement. But before we draw a firm conclusion on this, there is a need to validate the presented catalogues of small FDs.

The subject of small FDs is quite interesting. They are among the weakest signals and may be one of the most spectacular and intractable time-intensity changes in CR flux. While it is quite difficult to deal with high-amplitude FDs, timing the onset or time of FD minimum of small events is much more problematic. The same applies to the calculation of their amplitudes. If very large FDs at some NMs could appear as ordinary CR enhancement at some other locations on Earth (Belov 2008; Okike & Collier 2011; Dorman et al. 2018), then the variability of weak FDs around the Earth globe raises issues that remain on the cutting edge of CR intensity variation research. This is because the count rate dependence of a standard NM on altitude, cutoff rigidity, detector’s size, local meteorological parameters, like atmospheric pressure and thickness/mass of air column above the detector, effect of snow or wind, features of operations, CR anisotropy, signal superposition, and several other factors (Stoker, Raubenheimer & Walt 1972; Okike & Nwuzor 2020) do exert more pronounced effects on weak FD signals (e.g. Barouch & Bdoiaga 1975). These unpredictable factors would greatly complicate the magnitude estimation and timing of small FDs.

• Empirical estimation of FD event magnitude

  Though catalogues of high-magnitude FDs dominate the literature, a review of the existing works shows that approaches adopted by CR investigators to calculate their magnitudes have not been given detailed attention. The lack of adequate attention to event timing and magnitude estimation is even much more applicable in the case of small FDs. It is interesting to observe that despite the number of years Forbush events have been under study, there is no standard formulae for calculating the magnitude of FD events. As a result, almost every researcher develops their methodology as Oh et al. (2008) argue that there is no exact criterion for an FD event. Doubtlessly, the different versions of equations developed and employed by some of the researchers will add to the bias and contradictory results in many FD-based solar-terrestrial publications. As is demonstrated below, apart from the subjective equations used to calculate FD magnitude, it is also important to note that up to date, there are no standard formulae for timing Forbush events. For the first time, some of the equations employed in the field will be closely examined. This is of great relevance as it will further highlight the difficulties of dealing with small as well as big FDs. It will equally call the attention of the reading public to some of the reasons for the disputes among researchers in the field. It will also point to the need to validate existing FD lists. Most importantly, it will highlight the difficulties of selecting and timing small FDs. Two of the common equations employed by researchers that select FDs by the manual or semi-automated methods are presented below. These equations are used for the large and the rarely investigated small FDs. For clear illustration, however, the difficulties/demerits of timing and calculating event magnitudes with the available FD formulae will be demonstrated using large FDs.

where N|$_{R}$| is the reference level before the FD while N (t|$_{0})$| is the daily averaged minimum value during the FD (from Svensmark et al. 2016).

where |${\rm CR}_{q}$| represents the mean value of the CR data for any chosen period (from Tezari et al. 2016).

3 MOTIVATION

If manual/semi-automated detection of large events is fraught with numerous challenges as highlighted in Section 2, there is no doubt that we expect the worst scenario in the case of small FDs. Al2022 documents that the identification of small/weak FDs is one of the major challenges of manual/semi-automated techniques. It is interesting to note that accurate detection and timing of weak events was one of the major reasons for the implementation of the Bayesian blocks algorithm (Scargle 1998; Scargle et al. 2013). However, Al2022 explained that the algorithm may not be suitable for weak FD event selection. Thus, efforts to develop codes that can precisely time and calculate the magnitude of small FDs are ongoing (see Geppener & Mandrilava 2020, for example). The recent work of Poluianov et al. (2024) and others (e.g. Miroshnichenko 2018) which have moved the investigation of GLE from large to hidden/sub-GLEs are pointers to the fact that investigation of very small CR time-intensity increases [GLEs or other abnormal CR enhancement; e.g. Dorman et al. 2018)] or reductions (e.g. small/elusive FDs) is a promising field.

Further, Al2022 suggests that the GSM and the FAM are capable of detecting small amplitude FDs. The detection baseline of both codes was mentioned. For hourly CR count rates, the detection baseline of the GSM is 0.3 per cent whereas the FAM employed in Al2022 has a detection baseline of |$\lt 0.01$| per cent for both hourly and daily averaged data. Each of these degrees of accuracy is a great achievement in astrophysics. If confirmed with external FD event lists, they will certainly attract the attention of many researchers in the field. But before we conclude, there is a need to compare FD event catalogues selected with the two algorithms. Given the difficulties trailing manual/semi-automated identification of FDs as demonstrated in the previous section, coupled with the hypothetical report – that it is ‘impossible’ to detect small FDs from individual CR data (e.g. Belov 2008; Belov et al. 2018a), there is a need to validate the reported detection baseline of the two methods. The elusive small FDs are well suited to conduct such a test.

Moreover, the idea of combining CR data from NM located at different places on Earth has received some substantial criticism. Due to the contaminating influence of CR anisotropy, the time profile for the same FD may appear in different forms at different locations. Jordan et al. (2011) referred to FD data from different NMs as disparate time-series events, criticizing the idea of combining such signals. In this same vein, Sandstrom (1968) argued that the resulting mean for such combined signals may only be meaningfully taken as worldwide CR-time intensity variations if the event is worldwide in extent (observed by all NMs irrespective of their locations). This requirement implies that any changes in phases and event amplitudes are simultaneous and proportional at all NM stations. Since such complete signal coincidence between two or more stations is uncommon, a comparison of the GSM FD catalogue with those identified from separate NMs is required to clarify these speculations.

4 DATA AND ANALYSES

The daily and hourly CR data used in this work are available at http://cr0.izmiran.rssi.ru/common/links.htm. FD data selected using the GSM are downloaded from http://spaceweather.izmiran.

4.1 Noise in CR data

Generally, noise refers to an unwanted perturbation in the signal of interest (Barton & Hennelly 2019). Noise and attendant contamination is a commonplace in astronomy and astrophysics. Noise may appear as sharp spikes or other forms that distort spectra and may have a significant influence on post-processing as well as the final analysis results. Removal/subtraction of such artefacts/unwanted signals while introducing no other change to the signal/frequency of interest is usually a serious challenge and often requires some sophisticated programs (see Okike & Umahi 2019b, for a detailed discussion of the sinusoidal fidelity of the implemented Fourier harmonic software). The presence of noise in CR data may complicate the detection of FDs, especially small events.

But what exactly constitutes noise/nuisance in NM data? Why is the detailed analysis of the noise level not a commonplace analysis among CR scientists investigating FDs and other CR phenomena (Cane et al. 1993, 1996; Belov 2008; Oh et al. 2008; Dumbovic et al. 2011, 2012, 2024; Lee, Oh & Yi 2013; Belov et al. 2018a, b; Ugwu et al. 2024)? The first question is easy to address. Raw time-series CR data are composed of signals of different frequencies including periodic and aperiodic signals (see Section 2). But whether one or more of these signals are viewed as noise depends on the target of the researcher. For researchers investigating CR diurnal vectors using the traditional Fourier series and power spectral analyses (Krymsky et al. 1969; Pomerantz & Duggal 1971; Bemalkhedkar, Subramania & Razdan 1973; Sari et al. 1978; Mufti et al. 2011), FDs and GLEs are viewed as noise as they may lead to erroneous results. Similarly, investigators analysing FDs have serious problems disentangling the contributions from the CR diurnal anisotropies (see Okike 2020a, and the references therein). Not only that the amplitudes of CR diurnal anisotropies are comparable to the magnitude of FDs in some cases (Belov 2008), but diurnal anisotropies have serious obscuration/contamination effects, especially on small FDs (see also Richardson & Cane 2011). The time-intensity profile of raw CR data may also differ significantly from those of the harmonically filtered data (Okike 2020a).

Detection of small FDs in the presence of noise: One of the pioneer investigators (e.g. Barouch & Bdoiaga 1975) suggested that detection of small FDs requires two methods (1) averaging of CR time-series data over several stations, and (2) numerical filtering over a single NM. Some researchers have pursued the first method (e.g. Dumbovic et al. 2011; Belov et al. 2018a; GSM) using CR data assimilated from an array of NMs while others attempted the second (Laken & Calogovic 2013; FAM) using data from a single NM. These two methods are expected to remove/minimize the contributions from the diurnal anisotropies in raw CR data. However, each of these methods is fraught with pitfalls. The GSM method, for example, adopts the case study approach of combining raw CR data from different stations. Here, the phase shift and signal distortions arising from daily variations (viewed as noise when dealing with FDs) at each of the combined stations would have a pronounced negative impact on the timing, magnitude as well as number of FDs selected. Belov (2008) also outline other methods used to select FDs (e.g. relating CR intensity profile to interplanetary conditions).

A technique that efficiently handles the characteristic signal superposition in CR data was proposed in the 1930s. Bartels (1935) empirically showed that signals which exhibit periodicities, cycles, and recurrence tendencies should be subjected to harmonic analysis and statistical studies. The various signal variations (e.g. diurnal and 11-yr oscillations) show that CR data fit the bill. Raw CR signal should thus, be separated into different frequencies – the slowly/smoothed and the fast varying components – before selection of small/big FDs. Such complicated analytical transformation has been accomplished by some researchers (e.g. Okike & Umahi 2019b; Geppener & Mandrilava 2020; Starodubtsev et al. 2024, FAM). Whereas the fast-changing part contains the rapid reductions (FDs) and increases (GLEs), the slowly varying frequencies account for the diurnal anisotropies. FDs investigated in this work are selected from the high-frequency component of CR data.

Recently, Okike & Menteso (2024) also demonstrated that the 11-yr periodic oscillations observed in raw CR data could constitute a serious nuisance/noise in the analysis of FDs. Figs 2 and 3 of the article clearly show that the number and magnitude of FDs vary significantly between the raw and post-prepared CR data. This method of disentangling the Sun’s influence on CR data (Strauss & Engelbrecht 2023) was achieved using a high-pass filter (Harrison & Ambaum 2011). Such method of moving average is also employed in this work.

4.2 Manual selection of small FDs from daily and hourly CR averages

Identification of a small FD, either from daily or hourly CR data, is quite a challenging task. Figs 2 and 3 are presented to illustrate the similarities and differences between daily or hourly averages when investigators that identify FD manually employed them. The events presented were selected with the GSM. According to the FEID, five small events happened between 2003 September 13 and 21. The magnitude of the events for the 13th, 15th, 15th, 16th, and 21st of September are, respectively, 0.3, 0.5, 0.6, 1.5, and 0.7 per cent. Two events (0.5 and 0.6 per cent at 7:00 and 20:00, respectively) are detected on the 15th. The onsets of the events are marked with vertical lines on the diagrams. While data from many (10) stations are displayed in Fig.2 to illustrate intensity variations at different points on Earth and the implications of combining data from different NMs, events from only two stations are presented in Fig.3. Plotting more than two stations makes the diagram look blurred, preventing us from observing the variability patterns of interest at the NMs.

A careful inspection of Fig.2 shows that only two stations – APTY and MOSC – observed FD on 2003 September 13 as reported at the FEID. The rest of the stations rather observed increases on this date. The FD of the 15th was detected by seven of the stations. OULU, MOSC, and CLMX seem not to observe the event. The zero line (black dotted line) shows that MOSC did not see any FD between the 13th to 21|$^{\rm st}$| of September. The event of 2003 September 16 was the largest among these events but was only clearly observed at two stations, CLMX and PTFM.

The picture we have with the daily data seems to reflect the patterns observed in Fig.3. The intensity variations at these two stations look opposite at many points. It is obvious that combining the two signals will significantly affect the amplitude of the resultant signals. This implies that the amplitude of FDs calculated from the combined data may be seriously biased due to smoothing. The five vertical lines map the onsets of these events as reported at the FEID. But even with the vertical lines, it is still very difficult to visually detect event onsets here. It is easy to infer from the observed pits/depressions below the dotted horizontal line (zero line) in Fig.3 that many FDs that happened within the period may not have been detected by the GSM. It should be noted (see Section 4) that the GSM averages hourly CR data over many CR stations. As also illustrated in Fig.1, Fig.3 shows that the event onset is difficult to determine with precision. It is also obvious here that the FD minimum (marked unique T|$_{\rm min}$| in Fig.1) is also well defined in hourly data.

It is also important to note faction of FDs measured with CR hourly averages are also detectable with daily means. Out of the four small events (indicated by the first four vertical lines from the left of Fig.3), it is easy to see from Fig.2 that only one of the two events observed on the same day using hourly data (two events of 15th) is missing (due to averaging) in the daily data. Using the sophisticated method of Fourier harmonic analysis, Okike (2020a) presents the FDs selected from ten CR stations within this time. Table 1 of the paper shows that a series of FDs happened at different stations starting from 2003 September 4 to 30. Six of the FDs fall within 13th to 21|$^{\rm st}$| of September. Out of the 15 events that happened within the period, CLMX observed 7 while INVK detected only 4. The remaining 8 stations also detected different numbers of FDs within the period.

4.3 Automated selection of small FDs

• Daily CR averages

  Some significant differences/similarities between manual and automated methods will be highlighted here. Fig.4 illustrates event automatic selection from raw data (black line/empty small cycles) and Fourier transformed CR (blue line/filled cycles) data. For easy comparison with the FDs detected with the GSM, colour markers are used for the FDs selected from the Fourier transformed signal (FTS) in Fig.4. It should be noted, as indicated in Section 4, that the FTS and the red signal (diurnal wave) in Fig.4 are, respectively, the high and slowly varying components of the decomposed CR raw data. Note also that the original raw CR data (the black signal) are also plotted on the same figure for comparative reasons. (1) Blue-filled colour cycles mark FDs at the APTY station but not in the FEID (seven in number), (2) green-filled cycles stand for FDs at both APTY and FEID (these FDs are |$\gt 3$| per cent at the FEID, 10 in number), (3) red filled cycles stand for FDs at both APTY and the FEID but for FDs |$\lt 3$| per cent at the FEID (Note that the absolute values of FDs are presented in the FEID. By definition, FDs are negative values. Throughout this work, wherever FD magnitude measured by GSM or FAM are expressed as positive values for convenience). The black dotted line is drawn at −3 per cent of the graph to demarcate between big and small FDs. Most of the large FDs (green) at APTY are also big at FEID. But we can still notice two green circles above the dotted black line, implying that they are small FDs at APTY. The second green cycle from the left is a very small FD. The magnitudes and dates of these two small events at APTY are, respectively, |$-1.57$| per cent (2003 August 18) and |$-0.57$| per cent (2003 October 25). Their magnitudes and time of occurrence are recorded as 3.4 per cent (2003 August 17 at 14 h) and 5.6 per cent (2003 October 25 at 15 h) at the FEID. These two small events reveal the wide differences that exist between the event magnitudes of the two catalogues.

  The observed big differences between events calculated by the GSM and FAM were first noticed by Okike et al. (2021a). Using FDs selected from CLMX observatory through FAM, table 1 of the paper publishes event time and magnitude for events selected between 2003 and 2005. It should be noted that GSM timing follows the event onset whereas FAM tracks the time of minimum depression of an event. The table shows that the magnitude of some of the events at CLMX is twice their magnitudes at FEID. For example, the event of 2004 November 10 is −16.5 per cent at CLMX but it was calculated as −8.2 per cent using the GSM. The big event of 1/19/2005 was calculated as −24.2 per cent and −11.1 per cent, respectively, by FAM and GSM. These observed large differences in event magnitude of the two lists seem to be worse for small events. Event of 2004 December 13 (for FAM) and 2004 December 12 (for GSM) was reported as −5.5 per cent and −1.5 per cent, respectively. The magnitude of the small event (2003 February 17 by GSM, 2003 February 18 by FAM) was presented as 2.1 per cent at the FEID and 6.3 per cent at APTY station (automated approach).

  Many other significant differences may be inferred from the table. It is also important to note that only one set of FDs is presented at the FEID. The GSM selects FDs from raw CR data. But we have two catalogues of FDs in Fig.4. One is selected from the raw data whereas the other is from Fourier-transformed CR data. The FD data at the FEID are selected from the raw CR data without separating the contribution from CR anisotropy. Besides the effect of smoothing/leveraging problem (see figs 6 and 7 of Okike 2019b) that is inevitable when uniting/combining data from separate NMs. CR anisotropy is another factor that may play a key role in the differences between the catalogues at the FEID and those selected from Fourier decomposed CR data. This is because the signal from combined CR data may be mostly complicated/contaminated by the combined influence of CR anisotropies from the different locations. Fig.4 shows some significant differences between raw CR data and the Fourier-transformed CR data. These differences are also reflected in the number of FDs selected from both signals. Another major difference between the GSM and the FAM is that the GSM follows the case event study approach while the FAM adopts a statistical technique.

• Small sample hourly CR averages

  While it is visually hard to isolate FDs in Fig.3 following the event onset marked by the vertical lines, the point of maximal intensity reduction is clearer and easier to identify. The FD-Location algorithm calculates the magnitudes and the times of occurrence of almost all the depressions in Fig.5. While the GSM can only detect five FDs between 2003 September 11–21, the implemented algorithm selects 31 FDs within the same period. This implies that GSM detects only about 16 per cent of the events detected by the FAM. This is an indication that the current code is of higher efficiency than the GSM. The dotted black line in Fig.5 is the detection threshold CR (per cent) |$\le$| −1. Most of the dips/depressions not detected in Fig.5 are those above the detection baseline. The number of events detected by the code depends on the baseline used (Okike & Umahi 2019b; Okike 2021). If the baseline is reduced to −0.1 per cent or |$-$|0.01 per cent (as applicable in Fig.4), all the depressions, even those very close to the zero line will be isolated. Before or after normalization with any of the equations above (equations 1 and 2), the researcher undertakes the tedious method of searching for the onset of each of the events, isolating each event, noting the size of the depression and visually checking the time of maximal reduction for each. That is the case study approach illustrated in Figs 2 and 3. The automated method does not involve any of these manual tasks as all the needed steps are incorporated into the several subroutines in the program.

  Comparatively, the signals in both Figs 3 and 5 are identical, suggesting that the code implemented in Fig.5 leaves the form of the input signals unaltered. This implies that the phase and amplitudes of the input signals are the same as the output signals. A comparison of Fig.5 with 4 shows that FAM performs similarly with both daily and hourly averaged data. This is another great advantage over the manual/semi-automated methods.

• Large volume of hourly CR averages

For completeness, we present the performance of one of the algorithms with a larger volume of hourly (Fig.6) data containing 8760 data points. The FD detection code used in Fig.5 is applied to raw CR data as input whereas the code employed in Figs6 and 4 is applied to Fourier-transformed data as its input. A comparison of the two diagrams further confirms that our algorithm is capable of handling large volumes of data. There is also some interesting similarities between Figs4 and 6. Except for the large number of small and big FDs selected with the hourly data, almost all the patterns in Fig.4 are repeated in Fig.6. For example, the large event of 31 October are outstanding in the two figures. The shape of the diurnal wave curve also looks similar.

5 RESULTS AND DISCUSSION

5.1 Comparison of GSM and FAM FD catalogues

The performance of the GSM and the FAM were compared using both a daily and hourly basis in Section 4.3 using small sample data. A more comprehensive comparison is presented here.

• CR Daily averages

Fig. 7 is presented to illustrate some beautiful visual relationships between FDs selected by the two programs using data of different resolutions. Though FAM and GSM select events from daily and hourly averages here, the periods of high- and low-solar activities are conspicuously delineated by the two catalogues. While a large number of big and small FDs concentrated within the periods of high solar activities around 1990 and 2003, only a few small FDs happened within the time of minimum solar activities around 1996. The two catalogues clearly define the 11- and 22-yr solar cycle.

Two observable major differences between the two event lists are (1) the number of big and small FDs and (2) the magnitude of the large FDs (visual ranking). GSM, for instance, detected 250 big and 2722 small FDs whereas FAM selected 825 large and 280 small FDs within the same 22 and 23 solar cycle. This implies the GSM detects only about 30 per cent of the large FDs selected by FAM. On the other hand, FAM only selected 10 per cent of the small FDs identified by the GSM within the time. This suggests that the GSM is much more efficient in the identification of small FDs while the FAM performs far better than GSM in the selection of large FDs. Nevertheless, the illustrative cases presented in Figs 4 and 6 suggest that definitive conclusions regarding the efficiency of the two programs may not be reached with data of different resolutions.

Judging by the sizes of the large FDs, it is obvious that the two catalogues rank the detected large FDs differently. The two largest events are marked in the two panels. The event of 2003 October 29 is the largest for the GSM catalogue while the biggest event in the catalogue of FAM is the event of 1991 June 13. The second to the largest FD in the IZMIRAN catalogue is the event of 1989 October 20 whereas the event of 2003 October 31 is the second in the FAM’s catalogue.

• CR Hourly averages

Fig. 8 presents the FDs selected from the hourly averages by the two algorithms. The number of events selected by the FAM from the hourly data is significantly larger than those identified from the daily data. The number of big and small FDs selected by the FAM from hourly data are, respectively, 6738 and 7305. A relatively smaller event threshold [CR (per cent) |$\le$| −3] was used for the hourly data (e.g. Cane et al. 1996; Oh et al. 2008; Okike 2021). Since the GSM only utilizes hourly averages, the number of FDs identified by the GSM is the same in Figs 7 and 8. Compared with the 253 and 2722 FDs selected by GSM, it implies that the GSM detects only 4 per cent and 37 per cent of the big and small that happened within the period.

A few large events are marked. A comparison of such events in both panels gives the reader some perceptions of the closeness/disparity in the event timing and magnitudes estimation by the two methods. The three large events labelled suggest that there may be a good agreement in the event of big FDs. The largest event of 2003 October 29 was detected by GSM at 06:00 (onset) whereas its time of minimum was detected by FAM at 15:00 of the same day. The onset of the event of 1991 October 28 is at 15:00 (GSM). FAM sees the minimum at 20:00 h on the same day. The event onset of 1989 October 20 FD happened at 09:00 while FAM captured the FD minimum of the event at 22:00 h of the same day.

5.2 Further validation of the detection baseline of the GSM and the FAM

The task of validating the IZMIRAN FD catalogues with event lists selected by the FAM or other external investigators seems not to have received adequate attention. Besides the contributions of Okike et al. (2021a), Okike (2020a), and Okike & Alhassan (2021), there is a paucity of such investigations in the literature. One of the potential reasons is the difficulties of mining data from the large volume of data set at the FEID. Compared with all other existing event lists, no other FD lists contain up to 1 per cent of the FD catalogue at the FEID. Such an intimidating large catalogue requires the techniques of Big Data analysis (e.g Garofalo, Botta & Ventre 2017; Okike 2021) to handle. Rather than the conventional manual selection approaches, the selection and matching of events between the IZMIRAN event catalogue and any external event lists call for a specialized program.

Okike et al. (2021a) made the first bold step, albeit with a few event samples (31 events), of comparing (correlation analysis) FDs selected with the GSM with those identified with the automated approach. How does one extend such analysis to the Big FD Data presented in Figs 7 and 8? Inspection of table 1 of Okike et al. (2021a) shows that the FDs at the FEID were carefully matched with those selected by the automatic method. Though the correlation between the two catalogues is ostensibly high (0.82), larger samples are needed to make a firm decision. Additionally, most of the events among the 31 FDs are large FDs. It makes it hard to comment on the relationship between small amplitude events in the lists of Okike et al. (2021a). A large list of big and small FDs would help to confirm the detection baseline and efficiency of the two methods.

The method employed by Okike et al. (2021a) will be employed here to match events selected by GSM and FAM. Some of the event times indicated in Figs 7 and 8 clearly illustrate some of the steps. The large event of 2003 October 29, for example, was detected on the same day but at different times. The same applies to the other two big events marked in the diagram (events of 1991 October 28 and 1989 October 20). These events are the same and can be matched and the correlation between their magnitude tested as demonstrated by Okike et al. (2021a).

In view of the large volumes of data involved, manual association of events in the two lists will be very tedious and time-consuming. We developed a program that separately scans each catalogue, picking out the maximum or minimum intensity reduction (where there is more than one event in a day) in a specific day and the corresponding time (hour) of occurrence. Where only one FD is recorded in a day, the program simply selects the event, cataloguing the date, time, and event magnitude. After selecting/sorting the minimum (small) and the maximum (large) FDs for the GSM and FAM lists, the list of pairs of small or big FDs from both GSM and FAM are passed onto another algorithm – the coincident code. For the selection of small or big FDs from the two catalogues, FD (per cent) |$\le$| 3 or FD (per cent) |$\ge$| 3 with reference to GSM FD is used as a baseline. The list of large (160) and part of the small FDs (total number of small FDs is 1180) identified from the two catalogues are presented in Tables 1 and 2.

Another way of achieving the same aim is by averaging the hourly event over a day. While the recovery phase of FDs may last for some days, the onset and main phase of even the largest FDs happen within a day. This is much more applicable with hourly data as illustrated in Fig.8.

Tables 1 and 2 offer unprecedented opportunities for researchers who wish to test the consistency of the GSM and FAM catalogues. The two lists can be tested with solar-terrestrial parameters, for example. Further, a detailed inspection of the tables shows that the difference between the magnitudes calculated by the two programs is significant. The magnitudes of the three events marked in Fig.8 are presented in Table 1. For GSM and FAM, the magnitudes of the events of 1989 October 20 are, respectively, 23.40 and 24.26 per cent. There is a good agreement between the event magnitude here. Many other events register such close agreements. But there are also many cases where the magnitudes are significantly different. For example, in the event of 1991 October 28, the magnitudes are 17.18 for GSM and 53.27 per cent for FAM.

5.3 Quantitative estimate of signal-to-noise ratio in CR data

Given the difficulties of identifying small amplitude FDs in a given CR data, information on the signal-to-noise ratio (SNR) may further validate the FD events presented in this work. Though there is no global unique benchmark on the value of SNR, a large SNR generally implies that the signal is deemed significant rather than just a random variation. But the term ‘signal-to-noise’ ratio remains ambiguous until an investigator precisely defines what is considered ‘signal’ and ‘noise’ in a given data (e.g. Jeruchim & Wolfe 1989; Elkum & Shoukri 2008). This also suggests that the calculation of SNR varies between experimental data. In some laboratory measurements, for example, SNR is defined as the ratio of the average value to the standard deviation of the signal (i.e. SNR = mean/standard deviation). This type of SNR is just the reciprocal of the coefficient of variation (CV = standard deviation/mean). Nevertheless, the validity of signal variations measured using these statistical tools largely depends on the investigator’s knowledge of the dimensions/nature of the data (Schroder et al. 2012; Pelabon, Hilde & Gamelon 2020).

The complex nature of CR data, as noted in Section 4.1, makes quantitative analysis of the noise ratio a challenging task. The simple formula (SNR = mean/standard deviation or CV = standard deviation/mean) does not hold here. This as a result of the presence of some sporadic signals like FDs, GLEs, and other abnormal CR intensity enhancements, which often lead to irregular and unpredictable CR flux variations. Admittedly, noise analyses in CR data have yet to receive much attention in the field. This is because determining SNR in raw CR data requires signal decomposition, a feat that only a few investigators have achieved. Using quite a noisy CR data (minute resolution), Geppener & Mandrilava (2020) decomposed raw CR data from Inuvik (INVK) and Thule (THUL) station into different separate components, including the ‘signal’ and the diurnal components (‘noise’) [see panels c (signal) and d (noise); e (signal) and f (noise); g (signal) and h (noise) of Fig.4 of the article, for example]. Small amplitude FDs were detected from the signal (high-frequency part, c, e, and g). The authors calculated SNR as the ratio of the high-frequency component to the low-frequency part (diurnal component). Unfortunately, CR signal is not like other simple wave form such as sound waves or other transmission systems where the system output is composed only of two parts, ‘signal’ part and a singular ‘noise’ part (presumably, diurnal wave, in the case of Geppener and Mandrilava).

An effort to estimate SNR in this work starts with the declaration of what we consider noises in the raw CR data. As a result of the widely acknowledged superposition tendencies in raw CR data, whether a signal is considered a noise or a real signal depends on the signal of interest. Where FDs are signals of interest as in the current work, GLEs, diurnal variation, abnormal CR enhancement, 11-yr oscillations, and some longer periodicities are all viewed as noises. These different noise components highlight the complexities of calculating SNR in CR data. They, for example, question any estimate of SNR based on one component as attempted by Geppener & Mandrilava (2020). A holistic approach may be more pragmatic.

As noted in Section 4.1, complicated analytical transformations are required to isolate these signals. Three of these signals (raw CR data, FTS, and diurnal wave) are presented in Figs 4 and 6. It should be noted that two sets of FDs are calculated from the raw data and the FTS. While the FDs associated with the raw data are contaminated by the various noises indicated above, Fourier harmonic transformation and suitable high-pass filters have been used to account for many of these unwanted signals in the FDs selected from FTS. For example, the diurnal wave signal and the periodic 11-yr cycle are no longer parts of the components of the FTS.

Rather than estimating SNR with reference to only one noise component, we calculate SNR with reference to FTS and the raw data. Here, the FTS is regarded as the real/pure signal whereas the raw CR data are noisy. As noted earlier, a careful comparison of the two signals in Figs 4 and 6 shows that there are significant similarities as well as differences between the two signals. There are regions where the FTS and the raw data are in phase. They are out of phase in some parts. Some FDs are consistent in both whereas some are not. These differences are attributable to the presence and absence of some signals (or noise components) in raw and FTS, respectively. We note also that the graphic (visually elegant) presentation of the result of our detailed analytical transformation (FTS) with the raw time-series of CR data provides unambiguous result validation. This compares sharply with many publications where the input and output are usually incomparable with the raw time-series CR data (e.g. Sari et al. 1978; Tezari et al. 2016, GSM).

In the light of these, we roughly define the SNR as the ratio of FTS to the raw data. This may be done in three ways by employing (1) the whole time-series for the two signals, (2) only FDs that are consistent in the FTS and the raw signal, and (3) total events selected from the two signals. Application of methods 1, 2, and 3 to the results presented in Fig.4 yields SNR = 2.53, 1.39, and 1.49, respectively. Out of the 44 and 34 FDs measured with the FTS and raw data, respectively, 25 events are consistent in both signals. For the hourly data presented in Fig.6, SNR = 9.54, 1.61, and 1.61 for methods 1, 2, and 3, respectively. Of 1452 and 1364 FDs detected from FTS and raw data respectively, 1364 FDs are consistent in both signals.

The larger SNR associated with hourly data may indicate the differences in the two temporal resolutions (Lockwood 1971). It is also evidence that the timing and magnitude of FD events are more precise with hourly data.

There is yet another approach to quantifying the SNR in a given CR. This second method may be more complicated as it requires signal reconstruction. Here, all the signals, apart from the high-frequency component, removed from the raw data are to be reconstructed or added up as one signal (this should serve as the noise component). The SNR will then be calculated as the high-frequency ratio to this singular noise component. This may yield a better result. Nevertheless, reconstruction of all the signals that are filtered from the raw data with different subroutines in the current analysis may be quite involved. A simpler approach may be to first disable all other subprograms in the code, allowing only the subroutine that filters only the high-frequency component from the raw data. Here, all the remaining signals, including the diurnal and 11-yr oscillations may be lumped as one component (noise). For want of space, we will leave these indicated methods for some future work.

6 SUMMARY

Starting from Section 2, many potential biases/disputes that may arise from the commonly employed formulae were highlighted. While the subjective FD identification methods, which are the main source of some serious scholarly controversies in FD-based weather investigations are previously glossed over, the current effort is aimed at redirecting researchers in the field to the need to pay topmost attention to huge bias implications of the event catalogues employed in the analysis. Large FDs are usually conspicuous (as is evident in Fig.4). Such large depressions can easily be spotted without the aid of any computer program. However, the presented analysis confirms that complementary programs that can accurately time and correctly calculate the event magnitude have yet to be developed by researchers employing the traditional normalization equations as explained in Section 2.

If dealing with high-amplitude FDs is as difficult as demonstrated, then investigators attempting to identify the often hidden and elusive small FDs may have more problems to handle. The results presented here can explain why there are hardly any publications fully dedicated to the analysis of small amplitude FDs. Larger thresholds [CR (per cent) |$\ge$| 3] are generally used to identify FDs from hourly CR averages (e.g Cane et al. 1993, 1996; Oh et al. 2008). In the light of this, the efforts of the IZMIRAN team to identify FDs using a much smaller baseline [CR (per cent) |$\le$| 0.5] is a very bold step. But it should be realized that such low amplitude may be comparable or even smaller with the amplitude of pre-decrease that accompanies some large FDs (Hofer & Fluckiger 2000; Leerungnavarat & Ruffolo 2003; Ahluwalia, Ygbuhay & Duldig 2009). In fact, Sarbdeep (2017) report that the size of pre-decrease can be as large as 2–3 per cent. Worst still, the amplitudes of CR anisotropy can be as large as 10 per cent (e.g. Belov et al. 1979; Belov 2008). As may be realized from the current analyses, the mixture of these signals of similar or comparative amplitudes makes the selection of both small and large FDs from raw CR data quite a difficult task. There is, thus, a need to carry out a detailed validation study of FD lists containing very small amplitude events. The validation test is most important if such low-amplitude FDs are selected from hourly averaged data.

The GSM, for example, selected 253 large FDs for 22 and 23 Solar Cycles (1986–2008). This translates to 11 big FDs per year. This looks doubtful in view of the fact that the occurrence rate of the rare event, GLE, may be as high as 8 per year (Todd & Kniveton 2001). Visual inspection of Figs 4 and 6 shows that many large FDs occur in periods of high solar activities like 2003. The 825 and 6738 FDs selected from daily and hourly data through the automated method is a much greater improvement over the efficiency of the GSM. The baseline for selection with the averaged daily data is CR (per cent) |$\le$||$-$|0.01 whereas CR (per cent) |$\le$| −3 is used for the hourly data.

The number of small FDs detected by the GSM within this 23 yr period is 2722. This implies that the rate of occurrence of small events is |$\approx$| 118 yr⁻¹. This is an indication that the GSM is more efficient in the detection of small FDs than for big ones. The amplitudes of some of these events are as low as 0.3 per cent. The analyses presented here suggest some plausible reasons for the higher efficiency of the GSM for small FDs. First, many of the events listed as small events in the FEID may be FDs that appear large at some stations, look very small, or appear just like ordinary CR enhancement at some other locations. The amplitude of the resultant FDs will seriously be smoothed when data from such stations are combined. Suppose the amplitudes of the events are the same in all the stations [a rare or impossible situation, see also table 3 of Light et al. (2020)], phase shift arising from CR anisotropy at different locations may still impose some serious smoothing effect on the calculated event amplitude. Figs 2 and 3 clearly demonstrate that different stations observe different intensity variations at the time of the five FDs reported in the FEID. So the number of small FDs that will be detected within the period will be a function of the station. Even the behaviour of large and small FDs is clearly illustrated in Fig.1 using daily averaged data. Some large FDs may be seen by all the stations irrespective of their locations. Okike (2020a) experimentally demonstrated this (see their table 1). Out of the ten stations tested in the year 2003, there are cases where some events are observed at the same time by all the stations. But this is more applicable to big events. Nevertheless, the amplitudes of the same event vary appreciably between stations. Averaging the FD signal over the ten stations will yield a magnitude that may differ significantly from what is observed at each of the stations.

It is also interesting to observe from the figure that the small FD measured by NVBK station only looks like a very small CR enhancement at MOSC NM. Okike & Umahi (2019a) practically demonstrated that such enhancement reflects the presence of CR anisotropy. The anisotropy may be responsible for the missing small event at the station. If removed by the Fourier transformation technique, the hidden/obscured small event at MOSC may emerge. A closer inspection of table 4 of Okike (2020a) confirms that intensity variations between NMs have a more serious impact on small FDs than on big events. Many FDs of the magnitude in the range of |$\le$| 1 per cent are often seen by only a few stations. The table tends to further confirm the indication that bigger FDs tend to be global events whereas most small events are location-dependent.

It can be inferred from the results presented that one of the obvious drawbacks in the analysis of CR data is the manual or case study approach in the current era of Big Data analysis. Calculating the individual magnitude and event time of the large number of big and small FDs at the IZMIRAN is a herculean task. Such catalogue would have taken years to prepare since much manual labour is involved. If some of the improvements outlined by Belov et al. (2018a) are implemented, it is expected that some of the current lapses in the efficiency/accuracy of the GSM will improve. Additionally, the numerous advantages of the automated method over the GSM case study approach may call the attention of the IZMIRAN team to many other areas that the GSM needs improvement. In this era of Big Data analysis, occasioned by the preponderance of high-speed computers and sophisticated software, outbursts of technological advancements in data acquisition, for example, the GSM may advance from the semi-automated magnitude estimation and timing to complete automatic event selection approaches. New event catalogues that may result from the new versions of the GSM will provide an opportunity for further validation of the existing/old IZMIRAN FD catalogue. FAM, can, for example, handle both hourly and daily CR data. It can also select FDs from raw and Fourier harmonically transformed CR data. It can also analyse CR data assimilated from an array of NMs. It is also very fast and can analyse large volumes of data in less than a few seconds. The different versions of FAM and their catalogues allow us to conduct an array of validation tests.

NM measurement started around 1957. Some stations have accumulated CR data for over 60 yr. While the GSM or other manual methods could take quite a while to isolate a reasonable number of FDs from such a large volume of data, the current automated method can quickly select the FDs and other CR phenomena of interest. Geppener & Mandrilava (2020) assert that automatic detection of these sporadic effects in CRs provides an opportunity for detailed analysis of CR events at different locations on Earth. The detailed analysis presented using both hourly and daily averaged CR data suggests that such advantages make FAM more attractive than other FD event selection methods.

Though identification of CR intensity decreases (FDs) is a commonplace in the literature, noise analysis has yet to receive much attention. Following the traditional approach of selective identification of FDs and the associated phenomena, Geppener & Mandrilava (2020) estimated the SNR as a ratio of high-frequency signal to diurnal wave for a few isolated FD events. Consequent upon other superposed signals besides the high-frequency components and the diurnal variations, we offered different approaches. In the current statistical methods, one of the proposed methods define SNR as a ratio of high-frequency signal to the noisy CR raw data.

7 CONCLUSIONS

Following the outcome of the comprehensive comparison between the GSM and FAM, we conclude that the complete automated method of FD event selection and analyses is faster and more efficient than the manual/semi-automated techniques. The detailed and rigorous analyses performed by FAM, including the method of disentangling the contribution from the Sun and the Fourier harmonic analysis (which accounts for the diurnal anisotropies), suggests that development and implementation of varieties of algorithms should define the right pathway for CR events identifications, magnitude estimation, timing as well as statistical analyses in this era of Big Data analysis. Removal of other competing signals through signal decomposition indicate that event magnitude calculated by FAM is comparatively accurate. The technique of disentangling other frequencies that tend to obscure small FDs in raw CR data allows the FAM to efficiently detect previously hidden small amplitude FDs.

ACKNOWLEDGEMENTS

After addressing the comments of the unknown reviewers, we concluded that a second eye is needed to fine-tune a scholarly work. We are indebted to them. We also acknowledge the efforts of those who maintain http://cr0.izmiran.rssi.ru/.

DATA AVAILABILITY

The data used in this work are available at http://cr0.izmiran.rssi.ru/ and http://spaceweather.izmiran.ru/eng/.

Footnotes

References