Tsuchiya et al.
Progress in Earth and Planetary Science(2024) 11:26
https://doi.org/10.1186/s40645-024-00625-y

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open Access

Characteristics of temporal variabilityof long‑duration bursts of high‑energy radiation
associated with thunderclouds on the Tibetan
plateau
Harufumi Tsuchiya1* , Kinya Hibino2 , Kazumasa Kawata3, Munehiro Ohnishi3, Masato Takita3,
Kazuoki Munakata4, Chihiro Kato4, Susumu Shimoda5, Quanqi Shi6, Shuo Wang6, Chenyao Han6 andLiuming Zhai7

Abstract
From 1998 to 2017, neutron monitors located at an altitude of 4300 m on the Tibetan plateau detected 127
long-duration bursts of high-energy radiation in association with thunderclouds. These bursts typically lasted
for 10–40 min, and 89% of them occurred between 10:00 and 24:00 local time. They were also found to be more
likely to occur at night, especially during 18:00–06:00 local time period. The observed diurnal and seasonal variations
in burst frequency were consistent with the frequencies of lightning and precipitation on the Tibetan plateau. Basedon 19 years of data, the present study suggests that an annual variation in burst frequency has a periodicity of ∼ 16
years and a lag of ∼ 3 years relative to solar activity.
Keywords Thunderclouds, Particle acceleration, High-energy radiation, Time variability, Solar activity, Tibetan plateau*Correspondence:
Harufumi Tsuchiyatsuchiya.harufumi@jaea.go.jp
1
Nuclear Science and Engineering Center, Japan Atomic Energy Agency,
2‑4, Shirakata, Tokai‑mura, Naka‑gun, Ibaraki 319‑1195, Japan
2
Faculty of Engineering, Kanagawa University, Yokohama, Kanagawa
221‑8686, Japan
3
Institute for Cosmic Ray Research, University of the Tokyo, 5‑1‑5,
Kashiwanoha, Kashiwa, Chiba 277‑8582, Japan
4
Department of Physics, Shinshu University, Matsumoto, Nagano
390‑8621, Japan
5
RIKEN, 2‑1, Hirosawa, Wako, Saitama 351‑0198, Japan
6
Shandong Provincial Key Laboratory of Optical Astronomy
and Solar‑Terrestrial Environment, Institute of Space Sciences, Schoolof Space Science and Physics, Shandong University, Weihai 264209, China
7
National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100101, China

1 Introduction
In the 1920s, C. T .R. Wilson proposed that electrons inthunderclouds are accelerated to high energy in strong
electric fields and produce X-rays by bremsstrahlung (Wilson 1924, 1925). Since then, many observations have shown that lightning and thunderclouds
generate such X-ray signals, confirming that they areindeed powerful particle accelerators (Dwyer et al.
2012, and references therein). Beyond the Wilson prediction, bremsstrahlung gamma rays with a few tens of
MeV have been detected from lightning and thunderclouds. The detection of the high-energy photons suggests that lightning and thunderclouds can accelerate
electrons beyond a few tens of MeV inside them. Theoretical works (e.g., Gurevich et al. 1992; Dwyer 2003,
2007; Babich et al. 2004, 2010) have pointed out thatthe production of those high-energy radiations is due
to relativistic runaway electrons. Seed electrons produced by, for example, cosmic rays are thought to be© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

accelerated to relativistic energies when electric fields
exceed a critical threshold and become such runaway
electrons.
Solar activity influences the heliospheric magnetic
field, resulting in variations in the intensity of galactic cosmic rays reaching the Earth in an approximately
11-year cycle. Therefore, it is thought that solar activity,
by affecting the flux of galactic cosmic rays reaching the
Earth, also impacts the production of runaway electrons.
However, it remains unclear whether cosmic rays or solar
activity plays a role in producing the runaway electrons
responsible for high-energy bremsstrahlung gamma rays.
Bursts of high-energy radiation during thunderstorms
can be categorized into two types when classified simply
by their duration. One type is characterized by intense
short-duration bursts lasting for microseconds to milliseconds. The other type is a long-duration burst, whichlasts from a few seconds to a few tens of minutes andexhibits relatively fainter characteristics compared to theshort-duration bursts. Numerous measurements of theseshort-duration bursts have been taken by space- andground-based detectors and revealed several characteristics including the source altitude and their relation tolightning. In contrast to short-duration bursts, longduration bursts such as gamma-ray glows or terrestrial
ground enhancements (TGEs) have been observed lessfrequently until recently. However, observations madein the coastal area of the Japan Sea (Torii et al. 2002;
Tsuchiya et al. 2007a, 2011; Wada et al. 2021a), at highmountains (Torii et al. 2009; Tsuchiya et al. 2009; Chilingarian et al. 2010, 2011; Tsuchiya et al. 2012) and at highaircraft altitude (Østgaard et al. 2019; Kochkin et al.
2021) have led to increased detection of these long-duration bursts and have drawn attention to their characteristics, including their duration and their correlation withmeteorological phenomena.
The increasing amount of data on long-duration bursts
have allowed us to compile a comprehensive catalog ofsuch phenomena and to gain insight into their characteristics at various observation sites, including high mountain regions (Chilingarian et al. 2019) and coastal areasof the Japan Sea (Wada et al. 2021b). However, moredata are needed to explore whether there is a correlation between long-duration bursts and cosmic rays andto understand the meteorological and geographical factors that contribute to the generation of these bursts. By
studying these conditions, we can identify commonalities
among long-duration bursts and develop a deeper understanding of their production mechanisms. To this end,
we will present observational results obtained by neutron monitors (NM) at Yangbajing on the Tibetan plateau(TP) during 1998−2017 and then discuss the temporalvariability of long-duration bursts.

Page 2 of 14

2 Experiments
2.1 Overview

The Yangbajing NM has been in operation at the Yangbajing cosmic-ray observatory for more than two decades.
The observatory is located at an altitude of 4300 m (corresponding to an atmospheric depth of ∼ 600 g cm−2) in
the TP. In addition, electric field mills (EFMs) have been
deployed at the observatory in 2010 to study possible
correlations between variations in count rate measured
by a detector such as the Yangbajing NM and electricfields (EFs) (Amenomori et al. 2013). To clarify the pointsof the present work, we briefly explain their characteristics below.
2.2 Neutron monitor

The main purpose of the Yangbajing NM is to investigate
the ion acceleration at the solar surface and to monitor
galactic cosmic-ray intensity associated with the solar
activity (Miyasaka et al. 2005; Tsuchiya et al. 2007b). In
the present study, the NM is repurposed to examine theproduction mechanism of long-duration bursts of highenergy radiation associated with thunderclouds. Hereafter, the term “long-duration burst” is employed to referto the high-energy radiation detected by the Yangbajing
NM in association with thunderclouds.
As shown in Fig. 1, the Yangbajing NM consists of
28 NM-type BF3 counters surrounded by lead blocks
and polyethylene in the standard NM64 configuration.
Each NM unit has one BF3 counter with dimensions of
190 cm in length and 15 cm in diameter. The total areaof the Yangbajing NM is 32 m2. The outermost polyethylene serves the purpose of moderating incoming fastneutrons, while the embedded lead blocks breed themoderated neutrons via (n, xn) reactions to enhance thedetection efficiency for neutrons (x represents a number). When entering the BF3 counters, the moderated
neutrons undergo the (n, α) reaction: n +10 B → α +7 Li.
The cross sections of this reaction become larger as theFig. 1 Arrangement of the Yangbajing NM in a room
and a cross-sectional view of one unit, measured in centimeters

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

neutron energy approaches the thermal energy, thus
allowing efficient detection of neutrons in thermal toepithermal energy ranges. To further improve neutron
detection efficiency, the isotopic composition of 10 B ineach BF3 counter is enriched to 98% from a natural isotopic ratio of ∼ 20%. Charged particles produced by theabove reactions lose energy due to the ionization loss
in gas, resulting in anode signals in the counter. A dataacquisition system collects the output signals from eachcounter and registers the number of signals every one
second.
In our previous study (Tsuchiya et al. 2012), we determined the proportions of individual particles that contribute to the total count rate of the Yangbajing NM.
Secondary cosmic-ray neutrons and protons dominate
the total count rate with fractions of 83 and 12%, respectively. In contrast, leptons, including gamma rays andelectrons, contribute to it with only 5% [see also Clemand Dorman (2000)]. The previous study also indicatedthat the same type of NMs as the Yangbajing NM have asmall but non-negligible detection efficiency for gamma
rays through photonuclear reactions with lead blocks(γ +A Pb → n +A−1 Pb) (A = 206, 207, 208), with athreshold gamma-ray energy of 7 MeV (IAEA 2000).
Given these insights, we demonstrated that bremsstrahlung photons were responsible for the observed countincreases during thunderstorms in the Yangbajing NM,
rather than neutrons produced by photonuclear reactions in the atmosphere [e.g., Enoto et al. (2017)]. Therefore, for the present study as well, we assume that countincreases of the Yangbajing NM can be attributed primarily to bremsstrahlung photons with energy higher
than 7 MeV.
2.3 Electric field millElectric field data play a crucial role in understanding
the association of observed increases with thunderclouds and lightning. For this purpose, two BOLTECK
EFM-100 commercial electric field mills have been
operational at the observatory since 2010, positioned
25 m apart. One is situated at ground level, while theother is mounted atop an experimental building. The
vertical separation between them is approximately 3.4
m. The signals from both EFMs are transmitted to computers within the building via optical cables. These signals are recorded at an interval of every 0.1 s, providing
field strength below 100 kV m−1, with a measurement
resolution of 20 V m−1.

3 Analysis
To identify long-duration bursts, we performed several steps of analysis of data collected by the Yangbajing
NM from 1998 to 2017. First, we made a 5-minute countPage 3 of 14

history corrected for atmospheric pressure variations foreach day. Pressure fluctuations typically induce countchanges within ±2%. Second, we constructed an occurrence histogram of NM counts in every 5-minute counthistory, N5 min , and fitted a Gaussian function to this histogram to determine the mean value NBG and the standard deviation σ1day of the Gaussian function every day.
The resulting σ1day served as an estimate of the uncertainty in the 5-minute counts for each day. Third, we
calculated the statistical significance, σs, for each N5minusing the formula;σs =N5 min − NBG
2
N5 min + σ1day.

(1)This allowed us to assess whether the daily NM data contained count bins with σs > 4 . The probability of encountering a bin with a significance of 4 or higher by chance is
5 × 10−5. Therefore, out of the 288 bins in each 5-minutecount history, the number of bins with a significance of
4σ or greater is only 0.014. Among the N5min counts, wedefined the most prominent one as the peak count, Np,
in each 5-minute count history. This data set, which werefer to as the “potential burst set”, contains 135 events
that represent possible long-duration bursts associatedwith thunderclouds.
From the potential data set, we extracted a 5-minutecount history over a time span of ± 2 h centered on thepeak time “tp” when Np was recorded. This time intervalof ± 2 h is sufficient to cover the entire duration of eachburst and to estimate the background level of each burst.
To define the burst duration “td ”, we identified a continuous time range in which the statistical significance σsremained above 1 before and after the peak time tp. By
excluding all count bins in this td , two-time regions areleft in every extracted count history to estimate the background. The background level was determined by fitting
count bins in the two time regions with a quadratic function. The background level in td was then estimated byinterpolating the derived quadratic function.
After completing the above analysis, an eye scan was
performed to detect any suspicious events that may havebeen caused by irregular factors such as power failures.
As a result of this scan, eight events were identified assuspicious events in the potential burst set. Subsequently,
a total of 127 long-duration bursts were selected fromthe NM data collected between 1998 and 2017. This data
set is referred to as the final burst set. None of the eventsin the final burst set was found to be associated withsolar energetic particle events, including ground-level
enhancements (Vainio et al. 2017; Cohen and Mewaldt2018), suggesting that such a solar particle event does notcontribute to the production of long-duration bursts.

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

The current analysis is limited in the detection offaint bursts, because it only considers those with > 4 σ .
This selection criterion is one of the reasons for thedetection of only 127 events during the long observation period (1998−2017). This frequency is also likely
influenced by the higher NM threshold of 7 MeV andthe limited spatial illumination of a long-duration
burst. Gamma-ray detectors using NaI and BGO scintillators can readily capture long-duration bursts withenergies of a few MeV or less (Chilingarian et al. 2019;
Wada et al. 2021b), while these low-energy gamma
rays are not detectable by the Yangbajing NM. In
addition, it is known that a long-duration burst illuminates only a limited area (0.5–1 km) on the ground(Tsuchiya et al. 2011; Wada et al. 2019; Tsurumi et al.
2023). At the altitude of 4300 m, the mean free pathof gamma rays with energy of 10−50 MeV is approximately 700−900 m. Therefore, it would be more difficult to clearly detect long-duration bursts originating
significantly farther away from NMs than the mean
free path.

Page 4 of 14

4 Results and Discussion
4.1 Example of time profiles of long‑duration bursts

Figure 2 depicts examples of the 5-minute count histories
in the final burst set. It is evident that the individual counthistories exhibit significant count increases. Table 1 presents several key characteristics for each of 127 longduration bursts, including its net count increase denoted
as “ Ntot ” and the related statistical significance. The Ntot
is calculated by subtracting the interpolated backgroundfrom the total observed count in td . The observed countincreases are superimposed on gradual count changes
caused primarily by solar diurnal variation, which typically ranges within ±0.3% in amplitude. This variationarises from the anisotropy of galactic cosmic rays below
several tens of GeV in interplanetary space.
Unlike the gradual changes induced by the solar diurnal
variation, EF variations result in faster changes in the NM
count rate. Figure 3 shows examples of the relationshipbetween EF changes and observed count increases. The
EF intensity remains at ∼ 0.1 kV m−1 under fair weather
conditions, with its sign following atmospheric physics

Fig. 2 Examples of the NM count rate histories per 5 min in the final burst set. Each panel is labeled with the date of the event acquisition. The
horizontal axis depicts universal time (UT). Each error shown corresponds to a statistical 1σ . Red solid lines represent estimated background levels,
while two black dashed lines indicate a range of ± σ1day from the background level

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

Page 5 of 14

Fig. 3 Comparison between the BG-subtracted NM count rate and electric field (solid line). The abscissa depicts universal time (UT). The errors
quoted from the NM counts are statistical 1σconventions. A positive value denotes an EF directed
downward from the sky to the ground and vice versa. The
EF is found to exhibit significant variations lasting for
1−1.5h. While the count increases in the events (Fig. 3)
seem to coincide with periods of relatively large positiveEFs, the peak times of these count increases do not necessarily align with the peak times of the positive EFs. A
possible explanation could be that the alterations in the
EF within a thundercloud, responsible for electron acceleration, may not precisely synchronize with the observed
variations in the EF at the ground surface. Intense, sharp
peaks are also found in EF variations (e.g., 20150827 and20160617) and indicate the presence of lightning. Theselightning events causing significant peaks in EF variations do not appear to impact the observed long-duration
bursts. This is probably because the location of the lightning observed by the EFM is far from NMs. Therefore,
when investigating the relationship between EF and longduration bursts, it would be necessary to specify not only
the EF intensity but also the distance to a thundercloudor lightning. This will be our future task.
All other events detected after the EFM installations
are also found to have occurred under similar EF conditions (Additional file 1), suggesting a common underlying mechanism to produce a long-duration burst.
Typically, a thundercloud is considered to have a tripole

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

Page 6 of 14

Table 1 The parameters determined for individual events in the final burst set
ts (HHMM)ate (HHMM)b

Δtd

(UT)

(UT)

(s)

Ntot

Significancec

19990526

1130

1134

19990609

1430

1455

240

24866

15.8

1500

35669

19990620

0730

7.7

0755

1500

24092

19990629

6.9

1910

1925

900

17985

7.9

19990808

1405

1425

1200

15918

5.1

19990818

1330

1405

2100

32409

6.9

19990830

1300

1340

2400

41992

9.2

19990905

1355

1425

1800

40935

12.0

20000523

1950

2025

2100

39599

10.7

20000527

1040

1050

600

13721

6.5

20000701

1820

1835

900

31168

10.8

20000713

0835

0900

1500

44507

8.4

20000720

1225

1245

1200

25997

8.0

20000729

1450

1515

1500

26050

6.7

20000816

0820

0855

2100

39777

6.9

20000818

1320

1330

600

22382

6.4

20000818

1400

1415

900

14774

5.2

20000822

0800

0820

1200

28867

9.4

20010426

0715

0730

900

19924

8.8

20010609

1700

1735

2100

51037

11.4

20010620

1325

1345

1200

27694

7.2

20010625

1205

1215

600

11387

5.8

20010801

2005

2020

900

26538

10.0

20020518

1410

1420

600

12270

4.4

20020519

1650

1710

1200

14790

5.0

20020529

1550

1600

600

13043

6.0

20020602

2105

2115

600

15976

7.3

20020730

1610

1630

1200

31907

7.8

20030620

1434

1440

360

12416

4.1

20030628

0950

1015

1500

26251

5.8

20030630

1025

1050

1500

32280

7.3

20030709

0540

0550

600

15861

6.3

20030714

1530

1545

900

10919

4.0

20030820

1455

1515

1200

17700

5.6

20030822

1340

1405

1500

19572

6.3

20030822

1430

1445

900

37628

9.4

20030825

1250

1325

2100

46328

11.0

20030918

1700

1715

900

23264

11.0

20040203

1545

1615

1800

29535

8.0

20040609

2240

2250

600

26507

11.1

20040704

2025

2040

900

22875

6.6

20040725

0735

0800

1500

28833

8.6

20040731

1425

1445

1200

20889

4.7

20040803

1625

1645

1200

22040

5.4

20040804

2225

2255

1800

38885

9.0

20040809

1325

1335

600

18530

10.3

20040811

0825

0845

1200

44852

11.4

20040811

1725

1750

1500

26480

7.5

Date (YYYYMMDD)

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

Page 7 of 14

Table 1 (continued)ts (HHMM)ate (HHMM)b

Δtd

Ntot

Significancec

(UT)

(UT)

(s)

20040830

1600

1615

20040901

1535

1555

900

13001

5.2

1200

12259

20040904

1215

4.0

1235

1200

22654

20050508

6.6

1210

1230

1200

16474

5.9

20050605

0450

0510

1200

23276

7.6

20050615

1320

1340

1200

20656

5.5

20050702

1225

1235

600

47259

6.0

20050724

1520

1545

1500

9991

4.2

20050725

1835

1900

1500

29619

6.4

20050807

1410

1425

900

48742

13.2

20050807

1430

1445

900

13820

4.3

20050826

0720

0740

1200

16826

5.6

20050903

1120

1140

1200

22081

7.5

20050917

0710

0720

600

9444

4.3

20060511

1748

1754

360

10765

5.7

20060528

0535

0545

600

15920

7.0

20060627

1235

1250

900

15087

4.1

20060628

0555

0610

900

18245

5.8

20060808

1730

1740

600

23705

11.0

20060812

1715

1810

3300

11302915.7

20060829

0730

0800

1800

57789

15.0

20060922

0615

0625

600

17815

6.0

20060924

0839

0845

360

9566

5.4

20070701

1840

1900

1200

30533

9.8

20070713

1430

1445

900

22101

7.1

20070722

0615

0630

900

22137

7.8

20070727

1520

1540

1200

20633

5.6

20070824

1150

1200

600

16041

5.5

20070825

1455

1530

2100

86911

15.4

20080515

1525

1545

1200

20732

6.4

20080531

2125

2150

1500

33840

10.7

20080621

1945

1955

600

18923

7.1

20080711

0640

0650

600

14146

4.8

20080714

1225

1240

900

19914

5.9

20080827

1000

1030

1800

42310

8.5

20090628

1230

1240

600

13239

5.1

20090702

1000

1015

900

9734

4.0

20090702

1020

1030

600

19118

6.4

20090719

2200

2220

1200

43259

13.5

20090725

0650

0715

1500

21689

5.8

20090801

0540

0600

1200

15542

4.5

20090802

1355

1420

1500

26839

7.5

20090906

1000

1025

1500

25122

5.8

20100706

1855

1910

900

15802

5.8

20100722

0445

0505

1200

37639

12.0

20100823

1210

1240

1800

54236

11.1

20100919

1420

1440

1200

30433

8.6

20100924

0750

0820

1800

45447

11.8

Date (YYYYMMDD)

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

Page 8 of 14

Table 1 (continued)ts (HHMM)ate (HHMM)b

Δtd

Ntot

Significancec

(UT)

(UT)

(s)

20110710

1310

1345

20110811

1735

1745

2100

29362

8.3

600

26710

20120711

0605

8.2

0625

1200

30299

20120714

8.5

1750

1805

900

21427

6.2

20120803

2010

2025

900

33062

9.6

20120804

1730

1750

1200

23692

7.3

20120911

0550

0615

1500

25331

6.5

20121010

0645

0655

600

19303

6.0

20130627

1330

1400

1800

44102

7.9

20130902

0810

0825

900

20738

8.0

20140703

1025

1040

900

30253

5.8

20140708

0755

0805

600

15058

5.4

20140716

0835

0850

900

16548

5.4

20140720

1355

1405

600

31341

4.8

20140810

0405

0425

1200

27330

5.3

20140810

1900

1915

900

41085

9.8

20140821

1516

1522

360

12142

4.5

20140823

1040

1055

900

30624

6.5

20140911

1435

1455

1200

37654

10.2

20150827

1245

1300

900

19220

5.7

20160617

2025

2055

1800

24536

7.4

20160702

1755

1810

900

32135

8.2

20160704

1435

1510

2100

18502

6.3

20160710

1210

1220

600

41234

7.5

20160717

1220

1255

2100

24763

5.8

20160717

1348

1400

720

39823

8.5

20160801

0700

0720

1200

29004

6.5

20170705

1330

1340

600

17946

6.3

20170816

1305

1340

2100

50353

15.4

20170816

2030

2105

2100

46590

13.2

20170820

0805

0835

1800

58489

11.7

Date (YYYYMMDD)aStart timeb

End timec

Significance of Ntot

charge structure, comprising a lower positive charge
region (LPCR), a middle negative charge region, andan upper positive charge region (Cooray 2015). Electrons, located between the LPCR and the middle negative charge region, undergo the electric-field acceleration
toward the LPCR and emit high-energy photons throughbremsstrahlung directed to the ground. Based on measurements taken in the TP at an altitude of 4500 m above
sea level (a.s.l.), it was found that the cloud base altitude
is generally 1 km above the ground surface (Qie et al.
2005). In our previous study (Tsuchiya et al. 2012), we
examined a long-duration burst that occurred on 22

July 2010 (listed as 20100722 in Table 1), and found thatabout 90% of the NM count enhancement was caused bybremsstrahlung photons emitted by electrons accelerated in thunderclouds. This estimation assumed a cloudbase altitude of typically about 1 km above the groundsurface. Actually, the constitution ratio of these photons
varies according to the distance between the cloud baseand the ground, ranging from 85% at a distance of 5 km
to 95% at a distance of 0.3 km (Tsuchiya et al. 2012).
Therefore, the present bursts exhibit constitution ratiosof 85−95% if the cloud-base altitude is in between 0.3
and 5 km.

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

4.2 Duration# of events

Figure 4 presents the duration distribution for the final
burst set. Most of the observed duration ranged between
10 and 40 min, occasionally extending to ∼ 60 min. This
trend agrees with the typical life cycle of thunderclouds,
30−60 min, during the presummer and summer seasons.
Their mature stage, which is likely to produce lightning,
generally persists for 15–30 min (Ferrier and Houze
1989).
The ARGO-YBJ experiment, operating ∼ 200 m awayfrom the NM location, observed variations of the airshower rate during 2012 (Axikegu et al. 2022). Thesevariations lasted 14 to 55 min, and are in good agreement with our results. Count enhancements with similar
duration have been identified on Mt. Aragats (3250 ma.s.l.) and Mt. Lomnický Štít (2634 m a.s.l.), using multiple detectors such as NMs, a NaI detector, and a plastic scintillation detector. The count increases obtained by
NMs (Chilingarian et al. 2010, 2011) lasted ∼ 10 min, andmost enhancements of the NaI count in energy > 3 MeV
lasted for a few minutes to 50 min, with rare occasions
extending to 120 min (Chilingarian et al. 2019). Similarly, those obtained at Mt. Lomnický Štít lasted for 1–15
min (Chum et al. 2020). The typical durations within 50
min are in agreement with the present result. However,the > 120 min duration has never been observed at the
Yangbajing observatory. This discrepancy in burst duration may be attributed to two factors. One is the different
meteorological conditions between Mt. Aragats (3250 ma.s.l) and Yangbajing (4300 m a.s.l.): for example, successive generations of cells in thunderclouds might be more
pronounced on Mt. Aragats. This difference may resultin different life cycles for thundercloud-charged layers,
where electron acceleration takes place. The other is adifference in the energy threshold for photons of 7 MeV
for the Yangbajing NM and 3 MeV for their NaI detector. This difference in energy thresholds could also lead todifferent duration behaviors.
35
30
25
20
15
10
5
0
0

10

20

30

40

50 60 70
Duration (min)Fig. 4 Duration distribution of long-duration bursts in the final burst
set

Page 9 of 14

In contrast to high-altitude observations made during
the pre-summer or summer seasons, observations conducted at the Japan Sea in winter seasons have revealed
an alternative perspective on long-duration bursts,
which generally last only a few minutes (Torii et al. 2002;
Tsuchiya et al. 2007a, 2011; Wada et al. 2021b). According to Kitagawa and Michimoto (1994), tripole charge
structures become apparent during the mature stages of
winter thunderclouds. These tripole structures persist forless than 10 min during early or late winter and for evenshorter duration, less than a few minutes during midwinter. Thus, it is reasonable to postulate that differences in
the life cycles of thunderclouds are responsible for thenoticeable difference in burst duration among long-duration bursts during the summer and winter seasons.
4.3 Diurnal variation

The distribution of the onset times for the final burst set
is shown in Fig. 5. This distribution is clearly divided into
two sections: one covering the period from 00:00 to 10:00
local time (LT) and the other covering 10:00 to 24:00 LT.
LT is calculated as 6 h + universal time (UT), considering the geographical longitude of 90◦. In the total numberof observed bursts, 11% of them began at 00:00–10:00 LT
and the rest occurred at 10:00–24:00 LT. The latter time
region contains the period of increased convective activity in convective clouds over the TP as reported by Uyeda
et al. (2001) which showed that strong updrafts generated by land surfaces heated due to solar radiation in
TP result in the rapid development of convective clouds
during 09:00−13:00 LT in the premonsoon seasons and12:00−16:00 LT in the monsoon seasons. In addition, Qieet al. (2003) investigated lightning activity between 1998
and 2002 in TP using the lightning image sensor onboard
the Tropical Rainfall Measuring Mission. Their investigation indicates that 6% and 78% of lightning flashes in thediurnal lightning activity occur in 00:00−10:00 LT and
12:00−19:00 LT, respectively. Therefore, a clear correlation is evident between the distribution of the observed
burst start times and the temporal pattern of lightning
flashes.
Wada et al. (2021b) examined the onset time distribution of 70 long-duration bursts detected in the coastal
area of the Japan Sea over 4 winter seasons from 2015
to 2018. They divided the data into two parts: the daytime spanning 06:00−18:00 LT and the nighttime encompassing the remaining time period. They showed thatthe number of events in daytime is 15 and significantly
smaller than 55, the number of events in nighttime. The
present study also shows a comparable trend, indicating that the number of events during the day, 43, is lessthan the number of events during the night, 84, with aFraction (%)

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

18
16
14
12
10
8
6
4
2
0
0

2

4

6

8

10

12

14

16

18

20 22 24Start time (LT)

Fig. 5 Start time distribution of events in the final burst set (filled
histogram), plotted as a function of local time (LT) computed by 6 h+ UT. The filled circles represent the diurnal variation of lightning
activity in TP in 1998−2002 (Qie et al. 2003)

statistical significance of 3.6σ . This trend is supported tosome extent by observations at Mt. Aragats (Chilingarian et al. 2019). These results suggest that long-duration
bursts of high-energy radiation are likely to occur duringlocal nighttime hours. The nighttime phase corresponds
to the dissipation phase of thunderclouds, during which
the occurrence of strong electric fields capable of causing relativistic runaway electron avalanches is less likely.
Therefore, it is plausible that the long-duration bursts
observed at night could be attributed to the process ofModification Of Spectra as discussed by Chilingarian
et al. (2014) and Diniz et al. (2022).
4.4 Seasonal variation

Fraction (%)

Figure 6 shows the seasonal variation in the occurrences
number of the final burst set. Among them, 122 events(97% of the total 127 events) were observed between
May and September, corresponding to the premonsoon
and monsoon seasons in TP. The seasonal trend obtained

40
35
30
25
20
15
10
5
0

2

4

6

8

10

12
Month

Fig. 6 Distribution of months in which events occurred in the final
burst set (filled histogram). Filled squares and circles indicate
lightning activity and precipitation, respectively, during the years
1998−2002 in the central part of the TP (Qie et al. 2003)

Page 10 of 14

is similar to that of precipitation and lightning activity within the TP region (Qie et al. 2003). This similarity
suggests that long-duration bursts tend to occur during the rainy season when lightning is more frequent, as
expected.
According to the EF measurements from March 2010
to February 2012 (Amenomori et al. 2013), the total number of thundercloud occurrences at Yangbajing was 158
days. During this period, the Yangbajing NM detected
only seven long-duration bursts (Table 1). Interestingly,
Amenomori et al. (2013) showed that thunderclouds
were also observed in 54 days during winter seasons from
December to March. However, the Yangbajing NM did
not detect any long-duration bursts during this winterperiod, except only one recorded between 1998 and 2017(20040203 in Table 1). This infrequent detection during
winter suggests that the EF intensity due to thunderclouds may not be the sole factor governing the production of long-duration bursts.
The ARGO-YBJ experiment, conducted near the NM
location, detected twenty count enhancements during thunderstorms in 2012 between April and October (Axikegu et al. 2022). This period coincides withthe present result. Notably, four (20120714, 20120804,
20120911, and 20121010) of the six long-duration bursts
detected in 2012 (Table 1) align with the dates recordedby the ARGO-YBJ experiment. The effective area of
the Yangbajing NM (32 m2) is smaller than that of the
ARGO-YBJ detector (∼ 110 × 100 m2). A larger effective
area is likely to detect more long-duration bursts withnarrow illumination areas. Hence, the difference in effective area is considered one of the main factors contributing to the variation in the number of events detected in2012 (6 for the Yangbajing NM and 20 for the ARGO-YBJ
experiment).
Muraki et al. (2004) studied a seasonal variation usinga large-area meson monitor installed at Mt. Norikura(2770 m a.s.l.) in Japan. The meson monitor comprises
scintillation detectors, and primarily detects charged
particles but also has some sensitivity to neutral particles such as neutrons and gamma rays. Analyzing dataobtained from October 1990 to January 2002, they foundthat the derived seasonal variation matches the pattern of thunderstorm occurrence. The seasonal variation observed with the Yangbajing NM is similar to theirresult. This is probably because the two areas are influenced by the Asian monsoon. Chilingarian et al. (2019)
also showed a seasonal variation, with a notable peak inMay, which may probably be due to different meteorological conditions compared to those observed in the TP
and at Mt. Norikura.

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

4.5 Annual variation

In Fig. 7, we present an annual variation in occurrences
numbers of the final burst set (red histogram in the top
panel) and compare it with the annual variations of thesunspot number (black histogram in the top panel) andthe galactic cosmic-ray intensity (histogram in the bottom panel) to explore their possible correlations withlong-duration bursts. The sunspot number data weresourced from Sunspot Index and Long-term Solar Observations: https://​www.​sidc.​be/​silso/​home. For our investigation, we used Jungfraujoch NM data that are available
from the World Data Centre for Cosmic Rays (https://​cidas.​isee.​nagoya-​u.​ac.​jp/​WDCCR) , but annual variations of galactic cosmic-ray intensity are almost common
in all NM data. It has been hypothesized that galactic
cosmic rays play a role in the induction of thunderstormrelated events by providing seed electrons (Gurevich

Page 11 of 14

et al. 1992; Babich et al. 2007; Carlson et al. 2008; Gurevich and Karashtin 2013). As is well known, variations insunspot number reflect solar activity that has the 11-year
cycle, and is inversely correlated with variations of galactic cosmic-ray intensity at Earth. Thus, it is natural toconjecture that solar activity may influence the occurrence of long-duration bursts.
To quantify the annual variation of the occurrence
rate in the final burst set, we employed the following
functions for fitting: (1) a constant function, (2) a linear
function, and (3) a periodic function. Functions (1) and(2) are denoted fc (t) = a0 and fl (t) = a0 + a1 t , respectively. Here, a0 and a1 represent a constant and a slope,
respectively. The variable t shows the elapsed year since1998. The function (1) assumes that solar activity or cosmic rays exert time-independent effects on the observed
number of long-duration bursts. Function (2) assumes a

Fig. 7 Top: annual occurrence variation of the final data set (red histogram). The black histogram shows an annual variation in sunspot number
expressed in %. Solid red and black curves denote a periodic function of fp (t) and fsun (t), respectively, while dashed lines represent fc (t) and fl (t).The
error bar represents statistical 1σ.Bottom: the annual variation of cosmic-ray flux measured by neutron monitors located at Jungfraujoch. The NMdata were obtained from the following https://​cidas.​isee.​nagoya-​u.​ac.​jp/​WDCCR/​index.​html

Tsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

Page 12 of 14

Table 2 The fitting parameters determined for each function
χ2/νa

A

T

φ

a0

a1

Function

(%)

(yr)

(rad)

(yr)

(×10−1%/yr)

fc (t)−−−(8.8 ± 0.8) × 10−2

−

16/9

fl (t)−−−(1.0 ± 0.2) × 10−1

−1.5 ± 1.4

14/8

fp (t)

4.6 ± 1.3

16.4 ± 1.7−1.1 ± 0.4

0.100 ± 0.009

−

3.9/6

fsun (t)8.0 ± 0.2

12.57 ± 0.13

−0.22 ± 0.06

0.141 ± 0.004−5.8 ± 0.3

33/5

fcr (t)6.422 ± 0.009

11.772 ± 0.005

2.174 ± 0.002−2.920 ± 0.013

0.388 ± 0.001

50/5

a

ν is degree of freedom.

descending (or ascending) trend during the 1998−2017
period, based on the fact that the peak sunspot number
was smaller around 2013−2015 than during the periodaround 2000−2002. The last periodic function (3) isexpressed as


2π
t+φ ,
fp (t) = a0 + A sin(2)
T
where A, T and φ denote a normalization constant, aperiod, and a phase, respectively. As listed in Table 2, theresultant χ 2 /ν values (ν is the degree of freedom) indicatethat fp (t) provides the best fit to reproduce the derived
annual variation of the final burst set. This result implies
the potential presence of periodicity in the annual occurrence rate of the observed long-duration bursts.
For comparison, we evaluated periods of annual variations in the sunspot number and cosmic-ray flux as wellby fitting the following function to the variations
2π
t +φ .
fsun,cr (t) = a0 + a1 t + A sin(3)
TThis function considers a clear decrease (increase) in theamplitude of the sunspot number variation (cosmic-rayflux) over the years. The resulting curves of fsun (t) andfcr (t) are drawn in Fig. 7, and the parameters determined
are listed in Table 2. The evaluated periods (T) for thesunspot number and cosmic-ray flux deviate from theperiod estimated from the final burst set by 2.2σ and2.7σ (Table 2). In addition, by using the derived periods(T) and phases (φ ) in Table 2, we can calculate the peakyears of fp and fsun , and the year of the minimum of fcr,
each measured from 1998, as 6.9 ± 1.3 years, 3.58 ± 0.13
years, and 4.756 ± 0.003 years, respectively. From thesevalues, possible slight lags of fp with respect to fsun andfcr were estimated as 3.3 ± 1.3 years and 2.1 ± 1.3 years,
respectively. While the present analysis suggests a potential connection between long-duration bursts and solar
activity or cosmic rays, we need more data over a longer

time period before definitively confirming the periodicity
and delay.

5 Conclusions
Long-duration bursts were detected by the Yangbajing NM located at 4300 m a.s.l. during the period of
1998−2017. The detected bursts have a typical durationof 10 to 40 min. This duration distribution suggests thatelectrons undergo continuous acceleration to 10 MeV
or higher within a few tens of minutes. In the coastal
area of the Japan Sea, long-duration bursts have also
been observed in winter seasons and typically last fora few minutes. The difference in duration would result
from the distinct life cycles of winter and summer
thunderclouds.
The seasonal and diurnal variations in the occurrence
number of long-duration bursts agreed well with thosevariations of lightning and precipitation on the TP. Thisagreement justifies the selection and subsequent analysis of the Yangbajing NM data. The present work, basedon 19-year data, suggests the possibility that the annual
variation of long-duration bursts has a periodicity of ∼16 years and a lag of ∼ 3 years relative to solar activity.
To gain further insight into the observed annual variability, it would be necessary to conduct longer-termhigh-energy radiation observations coupled with comprehensive meteorological measurements.
The present work highlights the importance of NM
data for understanding the temporal variability andunderlying production mechanisms of long-duration
bursts of high-energy radiation associated with thunderclouds. Since the 1950s, numerous NMs have been
operational at various observatories around the world(Bütikofer 2018). These NM data would allow us tounravel the real connections between long-duration
bursts, cosmic rays, and solar activity.
Abbreviations
TP	Tibetan plateau
NM	Neutron monitor
EFM	Electric field millTsuchiya et al. Progress in Earth and Planetary Science(2024) 11:26

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40645-​024-​00625-y.
Additional File1. This file includes comparisons between long-duration
bursts detected in 2010–2017 (Table 1 in the main text) and EF variations,but not include the comparisons presented in the main text. Due toperiods of the EFM shutdown, EF variations could not be obtained for all
periods of 2010–2017.
Acknowledgements
We sincerely thank Prof. T. Shinoda (Nagoya Univ.) for giving information on
meteorological conditions on the Tibetan plateau.
Author contributions
HT, KH, and KK were responsible for data analysis, interpretation, and the
proposed writing of this paper. KH and KK installed the EFMs and performed
their maintenance. HT, KM, CK, MO, MT, SS, QS, SW, CH, and LZ contributed tothe maintenance of the Yangbajing NM. All authors read and approved thefinal manuscript.
Funding
This work was partly supported by JSPS KAKENHI Grant Number 21H01116.
Availability of data and materials
The datasets used and/or analyzed during the current study are available fromthe corresponding author on reasonable request.

Declarations
Competing interests
The authors declare that they have no conflict of interest.
Received: 6 December 2023 Accepted: 7 April 2024

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