An Improvement of the Method for Estimating the Lightning Current from Measured Electromagnetic Fields in Lightning Locating Systems

An Improvement of the Method for Estimating the Lightning Current from Measured Electromagnetic Fields in Lightning Locating Systems

Masashi TORII^* and Yoshihiro BABA^* (Received July 3, 2008)

Lightning locating systems (LLSs) provide lightning return-stroke peak currents estimated from measured magnetic or electric field peaks as well as lightning striking locations. Direct measurements of lightning currents on tall towers are used for testing the validity of field-to-current estimation equations employed in LLSs. The field and current peaks are usually assumed to be proportional to each other, where the proportionality coefficient is determined for lightning strikes to flat ground or a grounded object of negligible height. Therefore, these estimation equations are not applicable to lightning strikes to tall towers. Furthermore, in the case of lightning strikes to tall towers, as a result of transient process in the tower, current waveforms can differ significantly at different heights along the tower and can exhibit more than one peak. In such cases, the field-to-current estimation coefficient depends on current measurement location and on whether the first or second current peak is used. Thus, for calibrating LLSs using current measurements on towers, it is necessary to know appropriate far-field-to-current estimation equations or coefficients.

-G[YQTFU㧦 Electromagnetic field, lightning, lightning current, lightning return stroke.

ࠠ࡯ࡢ࡯࠼㧦 㔚⏛⇇㧘㔗㧘㔗㔚ᵹ㧘Ꮻㆶ㔗᠄

⪭㔗૏⟎ᮡቯࠪࠬ࠹ࡓߦ߅ߌࠆ㔗㔚ᵹផቯᴺߩᡷༀ

㠽 ੗ ᡽ ᔒ 㚍 ႐ ศ ᒄ

* Department of Electrical Engineering, Doshisha University, Kyoto Telephone : +81-774-65-6352, Fax : +81-774-65-6801, E-mail : [email protected]

㧝㧚✜⸒

⥄ὼߩ㔚᳇⃻⽎ߢ޽ࠆ㔗ߪ㔚᳇⸳஻ߦ᭽ޘߥ㓚ኂ ࠍ߽ߚࠄߔ㧚㔚᳇⸳஻ߩ⠴㔗⸳⸘ࠍㆡಾߦⴕ߁ߚ߼

ߦߪ㧘ߘߩ㔚᳇⸳஻߇㈩⟎ߐࠇࠆ࿾ၞߩ⪭㔗㗫ᐲ㧘 㔗㔚ᵹࡇ࡯ࠢ୯ߩ㗫ᐲಽᏓ╬ߦ㑐ߔࠆ⛔⸘⊛࠺࡯࠲

߇ᔅⷐߣߥࠆ㧚ߎߩࠃ߁ߥ࠺࡯࠲ߪ㧘ᦨㄭߢߪ⪭㔗

૏⟎ᮡቯࠪࠬ࠹ࡓ㧔Lightning Locating System㧚એਅ LLS㧕ߦࠃࠅᓧࠄࠇᆎ߼ߡ޿ࠆ㧚ߎߩࠪࠬ࠹ࡓߪ㔗

᡼㔚ߦ઻ߞߡ⊒↢ߔࠆ⏛⇇߹ߚߪ㔚⇇ࠍⶄᢙ࿾ὐߦ

⸳⟎ߒߚ⏛⇇߹ߚߪ㔚⇇࠮ࡦࠨ࡯ߢᬌ⍮ߒ㧘⪭㔗૏

⟎ࠍ࡝ࠕ࡞࠲ࠗࡓߢᮡቯߔࠆߣߣ߽ߦ㧘ᬌ⍮ߒߚ⏛

⇇ࡇ࡯ࠢ୯ H_M.peak߹ߚߪ㔚⇇ࡇ࡯ࠢ୯ Ez.peakߣᮡቯ

૏⟎㧔࠮ࡦࠨ࡯߆ࠄߩ〒㔌 d㧕߆ࠄ㔗㔚ᵹߩࡇ࡯ࠢ

୯㧔Ipeak §2ScdH_M.peak/v ߹ߚߪIpeak =2SH₀c²dEz.peak/v㧚ߚ ߛߒ㧘cߪశㅦ㧘vߪᏫㆶ㔗᠄ᵄㅴⴕㅦᐲ㧘H₀ߪ⌀ⓨ

ߩ⺃㔚₸㧕ࠍផቯߔࠆߎߣ߇ߢ߈ࠆ㧚਄⸥ߩ㔗㔚ᵹ

ផቯᑼ޽ࠆ޿ߪߘࠇߦઍࠊࠆታ㛎ᑼߪ㧘ᐔမߥᄢ࿾

㕙਄ߦု⋥ߥ㔗᡼㔚〝਄ࠍ㔗㔚ᵹᵄ߇৻ቯㅦᐲvߢ

਄᣹ߔࠆߣ઒ቯߒߡ᳞߼ࠄࠇߚ߽ߩߢ޽ࠆ㧚ߒ߆ߒ㧘

ࠝ࡯ࠬ࠻࡝ࠕߦ޽ࠆ㜞ߐ100 mߩGaisberg࠲ࡢ࡯ߦ ߅޿ߡ㗂ㇱઃㄭߢߩታ᷹㔚ᵹ߇LLSផቯ㔚ᵹߩ0.98

୚¹⁾㧘࠼ࠗ࠷ߦ޽ࠆ㜞ߐ160 mߩPeissenberg࠲ࡢ࡯

ߦ߅޿ߡߪ0.88୚²⁾ߣ߶߷╬ߒ޿ߩߦኻߒ㧘ࠞ࠽࠳

ߦ޽ࠆ㜞ߐ553 mߩCN࠲ࡢ࡯ߦ߅޿ߡߪ0.38୚³⁾ ߣታ᷹㔚ᵹ୯ߣ LLS ផቯ㔚ᵹ୯ߩ୯߇ᄢ߈ߊ⇣ߥ ߞߡ߅ࠅ㧘LLSߩ㔚ᵹផቯᑼߩౣᬌ⸛߇ᔅⷐߣߩᜰ

៰߇ߥߐࠇߡ޿ࠆ㧚

ᧄ⺰ᢥߢߪ㧘㔗᠄㜞᭴ㅧ‛߇ሽ࿷ߔࠆ႐วߦ߅ߌ ࠆ㜞᭴ㅧ‛ߩ㗂ㇱ߹ߚߪ⣉ㇱߩ㔗㔚ᵹࡇ࡯ࠢ୯ߣ᡼

኿㔚⇇߹ߚߪ⏛⇇ߩࡇ࡯ࠢ୯ߣߩ㑐ଥᑼࠍឭ᩺ߒ㧘 ߘߩᅷᒰᕈߦߟ޿ߡᬌ⸛ࠍⴕߥ߁㧚

㧞㧚㔗᠄㜞᭴ㅧ‛ߩሽ࿷ࠍ⠨ᘦߒߚᏫㆶ㔗᠄ߩ વㅍ✢〝ࡕ࠺࡞

⸘▚ࡕ࠺࡞

ᧄ⺰ᢥߩ⸘▚ߢ૶↪ߔࠆ㔗᠄㜞᭴ㅧ‛ߩሽ࿷ࠍ⠨

ᘦߒߚᏫㆶ㔗᠄ߩવㅍ✢〝ࡕ࠺࡞ࠍFig. 1ߦ␜ߔ㧚 㔗᠄㜞᭴ㅧ‛ߩ㜞ߐߪ㧘h = 0㧘100㧘160 ߅ࠃ߮

553 mߦ⸳ቯߒߚ㧚ߥ߅㧘h㧩0 ߪ㜞᭴ㅧ‛߇ሽ࿷ߒ

ߥ޿႐ว㧘ߟ߹ࠅᐔမᄢ࿾߳ߩ㔗᠄ࠍ㧘h㧩100 mߪ

ࠝ࡯ࠬ࠻࡝ࠕߩGaisberg࠲ࡢ࡯ࠍ㧘h㧩160 mߪ࠼ࠗ

࠷ߩPeissenberg࠲ࡢ࡯ࠍ㧘h㧩553 mߪࠞ࠽࠳ߩCN

࠲ࡢ࡯ࠍᗐቯߒߡ޿ࠆ㧚

Zgr

(Zch)

TL representing channel

TL representing tall object

Grounding impedance (Zob)

Utop

Ubot

h V0 (h,t)

Reference ground Ground surface

Fig. 1. A lightning strike to a tall grounded object of height h, represented by lossless transmission lines

connected in series with a lumped voltage source, V0 (h, t), and a lumped grounding impedance (Zgr).

Zgrߪធ࿾ࠗࡦࡇ࡯࠳ࡦࠬߢ޽ࠅ㧘ᧄ⺰ᢥߢߪ30 : ߣ⸳ቯߒߚ㧚Zchߪ㔗᡼㔚〝ࠍᮨᡆߔࠆવㅍ✢〝ߩ․

ᕈࠗࡦࡇ࡯࠳ࡦࠬߢ޽ࠅ㧘900 :ߣ⸳ቯߒߚ㧚Zobߪ 㜞᭴ㅧ‛ࠍᮨᡆߔࠆવㅍ✢〝ߩ․ᕈࠗࡦࡇ࡯࠳ࡦࠬ

ߢ޽ࠅ㧘300 :ߣ⸳ቯߒߚ㧚U_bot ߪ㜞᭴ㅧ‛ࠍਅะ߈

ߦવ៝ߔࠆ㔗㔚ᵹᵄߦኻߔࠆ⣉ㇱߢߩ෻኿ଥᢙߢ޽

ࠅ㧘U_topߪ㜞᭴ㅧ‛ࠍ਄ะ߈ߦવ៝ߔࠆ㔗㔚ᵹᵄߦ ኻߔࠆ㗂ㇱߢߩ෻኿ଥᢙߢ޽ࠆ㧚ߘࠇߙࠇᰴᑼߢ⴫

ߐࠇࠆ㧚

Z Z

Z Z

gr ob

gr ob

bot

U

Z Z

Z Z

ch ob

ch ob

top

U

Zgr=30 :㧘Zch=900 :㧘Zob=300 :ࠍ(1)㧘(2) ᑼߦઍ౉

ߔࠆߣ㧘Ubot = 0.9㧘Utop = í0.5߇ᓧࠄࠇࠆ㧚ᧄ⺰ᢥߢ ߪ㧘ߎࠇࠄߩ୯ࠍ૶↪ߔࠆ㧚

Fig. 1ߩࡕ࠺࡞ߦ߅޿ߡ㧘㜞᭴ㅧ‛ౝ㧔0 ” z ’” h㧕

ߩ㔚ᵹߪᰴᑼߢ⴫ߐࠇࠆ⁴⁾㧚

¦

ª ¸

¹

¨ ·

©

§

0

2 , '

2 ) 1 , ' (

n

sc n top n bot top

c nh c

z t h h I t

z

I U U U

»¼

¸º

¹

¨ ·

©

§

c nh c

z t h h I_sc

n top n bot

2 , '

1 1U

U (3)

ߎߎߢ㧘IscߪᏫㆶ㔗᠄߇㜞ዉ㔚₸㧔Zgr § 0㧕ߩᐔမ ᄢ࿾ߦ↢ߓߚ႐วߦ߅ߌࠆ㔗㔚ᵹ㧔⍴⛊㔗㔚ᵹ㧕ߢ

޽ࠅ㧘ᰴᑼߢ⴫ߐࠇࠆ㧚

0 ( 0 )

( 0 ) ,

s c ,

c h

V t

I t

Z

(4)

߹ߚ㧘㔗᡼㔚〝਄㧔 z’ • h 㧕ߩ㔚ᵹߪᰴᑼߢ⴫ߐࠇ ࠆ㧚

«¬

ª ¸

¹

¨ ·

©

§

¸

¹

¨ ·

©

§

v h t z h v I

h t z h I t

z

I _{sc top sc} '

' , 2 ,

) 1 , '

( U

»¼

¸º

¹

¨ ·

©

§

¦

1

1 ' 2

, ) 1 ( )

1 )(

1 (

n

sc top n top n bot top

top c

nh v

h t z h U I U U U

U (5)

v ߪᏫㆶ㔗᠄〝਄ߩ㔚ᵹᵄવ៝ㅦᐲߢ޽ࠅ㧘ᧄ⺰ᢥ ߢߪశㅦߩ1/3ߣ⸳ቯߔࠆ㧔v=c/3㧕㧚

㔗㔚ᵹ߅ࠃ߮㔗㔚⏛⇇ߩ⸘▚ᵄᒻ

ᧄ▵ߢߪ㧘Fig. 2ߦ␜ߔ2⒳㘃ߩ㔚ᵹᵄᒻࠍIscߣ ߒߡ↪޿㧘㔗᠄㜞᭴ㅧ‛㗂ㇱ߅ࠃ߮⣉ㇱ㧘㆙ᣇ㔚⇇㧘

⏛⇇ߩ⸘▚ࠍⴕ߁㧚ߥ߅㧘Fig. 2 ߩ┙ߜ਄߇ࠅㇱಽ ߇ᕆፋߥᣇߩ㔚ᵹᵄᒻߩࡇ࡯ࠢ୯ߪ10 kA㧘10-90㧑

┙ߜ਄߇ࠅᤨ㑆ߪ0.18 Ps㧘ᵄየ㐳ߪ30 Psߢ޽ࠆ㧚

ઁᣇߩ㔚ᵹᵄᒻߦߟ޿ߡߪ㧘ࡇ࡯ࠢ୯10 kA㧘10-90㧑

┙ߜ਄߇ࠅᤨ㑆1.0 Ps㧘ᵄየ㐳40 Psߢ޽ࠆ㧚

0 4 8 12 16

0 10 20 30 40 50 60

Time [Ps]

Current [kA]

Risetime=0.18 Ps Risetime=1.0 Ps

Fig. 2. Waveforms of lightning short-circuit current, Isc, with different 10-to-90% risetimes: 0.18 and 1.0 Ps.

Iscߩ┙ߜ਄߇ࠅᤨ㑆߇0.18 Ps߅ࠃ߮1.0 Psߦ߅ߌ ࠆ㜞᭴ㅧ‛⣉ㇱ߅ࠃ߮㗂ㇱߩ㔚ᵹᵄᒻࠍFig. 3߅ࠃ

߮4ߦ␜ߔ㧚Fig. 3߅ࠃ߮4ߩ(a) ߪh=100 m㧘(b) ߪ h=160 m㧘(c) ߪh=553 mߩ႐วߩ⸘▚ᵄᒻߢ޽ࠆ㧚 ߥ߅㧘ฦ࿑ߦߪ㧘Ყセߩߚ߼ h=0㧔ᐔမᄢ࿾㔗᠄㧕 ߩ႐วߩᵄᒻ߽␜ߒߡ޿ࠆ㧚߹ߚ㧘Fig. 3߅ࠃ߮4

Table 1. Peak values in kiloamperes of lightning current at the top and bottom of a tall object of different heights h=0, 100, 160, and 553 m.

Risetime = 0.18 Ps Risetime = 1.0 Ps Object

height, h top bottom top bottom

100 m 7.50

(10.6) 14.3 10.1

—— 11.1

160 m 7.50

(10.4) 14.3 10.6

—— 13.2

553 m 7.50

(9.24) 14.3 7.49

(9.70) 14.2

* Value in ( ) is the second or largest peak if present.

0 2 4 6 8 10 12 14 16

0 10 20 30 40 50 60

Time [Ps]

Current [kA]

Channel base at flat ground 100-m tower bottom

100-m tower top

(a) 100 m

0 2 4 6 8 10 12 14 16

0 10 20 30 40 50 60

Time [Ps]

Current [kA]

Channel base at flat ground 160-m tower bottom

160-m tower top

(b) 160 m

0 2 4 6 8 10 12 14 16

0 10 20 30 40 50 60

Time [Ps]

Current [kA]

Channel base at flat ground 553-m tower bottom

553-m tower top

(c) 553 m

Fig. 3. Current waveforms at the bottom and top of a tall object of different heights h for the 10-to-90%

current risetime being equal to 0.18 Ps.

ߩ㔚ᵹᵄᒻ߆ࠄ⺒ߺขߞߚࡇ࡯ࠢ୯ࠍTable 1 ߦ␜

ߔ㧚

Iscߩ┙ߜ਄߇ࠅᤨ㑆߇0.18 Psߩ႐วߩ㆙ᣇߢߩ

ု⋥㔚⇇ᵄᒻ㧔⸘▚ὐߪ㜞᭴ㅧ‛߆ࠄ᳓ᐔ〒㔌 50

km㧕ࠍFig. 5ߦ㧘᳓ᐔᣇะ⏛⇇ᵄᒻࠍFig.6ߦ␜ߔ㧚

߹ߚ㧘Iscߩ┙ߜ਄߇ࠅᤨ㑆߇1 Psߩ႐วߩု⋥㔚⇇

ᵄᒻࠍFig. 7ߦ㧘᳓ᐔᣇะ⏛⇇ᵄᒻࠍFig. 8ߦ␜ߔ㧚

0 2 4 6 8 10 12 14 16

0 10 20 30 40 50 60

Time [Ps]

Current [kA]

Channel base at flat ground 100-m tower bottom

100-m tower top

(a) 100 m

0 2 4 6 8 10 12 14 16

0 10 20 30 40 50 60

Time [Ps]

Current [kA]

Channel base at flat ground 160-m tower bottom

160-m tower top

(b) 160 m

0 2 4 6 8 10 12 14 16

0 10 20 30 40 50 60

Time [Ps]

Current [kA]

Channel base at flat ground 553-m tower bottom

553-m tower top

(c) 553 m

Fig. 4. Current waveforms at the bottom and top of a tall object of different heights h for the 10-to-90%

current risetime being equal to 1 Ps.

㔗᠄㜞᭴ㅧ‛⣉ㇱ߅ࠃ߮㗂ㇱߩ㔚ᵹࡇ࡯ࠢ୯ 㜞᭴ㅧ‛߇ሽ࿷ߔࠆ႐วߩ᭴ㅧ‛⣉ㇱߦ߅ߌࠆ㔚 ᵹࡇ࡯ࠢ୯Ibot..peakߪ㧘(3)ᑼࠃࠅ㧘

1 1

. 2 .

t o p

b o t p e a k s c p e a k b o t

I U I

U

| (6)

0 2 4 6 8 10 12 14

0 10 20 30 40 50 60

Time [Ps]

Electric field [V/m] Strike to 100-m tower

Strike to flat ground

(a) 100 m

-2 0 2 4 6 8 10 12 14

0 10 20 30 40 50 60

Time [Ps]

Electric field [V/m]

Strike to 160-m tower

Strike to flat ground

(b) 160 m

-4 -2 0 2 4 6 8 10 12 14

0 10 20 30 40 50 60

Time [Ps]

Electric field [V/m]

Strike to 553-m tower

Strike to flat ground

(c) 553 m

Fig. 5. Waveforms of vertical electric field EZ at d=50 km due to a lightning strike to a tall object of different

heights h for the 10-to-90% current risetime being equal to 0.18 Ps.

ߢਈ߃ࠄࠇࠆ㧚ߎࠇߦ㧘U_top = í0.5㧘U_bot= 0.9㧘Isc.peak=10 kAࠍઍ౉ߔࠆߣIbot.peak= 14.3 kAߣߥࠅ㧘Fig. 3 (a), (b), (c)ߦ߅ߌࠆ㜞᭴ㅧ‛⣉ㇱ㔚ᵹߩࡇ࡯ࠢ୯ߦ৻⥌ߔ ࠆ㧚

㜞᭴ㅧ‛㗂ㇱ㔚ᵹߦߟ޿ߡߪ㧘ᄢ࿾㕙߆ࠄߩ෻኿

ᵄߩᓇ㗀ߦࠃࠅࡇ࡯ࠢ୯߇2ߟሽ࿷ߔࠆᵄᒻߣߥߞ

0 5 10 15 20 25 30 35

0 10 20 30 40 50 60

Time [Ps]

Magnetic field [mA/m]

Strike to 100-m tower

Strike to flat ground

(a) 100 m

-5 0 5 10 15 20 25 30 35

0 10 20 30 40 50 60

Time [Ps]

Magnetic field [mA/m] Strike to 160-m tower Strike to flat ground

(b) 160 m

-10 -5 0 5 10 15 20 25 30 35

0 10 20 30 40 50 60

Time [Ps]

Magnetic field [mA/m] Strike to 553-m tower Strike to flat ground

(c) 553 m

Fig. 6. Waveforms of horizontal magnetic field HMat d=50 km due to a lightning strike to a tall object of

different heights h for the 10-to-90% current risetime being equal to 0.18 Ps.

ߡ߅ࠅ㧘╙2ࡇ࡯ࠢ߇╙1ࡇ࡯ࠢࠃࠅᄢ߈ߊߥߞߡ

޿ࠆ㧚h㧩0 m㧔ᐔမᄢ࿾㔗᠄ߩ႐วࠍ㒰߈㧘㜞᭴

ㅧ‛ߩ㜞ߐhߦ߆߆ࠊࠄߕ㧘╙1ࡇ࡯ࠢ୯߇㧘⚂7.5 kAߣߥߞߡ޿ࠆ㧚╙2ࡇ࡯ࠢ୯ߪ㧘h㧩100 m߅ࠃ

߮160 mߩ႐ว㧘⚂10.5 kA, h㧩553 mߩ႐วߢ⚂9.2 kA ߣߥߞߡ޿ࠆ㧚㔗㔚ᵹߩ┙ߜ਄߇ࠅᤨ㑆߇ 2h/c ࠃࠅዊߐ޿႐วߦߪ㧘╙1ࡇ࡯ࠢItop1.peakߪ(3)ᑼࠃࠅ㧘

0 2 4 6 8 10 12 14

0 10 20 30 40 50 60

Time [Ps]

Electric field [V/m]

Strike to 100-m tower

Strike to flat ground

(a) 100 m

0 2 4 6 8 10 12 14

0 10 20 30 40 50 60

Time [Ps]

Electric field [V/m] Strike to 160-m tower Strike to flat ground

(b) 160 m

-4 -2 0 2 4 6 8 10 12 14

0 10 20 30 40 50 60

Time [Ps]

Electric field [V/m]

Strike to 553-m tower

Strike to flat ground

(c) 553 m

Fig. 7. Waveforms of vertical electric field EZ at d=50 km due to a lightning strike to a tall object of different height h for the 10-to-90% current risetime being equal to 1 Ps.

1

1

. 2 .

t o p

t o p p e a k s c p e a k

I U I

| (7)

ߢਈ߃ࠄࠇࠆ. U_top = í0.5㧘Isc.peak=10 kAࠍઍ౉ߔࠆߣ㧘

Itop1.peak=7.5 kAߣߥࠅ㧘Fig. 3 (a), (b), (c)ߦ߅ߌࠆ㜞᭴

ㅧ‛㗂ㇱ㔚ᵹߩ╙1ࡇ࡯ࠢ୯ߦ৻⥌ߔࠆ㧚

╙2ࡇ࡯ࠢ୯Itop2.peakߦߟ޿ߡߪIsc(h, t)߇ࡇ࡯ࠢᓟ

߶߷৻ቯ୯ࠍ଻ߟ႐วߦߪ㧘(3)ᑼࠃࠅ㧘

0 5 10 15 20 25 30 35

0 10 20 30 40 50 60

Time [Ps]

Magnetic field [mA/m]

Strike to 100-m tower

Strike to flat ground

(a) 100 m

0 5 10 15 20 25 30 35

0 10 20 30 40 50 60

Time [Ps]

Magnetic field [mA/m] Strike to 160-m tower Strike to flat ground

(b) 160 m

-10 -5 0 5 10 15 20 25 30 35

0 10 20 30 40 50 60

Time [Ps]

Magnetic field [mA/m]

Strike to 553-m tower

Strike to flat ground

(c) 553 m

Fig. 8. Waveforms of horizontal magnetic field HMat d=50 km due to a lightning strike to a tall object of

different heights h for the 10-to-90% current risetime being equal to 1 Ps.

2

1 2 1

. .

t o p

t o p p e a k s c p e a k

b o t b o t t o p

I U I

U U U

|

u

(8)

ߢㄭૃߐࠇࠆ.ߎࠇߦ㧘U_top = í0.5㧘U_bot = 0.9, Isc.peak=10 kAࠍઍ౉ߔࠆߣ㧘Itop2.peak=10.9 kAߣߥࠅ㧘Fig. 3 (a) ߅ࠃ߮ (b)ߦ߅ߌࠆ㜞᭴ㅧ‛㗂ㇱ㔚ᵹߩ╙ 2ࡇ࡯ࠢ

୯ߦ৻⥌ߔࠆ㧚

એ਄ࠃࠅ㧘㜞᭴ㅧ‛਄ߢߩ㔗㔚ᵹߩࡇ࡯ࠢ୯ߪⷰ

᷹૏⟎㧔㜞ߐ㧕ߦଐሽߒ㧘ᩮరㇱ㧔z’=0)ߢᦨᄢߣߥ

ࠆߎߣ߇⏕⹺ߐࠇࠆ㧚

㧟㧚㔗㔚⏛⇇ࡄ࡞ࠬߩࡇ࡯ࠢ୯ߣ㔗㔚ᵹࡇ࡯ࠢ୯ ᐔမᄢ࿾߳ߩ㔗᠄ߦࠃࠆ㆙ᣇ㔚⏛⇇ߣ

㔚ᵹߩ㑐ଥᑼ

ᐔမᄢ࿾߳ߩ㔗᠄ߦ⿠࿃ߒߚ㆙ᣇߢߩု⋥㔚⇇ߩ

ࡇ࡯ࠢ୯ Ez..peak ߅ࠃ߮᳓ᐔᣇะ⏛⇇ߩࡇ࡯ࠢ୯

HM._peakߪᰴᑼߢㄭૃߢ߈ࠆ⁶⁾㧚

2

2 0

. .

z p e a k b p e a k

E v I

S H c d

| (9a)

.p e a k 2 b.p e a k

H v I

M ^| S c d (9b)

ߎߎߢ㧘vߪᏫㆶ㔗᠄㔚ᵹᵄߩવ៝ㅦᐲ㧘cߪశㅦ㧘

Ib.peakߪᐔမᄢ࿾㔗᠄ᤨߩᩮరㇱ㔚ᵹߩࡇ࡯ࠢ୯ߢ

޽ࠆ㧚ߎࠇࠄߩ2ᑼࠃࠅ㧘

2

2 0

. .

b p e a k z p e a k

I c d E

v

| S H (10a)

2

. .

b p e a k p e a k

I c d H

v ^M

| S (10b)

߇ᓧࠄࠇࠆ㧚ߎࠇߪ㧘ᐔမᄢ࿾㔗᠄ᤨߩ᷹ⷰ㔚⇇ࡇ

࡯ࠢ୯߅ࠃ߮⏛⇇ࡇ࡯ࠢ୯ߦၮߠߊ㔗㔚ᵹࡇ࡯ࠢ୯ ߩផቯᑼߢ޽ࠅ㧘LLSߢ↪޿ࠄࠇߡ޿ࠆ㔚ᵹផቯߩ ၮᧄᑼߢ޽ࠆ㧚

㔗᠄㜞᭴ㅧ‛㗂ㇱߩ㔚ᵹ╙ ࡇ࡯ࠢ୯ ߣ㆙ᣇ㔚⏛⇇ࡇ࡯ࠢ୯ߩ㑐ଥᑼ

Fig. 3ߩ㔚ᵹᵄᒻߣFig. 5ߩ㔚⇇ᵄᒻ߅ࠃ߮Fig. 6 ߩ⏛⇇ᵄᒻࠍ⷗Ყߴࠆߣ㧘㔚⇇߅ࠃ߮⏛⇇ߩࡇ࡯ࠢ

ߪh/cએౝߩᤨ㑆▸࿐ߢ↢ߓߡ޿ࠆ㧔hߪ㔗᠄᭴ㅧ‛

㜞ߐ㧘cߪశㅦ㧕㧚ߎߩߎߣߪ㧘㔚⇇㧘⏛⇇ߩࡇ࡯ࠢ

ߪೋᦼߦ㜞᭴ㅧ‛㗂ㇱߦᵹࠇࠆࡇ࡯ࠢ୯㧔╙1ࡇ࡯

ࠢ㧕ߢ᳿߹ࠅ㧘ᄢ࿾㕙ߢߩ෻኿ᵄߦᓇ㗀ߐࠇߥ޿ߎ ߣࠍ␜ߒߡ޿ࠆ㧚ߎߩߎߣ߆ࠄ㧘㜞᭴ㅧ‛ߩ╙1ࡇ

࡯ࠢ㔚ᵹItop1.peakߣ㆙ᣇ㧔d >> h㧕ߢߩု⋥㔚⇇ߩࡇ

࡯ࠢ୯Ez.peak߅ࠃ߮Mᣇะ⏛⇇ߩࡇ࡯ࠢ୯HM.peakߣߩ

㑆ߦߪᰴᑼ߇ᚑ┙ߔࠆ㧚

1 1

2 2

0 0

2 2

. . .

z peak top peak top peak

v c

E I I

c d c d

SH SH

| (11a)

1 1

2 2

.p e a k to p .p e a k t o p .p e a k

v c

H I I

c d c d

M ^| S S (11b)

਄ᑼߩ╙1㗄⋡ߪ㧘㜞᭴ㅧ‛㗂ㇱ߆ࠄ਄ะ߈ߦㅦᐲ vߢવ៝ߔࠆ㔚ᵹᵄߦ⿠࿃ߒߚ㔚⇇ߢ޽ࠅ㧘╙2㗄

⋡ߪ㜞᭴ㅧ‛㗂ㇱ߆ࠄਅะ߈ߦㅦᐲcߢવ៝ߔࠆ㔚 ᵹᵄߦ⿠࿃ߒߚ㔚⇇ߢ޽ࠆ㧚ߎࠇࠄߩ2ᑼࠃࠅ㧘

2 0 1

2

. .

t o p p e a k z p e a k

I c d E

v c

| S H

(12a)

1

2

. .

to p p e a k p e a k

I c d H

v c ^M

| S

(12b)

߇ᓧࠄࠇࠆ㧚ߎࠇࠄߪ㧘㜞᭴ㅧ‛㔗᠄ᤨߩ᷹ⷰ㔚⇇

ࡇ࡯ࠢ୯߅ࠃ߮⏛⇇ࡇ࡯ࠢ୯ߦၮߠߊ㜞᭴ㅧ‛㗂ㇱ 㔚ᵹߩ╙1ࡇ࡯ࠢ୯ߩផቯᑼߢ޽ࠆ㧚ᐔမᄢ࿾㔗᠄

ࠍኻ⽎ߣߒߚ(10a)㧘(10b)ᑼߣᲧߴࠆߣ㧘ᄌ឵ଥᢙߪ ߘࠇࠄߩv/(v+c) ୚ߣߥߞߡ޿ࠆ㧚଀߃߫㧘v=c/3ߩ ߣ߈ߦߪ㧘ߎߩᲧߪ0.25ߣߥࠆ㧚

Fig. 3 ߦ␜ߒߚ㔗᠄㜞᭴ㅧ‛㗂ㇱ㔚ᵹᵄᒻߩ╙ 1

ࡇ࡯ࠢ୯ߣ(12a)߹ߚߪ(12b)ᑼࠍ↪޿ߡ㆙ᣇ㔚⇇߹

ߚߪ⏛⇇ࡇ࡯ࠢ୯߆ࠄផቯߒߚ㔚ᵹࡇ࡯ࠢ୯ࠍ

Table 2ߦ␜ߔ㧚Table 2ߦ߅޿ߡ㧘┙ߜ਄߇ࠅᤨ㑆߇

0.18 Ps ߩ႐ว㧘ᬌ⸛ߒߚోߡߩ㜞᭴ㅧ‛ߩ㜞ߐ

㧔h=100, 160߅ࠃ߮553 m㧕ߦ߅޿ߡ㧘㔚⇇߅ࠃ߮

⏛⇇ࡇ࡯ࠢ୯߆ࠄផቯߒߚ㜞᭴ㅧ‛㗂ㇱߩ╙1ࡇ࡯

ࠢ୯ߪታ㓙ߩࡇ࡯ࠢ୯㧔7.5 kA㧕ߣ߶߷৻⥌ߒߡ޿

ࠆ㧚ߒ߆ߒ㧘┙ߜ਄߇ࠅᤨ㑆߇1 Psߩ႐ว㧘h=553 m

Table 2. First peak current values evaluated from Fig. 3 and those estimated using approximate expression (12a) or (12b) in kiloamperes of lightning current at the top of a tall object of different heights h=0, 100, 160, and 553 m.

Risetime = 0.18 Ps Risetime = 1.0 Ps Object

height, h Actual current

Estimated from field

Actual current

Estimated from field

100 m 7.50 7.45 10.1 5.40

160 m 7.50 7.52 10.6 6.61

553 m 7.50 7.56 7.49 7.56

ߦ߅޿ߡߩߺ߶߷৻⥌ߒߡ޿ࠆ߇㧘ߘࠇએᄖߩ႐ว ߦߪᄢ߈ߊ⇣ߥߞߡ޿ࠆ㧚ߎࠇߪ㧘(7)ᑼ޽ࠆ޿ߪ

(12a)㧘(12b)ᑼ߇㧘㔗㔚ᵹߩ┙ߜ਄߇ࠅᤨ㑆߇ 2h/c

ࠃࠅዊߐ޿႐วߦߩߺᚑࠅ┙ߟㄭૃᑼߢ޽ࠆߚ߼ߢ

޽ࠆ㧚

㔗᠄㜞᭴ㅧ‛㗂ㇱߩ㔚ᵹ╙ ࡇ࡯ࠢ୯ ߣ㆙ᣇ㔚⏛⇇ࡇ࡯ࠢ୯ߩ㑐ଥᑼ

㜞᭴ㅧ‛ߢ᷹ⷰߐࠇߡ޿ࠆ㔗㔚ᵹࡇ࡯ࠢ୯ߩ⛔⸘

࠺࡯࠲ߪᦨᄢ୯ߣߥࠆ╙2ࡇ࡯ࠢ୯ߦ㑐ߔࠆ߽ߩ߇

߶ߣࠎߤߢ޽ࠆߚ߼㧘E_z㧘H_Mߩࡇ࡯ࠢ୯߆ࠄ㗂ㇱ㔚 ᵹߩ╙2ࡇ࡯ࠢ୯ࠍផቯߢ߈ࠇ߫ታ↪਄᦭↪ߢ޽ࠆ㧚 (7)㧘(8)ᑼࠃࠅ㧘㔗㔚ᵹߩ┙ߜ਄߇ࠅᤨ㑆߇h/cࠃ ࠅዊߐ޿႐ว㧘㗂ㇱ㔚ᵹߩ╙2ࡇ࡯ࠢ୯ߪᰴᑼߩࠃ ߁ߦㄭૃߐࠇࠆ㧚

2

1

1 2 1

1

. .

. t o p

t o p p e a k s c p e a k

b o t b o t t o p

b o t b o t t o p t o p p e a k

I I

I U

U U U

U U U

|

u

(13)

(12a)㧘(12b)߅ࠃ߮(13)ᑼࠃࠅ㧘

2

1 2

. .

top peak bot bot top z peak

I c d E

v c U U U SH

|

(14a)

2

1 2

. .

top peak bot bot top peak

I cd H

v c ^M

U U U S

|

(14b)

߇ᓧࠄࠇࠆ㧚ᐔမᄢ࿾㔗᠄ࠍኻ⽎ߣߒߚ(10a)㧘(10b) ᑼߣᲧߴࠆߣ㧘ᄌ឵ଥᢙߪ(1+U_bot + ̓U_bot̓U_top) v/(v+c)

୚ߣߥߞߡ޿ࠆ㧚଀߃߫㧘v=c/3,̓ Ubot=0.9㧘Utop =í0.5 ߩߣ߈㧘ߎߩᲧߪ0.36ߣߥࠆ㧚ߎࠇߪ㧘CN࠲ࡢ࡯

㗂ㇱઃㄭߢߩ⋥ធ᷹ቯ㔚ᵹࡇ࡯ࠢ୯㧔╙2ࡇ࡯ࠢ୯㧕 ߣLLSߦࠃࠆផቯ୯ߩᲧ㧔ᐔဋ0.38㧕³⁾ߦ㕖Ᏹߦㄭ

޿㧚

Fig. 3 ߦ␜ߒߚ㔗᠄㜞᭴ㅧ‛㗂ㇱ㔚ᵹᵄᒻߩ╙ 2

ࡇ࡯ࠢ୯ߣ(14a)߹ߚߪ(14b)ᑼࠍ↪޿ߡ㆙ᣇ㔚⇇߹

ߚߪ⏛⇇ࡇ࡯ࠢ୯߆ࠄផቯߒߚ㔚ᵹࡇ࡯ࠢ୯ࠍ

Table 3ߦ␜ߔ㧚Table 3ߦ߅޿ߡ㧘┙ߜ਄߇ࠅᤨ㑆߇

0.18 Psߩ႐ว㧘㜞ߐh=100߅ࠃ߮160 mߩ᭴ㅧ‛㗂

ㇱߩ╙2ࡇ࡯ࠢ୯ߣ㔚⇇߹ߚߪ⏛⇇ࡇ࡯ࠢ୯߆ࠄផ ቯߒߚ㔚ᵹࡇ࡯ࠢ୯ߪ߶߷৻⥌ߒߡ޿ࠆ㧚h=553 m ߩ႐วߦߩߺ㧘ਔ⠪߇߿߿⇣ߥߞߡ޿ࠆߩߪ㧘(8)ᑼ

޽ࠆ޿ߪ(14a)㧘(14b)ᑼ߇㧘Isc(h, t)߇ࡇ࡯ࠢᓟ߶߷৻

ቯ୯ࠍ଻ߟ႐วߦߩߺ᦭ലߥㄭૃᑼߢ޽ࠆߩߦኻߒ㧘 Isc(h, t) ߩᵄᒻ⥄૕߇ࡇ࡯ࠢᓟߦ✭߿߆ߦᷫ⴮ߔࠆ ߚ߼ߢ޽ࠆ㧔Fig. 2ෳᾖ㧕㧚

Table 3. Second peak current values evaluated from Fig.

3 and those estimated using approximate expression (14a) or (14b) in kiloamperes of lightning current at the top of a tall object of different heights h=0, 100, 160, and 553 m.

Risetime = 0.18 Ps Risetime = 1.0 Ps Object

height, h Actual current

Estimated from field

Actual current

Estimated from field

100 m 10.6 10.8 — —

160 m 10.4 10.9 — —

553 m 9.24 11.0 9.70 11.0

㔗᠄㜞᭴ㅧ‛⣉ㇱߩ㔚ᵹࡇ࡯ࠢ୯ߣ

㆙ᣇ㔚⏛⇇ࡇ࡯ࠢ୯ߩ㑐ଥᑼ

(6)㧘(7)ᑼࠍ↪޿ࠆߣ㧘㔗᠄㜞᭴ㅧ‛⣉ㇱߩࡇ࡯ࠢ

㔚ᵹIbot.peakߪᰴᑼߢ⴫ߐࠇࠆ㧚

. .

bot peak bot top peak

I U I (15)

ߎߎߢ㧘(12a)㧘(12b)߅ࠃ߮(15)ᑼࠍ↪޿ࠆߣ㧘

. .

b o t p e a k b o t z p e a k

I c d E

v c

U S H

(16a)

. .

b o t p e a k b o t p e a k

I c d H

v c ^M

U S

(16b)

߇ᓧࠄࠇࠆ㧚ߎࠇࠄߪ㧘㜞᭴ㅧ‛㔗᠄ᤨߩ᷹ⷰ㔚⇇

ࡇ࡯ࠢ୯߅ࠃ߮⏛⇇ࡇ࡯ࠢ୯ߦၮߠߊ㜞᭴ㅧ‛⣉ㇱ 㔚ᵹࡇ࡯ࠢ୯ߩផቯᑼߢ޽ࠆ㧚ᐔမᄢ࿾㔗᠄ࠍኻ⽎

ߣ ߒ ߚ(10a)㧘(10b)ᑼ ߣ Ყ ߴ ࠆ ߣ 㧘 ᄌ ឵ ଥ ᢙ ߪ (1+Ubot)v/(v+c)୚ߣߥߞߡ޿ࠆ㧚଀߃߫㧘v=c/3, ̓Ubot=0.9 ߩߣ߈㧘ߎߩᲧߪ0.48ߣߥࠆ㧚

Fig. 3 ߦ␜ߒߚ㔗᠄㜞᭴ㅧ‛⣉ㇱ㔚ᵹᵄᒻߩࡇ࡯

ࠢ୯ߣ(16a)߹ߚߪ(16b)ᑼࠍ↪޿ߡ㆙ᣇ㔚⇇߹ߚߪ

⏛⇇ࡇ࡯ࠢ୯߆ࠄផቯߒߚ㔚ᵹࡇ࡯ࠢ୯ࠍ Table 4

ߦ␜ߔ㧚Table 4ߦ߅޿ߡ㧘┙ߜ਄߇ࠅᤨ㑆߇0.18 Ps

ߩ႐ว㧘ోߡߩ㜞᭴ㅧ‛ߩ㜞ߐߢ(16a)߹ߚߪ(16b) ᑼࠍ↪޿ߡផቯߒߚ㜞᭴ㅧ‛⣉ㇱߩ㔚ᵹࡇ࡯ࠢ୯ߪ

߶߷৻⥌ߒߡ߅ࠅ㧘ߐࠄߦFig. 3ߦ␜ߒߚ㜞᭴ㅧ‛

⣉ㇱߩ㔚ᵹࡇ࡯ࠢ୯ߣ߽߶߷৻⥌ߒߡ޿ࠆ㧚┙ߜ਄

߇ࠅᤨ㑆߇1 Psߩ႐วߦ߅޿ߡ߽㧘Ყセ⊛⦟ᅢߦ৻

⥌ߒߡ޿ࠆ㧚

Table 4. Peak current values evaluated from Fig. 3 and those estimated using approximate expression (16a) or (16b) in kiloamperes of lightning current at the bottom of a tall object of different heights h=0, 100, 160, and 553 m.

Risetime = 0.18 Ps Risetime = 1.0 Ps Object

height, h Actual current

Estimated from field

Actual current

Estimated from field

100 m 14.3 14.1 11.1 10.3

160 m 14.3 14.3 13.2 12.6

553 m 14.3 14.4 14.2 14.4

㧠㧚㆙ᣇ㔚⏛⇇ᵄᒻߦ߅ࠃ߷ߔᄢ࿾ዉ㔚₸ߩᓇ㗀 ᧄ┨ߢߪ㧘㆙ᣇ㔚⇇߅ࠃ߮⏛⇇ߦਈ߃ࠆᄢ࿾ዉ㔚

₸ߩᓇ㗀ߦߟ޿ߡ㧘ੑᰴర౞╴ᐳᮡ♽ߦ߅ߌࠆ FDTDᴺ⁷⁾ࠍ↪޿ߡᬌ⸛ࠍⴕ߁㧚

Ꮻㆶ㔗᠄߅ࠃ߮㔗᠄㜞᭴ㅧ‛ߪ╙2▵ߢ⺑᣿ߒߚ વㅍ✢〝ࡕ࠺࡞ߦࠃࠅ⴫⃻ߒ㧘Ꮻㆶ㔗᠄㔚ᵹᵄવ៝

ㅦᐲࠍv=c/3ߣ⸳ቯߒߚ㧚㔚ᵹᵄߩ10-90㧑┙ߜ਄߇ ࠅᤨ㑆ߪ1 Psߣߒߚ㧚FDTD⸘▚ߩߚ߼ߩ60 km × 20 kmߩ⸃ᨆⓨ㑆㧔ᐔ㕙㧕ߪ㧘৻ㄝ10 mߩᱜᣇᒻ࠮࡞

ߢಽഀߒߚ㧚߹ߚ㧘ᄢ࿾ߩෘߺߪ⴫⊹ᷓߐ (SfVP)^-1/2 (f=1 MHz, Vҏ=1 mS/mߢ16 m, Vҏ=0.1 mS/mߢ50 m)ࠃ ࠅ߽లಽߦᄢ߈ߊ⸳ቯߒߚ㧔1 km㧕㧚ᄢ࿾ቯᢙߪ㧘(i) ዉ㔚₸ ’㧘(ii) ዉ㔚₸V=10 mS/m㧘Ყ⺃㔚₸H_r=10㧘 Ყㅘ⏛₸P_r=1㧘(iii) V̓=1 mS/m㧘H_r=10㧘P_r=1㧘(iv) V=0.1 mS/m㧘Hr=10㧘Pr=1 ߣ⸳ቯߒߚ㧚ߘࠇߙࠇߩ႐วߦ ߅޿ߡ㧘㜞᭴ㅧ‛ߩ㜞ߐ h=0㧔ᐔမᄢ࿾㔗᠄㧕߅ࠃ

߮550 mߣߒ⸃ᨆࠍⴕߞߚ㧚߹ߚ㧘ធ࿾ࠗࡦࡇ࡯࠳

ࡦࠬߪZgr=30 :, 㔗᡼㔚〝ࠍᮨᡆߔࠆવㅍ✢〝ߩ․

ᕈࠗࡦࡇ࡯࠳ࡦࠬߪ Zch=900 :, 㜞᭴ㅧ‛ࠍᮨᡆߔ ࠆવㅍ✢〝ߩ․ᕈࠗࡦࡇ࡯࠳ࡦࠬߪ Zob=300 :ߣߒ ߚ㧚ߒߚ߇ߞߡ㧘㜞᭴ㅧ‛ߩ⣉ㇱߢߩ㔚ᵹ෻኿ଥᢙ

-4 -2 0 2 4 6 8 10 12 14 16

0 10 20 30 40

Time [Ps]

Electric field [V/m]

perfect conductor 10 mS/m 1 mS/m 0.1 mS/m

(a) Ez at d=50 km for h=550 m

-20 -10 0 10 20 30 40

0 10 20 30 40

Time [Ps]

Magnetic field [mA/m] perfect conductor 10 mS/m 1 mS/m 0.1 mS/m

(b) HMat d=50 km for h=550 m

0 1 2 3 4 5

0 10 20 30 40

Time [Ps]

Electric field [V/m]

perfect conductor 10 mS/m 1 mS/m 0.1 mS/m

(c) Ez at d=50 km for h=0

0 5 10 15

0 10 20 30 40

Time [Ps]

Magnetic field [mA/m]

perfect conductor 10 mS/m 1 mS/m 0.1 mS/m

(d) HMat d=50 km for h=0

Fig. 9. Waveforms of vertical electric field Ez and horizontal magnetic field HM at a distance of 50 km from a vertical lightning channel on lossy ground for different conductivity values, calculated using the 2D-cylindrical

FDTD method.

U_botߪ0.9ߢ޽ࠅ㧘਄ะ߈ߩવ៝ᵄߩ㜞᭴ㅧ‛㗂ㇱߢ ߩ㔚ᵹ෻኿ଥᢙU_topߪí0.5 ߣߥࠆ㧚߹ߚ㧘⸘▚ᤨ㑆

ࠬ࠹࠶ࡊߪ10 nsߣߒߚ㧚

d=50 kmߦ߅ߌࠆᄢ࿾⴫㕙ߩု⋥㔚⇇ᵄᒻEzߣM ᣇะ⏛⇇ᵄᒻHMࠍFig. 9ߦ␜ߔ㧚

ᤨೞ20 Psએ㒠ߩ㔚⇇㧘⏛⇇ߩᵄየㇱಽߦ߅޿ߡ ߪ㧘㔗㔚ᵹߩ┙ߜ਄߇ࠅᤨ㑆߅ࠃ߮ᄢ࿾ዉ㔚₸ߦଐ ሽߖߕ߶߷৻ቯߣߥߞߡ޿ࠆ㧚৻ᣇ㧘LLSߦ߅޿ߡ 㔗㔚ᵹߩࡇ࡯ࠢ୯ࠍផቯߔࠆ㓙ߦ↪޿ࠄࠇࠆ㔚⇇㧘

⏛⇇ߩᵄ㗡ㇱಽߩࡇ࡯ࠢ୯ߦߟ޿ߡߪ㧘ᄢ࿾ዉ㔚₸

ߩᓇ㗀ࠍฃߌߡ޿ࠆ㧚ᄢ࿾ࠍቢోዉ૕ߣ઒ቯߒߚ႐ วߦᲧߴߡ㧘ᄢ࿾ዉ㔚₸ࠍ10 mS/m㧘1 mS/m߅ࠃ߮

0.1 mS/mߣ⸳ቯߒߚ႐วߦߪ㧘㆙ᣇ㔚⇇㧘⏛⇇ߩࡇ

࡯ࠢ୯ߪ㧘ߘࠇߙࠇ5㧑㧘10㧑߅ࠃ߮50㧑⒟ᐲ߽ૐ ਅߒߡ޿ࠆ㧚ᐔမᄢ࿾߳ߩ㔗᠄ߩ႐วߦߪ㧘ᄢ࿾ዉ 㔚₸ߩᓇ㗀ߪૐᷫߐࠇࠆ㧚

એ਄ࠍ߹ߣ߼ࠆߣ㧘ᐔမᄢ࿾߳ߩ㔗᠄ߩ႐วߦߪ㧘

㆙ᣇ㔚⇇㧘⏛⇇ߩࡇ࡯ࠢ୯ߪ㧘ᄢ࿾ዉ㔚₸ߩᓇ㗀ࠍ ߘࠇ߶ߤฃߌߥ޿㧚৻ᣇ㧘㜞᭴ㅧ‛㔗᠄ߩ႐วߦߪ㧘 㔚⇇㧘⏛⇇ᵄᒻߩࡄ࡞ࠬ᏷߇ዊߐߊߥࠆߎߣߦ⿠࿃

ߒߡ㧘ᄢ࿾ዉ㔚₸ߩᓇ㗀ࠍࠃࠅᒝߊฃߌࠆߚ߼㧘વ

៝ߦࠃࠆᷫ⴮߽⠨ᘦߒߥߌࠇ߫ߥࠄߥ޿ࠤ࡯ࠬ߇Ⴧ ߃ࠆߣ⠨߃ࠄࠇࠆ㧚

㧡㧚⚿⸒

ᧄ⺰ᢥߢߪ㧘㜞᭴ㅧ‛߇ሽ࿷ߔࠆ႐วߩᏫㆶ㔗᠄

ߩવㅍ✢〝ࠍ↪޿ߡ㧘㆙ᣇ⏛⇇߅ࠃ߮㆙ᣇ㔚⇇ࡇ࡯

ࠢ୯ߣ㜞᭴ㅧ‛㗂ㇱߦ߅ߌࠆ㔗㔚ᵹߩ╙1ࡇ࡯ࠢ୯㧘 㔗㔚ᵹ╙2ࡇ࡯ࠢ୯߅ࠃ߮⣉ㇱߦ߅ߌࠆ㔗㔚ᵹࡇ࡯

ࠢ୯ߩ㑐ଥߦߟ޿ߡᬌ⸛ࠍⴕ޿㧘㆙ᣇ⏛⇇߹ߚߪ㔚

⇇ࡇ࡯ࠢ୯߆ࠄ㔗᠄㜞᭴ㅧ‛਄ߩ㔚ᵹࡇ࡯ࠢ୯ࠍផ ቯߔࠆᑼߩዉ಴ࠍⴕߞߚ㧚

㔗᠄㜞᭴ㅧ‛߇ሽ࿷ߔࠆ႐ว㧘ߘߩ⣉ㇱ߅ࠃ߮㗂 ㇱߢߩ෻኿ߩᓇ㗀ߢ㧘㔗㔚ᵹᵄᒻ߿ࡇ࡯ࠢ୯ߪ㧘᭴

ㅧ‛਄ߩ૏⟎ߦࠃߞߡᄌൻߔࠆߎߣࠍ␜ߒߚ㧚㔚ᵹ ᦨᄢ୯ߪ⣉ㇱߢ↢ߓ㧘ᐔမᄢ࿾㔗᠄ᤨߩᩮరㇱ㔚ᵹ ߩ1.4 ୚⒟ᐲߦ߽ߥࠆ㧚㗂ㇱߦ߅޿ߡߪ㧘ᄢ࿾㕙߆ ࠄߩ෻኿ᵄߩᓇ㗀ߦࠃࠅࡇ࡯ࠢ୯ߪ2ᐲ↢ߓ㧘╙2 ࡇ࡯ࠢ߇╙1ࡇ࡯ࠢࠃࠅᄢ߈ߊߥࠅ㧘ߘߩ୯ߪᐔမ ᄢ࿾㔗᠄ᤨߩᩮరㇱ㔚ᵹߩࡇ࡯ࠢ୯ߦㄭߊߥࠆ㧚㆙

ᣇ⏛⇇߅ࠃ߮㔚⇇ߪ㧘ᐔမᄢ࿾߳ߩ㔗᠄ᤨߦᲧߴ㜞

᭴ㅧ‛㔗᠄ᤨߦ߅޿ߡߪ㧘⚂3୚ߣߥࠆ㧔Ꮻㆶ㔗᠄

ᵄߩવ៝ㅦᐲ߇శㅦߩ1/3ߩ႐ว㧕㧚ߎࠇࠄߩߎߣ߆ ࠄ㧘ᐔမᄢ࿾㔗᠄ࠍኻ⽎ߣߒߚ㑐ଥᑼࠍ㧘㜞᭴ㅧ‛

㔗᠄ߦ⿠࿃ߒߚ㆙ᣇ⏛⇇߹ߚߪ㆙ᣇ㔚⇇ߩࡇ࡯ࠢ୯ ߆ࠄ㔗㔚ᵹߩࡇ࡯ࠢ୯ࠍផቯߔࠆߩߦㆡ↪ߔࠆߩߦ ߪේℂ⊛ߥ໧㗴߇޽ࠆ㧚

ߘߎߢ㧘㔗᠄㜞᭴ㅧ‛߇ሽ࿷ߔࠆ႐วߩ㆙ᣇ⏛⇇

ߩࡇ࡯ࠢ୯ HM.peak߅ࠃ߮㆙ᣇ㔚⇇ߩࡇ࡯ࠢ୯ Ez.peak

߆ࠄ㜞᭴ㅧ‛ߩ㗂ㇱߦ߅ߌࠆ㔗㔚ᵹ╙ 1 ࡇ࡯ࠢ୯

Itop1.peak㧘㔗㔚ᵹ╙2ࡇ࡯ࠢ୯Itop2.peak㧘߅ࠃ߮ਅ┵ߦ

߅ߌࠆ㔗㔚ᵹࡇ࡯ࠢ୯Ibot.peakࠍផቯߔࠆߚ߼ߩℂ⺰

ᑼࠍዉ಴ߒߚ㧚଀߃߫㧘㗂ㇱߦ߅ߌࠆ╙2ࡇ࡯ࠢ୯ ࠍ ផ ቯ ߔ ࠆ ᑼ ߪ Itop2.peak=(1+Ubot+UbotUtop)2Scd

HM.peak/(v+c)㧔Ubotߪ㜞᭴ㅧ‛⣉ㇱߩ㔚ᵹ෻኿ଥᢙ㧘Utop

ߪ㗂ㇱߩ㔚ᵹ෻኿ଥᢙ㧘vߪᏫㆶ㔗᠄ᵄߩવ៝ㅦᐲ㧕 ߢ⴫ߐࠇࠆ㧚ߎߩផቯᑼߩଥᢙߣᐔမᄢ࿾㔗᠄ࠍኻ

⽎ߣߒߚផቯᑼIb.peak=2ScdH_M.peak/v㧔I_b.peakߪᐔမᄢ࿾

㔗᠄ߩ႐วߩᩮరㇱ㔚ᵹࡇ࡯ࠢ୯㧕ߩଥᢙߣߩᲧߪ (1+U_bot+̓U_bot̓U_top)v/(v+c)ߣߥࠆ㧚ߎࠇࠄߩផቯᑼࠍ↪޿

ߡ㧘㆙ᣇ㔚⇇߅ࠃ߮⏛⇇㧔50 km㆙ᣇ㧕߆ࠄ㔗㔚ᵹ ߩ┙ߜ਄߇ࠅᤨ㑆߇h/c㧔hߪ᭴ㅧ‛ߩ㜞ߐ㧘cߪశ ㅦ㧕ࠃࠅዊߐ޿႐วߩ㗂ㇱ㔚ᵹ╙1㧘╙2ࡇ࡯ࠢ୯ ߅ࠃ߮⣉ㇱ㔚ᵹࡇ࡯ࠢ୯ࠍផቯߒߚߣߎࠈ㧘ኻᔕ▎

ᚲߩታ㔚ᵹࡇ࡯ࠢ୯ߣ⦟ᅢߦ৻⥌ߒߚ㧚߹ߚ㧘㜞᭴

ㅧ‛㗂ㇱ㔚ᵹߩ╙2ࡇ࡯ࠢ୯ࠍផቯߔࠆᑼߣᐔမᄢ

࿾ 㔗 ᠄ ࠍ ኻ ⽎ ߣ ߒ ߚ ផ ቯ ᑼ ߣ ߩ Ყ (1+U_bot+̓U_bot̓U_top)v/(v+c)ߦv=c/3㧘U_top=í0.5㧘U_bot=0.9ࠍ ઍ౉ߔࠆߣ㧘0.36ߣߥࠅ㧘㜞ߐ553 mߩCN࠲ࡢ࡯

㗂ㇱߩታ㔚ᵹࡇ࡯ࠢ୯㧔╙2ࡇ࡯ࠢ㧕ߣ⪭㔗૏⟎ᮡ

ቯࠪࠬ࠹ࡓLLSߦࠃࠆផቯ㔚ᵹߩᲧ㧔ᐔဋ0.38㧕ߣ

⦟ᅢߦ৻⥌ߔࠆߎߣࠍ␜ߒߚ㧚ߎߩߎߣߪ㧘㜞᭴ㅧ

‛㔗᠄ࠍኻ⽎ߦ LLS ߩ㔚ᵹផቯᑼߩ⹜㛎߿ࠠࡖ࡝

ࡉ࡟࡯࡚ࠪࡦࠍⴕ߁ߩߪ޽߹ࠅㆡಾߢߪߥ޿ߎߣ㧘

޽ࠆ޿ߪߎߩࠃ߁ߥ⹜㛎ࠍⴕ߁႐วߦߪ㧘ᧄ⺰ᢥߢ ዉ಴ߒߚᑼࠍ↪޿ࠆᔅⷐߩ޽ࠆߎߣࠍ␜ߒߡ޿ࠆ㧚 ߥ߅㧘ᧄ⺰ᢥߢ␜ߒߚࠃ߁ߦ㧘㔗㔚ᵹߩ┙ߜ਄߇ ࠅᤨ㑆߇h/cߩᢙ୚ࠃࠅ㐳޿႐วߦߪ㜞᭴ㅧ‛ߩ㗂 ㇱ߅ࠃ߮⣉ㇱߢߩ㔚ᵹࡇ࡯ࠢ୯ߪᐔမᄢ࿾㔗᠄ᤨߩ

ᩮరㇱ㔚ᵹࡇ࡯ࠢ୯ߣ߶߷৻⥌ߔࠆߚ߼㧘ᐔမᄢ࿾

߳ߩ㔗᠄ࠍኻ⽎ߣߒߚᓥ᧪ߩ㔚ᵹផቯᑼࠍㆡ↪ߒߡ

߽㧘⦟ᅢߦ㔗㔚ᵹࠍផቯน⢻ߢ޽ࠆ㧚㜞ߐ100 mߩ

࠲ࡢ࡯ߩ㗂ㇱߢߩታ᷹㔚ᵹߩࡇ࡯ࠢ୯ߣᓥ᧪ߩ㔚ᵹ ផቯᑼߢផቯߐࠇߚࡇ࡯ࠢ୯ߣߩ⋧㆑߇ 2㧑߅ࠃ߮

12㧑⒟ᐲߣዊߐ޿ߩߪ㧘ߎࠇ߇ℂ↱ߢ޽ࠆ㧚 ᧄ⎇ⓥࠍⴕ߁ߦ޽ߚࠅ㧘ߏᡰេ߅ࠃ߮ߏഥ⸒ࠍ⾦

ߞߚ㔎⼱ᤘᒄᢎ᝼㧘㐳ጟ⋥ੱᢎ᝼㧘᫪ᑧቁታ㛎⻠Ꮷ ߦᗵ⻢⥌ߒ߹ߔ㧚߹ߚ㧘ᧄ⎇ⓥߪ2007ᐕᐲหᔒ␠

ᄢቇℂᎿቇ⎇ⓥᚲ⎇ⓥഥᚑ㊄ߩ⵬ഥࠍฃߌߡⴕࠊ ࠇߚߎߣࠍ⸥ߒ㧘㑐ଥฦ૏ߦᗵ⻢⥌ߒ߹ߔ㧚

ෳ ⠨ ᢥ ₂

1) G. Diendorfer, and H. Pichler, “Properties of lightning discharges to an instrumented tower and their implication on the location of those flashes by lightning location systems,” Proc. 6th International Workshop on Physics of Lightning, Guadeloupe, France (2004)

2) G. Diendorfer, W. Schulz, and F. Fuchs, “Comparison of correlated data from the Austrian lightning location system and measured lightning currents at the Peissenberg tower,”

Proc. International Conference on Lightning Protection, Birmingham, UK (1998)

3) A. Lafkovici, A. M. Hussein, W. Janischewskyf, and K. L.

Cummins, “Performance analysis of the north American lightning detection network using CN tower lightning data,” Proc. 19th International Lightning Detection Conference, Tucson, Arizona, USA (2006)

4) Y. Baba, and V. A. Rakov, “On the use of lumped sources in lightning return stroke models,” J. Geophys. Res., vol.

110, no. D03101, doi: 10.1029/2004JD005202 (2005) 5) V. A. Rakov, “Lightning return stroke speeds,” J. Lightning

Res., vol. 1, pp. 80-89 (2007)

6) M. A. Uman, D. K. McLain, and E. P. Krider, “The electromagnetic radiation from a finite antenna,” American Journal of Physics, vol. 43, pp.33-38 (1975)

7) K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas and Propagation, vol. 14, no. 3, pp. 302-307 (1966)