... Exponential Rise Time NBE1, 20:24:14. VHF Power, log_e units. Amplitude, kb Exponential Rise, Fall Times 100 NBE1, 20:24:14

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1 3 NBE1, ::1 8 Exponentil Rise Time Amplitude, kb c Time, µ s NBE1, ::1 VHF Power, log_e units d Time, µ s Exponentil Rise, Fll Times Amplitude, kb - VHF Power, Ar.units Time, µ s 1 3 Time, µ s Supplementry Figure 1: Detiled time series dt for NBE1., INTF (lue) nd FA (red) wveforms for NBE1, showing clipping of the VHF signl y the digitiser. This did not ffect the ility of the INTF to determine the source directions, s the phse of the signls ws unchnged y the clipping., Exponentil increse in the VHF power during the first 1.5 µs of the NBE, prior to eing clipped. The red line corresponds to.3 µs initil rise time constnt. c, Expnded plot of the first few µs of the NBE, showing i) its rpid onset, ii) the simultneous occurrence of the FA sferic nd VHF rdition, indictive of the current eing produced y the rekdown, nd iii) the lck of detectle ctivity prior to the NBE onset. Both the VHF nd fst electric field signls were quiet down to the mient noise level of the INTF site, db elow their full scle mplitudes. The trnsient ripple in the FA wveform is due to periodic locl interference source, seen in Fig. d nd in Supplementry Fig.. d, Exponentil rise nd fll of the VHF power otined from the ttenuted VHF wveform present on the FA signl, digitised t the sme 18 MHz rte s the INTF signls. The overll rise nd fll time constnts were 1. nd.7 µs, respectively. 1

2 Supplementry Figure : Time series dt for NBE3., Overview of INTF nd FA wveforms., Expnded view of the first few microseconds of the NBE, showing its fst onset nd lck of prior ctivity, similr to NBE1.

3 Normlized Current.8... Doule exponentil current wveform NBE1 NBE3 Current, ka Current Along Brekdown Pth NBE1 NBE3 3 5 Time, µs 3 5 Distnce, m Supplementry Figure 3: Current wveforms., Doule exponentil current wveforms tht simulted the sferics for NBE1 nd NBE3, showing the difference in durtion of the two currents., Current versus propgtion distnce t successive µs time intervls, illustrting how the current for NBE3 ws sptilly more compct while the current for NBE1 ppered to e sptilly spred out reltive to the overll extent of the rekdown, consistent with the NBEs eing produced y succssion of rekdown events. 3

4 Altitude (km) 1 8 Lngmuir LMA on 5 Aug 13 :5:.3 :5:. :5:. :5:.8 1 Altitude (km) 8 - Est-West distnce (km) 8 North-South distnce (km) Supplementry Figure : LMA oservtions for the NBE flsh. Sme s Fig.1, except showing the first 1 ms of the ilevel IC flsh initited y NBE. Like NBE1, NBE (red circle) occurred t the se of the upwrd negtive leder of the flsh (green sources). The E-W nd N-S verticl projections show tht the negtive leder ws primrily verticl, consistent with the NBE lso eing verticl.

5 c E(t), V m -1 ; d = 5.3 km, h =. km I pk = ka, v = 9e+7 m s -1, z = 3 m, λ = 9 m, τ 1, =.5,.μs 5 3 NBE Oserved Rdition Induction Electrosttic Totl Qin, Coul * Qmom, C m/ Time, µs d s Current, ka 5 3 Doule exponentil current wveform Time, µs Supplementry Figure 5: Detiled oservtions for NBE., Overview of the INTF nd FA oservtions., Expnded view of the initil 7 µs of the NBE, showing i) the reltively grdul onset of the VHF ctivity, ii) the retrogressive upwrd development of the initil rekdown, iii) severl ttempted downwrd events s the dischrge intensified, nd iv) the lck of ctivity prior to the NBE s onset. c,d, simultion of NBE s sferic nd the two-pulse current wveform used in the simultion (see min text). 5

6 ΔE (V m -1 ) c Supplementry Figure : Initil ctivity of the NBE flsh., Detiled INTF nd FA oservtions for the first ms of the IC flsh initited y NBE, illustrting the two-stge nture of the negtive rekdown: i) grdul upwrd development during the 1.5 ms-durtion initil electric field chnge (IEC), ii) the fine structure of the first initil rekdown pulse (IBP) following the IEC, iii) the occurrence of the second NBE (downwrd ornge sources) t the eginning of the IBP, nd iv) the ccelerted upwrd development ssocited with the IBP.,c, INTF source loctions in the pln projection plne (Supplementry Fig. 15) nd in zimuth-elevtion formt, showing the upwrd negtive rekdown two-dimensionlly. The IEC (lue nd green sources) extended the dischrge 5 m t n estimted speed of 3 5 m s 1, nd the IBP (yellow nd red sources) extended the dischrge similr dditionl distnce t 1 m s 1. In this nd other figures, the INTF sources re coloured y time nd nd sized logrithmiclly y power.

7 18m 17m Supplementry Figure 7: Detiled INTF dt for NBE1., First 5 µs of NBE1, s in Fig. except expnded in time to etter illustrte the ltitude vriility of the NBE VHF sources, indictive of succession of rekdown events.,c, Projection plne nd zimuth-elevtion plots of the VHF sources, showing i) tht the NBE rekdown occurred t constnt zimuth, consistent with the positive rekdown eing verticlly downwrd, nd ii) tht the rdition sources following the NBE were directly ove the NBE strt point, consistent with eing produced y the onset of negtive rekdown. The horizontl distnce scle in pnel c) indictes the zimuthl rc length t the pln distnce of the dischrge. The elevtion scle corresponds to verticl distnce rther thn rc length. See Supplementry Fig. 1 for the uncertinty of the source loctions. 7

8 18m 19m Supplementry Figure 8: Detiled INTF dt for NBE., Expnded view of first 5 µs of the flsh (see lso Fig. 3 nd Supplementry Figs. 5 nd ).,c, Projection plne nd zimuth-elevtion loctions of the VHF sources. While the downwrd prt of the NBE occurred t constnt zimuth, the post-nbe sources ssocited with negtive rekdown hd lredy developed slightly wy from the strting region of the NBE. See Supplementry Fig. 17 for the uncertinty in the INTF source loctions. 8

9 m 1m Supplementry Figure 9: Detiled INTF dt for NBE3., Expnded time plot of the first 5 µs of the flsh (Fig. ).,c, Projection plne nd zimuth-elevtion loctions of the VHF sources, showing sustntil zimuthl spred in the VHF sources, oth during nd following the NBE, indictive of the positive rekdown eing lterlly distriuted, nd lso tilted somewht from verticl. See Supplementry Fig. 18 for the uncertinty in the INTF source loctions. 9

10 1 1 Lightning Initition Loctions 1 1 IC (51) NBE/INTF () NBE/LMA (9) NBE/(LMA) (3) Lightning Initition Heights y, km 8 Altitude, km 8 c 1 1 IC (51) NBE/INTF () NBE/LMA (9) NBE/(LMA) (3) INTF Site 5 x, km Lightning Initition Loctions d Time, min fter : CG (5) NBE/INTF (5) NBE/LMA () NBE/(LMA) (1) Lightning Initition Heights y, km 8 Altitude, km 8 CG (5) NBE/INTF (5) NBE/LMA () NBE/(LMA) (1) INTF Site 5 x, km Time, min fter : Supplementry Figure : Initil LMA sources for ll lightning flshes in the 5 August NBE storm. (Supplement to Fig. 5),, Pln loctions nd initition ltitudes vs. time for the IC flshes. c,d, Sme, except for CG flshes. NBEs 1 nd occurred in the concentrtion of events 5 km immeditely NE of the INTF (pnel ). NBE3 occurred s the first nd closest of three clustered IC flshes in smll susequent cell tht developed 3 km immeditely NNW of the INTF. The pln loction results show the tendency for IC flshes to hve their initition confirmed y INTF oservtions (red squres) when they were close to the INTF (lck tringle), ut this decresed with incresing distnce, due lrgely to the INTF recording eing triggered less often y ICs unless close. Due to the LMA s lrge deployment nd coverge re, it detected IC nd CG flshes eqully well independent of loction, llowing the initition of mny of the IC flshes to e identified from the LMA dt lone (ornge circles). By contrst, the monopolr electric field chnge of CG flshes enled INTF recordings to e triggered for most of the CG flshes nd to e used in their initition determintion. Of the 7 totl flshes, triggered the INTF recording, with 1 of 5 CG flshes eing so recorded, compred to 1 of 51 IC flshes. Note the cler demrction of the initition ltitudes of IC nd CG flshes, with the ICs typiclly eing initited etween 8 km MSL nd negtive CGs etween km. Severl susidence episodes occurred during the hour-long storm, during which time coupled ltitude decreses were seen in the CG nd IC initition heights. The episode etween nd 3 minutes ws ssocited with intensfied lightning ctivity nd the first two NBEs.

11 Altitude (km) 1 Lngmuir LMA on Aug 13 IC PC1 3:15: 3:15: 3:15: 3:15: 3:15:8 3:15:3 Altitude (km) Lngmuir LMA on Aug 13 1 c PC3 Low-lt. IC d IC 3::31 3::33 3::35 3::37 Altitude (km) 1 1 (+) 1 PC1 IC 8 (--) pts lt-histogrm Altitude (km) (+) 1 PC3 c 8(--) (--) 8 d (+) pts lt-histogrm North-South distnce (km) PC IC North-South distnce (km) 5-5 PC3 d 5-5 PC Est-Westdistnce (km) Altitude (km) -5 5 Est-Westdistnce (km) Altitude (km) Supplementry Figure 11: Precursor events on August., Lightning ctivity during s intervl etween 3:15: nd 3:15:3, showing the occurrence of precursor PC1 of Fig. (yellow circles) nd two other short-durtion dischrges, in reltion to the preceding nd susequent lightning flshes., Sme, except etween 3::31 nd 3::37, showing the occurrence of PC3 of Fig. (ornge circles). These nd the other circled PC events were cptured in the preflsh intervls of INTF recordings triggered y the susequent flshes. PC1 occurred immeditely ove the periphery of horizontlly extensive CG flsh tht followed s lter (red sources). PC3 occurred 1 s efore ilevel IC flsh (red sources), short distnce wy from the IC s upwrd chnnel nd immeditely elow upper positive chrge dischrged y the IC. Precursor d ws n uncommon low-ltitude event tht occurred 1.5 s efore nd immeditely elow midlevel negtive chrge dischrged y the IC. 11

12 Supplementry Figure 1: Detiled oservtions of the screening dischrge., Expnded time series dt for the temporlly-seprted upwrd positive rekdown events t the eginning of the ms-durtion screening dischrge of Fig. c, showing the retrogressive downwrd development of the successive events (dshed rrow)., Additionlly expnded dt for the first three events, showing the pprent speeds of the first nd second dischrges. Ech successive event hd decresed verticl extent ut slightly stronger pek VHF ctivity. c,d, Sptil development of the VHF rdition sources in zimuth-elevtion formt during the initil 5 nd 5 µs of the dischrge, respectively. Although the dischrge ws t 11.7 km pln distnce, due to its gret height (1. km), it ws ner 5 elevtion ngle reltive to the INTF t 3. km MSL. Uncertinties in the INTF source loctions re shown in Supplementry Fig.. 1

13 Source power sequence, IC events (NBE Storm) Source power sequence, PC events (NBE Storm) c Source power sequence, CG events (NBE Storm) VHF Power, dbw 3 VHF Power, dbw 3 VHF Power, dbw Time, µs fter initil source Time, µs fter initil source d Metric spce, IC events (NBE storm) e Metric spce, PC events (NBE storm) f 8 Time, µs fter initil source Metric spce, CG events (NBE storm) dbw Difference, P1 P (db) 3 dbw Difference, P1 P (db) 3 dbw Difference, P1 P (db) Log ( χ ) of initil source ν Log ( χ ) of initil source ν Log ( χ ) of initil source ν Supplementry Figure 13: Detiled nlysis of LMA dt for the 5 August 13 flshes. c, VHF source power sequences for the first 8 µs of the IC, PC, nd CG dischrges (sme s Fig. 7 c for August, except for the hour-long NBE storm). d f, Sme, except showing the oservtions in the metric spce of Fig. 7d f. Fewer PCs were produced y the NBE storm thn during the 3.5 min intervl of the August storms, ut the metrics indicted nerly ll were NBE-initited. Lrger numers of CG dischrges hd negtive first nd second source power differences P, nd thus were clssified s eing undetermined y the metric. As noted in connection with Fig. 7, this is likely n rtifct of rpid intensifiction of the rekdown. A lrger frction of ICs were indicted s eing NBE-initited metric-wise. 13

14 NBE1, mesurement t LBB, 97 km NBE3, mesurement t LBB, 97 km Digitil units Digitil units Time, microseconds c NBE, mesurement t LBB, 97 km Time, microseconds Digitil units Time, microseconds Supplementry Figure 1: Distnt sferic comprisons., Comprison of the simultion-predicted (red) nd oserved (lck) sferic for NBEs 1 nd 3 (Fig. ) t the 5-km distnt Luock, Texs sttion of the Los Almos Sferics Arry (LASA), 1 documenting tht the model-estimted rdition component for the NBEs is consistent with the distnt sferic. The predicted sferic tkes into ccount propgtion effects over finitely-conducting erth. The greement indictes the NBEs were verticlly oriented (horizontl rekdown would e strongly ttenuted t the mesurement distnce). c, Sme, except for NBE, simulted in Supplementry Fig. 5. The secondry pulse of the NBE sferic is not seen t the Luock sttion. Its mplitude my e overestimted in the simultion or its cuse not fully understood. 1

15 cos β. cos β cos α cos α Supplementry Figure 15: INTF source loction exmple., Direction cosine projection plne of the INTF oservtions, illustrting how the rdition sources re locted. The rrivl time differences etween pirs of ntenns constrins the source to lie long stright lines in the direction cosine plne, perpendiculr to the selines. The intersection of the lines gives the direction of the source. Geometriclly, the direction cosine plne corresponds to the equtoril plne of unit celestil hemisphere centered on the ntenn rry. 3, The inscried circle corresponds to the horizon nd its center to the zenith. The dshed circles correspond to 3 nd elevtion ngles nd shows tht the interferometer loctes sources less well elow 3 elevtion. The zimuth nd elevtion ngles re otined y projecting the solutions in the direction cosine plne up onto the celestil hemisphere., Zoomed-in view of the intersection. Noise nd/or multiple sources cuse the lines not to hve common intersection, ut to outline tringulr region. The solution is otined from lest-squre fit of the lines nd lies within the tringle. The size of the tringle provides mesure of the uncertinty in the source direction. For the exmple shown, the time differences of rrivl t the three selines were (τ 1, τ 3, τ 31 ) = (+.9,.15,.19) µs. The mximum nd minimum zimuth ngles were 5.8 nd.5 nd the elevtion ngles were nd , corresponding to pek-to-pek uncertinties of 1. in zimuth nd 1. in elevtion round the lest-squre vlue. For point source nd noise-free oservtions, the three time differences (i.e., the closure dely τ 13 going round the rry) dd to zero. For the exmple shown, the time differences dd to τ 13 =.7 µs, or.7 ns. The uncertinties provide mesure of the comined effects of noise nd non-loclized rdition sources. The oservtions indicte the uncertinty is primrily due to multiple sources rther thn ckground noise (e.g, Supplementry Figs. 1 nd 17). 15

16 18m 17m Supplementry Figure 1: Source loction uncertinties for NBE1. Sme s Supplementry Fig. 7, except showing the elevtion nd zimuth uncertinties of the VHF source loctions (lck verticl lines in pnel nd crosses in pnel c). For clrity, the uncertinties re overlid on top of the VHF sources in pnel ) nd ehind the sources in pnel c). Sources with centered dots in pnel ) hve smll uncertinty. The noticele increse in the elevtion uncertinty following the NBE (pnel ) nd lso in zimuth (pnel c) is due primrily to the negtive rekdown hving multiple sources, rther thn to their reduced power nd signl to noise rtio. This is seen from the first two sources t the eginning of the NBE eing s wek or weker thn the post-nbe ctivity, yet hving very smll elevtion uncertinties (..3 ). It indictes the initil rekdown of the NBE ws highly loclized, nd illustrtes the limiting ccurcy of the INTF mesurements. The elevtion uncertinties remin reltively smll during the initil prt of the downwrd NBE, ut increse for some of the sources towrd the end of the NBE, consistent with the ctivity occurring t multiple ltitudes. The sudden elevtion increse just fter. ms ( µs) is significnt uncertinty-wise nd coincides with the eginning of the prtil field recovery, further supporting the result tht the recovery signls the current hving died out eyond this time. 1

17 18m 19m Supplementry Figure 17: Source loction uncertinties for NBE. Sme s Supplementry Fig. 1, except for NBE. Agin, the uncertinties of the wek rdition t the eginning of the NBE re smll, indicting the initil rekdown ws highly loclized, nd providing seline for the uncertinty cused y ckground noise. The reltively smll uncertinties of the sources during the downwrd NBE indicte tht it ws primrily monotonic event, consistent with the NBE s nrrower current pulse (Supplementry Fig. 3). 17

18 m 1m Supplementry Figure 18: Source loction uncertinties for NBE3. Sme s Fig. 1, except for NBE3. The zimuthl uncertinty of the post-nbe negtive rekdown is noticely lrger, indictive of the rekdown hving wider horizontl extent. The zimuthl vriility is lso significntly lrger thn for NBEs 1 nd. 18

19 ΔE (V m -1 ) c d ΔE (V m -1 ) Supplementry Figure 19: Elevtion uncertinties for the INTF oservtions of the intermedite- nd weker-strength NBEs of Fig.. 19

20 ΔE (V m -1 ) c d ΔE (V m -1 ) Supplementry Figure : Elevtion uncertinties for the precursor nd screening dischrges of Fig. nd Supplementry Fig. 1.

21 Supplementry Note 1. Positive stremer speeds Experimentl studies of positive stremers in ir mesure their speeds to e one or two orders of mgnitude elow the oserved speeds of the fst positive rekdown. The highest reported speed is m s 1, mesured y Briels et l. 5 with 9 kv pulse cross cm point to plne gp t mient pressure. An pproximte verge vlue for the non-uniform electric field would e.5 m s 1, comprle to the rekdown strength of ir (3. V m 1 ). Allen nd Mikropoulos mde detiled oservtions of the speed of positive stremers in uniform electric field, nd investigted how the propgtion speed vried with the mient field E. The uniform field ws provided y prllel plte rrngement hving 1 cm gp. They expressed the oservtions in terms of the minimum field E st required to initite stle stremer, clled the stility field, nd the corresponding stility velocity v st of the resulting stremer. An electric field E st = 91 δ kv m 1 ws required to produce stremer of miniml initil energy, where δ is the frctionl ir density reltive to stndrd tmospheric conditions. The ssocited propgtion speed ws v st = m s 1. For stronger fields, the stremer speed v str ws well-fitted y cuic power lw dependence on E, ccording to ( ) E 3 ( ) E/δ 3 v str = v st = (1.5 5 ) E st.91 5 m s 1. (1) The mesurements were mde t mient pressure with electric fields etween 5 nd 8 kv m 1. The speed corresponding to 8 kv m 1 ws etween 5 nd 5 m s 1, depending on the mplitude nd durtion of the pulse used to initite the stremers from recessed point in the ground plne ( nd kv, nd 135 nd 7 ns, respectively). The question of interest is whether t stronger fields the cuic reltion would contine to hold, nd whether the propgtion speed cn rech the oserved vlues otined for the fst positive rekdown. To nswer the question it is instructive to evlute (1) for the stremer speed tht would e predicted if E is ssumed to e the rekdown field E k = (3. ) δ V m 1. Clling this speed v k, the nswer is tht the density dependence cncels, giving ( ) 3. v k = ( ).91 5 = m s 1. () Remrkly, this is the sme s the speeds of NBEs 1 nd 3, nd is close to the speeds estimted for the lesser-power dischrges. It is sed entirely on empiricl dt from lortory oservtions mde t ground level nd over restricted rnge of E field vlues. Agreement with the oservtions of the present study suggests tht (1) is vlid for fields up to nd possily eyond rekdown, nd tht the fst positive rekdown occurs t or ner E k, independent of ltitude. Tken t fce vlue, E/E k would e slightly ove unity when v str > v k, nd slightly less thn unity for v str < v k. In the super-criticl cse (e.g., for NBE or for the screening dischrge), the rekdown might e expected tke the form of n ioniztion wve rther thn discrete stremers. While this might hppen in some circumstnces, it should e noted tht the vlue of v st in (1) pplies to stremers hving miniml initil energy, nd tht the speeds for given vlue of E re incresed y fctor of two for initil energies corresponding to reltively smll potentils of kv (Fig. of Allen nd Mikropoulos). The oserved speeds would then e ttined t fields somewht elow rekdown. Overll, the picture tht emerges is tht positive stremers t the eginning of dischrge intensify the electric field up to or ner rekdown, nd then continue s result of self-generted field enhncement hed of the stremer system 7. Allen nd Mikropoulos showed tht the stremer speed stilized within few cm of eing initited, nd noted prticulrly tht speed invrince through the reminder of the gp indicted tht rnching hd negligile effect on the results. 1

22 Supplementry Note. Shortly efore this pper eing ccepted, Shi et l. 8 reported modelling results tht support the findings nd inferences of the present study tht the fst positive rekdown is stremer-sed. Their findings extend results otined in the erlier study y Liu et l. 9 to show tht positive stremers ) cn e initited from isolted hydrometeors t resonle mient field strengths nd storm ltitudes, ) exhiit exponentil growth up to speeds of m s 1 over short distnces ( MV potentil difference), nd c) develop oscilltory fluctutions in their wke tht would rdite in the high (HF) nd very high (VHF) frequency regimes. Supplementry References 1. Smith, D. A. et l. The Los Almos Sferic Arry: A reserch tool for lightning investigtions. J. Geophys. Res. 7, ACL ().. Stock, M. A. Brodnd interferometry of lightning. Ph.D. Disserttion, N.M. Inst. Mining & Tech., Socorro (1). 3. Rhodes, C. T., Sho, X. M., Krehiel, P. R., Thoms, R. J., & Hyeng, C. O. Oservtions of lightning phenomen using rdio interferometry. J. Geophys. Res. 99, (199).. Stock, M. G. et l. Continuous rodnd digitl interferometry of lightning using generlized cross-correltion lgorithm. J. Geophys. Res. Atmos. 119, (1). 5. Briels, T. M. P., Kos, J., Winnds, G. J. J., vn Veldhuizen, E. M. & Eert, U. Positive nd negtive stremers in mient ir: mesuring dimeter, velocity nd dissipted energy. J. Phys. D 1, 3 (8).. Allen, N. L. & Mikropoulos, P. N. Dynmics of stremer propgtion in ir. J. Phys. D 3, (1999). 7. Eert, U. & Sentmn, D. D. Stremers, sprites, leders, lightning: From micro- to mcroscles. J. Phys. D 1, 331 (8). 8. Shi, F., Liu, N. & Rssoul, H. Dynmics of reltive long positive stremer from n isolted hydrometeor. AGU Fll Annul Meet., Astrct AE1A-1 (15). 9. Liu, N., Kosr, B., Sdighi, S., Dwyer, J. R. & Rssoul, H. K. Formtion of stremer dischrges from n isolted ioniztion column t surekdown conditions. Phys. Rev. Lett. 9, 5 (1).