Journal of Research of the National Bureau of Sta ndards-D. Radio Propaga tion Vol. 63D, No.2, September- October 1959 Very-Low-Frequency Radiation Spectra of Lightning Discharges w. L. Taylor and A. G. Jean

(A pril 9, 1959) Spectral a nalyses are given of t he groundwa ve port ion of 33 sferic waveforms recorded from cloud-to-ground light ning discharges which occu rred at distances ranging between about 150 and 600 kilometers from Boulder, Colo. Frequencies of peak energy li e between 5 and 20 kilocycles p er second, which agree fa vorably wi t h other publi shed results. The average value of energy calculated from the groundwave pulses was found to be 26,600 joules, which is lower than va lu es derived from ot her experiments. Va rious param eters, such as the peak a mplitud e and duratio n of t he first half-cycl e, a re related to the radiated energy of the stroke. 1. Introduction 2. Equipment and Collection of Data Appleton et al. (1 92 6) were probably the first Sta tions at Boulder , Colo .; Salt La ke City, U tah ; workers to utilize the cathode-ray oscilloscope in and P alo Alto, Calif. ; were eq uippecl to record the stud ying the electromagnetic energy emitted from directions of arrival of atmospheric pulses, the lightning discharges. Following the developmen t pulse waveforms, and timing m arks from which the of radio communication techniques, it became times of arrival of individual pulses could be deter­ evid ent that the lightning discharge was the source mined. Atmospheric waveforms used in the spectral of interference to radio communication circuits . analyses were recorded from ver tical antennas. The In recent ~T ea r s, the radio signals emitted from overall amplitude response of the ver tical an tenna ligh tning disc harges, called atmospherics, or sferics, channel was constant within ± 1 db over the band­ have been utilized as a source of signals in propaga­ pass and sloped to 3-db cutoff points at frequencies tion studies at very-low radiofrequencies . of 1 and 100 kc. The phase response of this channel Various workers in England h ave been particularly closely approximated a linear function of frequency active in the u tili zation of sferics in propagation wi thin t he bandpass. studies, and it would be difFi ('.ul t and exhaustive A pair of vertical electrostatically shiclded loop to properly credi t all of tht lr accomplishments. an tennas, arranged at right angles to each other, However, as the work continued, it was learned were used in a direction-finding system a t each tha t some atmospheric waveforms could be in ter­ station. The overall bandpass of each loop-an tenna preted in te rms of the recep tion of a seri es of pulse channel extended from 1 to 100 kc, and closely ap­ due to successive refl ections between the ea r th proximated t hat of the vertical-an tenna channel. and th.e ionosphere. I t became eviden t that the The direction-Ending indications were ob tained charaeter of the atmospheric waveform observed using the en tire bandwidth of the loop-an tenna at great distances was materially altered by the channels. It was determined in earlier experi­ propagation eff ec ts, while at shorter ranges, the men ts [2] with wideb and direc tion finders, that in waveform was more represen tative of the source many cases the groundwave componen t of the fun ction. atmospheric could be discerned from the Sky wclve At the present time the use of atmospherics in components by virtue of differences in polarization propagation studies at the very-low radiofrequencies and times of arrival of the groundwave and skywave is common. NBS Boulder Laboratories havc es­ pulses.2 A time resolution of approximately 10 tablished a network: of stations [1]1 for this purpose, Msec is afforded by the wideband direction-finder , and the material presented in this paper resulted which is adequate to resolve the groundwave and from t he simultaneous observation of atmospherics skywave pulses. The direction of arrival of the at the Bureau recording sites. atmospheric, as indicated by the ver tically polan zed The obj ective of this paper is to present data groundwave component, should be virtually free on Fourier spectra of the electric fi eld strength of from error due to the presence of horizon tally polar­ signals radiated from return-stroke lightning di s­ ized componen ts in the atmospheric. charges. The radi ation spectra of lightning dis­ Timing marks derived from a secondary frequency charges were determined from observations of the standard, synchronized with the standard timing groundwave portion of the atmospheric. The pre­ emissions from station WvVV, were recorded on the cautions taken in identifying and utilizing ground­ atmosp heric waveform records. Using these timing wave pulses for this purpose arc described in this 2 E xcellent discussions regarding the lo cation of sforic sources through tho usc paper. o[ radio direetion.flllding have appeared in the literature: Ilorner [31. in particu­ lar, has discussed the probable sources of error in dircction.(jnding, in cluding that resulting from the reception of hori ~onta ll y polarized components of iono­ 1 Figures in braCkets indicate the literature references at the end o[ this paper. spheri C waves. 199

----' marks, the timc of arrival of atmospherics could be the induction field at frequencies near 1 kc. It was determined at each station to an accuracy of about desirable to limit the maximum observation range ± 1 msec. Atmospheric waveforms resulting from in order to minimize the distortion of the ground­ a particular lightning discharge were locat.ed on the wave pulse by propagation and to reduce the inter­ photographic records made at each station by virtue ference caused in the groundwave by the first-hop of their times of reception and directions of arrival. skywave pulse. The sweep of the oscilloscopes used in recording the The waveforms of two sferics, representative of atmospherics was activated by signals having those used in this analysis, are reproduced in figure amplitudes of about 50 mv/m or greater. Signals of la. The range to the source is approximately 165 smaller amplitude did not activate the sweep and km from both sferics 1 and 2. The groundwave therefore were not recorded. This feature provided portion of sf eric 1 is believed to comprise the first some discrimination against atmospherics of rela­ 110 I"sec of the approximate 450-.usec time base. tively low amplitude; such as those of distant origin The earliest evidence of the arrival of the first-hop as well as some local cloud-to-cloud and precursory skywave pulse in sferic 1 occurs at 147 I"sec. Note discharges. To minimize loss of early detail in the that the initial half cycle of the skywave pulse is waveform, a 24··l"sec delay line was used to delay negative, or opposite to the polarity of the first recording the signal un til after the sweep was initi­ half-cycle of the groundwave pulse. This reversal ated. The dynamic range of the recording equipment, in polarity of the initial part of the first-hop skywave in terms of the strength of a vertically polarized wave pulses evident in figures la and Ib is a consequence incident at the monopole antenna, extended from 0.2 of the pseudo Brewster angle in ionospheric reflec­ to 6 vim. Most of the analyzed atmospherics had tion. This phenomenon was discussed in an earlier peak field amplitudes approaching 1 vim. paper [1]. The locations of lightning discharges were deter­ The height of the ionospheric reflection was mined by triangulation, using the direction of arrival calculated to be about 65 km, corresponding to a indicated at each station. Due to the geometric range of 165 km and a 147-l"sec time interval between arrangement of the 3-station network, the locations the reception of the groundwave and the first-hop sky­ of lightning discharges which occurred near a record­ wave pulses. In this calculation, the ionosphere ing station are relatively inaccurate; however, for was assumed to be a homogeneous ionized medium distances greater than about 150 km, the error is with a sharp lower boundary [4]. estimated to be equal or less than 10 percent of the Note that sferic 2 is similar in character to sferic range. 1, but the groundwave is of larger amplitude and It was desired to identify waveforms on the photo­ longer duration. The first-hop skywave pulse was graphic records that res ulted from vertical lightning received before the entire groundwave pulse was discharges. Two tests that were used in an attempt recorded. It was necessary in such cases to complete to achieve this selection are described below. The the groundwave pulse as indicated by the dotted line relative amplitude of the vertical component of the before undertaking the spectral calculations. Since a electric field which would be registered at the appro­ very small fraction of the total area enclosed by the priate ranges from a vertical discharge was calculated waveform is contained under the sketched-in por­ using range information available from the direction­ tion, the error introduced into the spectral calcula­ finding "fixes," and from groundwave propagation tions is small. curves in the literature [15]. The source was con­ Waveforms of sferics 17 and 18/ which were re­ sidered to be vertically polarized if the relative ceived at ranges of 460 km under nighttime condi­ values of the observed and calculated pulse ampli­ tions, are given in figure lb. Note that in these tudes agreed within about 20 percent. 3 Numbers were assigned to the atmospherics in order of their selection for If a vertically polarized wave arrives at grazing analyses and each number associates an atmospheric with its spectrum. Sferics 1, 2, 17, and 18 were selected to represent the variability encountered in the incidence, the direction-finder response will approxi­ reception of the gronndwave pulses. The waveforms of the remaining atmos· mate a straight line inclined at an angle proportional pheries (sferies 3 through 16 and 19 through 33) are not presented in this report. to the azimuthal direction of arrival of the wave. +I .O ~-~-~-~-~ An incident wave consisting of both horizontal and +0.5 vertical components of the electric field will cause an elliptical direction-finding pattern to be produced. SF ERl e NO.17 The direction-finder responses to the atmospheric SFERle NO. I pulses which were selected for analyses indicated that the groundwave pulses were vertically polarized, and the first-hop skywave pulses were essentially, but not entirely, vertically polarized. Atmospheric SFERle NO. IS waveforms which satisfied both the "amplitude" SF ERie NO. 2 and "ellipticity" criteria outlined above were as­ sumed to result from vertical lightning discharges. (a ) (b) No sferics were analyzed which originated at 100 200 3011 400 0 100 100 300 400 distances less than 150 kill from Boulder, due, in TI ME,fL sec part, to limitations in the accuracy of "fixes" at FIGU R E L Representative atmospheric wavefo rms. short ranges, and also to minimize contributions by

200 35 {!a e Lhe Lime in terval between reception of the DISTAN CE: groundwave and Lhe first-hop skywave pulses is ;0 460 km Ie) about 97 /l ec compared to an interval of 147 /lsec in 25 20 figure 1a. As a conseq uence of the shorter time inLerval between the reception of the groundwave 20 and first-hop skywave pulses, a larger portion of the 15 groundwave pulses are concealed by the skywave 10 pul es than for the sferics 1 and 2. Prior to perform­ ing the spectral analyses of the groundwave pulses for sferics 17 and 18, the trailing edges of the ground­ DISTANCES: wave pulses were sketched in as indicated. A larger 12 If) W 17 8 19 - 4 60 km error r esulted in such cases; e.g., the area under the N' 22 823- 6 00 km DISTANCE ; 10 - sketched-in portion in sferic 18 is approximately 13 19 23 percent of the total area enclosed by the waveform of the groundwave pulse; however, this error is not considered to be serious in the present analyses. The ionospheric reflection height for these nigh t­ E time observations was calculated to be abouL 80 km, "u ~ using a range of 460 km and a time interval between > :t ~5 .---r--.,.---,,--,--..,----, DISTANCE : reception of groundwave and first-hop skywave w 24 o pulses of 97 /lsec. => ~ ~ 70 ..----,--,---r-r---,---, 3. Data Analyses ::;: DISTANCE :

0(£) = 0, for t ~ O , 18 DISTANCE : Ih) and the end of the pulse occurs aL t= T so Lhat 16 620 km

35 ..---,--,---,--,--.,.----, I~ 0 (£) = 0, for t ? T. JII 400km 12 Id) 27 The complex spectrum of Lhe pulse can be represenLed 25 10 by the Fourier in Legral 20 15 F (J)= J~T e- i27r /l 0 (t )clt, (1) 10 where.f represenLs the freq ueney in cycles pel' second 7 10 20 41) and £ is the time in seconds after the beginning of FREQUENCY. kc the pulse. The complex spectral components of the atmos­ FIGURE 2. Amplitude spectl·a oj atmospherics (see text). pheric were calculated at intervals of 1 kc on an elec tronic compu tel'. The absolute value, IFU) I, of the spectra of the groundwave pulses of individual atmospherics are given in figures 2a through 2h. q.uenci es in figure 2 fall within this range of frequen­ Fourteen of the analyzed pulses were received under CleS. daylight conditions from a storm approximately 165 With a knowledge of the complex spectrum FU) km from Boulder, and 19 pulses were received under of a groundwave pulse observed at distance d1, and nighttime conditions from ranges varying betwee n of the appropriate values of earth co nstants, it is 400 and 620 km from Boulder . The approximate possible to calculate the spectrum JF(j) I of a ground­ range at which each pulse was observed is indieatE'd wave pulse at a differen t range, d2, usi ng methods on the appropriate figure. evolved by Wait [14] . This rigorous method was not The frequencies of maximum energy for I"E't urn followed in t his paper, due to t he complex nature of stroke lightning discharges have been reported by a the calculations and the lack of adequate informa­ number of different workers 4 Their separate finding;s tion co ncerning earth co nstants. The less rigorous indicate that the frequency peaks occur in t he 5- to method used in normalizing the spectra jF'(j) I to a 20-kc region. It will be observed that the p eak fre- common distance is described below. The atmospheric pulses were recorded at distances • It is difficult to adequately rererenee all or the a va ilable literature dealiJlg with this subject. A relV representative re rerences l5-12] have been selected. betwee n 150 and 600 km and t heir spectral peaks 201 were attained at frequencies near 10 kc. A uniform The energy density, Ed, of the transient G(t) IS earth, having a conductivity of about 10- 2 mho/m , represented in joules/meter 2 by was assumed to exist along the propagation paths. R eferring to the curves of groundwave amplitude versus distance [15], it is evident for these values of (2) earth conductivity, distance, and frequency, that the signal amplitude decreases approximately at the in­ It was assumed t hat the curren t at the source was verse distance rate. Accordingly, the individual a simple linear dipole oriented along the vertical axis. spectra were referred to a common distance of 1 km The radiation component of the dipole electric fi eld by increasing each spectral component in proportion is proportional to cos (J , where (J is the angle of eleva­ to the observation range. The spectrum shown in tion measured from the horizontal. The vlf energy, figure 3 is the average of the individual spectra nor­ E T , in joules, radiated into the atmosphere was ob­ malized to this distance. The deviation of the indi­ tained by integrating the energy density Ed over the vidual spectra from the average is not very large surface of the radiation pattern of the source. Thus, which seems to support evidence in the literature [12 , 13] that the radiation spectra of return-stroke ( 211' 11' /2 li ghtning discharges do not vary a large amount from E7'= Jo Jo Edr2 cos3(Jd(Jdc/> (3) event to event. The l-km value was selected as a matter of convenience; the spectrum in figure 3 is = 4/37rr2E d , not intended to represent the actual distribution of amplitude with frequency at that distance. where (J is t he angle of elevation measured from the horizontal, c/> is the angle measured in the equatorial plane, and r is the distance in meters from the source 10000 ,----,------,,---,----,------,------, to the point of observation. Values of energy represented by each of the pulses, lj 1000 calculated using expression (3), are given in table 1. o t- T ABLE l. Very-low-frequency energy radiated into the al1ros­ ~ phere by return-stroke lightning discharges ~ 4000 a: o" z ET ~ ~ 1000 Sferie groundwave recorded at B oulder ..3- durillg daylight July 7, 1959

km kc j L ______165 10.0 2.2)<.10' 2 ______1000 L-___L- __----l ___ L-_L- __----:L- __-; 165 5.0 6.2XlO' 3 ______165 9.0 l. 7XlO' I 1 10 10 40 L ______165 7.0 5.5XlO' FREQUENCY, kc 5 ______165 9.0 1.8X lO' 6 ______165 5.5 2.1 X lO' FIGU RE 3. Average of amplitude spectra, normalized to 1 km. 7 ______165 9.5 1.1X 1O' 8 ______165 10.0 1. 5X 1O' 9 ______10 ______165 6.0 4.3X lO' 165 6.0 8.8XlO' The peak amplitude of this spectrum occurs at a lL ______165 7.5 6.9XlO' 12 ______165 9.5 1.3X IO; frequency of 6.5 kc; at frequencies below the peak, 13 ______165 10.0 1. 5X lO' the spectral amplitude is proportional to the 0.4 14 ______165 9.5 5. 9X 10' power of the frequency, while at frequencies higher Sferic groundwave recorded at Boulder than the peak, the spectral amplitude decreases as during nigh ttime July 26, 1958 the inverse 1.5 power of the frequency. The total energy available in a lightning discharge 15 ______400 7.5 2.1XI0' has been estimated to be about 2X 10 17 ergs [16]. 16 ______400 6.0 6.5X IO' 3L ______400 8.5 2.0XlO' This large amount of energy is partitioned into a 33 ______400 8.5 5.5XI0' number of different forms; for example, some energy 17 ______460 6.5 4.5X lO' is req uired to ionize the gas in the discharge channel, 18 ______460 5.5 2.9XlO' 19 ______460 5.5 6.2X lO' a larger portion is liberated as frictional heat ~n t~e 20 ______460 7.0 3.1XlO' 2L ______460 7.0 1. .1 X 10' movement of gaseous components, and some IS eVI­ 32 ______460 5.5 9.3XlO' dent as electromagnetic radiation, etc. An appreci­ 22 ______600 15.5 i.9X lO' able part of the energy is consumed in "ground losses" 23 ______600 12.0 1.1X lO' 24 ______due to the flow of induced currents in the earth [17]. 620 5. 5 1.1XlO' For the purposes at hand, it was desired to esti­ 25 ______620 7. 0 9.2X lO' 26 ______620 6.5 6.4XIO' mate the amount of vlf radio energy radiated into 27 ______620 9.0 1. 3X IO' 28 ______620 8.5 9.6XlO' the earth's atmosphere (i. e., exclusive of earth loss e~) 29 ______620 8. 0 6.4X lO' by the lightning discharges. This form of energy IS 30 ______620 6.5 6. 3XlO' a very small portion of the total amount available. 202 The average of these values of energy is 26,600 j. 1.3 On another occa ion l1O ], sferics were received from ~E IT=3.5X I07fO - 4D th understorms in a fron tal region extending through 1.2 T exas, Louisiana, and Oldahoma. The average of I the total radiated energy values calculated from 0 seven of these sferics was about 250,000 j ; the indi­ vidual values range from 130,000 to 500,000 j. Laby, "'" 1.0 ~ 0 0 et al. [ll], reported the average value of energy radi­ 0 o 0 ated from 35 sferics observed in Australia was 200,000 0 _" 0.9 ~ j . It appears that the sferics used in the present 0 0 <.!> 0 0 0 work: res ulted from less energetic discharges than ·0 0 0 -1 0.8 ~ those reported by Taylor and by Laby. It is not o 0 0 at all certain that the energy value reported here is o c o~ representative of return-stroke discharges from thun­ 0.1 derstorms occurring in the Rocky Mountain area. However, part of the differences between the energy 10 4 values quoted might have resulted from differences ET(JOULE S) in thunderstorm characteristics, differences in topog­ "'" raphy, earth conductivity, etc. FIGU RE 4. Frequency of spectTal peak veTS us total radiated The importance of land elevation in determining energy. thunderstorm characteristics was pointed out by Loeb [18]. In general, the lightning discharges used in this analysis occurred over land of higher eleva­ 103 f-----j------+-----+---:7""""----I tion than those previously reported by Taylor. It is not known in what area of Australia the lightning g o fiashes OCCUlTed that were used in Laby's analysis. W N It is interesting to note that the ratio of the total ~ energy available in a lighting discharge to the values ~ 1011----",...-4::...... -----+-----1------j o of electromagnetic energy radiated in to the atmos­ z phere is as large as 10 5 or 106 . 1 Er =O.o12 E ~! x A wide variation was noted in the detail of the o E individual groundwave pulses; however, most of them w consisted of two half-cycles. The first half-cycles 1 0 ~---~~---~~---~---~ were larger in amplitude and shorter in d UJo ation 101 103 1 0~ 105 106 than the corresponding values in the second half­ E T(JOULES) cycle. These two characteristics of the first half­ FIGU RE 5. Pulse amplit1ide verS1iS toiall'adiated en ergy. cycle would be expected to control the total radiated energy to a cer tain extent. After normalizing the observations to a l-km range, the relationships existing between various parameters mentioned above E were examined. Some of these comparisons are ~o 104~-----+-----~-~~--~-~ described below. w ~ -' (A) Frequency of spectral peak versus total radiated <{ ::;; energy. The relationship between the frequency of a: o z spectral peak (fo) and the total radiated energy (ET ) E is given in figure 4. Although the data points "- u scatter, there is a slight tendency for the more ~ 103 energetic sferics to attain energy peaks at the lower > frequencies. x"!:- ET = 0.0021 F(f)maxi'"8 o . (B) Peak amplitude oj sjerics versus total radiated E energy. The peak amplitude of the groundwave pulse (Emax) is plotted as a function of total radiated energy in figure 5. There is a close relationship be­ 102 ~----""""':------'-:------'-:--~ tween these parameters. The straight line drawn ~ ~ ~ ~ through the data points relate total radiated energy ET( JOULES) to the 2.4 power of the peak f"i eld str ength. FIGURE 6. Spectral peak verS1LS to/cll radiated energy. (C) Spectral peak versus total radiated energy. The relationship between the peak of the spectrum of the spectral peak. The frequency of the spectral the groundwave pulse, F(j)max, versus tbe total radi­ peak is not explicitly accoun ted for in this relation­ a ted energy of the pulse is given in figu re 6. A close ship. ~'elationship is indicated between these parameters. (D) L ength oj first half-cycle versus total radiated The straight line through the data poin ts indicates energy. In figure 7 the relationship between the that the energy is proportional to the l.8 power of length of the first half-cycle of the groundwave pulse 203 I termine values of propagation attenuation [10] and phase velocity of propagation [20 , 21]. f------

1.8 ------'-- The authors wish to acknowledge the mathematical 0 calculations made by L. J erome Lange and A. <) - Murphy, the preparation of the programing for the :x 1.7 1- o 0 :t rP V computer by H . H. Howe, and helpful conversations x ~ 0 ----- with Roger Gallet and J ames R. Wait during the 1.6 o 6' preparation of this paper. S'" ~ o 1.5 ~ 0 0 4. References 10- 13 lX '0.8 5 0 ~T '1I2 x [1) A. G. J ean, L . J. Lange, and J . R . Wait, I onospheri c 1.4 Y ~ refl ection coefficients at vlf from sferic measurements, Geofisica Pura e Appli cata 38, 147 (1957). I (2) R. A. H elliwell , A. G. Jean, a nd W. L. Taylor, Some 104 properties of lightning impulses which produce whistlers, Proc. IRE 46, 1760 (1958) . ET (JOU L ES) (3) F. Horner, The accuracy of t he location of sources of atmospherics by radio direction finding, Proc. Inst. FIG URE 7. L ength of first half-cycle vel·sus total radiated energy. Elec. E ngrs. (London) 101, Pt. III, 383 (1954) . (4) J. R. Wait and A. Murphy, Multiple reflections between (tx in microseconds) and the corresponding value the eart h a nd t he ionosphere in vlf propagation, Geofisica Pura e Applicata 35, 61 (1956). of total radiated energy is plotted. The r elative [5) C. E. R. Bruce a nd R. H . Golde, The light ning discharge, importance of the first half-cycle in determining J . Inst. Elec. Engrs. (London) 88, Pt. II, 487 (1941) . the energy is indicated in this plot and in figure 5, (6) H . Norinder, Variations of the electri c field in t he in which the peak amplitude of the groundwave vicini ty of lightning discharges, Arkiv Geofysik 1, 543 (1953). pulse is plotted as a function of total radiated (7 ) P. W. A. Bowe, Thc waveforms of atm ospherics and t he energy. propagation of very low frequency radio waves, Phil. The fi eld strength of a pulse is related to the rate Mag. r7] 42, 121 (1951) . of change of the source moment [1 3, 14, 19], hence, (8) F. W. Chapman and A. G. Edwards, Some observations on t he frequency spectrum of atmospheri c di st urbances flashes having rapidly rising curren ts would be due to t hundercloud discha rges a nd their effect on expected to produce sferics of high peak amplitude. resonant circuits, Proc. Union Radio Scientifi que The duration of the first half-cycle of the ground­ Internationale Comm. IV, No. 252 (1950) Zurich. wave pulse should correspond to the time at which (9) A. K impara, The typhoo n kezia a nd atmospherics, Proc. J apan Acad. 27, 366 (1951). the source current reached its maximum value. [10] W . L. Taylor a nd L . J. La nge, Some characteristics of H ence, sferics of large energy result from rapidly vlf propagation using atmospheric waveforms, Second Tising and long continuing source currents. It Conf. Atmospheric Elec. May 1958 (to be published would be expec ted that the more energetic discharges April 1959) . (11) T. H . Laby, J . J . McNeill , F . G. Nicholl s, and A. F. B. would produce sferics of longer duration, and a Nickson, Waveform energy a nd reflexion by the iono­ trong tendency of this nature is observed in the sphere of atmosphcrics, Proc. Roy. Soc. (London) clata; however, it was also observed that sferics [A)lH, l45 (1940) . representing l-elatively low values of energy attain (12) F. Chapman a nd R. C. V. Macario, Propagation of audio­ frcquency radio waves to great di stances, Nature 177, spectral peaks within the same frequency region, 930 (1956). 5- 20 kc, as those of larger en ergy . [13] A. D. Watt and E. L. Maxwell, Characteri stics of atmos­ The close relationship existing in figure 5 between pheri c noise from 1 to 100 kc, Proc. IRE 45, 787 (1957) . the peak amplit ude of the first half-cycle and total (14) J . R . Wa it, On the waveform of a radio atmospheric at short ranges, Proc. IRE 44,1052 (1956) . radiated energy suggests the possibility of gaining a (15) J. R. Wa it and H . H. Howe, Amplitude and phase curves useful estimate of energy by observing the peak for ground-wave propagation ill the band 200 cycles ampli tude of the groundwave pulse and by de­ per second to 500 kilocycles, NBS Ci rc. 574 (May 1956) . termining the distance to the fl ash. However, it is (16) C. W. All en, Astrophysical quantities, p. 123 (Univ. of London, Athlone Press , 1955). not known that this relationship will hold equally r17) J . R. Wait, personal communication. well at the higher energy levels. (18) L. B . Loeb, Thunderstorms a nd lightning strokes, p. 330 It would be of interest to compare the character­ Modern physics for the engineer by Royal Weller and istics of sferics originating (1) over land of different others (McGraw-Hill Book Co., Ncw York, 1954) . [19] H. A. Thomas and R. E. Burgess, Survcy of e x i ~ ting elevations and those originating over sea water, information and data on radio noise over the frequency and (2) from frontal and air-mass thunderstorms. ra nge 1- 30 Mc/s, D SIR Radio Research, Spccial This would aid in appraising the influence of topog­ Rept. 15, p. 38 (1947). raphy, earth conductivity, and meteorological factors [20) J. R. Wa it, Propagation of vcry-Iow-freq \l ency pulses to great distances, J . Rescarch NBS 61, 187 (1958) in determining the characteristics of sferics. RP2898. Atmospheric waveforms recorded at Boulder were (2 1) I a . L. AI'Pert and S. V. Borodina, Zhur . Ekspt l. i used in the presen t analysis. Simultaneous record­ TeOl·et. Fiz. (J. Exp. Theoret. Phys. U.S.S.R.) 33, ings of these atmospherics are also available from the 1305 (1957) . other stations located at Stanford and Salt Lake C ity. Analyses of this data is continuing to de- BOULDER, COLO. (Paper 63D2- 1S). 204