Oct 20, 1995 - rection finder with a technique to estimate the distance of the source. ..... CRDF is cathode-ray direction finder, and TPDF is time domain.
JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 100, NO. D10, PAGES 20,829-20,838, OCTOBER 20, 1995
Location of lightning dischargesfrom a single station V. A. Rafalsky,A. P. Nickolaenko, and A. V. Shvets Institute of Radio Astronomy, Ukrainian Academy of Sciences,Kharkov, Ukraine
M. Hayakawa SugadaizaSpaceRadio Observatory,Universityof Electro-Communications, Chofu, Tokyo, Japan
Abstract. A new computer-basedELF/VLF systemfor locatinglightning dischargeshas been developed.Both the arrival azimuthsof atmosphericsand the distancesto their sourcesare estimated.The direction-findingtechniqueusesthe Poyntingvector calculated directly in the time domain over the full band passof the receiver.Both the distanceof the lightningdischargeand the ionosphericheight can be estimatedfrom the phase spectrumof the first-ordermode of the Earth-ionospherewaveguide.The latter is approximatedwith a model function having the distanceand the height as the main parameters.Two wayswere appliedto obtain the spectrumof the first mode: the radial componentof the horizontal magneticfield was used,which containsonly a minor componentof the zeroth mode, or the mode decompositionproblem was solved.The systemhas been used to locate lightning sourcesin Africa and Asia from a scientificvessel during its voyagein the Atlantic and Indian Oceansin 1991. The overall uncertaintiesare estimatedto be a few degreesfor the sourcebearing,5% for distance,and 1% for the effectiveheight of the ionosphere;yet these estimatesneed an additionalconfirmationby comparisonwith independentand more exact techniques. 1.
Introduction
The problemof lightninglocationcanbe solvedby meansof either multistation or single-stationtechniques.Multistation techniquesare the most accurate,althoughthe facilitiesare of complicatedstructureand very expensive.They comprisea network of direction finders [Iwai et al., 1979; Krider et al., 1980; Orville et al., 1983; Hojo et al., 1989] or time-of-arrival sensors[Lewiset al., 1960;MacGormanand Rust, 1988]. It is much
more
convenient
to locate
the sources from
a
singlesite. Sometimesit is the only possibleway, e.g., for a systemon board an aircraft or a vessel.In this paper we will be concernedonly with single-stationtechniques. Single-sitelightninglocation systemsusuallycombine a direction finder with a techniqueto estimatethe distanceof the source.Accordingly,the presentwork includestwo relatively independentpartswhichare pertinentto directionfindingand distancefinding. Review of Direction-Finding Techniques
The historyof directionfinding(DF) for atmospherics began with the cathode-raydirectionfinder (CRDF) by Watson-Watt and Herd [1926]. This techniqueas well as almost all of more recent single-stationdirection finders are based on the measurementsof the full horizontalcomponentof magneticfield. This is measuredusuallyin a narrow frequencyband and is supposedto be ellipticallypolarizedwith the major axisof the polarizationellipsebeingorthogonalto the propagationdirection [see Heydt, 1982; Kononov et al., 1986, and references therein]. This basicassumptiondoesnot hold exactlyso that polarizationerrorsare the main problemsfor all single-station Copyright1995 by the American GeophysicalUnion. Paper number95JD01532. 0148-0227/95/95 JD-01532505.00
direction finders. There are two main causesof polarization errors [Yamashitaand Sao, 1974]:(1) deflectionof the source current from the vertical direction and (2) anisotropyof the Earth-ionospherewaveguide. The first cause dominates at closedistances,while the secondcauseis importantfor distant sources.
Some additional drawbacksarise when measuringthe azimuth of wideband sourcessuchas lightning dischargeswith a narrowbandreceiver.The first is that only a small part of the signalenergyis used,and the secondis the problem of selecting a properfrequency,becausedifferenttypesof atmospherics have a variety of spectrumshapesso that a universalobservation frequencycan hardly be found. A number of DF systemshave been proposedwith some differencesin the way of acquiringthe ellipseorientationin the coordinatesystemconnectedwith two orthogonalloop antennas.Adcock and Clarke [1947] suggestedthat only the initial part of the signalbe utilized for this purpose.This kind of simpletime domainprocessing enablesthe polarizationerrors to be reduced,providedthe time delaybetweenthe directwave and the wave reflectedonce from the ionosphereexceedsthe processingtime of the direction finder. The most commonly used systems[e.g.,Krider et al., 1976] apply this method. To derive the sourcebearing, Leavitt [1975] used Poynting vectormeasurements performedin the time domain,after the whistler signal passed through a narrowband filter. This methodaswell as the "full wave analysis"techniqueproposed by Okada et al. [1977] provide more accurateazimuth measurements,but both were developedfor quasi-monochromatic signalslike whistlersand therefore cannotbe applied directly to widebandsubionospheric signals. BurkeandJones[1992]usedthe three-fieldcomponentspectra of the ELF atmospherics (5-50 Hz) to constructthe Poynting vector and determine the sourcebearings. In this paperwe proposea new DF techniquefor ELF/VLF
20,829
20,830
RAFALSKY
ET AL.: SINGLE-SITE
atmosphericsbased on the time domain processingof three
LOCATION
OF LIGHTNING
This is accomplishedby meansof three-componentfield re-
fieldcomponents (horizontal magnetic H•candHy andvertical ception(verticalelectricand two orthogonalhorizontalmagelectricEz) in a wide frequencyband that is equivalentto the integrationof the Poyntingvector over all frequencies. Review of Distance-Finding Techniques
netic components)usingthe time domainPoyntingvector direction-findingprocedure,which is describedbelow, followed by the simulatedpivotingof the magneticantennaesystem.
The simplest among the single-sitedistancefinding techniquesis based on amplitude information [seeHorner, 1960; Ryan and Spitzer,1977; Kononov et al., 1986, and references therein]. In terms of this techniquethe amplitude of the incident atmospheric is supposedto be a function only of the distancefrom the lightning and assumesthat all sourceshave the same strength.Of course,the accuracyof suchmeasurements cannot be very high because of differencesbetween individual dischargecurrent moments within a thunderstorm
wherethe asteriskdenotescomplexconjugationand E(to) and It(to) are the frequencycomponentsof full electricand mag-
center or between
netic fields, derived from the time domain fields via Fourier
the centers.
A group of techniques,called E-H field analysis,uses a relationshipbetweenthe electric and magneticcomponentsof the near field [Runhke,1971;Kononovet al., 1986]or frequency dependenciesof such components[Korol and Nickolaenko, 1993]. Techniquesof this kind in principle are effectivefor short distanceswith the upper range limit of the order of 100 km.
2. Basic Concept of Time Domain Poynting Vector Direction-Finding Technique (TPDF) We considerthe Poyntingvector as follows: P(to) = Re[E(to) x H*(to)]
(1)
transformation:
E(to)=f E(t)e'•øtdt, H(to)=f••H(t)el•øtd (2)
Sao and Jindoh [1974] derived the distancesto distant sourcesusingthe delaybetweenthe arrival timesof ELF and VLF componentsin the "slow tail" atmospherics. We introducea "full" Poyntingvectorasan integralof P(to) An atmosphericwaveformis a set of multireflectedimpulses in the frequencydomain from the Earth and ionosphere.For some signalsthe reflections are distinguishableenough to obtain the time delays (3) between them. These delayscan be used to estimate the distance to the source, especiallythe delay between the direct wave and one-hopwave [seeLeafy, 1968].Unfortunately, only The magnitudeof thisvector describesthe total energyflux a small fraction of atmosphericscan be treated in this way. density, while its orientationindicatesthe averagedirectionof Hayakawa and Shimakura [1992] estimatedthe range to distant thunderstormsusing the temporal dependenceof the energyflow. The aboveequationsallow the followingtransformations: apparent signalfrequencyin tweek atmospherics.They simulated a pseudosferichaving two main parameters:reflection heightand distance.A comparisonbetweenthe two frequencytime dependenciesprovided estimatesof both the model pa-
H=fP(,o) d,o.
rameters.
A numberof techniquesare basedon the phasespectrumof atmospherics[see Inkov, 1973; Heydt, 1982, and references therein]. Systemsof this kind usuallycomprisethree narrowbandfilterswith equallyspacedcentralfrequenciesin the band 5-10 kHz. By measuringphasesin the channels,the parameter knownasthe groupdelaydifference(GDD) is obtained,which is supposedto be proportional to the distance.The coefficient of the proportionalityis taken from a model simulation.Two problemsare inherentin this approach.First is the assumption that the signalcomprisesa singlewaveguidemode. This is not adequatein many cases,especiallyfor propagationin nighttime conditions and/or excitation with a nearly horizontal source.The secondproblem is that the field phaseand correspondingGDD value of the first-order mode (supposedto dominateat the frequenciesof 5 to 10 kHz) dependsubstantially on the ionospheremodel. The new distance-findingtechniquedescribedin this paper alsobelongsto the phase-spectrumclass.To get rid of higherorder waveguidemodes, the frequency band is selectedbetween the cutoff frequenciesof the first- and second-order modes (1.9-3.2 kHz for nighttime conditions).Interference from the zeroth mode is eliminatedby selectingthe magnetic field componentwhichis parallel to the propagationdirection.
H--Ref [E(•o) xH*(•o)]d•o
(4)
The lastintegraloverdto is Dirac'sdeltafunction(5(t - •-); hencewe obtain finally the followingexpression.
II=f[E(t) xH(t)]dt The symbolRe is omitted here becausethe integrandis a real value.Equations(4) and (5) reflecta well-knownproperty of the integrals containing Fourier conjugate functions (Plancherelletheorem). When the field componentsare measuredat discretetime intervalsAt, the integralin (5) is replacedby a sum:
[l-- • [U(ti)X H(ti)]At.
(6)
RAFALSKY ET AL.: SINGLE-SITE LOCATION OF LIGHTNING
20,831
At a perfectly conductingground surface,only three field
components Hx, Hy, andEz remainnonzero,sothatwe have for the averageenergyflux:
source
IIx= - • Ez(t,) Hy(t,) At, l
IIy=• Ez(t,)Hx(t,)At. (7) l
The sourcebearing is found in the usual manner as the orientation of the vector which is oppositeto II. It is obvious now that one can acquirethe arrival direction in a wide frequencyband using direct time domain processing,obviating the tedious Fourier
transformation.
Omitting positive constantfactorswhich do not affect the sourcebearing,(7) can be rewritten as
x
IIx: - • Uz(t,)Uy( t,), l
IIy=• Uz( t,)Ux( t/),
Figure 1.
Coordinate system in the Earth-ionosphere
(8) waveguide.The x-y plane coincideswith the Earth surface,
l
whereUx, Uy, andUz aretheoutputvoltages of thechannels H x, Hy, andEz respectively. Relations(8) require that the followingconditionsbe satisfied: (1) the amplitudeand phaseversusfrequencycharacteristicsof the channelsare identical,and (2) the phaseversus frequency characteristicof channel is the same as for the H channels.The amplitudeversusfrequencycharacteristicof the E• andH channelsmay differ.To obtain (8), we modifiedthe initial definitionof the full Poyntingvector(3) to
while thez axisis directedupwardnormallyto the figureplane (not shown).
propagates.For a perfectlyconductingsystemthe phaseof this modeequalszero overthe entirewaveguide(SO - 1 in (11)) and is thereforeof no usefor distancefinding. In the frequencybandf• < f < f2(Af•2) the first-orderTM and TE modesalso propagate.The phaseversusfrequency dependenceof thesemodesaswell asof higher-ordermodesis determined by the quantitiesh and r. As we will see in the following,it is possibleto obtain the phasespectrumof the first-ordermode and match it with the functionof (11) to
11=f KE(oO)KH(oO)P(oo)doo, (9) estimate
whereKE(to) andKH(OO)are the amplitudeversusfrequency responsecharacteristics of the E• andH channels,respectively. This definitionis moreconvenientandnaturalwhenoperating with output voltagesrather than fields.
both h and r.
The radiationfieldsof the zeroth order (transverseelectromagnetic(TEM)) mode and higherTM modesarrivingfrom an arbitraryremote sourcelocatedwithin the waveguidehave threecomponents E•, H•,, andEr in the cylindrical coordinate
system of Figure1. The otherthreecomponents H•, E•,, and Hr correspondto TE modes. Thus two of the three nonvan-
3.
ishingfield components measuredon a perfectlyconducting groundplane,namelyEz andH•,, are the propertiesof TM
Basic Concept for Distance Finding
First, let us considera parallel plate and perfectlyconducting model of the Earth-ionospherewaveguide.Assumingan impulse•(t) as the sourcecurrent,the phaseof the nth mode of either the transversemagnetic(TM) or transverseelectric (TE) type is [Wait, 1962]
modes,while the third componentH r pertainsonly to the TE modes. Since TM waves do not have the zeroth-order mode,
we can use its phasespectrumfor the best fit procedure.It is apparentthat one shouldfirst solvefor the direction to enable calculatingthe waveformof the H,component. The aboveapproachremainsvalid for an arbitraryisotropic Earth-ionospherewaveguide.Equation (11) in this casemay whereSn = [1 - (n,r/kh)2]•/2, k - 2z'f/c is the wave be used as an acceptableapproximationto the phaseversus number,kSn is the horizontalcomponentof the wave vector, frequencyfunction.The valuesof S• are calculatedfrom the r is the source-observer distance,and h is the height of the dispersionequation [Wait, 1962] Earth-ionosphere waveguide.Equation(10) is valid when the 1 = RiRae -2tl•C"h (12) frequencyf exceedsthe n th cutoff frequencyof the guiding systemf• = nc/2h. The S• value is then real. whereRi andRe are the reflectioncoefficients fromthe ionIn practice,one never knowsthe actual time when a light- osphereandground,respectively, andCn = (1 - S•2)•/2 is ning dischargeoccurred;therefore we will relate the subse- the n th root of the modal equation(12). quent analysisto the time of the signalreception.In this case, The transcendentalequation(12) is solvednumericallyand (10) transformsinto remainsvalidbothfor TM andTE waveswhenthe appropriate Fn = krS n - 2 z'fr/c = kr( Sn - 1)
(11)
reflection
coefficients are substituted for the vertical and hor-
izontal wave polarizations,respectively.To find the reflection The first cutoff frequencyf• of the Earth-ionosphere coefficients, the usualtechniquehasbeen employedof layerwaveguidevariesfrom 1.5 to 2.5 kHz. At the frequencieslower by-layer impedance or admittance matrix recalculation than f• (referred to as Afol), only the zeroth-order mode [Budden,1961].
20,832
RAFALSKY
ET AL.: SINGLE-SITE
LOCATION
OF LIGHTNING
Figure 2 illustratesan example of atmosphericwaveforms receivedon January21, 1991, at 2031:46UT at geographical coordinatesof 19øSand 7øE (Guinea Gulf). The components in Figure 2 alreadycorrespondto r and ½directions,wherer is directedtoward the sourceand ½ is perpendicularto r (see
Figure1). The verticalscalesfor Hr andH, are equal.The components Ez andH, containa high-frequency initialpart,
2
4
6
whichHr doesnot have. The high-frequencyportion of the atmosphericis almost linearly polarized. Subsequently,the waveform of each componenttransformsinto a sequenceof multiple reflectedimpulseswith the repetitionfrequencyapproachingasymptoticallythe first cutoff frequencyf• of the Earth-ionosphere waveguide(about 1.7 kHz for this case). Amplitude spectraof the field componentsof this atmosphericare depictedin Figure 3 and indicatestronginterference betweenindividualwaveguidemodesproducingthe fine structureof the spectra.Sincethe phasedifferencebetweenthe modeschangeswith frequency,the spectracontainoscillating patternsbeginningat eachof the cutofffrequencies,the last of which are marked with arrows[seeNickolaenkoand Rafalsky, 1983]. An exceptionis the Af• 2 frequencyband for H• (the lowestplot), becausethisfield component,asexplainedabove, has very little of the zeroth mode. An analysisof the interferencepatternsreadilyprovidesan
8
estimate of the distance between
the source and observer. In
Time (ms)
fact, at a cutofffrequency,either of the Brillouin planewaves that composethe "new born" mode meets the waveguide boundariesnormally,sothat its phaseequalszero all alongthe waveguide.With increasingfrequencythe phaseof this mode increasesmore rapidly than that of the already propagating Hereinafter an exponentialmodel of the ionospherehas modes.At higherfrequenciesthe "newborn" modecatchesup been usedwith the followingelectrondensityprofile with the othersin phase.As this takesplace,the phasedifferN,, = 1 cm-3 e(z-h)/2 (13) ence changesfrom the value at the correspondingcutofffreFigure 2. Waveformsof three field componentsof an atmosphericreceivedon January21, 1991, 2031:46UT.
and effectiveelectron collisionfrequencyaltitude dependence
v,,/= 4 x 107s-• e(•'ø-z)/6'5, where h and z are measured
(14)
in kilometers.
To obtain the exactphase-frequency dependenceof a mode for both isotropicand anisotropicmodels,one shouldapplythe full expressionsfor the fields of a source.In doing so, the calculated dependence will vary slightly according to the source type.
4.
Measurement of Atmospherics
The experimentaldata used here were collectedon board the scientificvesselAcademician Vernadskyduring its 42nd expeditionthroughthe Atlantic and Indian Oceansduringthe period from Januaryto April 1991 [Lazebnyet al., 1992]. The verticalelectricand two orthogonalmagneticfield componentswere recordedsimultaneously. A kind of "ball antenna" [Ogawaet al., 1966] was usedfor the measurementof E z,
andtwoair coreloopswereusedfor theHx andH$ components. Three identical linear receiverswere used, one for each
channel,with a bandpassfrom 300 Hz to 13 kHz andproviding a gain of 50 dB. Received waveforms that exceededa fixed thresholdwere digitized with a 12-bit analog to digital computer (ADC) having the samplingrate of 100 kHz. Signal 2 4 6 8 10 waveforms2048 points long (20 ms) were then stored and Frequency (kHz) processedin a computer.The thresholdwas chosento record atmosphericsrelated to the most powerful lightning return Figure 3. Amplitude spectraof three field componentsfor strokes. the atmosphericin Figure 2.
RAFALSKY
ET AL.: SINGLE-SITE
LOCATION
OF LIGHTNING
20,833
Table 1. Resultsof Direction Finding for 16 Atmospherics Measured on April 10, 1991
(a)
Discrepancy,deg
! !
1
P
o
No.
Time, UT
Azimuth, deg
CRDFELF
CRDFVLF
TPDFELF
TPDFVLF
1 2 4 5 6 7 8 9 10 11 12 13 15 16
0121:30 0121:42 0122:27 0124:39 0124:50 0125:55 0126:30 0128:55 0130:20 0130:27 0131:48 0132:22 0132:59 0134:20
127.3 - 153.7 144.9 143.1 145.4 160.3 134.6 136.9 140.6 141.2 135.4 - 155.0 129.1 - 159.3
4.3 - 1.6 9.9 2.9 7.7 3.2 1.4 -47.4 2.8 -7.4 14.0 -2.8 -8.5 - 12.4
-1.7 4.5 3.5 2.1 -2.1 3.3 1.1 2.3 2.6 -11.1 2.1 - 1.7 -4.1 1.8
0.3 2.4 0.5 2.1 4.6 2.3 1.0 - 1.0 0.6 3.4 0.8 3.3 3.2 0.9
-1.6 - 1.6 -0.1 -2.6 -0.1 -2.5 -2.4 1.5 1.8 0.3 1.6 -2.5 -4.0 -0.4
CRDF is cathode-ray direction finder, and TPDF is time domain Poyntingvector direction finder.
180
(b)
lightning having mainly a horizontal componentof current moment rather than vertical discharges.This is the casewhen a higher-ordermode is excitedmore effectivelyfor frequencies in the vicinityof its cutofffrequency.Suchlightningis naturally expectedto be cloud-to-cloudor interclouddischargesrather than cloud-to-grounddischarges. On the other hand, such atmosphericsexhibit substantial -180 polarizationerrors.This is seenin Figure 4, where the spectra 2 4 6 8 10 of the amplitudeand orientationof the PoyntingvectorP(ro) are presentedversusfrequencytogether with the amplitude Frequency (kHz) spectrumof Ez. Each point in the spectracorrespondsto a Figure 4. (a) Spectraof Poyntingvector amplitude and E z measurementwith a narrowbanddirectionfinder. The apparfield componentand (b) the apparentazimuth for the atmo- ent azimuth indicatesseverepolarization errors, up to 90 despheric in Figure 2. Both graphs have the same frequency greesor even more at the frequencieswhere the amplitude of scale. the Poyntingvector is small or changesrapidly. The time domain technique proposed above averagesthe azimuths over the whole frequencyband with the weight being proportional quencyto zero. As a result the number of oscillationsin each to the amplitude of the vector. As a result the polarization pattern indicatesthe source-observerdistance,measuredin errors are substantiallyreduced. wavelengthsof the cutofffrequency.The atmosphericspectra The mostregularfrequenciesfrom the viewpointof polarizain Figure 3 are found to exhibit six or seven full oscillations tion errors are the bands below 1.5 kHz or above 7 kHz. Herestartingfrom the first cutofffrequencyof about 1.7 kHz, yielding a distanceestimate of 1000-1300 km.
It is reasonableto supposethat atmosphericsof the above Table 2. Resultsof Direction Finding for 12 Atmospherics type showingstrong intermode interference originate from Measured on February 26, 1991 Discrepancy,deg
lid
real
receive
= -20
-40
iELF 2
VLF 4
6
8
10
12
Frequency (kHz)
No.
Time, UT
Azimuth, deg
CRDFELF
CRDFVLF
TPDFELF
TPDFVLF
1 2 3 4 5 6 7 8 9 10 11 12
956:19 957:21 958:16 959:14 1000:16 1001:01 1001:48 1004:09 1005:04 1007:56 1009:46 1014:50
98.2 -82.1 94.2 95.9 94.0 -97.0 85.6 68.1 94.2 -93.6 84.6 179.3
1.4 -5.0 0.8 5.1 -5.6 -0.6 -5.3 4.0 -2.3 -0.5 -0.6 1.8
1.2 -5.0 0.8 5.1 -4.6 -0.4 - 1.8 3.1 74.1 4.5 -0.6 0.8
-3.9 -6.7 5.1 9.1 5.3 0.5 -0.7 - 1.3 -2.1 0.2 -3.0 5.1
0.4 -5.3 0.7 5.4 3.1 0.5 -0.5 0.2 0.9 -0.5 -0.1 -0.2
Figure 5. Amplitude-frequencycharacteristics of the real receiver and two simulated
receivers:
ELF
and VLF.
Abbreviations
as in Table
1.
20,834
RAFALSKY
5OO
-• 400
ET AL.: SINGLE-SITE
.........*......... .......
'F-
...........
(1•
,.- 300
--
,
•
..,..
:
,
i
OF LIGHTNING
__-b..... _............
.......
!
........... •--
!
: ....
0
LOCATION
,
_-
......
i
... _.......................
,
....!...............i'
z= 200
' i'-
0
E 100
......
_• .......
