Journal of Atmospheric and Solar-Terrestrial Physics · parameter is the length of the lightning...

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Journal of Atmospheric and Solar-Terrestrial Physics 71 (2009) 1877–1889

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Journal of Atmospheric and Solar-Terrestrial Physics

1364-68

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/jastp

On the NOx production by laboratory electrical discharges and lightning

Vernon Cooray a,�, Mahbubur Rahman a, Vladimir Rakov b

a Division for electricity and lightning research, Angstrom Laboratory, Department of Engineering Sciences, Box 534, SE-751 21 Uppsala University, Swedenb Department of Electrical and Computer Engineering, University of Florida, Gainesville, USA

a r t i c l e i n f o

Article history:

Received 19 February 2009

Received in revised form

16 July 2009

Accepted 22 July 2009Available online 3 August 2009

Keywords:

Nitrogen oxide

Lightning

Climate

26/$ - see front matter & 2009 Published by

016/j.jastp.2009.07.009

esponding author.

ail address: [email protected] (V. Coor

a b s t r a c t

Different approaches are used in estimating the global production of NOx by lightning flashes, including

field measurements carried out during thunderstorm conditions, theoretical studies combining the

physics and chemistry of the electrical discharges, and measurements of NOx yield in laboratory sparks

with subsequent extrapolation to lightning. In the latter procedure, laboratory data are extrapolated to

lightning using the energy as the scaling quantity. Further, in these studies only the return strokes are

considered assuming that contributions from other processes such as leaders, continuing currents,

M components, and K processes are negligible. In this paper, we argue that the use of energy as the

scaling quantity and omission of all lightning processes other than return strokes are not justified. First,

a theory which can be used to evaluate the NOx production by electrical discharges, if the current

flowing in the discharge is known, is presented. The results obtained from theory are compared with the

available experimental data and a reasonable agreement is found. Numerical experiments suggest that

the NOx production efficiency of electrical discharges depends not only on the energy dissipated in the

discharge, but also on the shape of current waveform. Thus, the current signature, can influence

extrapolation of laboratory data to lightning flashes. Second, an estimation of the NOx yield per

lightning flash is made by treating the lightning flash as a composite event consisting of several

discharge processes. We show that the NOx production takes place mainly in slow discharge processes

such as leaders, M components, and continuing currents, with return strokes contributing only a small

fraction of the total NOx. The results also show that cloud flashes are as efficient as ground flashes in

NOx generation. In estimating the global NOx production by lightning flashes the most influencing

parameter is the length of the lightning discharge channel inside the cloud. For the total length of

channels inside the cloud of a typical ground flash of about 45 km, we estimate that the global annual

production of NOx is about 4 Tg(N).

& 2009 Published by Elsevier Ltd.

1. Introduction

An assessment of the global distribution of nitrogen oxides isrequired for an adequate description of tropospheric chemistryand in the evaluation of the global impact of increasinganthropogenic emissions of NOx (Crutzen, 1970). In the mathe-matical models utilized for this purpose one needs to specify asinputs the natural as well as man-made sources of nitrogen oxidesin the atmosphere. Lightning is one of the main natural sources ofnitrogen oxides in the atmosphere, and it may be the dominantsource of nitrogen oxide in the troposphere in equatorial andtropical South Pacific regions (Gallardo and Rodhe, 1997). Thus, anaccurate quantification of nitrogen oxides production by thunder-storms is necessary for further development of the chemical

Elsevier Ltd.

ay).

models of the troposphere and in the evaluation of the effects ofthe man-made nitrogen emissions in the terrestrial atmosphere.

Due to the difficulty of making direct measurements of NOx

produced by natural lightning flashes, researchers have employedindirect methods to quantify the global production of NOx (Tuck,1976; Noxon, 1976; Chameides et al., 1977; Drapcho et al., 1983;Franzblau and Popp, 1989; Stith et al., 1999; DeCaria et al., 2000;Cook et al., 2000; Huntrieser et al., 2002, Zhou et al., 2005). Due toa large number of uncertainties involved in these methods, theestimates of global NOx production by lightning flashes availablein the literature vary by two orders of magnitude, from 1 to200 Tg(N)/year. In estimating lightning produced NOx by indirectmethods scientists have usually utilized the following twoprocedures: (1) a laboratory measurement of the number ofNOx molecules per unit energy for a laboratory spark is made andthe result is extrapolated to lightning by multiplying thismeasured value by estimated energy of lightning event. (2) Aground-based NOx measurement is made in the vicinity of anatural lightning flash and from it the source strength is

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Table 1Measured spark radii and values of k in Eq. (1) giving the best fit to data.

Reference Peak current (kA) Rise time (ms) Decay time (ms) r(tm) (cm) tm (ms) Value of k giving

the best fit,

�10�3

Flowers (1943) 17 8 60 0.8 8 0.37

18 6 60 0.7 6 0.35

22 3.3 60 0.615 3.3 0.41

26 8 60 0.9 8 0.35

Higman and

Meek (1950)

0.185 20 0.19 12 0.259

0.250 20 0.145 12 0.254

0.500 10 0.225 12 0.34

0.400 10 0.195 12 0.32

0.300 10 0.16 9 0.31

V. Cooray et al. / Journal of Atmospheric and Solar-Terrestrial Physics 71 (2009) 1877–18891878

estimated by making suitable assumptions concerning the fluiddynamics of the NOx flow from the source to the measurementpoint.

In studies of NOx production by lightning flashes, only returnstroke is assumed to be the NOx source and the effects, if any, ofleaders, continuing currents, M components, and K processes areneglected. Many studies have excluded cloud flashes from NOx

estimates assuming their contribution to be insignificant. Recentdirect measurements of NOx produced by triggered lightningflashes (Rahman et al., 2007) show, however, that it is not only thereturn stroke in ground flashes but also other slow processes suchas continuing currents are significantly contributing to theNOx production. This calls for a more thorough investigation ofthe problem including different processes in both ground andcloud flashes. In this paper, we attempt to conduct such aninvestigation. First we quantify the NOx production by differentdischarge processes of lightning flashes such as return strokes,leaders, continuing currents, and M components and subse-quently this information is utilized to quantify NOx productionby a typical lightning flash containing all these elements. Theresults are used to obtain a global estimate of the lightningproduced NOx. While performing this analysis we will alsoattempt to provide answers to the following important questionsrelated to the quantification of NOx emission by lightning flashes:(a) is the energy of discharge the correct scaling factor toextrapolate NOx emission from laboratory discharges to lightningflashes? (b) Does the shape of discharge current waveforminfluence the NOx emission? (c) What are the relative contribu-tions from leaders, return strokes, continuing currents, M

components, and K processes to the NOx production by lightningflashes? (d) Can one neglect the cloud flashes in evaluating theglobal NOx production?

2. NOx production by laboratory sparks

2.1. Radius of spark channels

According to Braginskii (1958), the radius of spark channel attime t, r(t), as a function of current is given by,

rðtÞ ¼ kr�1=6o i1=3t1=2 ð1Þ

where r(t) is in m, t is in microseconds, i is the instantaneouscurrent in the spark channel in kA, k is a constant, and ro is the airdensity at atmospheric pressure (1.29�10�3 g/cm3). In derivingthis expression, Braginskii assumed that the current increaseslinearly with time. However, the current in sparks decays afterreaching the peak value, and Braginskii noted that the value ofconstant k (originally set to 0.93�10�3) may have to be changed if

the equation is to predict the time variation of channel radius ofsparks. Cooray and Rahman (2005) have made a comparison ofthe results predicted by Eq. (1) with the constant suggested byBraginskii (1958) with the experimental data published byFlowers (1943) and Higman and Meek (1950) and found that itoverestimates the radius of spark channels. Table 1 gives channelradii observed in the experiment and constants k in Eq (1) thatgive the best fit to the experimental data. Based on thiscomparison, Cooray and Rahman (2005) estimated thatk ¼ (0.32870.05)�10�3. Recently, Perera et al. (2008) analysedthe diameter of spark channels of length 30 cm using aphotographic technique and the maximum channel diameter isobtained as a function of spark peak current for both positive andnegative polarities. Perera et al. (2008) compared the measuredmaximum channel diameter with the one obtained from Eq. (1)using the current waveform measured in the discharge as input.The results of that study confirm that the Braginskii’s originalconstant overestimates the channel diameter whereas theconstant suggested by Cooray and Rahman (2005) (i.e.0.328�10�3) provides a reasonable fit to the data. Based onthese experimental validations the value of the constantsuggested by Cooray and Rahman (2005) is used in the analysispresented here.

Lightning currents were directly measured on tall towers andat the triggered-lightning channel base (e. g., Berger, 1972; Fisheret al., 1993). Mathematical expressions to describe the waveformof typical first and subsequent return stroke currents recorded byBerger (1972) are found in CIGRE Study Committee 33 Report(1991) and Nucci et al. (1990). First let us utilize the typicalcurrent waveforms found in the above references to study howthe radii of the first and subsequent return strokes vary as afunction of peak current. Fig. 1 shows how the maximum radius ofthe channel given by Eq. (1) varies as a function of peak currentfor first and subsequent return strokes. Note that the radius of atypical first return stroke (with a peak current of 30 kA) is about2 cm and that of a typical subsequent stroke (peak current 12 kA)is about 1 cm. These values are in agreement with the radii ofreturn stroke channels estimated in photographic studies assummarized by Orville (1977a).

2.2. The volume of air heated in a spark channel

and its internal energy

Detailed studies of the temporal variation of temperature andpressure of lightning discharges and long laboratory sparks showthat the channel temperature reaches a peak of about25,000–30,000 K and the channel pressure is of the order of10 atm in a few microseconds after the commencement of currentflow through the channel (Orville, 1968a, b; Orville et al., 1967).

ARTICLE IN PRESS

0Peak Current, kA

0.005

0.01

0.015

0.02

0.025

0.03

0.035R

adiu

s, m (i)

(ii)

20 40 60 80

Fig. 1. The maximum radius of the channel as given by Eq. (1) as a function of peak

current for first (i) and subsequent (ii) return strokes. In these calculations the

typical current wave-shapes for first and subsequent return strokes found in the

literature were used.

V. Cooray et al. / Journal of Atmospheric and Solar-Terrestrial Physics 71 (2009) 1877–1889 1879

Then the channel plasma cools down mostly due to the channelexpansion, loss of heat due to radiation, and engulfing cold airfrom outer zones. This phase may last for about few tens ofmicroseconds. At the end of this phase the channel temperaturereduces to a value of about 15,000 K and the pressure inside thechannel attains the atmospheric pressure clamping down thepressure driven expansion of the channel. Experimental data thatsupport this scenario are provided, both for laboratory sparks andlightning flashes, by Orville (1968a, b, 1977b) and Orville et al.(1967). Another experimental observation that supports thisscenario is the following. The experimental data obtained byOrville (1968a) on the temperature of the lightning stepped leaderchannel show that at the formation of the step the channeltemperature increases to about 25,000–30,000 K. Subsequently,the temperature decreases to about 15,000 K and remains at thatlevel until the channel is retraced by the return stroke. Thetheoretical calculations of Paxton et al. (1986), Hill (1971) andPlooster (1971) also indicate that by the time the pressure insidethe spark channel reduces to the atmospheric pressure theaverage temperature in the channel is close to 20,000–15,000 K.After the pressure equilibrium is reached, the cooling of thechannel takes place mainly due to the entrainment of cold airacross the channel boundaries into the hot core of the channeleffectively reducing the diameter of the hot core (Hill et al., 1980).Similarly, Eq. (1) predicts that the spark channel expands initiallywith time and its maximum radius is attained in a fewmicroseconds to a few tens of microseconds, depending on thepeak and the duration of current. After this, the radius of the hotchannel decreases, while the channel resistance starts to increasewith time. Based on the experimental and theoretical data(Orville, 1968a, b; Paxton et al., 1986; Orville et al., 1967; Hill,1971; Plooster, 1971), we assume in our analysis that the pressurein the channel at the time of maximum radius is close toatmospheric pressure and that the average temperature of the hotair in the channel at this time is close to 15,000 K. In reality, thechannel temperature is not uniform across the cross section of thechannel. But the theoretical calculations of Paxton et al. (1986)and Hill (1979) indicate that after a few tens of microseconds theradial temperature distribution is relatively flat with a sharpdecrease to ambient temperature at the channel boundaries. Thisjustifies the use of an average value to describe the channel

temperature. Further, the temperature of 15,000 K estimated byOrville (1977b) when the channel was close to pressureequilibrium is the average temperature across the channeljustifying our selection of 15,000 K as the average temperature.Thus, we assume that in a cylindrical spark channel the volume ofair, V, heated to a temperature of about 15,000 K is given by

V ¼ lp r2max ð2Þ

where l is the length of the spark and rmax is the maximum radiusof the spark channel given by Eq. (1) with k ¼ 0.328�10�3.

2.3. NOx production in spark channels

It is believed that in an electrical discharge mainly NO is beingproduced through a series of high temperature reactions, which isconfirmed by different laboratory experiments. Depending on thepresence of excess O2 and O3 and the residence time theexperimentally found NO/NOx ratios vary significantly. However,the total number of molecules of NOx (NO+NO2) produced by adischarge is equal to the total number of NO molecules producedin the discharge, which is calculated in this section.

As mentioned previously, a procedure outlined by Borucki andChameides (1984) has been adopted to quantify the number of NOmolecules that will be ‘‘fixed’’ as the discharge channel coolsdown to ambient temperature. The amount of NO produced by adischarge via high temperature reactions is determined by thefreeze-out temperature, Tf. This temperature is defined as follows:let us denote by tNO(T) the time required by NO to reachthermodynamic equilibrium at a given temperature, T. Thefreeze-out temperature is defined in such a way thattNO(Tf) ¼ tT(Tf) where tT(T) is the characteristic cooling time ofthe heated gas. When T4Tf then tNO(Tf)otT(Tf) and the chemicalreactions are fast enough to keep NO in thermodynamicequilibrium. If ToTf then tNO(Tf)4tT(Tf) and chemical reactionsare too slow to adjust to the rapidly decreasing temperature. Inthis case the amount of NO at Tf in the mixture is frozen out. Thus,if N is the number of air molecules heated above Tf, the number ofNO molecules generated by the process, MNO, is given by

MNO ¼ N f ðTf Þ ð3Þ

where f(Tf) is the fraction of NO molecules in the gas attemperature Tf (Chameides, 1986; Borucki and Chameides, 1984).

The value of Tf depends on the cooling rate of the gas in thedischarge. For lightning-like discharges Tf and corresponding f(Tf)were estimated to be around 2660 K and 0.029 respectively(Chameides, 1986; Borucki and Chameides, 1984). These valueshave been used in the calculations presented here. In order toevaluate MNO it is necessary to evaluate N, the number ofmolecules heated above Tf, which can be found from the followingequation

N ¼ VðEh=Ef ÞNoðTo=Tf Þ ð4Þ

where V is the volume of hot air in the discharge channel given byEq. (2), Eh and Ef are the internal energy of air per unit volume atthe temperatures Th and Tf, respectively, To is the standardtemperature and No is the number of molecules per unit volumeat standard temperature and pressure. In the calculations we haveassumed that Th ¼ 15,000 K, Tf ¼ 2660 K, To ¼ 273 K andNo ¼ 2.69�1025 m�3. In deriving Eq. (4) we have assumed that,as the channel cools after reaching the pressure equilibrium dueto the entrainment of cold ambient air into the discharge channel,not much of the energy escapes the channel as radiation.Moreover, in the derivation we have neglected the production of

ARTICLE IN PRESS


NO, if any, by the shock wave generated by the discharge.Both these assumptions are supported by the calculations of Hillet al. (1980). The number of NO molecules produced by thedischarge is then given by

MNO ¼ f ðTf ÞVðEh=EdÞNoðTo=Tf Þ ð5Þ

The values of Eh and Ef are calculated using the set of equationsgiven by Plooster (1970, 1971) describing the variation of internalenergy of air as a function of temperature and pressure. Thus, ifthe current waveform in the discharge channel is known, thenEqs. (1)–(5) can be used to evaluate the number of NO moleculesproduced by the discharge.

2.4. Efficiency of NOx production in sparks with different current

wave-shapes

Let us now check the validity of Eq. (5) by comparing itspredictions with the available experimental data. The efficiency ofNOx production by electrical discharges is evaluated by Chameides(1979), Levine et al. (1981), Peyrous and Lapeyre (1982), Boruckiand Chameides (1984), Rehbein and Cooray (2001), Wang et al.(1998) and Rahman et al. (2008). Unfortunately, only in a fewcases the current waveform associated with the electric dis-charges used in the experiment is given. These are the studiesconducted by Wang et al. (1998), Rehbein and Cooray (2001), andRahman et al. (2008). The current waveform associated with thesparks analysed by Wang et al. (1998) has a rise time of 30ms anda decay time (time taken by the current to decay to 1/2 of its peakvalue) of 400ms. The current waveform associated with the sparksin the experiment conducted by Rehbein and Cooray (2001; thecurrent waveforms are given in Rehbein, 1999) was oscillatorywith a frequency of 2.8 MHz and decay time of 2ms. The currentwaveform in the spark experiments conducted by Rahman et al.

100

Peak Current, A

1E+017

1E+018

1E+019

1E+020

1E+021

1E+022

NO

x m

olec

ules

/m

(a)

(b)

(c)(d)

(e)

1077

1000 10000 100000

Fig. 2. NOx production efficiency of laboratory sparks and lightning return strokes

as a function of peak current. (a) Theoretical prediction based on the current

waveform of the study conducted by Wang et al. (1998), (b) prediction based on

the typical first return stroke current waveform, (c) prediction based on the typical

subsequent return stroke current waveform, (d) prediction based on the current

waveform in the sparks studied by Rahman et al. (2008) and (e) prediction based

on the current waveform in the sparks studied by Rehbein and Cooray (2001). The

experimental data corresponding to different studies (Rehbein and Cooray: hollow

triangles; Wang et al.: hollow circles; Rahman et al.: solid circles) are also shown

in the figure.

(2008) had a rise time of about 0.3ms and a decay time of about25ms. The NOx production per unit length by these discharges isevaluated using the equations presented in the previous sectionand the results, together with the experimental data, are shown inFig. 2. First note that there is a reasonable agreement between theexperimental data and the theory. Second, note how the NOx

production depends on the wave-shape of current. For a givenpeak current, a current with a longer duration gives rise to moreNOx than a current with a shorter duration. The reason for this isthat the volume of the discharge channel increases withincreasing the duration of current waveform. Since the volumeof the discharge channel is a measure of the internal energyretained in the discharge channel, in long-duration currents moreenergy goes into the internal energy of the discharge than in shortduration currents. As the internal energy of the dischargeincreases the mass of air that is being heated beyond theNOx freeze-out temperature also increases leading to a higherNOx production. To the best of our knowledge, this is the first timethat the dependence of NOx production on the shape of thecurrent waveform flowing in the discharge channel is explicitlyrecognized.

2.5. NOx production in sparks as a function of energy

In order to calculate the energy dissipated in the dischargechannel we will employ again the spark discharge channel modelof Braginskii (1958). Two simplifying assumptions made indeveloping this model are: (a) the conductivity of the channel isuniform across the channel cross section. (b) The conductivity ofthe channel does not vary as a function of time. With theseassumptions the energy dissipated in the discharge channel isgiven by

U ¼ l

Z 10

i2ðtÞ

prðtÞ2sdt ð6Þ

where s is the effective conductivity of the spark channel, r(t) isthe radius of the channel at time t (given by Eq. (1)) and l is thelength of the channel. Braginskii (1958) recommended the use ofE104 S/m as the effective conductivity of the channel.

In order to test the validity of this equation, the energy in thesparks studied by Rahman et al. (2008) was evaluated byintegrating the product of voltage and current waveforms. For35 current waveforms the total energy calculated from the aboveequation agrees within 15%, when the value of s is assumed to be0.65�104 S/m. Paxton et al. (1986) studied the development oflightning channel taking into account the detailed physics of thecomplex electro-hydrodynamic and thermodynamic processes.The current waveform used by Paxton et al. had a linear rise topeak followed by an exponential decay. The peak value, rise time,and decay time of the current waveform used by Paxton et al.were 20 kA, 5ms, and 50ms, respectively. The calculated totalenergy dissipation in the discharge up to 50ms was about 5 kJ/m.Eq. (6) for the same current predicts the same energy dissipationwhen s ¼ 104 S/m. These comparisons suggest that Eq. (6) cangive a reasonable value for the total energy dissipated in thedischarge for values of s ranging from 0.65�104 to 104 S/m. In thecalculations to follow we will use s ¼ 0.8�104 S/m.

Fig. 3 depicts the energy dissipation per unit length inelectrical discharges having current signatures similar to thoseof typical first and subsequent strokes, as a function of peakcurrent. According to Fig. 3 typical first and subsequent returnstrokes will dissipate about 20 and 2.5 kJ/m, respectively, inchannel sections close to ground.

ARTICLE IN PRESS

0Peak Current, kA

0

20000

40000

60000

80000E

nerg

y, J

/m

(i)

(ii)

20 40 60 80

Fig. 3. The energy dissipation per unit length in (i) first return strokes and

(ii) subsequent return strokes as a function of peak current.

1Energy, (J/m)

1E+017

1E+018

1E+019

1E+020

1E+021

1E+022

NO

x mol

ecul

es/m

(a)

(b)

(c)

10 100 1000 10000 100000

Fig. 4. NOx production efficiency of laboratory sparks and lightning return strokes

as a function of the energy dissipated in the discharge. (a) Theoretical prediction

based on the current waveform of the study conducted by Wang et al. (1998),

(b) prediction based on the current waveform in the sparks studied by Rahman

et al. (2008) and (c) prediction based on the current waveform in the sparks

studied by Rehbein and Cooray (2001). The experimental data corresponding to

different studies are also shown in the figure.


In Fig. 4, the calculated yield of NOx as a function of the energydissipated in the discharge is depicted for current waveformscorresponding to the experiments conducted by Wang et al.(1998), Rehbein and Cooray (2001), and Rahman et al. (2008). Forcomparison purposes the experimental data are also shown in thesame diagram. It is important to note that the experimentalevaluation of the energy dissipated in spark channels is not trivial.Errors may result from the measurement of voltage across thespark channel either due to inductances in the circuit or due to theresponse characteristics of high-voltage dividers. Moreover, forlarge currents the discharge channel transverse diameters mayreach several centimetres and in the case of short gaps (about3 cm), as in the case of Wang et al.’s (1998) study, the electrodeeffects may influence the total energy measured. Nevertheless, asone can see in Fig. 4, there is a reasonable agreement between thetheory and experiment. One important conclusion that can bemade from the results of this analysis is that the energy dissipated

in the discharge cannot be used as a scaling factor in extrapolatinglaboratory data to lightning. The reason for this is that for a givenenergy the NOx production efficiency of a spark depends on thewaveform of the discharge current.

3. NOx production in discharges containinglong duration currents

Currents having relatively long durations ranging from severalmilliseconds to hundreds of milliseconds are associated withdifferent lightning processes. One such process is the steppedleader. A stepped leader may carry currents of tens to hundreds ofamperes with durations of some tens of milliseconds. Longduration currents initiated by return strokes and flowing alongthe channel to ground are known as continuing currents.Discharge processes taking place inside the cloud can alsogenerate long duration currents.

The theory presented in Section 2.3 cannot be applied tocalculation of NOx production in channels carrying long durationcurrents. When the current duration is long, ample time isavailable for the mixing of cold air into the discharge channelwhile the current is still flowing in the channel. Thus, the energydissipated in the channel is continuously being utilized to heatcold air coming into the channel. At the same time hot air leavingthe channel as it cools down, creates NOx in gas volumes adjacentto the discharge channel. In the case of long duration current thisturbulent mixing of cold air into the channel and hot air leaving ithas to be taken into account in the calculation of NOx production.This prevents us from using the procedure for calculating theNOx production in spark channels, described in Section 2.3. Recentmeasurements conducted by Rahman et al. (2007) show that theNOx production by steady currents in rocket-triggered lightning isproportional to the charge transferred along the channel. Accord-ing to their measurements the NOx production efficiency of longduration currents is equal to about 2�1020 molecules/m/C.

4. NOx production in streamer discharges

The propagation of leaders in long laboratory sparks andlightning are facilitated by streamer discharges taking place at theforward moving leader tip. Streamer discharges may also beresponsible for the leakage of charge from the hot leader channelcore, which is at extremely high potential, into the corona sheath.The air temperature in a streamer is close to the ambienttemperature whereas the electron temperature can be several tensof thousands of Kelvin. The collision between energetic electrons andneutral molecules leads to the dissociation of N2 and O2 in thestreamer discharges and the resulting chemistry gives rise to bothNOx and O3. However, the theory developed for the NOx generationin hot sparks cannot be utilized here, because the NOx productionprocess is not controlled by temperature variation. Recently, Coorayet al. (2008) demonstrated that a theory developed for studyingNOx production by solar proton events (Crutzen, 1970; Nicolet, 1975)could be utilized to calculate the NOx production from corona andstreamer discharges. According to this theory, the NOx productionrate is approximately equal to the rate of production of ion pairsduring the proton impact. Since the bulk of ionization in such eventsis produced by secondary electron impacts, Cooray et al. (2008)applied the same concept to study the NOx production in lowpressure gas discharges, corona discharges, and streamer dischargesin which the source of ionization is the electron impacts. Let usassume that the radius of the streamer channel is Rs and the numberof charge particles at the streamer head is N. Since the number ofionizing events created by a streamer in moving a unit length is

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equal to N/2Rs, according to Cooray et al. (2008), the number of NOx

molecules produced by a streamer in propagating a unit distance isgiven by kN/2Rs, where k is the number of NOx molecules generatedper ionizing event. Using experimental data for corona Cooray et al.(2008) demonstrated that kE1 for positive polarity and kE0.6 fornegative polarity.

5. NOx production in ground lightning flashes

Having outlined the procedure to evaluate the efficiency of NOx

production in sparks, continuing currents, and streamer dis-charges we are now in a position to incorporate them all into asingle model that can be used for evaluating the NOx productionby lightning flashes.

5.1. The model of a ground lightning flash

As summarized by Cooray (2003), a ground flash is initiated by anelectrical breakdown process in the cloud that is called the preliminary

breakdown. This process leads to the creation of a column of chargecalled the stepped leader that extends from cloud to ground in astepped manner. On its way towards the ground a stepped leader maygive rise to several branches. Once the connection of the steppedleader to ground is made, a nearly-ground-potential wave and theassociated luminosity wave travels along the leader channel towardsthe cloud at a speed comparable to that of light. This wave is calledthe return stroke. Although the current signature associated with thereturn stroke proper tends to have duration of a few hundredmicroseconds, the return stroke current may not go to zero within thistime, and a low-level current may continue to flow for tens tohundreds of milliseconds. Such long duration currents are calledcontinuing currents. Continuing current longer than 40 ms tend tofollow subsequent (as opposed to first) strokes, described below. Thearrival of the first return stroke front at the cloud end of the returnstroke channel leads to a change of potential in the vicinity of thispoint. This change in potential may initiate a positive discharge thattravels away from the upper end of the return stroke channel (the so-called J-process). When a fresh discharge is created in the previouslyionized channel, the process that follows depends on the conditionsalong the channel. If the channel carries a continuing current therewill be a wave that travels towards the ground and produces areflection there. This process is called the M component. If the channelcarries essentially no current, the downward-moving wave may takethe form of dart leader that travels towards the ground and produces areturn stroke there. Such return stroke is called the subsequent return

stroke. Processes similar to those occurring after the first returnstrokes may also take place after subsequent return strokes.Unsuccessful dart leaders and other transient processes involvingin-cloud channels are referred to as K changes.

In evaluating the NOx production by a ground flash one has toconsider all these processes. In the present study, an attempt ismade to include the various lightning processes in the estimationof the global NOx production by ground flashes. In this evaluation,a ground flash is represented by the following model. Thegeometry of the lightning channel consists of a vertical sectionof height H and a horizontal section of length L. The horizontalchannel which is located in the cloud consists of n branches ofequal lengths. Each branch is created by a leader discharge andduring its creation the leader current is confined to that particularbranch i.e. it does not flow along other branches. In lightningflashes giving rise to continuing currents the source is confined toa single branch i.e. the current passes through a branch andfollows the vertical channel to ground. Processes to be taken intoaccount are the leaders, return strokes, continuing currents, andM components in the vertical channel section and leaders and

K changes in the horizontal channel sections. A cloud flash isrepresented by two networks of horizontal channels, one in thepositive charge region and the other in the negative, connected toeach other by a vertical channel. The geometry of the horizontalchannels is identical to the one assumed for ground flashes.

5.2. NOx production in different processes in ground flashes

5.2.1. Leaders

5.2.1.1. Corona sheath. A leader channel consists of a hot coresurrounded by a corona sheath. The corona sheath is createdthrough the action of streamer discharges and the chargedeposited in the corona sheath by the streamers is supplied by thecurrent flowing in the hot core. Both these processes (i.e. streamerdischarges and current flow along the core of the leader) have tobe considered in evaluating the NOx production by leaderdischarges. In this section we will concentrate on the former.

According to bidirectional leader concept, the vertical channelof a negative ground flash is forged by negative stepped leadersand the channels in the cloud are created by positive leadersmoving away from the point of origin of the flash. In the analysisto follow we assume that the magnitude of the charge depositedper unit length of the leader channel is the same on both verticaland horizontal channels. Let us denote this by r. We also assumethat most of this charge resides in the corona sheath and thetransport of this charge into the corona sheath is mediated bystreamers. Since most of the charge of the streamer is located atthe head of the streamer (Gallimberti, 1979), the number ofstreamers, Ns, per unit length of the leader channel is

Ns ¼ r=eNhead ð7Þ

where Nhead is the charge on the head of the streamer channel.Applying the Gauss law over a cylindrical surface encompassingthe whole corona sheath, one obtains the radius of the coronasheath, Rc+, as

Rcþ ¼ r=ð2peoEsþÞ ð8Þ

where Es+ is the critical background electric field necessary for thepropagation of positive streamers. Note that in writing down theabove equation we assume that all the charge in the corona sheath islocated inside the radius Rc+ and the electric field at this outer edgeof the corona sheath is equal to Es+. If the electric field in thestreamer region remains constant at this critical electric field, inorder to satisfy the boundary conditions in coaxial geometry thevolume charge density in the streamer region should decreaseinversely with radius. Since most of the streamer charge is located atits head, this condition requires the number of streamers moving outfrom the central conductor to decrease linearly with radial distance.In other words the number of streamers having a given length l istwo times the number of streamers of length 2l provided that 2loRc.Thus, streamers travel, on average, a distance of Rc/2 in creating thecorona sheath. Using the expression for the number of NOx

molecules generated by a single streamer in moving a unit lengthderived previously, we find the number of NOx molecules created bypositive streamers per unit length of positive leader channel, Zstr+, as

Zstrþ ¼ kþr2=8peoeEsþRs ð9Þ

where k+ is the number of NOx molecules generated per ionizingevent in positive discharges. Similarly, the number of NOx moleculesgenerated by negative streamers per unit length of the negativeleader channel is given by

Zstr� ¼ k�r2=8peoeEs�Rs ð10Þ

ARTICLE IN PRESS


where the parameters have the same definition as in previousequation but corresponding to negative streamers. Thus the totalnumber of NOx molecules generated by corona sheath of the leadersin the whole ground flash is given by

NOx�leader sheath ¼ Zstr�H þ ZstrþL ð11Þ

The charge per unit length of lightning stepped leaders isexpected to be in the range of 0.0005–0.001 C/m. In thecalculations, we assumed that r ¼ 0.005 C/m. The values of Es+

and Es� are equal to 500 kV/m and 1 MV/m respectively (LesRenardi�eres Group, 1974). We assume that N ¼ 108 (Gallimberti,1979). We also assumed that the values of k� ¼ 0.6 and k+ ¼ 1.0are independent of pressure. Recall that k� and k+ refers to thenumber of NOx molecules created by an ionizing event. Theassumption is based on the study of Jackman et al. (1979) whosetheoretical calculations predict that NOx molecules per ionizingevents does not change significantly with increasing altitude andhence with pressure. We have also assumed that the values of Es+

and Es� do not vary with pressure. In reality they decrease linearlywith pressure but that effect is somewhat compensated by theincrease in the size of the streamer head with decreasing pressure.Substituting these values in Eq. (9), we obtain Zstr+E2�1020 forr ¼ 0.0005 C/m.

5.2.1.2. NOx production in the hot core of the leader. The averagespeed of propagation of lightning stepped leaders is about2�105 m/s and to supply a charge per unit length equal to0.0005 C/m the current flowing along the hot core should be about100 A. As the leader progresses, this current will continue to flowin any given channel section as long as the conditions are suitablefor the continuous propagation of the leader head. Let us re-present the current flowing along the stepped leader channel byIls. If the charge density along the leader channel is constant andequal to r then Ils ¼ vr where n is the speed of propagation of thehead of the leader channel. Let Zlea be the number of NOx mole-cules generated per unit length per unit charge by the currentflowing in the core of the leader channel. Thus the number of NOx

molecules generated by a given section of the leader channel dueto this current is ZleaIlstd where td is the time over which a currentof amplitude Ils flows along the core of the channel section. Con-sider the vertical channel of length H. In a channel element oflength dz located at a height (H�z) above ground level the dura-tion of this current is (H�z)/vs, where vs is the speed of progres-sion of the leader head. Note that this time is equal to the timeneeded for the leader head to travel the distance from the channelelement to the ground. The total number of NOx molecules gen-erated in the channel element by the core current after correctionfor the pressure is ZleaIlsðH � zÞe�z=lp dz=vs. The total contributionfrom the vertical channel section can be obtained by integration ofthis expression from 0 to H. In constructing the above equation wehave assumed that the atmospheric pressure decreases ex-ponentially with height with a decay height constant lp and theefficiency of NOx production by hot discharges decreases linearlywith pressure (Zipf and Prasad, 1998; Rahman and Cooray, 2008).

The evaluation of the contribution to the NOx production fromnon-vertical in-cloud channels is more complicated. The channelsystem inside the cloud may consist of many branches and at a giventime only a few of these branches may be developing (Shao et al.,1995; Shao and Krehbiel, 1996; Thomas et al., 2004) and hence thecore current is active only along those branches at that time. Thus,one problem in evaluating the NOx production in the core of thenon-vertical in-cloud channel is the difficulty of knowing the lengthof the channel sections in which the current is flowing at a giventime. Consider that the non-vertical in-cloud channels comprise n

identical branches connected to the top of the vertical channel. Wepresume that these channels in the cloud are also created byprocesses similar to that of lightning leaders observed in groundflashes, and therefore, their current and speed of development arealso identical to those of these leaders. As mentioned in Section 5.1we assume that the core current will flow in each branch only whenthat particular branch is being formed. In reality, core current maypass from an active branch to a previously formed branch thusincreasing the total length of the channel sections supporting a corecurrent at a given time. Consider the development of a horizontalchannel section inside the cloud. Let us direct the coordinate x alongthe channel section. Consider an element dx on this channel locatedat a distance x from the origin of the section. In this element, thecurrent flows for a duration of (l�x)/vs where vs is the speed ofdevelopment of the channel and l is the length of the channel. Thusthe number of NOx molecules produced in this channel element is

ZleaIlse�H=lp ðl� xÞdx=vs. The total NOx production in the channel

section can be obtained by integrating the above expression from 0

to l. The result of this integration is ZleaIlsl2e�H=lp=2vs. Since we have

assumed that there are n identical branches and the total length ofthe horizontal channels is L the number of NOx molecules producedby the current flowing through the core of the channels inside the

cloud is given by ZleaIlsL2e�H=lp=2vsn. A similar procedure can be

used to evaluate the NOx production along the vertical section of theleader channel but the mathematics is slightly more complicateddue to the fact that the pressure varies along the channel. Afterapplying the mathematics one can show that the total number ofNOx molecules produced by the core current in the stepped leaderchannel of the ground flash (including the branches in the cloud) is

NOx�sl�core ¼ZleaIlslpH

vs1� e�H=lp

� �þZleaIls

vs

� l2p � lpe�H=lp H þ lp

� �� þZleaIls

2vsnL2e�H=lp ð12aÞ

Using the same procedure the number of NOx moleculesproduced in the dart leader channel core can be written as

NOx�dl�core ¼ZleaIldlpH

vdð1� e�H=lp Þ þ

ZleaIld

vd

� l2p � lpe�H=lp H þ lp

� �� ð12bÞ

where Idl is the current in the dart leader and vd the speed of dartleaders. To evaluate this equation it is necessary to have values forZlea, n, vs, Ils, vd and Ild. As pointed out in Section 3, the efficiency ofNOx production by long duration currents is about 2�1020

molecules/m/C. We assume that this is also true for the currentsflowing along the leaders channels, i.e. Zlea ¼ 2�1020 molecules/m/C. This assumption is justified because, like continuingcurrents, leaders also support currents with amplitudes on theorder of hundred amperes or more for durations of manymilliseconds depending on the time of travel. The channelstructure inside the cloud, as revealed from interferometricstudies, can be approximated by a few large channels connectedto the main channel (Shao et al., 1995, Shao and Krehbiel, 1996).Thus, the value of n may lie in the range of, say, 3 to 10. Opticalobservations of the stepped leaders and the interferometricstudies show that the speed of development of stepped leaderchannels in virgin air, v, is about 2�105 m/s (Schonland, 1956;Shao et al., 1995). Measurements conducted with both natural andtriggered lightning show that the speed of dart leaders is about107 m/s (Schonland et al., 1935; Orville and Idone, 1982; Wang etal., 1999). The currents in either the stepped leaders or dart

ARTICLE IN PRESS


leaders cannot be measured directly. But, inferences based onelectric field measurements show that stepped and dart leadersare associated with currents of the order of 100 A and 1 kA (Idoneand Orville, 1985; Cooray et al., 1989; Kodali et al., 2005),respectively.

5.2.2. Return strokes

In assessing the NOx production by first and subsequentstrokes we make the following assumptions. (a) The shape of thecurrent waveform at the channel base of the first and subsequentreturn strokes are similar to the typical waveforms constructed byCIGRE Study Committee 33 (1991) and Nucci et al. (1990). (b) Thereturn stroke peak current decreases linearly along the verticalsection of the channel and reducing to zero amplitude at the cloudend of the vertical channel. (c) The return stroke channel isvertical from ground level to the height of the charge centre, H.With these assumptions the NOx produced by the first returnstroke after correcting for the decrease in pressure with height is

NOx�fr ¼ Zfrlp 1�lp

Hþlp

He�H=lp

� �ð13Þ

where Zfr is the number of NOx molecules produced by a unitlength of the discharge at atmospheric pressure having a currentidentical to that of a typical first return stroke. In the calculationwe assume that the peak current of a typical first return stroke is30 kA. Note that, as depicted by curve b in Fig. 2, NOx productiondepends on the peak current of the first return stroke. From thisfigure we estimate that Zfr ¼ 5.9�1020 molecules/m. Similarly,the number of NOx molecules generated by a subsequent returnstroke is given by

NOx�sr ¼ Zsrlp 1�lp

Hþlp

He�H=lp

� �ð14Þ

where Zsr is the number of NOx molecules produced by a unitlength of the discharge at atmospheric pressure having a currentidentical to that of a typical subsequent return stroke. In thecalculation we assume that the peak current of a typicalsubsequent return stroke is 12 kA. Note again that, as depictedby curve c in Fig. 2, NOx production also depends on the peakcurrent of the subsequent return stroke. From this figure weestimate that Zsr ¼ 1.4�1020 molecules/m.

The use of return stroke current instead of the energydissipated in return strokes as an input parameter in quantifyingNOx production in return strokes, as done above, has at least oneimportant advantage. The energy dissipated in lightning flashescannot be measured directly but has to be inferred by indirectmethods leading to large inaccuracies in the estimated NOx

production. On the other hand, the current at the channel base ofground flashes can be measured and a large amount of data onthis parameter is available in the literature.

In deriving Eqs. (13) and (14) it has been assumed that thereturn stroke peak current decreases with height. The experi-mental observations show that the luminosity of both first andsubsequent return strokes decreases with height indicating thatthe return stroke current peak also decreases with height (Jordanand Uman, 1983; Schonland, 1956). Of course, since the exactnature of how the return stroke peak current decreases withheight is not known, one has a freedom to select any other form ofdecay for the peak current than the linear decay assumed in thecalculation. However, the expression describing a linear decaywith current amplitude decreasing to zero at cloud level involvesonly one parameter, i.e. height of the vertical channel, and it alsospecifies the boundary conditions for the current at the cloud endof the channel. Moreover, the linear decay has been shown to

produce electric fields at both far and close distances that aresimilar to those measured when used in return stroke models(Rakov and Dulzon, 1987; Thottappillil et al., 1997).

5.2.3. M components and K processes

As pointed out earlier, the development or extension of thelightning channels located inside the cloud are mediated byleaders. As these leaders develop the changes in the potential atthe extremities of the leader may causes K processes that travelalong the channel reducing the potential differences. The inter-ferometric observations indicate that it is usual to have a few K

processes in the developing stage of a given channel section (Shaoet al., 1995, Shao and Krehbiel, 1996). Thus, if Zm is the number ofNOx molecules produced per unit length of the channel by a K

process then the total number of NOx molecules generated by K

processes during the development of the channels inside thecloud after correction for the pressure is ZmnkLe�H=lp . In thisexpression nk is the number of K changes taking place in thedevelopment of a particular branch. In writing down the aboveexpression we have also assumed that the current associated witha given K occurring during the development of a given branchtravels only along that branch. In the calculations to be conductedlater we assume that nk ¼ 3. Thus, the total number of K changesper flash is equal to nnk where n is the number of branches in thechannel. In a lightning flash with five branches in the cloud thetotal number of K changes would be 15. If these K changes end upin a channel carrying a continuing current to ground then theresulting current will propagate to ground as an M component.The number of NOx molecules produced in the vertical channel bythe M components after correction for the pressure is given bynmZmlpð1� e�H=lp Þ where nm is the number of M componentstraveling along the vertical channel of a typical ground flash. Notethat we have assumed that the NOx production efficiency of atypical K change is identical to that of a typical M component. Thisassumption is not unreasonable since, as mentioned above, theyshare a common origin and therefore they probably have similarcurrents. The total number of NOx molecules generated by K

changes and M components after the pressure correction is

NOx�m ¼ nmZmlpð1� e�H=lp Þ þ nkZmL e�H=lp

h ið15Þ

Now, let us evaluate the magnitude of Zmk. A typical M

component current has a more or less symmetric bell-shapedwaveform with a rise time of about 400ms and a peak of about160 A (Thottappillil et al., 1995). Calculations done with such acurrent waveform show that Zmk ¼ 2�1020. M components travelalong the vertical channel carrying continuing currents. In atypical ground flash having a continuing current, M componentmay out-number the number of return strokes by 1–4. Therefore,a typical ground flash containing continuing currents may supportabout 16 M components along the vertical channel. In making theabove statement we have assumed that a typical ground flashcontains four return strokes. On the other hand, the percentage ofground flashes containing long (longer than 40 ms) continuingcurrents is about 30–50% (Rakov and Uman, 2003; Saba et al.,2006). This fixes the value of nm to about 5.

5.2.4. Continuing currents

In the model under consideration we assume that thecontinuing currents are flowing only through the vertical sectionof the ground flash. Of course, they also flow along horizontalchannels but our knowledge at present on how continuing currentis distributed in channels in the cloud is rather meager. In thiscase the total number of NOx molecules generated by these

ARTICLE IN PRESS

0Charge neutralized, C

1024

1025

1026

1027

Num

ber o

f NO

x mol

ecul

es

0

Horizontal channel length, km

a

b

c

d

e

f

20 40 60 80 100

10 20 30 40 50

Fig. 5. The number of NOx molecules produced by different processes associated

with a ground flash as a function of horizontal channel length. (a) Total, (b)

streamers in corona sheaths, (c) core current in leaders, (d) M components and K

changes, (e) continuing currents and (f) return strokes (four strokes). The vertical

channel length is assumed to be 5 km and the number of main branches in the

cloud is assumed to be 5.


continuing currents in a ground flash after pressure correction isgiven by

NOx�cv ¼ kcZconIcontclpð1� e�H=lp Þ

h ið16Þ

where Zcon is the number of NOx molecules produced per secondby a unit length of the discharge channel carrying continuingcurrent, Icon is the magnitude of continuing current, tc is thetypical duration of continuing current, and kc is the fraction ofground flashes that support continuing currents. In the calcula-tions we assumed that Zcon ¼ 2�1020 molecules/m/C (see Section3). According to experimental data, about 30–50% of the lightningflashes contain continuing currents and the amplitude and theduration of a typical continuing current are about 100 A and100 ms, respectively (Rakov and Uman, 2003; Saba et al., 2006).Thus, kc ¼ 0.3 and tc ¼ 0.1 s.

The exact nature of the source that drives continuing currentalong the vertical channel is not known. Most likely the source isthe development and the charge transfer along the upper channelsections. Since we have taken this activity into account in Section5.2.1 under leaders it is reasonable to consider only the verticalchannel here.

5.2.5.. NOx production in a typical negative ground flash

One can sum the contributions to the NOx production fromdifferent processes taking place in a ground flash as done in thefollowing equation:

NOx�ground ¼ Zstrlpð1� e�H=lp Þ þ ZstrLe�H=lp þZleaIlslpH

vsð1� e�H=lp Þ

þZleaIls

vsðl2

p � lpe�H=lp ½H þ lp�Þ þZleaIls

2vsnL2e�H=lp

þnsZleaIldlpH

vdð1� e�H=lp Þ þ

nsZleaIld

vdðl2

p � lpe�H=lp H þ lp��

þZsrnslp 1�lp

Hþlp

He�H=lp

� �þ nmZmlpð1� e�H=lp Þ

þnkZmLe�H=lp þ kcZconIcontclpð1� e�H=lp Þ ð17Þ

We made an attempt above to specify numerical values for theconstants that appear in this equation. One has to admit, ofcourse, that our knowledge on the numerical values of differentparameters is not complete and more work has to be done beforethe above equation could be applied with confidence. However,this equation provides a foundation on which the procedure toestimate NOx production in lightning flashes could be built as oneobtains more information concerning the parameters. In Appen-dix 1 we have summarized our current knowledge on each of theparameters that appear in Eq. (17).

Note that since M components are discharges propagating inchannels carrying continuing currents one may wonder whetherthe contribution from M components to the NOx production isalready taken into account in the production of NOx by continuingcurrents. The reason why we have included both contributions(i.e. continuing currents and M components) in the aboveequation is the following. The lightning channel becomes moreluminous when M components are traveling through it. Thisshows that they cause additional atomic excitation and ionizationbecause the channel becomes luminous while they propagatealong it. Furthermore, the optical observations show that duringthe propagation of the M components the diameter of the channelthrough which a continuing current is already propagating

gradually increases from about 0.5 cm to about 3 cm (Idone,1992). Moreover, M components were also observed to producethunder (Rakov et al., 2000). Thus it is reasonable to assume thatthe M component will enhance the NOx production beyond theNOx production level of the continuing current during its passagethrough the channel. This justifies adding the contribution of theM components to that of the continuing current. The samereasoning applies to the addition of the contribution from K

processes to the NOx yield from the leader currents flowingthrough the hot core of the developing leaders.

Now, let us illustrate the use of Eq. (17). In Fig. 5 we havedepicted the contributions from leaders (separated intocontribution from streamers in the corona sheath and currentflow along the core), return strokes, M components, K processes,and continuing currents as a function of the horizontal channellength L. First, note that the contributions from return strokes andthe continuing currents do not vary with increasing length of thehorizontal channels because these currents are assumed topropagate only along the vertical channel. Second observe thatthe return strokes produce the least contribution to the NOx

production whereas the largest contribution is made by leaderswith the current flowing along the core being the maincontributor. More than 90% of the contribution to the NOx

production is coming from leaders, M components, and K

processes. Leaders alone contribute about 50% to the NOx

production. Note that these observations are true also forhorizontal channel lengths as short as 10 km. On the other hand,in the literature, the return stroke is often assumed to be the NOx

source in ground flashes. Our study shows that this assumption isincorrect. Using VHF lightning channel mapping technique,Laroche et al. (1999) observed that the mean total channellength in over 20,000 cloud and ground flashes is 45 km. Takingthis length as a typical value the results presented in Fig. 5 showthat an average ground flash with four return strokes willgenerate about 4�1025 NOx molecules per flash.

ARTICLE IN PRESS


1024

1025

1026

1027

Num

ber o

f NO

x mol

ecul

es

0Horizontal channel length, km

a

b

c

d

e

10 20 30 40 50

20 40 60 80 100

Fig. 6. The number of NOx molecules produced by different processes associated

with a cloud flash as a function of horizontal channel length. (a) Total,

(b) streamers in corona sheaths, (c) core current in leaders, (d) K changes and

(e) continuing currents. The vertical channel length is assumed to be 5 km long and

the number of main branches in the cloud is assumed to be 5.


6. NOx production by cloud flashes

Cloud flashes normally occur between the main negative andupper positive charge regions of the cloud. Much of theinformation available today on the mechanism of the cloud flashis based on electric field measurements. Also Proctor (1981, 1991,1997), Shao et al. (1995), and Shao and Krehbiel (1996) madeimportant discoveries utilising VHF radio imaging techniques.Based on this information Cooray (2003) summarized theactivities during a cloud flash as follows (see also Rakov andUman, 2003).

The cloud flash commences with a movement of negativeleader discharge from the negative charge region towards thepositive one in a more or less vertical direction. The verticalchannel develops within the first 10–20 ms from the beginning ofthe flash. This channel is a few kilometres in length and itdeveloped with a speed of about 2.0�105 m/s. Even after thevertical channel was formed, one could detect an increase in theelectrostatic field indicative of negative charge transfer to theupper levels along the vertical channel.

The main activity after the development of the vertical channelis the horizontal extension of the channels in the upper level (i.e.,the channels in the positive charge region). These horizontalextensions of the upper level channels are correlated to the briefbreakdowns at the lower levels, followed by discharges propagat-ing from the lower level to the upper level along the verticalchannel. Thus the upper level breakdown events are probablyinitiated by the electric field changes caused by the transfer ofcharge from the lower levels. For about 20–140 ms of the cloudflash, repeated breakdowns occur between the lower and upperlevels along the vertical channel. These discharges transportednegative charge to the upper levels. Breakdown events of this typecan be categorised as K changes. In general, the vertical channelsthrough which these discharges propagate do not generate anyradiation in the VHF range, which indicates that they areconducting. This is so because, in general, conducting channelsdo not generate VHF radiation as discharges propagate alongthem. Occasionally, however, a discharge makes the verticalchannel visible at VHF and then the speed of propagation can beobserved to be about (0.5–3)�107 m/s, typical of K changes. Thisactive stage of the discharge may continue to about 200 ms.

In the latter part of this active stage (140–200 ms), significantextensions of the lower level channels (i.e. the channel in thenegative charge region) take place, but they occur retrogressively.That is, successive discharges, or K changes, often start justbeyond the outer extremities of the existing channels and thenmove into and along these channels, thereby extending themfurther. These K changes transport negative charge from succes-sively longer distances to the origin of the flash, and sometimeseven to the upper level of the cloud flash as inferred from VHFemissions from the vertical channel. Sometimes, these K changesgive rise to discharges that start at the origin of the flash and moveaway from it towards the origin of the K changes. Such dischargescan be interpreted as positive recoil events that transport positivecharge away from the flash origin and towards the point ofinitiation of the K change. At the final part of the discharge thevertical channel and the upper level channels were cut off fromthe lower level channels. This is probably caused by the decreasein the conductivity of the vertical channel. The above descriptionshows that a cloud flash can be described as an electrical activitythat collects the charge from the main negative charge centre andredistribute it in the positive charge centre after transporting italong a more or less vertical channel. The recent observationsbased on 3D interferometry also confirm the basic features ofcloud flashes described above (Lojou and Cummins, 2005; Lojouet al., 2008; Coleman et al., 2003; Morimoto et al., 2005). It is also

important to mention here that, since positive discharges do notradiate efficiently in HF and VHF, the channels created by positivedischarges could be detected only when negative recoil dischargestravel along them. Thus the channel structure of lightning flashesinside the cloud available today may not be complete.

Let us assume that the total length of the channels in thenegative charge centre is equal to that in the positive chargecentres. Denote this length by L. Assume further that thesechannels are oriented in a horizontal direction. The electricalactivity taking place in the negative and positive charge centresduring a cloud flash are not very different from the electricalactivity taking place in the negative charge centre in the case of aground flash (i.e. creation and extension of channels by leadersand intermittent occurrence of K changes). Taking into accountthe fact that the atmospheric pressure is different at the heightswhere negative and positive charges are located in a cloud, we candescribe the NOx production by a cloud flash by the followingequation.

NOx�cloud ¼ ZstrLe�Hn=lp þ ZstrLe�Hp=lp þZlea

2vnIleaL2e�Hn=lp

þZlea

2vnIleaL2e�Hp=lp þ nkZmLe�Hn=lp þ nkZmLe�Hp=lp ð18Þ

where Hn is the height of the negative charge centre and Hp is theheight of the positive charge centre. We assume that Hp ¼ 10 km.The results obtained for different values of L are shown in Fig. 6. Inmany studies dealing with the global production of NOx theassumption is made that the cloud flashes do not contributesignificantly to the NOx production in thunderstorms. Thisassumption was challenged previously by Gallardo and Cooray(1996). There are also field measurements showing theimportance of cloud flashes in NOx production. For example,airborne measurements of Dye et al. (2000) show that NOx from astorm that produced exclusively cloud discharges was comparableto other observations where both cloud and ground discharges areoccurring. Further, the modelling of airborne NOx measurementsby DeCaria et al. (2000, 2005) show that intra-cloud lightning (or

ARTICLE IN PRESS


0

2

4

6

8

10

12

Ann

ual N

Ox

yiel

d, T

g (N

)

0

Horizontal channel length, km

10 20 30 40 50

20 40 60 80 100

Fig. 7. Annual production of NOx by lightning flashes as a function of horizontal

channel length. The flash rate is assumed to be 100 per second, the vertical channel

length in ground flashes is assumed to be 5 km and the number of main branches

in the cloud is assumed to be 5.


the intra-cloud part of the ground flashes) was the dominantsource of NOx for the thunderstorms investigated in the study. Theresults presented in Fig. 6 show that for a given channel lengthboth the ground flash and the cloud flash generate more or lessequal number of NOx molecules.

7. Global production of NOx by lightning flashes

The results presented above can be used to evaluate the globalproduction of NOx by lightning flashes if the flash rate of thelightning flashes is known. In the analysis we have not treatedpositive flashes separately but indirectly assumed that the NOx

production from a typical positive flash is similar to that of a typicalnegative flash. In the literature the flash rate is assumed to lie in therange of 40–300 flashes per second (Turman and Edgar, 1982;Christian et al., 2003). In the results to be presented we assumed aglobal lightning flash rate of 100 per second. There is no reason toseparate the flash rate into ground and cloud flashes because bothtypes of flashes produced more or less the same amounts of NOx. InFig. 7 we have depicted the annual NOx production by lightningflashes as a function of the horizontal channel length. If one assumesan average total channel length of 45 km for a lightning flash, theglobal NOx production by lightning flashes will be about 4 Tg(N)/year. One has to understand that the global lightning flash frequencyis not a constant and it may vary from one year to another.More over the number 100 flashes/s is based on thunderstormobservations and satellite data suggest values in the range of40–300 flashes/s. But, of course this estimation too depends on thedetection threshold level of the satellite and the possible screeningof optical radiation by cloud cover. The important point however isthat the NOx production rate is proportional to the global lightningflash frequency. The number 4 Tg(N)/year is based on 100 flashes/sand if it varies say between 40 to 300 flashes/s, the gobal NOx

production rate will also vary between about 2 to 12 Tg(N)/year. Leeet al. (1997) studied the various sources and sinks of NOx in theatmosphere and concluded that the contribution from lightning

should be in the range of 4–8 Tg(N)/year. Our results agree with thisprediction. The present global estimates of NOx based on theoreticaland laboratory studies vary between 1 Tg(N)/year to about100 Tg(N)/year. The two orders of magnitude variation in thisestimate is due to the different results obtained for the NOx

production efficiency of laboratory discharges and the differentvalues assumed for the energy dissipation in lightning flashes. Aspointed out previously, the variation in the efficiency of NOx

production in laboratory discharges is probably due to thedifferences in the current waveforms associated with thesedischarges. The energy dissipation in lightning flashes is aparameter that cannot be measured directly and therefore is not agood scaling quantity in NOx studies. Our estimate is free from boththese drawbacks. Another interesting point of our study is theobservation that most of the NOx production in lightning flashes isdue to cloud flashes or the cloud portion of ground flashes. Thus theinjection of NOx by thunderstorms into the atmosphere takes placeprimarily at a height of 5–10 km. The theoretical studies conductedby Gallardo and Rodhe (1997) show that in order to account forthe nitrate deposition in the remote marine regions the strength ofthe NOx source due to lightning should be about 5 Tg(N)/year and thesource should be located at the cloud height. Our study confirms thisinference.

8. Conclusions

The results presented in this paper show that the NOx

production efficiency of electrical discharges depends not onlyon the energy dissipated in the discharge but also on the shape ofthe current waveform. This provides an explanation for thedifferent values of NOx molecules/J obtained by different research-ers in different experiments. Thus, energy dissipated in adischarge is not suitable as the scaling quantity for extrapolatingthe laboratory data to lightning flashes. In this paper, we present atheory which can be used to evaluate the NOx production inelectrical discharges, if the discharge current is known. The resultsobtained are compared with the available experimental data and agood agreement is found between theory and experiment. Thestudy shows that the primary contribution to NOx from thunder-storms is coming from the electrical activity inside the cloud, withonly a small fraction being contributed by return strokes. Usingthe proposed theory, we estimated the global NOx production bylightning flashes taking into account different lightning processessuch as leaders, return strokes, M components, K changes andcontinuing currents. The results show that the efficiency of NOx

production in ground flashes and cloud flashes are similar and foran average total channel length of 45 km the global production ofNOx by lightning flashes, based on lightning flash frequency of100 flashes/s, is about 4 Tg(N)/year.

Appendix 1

Zstr: the number of NOx molecules generated in the corona sheathduring the creation of a leader channel. The currentestimate is 2�1020 molecules/m

Zcon: the number of NOx molecules generated per unit length perunit charge by a continuing current. The best estimate is2.0�1020 molecules/m/C.

Zlea: the number of NOx molecules generated per unit length perunit charge by a the leader current flowing through thechannel core. The best estimate is 2.0�1020 molecules/m/C.

lp: the decay height constant for the atmospheric pressure. This isequal to 8500 m.

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H: the height of the negative charge centre. The value used in thecalculations is 5000 m.

Hp: the height of the positive charge centre. The value used in thecalculation is 10,000 m.

L: the total length of the horizontal sections in the cloud. Currentestimates place it some where between 30–50 km.

Zfr: the number of NOx molecules generated per unit length in adischarge channel carrying a current waveform similarto that of a typical first return stroke. The best estimateis 5.9�1020 molecules/m.

Zsr: the number of NOx molecules generated per unit length in adischarge channel carrying a current waveform similarto that of a typical subsequent return stroke. The bestestimate is 1.4�1020 molecules/m.

Zs: the number of subsequent return strokes in a typical groundflash. The best estimate is 3.

Zm: the number of NOx molecules generated per unit length in adischarge channel carrying a current waveform similarto that of M component. The best estimate is 2.0�1020

molecules/m.nk: the average number of K changes taking place during the

development of a given channel branch in the cloud. It isassumed to be 3.

nm: the average number of M components in a typical groundflash. The best estimate is 5. This number is based on thefact that a ground flash with a continuing current cansupport about 16 M components and about 30% of theground flashes contain continuing currents.

kc: the fraction of ground flashes containing continuing currents.The best estimate is 0.3.

tc: the average duration of continuing current. The best estimateis 100 ms. This figure is actually valid for long continuingcurrents.

Icon: magnitude of typical continuing current. The best estimate is100 A.

Ils: magnitude of typical stepped leader current. The best estimateis 100 A.

Ild: magnitude of typical dart leader current. The best estimate is1 kA.

vs: the average speed of development of lightning leader channelsin virgin air inside the cloud. The best estimate is2�105 m/s.

vd: the average speed of dart leaders. The best estimate is 107 m/s.n: the number of major branches inside the channel. The available

VHF interferometric images show that it may vary fromabout 3–10. It is assumed to be 5.

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