Atmospheric Research 98 (2010) 327–340

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Further laboratory investigations into the Relative Diffusional Growth Ratetheory of thunderstorm electrification

C. Emersic ⁎, C.P.R. SaundersSchool of Earth, Atmospheric and Environmental Sciences, The University of Manchester, Simon Building, Manchester, UK

a r t i c l e i n f o

⁎ Corresponding author. Tel.: +44 161 306 2488.E-mail address: christopher_ce@hotmail.com (C. E

0169-8095/$ – see front matter © 2010 Elsevier B.V.doi:10.1016/j.atmosres.2010.07.011

a b s t r a c t

Article history:Received 3 March 2010Received in revised form 18 June 2010Accepted 12 July 2010

Predictions from the Relative Diffusional Growth Rate theory have allowed us to furtherexamine controls over the sign of graupel charge in laboratory experiments involving collisionsbetween ice crystals and riming graupel. This has been achieved primarily through the use oftwo-cloud experiments in which a supercooled droplet cloud and an ice crystal cloud aremixedtogether. A range of crystal-cloud nucleation techniques has enabled substantial control overthe preconditioning of ice crystal surface growth rates such as to control transient rapid crystalgrowth on mixing with a droplet cloud prior to interaction with a riming target. We havequalitatively identified the effects that crystal surface growth rate and size have on the rate oftransient rapid growth after mixing. Crystals with higher surface growth rates in environmentsnearer to water saturation reduce the effect of transient rapid growth on mixing leading topositive graupel charging. Crystals with lower surface growth rates in environments nearer toice saturation enhance transient rapid growth on mixing – particularly for smaller crystalsizes – to promote negative graupel charging. This is consistent with the Relative DiffusionalGrowth Rate theory which has been developed frommany laboratory studies and shows that incollisions between ice particles, the surface growing faster by diffusion charges positively.Using both the shortest and longest nucleation techniques developed, it was possible to extendnegative charging to approximately −20 °C and −14 °C respectively. Being able to controlcloud microphysics and determine its effect on charge sign has led to the conclusion thatnumerical models of thunderstorm charge development need to take account of the wide rangeof specific microphysical conditions and their effects on cloud particle charging throughoutmany regions and the lifetime of a thunderstorm.We also provide evidence in support of new interpretations of the results of other researchersby using predictions of the Relative Diffusional Growth Rate theory to enable the developmentof experimental techniques to promote negative graupel charging to record high temperatures,and consequently allow negative charging at any sub-zero temperature applicable tothunderstorms.

© 2010 Elsevier B.V. All rights reserved.

Keywords:Ice crystalGraupelChargingRimingRelative Diffusional Growth Rate theory

1. Introduction

The Relative Diffusional Growth Rate theory remains themost successful explanation of charge transfer in laboratorycloud chamber experiments in which ice crystals reboundfrom a riming target representing a falling graupel pellet. The

mersic).

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success of this theory is based on almost 25 years ofsupporting laboratory evidence (Keith and Saunders, 1990;Saunders et al., 1991, 2004, 2006; Brooks et al., 1997;Saunders and Peck, 1998; Pereyra et al., 2000; Mitzevaet al., 2005; Emersic, 2006). The theory was empiricallydetermined by Baker et al. (1987) and states that: “During iceparticle collisions, the particle whose surface is growingfastest from vapour diffusion at the instant of collision willcharge positively on particle separation”. The mechanism

328 C. Emersic, C.P.R. Saunders / Atmospheric Research 98 (2010) 327–340

operates independently of any pre-existing electric field andsimply relies on collisions between ice particles with avapour-grown surface. Many observational and simulationstudies of storms have also supported the hypothesis thatgraupel and ice crystals are the species that play the mostvital role in the electrification of storms and occurrence oflightning (e.g. Dye et al., 1986, 1988; Ziegler et al., 1991;Bringi et al., 1997; Black and Hallett, 1999; Bruning et al.,2007). This field-independent graupel–ice crystal interactioncharging process described by the Relative DiffusionalGrowth Rate theory is now widely considered to be theprinciple charging mechanism in thunderstorms; however, itis often misnamed in the literature as the ‘non-inductive’theory.

This paper sets out to examine the Relative DiffusionalGrowth Rate theory further, using it to make predictionsabout the microphysical controls of charge transfer duringcollisions between graupel particles and ice crystals. This isdone by using experimental techniques known to influencecharge transfer and by developing new ones based onpredictions from the theory. In particular, this paper expandson the work of Saunders et al. (2004, 2006), and providesfurther support to justify a reinterpretation of the results ofTakahashi (1978).

The primary experimental methodology in the materialpresented here involves the explicit use of two-cloud-mixing experiments akin to the work of several others(Pereyra et al., 2000; Saunders et al., 2004, 2006). Suchexperiments involve the generation of two separate clouds,one of supercooled water droplets and one of ice crystals;these clouds are then mixed together for a brief time priorto interaction with a riming target. This is in contrast tosingle-cloud experiments in which crystals always share anenvironment with a continuous supply of supercooledwater droplets (Takahashi, 1978; Jayaratne et al., 1983;Keith and Saunders, 1990; Saunders et al., 1991; Brooks etal., 1997; Saunders and Peck, 1998). When crystals grow ina separate cloud, initially containing supercooled waterdroplets and a given liquid water content, the vapoursupply available for crystal growth via the Bergeron–Findeisen process becomes substantially reduced due tocompetition amongst the crystals for the available vapour(e.g. Rogers and Yau, 1989). The environment becomes sub-water saturated, and the crystals can therefore be subjectedto growth in an environment between ice andwater saturation,with a bias toward ice saturation. The consequence of this isthat the growth rate of the crystal surface reduces, and thesurface becomes colder than it would otherwise have been hadit originally grown in an environment above water saturationbecause of the reduced release of the latent heat of fusionassociated with limited growth. When crystals preconditionedin this way are introduced into a new environment that is at orabove water saturation (e.g. by mixing with a droplet cloud),the crystals experience a rapid, but transient growth. Thegrowth is rapid because the lower surface temperature reducesthe equilibrium surface vapour pressure over the ice crystalsurface, and the rapid growth is transientdue to the subsequentrapid increase in surface temperature associated with the nowincreased release of latent heat of fusion, ultimately increasingthe surface vapour pressure. After mixing, the crystals respondto the new environment, with an increased growth rate, on

timescales of the order of microseconds (Pruppacher and Klett,1978) and then take additional time of the order of tens ofmilliseconds to reach thermal equilibrium with the newenvironment (Saunders et al., 2004). If the crystals collidewith the target prior to thermal relaxation during the brief timethat their growth rate is enhanced, then in accordancewith theRelative Diffusional Growth Rate theory, they aremore likely tocharge positively on separation, leaving the target with anequal and opposite negative charge. There is no net chargetransfer if the crystals do not separate and instead stick to thetarget surface. However, if thermal equilibrium of the rapidlygrowing crystals is achieved after mixing but before theyinteract with the target, then the growth rate of the crystals atinteraction time will be reduced and the crystals will havereverted to being single-cloud-like in nature. To be clear, theunique properties of the two-cloud rapid-growth phenomenononly exist briefly, and must be engineered to be utilised withinthe available timewhen testing the RelativeDiffusional GrowthRate theory. The phenomenon has been observed and tested ina number of recent previous studies (Pereyra et al., 2000;Saunders et al., 2004, 2006).

Two-cloud experiments have proven to be important forour understanding of microphysical charge transfer processesand examining the Relative Diffusional Growth Rate theory;single-cloud experimental setups, as we have used in paststudies, are limited in their ability to provide insight about thegoverning microphysics leading to charge transfer. Thetransient rapid-growth phenomenon associated with two-cloud experiments allows for much more extensive exami-nation and understanding of universally-applicable electro-microphysics that affect resulting charge transfer in allexperimental situations, whether single- or two- cloud. Thedirect benefits of two-cloud experiments in testing the RelativeDiffusional Growth Rate theory are demonstrated in this paper.One final note: It is traditional in thunderstorm electrificationpapers of this kind, that when reference is made to chargetransfer, the sign convention is always with respect to graupelunless otherwise specified; negative charging implies thegraupel charges negatively.

Section 2 describes the equipment used in the experi-ments, and discusses the development and characterisationof all experimental techniques employed. Section 3 describesthe experiments themselves and the results obtained, withSection 4 mirroring a similar structure to discuss the findingsand their implications. Section 5 provides a succinct conclud-ing summary of the research.

2. Experimental setup

This section is presented in two distinct parts. The firstdiscusses the instrumentation used in the experiments; thesecond presents the development and characterisation ofseveral cloud nucleation techniques used to generate crystalswith a range of surface properties prior to their mixing withthe droplet cloud.

2.1. Experimental apparatus and basic procedure

Experiments were performed in the Manchester cloudchamber located within a cold room capable of reachingtemperatures down to −40 °C. The cold room measures

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3 m×2 m×4 m and the cloud chamber inside measures0.9 m×1.5 m×2 m respectively (Fig. 1). This chamber wassplit into two halves with a sheet of thin plastic to create acrystal-cloud chamber and a droplet-cloud chamber. Asealable orifice was created to ease accessibility betweenthe two chambers during experimental preparations. Cali-brated thermocouples are symmetrically placed at a numberof heights within the two chambers, namely roof-level,target-level, and floor-level. A water boiler is located beneatheach of the two chambers to generate cloud. Airflow throughthe tubes is generated using an air pump, drawing out thecloud. The pump speed is adjusted using a voltage controller,with air speed set to 6 m s−1. Continuous pump operationand a three-way valve were used to provide near-instant airflow to avoid the effects of low particle acceleration during airpump initiation.

Ice crystal clouds are generated in the crystal chamberusing a number of techniques discussed in Section 2.2.However, they all involve cooling part of a cloud of super-cooled water droplets to below the homogeneous freezingtemperature to cause ice nucleation. This is either achievedusing liquid nitrogen-cooled wires, an open pot of nitrogen,or rapid adiabatic expansion of a small volume of compressedair. The cloud is considered ready for experimental use andextraction when it first becomes entirely visually glaciated,and the crystal number concentration is at its highest beforeany significant sedimentation. The time of this condition afternucleation (and the crystal surface properties) was depen-dent on the choice of nucleation technique, and is discussedin more detail in Section 2.2.

A cylindrical metal rod of diameter 3 mm and length40 mm is housed vertically inside tubes of internal diameterof 42 mm and acts as a target for the cloud particles,

Fig. 1.Manchester cloud chamber. A: Riming target rod and charge amplifier;B: Crystal tube; C: Droplet tube; D: Opening between chambers; E: chamberseparator; F: Vapour and droplets; G: Crystal boiler source; H: Droplet boilersource; J: Crystal chamber; K: Droplet chamber; L: Airflow to external airpump; T: Thermocouples.

simulating a riming hailstone (Fig. 2). It is connected to asensitive electrometer which detects charge transferred tothe rod during collision–separation events between the icecrystals and the riming target. The output from the amplifieris fed to a chart recorder which plots the magnitude andpolarity of the charge transferred to the rod with time (thecurrent).

As the separate liquid and ice clouds are drawn out of theirchambers through the pipes, they are mixed prior tointeracting with the target rod. The two clouds are broughttogether in the piping system and mix for a spatial distanceof about 10 cm before reaching the target rod at a speed of6 m s−1, which is comparable with the relative terminalvelocity between colliding particles in the updraft regions ofnatural thunderclouds (Locatelli and Hobbs, 1974). Calcula-tions of the Reynolds number indicate that the cloud is wellmixed by this time. The brief mixing time of about 1.6 ms ismuch less than the thermal relaxation time of the crystals(tens of milliseconds (Saunders et al., 2004) and therefore theexperiments can take advantage of the two-cloud rapidcrystal growth phenomenon.

The droplet cloud is the primary contributor to the riming ofthe target rod; the collected crystals were shown in auxiliaryexperiments to contribute negligible mass compared withdroplet collection. The parameter ‘effective water content’ isused in these experiments, as this is ameasure of that portion ofthe cloud liquid water content (LWC) actually collected by therimer during the accretion time, and thus influences the surfaceproperties of the rimer. The effectivewater content is calculatedas a product of the cloud liquid water content (W) and thecollection efficiency (E) of the target rod, which has a valuebetween 0 and 1, and is affected by the rod geometry, air speed,and droplet size, amongst other parameters (Ranz and Wong,1952). The effectivewater content is thus given the symbol EW,andhas densityunits of gm−3. Brooks et al. (1997) showed thatrime accretion rate (RAR) – the product of EW and velocity(V) – was also a fundamental parameter to use because thecharge transferred during collisions was the same for a givenvalue of RAR, regardless of the permuted values of the productof EW and V. This parameter allows velocity independence inexperiments; however, in the experiments presented here,only a single airspeed of 6 m s−1 was used, and so EW wasselected in the interests of simplicity. EW was determined bymeasuring the mass of rime accreted on the target rod duringeach experimental riming time, taking account of thecorresponding volume swept out by the projected surfacearea of the rod. The collected ice mass was determined byweighing the rimed target rod at the end of each experimentusing a sensitive balance, and comparingwith the unrimed rodweight. The riming time in all experiments here was the sameat 30 s.

The pipes within the cloud chamber (Fig. 1) lead outthrough the external wall of the cold room and through aCloud Particle Imager (CPI) probe. The CPI is an instrumentused here to gather particle size distribution data from themeasured cloud particles, and is acting as a substitute for thecontinuous formvar replicator used in earlier studies. Theprobe was designed for airborne sampling of natural clouds,but adequately serves laboratory use (Connolly et al., 2007).All measurements using the CPI were corrected for oversizingusing the correction algorithms of Connolly et al. (2007).

Fig. 2. Target rod and cloud extraction tube. A: Cross-sectional view; B: Side view.

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2.2. Characterising nucleation techniques

The vapour content in the crystal chamber and the surfacegrowth rate of the crystals are controlled by the presence ofsupercooled water droplets and by the choice of nucleationtechnique. A longer nucleation time produces a greaternumber of crystals which compete more for the availablevapour and result in slower growing and thus relativelycolder crystals; conversely shorter nucleation times producerelatively fewer and therefore larger, faster growing, rela-tively warmer crystals.

Quantitative knowledge of crystal surface properties is notin focus here, nor realistically attainable due to experimentaluncertainties and the distributions in crystal sizes produced.What is of interest and reproducible, is the qualitative,relative, difference in the surface properties of crystalsgenerated at a given temperature by the various nucleationtechniques. It is this qualitative, relative, difference that canbe used to examine the resulting charging and test theRelative Diffusional Growth Rate theory.

All crystal clouds are grown from a droplet cloud with aninitial EW of b0.5 g m−3 (corresponding, from test rodgeometry and the droplet spectrum (Ranz and Wong, 1952),to equate to a LWC of approximately b1 g m−3), which was avalue optimised for minimum chamber heat input, andproviding sufficient LWC to allow for a range of crystalgrowth rates given a particular choice of nucleation tech-nique. Seven different nucleation techniques were used in theexperiments presented here and covered the full spectrum ofcorresponding crystal surface growth rates. The characterisa-tion of the crystals produced by each nucleation technique isdiscussed below. Two different classes of nucleation tech-nique were used: single- and double-nucleation techniques;each will be addressed in their own subsection.

2.2.1. Single-nucleation techniquesSingle-nucleation techniques involve generating a cloud

of supercooled water droplets, nucleating once, and allowingthe crystals to grow. The nucleation techniques are distin-guished by the effective length of time the nucleation processlasts, and this controls the number of crystals generated.There are five single-nucleation techniques that producedistinct relative crystal surface growth rates.

Nucleation technique A involved leaving an open pot ofliquid nitrogen in the cloud to continuously nucleate.Nucleation techniques B–D involve inserting a liquid nitro-gen-cooled rod (about −200 °C) into the cloud of super-cooled water droplets, each for a different length of time.Nucleation technique B involved inserting the rod andwafting it around for approximately 3 s — this producedresults comparable to nucleation technique A. Nucleationtechnique C involved inserting the rod and keeping it steadyfor approximately 1 s; nucleation technique D involved a verybrief stab of the rod into the cloud. Nucleation technique Einvolved the use of a syringe to adiabatically expand a smallvolume (2 ml) of compressed ambient air to locally cool aportion of the supercooled water droplet cloud to below thehomogeneous water freezing temperature.

A cloud of supercooled water droplets was generated inthe crystal chamber and left to equilibrate for 10 minwith theboiler left on continuously during experiments. The cloudwasnucleated with a chosen nucleation technique, and the crystalcloud sampled during the time corresponding to the time ofcrystal extraction (and target riming) in charge transferexperiments (Section 3). This procedure was repeatedmultiple times for a given nucleation technique and cloudtemperature to test reproducibility, and was performed foreach of the five nucleation techniques, for each of severaltemperature bands ranging from −10 °C to −30 °C inapproximately 5 °C increments. The growth rate of crystalsat−5 °C is sufficiently slow that distinguishing droplets fromcrystals using the CPI probe data was difficult; formalcharacterisation could therefore not be completed for thistemperature range. However, the general relative trends infindings, which were consistent at all other temperatures,could be extrapolated to this temperature range with goodconfidence.

In formal charge transfer experiments (Section 3), thecloud temperature is often not precisely at the temperaturesused in the calibration, and Table 1 shows the temperatureband classifications used in attributing these calibrations.

Once nucleated, a cloud of growing crystals has a dis-tributed range of crystal sizes. The mode of size distributionhistograms (averaged over 10 s bins of sample time) wasused as the measure of the typical crystal size as a function oftime, to determine the growth rate of crystals in each of the

Table 1Classification of measured cloud temperature relative to calibrationtemperature banding.

Measured cloud temperature (°C) Calibration temperature band (°C)

−4.0–−7.9 −5−8.0–−12.4 −10−12.5–−17.9 −15−18.0–−22.4 −20−22.5–−27.4 −25−27.5–−32.5 −30

ig. 3. The average crystal growth rate produced by the range of single-ucleation techniques at different temperatures, ranging between 0 and.8 μm s−1. The important feature of this figure is the qualitative, relativecrease in growth rate as the nucleation time is reduced, and not thearticular absolute values of crystal surface growth rates. This relativecrease in growth rate with reducing nucleation time at a given temperatureconsistent and experimentally reproducible at all temperature ranges.

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crystal clouds. Calculations of crystal collision efficiency usingthe equations of Ranz and Wong (1952), and the magnitudeof charge transferred per event (collision and separation) as afunction of crystal size, using the charge transfer equations ofKeith and Saunders (1990), revealed that the concentration ofcrystals in each size range in typical average size distributionstransferred the same order of magnitude of charge, validatingthemeasure of the distribution'smodal size as a characteristicindicator of crystal growth rate that accommodates thecloud's internal variations.

As discussed in the second paragraph of Section 2.1, thecrystal cloud is considered ready for mixing during chargetransfer experiments (Section 3) when it first becomes visuallyentirely glaciated (the droplets disappear indicating approach-ing ice saturation) and the crystal number concentration is at itshighest before any significant sedimentation. The time of thiscondition after nucleation was dependent on the choice ofnucleation technique, and the 30 s extraction period in whichcloud mixing and target riming occur, is described in Table 2.Note that nucleation techniques F and G are discussed inSection 2.2.2 but are listed here for consolidation.

The average growth rate of crystals produced by thesesingle-nucleation techniques prior to mixing at differenttemperatures are shown in Fig. 3, and range in value between0 and 0.8 μm s−1.

As discussed in the first paragraph of Section 2.2, theimportant aspect of Fig. 3 is that the growth rate of crystals, at agiven temperature, qualitatively increases for shorter nucle-ation times. This relative trend in growth rate is consistent andreproducible over all temperature ranges, and it is thisqualitative, relative difference that is of interest when laterused in examining the Relative Diffusional Growth Rate theoryof charging. The particular quantitative growth rate is differentwith temperature for any one given nucleation technique, butthis is not relevant for testing expectations of the theory; again,only how the crystal growth rates at a given temperature

Table 2List of times when the crystal clouds were extracted and used in chargetransfer experiments for the different nucleation techniques.

Nucleation technique Time of charge transfer(seconds after nucleating)

A 180–210B 180–210C 120–150D 90–120E 90–120F 90–120G 90–120

Fn0inpinis

qualitatively vary as a function of nucleation technique is ofinterest. As discussedmore in Section 1, it is expected from thetheory that longer nucleation times – producing lower crystalsurface growth rates –will promote enhanced negative graupelcharging. Neither these experiments, nor the Relative Diffu-sional GrowthRate theory, allowprecisenumerical calculationsof the amount of charge transferred, and this is not in focushere.

Given the averaged trends of crystal growth rate, it ispossible to calculate the supersaturation the crystals experi-enced from the environment by virtue of that measuredgrowth, by using the crystal growth rate equations of Mason(1953). The derivation for both spherical and circular diskshaped ice crystals is shown in Appendix A. From ourmeasurements of crystal growth rate, the average supersat-uration experienced by the crystals just prior to mixingwith adroplet cloud in charge transfer experiments (Section 3) wascalculated for each nucleation technique at each examinedtemperature (Fig. 4). Crystal cloud experienced supersatura-tion values range between 0 and 0.4% with respect to ice.

Again, as with Fig. 3, the important aspect of Fig. 4 is thequalitative, relative difference in supersaturation for eachnucleation technique at a given temperature. The absoluteexperienced-supersaturation values as a function of nucle-ation technique for a given temperature, or the differences inmagnitude of experienced-supersaturation for a given nucle-ation technique as a function of temperature, are of no concernin using the different crystal clouds to examine the RelativeDiffusional Growth Rate theory.

Both Figs. 3 and 4 show that the qualitative, relativedifference in crystal surface growth rate and experienced-supersaturation as a function of nucleation technique for agiven temperature is correlated consistently with the nucle-ation time. Given this, it is possible to test the RelativeDiffusional Growth Rate theory by introducing the differentcrystal clouds to a droplet cloud with a much highersupersaturation, causing sudden rapid crystal growth, whoserate is governed by the relative difference in preconditionedsurface temperature (via initial growth rate, as discussed inSection 1), dictated through the choice of nucleation technique.

Fig. 4. The average experienced supersaturation (with respect to ice) of crystalsprior to mixing with the droplet cloud, for a given nucleation technique andcloud temperature. Experienced supersaturation values range between 0 and0.4% over ice. Only the qualitative, relative difference in the trend of the averagesupersaturation experienced by a crystal produced at a given temperature bythe different nucleation techniques is important; longer nucleation timesproduce crystals experiencing supersaturation values closer to ice saturation aany given temperature. The relative increase in experienced supersaturation asa function of nucleation technique at a given temperature is consistent for altemperatures.

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t

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It is expected that longer nucleation times will promoteenhanced negative graupel charging. These experiments arepresented in Section 3 — and Section 3.2 in particular.

Table 3Calculated total charge transferred by small crystals produced in double-nucleation techniques in a typical experiment using equations of Ranz andWong (1952), and Keith and Saunders (1990).

Nucleationeventnumber

Average crystalsize at extractiontime (μm)

Efficiency ofcrystalimpaction

Typicalcrystalcount

Total chargetransferred(fC)

First 55 91% 815 2119Second 27 73% 200 36

2.2.2. Double-nucleation techniquesDouble-nucleation techniques are more complex than

single-nucleation techniques, and as their name suggests,they involve nucleating a cloud of supercooled water dropletstwice before crystal extraction. They were developed toexamine elements of the Relative Diffusional Growth Ratetheory; a detailed explanation of the scientific background isoutlined fully in Section 3.1. In brief however, the objective ofthe charge transfer experiments associated with double-nucleation is to examine, qualitatively, the indirect effects oncharging of crystal size in two-cloud experiments, byexamining the effect of crystal size on transient rapid growthduring cloud mixing (discussed in detail in Section 1). Forthese experiments, two nucleation techniques were devel-oped that created clouds of either small or large crystals, andthe crystals in both cases were growing slowly in conditionsvery near ice saturation immediately prior to mixing.

The first nucleation event in the double-nucleation pro-cess was a single-nucleation technique selected based on thecrystal size requirements at extraction time. Later, when thecrystals were approaching the desired size, a second andmuch longer nucleation event occurred to ensure the rapidremoval of all remaining vapour via increased Bergeron–Findeisen processes (Rogers and Yau, 1989). This resulted inthe slowest growth of the originally nucleated crystals,subjecting them to an environment at approximately icesaturation. For nucleation technique F, the first nucleationevent was performed using nucleation technique C followedby nucleation technique B to produce small, slow growingcrystals. For nucleation technique G, nucleation technique Ewas followed by nucleation technique B to produce large,slow growing crystals.

The initial procedure was to generate a cloud of super-cooled water droplets in the crystal chamber which was leftto equilibrate for 10 min. The cloud was then nucleated forthe first timewith either nucleation technique C or nucleationtechnique E depending on which double-nucleation tech-nique was being characterised (correspondingly F or Grespectively). One minute after the first nucleation event,the vapour and droplet source from the boiler was stoppedand cloud was simultaneously nucleated again using nucle-ation technique B to reduce the remaining traces of vapour inthe chamber. The crystal cloud was sampled during the timecorresponding to the time of crystal extraction and riming informal charge transfer experiments (Section 3.1), namelybetween 90 and 120 s after the first nucleation (Table 2). Thecalibration procedure was repeated multiple times for eachof the two double-nucleation techniques and cloud tem-peratures to test reproducibility. These two double-nucle-ation techniques were only used within a temperature rangefrom −15 °C to −20 °C in charge transfer experiments(Section 3.1), and therefore only those two temperatureswere calibrated. As with the single-nucleation techniques, thesame temperature banding scheme was used, as outlined inTable 1.

Note that for nucleation technique F, the first nucleationwas purposely not one of the longer nucleation techniques Aor B, to ensure slightly larger crystals at extraction time,which for these double-nucleation techniques was 30 searlier than for the comparable single-nucleation technique.These larger crystals enabled better detection by the CPIprobe to increase confidence in our observations for this morecomplex and difficult crystal engineering. It was onlyimportant that the resulting crystals were qualitatively,relatively smaller than those of nucleation technique G, in acomparable environment.

The second nucleation event, besides affecting existingcrystals, also produced new crystals. These were shown tohave insignificant charge contribution by calculating thecollision efficiency for the size of secondary-nucleationcrystals during the crystal extraction time. Using theequations of Ranz and Wong (1952), this was shown to bearound 73%. The charge transfer per event equation of Keithand Saunders (1990), and the corrected size distributionconcentrations given by the CPI for the appropriate size bin(Connolly et al., 2007), were used to calculate the total chargecontribution of these small crystals (Table 3). The total chargecontribution is negligible, so they do not contaminate thecharging results.

In double-nucleation experiments, an identical sizingprocedure was used as in the single-nucleation case, using

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the mode of the distributions with time as a general sizeindicator. From this, it was possible, as in Section 2.2.1, tocalculate the average crystal surface growth rates andcorresponding experienced-supersaturation for each nucle-ation technique at each temperature. Table 4 confirms that thecrystals did have the properties they were engineered for, andwere suitable for use in the associated charge transferexperiments. The crystals produced by both double-nucleationtechniques are experiencing ice-saturated conditions prior tomixing at extraction time, and are growing slowly therefore,but are comparable in their growth rates. The crystals producedby nucleation technique F are considerably smaller than thoseproduced by G, and therefore the effects of size on charging intwo-cloud experiments can be determined.

3. Experiment summary and results

Three sets of experiments were performed to examineelements of the Relative Diffusional Growth Rate theory;all involving the mixing of two separate clouds. Each experi-ment set is discussed in the following separate subsections;the experimental discussions (Section 4) are also sectionedaccordingly.

3.1. Effects of crystal size in two-cloud experiments

Through the use of two-cloud experiments, research hasshown, in accordancewith theRelativeDiffusionalGrowthRatetheory, that rapid growth of crystals resulting frommixing intoa droplet cloud before interacting with a target, promotesnegative graupel charging (Saunders et al., 2004, 2006). (Thedetails of this process and the importance of two-cloudexperiments are discussed more thoroughly in Section 1.)However, crystal radial growth rate is inversely proportional toits size, and therefore larger crystals are expected to respondless severely to this rapid growth on cloud mixing.

In the two-cloud experiments of Saunders et al. (2004), itwas shown that small, slow growing, and therefore relativelycolder crystals (generated by using the equivalent ofnucleation technique B, Section 2.2.1) when mixed with thedroplet cloud prior to target interaction gave rise to negativerimer charging. When crystals, generated by nucleationtechnique B, were allowed to grow faster and heat up bythe introduction of more vapour and droplets into the crystalcloud a few seconds prior to mixing with the droplet cloud,those crystals led to positive charging, despite remainingcomparable in size. This supported the Relative DiffusionalGrowth Rate theory, and also revealed that the crystal surfacegrowth rate (and therefore surface temperature) is an

Table 4Summary of crystal properties for double-nucleation techniques F and G. Temperatusurface growth rates of crystals from both nucleation techniques at both temperatsaturation. Crystals from nucleation technique F are smaller than nucleation techni

Temperature (°C) Nucleationtechnique

Average crystal size duringextraction time (μm)

Averagsurface

−15 °C F 46 −0.02G 66 0.05

−20 °C F 46 0.06G 60 0.01

influential factor on the transient rapid growth and resultingcharge transfer in two-cloud experiments. However, howsignificantly the effect of transient rapid growth is affected,qualitatively, by crystal size and therefore how crystal sizeindirectly affects the resultant charging in two-cloud experi-ments, were not determined in the experiments of Saunderset al. (2004). While clouds of small, slower growing and thusrelatively colder crystals could be generated in the experi-ments of Saunders et al. (2004), slower growing large crystalscould not, and such crystals were a necessary requirement ofsuch an investigation. A more advanced engineering of thecrystal-cloud conditions was required. Using the double-nucleation techniques characterised in Section 2.2.2, it ispossible to produce the required slow growth conditions andrelatively colder crystals at both large and small sizes, and tothen examine how crystal size affects charge transferfollowing transient rapid growth after two-cloud mixing.

The experimental procedure for the charge transferexperiments was similar to that used to characterise thedouble-nucleation techniques. In addition, a separate dropletcloud was prepared, with liquid water content adjusted toprovide the desired EW. Nucleation techniques F and G wereused to control resulting crystal size (Table 4). The resultingcharge transfer to graupel plotted in EW–T parameter spacefor the temperature range for each double-nucleationtechnique revealed that the influence of crystal size doesaffect the transient rapid growth (Fig. 5). The lines drawn onthe figure separate positive from negative graupel chargingand are called Charge Sign Reversal Lines. It can be seenthat, as expected, increasing crystal size does diminish theinfluence of transient rapid growth to promote positivegraupel charging in accordance with the Relative DiffusionalGrowth Rate theory.

3.2. Reversal line control

As discussed in Section 3.1 Saunders et al. (2004)determined, using two-cloud experiments, that the choiceof nucleation technique applied to the crystal cloud couldaffect the resultant charging; longer nucleation times tendedto promote negative graupel charging. Expanding on this,Saunders et al. (2006) succeeded in producing clouds ofcrystals with sufficiently low growth rates that when mixedwith the droplet cloud, negative charging at higher values ofEW and temperature was achieved, relative to reversal linesfound by other researchers (Fig. 6); different researchers haveused a variety of different experimental techniques inacquiring their reversal lines.

res chosen to be around the reversal line; see Section 3.1. Pre-mixing crystalures are approximately zero due to the environment being very close to iceque G, however, as intended.

e pre-mixing crystalgrowth rate (μm s−1)

Average crystal-experienced supersaturationover ice during extraction time (%)

−0.03−0.030.020.00

Fig. 5. Charge transferred to graupel as a function of EW and cloud tem-perature for smaller and larger crystals. Plot A is associated with nucleationtechnique F (smaller crystals); plot B with nucleation technique G (largercrystals). Both nucleation techniques produce slow growing crystals prior tomixing to enhance the effects of transient rapid growth. As expected fromthe Relative Diffusional Growth Rate theory, negative graupel charging ispromoted to higher temperatures for smaller crystals.

Fig. 6. Summary of reversal lines found by recent experimental research(Takahashi, 1978; Saunders and Peck, 1998; Pereyra et al., 2000; Saunders et al.2006). Different experimental conditions give rise to different reversal lineswhich are highly sensitive to the specificmicrophysical environment governingsurface growth of the interacting particles. The lines of Pereyra et al. andSaunders et al. were explicitly two-cloud experiments. Saunders and Peck useda single-cloud setup. Takahashi used a single cloud also, but had two-cloud-likeresults. This is discussed in Section 3.3. The Relative Diffusional Growth Ratetheory is providing predictive clues into the sensitivities of the measurablelaboratory parameters which affect these lines.

334 C. Emersic, C.P.R. Saunders / Atmospheric Research 98 (2010) 327–340

Our increasing understanding of the Relative DiffusionalGrowth Rate theory allows us to predict that by varying onlythe nucleation technique in two-cloud experiments, thereversal line can be altered. Longer nucleation times shouldpromote negative charge transfer at higher temperatures byvirtue of producing slower growing crystals, which respondmore substantially on mixing with the droplet cloud to growmore rapidly prior to target collision. With the range of newnucleation techniques available here (Section 2.2.1), experi-ments were performed which examined the limits to whichnegative graupel charging could be promoted by alteringnucleation technique alone. These experiments were stan-dard two-cloud experiments following the procedure out-lined in Section 2.1 and used the longest and shortestnucleation technique available — namely nucleation techni-ques A and E (Section 2.2.1).

The polarity of charge transfer to the target rod wasplotted on a graph of effective water content and cloudtemperature for each of the two nucleation techniques(Fig. 7). Fig. 7A shows that for the longest nucleation time,negative graupel charging could be extended to temperaturesof approximately −14 °C. With the shortest nucleation time,it was found that the reversal line moved to lowertemperatures around −20 °C, (Fig. 7B). So, by selecting the

,,

longest and shortest nucleation times available, the temper-ature limit of negative graupel charging could be altered byover 5 °C.

3.3. High temperature negative graupel charging

Increasing the nucleation time in the two-cloud experi-ments described in Section 3.2, extended negative graupelcharging to an upper limit of approximately −14 °C. In theexperiments of Takahashi (1978) however, negative graupelcharging was noted at higher temperatures. Following theexamination by Saunders et al. (2006) of the likely micro-physical conditions in the experiments of Takahashi (1978),we used the Relative Diffusional Growth Rate theory topredict that increasing the supersaturation of the dropletcloud in two-cloud experiments would, on cloud mixing,extend negative graupel charging to higher temperaturesthan achieved in the experiments of Section 3.2.

Increasing the droplet-cloud supersaturation is possible intwo ways: briefly increasing the droplet boiler power a fewseconds before cloud mixing, or decreasing the droplet-cloudgrowth time. The former method had the disadvantage ofincreasing the minimum EW. Sensitivity tests showed thatyounger droplet clouds promoted enhanced negative graupelcharging, which the Relative Diffusional Growth Rate theoryindicates is due to faster growing crystals during cloudmixing, all else being the same. Crystals grow only from directdeposition of vapour onto their surface, thus this implied thatthe younger droplet clouds had greater vapour contents,although it was not possible to directly measure humidityhere. Larger vapour contents would be expected at firstbecause the boiler is initially set to a high input power until

Fig. 7. EW–T plots of charge transferred to the rimer using nucleationtechniques A and E – the extremes of crystal surface growth rate that can beengineered, from slowest to fastest – to examine the effect this has onreversal line control. As predicted by the Relative Diffusional Growth Ratetheory, the longer nucleation technique (A) promotes enhanced negativegraupel charging to temperatures of approximately−14 °C at warmest. Over5 °C in reversal line temperature control can be gained by choice ofnucleation technique alone.

ig. 8. By using younger droplet clouds containing a greater amount of waterapour and nucleation technique D, the mixing of the clouds in two-cloudxperiments yields a promotion of negative graupel charging to highermperature values than have ever been achieved before (plot B), supportinge qualitative predictions of the Relative Diffusional Growth Rate theory.he reversal line of the effective two-cloud experiments of Takahashi (1978)also shown for reference. In plot A, standard 10-min clouds were used inhich the vapour content was lower, resulting in the expected positivearging in the same region.

335C. Emersic, C.P.R. Saunders / Atmospheric Research 98 (2010) 327–340

full and vigorous boiling is observed, then reduced in value toprovide the desired EW over the following 5 or 10 min. Usingdroplet clouds grown for 5 min was the chosen method toincrease droplet-cloud vapour content.

The experimental procedure employed involved the use ofnucleation technique D (Section 2.2.1) in the crystal cloud, andthe standard experimental technique outlined in Section 2.1—

with the exception that the droplet clouds were only grownfor 5 instead of 10 min. This was compared with the sameexperimental process in which droplet clouds were grown forthe full 10 min.

5-min droplet clouds led to negative graupel charging athigh temperatures (Fig. 8B). Negative charging was noted atthe upper temperature limit of measurable crystal growth inthe chamber; this is the first instance of such high tem-perature negative graupel charging in the literature. Thispromotion of negative charging was also achieved withoutusing a longer nucleation time, suggesting there was room foreven greater promotion of negative charging.

4. Discussion

The layout of the discussion follows that of the resultssection.

FvetethTiswch

4.1. Effects of crystal size in two-cloud experiments

Expanding on the work of Saunders et al. (2004, 2006), wesuccessfully engineered techniques to allow sufficient controlover the crystal surface growth rates to distinguish the effectsof crystal size on their subsequent transient rapid growth onmixing with a droplet cloud (discussed in detail in Section 1).By growing crystal clouds using a double-nucleation tech-nique (Section 2.2.2), which enabled the crystals to experi-ence low growth conditions near ice saturation immediatelyprior to mixing and were thus relatively colder from thereduced latent heat of fusion, the subsequent transient rapidgrowth effect was maximised. Enabling this rapid growthcondition for both large and small crystals allowed theinfluence of size on that rapid growth to be examined, andthus also the indirect effects of size on resulting chargetransfer in two-cloud experiments. This was not possible inthe experiments of Saunders et al. (2004) because the growthrate of both large and small crystals was sufficiently highprior to mixing that the effect of rapid transient growth wasminimised, and they were unable to draw conclusions aboutthe influence of crystal size. In accord with the standardtheory of crystal diffusional growth rate as a function of size,

Fig. 9. Diagram of chamber used by Takahashi (1978) (adapted). In thoseexperiments, water droplets and vapour entered from the lower portion othe chamber (A). Continuous nucleation to produce ice crystals occurred at BGrowing crystals travelled through the chamber, isolated from the droplestream (C). Crystals were then reintroduced to the droplet stream, andexperienced rapid growth (D), akin to two-cloud experiments, beforeinteracting with the rotating target. The resulting charge transfer produceda two-cloud-like charge reversal line (Fig. 6).

336 C. Emersic, C.P.R. Saunders / Atmospheric Research 98 (2010) 327–340

smaller crystals were observed here to respond better thanlarger crystals to environments conducive to transient rapidgrowth, and ultimately further promote negative graupelcharging to higher temperatures.

In summary, the effects of crystal size on charge transfer intwo-cloud experiments in which transient rapid growthoccurs, are only significant when the crystals are relativelycold due to their growth in conditions near ice saturationprior to mixing. If crystals are growing more rapidly inconditions closer to water saturation and are thereforerelatively warmer, the effect of transient rapid growth isdiminished, and thus the influence of size on that transientrapid growth is less pronounced. Faster growing, warmercrystals – large or small – prior to mixing, promote positivegraupel charging; slower growing, colder crystals – large orsmall – prior to mixing promote negative graupel charging,but more so for smaller crystals. These relationships arequalitative, and it is not possible in these experiments toquantify these phenomena. They are however, in agreementwith the Relative Diffusional Growth Rate theory.

4.2. Reversal line control

Saunders et al. (2004) pioneered the use of multiplenucleation techniques in cloud charging experiments, and thiswas further developedby Saunders et al. (2006). The increase inunderstanding of the Relative Diffusional Growth Rate theorythat these two works provided led to the development of aspectrum of nucleation techniques (Section 2.2.1) that allowedbetter control over the crystal surface growth rates. By usingtwo-cloud experiments, it was possible to utilise the precondi-tioning of the crystal surface states that these nucleationtechniques allowed, to control the reversal lines. As predictedby the Relative Diffusional Growth Rate theory, longernucleation times promoted negative graupel charging, whichcould be increased from a temperature of −20 °C — producedusing the shortest nucleation time, to approximately−14 °C—

produced using the longest nucleation time.Using the same experimental equipment, different forms

of reversal line can be produced — such as the single-cloudexperiments of Saunders and Peck (1998), to the double-cloud results here and in other works (Saunders et al., 2004,2006). We have acquired substantial control over theengineering of the reversal lines, and thus the specificmicrophysics they represent prior to collision; the micro-physics is critical to the resulting charge transfer. This revealsthat whenmodelling charge separation in natural storms (e.g.Helsdon et al., 2001; Mansell et al., 2005), it is unrealistic touse single, static reversal line parameterisations whicheffectively assume that a storm's microphysical environmentis homogeneous and omnitemporal. We suggest that untildynamic reversal line parameterisations are completed, thebest approach is to hybridise parameterisation schemes:employ multiple, appropriate, schemes which best representthe microphysical environment at a given time and place,aided by the Relative Diffusional Growth Rate theory.

4.3. High temperature negative graupel charging

Saunders et al. (2006) suggested that the originalexperiments of Takahashi (1978) were two-cloud-like in

nature, despite only a single cloud being used. The chargereversal lines of Saunders et al. (2004) and Pereyra et al.(2000) were similar in profile to the line Takahashi hadproduced, and this gave clues that the microphysical setup inTakahashi's experiments may have been two-cloud-like innature. Therefore, a closer examination of the chamber usedby Takahashi (Fig. 9) and recent understandings of the effectsof mixing two clouds to test the Relative Diffusional GrowthRate theory, led Saunders et al. (2006) to suggest anexplanation of a possible lifecycle of crystals in Takahashi'schamber. The suggestion was that as crystals were continu-ously nucleated by dry ice at the chamber's side, they grew ina region where vapour supply was limited and experiencedan environment close to ice saturation (Fig. 9). These crystalsthen travelled into a different section of the chamber inwhichthere was a rising vapour and droplet stream, which mayhave been similar to two-cloud mixing. On entering thedroplet stream, the crystals experienced transient rapidgrowth and struck the target before thermally relaxing inthe new environment to give the observed two-cloud-likereversal line that was observed (Fig. 6).

In testing the Relative Diffusional Growth Rate theory forpromotion of negative graupel charging when nucleationtime was increased in two-cloud experiments (Section 3.2), itbecame clear that maximising nucleation time alone couldnot promote negative charging to temperatures aboveapproximately −14 °C. Yet Takahashi (1978) had achieved

f.t

337C. Emersic, C.P.R. Saunders / Atmospheric Research 98 (2010) 327–340

negative charging to temperatures as high as −8 °C. TheRelative Diffusional Growth Rate theory allowed us to predictthat promoting negative graupel charging to higher tem-peratures required an increase in the supersaturation of thedroplet cloud in two-cloud experiments. Such high supersat-uration values were likely to exist in the pure droplet streaminto which the crystals were introduced in the experiments ofTakahashi (1978). Increasing droplet-cloud supersaturationprior to mixing was briefly investigated by Saunders et al.(2006) and produced negative charging at temperatures ashigh as −7.7 °C. The increased supersaturation generated inthe droplet cloud here to examine this further, producednegative graupel charging at higher temperatures than havebeen observed previously in the literature. This was evenachieved without using the longest nucleation techniqueavailable, highlighting the substantial influence of theincreased supersaturation on the resulting transient rapidcrystal growth on mixing. In essence, it is possible to achievenegative charging at any temperature desired, throughcareful choice of experimental setup that alters the micro-physics affecting the surface growths of the two interactingparticles.

Promoting negative charging to such high temperatures,exceeding the limits found in Takahashi (1978), stronglysupports the idea that his experiments were two-cloud-likein nature despite only using a single cloud. That high tem-perature negative charging was achieved based on predic-tions by the Relative Diffusional Growth Rate theory stronglysupports the theory and its predictive ability. The theory incombination with the use of two-cloud experiments hasallowed us an unprecedented level of control over the chargetransfer reversal lines, and more importantly, an understand-ing of the microphysical processes involved.

5. Conclusions

The overarching goal of this paper was to further examinethe predictive value of the Relative Diffusional Growth Ratetheory, which states that: “During ice particle collisions, theparticle whose surface is growing fastest from vapourdiffusion at the instant of collision will charge positively onseparation”. This is an empirical observation first reported byBaker et al. (1987), and is supported by almost 25 years oflaboratory experiments. Predictions from the theory werecontextualised primarily by extending the works of Saunderset al. (2004, 2006), and in understanding better the results ofTakahashi (1978).

All the experiments presented here were two-cloudexperiments; that is, they involved the creation of separatedroplet and crystal clouds whichwere brought together beforeinteractions with the target rod acting as a riming graupelparticle; full details of the microphysical processes thisgenerates are discussed in Section 1. Two-cloud experimentshave been shown to be very important for testing the RelativeDiffusionalGrowthRate theory, as they allowanexaminationofa wider range of microphysical conditions than single-cloudexperiments. Only by this extended examination can a fullerunderstanding of the theory and the general microphysicalproperties involved in charge transfer be identified; thegoverningelectro-microphysicsof thismechanism is applicableto all experimental and natural situations. A great deal of work

has concentrated on characterising a range of nucleationtechniques to control environmental conditions and dictatethe preconditioning of the surface state of crystals prior tomixing with the droplet cloud. The importance of this washinted at by Saunders et al. (2004, 2006) and is expanded fullyhere to provide many additional advantages.

We have shown the factors affecting charge transfer byusing two-cloud experiments and the range of nucleationtechniques to precondition crystals, causing transient rapidgrowth on cloud mixing. Specifically, the surface growth rate(and thus temperature) of crystals determines the significanceof the transient rapid growth; relatively colder surfaces, due totheir reduced growth rate prior to mixing, respond better andgrow faster on mixing. New to this study is the effect of size ontransient rapid growth; in the situation where rapid growth ispronounced for lower surface temperatures, larger crystals actto diminish somewhat the significance of this rapid growthrelative to smaller crystals, in agreement with standard crystalgrowth theory. The effects of size on transient rapid growth isinsignificant when the crystals grow at or above watersaturation (akin to single-cloud experiments), as there is verylittle transient rapid growth under such conditions. In relationto crystal surface preconditioning prior to cloud mixing,relatively faster growing crystals (large or small) in environ-ments closer to water saturation are observed to promotepositive graupel charging onmixing; relatively slower growingcrystals (large or small) in environments nearer ice saturationtend to promote negative charging on mixing, but more so forsmaller crystals. This is in full agreement with the RelativeDiffusional Growth Rate theory.

A careful choice of length of nucleation time of the crystalcloud in two-cloud experiments allowed some control in thetemperature at which negative charging occurs. The shortestnucleation times promoted negative charging no warmerthan −20 °C; the longest nucleation times successfullypromoted negative graupel charging to increased tempera-tures of approximately −14 °C. This ability to control thecharge reversal line, and thus the associatedmicrophysics hasimportant implications for numerical models of thunder-storm electrification. Currently, numerical models haveapplied a single reversal line, representing specific electro-microphysical conditions, to all parts and times of that storm.This, in effect, is implying that electrically, the microphysicalenvironment of the examined storm is homogeneous andomnitemporal, which is unlikely to realistically representnature. We suggest that until dynamically variable reversalline parameterisations, tailored as appropriate to the spatialand temporal local storm conditions become available,numerical models employ a range of established reversallines that are more representative of the local microphysics ata given place and time, assisted by the Relative DiffusionalGrowth Rate theory.

Further evidence has been presented here that supportsthe suggestion by Saunders et al. (2006) that the reversal lineof Takahashi (1978) is representative of there being two-cloud-like conditions present in the chamber used, despiteonly having used a single cloud. The profile of the reversal lineof Takahashi (1978) was very similar to the reversal linesfound by other researchers who used a two-cloud setup. There-examination of the likely microphysical conditions in theexperiments of Takahashi (1978) as proposed by Saunders

338 C. Emersic, C.P.R. Saunders / Atmospheric Research 98 (2010) 327–340

et al. (2006) was in agreement with a prediction here fromthe Relative Diffusional Growth Rate theory that increasingvapour content in the droplet cloud of two-cloud experi-ments would promote negative graupel charging to highertemperatures than long nucleation techniques alone couldprovide. Testing this experimentally here revealed thatnegative charging could be promoted beyond the limit ofapproximately −14 °C (Saunders et al., 2006) and −8 °C(Takahashi, 1978), to record high temperatures of approxi-mately −5 ° C — warmer than which, it becomes moredifficult to reliably grow crystals in a cloud chamber. It waspossible to promote negative charging to any temperaturedesired by a combination of crystal-cloud nucleation tech-nique and increasing droplet-cloud vapour content in two-cloud experiments. This represents an unprecedented level ofcontrol over the charge reversal lines, and an understandingof the associated microphysical conditions from use of theRelative Diffusional Growth Rate theory.

In closing, this paper has provided multiple verifiedexamples of the predictive value of the Relative DiffusionalGrowth Rate theory, and further supports its role as a leadingcandidate charging mechanism to explain the electrification ofthunderstorms. We recognise however, as its name suggests,that the theory is only capable of providing qualitativeexplanations for the polarity of charge transfer. It offers noability to quantitatively predict the magnitude of chargetransferred during ice particle collisions, nor insight intoexplicit physical, microscopic charge transfer processes. Weare hoping to address these areas in upcoming papers.

Acknowledgements

We would like to thank NERC for funding the PhD fromwhich this paper content originates. Additionally, we thankMr. Peter Kelly for his assistance in engineering multipleaspects of the experimental equipment used in this research.

Appendix A

Presented is a derivation of an expression of thesupersaturation that crystals would have experienced intheir environment given their measured growth, using thecrystal growth rate equations of Mason (1953).

A.1. Nomenclature (SI units)

C Electrostatic capacity of the crystalsD Diffusion coefficient of water vapour in airdmdt

Rate of change of crystal mass

drdt

Rate of change of crystal radius

ei(T) Saturation vapour pressure over iceκ Thermal conductivity of airLs Latent heat of sublimationm Mass of ice crystalr Radius of ice crystalr0 Crystal radius at prior time intervalr1 Crystal radius at subsequent time intervalRv Gas constant for water vapour treated as an ideal

gas (461.5 J kg-1 K-1)

Si Supersaturation with respect to iceSw Supersaturation with respect to waterρ Density of ice crystalσS Experienced supersaturation (using spherical

approximation)σD Experienced supersaturation (using disk

approximation)t0 Prior time intervalt1 Subsequent time intervalT TemperatureV Volume of crystal

A.2. Calculation

Ice crystal growth rate equation of Mason (1953):

dmdt

=4πCσs

f Tð Þ

where:

f tð Þ = L2sκRvT

+RvTei Tð ÞS

!:

When the crystal is approximated as a sphere, C≡r

dmdt

=4πrσs

f Tð Þ :

Also, m = ρV = 43πρr

3:

Thus

dmdt

= 4πρr2

and

dmdt

=dmdr

drdt

= 4πρr2drdt

:

Hence:

dmdt

=4πrσS

f Tð Þ = 4πρr2drdt

→drdt

=σS

ρrf Tð Þ

∴∫rdr = σS

ρf Tð Þ∫dt

12 r

2 + r0 = σStρf Tð Þ where r0≅0.

Therefore:

σS =ρr2f Tð Þ

2t:

When the crystal is approximated as a circular disk, C≡ 2rπ :

339C. Emersic, C.P.R. Saunders / Atmospheric Research 98 (2010) 327–340

Following the above procedure:

dmdt

=4πCσD

f Tð Þ ≡4π 2rπ σD

f Tð Þ =8rσD

f Tð Þ :

Also

m = ρV = ρ πr2h� �

:

Thus,

dmdr

= 2πρhr

and

dmdt

=dmdr

drdt

= 2πρhrð Þdrdt

:

Hence:

dmdt

=8rσD

f Tð Þ = 2πρhrð Þ drdt

→drdt

=4σD

πρhf Tð Þ

∴r = ∫ drdt dt = ∫ 4σD

πρhf Tð Þ dt =4σDt

πρhf Tð Þ + c where c≅0.

Therefore:

σD =πρhrf Tð Þ

4t:

Findings by Latham and Saunders (1970) suggest thatplate-like crystal depths are typically one third of theirdiameter.

If

h =13d =

23r : ⇒σD =

πρr2f Tð Þ6t

=π3σS≅σS:

Thus, spherical and disk approximations are comparable.When using these equations for generating the supersatura-tion curves, it was necessary to consider the supersaturationvalue over 10 s intervals, corresponding to the averaging ofthe crystal growth rates, and measured from the previousinterval rather than from the origin. This was so the cal-culated supersaturation was more accurately representativeof what was experienced during the local time period ofmeasurement, rather than representing an average fromnucleation up to a given time. Thus the integrals above weregiven boundary conditions and re-evaluated.

∴∫r1r0rdr =

σS

ρf Tð Þ∫t1t0dt

12r2jr1

r0=

σS

ρf Tð Þ tjt1t0

12

r21−r20� �

=σS t21−t20� �ρf Tð Þ

Therefore:

σS =ρf Tð Þ r21 � r20

� �2 t21 � t20� � :

The above expression is used to calculate the experiencedsupersaturation values from the measured crystal size, ulti-mately used in Fig. 4.

References

Baker, B., Baker, M.B., Jayaratne, E.R., Latham, J., Saunders, C.P.R., 1987. Theinfluence of diffusional growth rates on the charge transfer accompanyingrebounding collisions between ice crystals and soft hailstones. Q. J. R.Meteorol. Soc. 113, 1193–1215.

Black, R.A., Hallett, J., 1999. Electrification of the hurricane. J. Atmos. Sci. 56,2004–2028.

Bringi, V.N., Knupp, K., Detwiler, A., Liu, L., Caylor, I.J., Black, R.A., 1997.Evolution of a Florida thunderstorm during the Convection andPrecipitation/Electrification Experiment: the case of 9 August 1991.Mon. Weather Rev. 125, 2131–2160.

Brooks, I.M., Saunders, C.P.R., Mitzeva, R.P., Peck, S.L., 1997. The effect onthunderstorm charging of the rate of rime accretion by graupel. Atmos.Res. 43 (3), 277–295.

Bruning, E.C., Rust, W.D., Schuur, T.J., MacGorman, D.R., Krehbiel, P.R., Rison,W., 2007. Electrical and polarimetric radar observations of a multicellstorm in TELEX. Mon. Weather Rev. 135 (7), 2525–2544. doi:10.1175/MWR3421.1.

Connolly, P.J., Flynn, M.J., Ulanowski, Z., Choularton, T.W., Gallagher, M.W.,Bower, K.N., 2007. Calibration of the cloud particle imager probes usingcalibration beads and ice crystal analogs: the depth of field. J. Atmos.Oceanic Technol. 24 (11), 1860–1879.

Dye, J.E., Jones, J.J., Winn, W.P., Cerni, T.A., Gardiner, B., Lamb, D., Pitter, R.L.,Hallett, J., Saunders, C.P.R., 1986. Early electrification and precipitationdevelopment in a small isolated Montana cumulonimbus. J. Geophys.Res. 91, 1231–1247.

Dye, J.E., Jones, J.J., Weinheimer, A.J., Winn, W.P., 1988. Observations withintwo regions of charge during initial thunderstorm electrification. Q. J. R.Meteorol. Soc. 114, 1271–1290.

Emersic, C., 2006. Investigations into thunderstorm electrification processes.Physics and Astronomy. The University of Manchester, Manchester, UK.

Helsdon, J., Wojcik, W.A., Farley, R.D., 2001. An examination of thunderstorm-charging mechanisms using a two-dimensional storm electrificationmodel. J. Geophys. Res. 106 (D1). doi:10.1029/2000JD900532.

Jayaratne, E.R., Saunders, C.P.R., Hallett, J., 1983. Laboratory studies of thecharging of soft-hail during ice crystal interactions. Q. J. R. Meteorol. Soc.109, 609–630.

Keith, W.D., Saunders, C.P.R., 1990. Further laboratory studies of the chargingof graupel during ice crystal interactions. Atmos. Res. 25 (5), 445–464.

Latham, J., Saunders, C.P.R., 1970. Experimental measurements of collectionefficiencies of ice crystals in electric fields. Q. J. R. Meteorol. Soc. 96 (408),257–265. doi:10.1002/qj.49709640808.

Locatelli, J.D., Hobbs, P.V., 1974. Fall speeds and masses of solid precipitationparticles. J. Geophys. Res. 79 (15), 2185–2197.

Mansell, E.R., MacGorman, D.R., Ziegler, C.L., Straka, J.M., 2005. Chargestructure and lightning sensitivity in a simulated multicell thunder-storm. J. Geophys. Res. 110 (D12). doi:10.1029/2004JD005287.

Mason, B.J., 1953. The growth of ice crystals in a supercooledwater cloud. Q. J. R.Meteorol. Soc. 79, 104–111.

Mitzeva, R.P., Saunders, C.P.R., Tsenova, B., 2005. A modelling study of theeffect of cloud saturation and particle growth rates on charge transfer inthunderstorm electrification. Atmos. Res. 76, 206–221.

Pereyra, R.G., Avila, E.E., Castellano, N.E., Saunders, C.P.R., 2000. A laboratorystudy of graupel charging. J. Geophys. Res. 105, 20803–20812.

Pruppacher, H.R., Klett, J.D., 1978. Microphysics of clouds and precipitation.Reidel, London, UK.

Ranz, W.E., Wong, J.B., 1952. Impaction of dust and smoke particles onsurface and body collectors. Ind. Eng. Chem. 44, 1371–1381.

Rogers, R.R., Yau, M.K., 1989. A Short Course in Cloud Physics, 3rd ed. Elsevier,New York. 293 pp.

340 C. Emersic, C.P.R. Saunders / Atmospheric Research 98 (2010) 327–340

Saunders, C.P.R., Peck, S.L., 1998. Laboratory studies of the influence of therime accretion rate on charge transfer during crystal/graupel collisions.J. Geophys. Res. 103, 13949–13956.

Saunders, C.P.R., Keith, W.D., Mitzeva, R.P., 1991. The effect of liquid water onthunderstorm charging. J. Geophys. Res. 96, 11007–11017.

Saunders, C.P.R., Bax-Norman, H., Avila, E.E., Castellano, N.E., 2004. Alaboratory study of the influence of ice crystal growth conditions onsubsequent charge transfer in thunderstorm electrification. Q. J. R.Meteorol. Soc. 130, 1395–1406.

Saunders, C.P.R., Bax-Norman, H., Emersic, C., Avila, E.E., Castellano, N.E.,2006. Laboratory studies of the effect of cloud conditions on graupel/crystal charge transfer in thunderstorm electrification. Q. J. R. Meteorol.Soc. 132, 2653–2673.

Takahashi, T., 1978. Riming electrification as a charge generation mechanismin thunderstorms. J. Atmos. Sci. 35, 1536–1548.

Ziegler, C.L., MacGorman, D.R., Ray, P.S., Dye, J.E., 1991. A model evaluation ofnon-inductive graupel-ice charging in the early electrification of amountain thunderstorm. J. Geophys. Res. 96, 12833–12855.