A laboratory study of the influence of ice crystal growth conditions on subsequent charge transfer in thunderstorm electrification

Transcription

1 Q. J. R. Meteorol. Soc. (2004), 130, pp doi: /qj A laboratory study of the influence of ice crystal growth conditions on subsequent charge transfer in thunderstorm electrification By C. P. R. SAUNDERS 1, H. BAX-NORMAN 1,E.E.AVILA 2 and N. E. CASTELLANO 2 1 Physics Department, University of Manchester Institute of Science and Technology, UK 2 Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Argentina (Received 16 July 2003; revised 3 February 2004) SUMMARY Laboratory studies of a thunderstorm charging mechanism involving rebounding collisions between ice crystals and riming graupel pellets, have shown the importance of the growth conditions of the interacting ice particles on the sign of the charge transferred. The present study shows a new result: if an ice crystal is not in thermal equilibrium with the environment (immediately following the mixing of two clouds at different saturations) the crystal surface may experience an enhanced growth rate that can influence the sign of the charge transfer and promote negative rimer charging. Furthermore, when an ice crystal in ice saturation conditions is introduced to a cloud at water saturation, leading to transient growth and heating, the period of thermal nonequilibrium is shown to be sufficiently brief that the enhanced negative rimer charging is short lived. These results suggest that the earlier conclusions of Berdeklis and List that the cloud saturation conditions around a growing ice crystal impart to the crystal surface a property that is carried with it and that influences the sign of subsequent charge transfer are unfounded. The discrepancy is because in their laboratory simulations of thunderstorm conditions there is adequate time for the growing ice crystal surface to come to equilibrium with its environment. The established concept of the relative diffusional growth rate of the interacting surfaces controlling the sign of charge transfer, such that the faster growing surface charges positively, is consistent with the observations. KEYWORDS: Cloud saturation Graupel Ice particle growth Thunderstorm charging 1. INTRODUCTION Many laboratory experiments have shown that charge is transferred when ice crystals rebound from riming ice pellets (Reynolds et al. 1957; Takahashi 1978; Hallett and Saunders 1979; Jayaratne et al. 1983; Saunders et al. 1991; Saunders and Peck 1998; Pereyra et al. 2000; Berdeklis and List 2001). The sign of the charge transfer has been shown to depend on the cloud temperature and water content, and the results have been used to suggest a method by which thunderstorms become electrified when falling graupel particles collect supercooled water droplets and encounter ice crystals that separate charge during collisions. The results show that riming graupel pellets tend to charge positively at high temperatures and the crystals charge negatively, while at low temperatures the charge transfers are reversed. The critical temperature for charge sign reversal depends on the amount of rime accreted as measured by the effective liquid water content, as indicated by the results of Pereyra et al. (2000) and shown in Fig. 1. Jayaratne et al. (1983) suggested that this mechanism could account for the normal thunderstorm dipole structure; at low temperatures positively charged ice crystals are carried up in the updraught, while the negatively charged graupel falls to form the negative charge centre from which lightning is initiated. Furthermore, the often observed lower region of positive charge could be due to graupel being charged positively in regions of higher temperatures to produce the thunderstorm tripole charge distribution (Williams 1989). Of relevance to the present study is the suggestion by Hallett and Saunders (1979) that the sign of charge transfer is influenced by the physical state of the rime surface, and its vapour pressure excess or deficit relative to the environment. Corresponding author: Physics Department, UMIST, Sackville Street, Manchester M60 1QD, UK. clive.saunders@umist.ac.uk Member of CONICET (Consejo de Investigaciones Científicas y Técnicas, Argentina). c Royal Meteorological Society,

2 1396 C. P. R. SAUNDERS et al. 4 Target positive + Effective Water Content g m Target negative... + _ Temperature o C Figure 1. Rimer charge sign as a function of temperature and effective liquid water content, EW. The continuous line is the boundary between positive and negative rimer charging zones from Pereyra et al. (2000). The vertical dashed lines at EW < 1gm 3 represent the range of EW values over which a particular charge sign was observed by Berdeklis and List (2001) together with two isolated results (+ ). This concept was extended by Baker et al. (1987) to take account of the growth rate of the ice crystals involved in the charge transfer collisions. The laboratory studies referred to above have been performed in cloud chambers of various designs, but the essential features are as follows: water vapour is introduced to a cold volume where it condenses to form a cloud of supercooled droplets; the cloud is nucleated by introducing a very cold source, or by rapid expansion, to initiate ice crystals that grow from the available vapour; the cloud of crystals and droplets is then drawn past a target representing a graupel pellet, or the target is moved through the cloud, while the charge transferred to the target is measured. Studies by Pereyra et al. (2000) showed that during crystal collisions with a riming graupel target, the target tends to charge negatively at low temperatures, the charge sign threshold being controlled by the value of effective liquid water content (EW; the portion of the cloud liquid water content swept out and collected by the target) as shown in Fig. 1. The charge sign boundary in this figure is similar to that noted by Takahashi (1978). In laboratory studies by Berdeklis and List (2001) the ice crystals were grown in a separate cloud chamber, then introduced to a wind-tunnel airstream carrying supercooled water droplets towards a fixed target where charge transfer occurred, as shown in Fig. 2. Their results in Fig. 1 show the charge sign over a range of values of EW at each of the temperatures studied. These results are in general agreement with those of Pereyra et al. (2000); however, as can be seen from the figure, Berdeklis and List used only a small range of low values of EW compared with other studies. Berdeklis and List (2001) also presented some results that indicated a dependence of the sign of charging on the growth conditions of the ice crystals. When the crystals were grown in cloud conditions near water saturation the target charged more negatively,

3 CHARGE TRANSFER IN THUNDERSTORM ELECTRIFICATION 1397 Ice Crystal Chamber Target Droplets Boiler Wind Tunnel Figure 2. Schematic of the wind-tunnel and ice crystal chamber, after Berdeklis and List (2001). The test section, of width m, houses the riming target connected to an electrometer. whereas crystals grown in conditions near ice saturation charged the target more positively. Berdeklis and List concluded that the initial growth condition of the crystals is important in controlling the sign of the subsequent charge transfer. This conclusion is in disagreement with other studies, that have found the charge transfer sign to be related to the relative diffusional growth rates of the interacting ice surfaces at the moment of collision (Baker et al. 1987) rather than to the history of the ice crystal growth condition. Moreover, the Berdeklis and List conclusion implies that an ice crystal can carry a memory of its surface growth condition, even after being subjected to changes in its local environment while en route to the target. In their experiments the crystals were drawn into the wind-tunnel via a tube of length 5 m cooled by dry ice; they were then mixed into the wind-tunnel droplet cloud, which would have provided water saturation conditions leading to crystal growth before reaching the target. A characteristic that is conserved for a sufficient time to be carried from the growth chamber to the target is the crystal shape, although Berdeklis and List do not report on the crystal morphology in their experiments. Crystals grown in high supersaturation conditions tend to become dendritic, while low supersaturations lead to unbranched plates or columns (Hallett and Mason 1958). However, Jayaratne et al. (1983) found no influence of crystal type (plates or columns) on the sign of charge transfer. Furthermore, Keith and Saunders (1990), using large crystals grown in a high supersaturation that led to the development of dendritic arms, found no difference in charge sign results compared with small crystals of plate or column type grown at lower supersaturation. Because of the important consequences of the Berdeklis and List (2001) result to the concepts of particle charging in thunderstorms, the following experiments were designed to test the effects of initial and subsequent crystal growth conditions on the

4 1398 C. P. R. SAUNDERS et al. Pump Ice Crystals Droplets Boiler Boiler Plan View of UMIST Cloud Chambers Amplifier Target Side View of Riming Target in Tube End View Figure 3. Plan view of the droplet and ice crystal cloud chambers at UMIST together with views of the riming target in the airflow tube. sign of charge transfer. Separate ice crystal and droplet growth chambers were used with independent control of the cloud conditions. Mixing of the two clouds will have produced conditions between ice and water saturation. For this aspect of their studies Berdeklis and List concentrated on temperatures around 14 C and values of EW around 0.5 g m 3, with crystal sizes between 50 and 100 µm; consequently similar conditions were used in the present work. 2. THE EXPERIMENTS AND RESULTS To permit the mixing of ice crystals into a cloud of droplets, as in the experiments of Pereyra et al. (2000) and Berdeklis and List (2001), the 2 m tall cloud chamber in the University of Manchester Institute of Science and Technology (UMIST) laboratory in Manchester is divided vertically to create two separate chambers each of horizontal dimensions 1 m 0.75 m, as shown in Fig. 3. Vapour sources produce a cloud of droplets in each chamber. In one cloud chamber of supercooled droplets ice crystals are initiated by brieflyintroducinga finemetalwire cooledin liquid nitrogen. Afterallowing the crystals to grow for a few minutes, the cloud of crystals and the droplet cloud from the other chamber are drawn together via a Y tube so that the two clouds mix. The resultant cloud then encounters a 4 mm diameter metal rod target that represents a falling small hail or graupel pellet. The cloud particles are drawn past

5 CHARGE TRANSFER IN THUNDERSTORM ELECTRIFICATION Effective Water Content gm Temperature o C Figure 4. Predominant positive rimer charging in the UMIST chambers indicated by +. The ice crystals were grown in a cloud near water saturation, then introduced to the droplet cloud on the way to the target. The dot represents negative charging. thetargetat6ms 1, being a typical fall-velocity of graupel pellets in thunderstorms. The charge transferred during the brief crystal/graupel collisions is detected by a current amplifier connected to the target. The principal contribution to the cloud water content encountered by the riming target comes from the droplet cloud whose liquid water content (LWC) was adjusted to provide the required values of EW, which were determined by weighing the rime ice formed on the target. Two situations were examined, to match the cloud saturation conditions at temperatures around 14 C as described in the work by Berdeklis and List (2001). In one the crystals were allowed to grow for several minutes in a plentiful supply of vapour, while in the other they grew in a low vapour supply. The first case was achieved by nucleating the supercooled droplet cloud briefly with the cooled wire in order to produce only a few crystals, leading to low competition for vapour. In the second case, the nucleating wire was used extensively in a cloud with low water content in order to initiate many crystals that would compete for vapour, and consequently grow at a lower rate. For the initial high growth rate conditions the target generally charged positively, as shown in Fig. 4; the lone negative point suggests that cloud conditions approached those of the negative zone in the results of Pereyra et al. (2000) in Fig. 1. Whereas, if the crystals were initially grown at a lower rate the target charged negatively, as shown in Fig. 5. As these results were the opposite of those reported by Berdeklis and List, differences between the laboratory procedures in the two studies were examined. The principal difference is that in the Berdeklis and List chamber the ice crystals have a 6 m path to the target, giving them a passage time of a few seconds during which they encounter the dry-ice cooled pipe and the wind-tunnel droplet cloud; in the present work the mixing path is 0.14 m long. In order to study the effect of mixing time, the ice crystals were grown in the usual way, with the same low vapour supply and plentiful supply of crystals

6 1400 C. P. R. SAUNDERS et al. 2.0 Effective Water Content gm Temperature o C Figure 5. Ice crystals grown in a cloud near ice saturation then introduced briefly to the droplet cloud on the way to the target. Points represent negative charging of the riming target, commensurate with transient growth. 2.0 Effective Water Content g m Temperature o C Figure 6. Predominant positive charge transfer to the riming target after crystals were grown in a cloud initially near ice saturation, with water droplets then added to the crystal chamber for a few seconds (longer than the crystals transient growth time) before the crystals were introduced to the other droplet cloud on the way to the target.

7 CHARGE TRANSFER IN THUNDERSTORM ELECTRIFICATION 1401 that would lead to a negatively charged target, as above. However, just before drawing the crystals to the target, the vapour supply to the crystal chamber was increased for a few seconds to simulate the passage of the crystals through the droplet cloud on the way to the target in the Berdeklis and List experiments. On drawing these crystals, together with the droplets from the other chamber, to the target it was found to charge positively, as shown in Fig. 6. An even longer exposure of the crystals to high supersaturation before being mixed with the droplet cloud, always led to positive charging of the target. 3. DISCUSSION These experiments have shown that any preconditioning experienced by growing ice crystals as a function of their local supersaturation condition is overcome when they are mixed into an environment having a higher supersaturation. The characteristic time for vapour diffusion for a crystal surface of radius a to respond to a changed local environment is of the order of a 2 /πd v (Pruppacher and Klett 1978) where D v is the diffusion coefficient for water vapour. For our small crystals this is of order 10 6 s. Thus, in nature and in all laboratory experiments the crystal growth rate responds rapidly to the vapour content of a new environment. In the present experiments, when the crystals grow slowly in conditions near to ice saturation and are then exposed to a higher supersaturation on mixing into the droplet cloud, their growth rate increases, which influences the sign of charge transfer. According to the Baker et al. (1987) charging hypothesis, the ice particle surface growing fastest by vapour diffusion charges positively during a brief collision, hence the slower-growing target charges negatively, as shown in Fig. 5. However, as shown by the laboratory experiments (see Fig. 6) in which vapour is reintroduced to the crystal cloud for long enough to allow the crystals to equilibrate, the effect of the faster growth rate on the sign of charging is short-lived. We need to take into account the effect of the heating of an ice crystal growing by diffusion due to the release of latent heat associated with vapour deposition. The crystals initially grown in conditions near ice saturation have an equilibrium temperature below the temperature of an ice crystal growing at water saturation (both clouds being at the same ambient temperature). So, on mixing into the droplet cloud the crystals experience an enhanced growth rate, because their temperature is below the equilibrium value. Of course the effect is transient, and lasts only as long as it takes the now faster growing crystal to warm up sufficiently to reduce its growth rate to the value appropriate to the existing supersaturation. The limiting factors on the enhanced growth driven by temperature difference are: the passage time in the Y mixing tube, which is about s at a velocity of around 6 m s 1 ; and the thermal relaxation time, which for a crystal of radius 50 µm is of order s at a cloud temperature around 15 C (the calculation is shown in the appendix). Thus the crystals maintain a high growth rate during collisions with the target, which charges negatively. On the other hand, in the experiments in which vapour is reintroduced to the crystal cloud for a few seconds following an initial low growth rate of the crystals, there is sufficient time available for the transient high growth rate to reduce to the normal growth rate before the crystals and the droplet cloud from the other chamber are mixed on the way to the target, so the target charges positively as shown in Fig. 6. In the experiments of Berdeklis and List (2001) the passage time of the crystals through the droplet cloud was around s, which, according to the thermal relaxation analysis presented in the appendix, is sufficient for their crystals of 50 to 100 µm diameter to reach thermal equilibrium with their new environment, and so to grow and charge independently of the original growth conditions.

8 1402 C. P. R. SAUNDERS et al. Berdeklis and List (2001) reported negative rimer charging when the crystals were grown in conditions near water saturation. An explanation for this may be associated with the fact that a slight increase in EW, at the low values of EW used by Berdeklis and List, can reverse the rimer charge sign from positive to negative, as shown by the lower portion of the Pereyra et al. (2000) charge reversal line in Fig. 2. In order to maintain water saturation conditions in the crystal chamber, a higher LWC would have been required, which may also have provided an extra source of droplets when drawn into the wind-tunnel with the crystals. This extra LWC would have contributed to the value of EW experienced by the target, favouring negative charging. In their work, Berdeklis and List did not measure EW by weighing the accreted rime on the target as in the present experiments, they determined the LWC value from the water spray nozzle flow rate into the wind-tunnel. In their study of the effect of crystal growth conditions, Berdeklis and List (2001) concentrated on temperatures around 14 C, where positive and negative charge transfers were noted as above. They also reported negative rimer charging at 21 C, with strong negative charging in conditions near water saturation in the crystal chamber. These results could be associated with the larger crystals resulting from the higher growth rate in the conditions of high supersaturation. Keith and Saunders (1990) found a strong dependence of the magnitude of charge transfer on crystal size. Berdeklis and List quote values for crystal sizes in the range 50 to 100 µm, but they do not refer to the details of their crystal sizes for specific experiments, so a definite conclusion here is not possible. 4. CONCLUSIONS In experiments reported by Berdeklis and List (2001), ice crystals grown in cloud conditions near ice or water saturation were drawn through a cloud of droplets before encountering a riming target where charge transfer occurred. They reported that the initial crystal growth conditions control the sign of subsequent charge transfer. These results are at odds with the concept of the charge sign being controlled by the relative diffusional growth rates of the interacting ice surfaces at the time of collision. Experiments performed here to test the hypothesis, showed that when there is adequate time for mixing of ice crystals and droplets to allow the ice crystal surfaces to respond to the given cloud conditions, the sign of charge transfer is not affected by the initial growth conditions experienced in the crystal chamber. Evidence was found to show that crystals grown in conditions of low saturation do experience a sign of charge transfer dependent on those conditions, but only when subjected briefly to conditions of high supersaturation for too short a time to come to thermal equilibrium; the transient higher growth rate then leads to the negative charging of a riming graupel target. In thunderstorms such non-equilibrium situations may exist when two cloud airstreams of different origins mix ice crystals and water droplets together before encountering a riming graupel pellet. Dye et al. (1986) concluded from their thunderstorm observations that the updraught downdraught transition zone between 10 and 20 C may be a preferred location for charge generation associated with ice particle collisions. Thus, the interacting cloud particles are generated in different environments that may permit transient charging behaviour following mixing. Often, however, there may be sufficient time for mixing to allow the ice crystals to come to thermal and vapour equilibrium with the local conditions, and to grow at the appropriate steady-state rate. Further analysis is needed of the origins of cloud particles involved in charge transfer, the mixing process and mixing times in a variety of situations relevant to

9 CHARGE TRANSFER IN THUNDERSTORM ELECTRIFICATION 1403 thunderstorm electrification. In all cases studied here the sign of the charge transferred to the target is consistent with the relative growth-rate hypothesis first propounded by Baker et al. (1987), which states that for two colliding ice surfaces the one growing faster by vapour diffusion charges positively. This implicitly requires the controlling relative diffusional growth rate to apply to both of the interacting ice particle surface conditions at the moment of collision. ACKNOWLEDGEMENT This work was supported by the Natural Environment Research Council, UK. APPENDIX Calculation to obtain the thermal relaxation time for ice particles The calculation shown here is to obtain the thermal relaxation time for ice particles growing initially at ice saturation and then introduced to an environment at water saturation at the same temperature. The method is to determine the temperature as a function of position r,andtimet, inside the volume of an ice crystal of radius a,growing by the diffusion of water vapour. The conditions of the problem are: (i) The crystal is a sphere with radius a and volumetric density ρ. (ii) Initially, the crystal is in equilibrium, with its vapour at temperature Ta in an environment at ice saturation with vapour density ρ i (Ta). (iii) Later, the crystal is placed in an environment at temperature Ta at water saturation with vapour density ρ w (Ta). The temperature distribution, T(r,t), established in the volume of the sphere, must satisfy the following equation: κ 2 T = T t, (A.1) with κ = k/ρ i C,wherek, ρ i and c are the thermal conductivity, density and specificheat of the ice respectively. The boundary condition is: k T r + LsD r=a a (ρ i(t r=a ) ρ w (Ta)) + (T r=a Ta) k a a = 0, (A.2) where: k( T )/( r) r=a is the net radial heat flux thought the sphere surface; (LsD/a) (ρ i (T r=a ) ρ w (T a)) is the net heat flux released by water vapour deposition on the surface, Ls isthespecificheat of sublimation of ice, D is the diffusion coefficient of vapour of water in air, and ρ w is the density of water; (T r=a Ta)k a /a is the sensibleheat flux exchange by convection and conduction through the air, where k a is the air thermal conductivity. The initial condition is: T(t = 0,r)= Ta. (A.3) The expressions used for ρ i (T ) and ρ w (Ta) are those corresponding to the Clausius Clapeyron equations. In order to solve the problem, ρ i (T ) was approximated by a Taylor series about Ta. The error in this approximation is not greater than 1% when (T Ta)<3 C.

10 1404 C. P. R. SAUNDERS et al. a=200 m a=150 m a) a=100 m a=75 m a=50 m t e [s] a=25 m a=10 m Ta [ o C] 1.00 Ta= -5 o C Ta= -10 o C Ta= -15 o C Ta= -20 o C Ta= -25 o C Ta= -30 o C Ta=-30 o C b) t e [s] 0.10 Ta=-5 o C a [ m] Figure A.1. Thermal relaxation time t e, for ice particles of radius a, initially in a steady state at ice saturation at the environment temperature Ta, then subjected to an environment at the same temperature but at water saturation that produces transient growth. (a) Shows t e against Ta for different a, and (b) shows t e against a for different Ta. Note that a 50 µm radius ice sphere at 15 C has a thermal relaxation time of around s. Working with this approximation, Eq. (A.2) can be written as: k T r + LsD ( r=a a (ρ ka i(ta) ρ w (Ta)) + (T r=a Ta) a + LsD ) ρ i a T = 0. T =Ta (A.4)

11 CHARGE TRANSFER IN THUNDERSTORM ELECTRIFICATION 1405 The solution of Eq. (A.1) using Eqs. (A.3) and (A.4) is: T(r,t)= Ta + Fo H { ( ) } Ha 2 2 Fo (α n a) 2 + k 1 )( kr Ha n=1 { ( Ha (α n a) 2 + k 1 k )} exp( α2 n κt) α 2 n sin(α n a) sin(α n r), (A.5) where Fo = LsD ( a (ρ ka i(ta) ρ w (Ta)), H = a + LsD ) ρ i a T, T =Ta and α n is the nth root of the equation: ( ) Ha α n a cot(α n a) + k 1 = 0. (A.6) Time t e is assumed to be the time taken for the sphere surface to reach 95% of the final equilibrium temperature (t ). (T(r a, t ) = Ta + Fo/H = constant.) In Figs. A.1(a) and (b), t e is given for different radii of the ice sphere and different air temperatures. These figures show that t e increases with a and decreases with Ta. The order of magnitude of t e is in the range milliseconds to seconds. REFERENCES Baker, B., Baker, M. B., Jayaratne, E. J., Latham, J. and Saunders, C. P. R The influence of diffusional growth rates on the charge transfer accompanying rebounding collisions between ice crystals and soft hailstones. Q. J. Meteorol. Soc., 113, Berdeklis, P. and List, R The ice crystal graupel collisional charging mechanism of Dye, J. E., Jones, J. J., Winn, W. P., Cerni, T. A., Gardiner, B., Lamb, D., Pitter, R. L., Hallett, J. and Saunders, C. P. R. thunderstorm electrification. J. Atmos. Sci., 58, Early electrification and precipitation development in a small isolated Montana cumulonimbus. J. Geophys. Res., 91, Hallett, J. and Mason, B. J The influence of temperature and supersaturation on the habit of ice crystals grown from the vapour. Proc. R. Soc. London, A247, Hallett, J. and Saunders, C. P. R Charge separation associated with secondary ice crystal production. J. Atmos. Sci., 36, Jayaratne, E. R., Saunders, C. P. R. and Hallett, J Laboratory studies of the charging of soft hail during ice crystal interactions. Q. J. R. Meteorol. Soc., 109, Keith, W. D. and Saunders, C. P. R Further laboratory studies of the charging of graupel during ice crystal interactions. Atmos. Res., 25, Pereyra,R.G.,Avila,E.E., Castellano, N. E. and Saunders, C. P. R A laboratory study of graupel charging. J. Geophys. Res., 105, Pruppacher, H. R. and Klett, J. D Microphysics of clouds and precipitation. Reidel, London, UK Reynolds S., Brook, M. and 1957 Thunderstorm charge separation. J. Meteorol., 14, Gourley, M. F. Saunders, C. P. R. and Peck, S. L Laboratory studies of the influence of the rime accretion rate on charge transfer during crystal/graupel collisions. J. Geophys. Res., 103, Saunders, C. P. R., Keith, W. D. and Mitzeva, R. P The effect of liquid water on thunderstorm charging. J. Geophys. Res., 96,

12 1406 C. P. R. SAUNDERS et al. Takahashi, T Riming electrification as a charge generation mechanism in thunderstorms. J. Atmos. Sci., 35, Williams, E. R The tripole structure of thunderstorms. J. Geophys. Res., 84,