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OCR for page 114
t
Charging Mechanisms in Clouds
anc! Thunderstorms
9
INTRODUCTION
KENNETH V. K. BEARD
. University of Illinois at Urbana-Champaigrz
HARRY T. OCHS
Illinois State Water Survey
Since the time of Benjamin Franklin, a major diffi-
culty in identifying the causes of cloud electricity has
been our inability to obtain adequate measurements
within clouds. This observational problem is now being
remedied by modern electronics and instrumented air-
craft. More quantitative theories of charging have be-
come available since the 1940s along with our improved
understanding of the atmosphere. In addition, better
laboratory simulations of cloud physics in recent dec-
ades have led to improved measurements of microscale
charge separation. With all these advances we should
not be surprised to find that the number of possible
charging mechanisms has proliferated. Thus, a modern
task has been to sort through the possible mechanisms in
trying to identify their relative contribution to cloud
electrification (Mason, 1972; Latham, 1981; Taka-
hashi, 1982~. A major purpose of this chapter is to de-
scribe the mechanisms that charge cloud and precipita-
tion particles. We also evaluate their relative role in
cloud-scale electrification and assess our state of knowl-
edge. A broader evaluation of cloud electrification is
found in Chapter 10 of this volume.
There are two major categories of charging mecha-
nisms: the microscale separators, which ultimately lead
to charged cloud and precipitation particles, and the
~4
cloud-scale separators, which can result in field intensi-
fication and lightning. The first category includes the
creation of ion pairs in the air and charge separation on
individual cloud and precipitation particles. These
mechanisms are coupled with other microscale separa-
tors to produce net charges on cloud and precipitation
particles, for example the attachment of ions by diffu-
sion to cloud drops and the charging that results from
particle collisions. Once the cloud and precipitation
particles become appreciably charged, a larger scale
separator such as differential sedimentation is needed to
create electrification on the cloud scale. Convection can
also act as a cloud-scale separator by redistributing ions
and particles. Much of the emphasis in this chapter will
be on describing the microscale separators that produce
the charged cloud and precipitation particles.
In discussing the charging mechanisms we consider
the electrification of convective clouds. These clouds
can produce spectacular displays of lightning and are
the most important cloud link in the global electric cir-
cuit. We start the discussion of charge separation in the
simple environment of a small cumulus cloud. This non-
precipitating cloud stage is followed by sections on the
rain stage and hail stage. An abbreviated discussion of
the charging mechanisms associated with these three
stages is found in the evaluation section of this chapter.
OCR for page 115
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS
CLOUD STAGE
As the first clouds form on a warm summer afternoon,
the environment is already set for cloud electrification.
The air is filled with ions whose concentrations and mo-
bilities determine the effective conductivity of the atmo-
sphere. In many practical situations the air is an electric
insulator, but the conductivity is large enough to permit
a relaxation time of less than 7 minutes for discharging
the lower atmosphere (Israel, 1971~. The discharge cur-
rent results from the drift of small ions with the mass of a
few molecules. Charge separation begins immediately
when a field is applied to a mixture of positive and nega-
tive ions. Within a cloud the usual result of ion motion is
capture by water droplets.
The electric background in which the cloud forms
contains vertical gradients in ion concentration with a
negative charge at the Earth's surface that is maintained
by thunderstorms. The electric field above the ground is
reduced by a screening layer of positive ions attracted by
the Earth. Positive ions from aloft accumulate near the
ground because the field-induced drift is reduced by col-
lisions as the density of the air increases. Capture of ions
by aerosols greatly reduces the drift velocity and, during
times of heavy pollution, 500 V/m have been measured
between the positive space charge and the ground. A
field of 130 V/m is more typical of a summer day with a
well-mixed boundary layer. This is reduced by about 1
order of magnitude at a 3 km height. Thus, a fresh cu-
mulus cloud forms in an environment of vertical gradi-
ents in space-charge density, electric field, ion concen-
tration, and conductivity (see Figure 9.1~. The field is
oriented toward negative earth with a strong increase in
positive space charge below 1 km and a small ion con-
centration and conductivity that increase with height.
In this electric environment there are several ion cap-
ture mechanisms that lead to charged droplets in shal-
low cumulus clouds. In the following discussion, micro-
scale charge separation is described for diffusion
charging, drift charging, and selective ion charging.
The cloud-scale separation of charge for these nonpre-
cipitation clouds is discussed below under drift charg-
ing.
Diffusion Charging
For the early stage of cloud charging we consider the
collection of ions by cloud droplets. The ion-transport
equation on the microscale near a cloud droplet gives
the charge flux (C/m2 see) or the current density for an
ion component as
Hi = piU + PiBiE - DiVpi, (9.1)
~5
SPACE CHARGE DENSITY (p), CONDUCTIVITY (A),
pC m ~3 pC v-1 s~1 m~1
0.01 0.02 0.05 0.1 0.2 0.5 1 2 5
7 1 1 1 1 / /1 1
I
I 3
o
q
l 11 / ~
1 2 5 10 20 50 100 200 500
SMALL ION CONCENTRATION (n), ELECTRIC FIELD (E),
per 0.01 cm3 V m~1
FIGURE 9.1 Average electric properties of the lower atmosphere
during fair weather. The variation of the electric field with height is
due to Gish (e. g., see Pruppacher and Klett, 1978~. The space charge
density is a direct result of Gauss's law, whereas the conductivity is
obtained by assuming a constant current (2. 7.pC m ~ ~ see ~ Id. The con-
centration of small ions is proportional to the conductivity and varies
inversely with the ion mobility.
where Pi is the ion-charge density (C/m3) of a particular
species, U is the air velocity, Bi is the ion mobility (about
2 x 10 ~ 4 m2/V see for small ions in the lowest few kilo-
meters), E is the electric field, and Di is the molecular
diffusivity (m2/sec). The flux term for the microscale
airflow (piU) is relatively weak because of the low fall
speed for cloud droplets. In addition the field is small
enough in the cloud stage to ignore the ion drift term
(piBiE). Thus the charging of small cloud droplets is
found by evaluation of the standard diffusion equation.
An important consequence of diffusion charging is a
reduction of ion concentration within the cloud by sev-
eral orders of magnitude. The time constant for deple-
tion can be obtained from the solution to the diffusion
equation for a steady-state attachment of ions to a cloud
of similar size droplets. The solution is
Pi = Pie expel - 4 7rRDiNt), (9. 2)
where R is the droplet radius and N is their concentra-
tion. For a typical size and concentration in the cloud
OCR for page 116
116
stage (10 ,um, 100 cm-3), the depletion time constant,
t = (4,rRDiN) ~ i, is 10 sec. Thus equilibrium is achieved
rapidly, and the local concentration in clouds can be
approximated by a steady-state balance between pro-
duction by cosmic rays and depletion by recombination
and attachment to cloud droplets (Chiu and Klett,
1976).
The amount of charge on a cloud droplet from kinetic
theory is a Gaussian-like (Boltzmann) distribution cen-
tered on zero charge for equal concentration of positive
and negative ions. As is evident by the positive space
charge near the ground, the ion mixture is not always
neutral. In such cases a net charge is collected by drop-
lets. For the zero-centered distribution the rms Boltz-
mann charge can provide an estimate for the magnitude
attained in diffusion charging:
Q = (8 7re0RkT)~/2, (9.3)
where c0 is the permittivity of air (8.85 x 10- 12 F/m), k
is the Boltzmann constant (1.38 x 10-23 ]/K), and T is
the temperature (Gunn, 1957~. This equation can be in-
terpreted as a balance between the stored electric energy
on the droplet (1/2 Q214,re0R) and the thermal motion
energy of the ions (kT). When the Boltzmann charge is
evaluated for a typical droplet size in the cloud stage (R
= 10 ,um), the rms charge in number of electrons is ne =
6Ri'2 (,um) = 19. This result is consistent with the spread
in droplet charge measured for nonconnective clouds
with low electric fields (Gunn, 1957~.
Drift Charging
Larger-scale transport of ions is characterized by cur-
rents from bulk and eddy transport of ions along with
the field-driven drift. The charge-flux equation is the
larger-scale version of Eq. (9.1)
Ji = piU + piBiE - KVpi, (9.4)
where K is the eddy diffusivity (m2/sec). If we consider
just the drift of ions in the ambient field we find that the
vertical drift current (piBiE) at cloud top and cloud base
must result in an accumulation of positive and negative
space charge, respectively (Figure 9.2~. An electric bal-
ance is achieved fairly rapidly as a screening layer forms
with the capture of incoming ions by cloud droplets.
The field within the cloud is increased by the charge that
accumulates at the boundary.
The amount of charge on droplets in this region can
be estimated by considering diffusion capture by ions of
only one sign. The maximum charge captured is found
from the amount needed to neutralize the induced
KENNETH V. K. BEARD and HARRY T. OCHS
a b c
1J+
J
/ :: ii ~//////////
FIGURE 9.2 Electrification of a model cumulus cloud (after Chin
and Klett, 1976): a, vertical drift currents reflecting the ion deficits
with the cloud; b, resultant charge accumulation and field enhance-
ment from ion drift; c, effect of convective transport on charges and
field.
charge (of opposite sign) from polarization in the elec-
tric field:
Q= 127re0R2E. (9.5)
The capture of ions from the drift current during the
cloud stage, for example at cloud base (Figure 9.2b),
results in ne = 0.002 R2 (,um) E (Vim) = 20 for R = 10
,um and E = 100 V/m. This charge is comparable with
the Boltzmann charge given by Eq. (9.3). However
charge generation from drift into cloud edges increases
with R2 in contrast to the dependence of Eq. (9.3). Thus
charges of several hundred electrons are readily attained
for somewhat larger cloud droplets by diffusion of ions
of one sign to polarized drops. Somewhat later in this
section we shall find out that the size and field depen-
dence given by Eq. (9.5) also applies within clouds for
ion capture by polarized drops and for the breakup of
these drops.
In addition, for the cloud stage we must also consider
the role of the bulk and eddy transport terms in Eq.
(9.4). For diffusion charging and the simple convective
pattern, illustrated in Figure 9.2c, convection trans-
ports negative charge upward within the core and car-
ries positive charge downward along the edges (Chiu
and Klett, 1976). The effect of eddy diffusion in this sim-
ple model is to smooth the charge distribution produced
by the bulk transport and ion drift. When all three terms
in Eq. (9.4) are included, the field is enhanced within
the cloud but is not so strong as the pure drift case.
For this early stage of cloud electrification, drift
charging of droplets with negative charge at cloud base
and positive charge at cloud top is apparently the domi-
nant mechanism. The current into cloud base from drift
OCR for page 117
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS
is p B E, and the current from convection is U. where
p = p + - p is the space charge. (The value of p is ap-
proximately one half the small ion concentration, be-
neath cloud base, times a unit charge.) The ratio of drift
to convection is 7.5 (using the values for p, n, and E on
Figure 9. 1 at 1 km and B = 2.2 x 10 - 4 m2/V see and U
= 1 m/see) clearly showing the dominance in the drift of
negative ions into cloud base over the upward convec-
tion of positive space charge. The ratio decreases as the
cloud base is lowered and is less than unity for bases be-
low about 300 m. The calculations of Chiu and Klett for
a cloud base at 10 m show the dominance of convective
transport of positive space charge over drift into cloud
base. They found a positive core, but drift still domi-
nated the charging process in the upper cloud with posi-
tive charges at cloud edges similar to Figure 9.2c. Thus,
for the majority of cases in the cloud stage, drift charg-
ing is the most significant electrification mechanism.
Convection and eddy diffusion in the single-cell pattern
investigated by Chin and Klett generally weaken elec-
trification by redistributing and mixing the drift-gener-
ated charge
.
The charge acquired by droplets in the cloud stage has
been from diffusion of ions within the cloud and drift
charge at cloud edge.
Selective Ion Charging
When equal numbers of positive and negative ions are
present there can be a preferred attachment of one sign
if the droplet is polarized (Wilson effect). The governing
equation for the microscale transport t given by Eq.
(9.1~] has two classes of solutions (Whipple and
Chalmers, 1944~. In the case of "fast ions" the down-
ward drift of positive ions exceeds the fall speed of the
droplet (B + E > V) and ions of both signs are captured
at nearly the same rate (Figure 9.3a). The droplet size
where B + E = U in the lowest few kilometers is R = 1
,um for E = 10 V/m. Since most droplets in shallow cu-
mulus clouds are larger than 4 ,um, ions are captured
selectively by the Wilson effect. Larger droplets will ac-
quire a negative charge by the preferential attraction of
negative ions, as shown in Figure 9. 3b for the "slow ion"
case (B + E < U).
The maximum charge acquired by droplets for the
Wilson effect is
Q = 2 7re0R2E . (9. 6)
This is only one sixth the diffusion charge from the drift
current given by Eq. (9.5) and yields a negative charge
equivalent to 36 electrons for the largest cloud droplets
(R = 100 ,um) and a downward directed field of 10 V/m.
~7
a
U
t B_E
b
1i
~ ll
E
~ \, 7
~ t t
|B+E I '~ - I
'\' \\~'
FIGURE 9.3 Selective ion capture from droplet polarization in a
downward-directed field (Wilson effect): a, fast-ion case B+E > By;
b, slow-ion case (B. + E < ~ with trajectories Even by dashed curve.
Thus the largest cloud droplets are charged for the Wil-
son effect to a magnitude of about the rms Boltzmann
charge.
In our cumulus scenario the cloud is only about 1 km
deep with a central updraft speed of 1 to 2 m/see; there-
fore the small drops that we are considering are carried
upward. When the cloud depth increases to about 3 km,
drops become large enough to be detected by radar.
This is a common circumstance for summer cumulus
clouds in mid-latitudes. The cloud top would lie below
the level where droplets readily freeze except over ele-
vated terrain or in a more northern climate. The drops
associated with the initial radar echo are still quite small
and unable to fall out of the cloud. However, we con-
sider the time of the first radar echo as the beginning of
the rain stage. In the following section we examine the
charging mechanisms associated with drizzle drops and
raindrops: selective ion charging, breakup charging,
and induction charging.
RAIN STAGE
Selective Ion Charging
When we make the transition to the new stage, micro-
scale separation of charge becomes more powerful be-
cause of the Ret dependence of charge captured by polar-
ized drops tEqs. (9.5) and (9.644. As the drizzle drops
begin moving downward in the cloud a larger scale sep-
aration of charge can result as drizzle drops capture neg
OCR for page 118
118
alive ions (Wilson effectJ and the excess positive ions be-
come attached to cloud droplets. The enhanced electric
field within the cloud would provide a positive feedback
to the Wilson effect by increasing the polarization on the
drops. If the field should reach about 10 kV/m the ion
drift velocity would increase to a few meters per second.
This is the situation where the velocity of positive ions is
about the same as the fall speed of small raindrops. Con-
sequently generation by selective ion charging and the
simple feedback mechanism for the Wilson effect is lim-
ited. iThe same limit does not apply to diffusion charg-
ing at cloud edges, Eq. (9.5~.
In the rain stage, microscale separation of charge
from ion capture continues while new mechanisms
make their appearance. The role of convection remains
central to cloud development as well as the motion of
charged droplets within the updraft. Transport and
drift are important factors in ion movement within the
cloud and to droplets at the boundaries. The Wilson ef-
fect appears to be responsible for some of the field en-
hancement but must be considered along with the addi-
tional mechanisms of breakup charging and induction
charging.
Breakup Charging
The collisions between drizzle (R = 100-1000 ,um)
and cloud droplets (R = 10-100 Am) usually result in
coalescence growth and the production of rain. In con-
trast the collisions between raindrops (R = 1-6 mm) and
drizzle often result in only transient coalescence fol-
lowed by fragmentation. Such events can result in
charged drops in the presence of an electric field. The
polarization charge of one sign on a spherical drop is
Q = 3 7reoR2E. (9. 7)
This equation gives the net positive or negative charge
that can be separated by "slicing" a polarized drop in
half. To apply Eq. (9.7) to the rain stage, consideration
of some details of drop collisions and the role of the elec-
tric field follows.
Four general kinds of breakup phenomena are illus-
trated in Figure 9.4 (neck, sheet, disk, and bag) based on
the laboratory study of McTaggart-Cowan and List
(1975~. The amount of charge separated in bag breakup
is given approximately by Eq. (9.7) (Matthews and Ma-
son, 1964), but the charge has not been determined for
the other cases shown in Figure 9.4. The most frequent
kinds of breakup result after a vertical elongation of the
coalesced drop pair followed by a neck or sheet that
tears into numerous droplets. This is not the ideal "slic-
ing" required for Eq. (9.7~. For example, an elongation
increases the polarization charge by a factor of 4 if the
KENNETH V. K. BEARD and HARRY T. OCHS
a b
NECK SHEET
(27%) (55%)
o
0 0
o
o
c d
DISK BAG
( 18%) (< 1/2%)
O ~ . O O
. O to .
· . . · - . -
· . ... .
. :. ~ : .' .:
· . . . .. -
. . .e ~ .0 ..
.o: .e O o O
00 0~. 0
~ · 0
0 ~
FIGURE 9.4 The four observed breakup types with percentages of
occurrence: a, neck; b, sheet (two views taken perpendicular to each
other); c, disk; d, bag (from McTaggart-Cowan and List, 1975).
distorted drop is modeled as a prolate spheroid with a
major axis of 5 times the spherical diameter. Thus Eq.
(9.7) gives a rather conservative estimate of the micro-
scale charge separation in breakup.
An important feature of breakup collisions is that they
occur slowly compared with the charge-relaxation time
(i.e., the time required to redistribute the charge). The
breakup time is given roughly by the raindrop diameter
divided by the velocity difference between the colliding
drops (about 0.5 msec). In contrast, the charge relaxa-
tion time for pure water is about 100 times faster and for
rainwater with impurities, 104 to 106 times faster. Thus,
the distribution of polarization charge on a distorting
raindrop is in approximate equilibrium with the electric
field.
In breakup charging, the electric field separates
charge on individual drops by polarization, breakup
separates charge between colliding drops, and gravity
separates charge on a large scale. The sheet breakup
shown in Figure 9.4b, with a downward directed field,
will result in a positive charge on the large fragment (R
> 1 mm) given approximately by Eq. (9.7) and a nega-
tive charge of the same magnitude distributed over the
small fragments (R ~ 100 ,um). The difference in fall
speed between these sizes (6 to 10 m/see) gives the cloud-
scale separation rate.
Although breakup charging contains the microscale
and cloud-scale mechanisms of charge separation neces-
sary for cloud electrification, it does not reinforce the
existing field. However, it may contribute significantly
to drop charging found in both the rain and hail stages.
OCR for page 119
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS
Induction Charging
In addition to coalescence and breakup, the collision
between drops can result in interactions where the two
drops bounce apart. The amount of charge transferred
between drops that are polarized depends on the contact
angle relative to the field, the contact time, the charge
relaxation time, and the net charge on the drops as well
as the magnitude of the polarization. Induction charg-
ing was first considered by Elster and Geitel (see
Chalmers, 1967) for contact between a large and small
sphere along a line parallel to the field. Later studies
included the effects of image charges, contact angle,
and net charge with extensions of theory to ice particles.
In the rain stage we will consider only induction charg-
ing for drops while reserving the ice aspects of this mech-
anism for the had! stage.
The importance of contact angle is immediately obvi-
ous from the induced surface charge on a conducting
sphere in a uniform electric field given by 3,rcoE cos ~
and shown schematically on Figure 9.5a. However, the
contact angle is a hydrodynamic problem of two defor-
mable bodies in a gaseous medium with its own set of
governing parameters. Even in the absence of electric
effects, such interactions are understood only in terms of
broad categories in a manner similar to the breakup
phenomena. For example, contact angles of 50-90° are
associated with bouncing drops, and angles of 60-80°
with partial coalescence. These phenomena occur over
sizes intermediate to the ranges for coalescence and
breakup. Laboratory experiments indicate bouncing
between large and small drizzle drops and partial coa-
lescence between drizzle and large cloud drops. We will
emphasize the charge transfer between dissimilar sizes,
as the above ranges suggest. Interactions between simi
a
_>
E
b
E
- . 1
+/
FIGURE 9.5 Charge transfer by the induction mechanism for collid-
ing drops in a downward-directed field: a, charge distribution on a
polarized drop; b, contact at moderate angle; c, charge generation
after separation.
119
tar size drops are relatively unimportant because their
similar fall speeds lead to infrequent collisions.
The maximum charge on a large drop (R) acquired by
collision with a small drop (r) for dissimilar sizes is given
approximately by
Q = 12 cos ~ 7re0r2E.
(9.8)
If we assign an average contact angle of 70 (whereby
12 cos ~ = 4), the result is similar to Eqs. (9.6) and (9.7)
except for the scaling by r2 instead of R2. It should be
obvious from the r2 dependency that the induction
mechanism is not a powerful means of direct charge sep
aration. However, as Figure 9.5 demonstrates, the mi
croscale charge separation followed by differential sedi
mentation reinforces the existing field. Therefore the
induction mechanism may be capable of significant
charge separation on the cloud scale through positive
feedback to Eq. (9.8~.
There are several possible limitations on induction
charging between drops. First, charge transfer must oc
cur on a time scale compatible with contact. When we
consider the interaction between drizzle drops and large
cloud droplets, appropriate for partial coalescence or
bouncing, the contact time ranges from 1 to 50 ,usec.
This is several orders of magnitude longer than the
charge-relaxation time for cloud and rain water. There
fore the contact time is not a limitation for charge trans
fer between drops.
A second possible limitation occurs because an elec
tric field can transform partial coalescence (or bounce)
into complete coalescence. This effect has not been stud
ied in detail; however, laboratory simulations of induc
tion charging (Jennings, 1975) showed that the separa
tion probability is reduced by an order of magnitude
when the field is increased from 10 kV/m to 30 kV/m.
Other studies with charged drops of similar sizes show
suppression of bounce at charges comparable with those
induced by the above fields. Hence, there is evidence
suggesting a limit on induction charging but at fields
well above those found in the rain stage (typically less
,2~, than 1 kV/m).
JO A third possible limitation, one that applies to bounc
,' ing drops but not to partial coalescence, is that charge
transfer must occur across an air gap. Transfer mecha
nisms such as field emission or corona, in a small air gap,
usually require very high fields (greater than 107 V/m).
Since the field between drizzle drops is enhanced by in
duced charges by a factor of only about 50 to 500, thun
derstorm fields appear to be required for charge transfer
across the air gap between bouncing drops. However,
neither charge transfer between bouncing drops nor the
limitation of field-induced coalescence have been ade
quately investigated.
OCR for page 120
120
Drop charging occurs in the rain stage from drift
charging at cloud edges and selective ion capture within
the cloud. The latter mechanism enhances the electric
field by gravitational separation of negatively charged
precipitation drops and positively charged cloud drop-
lets. In addition, breakup charging of colliding drops
may result in significant charges on raindrops and driz-
zle drops. Since fields are weak in the clouds we have
considered, induction charging is ineffective. However,
under the special circumstance of deep (warm) convec-
tion, as discussed in the evaluation of charging mecha-
nisms, induction may lead to higher fields through a
positive feedback.
As the cloud top rises above the freezing level the
newly formed cloud droplets, as well as drizzle drops
carried in the updraft, remain in the liquid state. Soon
some of the larger drops freeze until, at about the
- 15°C level, the cloud top takes on a fuzzy outline indi-
cating a substantial number of ice particles. Such a gla-
ciated cloud usually undergoes a growth spurt from the
release of latent heat. If the air above is not too warm,
convection may continue up to the base of the strato-
sphere, resulting in an intense thunderstorm.
Typically on a day that has isolated thunderstorms,
the first cumulus clouds in the early afternoon reach
only the cloud stage. Somewhat later cloud tops are
higher and reach the rain stage. It is often not until mid-
dle afternoon that cloud tops are high enough to glaci-
ate. This is the onset of the hail stage, since what follows
is the beginning of hail-like precipitation as droplets col-
lide and freeze onto larger ice particles.
HAIL STAGE
The glaciated portion of the cloud contains ice crys-
tals in a saturated vapor environment maintained by the
presence of more numerous cloud droplets. Since the
saturation vapor pressure for ice is less than water, the
ice crystals grow rapidly by vapor diffusion. As the ice
crystals grow larger than about lOO ,um, they begin to
collect cloud droplets. This riming process continues
within the upper portion of the cloud until the particles
are transformed into soft hail (also termed "snow pel-
lets" or "graupel"~. These ice particles are not nearly so
dense or large as typical hailstones. When the size and
liquid water concentration are large enough, the accre-
tion of water occurs too rapidly for immediate freezing.
Water will then infiltrate the rime structure and in-
crease the particle mass, fall speed, and growth rate. In
a strong updraft the water in soft hail may refreeze
higher in the cloud, resulting in ice pellets (i.e., small
hailstones). Further growth by riming may be followed
by a descent to a region where wet growth can again
KENNETH V. K. BEARD and HARRY T. OCHS
occur. A cycle of wet and dry growth may be repeated
several times to produce the multiple layering found in
larger hailstones (see also Chapter 7, this volume).
The above description for the growth of soft hail and
hailstones indicates the complexity of particle interac-
tions in the hail stage. Although the growth of ice pre-
cipitation is governed by the collection of cloud drop-
lets, the charging of ice precipitation appears to be
linked to collision with smaller ice particles (Gaskell and
Illingworth, 1980; Latham, 1981; Jayaratne et al.,
1983~. Therefore, we will consider the separation of
charge for collisions of precipitation, such as soft hail
and hailstones, with frozen drops and ice particles.
First, the induction charging discussed for the rain stage
will be extended to drops and ice particles rebounding
from ice precipitation with dry or wet surfaces. Then we
discuss thermoelectric charging and interface charging.
Induction Charging
The concept of induction described for the rain stage
can be applied in the hail stage after considering a few
alterations. Of primary importance is the charge relaxa-
tion time for ice that is a factor of 1000 slower than for
liquid water. Theoretical estimates by Gaskell (1981)
for charge transfer between a 100-,um ice sphere and a
much larger one, including the effect of a surface con-
ductivity, yield a relaxation time constant of ~ = 100
,usec, which is much longer than an estimated contact
time of less than 1 ,usec. Since-the amount of charge
transferred during contact is proportional to 1 - e- tie,
an ice sphere charges at less than one hundredth the rate
of a comparable water drop. This would increase the
induction-charging time from a few minutes for drizzle
drops to several hours for ice pellets. However, induc-
tion charging of wet hail would proceed to the maxi-
mum amount in Eq. (9.8) about as rapidly as in the wa-
ter-drop interactions.
Another aspect of induction charging is the effective
contact angle found from the average over the range of
bouncing interactions. In the rain stage the average is
about 70° for collisions between large and small drizzle
drops. Experimental measurements of charge separa-
tion for larger precipitation particles (both water drops
and ice spheres) colliding with cloud droplets indicate
that the average contact angle is greater than 85 (e.g.,
see Jennings, 1975; Gaskill, 1981) . In contrast, ice parti-
cles almost always separate after colliding with hail, re-
sulting in an average contact angle of 45°.
When we consider both the effects of contact angle
and charge relaxation, we can compare the strength of
induction charging for various particle interactions in
the hail stage. For collisions between dry hail and ice
OCR for page 121
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS
particles the relaxation time is too long to permit charg-
ing to the maximum value given by Eq. (9.8~. As stated
above, the charge attained by an ice pellet is less than
one hundredth that of drizzle in a comparable time. In
addition, the average contact angle of 45° yields only a
factor-of-2 increase over the 70° angle assumed for driz-
zle. Thus, induction charging between dry hail and ice
particles is severely limited by the long relaxation time
for ice.
In collisions between wet hail and cloud drops or ice
crystals, charge relaxation should be controlled by liq-
uid water and the charging rate comparable to induc-
tion in the rain stage. The maximum charge attained
would be governed by the average contact angle in Eq.
(9.8) of over 85° for wet hail and cloud droplets (or small
drizzle drops) and 45° for wet hail and rebounding ice
crystals. Thus, the most powerful interaction for induc-
tion charging in the hail stage would appear to be colli-
sions between wet hail and ice crystals.
Thermoelectric Charging
Up to this point, we have discussed mechanisms that
depend on the ambient electric field. We now turn to
charge transfer between cloud and precipitation parti-
cles where an external field is unnecessary. This class of
microscale separation mechanism originates from in-
trinsic charge carriers and their relationship to bulk
properties. Thermoelectric charging is the result of a
thermally induced gradient in the concentration of car-
riers that transport positive and negative charges. For a
linear gradient in temperature, the steady-state balance
between carrier diffusion and drift produces a field of E
= kdTldx with an empirically determined coefficient of
k = 2 mV/°C (Latham and Mason, 1961~. The corre-
sponding surface charge density from Gauss's law is
about (10- is C/cm °C) dT/dx (where the gradient is in
degrees per centimeter). We can estimate the steady-
state charge (in coulombs) for a short ice cylinder of ra-
dius r by
Q= 10-isr/`T
(9~9)
for a temperature difference AT (°C) across a length of
err (cm) and a surface charge on an area of errs.
In the hail stage a temperature gradient would occur
during the contact between a precipitation particle,
warmed by the freezing of rime (e.g., soft hail) and a
smaller particle. A negative charge would be transfer-
red to the precipitation particle with Q = 10- i6 C for a
small particle using r = 100 ,um and with a rather large
temperature difference of /i T = 10°C. Thus, the charg-
ing in a single collision is rather insubstantial when com
121
pared with values of greater than 1 pC measured for soft
hail in thunderstorms.
These estimates of thermoelectric charging are fur-
ther reduced when we account for the limitation im-
posed by transient contact. Both theory and experiment
show that about 10 msec are required to reach a maxi-
mum charge comparable to Eq. (9.9) (Latham and
Stow, 1967~. Since the contact time between precipita-
tion and cloud particles is many orders of magnitude
smaller we can reasonably expect that our estimate of
10-16 C for a single collision would be reduced to well
below 10- i~ C. Even under the most favorable condi-
tions (i.e., 104 collisions within 20 minutes for high ice
crystal concentrations at 100 per liter), the accumulated
charge would be less than 10- i4 C.
In contrast to the estimate of considerably less than
10- i~ C per event for thermoelectric charging, recent
laboratory studies have yielded up to 0.3 pC per colli-
sion between a small ice particle and a simulated hail-
stone (Gaskell and Illingworth, 1980~. Thus, there is ev-
idence to demonstrate that mechanisms far more
powerful than thermoelectric charging are at work in
the hail stage.
Interface Charging
Two types of interface charging will be discussed:
freezing potentials involving impurities and contact po-
tentials.
Charge can be transferred across a freezing interface
by selective incorporation of ions, originating from dis-
solved salts and gases, into the advancing ice. In the
steady state, a balance is reached between the selection
process and the relaxation of charge in the ice. A tran-
sient in potential is observed when a plane interface ad-
vances past an electric probe. Early workers measured
large potentials in the freezing of aqueous solutions con-
taining naturally occurring salts over the range of con-
centrations found in precipitation (Workman and Rey-
nolds, 1948~. Subsequent researchers have made more
refined measurements and developed a theoretical de-
scription of freezing potentials (e. g., see Caranti and I1-
lingworth, 1983a). Others have investigated charge
transfer between solution drops and simulated hail-
stones (e.g., Latham and Warwicker, 1980~. As a result
of these later studies and related ones (Gaskell and I1-
lingworth, 1980; layaratne et al., 1983; Caranti and I1-
lingworth, 1983b), the role of interface charging in hail-
stage electrification is being clarified.
As indicated above, two methods are used to study
interface charging: (1) potentials are measured as a
function of solute impurities and supercooling, with dif-
fering growth rates and interface areas; and (2) transfer
OCR for page 122
122
of charge is measured for collisions between particles
and a much larger "target" electrode coated with ice as a
function of solute impurity, supercooling, and speed of
impacting drops. Other conditions have also been var-
ied, such as the target temperature and the riming rate
of the target for a mixture of supercooled drops and ice
crystals. Investigation of these various parameters cov-
ers many of the conditions found in the hail stage and
helps to sort out contributions of freezing potentials
from contact potentials and the thermoelectric effect.
Recent studies have shown that interface potentials
for bulk solutions near 0°C are substantially reduced by
supercooling, apparently from the effects of the den-
dritic interface (Caranti and Illingworth, 1983a). Po-
tentials could not be measured for 100-,um-diameter
droplets, in the range - 1 to - 20°C, impacting on an
ice substrate because the potential was either too small
(less than 100 mV) or it decayed too rapidly (in less than
5 msec). A reduction in charge transfer was also found
by Latham and Warwicker (1980) for millimeter-size
drops splashing from ice targets in comparison with ear-
lier findings for drops not completely cooled by the air
(Workman, 1969~. In fact, the charging was of the
wrong sign for the freezing of sodium chloride solutions
and independent of concentration, indicating that the
freezing potential was not the dominating mechanism.
A more likely cause was a common form of interface
charging associated with the disruption of an air-water
interface (i.e., spray electrification). The charges on the
air-water interface are readily overwhelmed by polar-
ization charges. For example, Latham and Warwicker
(1980) found that charge transfer was substantially in-
creased by applying a field of only 100 V/m.
As the above comparisons demonstrate, the relative
importance of charge transfer during the freezing of
aqueous solutions is greatly diminished by supercooling.
The effect of dissolved ions on charging seems to be neg-
ligible in the splashing of supercooled solution drops
from ice targets. However, the above considerations do
not rule out the freezing potential as a factor in the
transfer of charge for a target collecting solution drops
and also colliding with ice crystals.
Before examining collisions involving ice crystals dur-
ing rime formation, we will consider the transfer of
charge between an ice-coated target and rebounding ice
particles in the absence of droplets. Experiments have
shown that a target of ice accumulates either negative or
positive charge in collision with ice particles depending
on whether the target surface has undergone sublima-
tion or deposition (Buser and Aufdermaur, 1977~. It was
concluded from an additional experiment that the con-
dition of the surface was controlling the charge transfer
rather than a thermal gradient as would have been ex-
pected for the thermoelectric effect. Buser and Aufder
KENNETH V. K. BEARD and HARRY T. OCHS
maur (1977) also found that the transfer of charge be-
tween ice particles and targets of various metals was
proportional to the contact potential. Thus variations in
the surface state and, in particular, the free energy of
the charge carriers is a major factor in this type of charge
separation. The differing signs in the ice-target experi-
ments can be attributed to differing surface characteris-
tics of the target. The surface exposed during sublima-
tion was composed of ice originally formed near 0°C,
whereas a frosted surface was produced by deposition at
the experimental condition of - 45°C.
More recently Gaskell and Illingworth (1980) studied
interface charging in the temperature range from - 5 to
- 25°C. They also found negative charging for a sub-
liming target and positive charging during deposition
without any direct evidence of the thermoelectric effect.
Frozen droplets of 100-,um diameter transferred charges
of about - 0.015 pC for sublimation and + 0.10 pC for
deposition. Little variation in charging was found over
the temperature range or when the ice target contained
ion impurities. These results are consistent with inter-
face charging by a contact potential mechanism
whereby the surface states of the charge carriers differ
between the smooth surface formed near 0°C, exposed
during sublimation, and the frosted surface formed by
deposition. Additional support for the contact potential
hypothesis comes from measurements of the effects of
impact velocity and droplet size on charging, since the
transfer of charge was found to increase with both of
these parameters in a manner consistent with an in-
crease in contact area (Gaskell and Illingworth, 1980~.
Charging was also examined by Gaskell and I1-
lingworth (1980) for a target undergoing simultaneous
collisions with ice particles of 100 ,um diameter and su-
percooled droplets at low to moderate liquid water con-
tents (0.05 to 0.85 gamy. The charge transferred to the
target was positive at - 5°C and negative at - 15°C
with the transition near - 10°C. The sign reversal was
possibly caused by changes in the contact potential with
rime structure at different temperatures (Caranti and
Illingworth, 1980~.
An estimate of interface charging in collisions be-
tween various sizes of cloud and precipitation particles
can be obtained from the work of Gaskell and I1-
lingworth (1980) in which the charge was found to be
related to the contact area through the impact speed and
ice particle size. In the following formula, we have com-
bined their relation for impact velocity (Q ~ Ut 6) with
an expression for the velocity of hail (U ~ R08, e.g., see
Pruppacher and Klett, 1978) and have included their
scaling for ice particle size (Q ~ ri 7~:
Q= FR~.3r~.7
(9.10)
OCR for page 123
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS
The factor F is a function of the interface potential, de-
pends on the nature of the contact surfaces, and may be
evaluated from laboratory data. For example, in the
riming experiment of Gaskell and Illingworth (1980) the
collisional charge was Q ~ - 0.04 pC in the range - 15
to - 20°C for r = 50 Em end R = 0.43 cm (e size with a
terminal velocity at the laboratory impact speed, 8 m/
see). Thus, for the interface conditions corresponding to
these experiments the factor for the interface potential is
F = - 970 (with Q in picocoulombs and the radii in
centimeters).
The latest investigation of ice crystals rebounding
from riming targets provides additional evidence for in-
terface charging (Jayaratne et al., 1983~. In this study
the target electrode was moved through a cloud of su-
percooled droplets that was seeded to produce ice crys-
tals. Charging of the target began shortly after seeding
and ended after about 4 minutes when the ice crystals
settled out of the cloud. At low liquid-water contents the
maximum current was positive at a temperature below
about - 10°C and negative at temperatures above, in-
dicating a reversal in sign of the charge in a manner sim-
ilar to that of Gaskell and Illingworth (1980~. The
results of Jayaratne et al. are difficult to interpret in
terms of charge transfer because of transients in the ice
crystal size, the liquid-water content, and the current
measured at the target. However, the charge was esti-
mated for single events by the investigators from the tar-
get current and ice crystal concentration. In one case
they estimated Q ~ 0.01 pC for an ice crystal size of 125
Em diameter, where the target speed was 2.9 m/see, the
temperature - 6°C, and the liquid-water content 2 g/
m3. The factor for the interface potential that corre-
sponds to these experimental conditions is F = 870 (with
Q in picocoulombs and the radii in centimeters).
The variation in the sign-reversal temperature with
liquid-water content was attributed to changes in the
freezing process or to variations in the structure and
density of the rime. This view is consistent with inter-
face charging by the contact potential mechanism.
However, sufficient data are unavailable to express the
factor for the interface potential as a function of the rim-
ing rate or fundamental parameters such as temperature
and liquid-water content.
Another aspect investigated by Jayaratne et al. (1983)
was the variation in charging with solute impurities in
the cloud droplets. For cloud water containing natural
amounts of sodium chloride they determined that about
- 0.003 pC was transferred by ice crystals of 50-,um di-
ameter at - 10°C and 1 g/m3. A charge of the same
magnitude but of the reverse sign was found for ammo-
nium sulfate under the same conditions. At - 20°C the
charge was - 0.08 pC for sodium chloride and + 0.08
pC for ammonium sulfate. It should be noted that with
123
these impurities there was no sign reversal in charging
over the temperature range investigated ~ - 4 to
- 20°C). The factor for the interface potential based on
the sodium chloride measurements is F ~ - 1100 for
- 10°C and F ~ - 3100 at - 20°C. The corresponding
factors for the ammonium sulfate measurements are the
same but have a positive value.
In contrast to the above study, Caranti and I1-
lingworth (1983b) found that solute impurities at natu-
ral concentrations did not have a measurable effect on
the contact potential of a riming substrate. Thus there
seems to be contradictory evidence on the role of solutes
in contact charging. A direct comparison between these
two studies may be inappropriate because the rime
structure and the resultant factor for the interface po-
tential may have been affected by differing experimen-
tal conditions. If the solute influenced the rime structure
in the experiments of layaratne et al. (1983) either di-
rectly during the freezing or indirectly by alternating
the cloud properties, then their results would have been
affected by the contact potential mechanism.
In summary, interface charging occurs between rim-
ing precipitation particles and ice crystals with a nega-
tive charge acquired by the precipitation for tempera-
tures below about - 15°C or - 20°C depending on the
liquid-water content. The separation of charge appears
to result from an interface potential with an amount
given by Eq. (9.10) that incorporates the variation in
contact area through the ice crystal size and hail size
(i.e., impact speed). The interface potential enters Eq.
(9.10) through an empirical factor, F. Natural amounts
of solute also affect the magnitude and sign of charging.
However, it is unclear whether the resultant change in
interface potential occurs as a freezing potential or indi-
rectly as a contact potential through an altered rime
structure.
Before applying the results of these laboratory find-
ings to the hail stage we first consider the appropriate
value of the factor for the interface potential. In the
evaluations presented here F was found to be in the
range - 3100 to + 3100. Thus the charge obtained by a
precipitation particle of R = 1 mm in a collision with an
ice particle of r = 50,um has a range, according to Eq.
(9.10), of - 0.02 to + 0.02 pC. This range is increased to
+ O.15 pC for R = 2 mm and r = 100,um. These calcu-
lated values also correspond to the measured range pre-
sented in this section because the particle sizes corre-
spond approximately to the experimental sizes (r) and
impact speeds. For a particular application to the hail
stage we consider a situation similar to the experiment of
Gaskell and Illingworth (1980) at low to moderate liq-
uid-water contents and in the temperature range - 15
to - 20°C. For this set of conditions the type of rime is
appropriate for soft hail. The estimated charge transfer
OCR for page 124
124
red to a soft hail particle (R = 1 mm) by an ice particle (r
= 50 ~m) is - 0.006 pC using F = - 970 (determined
previously for this experiment).
Since contact charging happens much more rapidly
than discharging of net charge between particles by con-
duction, a buildup of charge can readily occur in multi-
ple collisions. A charge of 20 pC could accumulate un-
der favorable conditions with ice crystal concentrations
of 100 per liter after 3000 collisions (or about 6 minutes).
This amount is comparable with negative charges found
on ice precipitation in highly electrified regions of thun-
derstorms (e.g., see Latham, 1981~. Thus, interface
charging appears to be capable of microscale charge
separation in amounts that can account for a major as-
pect of thunderstorm electrification. However, the wide
range and sign variation for the interface factor (and
charge) found in laboratory studies seems to be at odds
with observations of the predominantly negative charge
center for thunderstorms. It is apparent that additional
laboratory measurements along with more detailed
field observations are required to sort out the discrep-
ancy. The relation of the interface factor (F) to tempera-
ture, liquid-water content, and impurities must be
known before interface charging can be reliably applied
to the variety of conditions in the hail stage.
This completes our detailed! discussion of microscale
charge separation. We have gone from diffusion charg-
ing in the cloud stage to the more complex mechanisms
involving precipitation in the rain and hail stages. In the
following section we consider the relative importance of
these mechanisms, and in particular, we evaluate their
contributions by comparison with observations of
clouds and thunderstorms.
EVALUATION
The requirements for a satisfactory explanation of
charge separation in clouds and thunderstorms are
fairly well known (e.g., Mason, 1972; Latham, 1981;
Takahashi, 1982~. Any theory must be capable of ex-
plaining microscale and cloud-scale charge separation
on a suitable time scale. For a fairly complete assessment
of charge-separation mechanisms, we need to take into
account the evolution of charges and fields, and their
interactions, in at least two dimensions. Such an evalua-
tion is well beyond the scope of this paper (see Chapter
10, this volume, on cloud modeling.) What we can do
here is reiterate some of the pronounced strengths and
weaknesses for the various charging mechanisms. We
can also indicate where model studies would be helpful
in quantifying our gross conclusions and point to areas
in need of further laboratory or field research. In mak-
ing our evaluation we consider the major requirements
KENNETH V. K. BEARD and HARRY T. OCHS
for an adequate theory of charge separation in three
stages: (1) the cloud stage for small cumulus clouds that
contain only cloud droplets and drizzle drops; (2) the
rain stage for larger cumulus clouds that contain rain-
drops formed by accretion of cloud droplets; and (3) the
hail stage for the upper regions of large cumulus clouds
where precipitation (notably, soft hail) is formed by ac-
cretion of supercooled droplets.
Cloud Stage
Electrification is generally weak in the cloud stage.
Ion mechanisms dominate because of the absence of pre-
cipitation and their associated charge-separation mech-
anisms. Charges have been observed to range from
about 1 to 20 electrons for small cloud droplets with a
normal distribution centered near zero charge. Values
of the average charge magnitude are indicated in Figure
9.6 by region Car from measurements in stratocumulus
clouds (Phillips and Kinzer, 1958~. The observations
agree with a Boltzmann equilibrium (line c) after the
~n-9
._ ~
,o-lo~
10_7,
-12
lo-13
E
o 10-14
L)
la
1n-l5
n-17
1o-l9 _
2um 5 1 n 20
PARTICLE DIAMETER
- . _ 50 100 200 500 lmm 2 5 10 20
I ~j 1 1 1 I I ~6
-100pC
-10pC
-1pC
-0.1 pC
-0.01 pC
ELECTRIC FIELD
Drift Schaive Breakup
Charging Ion Charging Charging
Line (Eq 5} (Eq 6) (Eq 7)
6 100 kV/m 600 kV/m 400 kV/m
S 10 kV/m 60 kV/m 40 kV/m
4 1 kV/m 6 kV/m 4 kV/m
3 100 V/m 600 V/m 400 V/m
2 10 V/m 60 V/m 40 V/m
1 1 V/m 6 V/m 4 V/m
1o-o
1n-1
10-2
/// /.~ /1
- 1e 1 1 1 1 1 1 1
1 Am 2 5 10 20 50 100 200
PARTI CLE RADI US
Q(C) - 8.4 x 10-'5 R'~ (mm)
5(C} - 3.8 x 10-39 R0 6(/lm}
la'
10-5
10-6
_ 10-7
in-8
_ in-9
._
1 1 1 1
500 lmm 2 5 10
FIGURE 9.6 Average charge magnitude for cloud and precipitation
particles. Regions C1 and C2 show cloud stage (after Phillips and Kin-
zer, 1958; Gunn, 1957), regions Rat and Ret show rain stage for shallow
and deep convection (after Takahashi, 1973a, 1978), and regions HI
and H show hail stage (after Takahashi, 1973a; Latham, 1981). Lines
labeled c, T. and h are from equations given by lower inset. Lines 1
through 6 have ROE dependence on charge (see upper inset for corre-
sponding mechanisms and fields).
OCR for page 125
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS
rms charge given by Eq. (9.3) is converted to a mean
deviation (see lower inset on Figure 9.6 for the corre-
sponding Q equation). We can expect that the charge
distributions for large cloud drops would be skewed (no
longer centered on zero charge) with higher averages as
indicated by region C' from the influence of the electric
field by drift charging at cloud edges and selective ion
charging. Note that charging under the influence of the
electric field is depicted on Figure 9.6 by the lines la-
beled 1 through 6. The corresponding values of electric
field for three mechanisms are found in the upper inset.
For example, line 2 shows the charge magnitude for
drift charging at cloud base (or top) in a field of 10 V/m
and selective ion charging in a field of 60 V/m.
For a small cumulus, charge separation in the cloud
stage is consistent with microscale ion capture and
cloud-scale convective transport of charge. This combi-
nation can account for such features in the cloud stage as
the negative core and positive edges. It can also explain a
positive charge in the base of a cloud very near to the
ground. Charging by ion capture appears to be limited
by cosmic-ray production within the cloud (Wormell,
1953) and transport from outside, and therefore addi-
tional mechanisms are required to produce the fields
and charges found in the rain stage and hail stage.
Rain Stage
Electrification in convective clouds of less than about
3 km deep is characterized by the drop charges for the
rain stage indicated in Figure 9.6 by region Rat (Taka-
hashi, 1973a). The mean value (Q) is approximated by
the straight line proportional to Ri 3 (i.e., line r with
equation shown on lower inset from Pruppacher and
Klett, 1978~. Since the electric field associated with
these clouds is often 10 to 100 V/m, it is apparent from
Figure 9.6 that drift charging (lines 2 and 3) and also
selective ion charging and breakup charging can pro-
duce charges of the observed magnitude (Q) for drizzle
and raindrops (R > 100,um). What is not so apparent is
how cloud drops and small drizzle drops acquire their
relatively high charge in the rain stage. One possibility is
by evaporation of drops with higher charge. Other ex-
planations involve selective ion capture from the effects
of surface potentials (Takahashi, 1973b; Wahlin, 1977~.
However, the details of these mechanisms are poorly un-
derstood, and consequently their role in drop electrifi-
cation remains uncertain. Additional research is needed
to clarify the microscale-separation mechanisms respon-
sible for charging cloud drops and drizzle drops.
Another aspect of electrification in the rain stage is
the predominant sign of charge for cloud drops, drizzle,
and raindrops. We can consider charge separation for a
125
convective cloud of about 3 km deep (after Takahashi,
1982~. The trajectories of drizzle and raindrops are de-
picted in Figure 9.7 to indicate differences for the pre-
ferred sign of charge. The drizzle drop is in a region of
lower updraft speed (dashed arrow), which results in a
shorter growth time within the cloud. Negative charg-
ing occurs by the Wilson effect (for a downward-di-
rected field) and by drift current at cloud base. In addi-
tion, drizzle may be produced by breakup of raindrops,
resulting in negatively charged drizzle for the field near
and below cloud base. Raindrops become electrified
positively by breakup charging. At an earlier time, rain-
drops near cloud top may also acquire a positive charge
from the capture of droplets.
Although this picture of drop trajectories in Figure
9.7 is greatly simplified it does illustrate some essential
differences that can occur in growth histories and in the
resultant charge-separation mechanisms for cloud drop-
lets, drizzle drops, and raindrops. Our conclusions
about the predominant sign of charge, based on trajec-
tories and separation mechanisms, are consistent with
extensive observation of tropical cumulus clouds (e.g.,
see Takahashi, 1982~. These observations show a pre-
dominance of positive droplets near cloud top and nega-
tive drizzle drops and positive raindrops within and be-
low the cloud.
~DRtFT(+)
If// ~
+ SELECTIVE tON
i, CAPTURE (-}
DRIZZLE
~1,,tL.,~
DRIFT (-) ~ ~
. · ~
/~' `~+)
tRAINDROPS ~ BREAKUP (do)
1 (3 BREAKUP (-)
~: ~ : ~ ~ ~
FIGURE 9.7 Rain-stage electrification based on simplified growth
histories for drizzle and raindrops (modified from Takahashi, 1982).
Air currents are shown by dashed arrows and ion drift currents by
heavy arrows.
OCR for page 126
126
A fascinating aspect of electrification in the rain stage
is the reported occurrence of lightning for clouds
warmer than 0°C (e.g., see Moore et al., 1960~. The
evidence is incomplete because this phenomenon has not
been verified by in situ measurements of cloud tempera-
ture. Such lightning is apparently restricted to the trop-
ics and probably occurs only in clouds that are deeper
than discussed above. For warm clouds of about 5 km
depth average charges are typified by region R2 shown
on Figure 9.6 (Takahashi, 1978~. These charges were
measured at the ground with associated fields of less
than 1 kV/m. Drift charging, selective ion capture, and
breakup charging can probably account for such high
charges providing the fields in or around the cloud reach
about 1 kV/m. (Fields as large as 3 kV/m were measured
from an aircraft in the vicinity of warm cloud lightning
by Moore et al., 1960.) There is also the possibility that
induction charging could contribute to the field intensi-
fication within the cloud, but the enhancement of drop
coalescence in fields of 30 kV/m suggests that lightning
cannot be achieved by induction alone. We should keep
in mind, however, that induction charging has been in-
vestigated for only a narrow range of drop sizes and that
lightning in deep (warm) convection has not been stud-
ied in detail. Therefore, additional research on charge
separation mechanisms is required to understand the
strong electrification that occurs in deep warm clouds.
Hail Stage
There are three aspects of charging in the hail stage
that must be explained: (1) the observed region of nega-
tive charge, (2) the buildup of fields, and (3) the average
values of charge. Regions of negative charge lie gener
FIGURE 9.8 Schematic diagram illustrat-
ing the levels and distribution of charge
sources for ground-flash lightning observed
for summertime in Florida and New Mexico
and for wintertime in Japan (from Krehbiel et
al., 1983).
KENNETH V. K. BEARD and HARRY T. OCHS
ally between the - 10 and - 25°C level even in winter
thunderstorms, as illustrated by the location of light-
ning sources shown on Figure 9.8 (from Krehbiel et al.,
1983~. The space-charge densities associated with the
region of negative charge average about 1 C/km3 from
estimates based on lightning currents and particle
charges (Latham, 1981~. The second aspect of charging
in the hail stage is the development of large electric
fields. The maximum fields measured in thunderstorms
are consistent with estimates of the requirement for
lightning initiation (about 400 kV/m).
The average magnitude of charge on individual parti-
cles (Q) in the hail stage is shown on Figure 9.6 by region
Hi for cloud droplets and region H2 for precipitation
particles, with line h giving an approximate Q from
Grover and Beard (1975~. The charges on raindrops are
in the lower portion of H2 (after Takahashi, 1973a),
whereas charges on solid precipitation reside in the up-
per portion of H2 (Latham, 1981~. In both cases the av-
erage for the negative charges usually exceeded the posi-
tive charges by a significant amount, with charges on
individual particles sometimes in excess of 100 pC. As a
result of the high fields found in the hail stage, breakup
charging would be highly efficient (Figure 9.6, line 6),
with the sign depending on the orientation of the local
field. (Note that a variety of field orientations must oc-
cur within thunderstorms around charge centers, see
Figure 9.8.) Drift charging would also be efficient in
strong fields if ion concentrations are enhanced by co-
rona from ice crystals (Griffiths and Latham, 1974~.
Thus the generally high charges found on cloud and pre-
cipitation particles are probably an indication of field-
driven mechanisms that separate charge on the micro-
scale. For the causes of high fields we will consider the
20
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SUMMER STORMS
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OCR for page 127
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS
microscale and cloud-scale mechanisms that lead to the
negative-charge region observed to occur between - 10
and - 25°C.
We first evaluate convection charging, which has
held a controversial position among theories of thunder-
storm electrification (e.g., see arguments in Mason,
1976; Moore, 1977~. These theories, proposed by Grenet
(see Chalmers, 1967) and Vonnegut (1955), rely on the
transport by updrafts and downdrafts of space charges
and screening layers. In the hail stage, with a highly
electrified cloud, the charge from the positive corona at
the ground is carried into the cloud base and by the up-
draft, to the cloud top where it attracts a negative
screening layer. The downdrafts carry the negative
charge back toward the cloud base to strengthen the
negative field between the cloud base and the ground,
thus enhancing the positive corona. The notion of nega-
tive charge in downdrafts has been reintroduced in the
form of nonrandom mixing from the cloud top by Tel-
ford and Wagner (1979) to provide a qualitative expla-
nation for a negative-charge region near the - 10°C
level.
This picture of descending negative charges appears
to be at odds with the early stages of convective electrifi-
cation modeled by Chiu and Klett (1976~. They found a
positive screening layer at a cloud top and positive de-
scending charges. Convection and mixing were found to
weaken the field within the cloud. Since Chiu and Klett
did not expect their model outcome to change apprecia-
bly for clouds deeper than 5 km, it is difficult to envision
how convective (single-cell) transport could be the
source of strong electrification. However, in the hail
stage with multicell convection and with corona from
precipitation, the ion concentrations would differ con-
siderably from the model of Chiu and Klett. Thus, a
better model is required to evaluate the importance of
convection in highly electrified clouds.
Another criticism of convection charging is that up-
drafts and downdrafts may disorganize their associated
charges through mixing (e. g., see Chalmers, 1967) . The
study of Chiu and Klett clearly shows that single-cell
convection with eddy diffusion diminishes the electric
field within the cloud. If we picture cloud turrets as con-
vective cells (similar to Figure 9.2) with interspersed up-
drafts and downdrafts, then the possibility for disorgan-
ization by mixing between adjacent charge regions
becomes rapidly apparent. Questions regarding the im-
portance of mixing in cloud electrification probably will
not have a satisfactory answer until we have more quan-
titative models of turret scale motions and entrainment.
In addition, the common occurrence of a negative
charge center near - 15°C suggests that transport of
ions and charged particles by convection is not so impor
127
tent as microscale charge separation involving ice parti-
cles.
In evaluating induction charging in the hail stage, we
consider that the most efficient microscale interactions
are collisions between wet hail and ice particles. The
maximum charge according to Eq. (9.8) is about 1 pC in
the limiting field of 400 kV/m for a particle of 100-,um
radius and 10 pC for a 300-,um particle. Since the wet
growth of hail requires sizes larger than about 10 mm
diameter, the induction limit of 1 to 10 pC even for R =
10 mm is well below the charge expected from ion cap-
ture in high fields (see line 6, Figure 9.6~. Thus, induc-
tion charging cannot be directly responsible for the av-
erage charges (1 to 100 pC) found on precipitation
particles (0.5 to 2 mm radius) in the hail stage.
Another aspect of the induction charging of wet hail is
its importance to the region of negative charge near the
- 15°C level. For hailstones with a maximum charge of
10 pC at a maximum concentration of 1 m ~ 3, the result-
ing space-charge density is 0.01 C/km3. This estimate of
the maximum charge density is several orders of magni-
tude smaller than a charge of about 1 C/km3 found from
measurements of particles and from estimates based on
lightning currents. Although the induction mechanism
provides negative charge on precipitation particles and
field intensification through feedback, it appears to be
too weak to account for the charge densities associated
with the hail stage. Its shortcomings are twofold: the
maximum charge is limited by the effects of size and
contact angle given in Eq. (9.8), and the charge density
is limited by the instrinsically low concentration of hail-
stones. The microscale separation mechanism in the
negative-charge region is probably associated with
smaller precipitation particles (e.g., soft hail), because
their higher concentration could lead more easily to a
sufficient charge density. For example, particles at a
concentration of 100 m ~ 3 carrying 10 pC would result in
a more realistic 1 C/km3.
The charging of soft hail has been simulated in the
laboratory by collisions between ice particles and an ice
electrode in the process of riming (Gaskill and I1-
lingworth, 1980; Jayaratne et al., 1983~. Although our
understanding of the separation mechanism is incom-
plete, the evidence points to interface charging from
contact potentials with freezing potentials having a sec-
ondary role. Investigations of temperature effects in the
above studies have ruled out thermoelectric charging.
The formula applicable to these results scales with con-
tact area and is the same as line r on Figure 9.6 when
evaluated for an ice particle of r = 60,um. Thus charge
transfer for individual collisions between soft had! and
small ice particles is around 0.01 pC. Since contact time
is relatively short compared with the time required to
OCR for page 128
128
discharge colliding particles by conduction, an accumu-
lation of charge can occur in multiple collisions. In this
manner an increase of 3 orders of magnitude, well into
region H2, may be attained with high concentrations of
ice crystals in several minutes.
A key result of the above experiments is a reversal in
the sign of charging at temperatures of - 10 to - 25°C
depending on liquid-water content. Riming particles
acquire negative charges if colder than the reversal tem-
perature and positive if warmer. Thus, soft hail would
be charged negatively above the reversal level in the
cloud and positively below this level.
Jayaratne et al. (1983) postulated that descending
precipitation particles should have their maximum neg-
ative charge near the reversal level and that rebounding
ice crystals carrying negative charge from below would
also contribute to the negative region. The fields di-
rected toward the reversal level would intensify during
the process of charge separation by differential sedimen-
tation.
There are many features of interface charging that
need clarification before we can feel comfortable with
the above description of charging in the hail stage. First,
the roles of temperature, liquid-water content, and so-
lutes are poorly understood. These appear to influence
contact potential through changes in rime structure.
TABLE 9.1 Charge Separation in Clouds and Thunderstorms
KENNETH V. K. BEARD and HARRY T. OCHS
(Solutes may also affect interface charging by transient
freezing potentials. ~ Second, the details of charge trans-
fer have not been explained, although the charge carri-
ers are probably associated with the contact surfaces.
This concept is consistent with a rapid transfer of charge
that scales with contact area. Finally, our recently ac-
quired understanding of interface charging, even
though somewhat limited, cannot be adequately as-
sessed until it is placed within the framework of a multi-
dimensional cloud model.
CONCLUSIONS
The charging mechanisms in clouds and thunder-
storms are varied and numerous. Some are simple and
readily appreciated, whereas others are complex. Sev-
eral important mechanisms are poorly understood.
Feedback readily occurs through changes in ion concen-
tration and the electric field making it difficult to iden-
tify the primary causes for electrification. However,
some simplification can result by considering the charg-
ing mechanisms in three stages of cumulus cloud devel-
opment: the cloud, rain, and hail stages.
The charging mechanisms discussed in this chapter
are summarized in Table 9.1. Each mechanism is listed
with the microscale and cloud-scale separators (with
Mechanism Microscale Cloud Scale Major Roles
1. Diffusion charginga Ion capture by Removes ions within
diffusion cloud
2. Drift chargings h Ion capture in Drift currents Charges particles
drift currents Convection Enhances field
(Sedimentation)
3. Selective ion Ion capture by Sedimentation Charges particles
charging' 'I polarized crops (Convection) Enhances fields
4. Breakup charging'' Collisional Sedimentation Charges drops
breakup of (Convection)
polarized drops
5. Induction charging`' f Charge transfer Sedimentation Charges particles
between polarized (Convection) Enhances field
particles
6. Convection chargingd ~ h Space-charge Convection Enhances field
production (Charges particles)
Ion capture in
drift currents
7. Thermoelectric charging) Charge transfer Sedimentation (Charges particles)
between particles of (Convection)
differing temperatures
8. Interface charging) k Charge transfer Sedimentation Charges particles
between particles (Convection) Enhances field
involving contact
potentials
(freezing potentials)
aGunn (1957); bChiu and Klett (1976); CWilson (1929); dChalmers, (1967); eMatthews and Mason (1964); fElster and Geitel (1913); "Grenet
(1947); hVonnegut (1955); 'Latham and Mason (1961); iWorkman and Reynolds (1948); Abuser and Aufdermaur (1977~.
OCR for page 129
CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS
items of secondary importance shown in parentheses).
Charging appears to be well described by diffusion,
drift, and selective ion capture for the nonprecipitating
cloud stage (mechanisms 1-3~. The situation in the rain
stage is complicated by the addition of breakup and in-
duction (mechanisms 4 and 5~. We suspect that drift,
selective ion capture, breakup, and induction are re-
sponsible for charges and fields in shallow clouds. How-
ever, it is difficult to find an explanation for the stronger
electrification in convective clouds over a few kilome-
ters deep. The basis of lightning from clouds with tops
warmer than freezing remains a mystery. A major prob-
lem in the rain stage is that our knowledge of the sus-
pected mechanisms is still rather rudimentary. There is
clearly a need for additional research on changing by
ions, breakup, induction, and convection to understand
the electrification of warm clouds.
In the hail stage we add thermoelectric and interface
charging (mechanisms 7 and 8~. Recent laboratory stud-
ies of charge transfer involving ice particles rebounding
from simulated hailstones in the process of riming have
shown that interface charging is the dominant mecha-
nism. The roles of temperature, liquid-water content,
and solutes are most likely important in altering the
rime structure and thereby the contact potential and
contact area. More research is required to understand
these effects and the details of charge transfer.
The electrification process becomes more complex as
a cloud develops. The cloud stage involves mechanisms
1-3, whereas the rain stage includes 1-6. All the mecha-
nisms listed in Table 9.1 may occur in the hail stage. We
might ask, as many have before us, which separation
mechanisms are essential to cloud electrification. The
answers, if we had them, would depend on which aspect
of cloud electrification we consider. For example, the
essential mechanism for lightning depends on whether
we are looking at the field development in the rain or
hail stages or whether we are concerned with the charge
centers associated with cloud-to-ground, in-cloud, or
cloud-to-cloud lightning. Yet another aspect of light-
ning is the mechanism that initiates the stroke. Clearly
the idea of an "essential" mechanism is an oversimplifi-
cation. A more useful approach is to examine the inter-
dependencies. We should be asking how the various
charge-separation mechanisms are related. Some an-
swers should be forthcoming as we incorporate the
knowledge gained from recent laboratory studies of in-
dividual mechanisms into models of cloud electrifica-
tion and compare the findings to field observations.
With continued progress in laboratory, field, and mod-
eling research we should achieve, in the next decade, a
much improved perspective of the charging mechanisms
in clouds and thunderstorms.
129
ACKNOWLEDGMENTS
We appreciate the helpful comments of Bernice Ack
erman, David Johnson, Anthony Illingworth, and an
anonymous reviewer. This review was supported in part
by a grant from the National Science Foundation under
ATM-83-14072.
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.. . .
Representative terms from entire chapter:
charge transfer
