|
Items in cart [4] |
Questions? Call 888-624-8373 |
| Copyright © 2009. National Academy of Sciences. All rights reserved. Terms of Use and Privacy Statement |
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 131
Moclels of the Development of the
Electrical Structure of Clouds
10
INTRODUCTION
ZEV LEVIN
Tel Aviv University
ISRAEL TZUR
National Center for Atmospheric Research
Thunderstorms are highly variable in their intensity,
dimensions, composition, and electrical structure. Some
generalizations can be made about them, however. The
lightning activity follows strong vertical air currents
and precipitation. As a consequence of this correlation,
lightning is most frequently observed in cumulus clouds,
rarely in stratus clouds, and never in isolated cirrus
clouds. Both satellite and ground observations reveal
lightning activity at all latitudes between 60° N and 60°
S with the most frequent occurrence at low latitudes and
over land. The high occurrence rate over land is be-
lieved to be related to the more connectively unstable
conditions normally present over land. In high lati-
tudes, the lightning frequency decreases because of the
reduced convection from colder surfaces and the re-
duced absolute humidity.
Most thunderstorms contain both water drops and ice
crystals, they usually have mass contents (water + ice)
greater than 3 g/m3, and they have precipitation rates
(involving particles larger than 100 ,um) in excess of 20
mm/in. Although lightning has been observed most often
in clouds containing both ice and water, there have been
a few observations of lightning from all-water clouds
(e.g., Lane-Smith, 1971~. Lightning has been observed
in clouds that are completely at temperatures below
131
0°C, but these clouds usually contain both supercooled
water droplets and ice.
The complexity of the processes leading to the devel-
opment of both the precipitation and electrical struc-
ture in the clouds makes it impossible to construct or
validate theories of cloud electrification from simple
field experiments. It is only through the complementary
efforts of laboratory experimentation, field observa-
tions, and mathematical simulations that we can hope
to understand the physical processes involved in thun-
derstorms. A recent review by Latham (1981) summa-
rized some of the main observations of thunderstorm
electrification in a coherent fashion, and we refer the
interested reader to it.
Improved understanding of the major processes lead-
ing to the buildup of strong electrical fields and their
mutual interaction with precipitation can lead to better
forecasting of thunderstorm activity for use in aviation
and protection of forested areas, to the development of
methods for artificially modifying lightning activity,
and even to the development of more efficient rain-en-
hancement operations.
As an ultimate test of the various theories of how elec-
trical charge separates in thunderclouds, it would be
necessary to design a model that simulates as accurately
as possible the three-dimensional and time-dependent
nature of the cloud and its environment, including the
OCR for page 132
132
microphvsical development of the liquid and solid
phases in the cloud and all the possible electrical pro-
cesses that are operating. These requirements are not yet
attaintable with our current state of knowledge and
available computers. The number of processes involved
and the large range of scales (from the molecular level to
the dynamic scale 1000 m) cannot all be included in a
single model. Therefore, attempts have been made to
deal with the problem of the development of the electri-
cal structure of clouds by emphasizing some processes
and ignoring others. A few models, for instance, simu-
late the microphysical processes only, neglecting the
macroscale dynamics altogether, whereas others have
gone to the other extreme and simulate the dynamics in
detail while simplifying the microphysics dramatically.
To fill in the gap, some modelers have tried to deal with
both the microphysics and the dynamics with sacrifices
at both ends of the scale.
We will review some of these models, try to establish a
common denominator from their results and conclu-
sions, and d-raw attention to some unanswered points
that need further work.
GENERAL REQUIREMENTS FROM
ELECTRICAL MODELS OF
THUNDERCLOUDS
The validity of any thunderstorm model is deter-
mined by its ability to simulate observed features. Ow-
ing to the large natural variability of the various pro-
cesses in thunderclouds, it is difficult to find a "typical"
storm with which all models could be compared. It is
possible, however, to list some common observed fea-
tures to use as general criteria for such comparisons.
The following summary by Mason (1971) of the basic
thunderstorm observations still appears to be valid:
1. The average duration of precipitation and electri-
cal activity from a single cell is about 30 min.
2. The average electric moment destroyed in a light-
ning flash is about 100 C km, the corresponding charge
being 20 to 30 C.
3. In a large, extensive cumulonimbus, this charge is
separated in a volume bounded approximately by the
- 5°C and - 40°C levels and has an average radius of
perhaps 2 to 3 km.
4. The negative charge resides at altitudes just above
the - 5°C isotherm. Krehbiel et al. (1979) observed that
the negative charge transferred by lightning originates
from regions between -10°C and -17°C, indepen-
dent of the height above ground and regardless of the
geographical location of the thunderstorm. The main
positive charge is situated several kilometers higher. An
ZEV LEVIN and ISRAEL TZUR
other subsidiary small positive charge may also exist
near cloud base, centered at or below the 0°C level.
5. The charge-separation processes are closely associ-
ated with the development of precipitation, probably in
the form of soft hail (particles containing both liquid
water and ice).
6. Sufficient charge must be separated to supply the
first lightning flash within 12 to 20 min of the appear-
ance of precipitation particles of radar-detectable size
(d-200,um).
MECHANISMS OF CHARGE SEPARATION
For space-charge centers to build up in clouds, charge
must be separated first in the microscale, and then
larger-scale processes can act to separate the opposite
charges in space. When accomplished, this dual-scale
process leads to the buildup of a space-charge distribu-
tion similar to that in Figure 10.1.
In thunderclouds the charge separated on a micro-
scale by particle interactions is subsequently separated
on a macroscale with the help of convection and gravita-
tional settling. Convection plays a role in cloud particle
growth by forcing the condensation of water vapor until
the particles are large enough to coalesce. Some of the
interactions between cloud particles, particularly those
followed by rebounding, may result in charge separa-
tion (as will be discussed later). These charges are then
separated by differential terminal settling velocities.
The larger particles, which carry predominantly one
~ t ~ Conduction, JE
cam--W! t~-
12 km + + + (-25to -60°C)-
1\
7 km
Charge ma/
Separation /
Current ~
- l _ _ _ (- 10° to - 20° C )
~ /~- + + _ (0°to-5°C)
Lightning, JL?4/ poloist I I I I I I ~ ~ PreC;P;tOt;On, JP
Convection Discharge, l I I
~ 1'', ;; | | ~ ~convection, JC
of Wf We'd W/f elf f /7'f elf Wf Wf ,^/7,'7
FIGURE 10.1 A schematic of the main space-charae distribution
and currents in a thundercloud.
OCR for page 133
\IODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS
sign of charge, fall faster and farther down with respect
to the convected air, leaving the oppositely charged
smaller particles above.
As the charge centers build up, discharging mecha-
nisms become more effective, and these should be in-
cluded in any complete description of cloud electrifica-
tion. Two kinds of discharge are possible: (1) discharge
by collisions between drops and ions of opposite polarity
and (2) discharge by collision and coalescence with
cloud particles of opposite charge (see Colgate et al.,
19771. The first mechanism depends on the electrical
conductivity of the small ions (\ = nek, where n is the
ion number density, e is the electronic charge, and k is
the electrical mobility) and on the ion diffusivity. Often
ions of different polarities have different diffusivities;
those with higher diffusivity attach preferentially to
cloud and free aerosol particles. However, after some
charge is built up on a cloud particle, further ion diffu-
sion to it will be limited.
Another factor affecting ion attachment to cloud par-
ticles is the electric field in the cloud. Strong fields will
move free ions from one region to another. In so doing,
they also increase the conduction currents and, hence,
the discharge of cloud particles. In addition, when the
electric field exceeds about 50 kV/m, corona discharge
begins near the corners of ice crystals and high concen-
trations of ions are generated. These ions increase the
electrical conductivity and help to prevent or slow down
the further buildup of the space charge.
The other discharge mechanism (collection of oppo-
sitely charged cloud particles) takes place at all stages of
particle growth. This mechanism is enhanced if the in-
teracting particles are highly charged, have opposite po-
larity, and when the ambient field is strong. In this case
the collection efficiency increases by increasing the colli-
sion efficiency (Coulomb attraction changes the trajec-
tories of particles relative to each other) or by increasing
coalescence efficiency (not allowing bouncing, and
hence no charge separation, to occur) or by both.
Therefore, for a charge mechanism to be effective, it
has to separate sufficient charge at a rate sufficiently
high to overcome these discharge processes. The many
charge-separation mechanisms and their complexity re-
quire a detailed discussion that is beyond the scope of
this chapter. We recommend that the interested reader
refer to Chapter 9 (this volume) by Beard and Ochs and
to Mason (1971~.
The various charging mechanisms that have been
proposed as possible major contributors to electrifica-
tion of thunderstorms can be divided into two major
classifications: (1) precipitation mechanisms requiring
particle interactions with subsequent space-charge sep-
aration by gravitational sedimentation and (2) ion at
133
tachment to cloud or precipitation particles and then
charge separation by either gravitational settling or by
atmospheric convection (updrafts or downdrafts).
Mechanisms from group (1) above are divided into two
major subprocesses inductive and noninductive. Most
models to date treat these mechanisms with various de-
grees of detail. On the other hand, only a few models are
available that treat the ion convective process. Conse-
quently, since the intention here is to review the present
state of knowledge in modeling electrical development
in clouds, most of the emphasis is placed on the models
dealing with the precipitation mechanisms. As discussed
later, there are still a great many questions that these
models cannot answer.
Inductive Process
Charge can be separated by the inductive process dur-
ing rebounding collisions of particles embedded in an
electric field. This mechanism, which is relatively sim-
ple to formulate, was treated intensively in cloud elec-
trification models. According to Sartor (1967) and Scott
and Levin (1975) the amount of charge that is separated
per collision by this process is
AQ = t-4~0E~r2cos~ + (co + 1)Q + ~q]
[1 - exp(-tc/~] (10.1)
In this equation /`Q represents the charge transfer to the
large particle as a smaller particle o-f radius r collides
and rebounds in an electric field E (defined as positive
when a positive charge is overhead), making an angle ~
between the field and the line connecting the centers of
the particles at the point of separation; ~ and ~ are con-
stants that depend on the ratio of sizes of the colliding
particles (Ziv and Levin, 1974~; Q and q represent the
initial charge on the particles before the interaction; tc is
the contact time of the colliding particles and ~ the relax-
ation time of the charge carrier ~ = ccolK' where ~ and K
are the dielectric constant and the electrical conductiv-
ity, respectively; and c0 is the permittivity of free space).
The first term on the right-hand side of Eq. (10.1)
represents the charge that is transferred from the small
to the large particle because of the inductive polariza-
tion effect. One can see that the stronger the field or the
larger the size of the smaller particle, the larger is the
charge separated. The constant ~ represents the en-
hancement of the electric field around the colliding par-
ticles, as compared with the the ambient field. Particles
may collide at the head-on position but will skid or roll
on each other and finally separate at the angle I. For
water drops, ~ may vary between 50° and 90° (Levin
and Machnes, 1977~. Large liquid particles sometimes
OCR for page 134
134
may also be separated at ~-90°, leading to their dis-
charge (Al-Seed and Saunders, 1976~. On the other
hand, nonspherical solid or liquid particles can separate
larger charges by the inductive process as a result of the
much enhanced electric fields near them (Censor and
Levin, 1974~.
The second and third terms on the right side of Eq.
(10.1) represent the limitation of charge transfer due to
the initial charge on the large (Q) and small (q) parti-
cles, respectively. The constant co then is a geometrical
factor that represents the effect of the capacitance of the
two on the charge transfer.
The last term on the right represents the limitation to
charge transfer due to the electrical conductivity of the
materials that compose the particles (Sartor, 1970;
Caranti and Illingworth, 1983; Illingworth and Caranti
1984~. Ice particles at low temperatures, for example,
have low bulk and surface electrical conductivities that
lead to longer relaxation times r. This means that in any
given collision there is the possibility that not all the
available charge will be transferred, since the contact
time tc might be shorter than I. Indeed a recent labora-
tory study by Illingworth and Caranti (1984) on the de-
pendence of charge transfer during ice-ice collisions on
the surface conductivity of ice, suggests that for ice-ice
interactions the inductive mechanism is not efficient.
Interactions of two particles can result in either collec-
tion or rebound. To describe the probability of these two
end results a collision efficiency, Ed, and a coalescence
efficiency, E2, are defined. Ed represents the probability
of two cloud particles to interact, and E2 represents the
probability of the interacting particles to coalesce.
Therefore, the collection probability is Ed E2, and the
rebound probability is (1 - EATEN. To separate charge
an electrical contact among rebounding particles must
be achieved. Only a fraction, E3, of the particles that
collide and rebound make such electrical contact. We
will refer to E3 as the electrical contact probability.
Therefore, the probability for separating charge be-
tween two cloud particles is P = EM - E2)E3.
The rate of charge buildup on the large particles per
unit volume as a result of collisions of particles can be
expressed as
dQ/dt= 7r(R + r)2(V- v)Nn(Pl\Q - E~E2qj,
(10.2)
where R and r are the radii of the large and small parti-
cles, respectively, V and v are their fall speeds, and N
and n are their concentrations. The term P1\Q repre-
sents the charge separated per interaction, while E~E2q
accounts for the discharge of the large particles resulting
from collection of oppositely charged particles (Scott
and Levin, 1975~.
ZEV LEVIN and ISRAEL TZUR
Noninductive Process
Many noninductive mechanisms have been proposed
to explain the formation of electricity in thunderstorms.
Among the most powerful are the thermoelectric effect
(Reynolds et al., 1957; Latham and Mason, 1961),
freezing potentials (Workman and Reynolds, 1948),
and contact potentials (Buser and Aufdermaur, 1977;
Caranti and Illingworth, 1980~. All of these rely on the
electrochemical nature of water or ice for charge sepa-
ration.
Thermoelectric Effect Charge separation results
from interactions of ice particles of different surface
temperatures. On contact the temperature gradient
across the surface causes the H + ions to migrate from the
warmer particle to the cold one, leaving OH- ions on
the warmer ice particle. Subsequent rebound of these
particles will result in charge separation. The amount of
charge separated in this process depends on the temper-
ature and the temperature gradient. In most models, the
value of the charge separation per interaction is taken as
a constant, regardless of the temperature or tempera-
ture gradient.
Freezing Potentials Workman and Reynolds (1948)
and Pruppacher et al. (1968) observed that high electri-
cal potentials develop across an ice-water interface
when the water contains small amounts of impurities
(~ 10-5 molar). These potentials develop as a result of
preferential incorporation of certain ions from the solu-
tion into the ice lattice, leaving the ice and the liquid
solution oppositely charged. In clouds, if such a situa-
tion occurs, fragments of the solution can be thrown off
as a result of the impact of other particles. These frag-
meets carry away charge of one sign, leaving the ice par-
ticle with the opposite charge. Gravitational settling
can then separate the two charges in space.
These early works suggested that the magnitude and
sign of the separated charge depend critically on the
amount and type of impurity used. Various laboratory
experiments conducted to simulate this charging mech-
anism have resulted in a surprisingly wide range of
charge transfer. Most investigators (e.g., Weickmann
and Aufm Kampe, 1950; Latham and Mason, 1961)
measured charging rates that correspond to roughly 3 X
Jo- 16 to 3 X 10- Is C per collision. Schewohuk and Iri-
barne (1971) observed about 10-~ C per collision for
very large water drops (R = 2.9 mm), a value that de-
creased as the drop size and impact velocity decreased.
On the other hand, they observed very little dependence
on impurities but much stronger dependence on temper-
ature. In most of these experiments the rebounding
OCR for page 135
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS
droplets received positive charge, leaving the target ice
negatively charged.
In experiments by Latham and Warwicker (1980),
these general findings were confirmed, but a maximum
charge of only 10- ~4 C per collision was observed with
slightly smaller drops, in conformity with most other
investigations. It is also clear from these experiments
that the charge separation is more a function of drop size
than of impurities.
Contact Potentials Buser and Aufdermaur (1977)
and more recently Caranti and Illingworth (1980) ob-
served that a surface potential develops during riming of
supercooled water droplets on ice. This surface poten-
tial increases steadily with decreasing temperature
down to - 10°C and remains constant to - 25°C.
Caranti and Illingworth (1980) also observed that im-
purities, such as NH4OH, NaCl, or HE, made no detect-
able difference in the surface potentials. In clouds,
charge could be transferred by collisions and subsequent
rebounds of small unrimed ice crystals with a surface
potential near zero from the surface of a rimed crystal
with negative surface potential.
The electric charge buildup by each of the noninduc-
tive processes can be expressed as in Eq. (10.1), except
that ~Q has the form
Q = ~ - A + (co + 1)Q
+ ~q]~1 - exp( - tclr)], (10.3)
where A is the charge transfer per collision resulting
from one of the above mechanisms. The value of A for
small cloud particles varies from 10- i5 to about 10- i4 C
per collision, depending on the type and size of the parti-
cles and on temperature (Takahashi, 1978~. Owing to
the lack of comprehensive data about the charge trans-
fer as a function of size and temperature, all available
numerical models take this value as a constant.
One should keep in mind that the charge buildup by
both the inductive and the noninductive processes de-
pends on the interaction probabilities Em, E2, and E3 and
on the ratio tclr. In the models, the values of Em, E2, and
E3 have to be specified. A detailed discussion of the
probabilities and the way they are calculated and mea-
sured is beyond the scope of this paper. The interested
reader is referred to Pruppacher and Klett (1978, Chap-
ter 14) for details.
The collision efficiency Em of water drops used in the
numerical models is based on calculations of particle
trajectories (e. g., Davis and Sartor, 1967~. A few calcu-
lations are available for collisions of ice particles with
water drops and with other crystals. These are limited
owing to the complex geometrical shapes of the ice crys-
tals and their dependence on temperature.
135
The coalescence efficiency of water drops or ice crys-
tals has not been theoretically evaluated and is deter-
mined by experimental measurements. For water
drops, the coalescence efficiencies of Whelpdale and
List (1971) and Levin and Machnes (1977) are often
used. These values vary from almost zero for interac-
tions of large drops among themselves to a value close to
unity for interactions of very small drops with large
ones. The experiments on interaction of ice particles
with water drops did not differentiate between collision
and coalescence and only measured the end result such
as collection (EWES or rebound teat - Ells (e.g., Auf-
dermaur and Johnson, 1972, and some other works sum-
marized by Pruppacher and Klett, 1978~. Aufdermaur
and Johnson (1972) observed that rebound occurred on
only about 1 percent of the impacting drops; this im-
plied about a 99 percent collection. However, this ex-
periment was conducted with a limited range of drop
sizes and temperatures. Unfortunately, not enough in-
formation is available on this parameter.
The values of E3 are the least known, and a large
range of values is usually tested in the models.
To simplify things, some models do not use the de-
tailed formulation of Em, E2, and E3, but rather combine
theminto one parameter(P= EN - E2)E3.Therelax-
ation time for charge transfer between the interacting
particles, I, depends on their electrical conductivity.
This conductivity, either surface (electrons) or bulk
(ions), is temperature dependent. The relaxation time of
ionic charge transfer of pure ice decreases from 6.8 X
10 ~ 3 see at - 10° C to 2.8 X 10 - 2 see at - 19° C (Sartor,
1970~. However, for slightly impure ice (doped with 3
X 10-6 M chloride, for example) this relaxation time
will be shortened by two orders of magnitude but be-
come more temperature dependent (Gross, 1982~. The
relaxation time of charge transfer by surface electrons
on the other hand is believed to be about 30 times shorter
than bulk ions. It is therefore the surface electrons that
are probably responsible for the transfer of charge dur-
ing interactions of ice particles (Gross, 1982~.
The contact time tc has been estimated to vary be-
tween 10-4 to 10-6 see (Sartor, 1970; Caranti and I1-
lingworth, 1980~. Therefore, the ratio tclr will vary
with temperature by a few orders of magnitude. As the
temperature decreases, the factor t1 - exp(- tclr)] in
Eqs. (10.1) and (10.3) inhibits the charge transfer. For
water drops, this factor is almost unity, because water
has a higher conductivity than ice.
CHARGING BY ION ATTACHMENT
Attachment of ions to cloud particles can also charge
them. Three kinds of mechanisms should be considered:
ion diffusion, ion conduction, and ion convection. Dif
OCR for page 136
136
fusion of ions through air is a function of the tempera-
ture and the sizes of the ion. At altitudes typical of thun-
derstorms, negative ions have a diffusivity about 25-40
percent larger than that of positive ions. This would sug-
gest that at the early stages of cloud development, when
all other charge mechanisms are not effective, charge
separation by ions would dominate.
At later stages when the strength of the electric field
increases, ions can be conducted to the cloud particles
because of the electrical forces (ion conduction). At the
same time ions can be transported toward the particles
because of the relative velocities between them. Wilson
(1929) pointed out that ions, which move because of the
presence of the electrical forces and the air flow, selec-
tively interact with cloud particles moving under the
action of gravity and air flow (ion convection). This se-
lective ion current depends on the fall speed of the parti-
cle, its charge, and the magnitude and direction of the
external electric field.
The attachment of ions to cloud particles reduces
their concentration and the electrical conductivity.
Phillips (1967) calculated the electrical conductivity ex-
isting in electrified clouds under a quasi-static situation.
His calculations were based on the balance between the
ion production from cosmic-ray ionization, the rate of
ion loss from ion recombination, and ionic diffusion and
conduction to cloud particles. Similar formulation was
used by Griffithes et al. (1974) for calculating the elec-
trical conductivity for three different cloud types cu-
mulus congestus, strato-cumulus, and fog. They con-
cluded that a decrease in conductivity of about 3 orders
of magnitude occurred under highly electrified condi-
tions. This decrease was found to be sensitive to varia-
tions in the liquid-water content and the electrical field
but only slightly affected by changes in altitude, particle
charge, and the manner in which the charge is distrib-
uted over the size spectrum. When a secondary source of
ion production, resulting from corona currents emitted
from ice particles under the influence of a strong electric
field, was introduced into the calculations, a large in-
crease in conductivity was predicted.
The process of ion attachment to cloud particles con-
tinues until enough charge is accumulated, at which
point any additional charge can be quickly neutralized
by attachment of ions of opposite charge. Some charge
on the cloud particles often exceeds this saturation
threshold value owing to charging by other mecha-
nisms, so that within the main charge centers of the
cloud ion attachments will generally act as discharge
processes.
When the cloud is electrified the conducting environ-
ment reacts. Atmospheric ions that have the same polar-
ity as the charge center within the cloud will be re
ZEV LEVIN and ISRAEL TZUR
pelted, while those with an opposite polarity will be
conducted from the surroundings toward the cloud. The
ions that enter through cloud boundaries are attached to
cloud particles and generate a charged screening layer.
This process was first recognized by Grenet (1947) and
independently by Vonnegut (1955~. Brown et al. (1971)
and Klett (1972) presented detailed calculations of the
charge distribution and accumulation process in the
screening layer.
Recently it has been suggested (Wahlin, 1977) that
negative ions not only have higher mobility than posi-
tive ones but also have higher electrochemical affinity to
surfaces and will rapidly attach to cloud particles.
Therefore, negative ions that are brought, along with
positive ions, into the cloud by an updraft, will prefer-
entially attach to cloud particles near cloud base, leav-
ing the free positive ions to be carried to cloud top. This
mechanism also relies on falling precipitation particles
and updraft for charge separation to occur. Without
large precipitation particles falling with respect to the
updraft, all the charges (negatively charged particles
and positive free ions) would occupy the same volume
and mask each other completely. However, this mecha-
nism is probably too weak to produce strong fields dur-
ing cloud development, since the ion concentration pro-
duced by cosmic rays below the cloud base is too low to
produce extensive charge separation (Wormell, 1953~.
A mechanism that also relies on atmospheric ions for
the charging but does not require gravitational settling
of precipitation particles for charge separation, is the
convective model proposed by Vonnegut (1955~. It de-
pends on air currents to bring abundant positive ions
from the ground up to cloud level. Cloud droplets that
collect these ions at the cloud base carry them to the
cloud top in the updrafts. The resulting region of posi-
tive charge, according to Vonnegut, will preferentially
attract negative ions from the free atmosphere above to
form a screening layer at the cloud top. Downdrafts,
produced by the vortex circulation of the air in the
cloud, which is enhanced by the negatively buoyant air
created by overshooting the thermal equilibrium point
and by the evaporation of cloud particles at the cloud
top, will transport the negative ions down to the cloud
base, forming a vertical electrical dipole.
Latham (1981) suggested that the convective mecha-
nism plays only a minor role in the charging of thunder-
storms because rates of ion production by cosmic rays
are far too small to produce enough charge that can be
separated and produce lightning. On the other hand,
calculations by Martell (1984) suggested that the ion
pair production over continental surfaces is greater than
that produced by cosmic rays by more than an order of
magnitude because of the decay of radioisotopes. If
OCR for page 137
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS
these calculations are confirmed experimentally, the IOOO
relative contribution of the convective mechanism will
have to be re-examined.
SURVEY OF THEORETICAL MODELS
Parallel-Plate Models
Parallel-plate models are the simplest models of cloud
electrification. They completely ignore the contribu
tions of the air motions and focus on the microphysics.
However, even in this area they consider only a small
fraction of the microphysical processes that take place.
To simplify things, they assume that any charge sepa
rated in the charging volume is accumulated on two
parallel plates, simulating the centers of the space
charges in the cloud. Therefore, the models cannot pre
dict the vertical structure of the charges in the cloud.
The cloud is assumed to be composed of water drops
alone, ice crystals with hail pellets, or a combination of
them. The simplest of these models allows the particles
to grow with time at preassigned rates (Mason, 1972),
whereas the more detailed models allow the growth to
proceed by semicontinuous (Ziv and Levin, 1974) or sto
chastic interactions (Scott and Levin, 1975~. These
models do not explicitly consider the effect of ions on the
charging but assume discharge of particles (owing to at
tachment of ions of opposite signs) that exponentially
depends on the field. All these models tested the effec
tiveness of the inductive process only.
Mason (1972) and Sartor (1967) assumed that charge
is separated by collisions of ice crystals and hail pellets.
They concluded that the inductive process is a very pow
erfu] one and is capable of separating enough charge for
the field to reach a few kilovolts per centimeter in about
500-600 sec.
Scott and Levin (1975), who treated the particle
growth in more detail, concluded that the inductive
process could account for the first lightning of a thun
dercloud provided the electrical contact probability,
E3, is greater than 0.1 (see Figure 10.2~. That is, of the
cloud particles that do make contact and then rebound,
about 10 percent need to separate charge in order for the
process to be effective. For water drops, the value of the
charge separation probability, which contains E3 in it, is
thought actually to be lower than 0.1, thus making this
process ineffective in producing enough charge separa
tion. For ice-ice collisions, on the other hand, this effi
ciency could be as high as 0.9. There is still great uncer
tainty as to its value for water drops colliding with ice
pellets.
As mentioned before, the charge transferred per colli
sion of ice particles should decrease with decreasing
137
500
100
- ' ' ' ' 1 ' ' ' ' I ' ' ' ' 1 ' '
- rF=40, E3 =1~
1// ~0.3
_ E3 -0.8 111 / TF =54. E3=O.S
/ F<=ll93 E3 =0.1
/
OF = 173, E3 =0.05
0 500 1000 1500
TIME (s)
FIGURE 10.2 The growth of the electric field as a function of time
under the inductive process with water drops only and calculated by
the infinite cloud model of Scott and Levin (1975~. The different
curves represent different values of E3, the electrical contact effi-
ciency. The values of IF correspond to the time constants during the
time of the maximum growth rate of the electric field.
temperature. Ziv and Levin (1974) simulated this fea-
ture for ice-ice collisions and found greatly diminished
charge and field buildup.
Other important factors determining the electrical
development in clouds are the relative sizes of the collid-
ing particles and the number of concentrations of the
cloud elements. The first factor affects the charge that is
separated per collision, since the charge transferred in-
creases with increasing size of the rebounding particle.
The second factor affects the number of collisions and,
hence, the rate of charge (and field) buildup. When in-
tense precipitation occurs (rates ~ 30 mm/in) the field
can develop to large values with the inductive process
only. However, for smaller precipitation rates (smaller
particles and lower concentrations) it takes longer than
the times set by the criteria above for the field to
buildup.
OCR for page 138
138
One-Dimensional Models
Illingworth and Latham (1975) correctly pointed out
that horizontally infinite parallel-plate models overesti-
mate the electric-field development because they lack a
finite horizontal extent for the cloud. They constructed
a simple one-dimensional model in which precipitation
ice particles descended from the cloud top downward
and interacted with smaller ice crystals (Illingworth and
Latham, 1977~. During these interactions, charge was
separated by either inductive or noninductive processes.
The linear dependence of the charge separation in the
noninductive process [Eq. (10.3~], and its independence
of the ambient field, caused the field to grow early in a
linear fashion (see Figure 10.3~. The inductive process,
on the other hand, started later since it relies on the mag-
nitude of the ambient field. Superposition of the two
processes led to both a rapid linear field development in
the early stages as a result of the noninductive process
and a subsequent enhancement of the field owing to the
inductive process. One of the important results of this
300
I00
30
10
1 1 1/ 1 / _
//
0 400 800 1200 1600 2000
t (s)
FIGURE 10.3 The variation of the maximum field Em with time for
the ice-ice noninductive charging mechanism (curve 1), the ice-ice in-
ductive charging mechanism (curve 3), and the combined ice-ice
mechanisms (curve 2). From Illingworth and Latham (1977~.
ZEV LEVIN and ISRAEL TZUR
simple model is its ability to predict the vertical dipole in
the cloud and even the small positive pocket at cloud
base.
Tzur and Levin (1981) developed a much more de-
tailed model that included a macroscale dynamical
framework in one-and-a-half dimensions (height as an
independent variable and a finite cloud radius with lat-
eral mixing) and fully interactive microphysics of the
precipitation development. Electrically the model
treated in great detail free ions and their attachment to
cloud particles and inductive and some noninductive
processes with both ice and water, all in a time-depen-
dent frame. From the results of the model Tzur and
Levin concluded that charge separation in the liquid
section of the cloud is not likely to be effective since the
efficiency of bouncing and charge separation by water-
water interaction is probably low. Similarly, collisions
between ice particles and ice pellets in the absence of
water droplets, either by the inductive or thermoelectric
effects, namely, near the cloud top (temperatures
~ - 25°C), are not likely to contribute greatly to cloud
electrification either tsee Figures 10.4(a) and 10.4(b)~.
This is because of the small value of tilt at these temper-
atures (Iow surface and bulk electrical conductivities in
ice) . Also, at these altitudes the number of ice particles is
relatively low, reducing the collision frequency and the
charge separation.
At higher temperatures (about -10°C or warmer)
ice particles interact with both ice crystals and water
droplets. From the model results, Tzur and Levin con-
cluded that the collisions of the ice crystals with water
drops, by a mechanism such as the Workman-Reynolds
effect, are very effective charge separators isee Figure
10.4(c)] owing to the large concentration of water drop-
lets as compared with that of ice.
Comparison of Figures 10.4(a) and 10.4(c) shows that
the charging rate by the inductive process changes rap-
idly with time once charging starts. On the other hand,
the charging rate by the noninductive mechanism is al-
most constant with time, in agreement with the recent
measurements by Krider and Musser (1982~. These mea-
surements show that the total currents (Maxwell cur-
rents) below electrified clouds remained fairly constant
with time while at the same time the electric field in the
cloud increased by a few orders of magnitude.
Testing the inductive process revealed that very high
fields and large charges can be produced only after 3000
see from cloud initiation isee Figure 10.5(a)] or about 20
min after precipitation particles appeared in reasonable
concentration for radar detection. As in the case of the
simpler model of Illingworth and Latham (1977), the
noninductive process produced linear field develop-
ment. However, as opposed to Illingworth and Latham
OCR for page 139
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS
11
1O
91
8 _
7 --3o
I 6 ~
I 5 _-20
-lo
O _
4
3
2 _
11:
10~
9L
TIC 7
_ ~
I 6
5
8
4
3
2
11
1O
9
8
_. 7
I
6
5
4
3
, . . . ,
_ INDUCTIVE CHARGING (a) _
DROPS - ICE
_ 6XIo-llXlo-a(cm-35
T°C
it_
o
l - ~1 1 1 1 1 1 -
I I I ~I I
TllERMOELECTRIC EFFECT ~ b ~ _
2.5 x 10-~3 x 1O-a ~ C m~3 5-1,
-30
-20
-10
n
~~
_ WORKMAN-REYNOLDS EFFECT ( C)
7 x 10- 1 1 x 1O-a (C m~3 ~ I
T.C
--3o _
_-20 ~ ~x
_
-10 _
O _
2 _ - _
1- , 1 , 1 , I , -
1000 2000 3000
TIME ( s)
139
(1977), who assumed that only ice-ice collisions separate
charge, Tzur ant] Levin (1981) assumed that charge sep-
aration by ice-ice collision is temperature dependent,
and hence less effective than interactions of ice and wa-
ter, which occur at warmer temperatures. Although the
noninductive mechanism that they considered is the
Workman-Reynolds process, any electrochemical pro-
cess in which charge is separated by interaction of ice
pellets and water droplets during riming is applicable to
these calculations.
Ions contributed only slightly to charge buildup, ei-
ther by diffusion to charged particles or by conduction.
Their contribution can be pronounced, on the other
hand, in the early stages of the cloud buildup, when
droplets are very small, and during rain below the cloud
base. This latter charging of raindrops becomes signifi-
cant when the field near the ground passes the threshold
for corona discharge. During this stage the charge of
raindrops can be greatly modified by attaching of oppo-
sitely charged ions to them.
A closer look at the charge structure produced by the
noninductive process iFigure 10.5(a)] reveals that a
"classical" dipole develops with a negative charge center
at about - 8°C and with the main positive charge cen-
ter at higher altitudes (about -18°C) (see Figure 10.5
at t = 2400 see). Large fields are already formed by
2500 see after cloud initiation (about 10 min after pre-
cipitation particles appear), and with precipitation
rates less than 20 mm/in. A positive charge pocket de-
velops near the cloud base at temperatures warmer than
O°C.
On the other hand, the inductive process alone delays
the field buildup for about 3000 sec. It produces the neg-
ative charge center between about - 10 and - 20°C
and the positive charge center still higher up at tempera-
tures lower than - 20°C isee Figure 10.5(b)~. A positive
pocket extending from the - 5°C isotherm to the cloud
base is also found. This means that the noninductive
mechanism produces space-charge centers at slightly
lower altitudes, at earlier times, and with lower precipi-
tation rates than does the inductive process.
FIGURE 10.4 (a) The charging rate in coulombs per cubic meter per
second by the ice-water inductive process as a function of height and
times from Tzur and Levin (1981~. The value of each contour is 6 X
10- ~ x 10-~ with ax displayed near each one. Note that the charging
rate rapidly varies with time and reaches a maximum value at about
3000 sec. (b) The charging rate by the ice-ice thermoelectric (nonin-
ductive) effect. Note that the values of the contour are two orders of
magnitude smaller than in (a). (c) The charging rate by the ice-water
(noninductive) Workman-Reynolds effect. Note that the values of the
contours are similar to those of (a). Also note that charging starts early
and tends to remain fairly constant with time for most of the lifetime of
electrical production.
OCR for page 140
40
10
1 1 1 1
DROP AND ICE CHARGE (a)_
+ 4 x 10-9 x 1O-a ( C / ma )
NONINDUCTIVE PROCESSES _
8 t T C 2.5_ ¢
E ~ ~o ~
'°r
9L
8
7
Y 6
I 5
llJ
3
1 1 1 1 1 1
DROPS AND ICE CHARGE (b)
+ 6 x 10 9 x 10 a ( C / ma )
INDUCTIVE PROCESS
3.5 ( All,
(` "
~7
1000 2000 3000 4000
TIME (s)
FIGURE 10.5 (a) The net charges in coulombs per cubic meter on
cloud and precipitation particles (ice and water) resulting from the ice-
water noninductive process, as a function of height and time, from
Tzur and Levin (1981~. Solid lines represent net positive charges, and
dashed lines represent net negative charges. The value of each contour
is given by + 4 X 10 ~ 9 X 10 ~ ~ with ax displayed next to each one. Note
that the maximum charges are produced around t = 2500 see with
negative charge near - 10°C and positive charge around - 25°C. An-
other small positive charge appears just below the 0°C level. (b) As in
(a) except for the inductive (ice-water) process. Note the delay in the
development of the space charges as compared with (a).
A combination of the two processes produced strong
field and space-charge distributions, which are almost a
linear superposition of the two individual cases. Specifi-
cally, a strong field develops early (t ~ 2500 see) but is
enhanced later (t ~ 3000 see). Since the inductive pro-
cess begins to operate when the field is stronger, a new
space-charge center (negative charge) is produced at the
ZEV LEVIN and ISRAEL TZUR
cloud top. This charge center, as with all other charge
centers, then descends as precipitation falls. At a partic-
ular height it seems as if the charges switch signs with
time. This implies that at this stage the inductive process
is so effective that charged particles falling below a cer-
tain space-charge volume are rapidly charged oppo-
sitely owing to the reversal of the field direction below
the charge center. Had the effectiveness of the inductive
process been reduced, the charge centers might have
spread out over a greater cloud depth and would have
prevented the field reversal.
One of the limitations, of course, of the one-dimen-
sional, time-dependent models is their poor simulation
of the air circulation within the cloud and the entrain-
ment of air from the environment on the sides and top.
Since in this model any mixing in of drier air, or detrain-
ment of cloudy air, is immediately averaged over the
entire layer of the cloud, it actually affects the whole
cloud development in the model, as compared with na-
ture, where relatively smaller effects are produced by
mixing at cloud edges only. For a better simulation of
these effects, two- or three-dimensional models are
needed.
Two-Dimensional Models
Two-dimensional models have been developed to im-
prove the simulation of the macroscale dynamics and its
effect on the charge distribution and electrical develop-
ment.
Chin (1978) simulated a vortex-type thunderstorm in
a two-dimensional, time-dependent axisymmetric mod-
el. In his model, only water drops were considered,
and charge was allowed to develop via the inductive
process and ion attachment. Cloud microphysics was
not dealt with in detail, and cloud water was converted
to precipitation particles, of a preassigned distribution,
by a parameterized formulation. In each time step in the
model, the number of possible particle interactions was
calculated based on known collision efficiencies. From
it a net charge separation was derived. Simultaneously,
ion attachment by diffusion and conduction was per-
mitted to take place, and the total net charge at each At
was found. Chiu's results also indicate that the inductive
process could be a very effective charge separation
mechanism, provided that large precipitation rates are
present. The results also indicate the development of a
vertical dipole of a proper "classical" polarity with an
additional small positive space charge near the cloud
base. As in the one-and-a-half-dimensional model of
Tzur and Levin (1981) large charges and strong fields
developed only after rain formed. The evolution of the
horizontal electric field, with a maximum at 30 min. is
OCR for page 141
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS
RADIAL ELECTRIC FIELD ( V m~l)
' 1 ' I I l l l l l
7_2 ~ (a) 14min. _ ~ (b) 18 min. ~ ~ (c) 22 min.
6.4 _
5.6
4.8 _
E 4.0
FIGURE 10.6 Evaluation of the radial elec- A
trio field, from Chiu (1978). (a) At 14 min. 3.2
Contour interval is 2 V/m, and the range is
- 14 to 0 V/m. (b) At 18 min. Contour inter- 2.4
vat is 10 V/m, and the range is - 70 to 30 V/
m. (c) At 22 min. Contour interval is 200 V/ I.6
m, and the range is - 1000 to 200 V/m. (d) At
26 min. Contour interval is 103 V/m, and the ° ~
range is ( - 4 - 2) X 103 V/m. (e) At 30 min. O
Contour interval 2 X 103 V/m, and the range
is -6to6 x 103V/m.
shown in Figure 10.6. The effect of ions, either by diffu-
sion in the early stages or by conduction at the later
stages, was found to be relatively small and did not sig-
nificantly alter the charging of the cloud. The entrain-
ment of ions from cloud sides and tops did not greatly
modify the electrical development.
Heldson (1980) used the same model for a two-dimen-
sional slab cloud and simulated the effect of artificial
chaff seeding for the prevention of lightning. The intro-
duction of chaff into the cloud creates centers for ion
production by corona discharge as the electric-field
strength approaches that needed for lightning. The
results of the model suggest that the presence of excessive
ions at this stage increases the cloud electrical conduc-
tivity and enhances the discharge of the cloud particles.
This in turn prevents the further buildup of the electric
field and charges. The results of this model demonstrate
one practical use for modeling of electrical processes in
thunderclouds.
Thunderstorms usually contain both water and ice.
The models of both Chin and Heldson are therefore lim-
ited since no ice formation was simulated even though
the clouds in their models reached heights where ice is
usually found.
Kuettner et al. (1981) developed another two-dimen-
sional model. Their model superposes a kinematic flow
model, including cloud particle growth, on an electrical
charge separation model. The cloud model uses either
vortex or shear flow to simulate a steady-state flow con-
figuration. Precipitation ice particles were introduced
about 1 km above the cloud base and allowed to be
moved with the airflow. During their ascent and de-
scent they grew by collecting cloud droplets and sepa-
rated charge through rebounding collisions of either wa
, ~
0 0.8 1.6 2.4 0 0.8 1.6 2`
141
M ...
~F JO
0 0.8 t.6 2.4 0 0.8 1.6 2.4 0 0.8 1.6 2.4
r (km)
1 1 1 ~
g,0 min.~
it_
1~~o~
411~\ \ \
1' 1 \
41 ~1_
- ~ 400 / ~
_ ~_
'0%, 1, I,
ter droplets or small ice crystals. The model did not
consider ion attachment or particle growth by conden-
sation. Particle growth by collection was calculated
with a constant probability of charge separation. The
model also did not address the problem of entrainment
or turbulent diffusion. However, the merit of this model
is its relative simplicity and the capability of testing the
electrical development under different airflow condi-
tions such as those observed in the field. The results of
this model point out that the noninductive process, in-
corporating ice-water and to some extent ice-ice interac-
tions with an average value of observed charge separa-
tion per collision, can produce an electrical dipole at
realistic altitudes but cannot enhance the field to a value
comparable with the breakdown value.
On the other hand, the inductive process, involving
charge separation by ice-water interactions, produced
very high fields but generated a very complex space-
charge configuration. The complex field and space-
charge structure arises as a consequence of the high effi-
ciency with which the inductive process operates when
large precipitation particles appear. As these large par-
ticles descend through a space-charge center and be-
come exposed to an electric field of opposite direction,
their charge polarity reverses in response to the reversal
of the electric field.
Combination of the inductive with the noninductive
mechanisms produced both a proper charge distribution
and a rapid growth of the field. The results of Kuettner
et al. (1981) suggest that charge separation processes in-
volving ice-ice collisions are not very powerful, being
limited by both the long relaxation time of the charge
carriers and by the relatively low concentration of ice
crystals (resulting in low collision rates). In addition, in
OCR for page 142
142
agreement with the other two-dimensional models, this
model demonstrates that both strong horizontal and
vertical fields can be produced by charge separation
mechanisms that depend on precipitation. The horizon-
tal fields are generated by horizontal displacement of
the charged particles by the air circulation. Even under
very weak shear conditions the space-charge centers
were found to be displaced horizontally and produce
very strong horizontal fields even close to the cloud base.
The presence of the shear was found to smooth the de-
velopment of the charge centers by limiting mixing of
precipitation particles of opposite charges.
Takahashi (1979) developed a two-dimensional,
time-dependent mode! of a small warm cloud, which
treats the microphysics and the macroscale dynamics in
detail. Electrification due to the inductive mechanism
and to ion attachment by diffusion and conduction is
considered in a way that seems to explain the weak elec-
trification of warm maritime clouds. The most impor-
tant mechanism responsible for charging in such clouds,
according to this model, is the attachment of ions to
cloud and precipitation drops. This attachment is signif-
icantly enhanced during condensation and evaporation.
During the former, positive ions are preferentially in-
corporated into the growing drops, whereas during
evaporation negative ions are preferentially attached.
In an attempt to evaluate the effectiveness of the con-
vection electrification process, Ruhnke (1972) and Chiu
and Klett (1976) developed two-dimensional, axisym-
metric steady-state models. Ruhnke calculated the elec-
tric fields and charges that arise from ion attachment to
cloud water in solenoidal flow, intended to represent
the flow in an isolated convective cloud. The actual
cloud volume (where liquid water exists) was assumed
to be spherical and to be entirely within the updraft.
Space charge arises owing to local differences in electri-
cal conductivity. These differences stem from attach-
ment of ions to cloud particles (assumed to depend only
on liquid-water content), which form ion currents con-
sisting of both conduction and convection currents. By
assigning a specific liquid-water content and a relation
between it and ion conductivity, Ruhnke avoided deal-
ing with interactions between ions and cloud droplets.
The steady-state assumption precludes any detail of the
initial development of the convective electrification.
His results show that only very small fields can be devel-
oped by this process.
Chiu and Klett (1976) improved on this model by us-
ing a more realistic convective circulation in which the
updraft was within the cloud and the downdraft was at
its edges. They also considered the effect of turbulent
diffusion in addition to conduction and convection cur-
rents on the transport of ions. Attachment of ions to
ZEV LEVIN and ISRAEL TZUR
cloud drops was affected by the liquid-water content
and by the ambient electric field. Chiu and Klett's
results show that convective electrification by itself can-
not explain the strong electrification in thunderclouds.
One should bear in mind that the terms that are highly
variable with time such as the rate of charge buildup,
especially at the later stages of thunderstorm develop-
ment, are ignored in these steady-state models. In a fully
developed time-dependent model, such terms may mod-
ify the above conclusions. In addition, the dynamics
used in the convective models is parameterized and may
not be realistic enough to simulate the real convective
charging process that is highly dependent on cloud dy-
nam~cs.
Three-Dimensional Models
To date, only one three-dimensional, time-dependent
model of an electrical cloud has been developed
(Rawlins, 1982~. This model uses pressure as the vertical
coordinate with grid spacings of 50 mbar vertically and
1 km horizontally. The microphysical parameterization
of Kessler (1969) is used to describe the growth of cloud
particles into precipitation size. Ice, initiated by ice nu-
clei that freeze the supercooled water drops, is repre-
sented by three size classes: 0-100,um, 100-200,um, and
200-300 ,um in radius. Hail is designated as ice greater
than 300,um in radius, and it is forced to be distributed
exponentially in size (Marshall and Palmer, 1948~.
With this model Rawlins tested the effectiveness of
various electrical processes, such as the inductive and
the contact surface potential (noninductive) mecha-
nisms. He assumed that ion attachment to cloud parti-
cles can be ignored altogether. He concluded that the
noninductive process is able to produce fields of high
enough intensity to initiate lightning within about 20
min after precipitation begins. This process produced a
"classical" dipole tsee Figure 10.7(a)] but without the
small positive charge center closer to the cloud base.
The inductive process, involving ice-ice collisions,
was capable of producing strong fields only in the pres-
ence of high concentrations of ice particles and only 30
min after precipitation particles appeared. With this
process, a very complex space-charge structure emerged
isee Figure 10.7(b)] as was also found by Kuettner et al.
(1981~. Allowing ice crystals to rebound more than once
from ice pellets reduced the calculated maximum field
to below that needed for lightning "compare the values
of E- in Figures 10.7(a) and 10.7(b)~.
However, one should note that the same restriction of
multiple collisions was not applied to Rawlins's calcula-
tions of the noninductive process. Multiple collisions, if
OCR for page 143
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS
400
600
700
A, 500
LL
cr
~ 600
An
I3J
700
(a)
E SOD
-50 0 50 -50 0
50 100 -200 0 200
Qp(C)Qc(C) Ez(kV m~l )
(b
400 _ I \T I I _ ~
-10 0 10-10 0 10 20 -50 0 50
Qp(C)Qc (C) Ez(kV m~')
1
FIGURE 10.7 The vertical distribution of space charges on precipi-
tation, Qy, and cloud, Qc, particles and the vertical electric field, from
Rawlins (1982~. (a) Ice-ice noninductive charging mechanisms after 36
min of cloud growth with charge separation per collision of Q = 10 fC.
(b) Ice-ice inductive process after 44 min of cloud growth. Note the
simple dipole structure and the intense field in (a) as compared with
the more complex structure and weaker field in (b), implying the inef-
fectiveness of the inductive process under the assumptions of this
model.
allowed for, will restrict charge transfer during particle
collisions regardless of the process considered.
DISCUSSION
From this survey, it is clear that present models can
describe both the electrical development and the growth
of precipitation in some detail. An interesting common
conclusion of all the models is the insensitivity of the
results to small changes in free ion concentration or con-
ductivity. These parameters do become important dur-
ing the early stages of cloud development and below the
cloud base during rain. They are probably also impor-
tant just at the onset of lightning or immediately after
143
ward, but none of the models described here has dealt
with this complex problem.
The emergence of the more complex models of two or
three dimensions provides a clear visualization of the
ability of the precipitation charging mechanisms to pro-
duce strong horizontal displacement of charges. These
are often found in clouds and frequently lead to horizon-
tal lightning strokes. It was shown that such numerical
models could also be used to test the feasibility of pre-
venting lightning by limiting the electric field growth.
Multidimensional models can also greatly aid interpre-
tation of the results of field experiments such as chaff
dispersal in real clouds because they incorporate more
realistic air circulations than do one-dimensional
models.
One of the main purposes of all the models discussed
here is to test the various proposed mechanisms of
charge separation in clouds. It seems that now that the
models are capable of simulating the main features of
the electrical charge separation in the cloud in a frame-
work that combines air circulation and precipitation
growth, however, reliable values for some of the various
parameters are desperately needed. In particular, the
electrical contact probabilities of the various particles
(primarily ice with water and ice with ice), the coales-
cence probabilities, the relaxation time of the charge
carriers on ice as a function of temperature, and the
length of time the particles actually make contact before
rebounding are all essential, and not yet known, for
evaluating the effectiveness of the various mechanisms.
Such parameters can only be obtained by careful labo-
ratory experiments.
Despite the uncertainties in the values of the main pa-
rameters involved in the precipitation processes of cloud
electrification, it is still impressive to see that virtually
all of the models appearing within the past 10 years,
regardless of their complexity, agree that precipitation
mechanisms can explain the main features observed in
thunderclouds. They explain the presence of the space-
charge centers at the proper altitudes and temperatures.
They show that strong fields can be developed within 20
to 30 min of the appearance of precipitation in the
cloud. Some show that noninductive charge separation
processes teither ice-ice (Rawlins, 1982) or ice-water
(Tzur and Levin, 1981~] can produce very strong fields
with low precipitation rates as is sometimes observed in
nature (Gaskell et al., 1978~. In addition results with
noninductive processes show that the electric field
grows linearly with time, as observed by Winn and
Byerly (1975~. These results also agree with the recent
measurements of Krider and Musser (1982), which sug-
gest that the charging rates in thunderclouds are inde-
pendent of the field and fairly constant with time iFig
OCR for page 144
144
ure 10.4(c)~. However, the observations of Williams and
Lhermitte (1983) pointed out that the Musser and Kri-
der results can also be explained by the convective
charge transport. Their observations showed that fall-
ing precipitation may not be the only cause for the elec-
trification of thunderstorms. All the models agree that
the inductive process requires higher precipitation rates
in order to operate effectively. Some models show that
the most effective method to produce strong fields is to
let both inductive and noninductive mechanisms oper-
ate simultaneously. While noninductive mechanisms
can be powerful, particularly early in the development
of the electric field, it is difficult to see how one can
ignore the inductive process altogether. This process
should operate in general whenever an ambient electric
field is present. In some cases, it may discharge the par-
ticles, while in others it will charge them, but it should
always operate. If, on the other hand, its effectiveness is
very low, as reported by Illingworth and Caranti
(1984), it will not be felt in the cloud. Thus if a charge
greater than that predicted by Eq. (10.1) is found on
some of the particles (Christian et al., 1980), the induc-
tive process should have discharged them. Since such
charges were observed, it must be concluded that in
these cases the inductive process did not effectively oper-
ate.
Most investigators seem to feel that charge separation
through interactions among water drops only is not ef-
fective since most collisions result in coalescence, thus
limiting the possibilities for charge separation. Never-
theless, laboratory experiments (Levin and Machnes,
1977; Beard et al., 1979) suggest that the coalescence
efficiency is far from being understood, so the role of
water-drop interactions should not yet be ignored com-
pletely.
Laboratory measurements of the surface potentials of
ice under various growth conditions (Buser and Aufder-
maur, 1977; Caranti and Illingworth, 1980) reveal the
complexity of the charge-transfer problem. Again, ad-
ditional experiments are needed to resolve the depen-
dence of charge separation by this process on tempera-
ture and on the strength of an external electric field.
In spite of the fact that the numerical models thus far
rule out convective electrification as an effective mecha-
nism for producing strong fields by itself, it must be em-
phasized that these models are only quasi-static and con-
tain parameterized dynamics. To simulate this
mechanism effectively, more detailed cloud dynamics,
ion convection and conduction, and precipitation pro-
cesses must be included. Thus far, no such model has
been developed. Such a detailed model is urgently
needed, especially following the recent experiments by
Vonnegut et al. (1984) that reversed the polarity of a
ZEV LEVIN and ISRAEL TZUR
thundercloud by emitting negative ions from a long ca-
ble electrified to 100 kV and suspended below the cloud.
Their observations suggest that the negative ions pene-
trated the cloud, ascended to the cloud top, and at-
tracted positive ions from the free atmosphere above
and were carried down by the air currents to the cloud
base thus reversing the previous polarity of the cloud.
If the ion concentration was too small to produce this
effect, it is still possible that the additional ions changed
the initial conditions of the cloud electrification, which
led to the reversal in the cloud polarity.
With the newly available data and faster computers
we can look forward to a new generation of models in-
corporating cloud microphysics and dynamics together
with the convection and precipitation electrification
mechanisms.
REFERENCES
Al-Saed, S. M., and C. P. R. Saunders (1976~. Electric charge transfer
between colliding water drops, J. Geophys. Res. 81, 2650-2654.
Aufdermaur, A. N., and D. A. Johnson (1972~. Charge separation due
to riming in an electric field, Q. J. R. Meteorol. Soc. 98, 369-382.
Beard, K. V., H. T. Ochs III, and T. S. Tung (1979~. A measurement
of the efficiency for collection between cloud drops, J. Atmos. Sci.
36, 2479-2483.
Brown, K. A., P. R. Krehbiel, C. B. Moore, and G. N. Sargent (1971~.
Electrical screening layers around charged clouds, J. Geophys. Res.
76, 2825-2835.
Buser, O., and A. N. Aufdermaur (1977~. Electrification by collisions
of ice particles on ice or metal targets, in Electrical Processes in At-
mospheres, N. Dolezalek and R. Reiter, eds., Steinkopff, Darm-
stadt, p. 294.
Caranti, J. M., and A. J. Illingworth (1980~. Surface potentials of ice
and thunderstorm charge separation, Nature 284, 44-46.
Caranti, J. M., and A. J. Illingworth (1983~. Frequency dependence of
the surface conductivity of ice, J. Phys. Chem. 87,4078-4083.
Censor, D., and Z. Levin (1974). Electrostatic interaction of axisym-
metric liquid and solid aerosols, Atmos. Environ. 8, 905-914.
Chiu, C. S. (1978~. Numerical study of cloud electrification in an axi-
symmetric liquid and solid aerosols, J. Geophys. Res. 83, 5025-
5049.
Chiu, C. S., and J. N. Klett (1976~. Convective electrification of
clouds,J. Geophys. Res. 81, 1111-1124.
Christian, H., C. R. Holmes, J. W. Bullock, W. Gaskell, J. I1-
lingworth, and J. Latham (1980~. Airborne and ground-based stud-
ies of thunderstorms in the vicinity of Langmuir Laboratory, Q. J.
R. Meteorol. Soc. 106,159-174.
Col~ate, S. A., Z. Levin, and A. G. Petschek (1977~. Interpretation of
thunderstorm charging by polarization induction mechanisms, J.
Atmos. Sci. 34,1433-1443.
Davis, M. H., and J. D. Sartor (1967~. Theoretical collision efficiencies
for small cloud droplets in Stokes flow, Nature 215, 1371-1372.
Gaskell, W., A. J. Illingworth, J. Latham, and C. B. Moore (1978).
Airborne studies of electric fields and the charge and size of precipi-
tation elements in thunderstorms, Q. J. R. Meteorol. Soc. 104, 447
- - 460.
Grenet, G. (1947~. Essai d'explication de la charge electrique des
nuages d'orages, Ann. Geo phys. 3, 306-310.
OCR for page 145
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS
Griffithes, R. F., J. Latham, and V. Myers (1974~. The ionic conduc-
tivity of electrified clouds, Q. J. R. Meteorol. Soc. 100, 181-190.
Gross, G. W. (1982~. Role of relaxation and contact times in charge
separation during collision of precipitation particles with ice tar-
gets, J. Geophys. Res. 87, 7170-7178.
Heldson, J. H., Jr. (1980~. Chaff seeding effects in a dynamical-electri-
cal cloud model, J. Appl. Meteorol. 19, 1101-1183.
Illingworth, A. J., and C. M. Caranti (1984~. Ice conductivity re-
straints on the inductive theory of thunderstorm electrification, in
Conference Proceedings, VII International Conference on Atmo-
spheric Electricity, American Meteorological Society, Boston,
Mass., pp. 196-201.
Illingworth, A. J. and J. Latham (1975). Calculations of electric field
growth within a cloud of finite dimensions, J. Atmos. Sci. 32, 2206-
2209.
Illingworth, A. J., and J. Latham (1977~. Calculations of electric field
growth, field structure and charge distributions in thunderstorms,
Q. J. R. Meteorol. Soc. 103, 231-295.
Kessler, E. (1969~. On the Distribution and Continuity of Water Sub-
stance in Atmospheric Circulation, Meteorol. Monogr. Vol. 10, No.
32, American Meteorological Soc., Boston, Mass., 84 pp.
Klett, J. D. (1972~. Charge screening layers around electrified clouds,
J. Geophys. Res. 77, 3187-3195.
Krehbiel, P. R., M. Brook, and R. A. McCrory (1979~. An analysis of
the charge structure of lightning discharges to ground, J. Geophys.
Res. 84, 2432-2456.
Krider, E. P., and J. A. Musser (1982~. Maxwell currents under thun-
derstorms,J. Geophys. Res. 87,11171-11176.
Kuettner, J., Z. Levin, and J. D. Sartor (1981~. Inductive or noninduc-
tive thunderstorms electrification, J. Atmos. Sci. 38, 2470-2484.
Lane-Smith, D. R. (1971~. A warm thunderstorm, Q. J. R. Meteorol.
Soc. 97, 577-578.
Latham, J. (1981~. The electrification of thunderstorms, Q. J. R. Me-
teorol. Soc. 107, 277-298.
Latham, J., and B. J. Mason (1961). Generation of electric charge
associated with the formation of soft hail in thunderclouds, Proc. R.
Soc. London A260, 537-549.
Latham, J., and R. Warwicker (1980~. Charge transfer accompanying
the splashing of supercooled raindrops on hailstones, Q. J. R. Me-
teorol. Soc. 106, 559-568.
Levin, Z., and B. Machnes (1977~. Experimental evaluation of the
coalescence efficiencies of colliding water drops, Pure Appl.
Geophys. 115, 845-867.
Marshall, J. S., and W. M. K. Palmer (1948~. The distribution of rain-
drops with size, J. Meteorol. 5, 165-166.
Martell, E. A. (1984~. Ion pair production in convective storms by
radon and its radioactive decay products, in Conference Proceed-
ings, VII International Conference on Atmospheric Electricity,
American Meteorological Society, Boston, Mass., pp. 67-71.
Mason, B. J. (1971~. The Physics of Clouds, Oxford Univ. Press, Cam-
bridge, 671 pp.
Mason, B. J. (1972~. The physics of thunderstorms, Proc. R. Soc. Lon-
don A327, 433-466.
Phillips, B. B. (1967~. Ionic equilibrium and the electrical conductiv-
ity in thunderclouds, Mon. Weather Rev. 95, 854-862.
Pruppacher, H. R., and J. D. Klett (1978~. Microphysics of Clouds and
Precipitation, Reidel, Dordrecht, 714 pp.
]45
Pruppacher, H. R., E. H. Steinberger, and T. L. Want (1968). On the
electrical effects that accompany the spontaneous growth of ice in
supercooled aqueous solutions, J. Geophys. Res. 73, 571-584.
Rawlins, F. (1982). A numerical study of thunderstorm electrification
using a three dimensional model incorporating the ice phase, Q. J.
R. Meteorol. Soc. 108, 778-880.
Reynolds, S. E., M. Brook, and M. F. Gourley (1957~. Thunderstorm
charge separation, J. Meteorol. 14, 426-436.
Ruhnke, L. H. (1972~. Atmospheric electron cloud modeling, Me-
teorol. Res. 25, 38-41.
Sartor, J. D. (1967). The role of particle interactions in the distribution
of electricity in thunderstorms, J. Atmos. Sci. 24, 601-615.
Sartor, J. D. (1970~. General Thunderstorm Electrification, National
Center for Atmospheric Research, Boulder, Colo., p. 99.
Schewchuk, S. R., and J. V. Iribarne (1971~. Charge separation dur-
ing splashing of large drops on ice, Q. J. R. Meteorol. Soc. 97, 272-
282.
Scott, W. D., and Z. Levin (1975~. Stochastic electrical model of an
infinite cloud charge generation and precipitation development, J.
Atmos. Sci. 32,1814-1828.
Takahashi, T. (1978). Riming electrification as a charge generation
mechanism in thunderstorms, J. Atmos. Sci. 35, 1536-1548.
Takahashi, T. (1979~. Warm cloud electricity in a shallow axisymmet-
ric cloud model, J. Atmos. Sci. 31, 2236-2258.
Tzur, I., and Z. Levin (1981). Ions and precipitation charging in
warm and cold clouds as simulated in one dimensional time-depen-
dent models, J. Atmos. Sci. 38, 2444-2461.
Vonnegut, B. (1955~. Possible mechanism for the formation of thun-
derstorms electricity, in Proceedings International Conference At-
mospheric Electricity, Geophys. Res. Paper No. 42, Air Force Cam-
bridge Research Center, Bedford, Mass., p. 169.
Vonnegut, B., C. B. Moore, T. Rolan, J. Cobb, D. N. Holden, S.
McWilliams, and G. Cadwell (1984~. Inverted electrification in
thunderclouds growing over a source of negative charge, EOS 65,
839.
Wahlin, L. (1977~. Electrochemical charge separation in clouds, in
Electrical Processes in Atmospheres, H. Dolezalek, and R. Reiter,
eds., Steinkopff, Darmstadt, p. 384.
Weickmann, H. K., and J. J. Aufm Kampe (19SOj. Preliminary exper-
imental results concerning charge generation in thunderstorms con-
current with the formation of hailstones, J. Meteorol. 7, 404-405.
Whelpdale, D. M., and R. List (1971). The coalescence process in rain
drop growth, J. Geophys. Res. 76, 2836-2856.
Williams, E. R., and R. M. Lhermitte (1983). Radar tests of the pre-
cipitation hypothesis for thunderstorm electrification, J. Geophys.
Res. 88, 10984-10992.
Wilson, C. T. R. (1929~. Some thundercloud problems, J. Franklin
Inst. 208, 1-12.
Winn, W. P., and L. G. Byerly III (1975~. Electric field growth in
thunderclouds, Q. J. R. Meteorol. Soc. 101, 979-994.
Workman, E. J., and S. E. Reynolds (1948). Suggested mechanism for
the generation of thunderstorm electricity, Phys. Rev. 74, 709.
Wormell, T. W. (1953~. Atmospheric Electricity: Some recent trends
and problems, Q. J. R. Meteorol. Soc. 79, 3.
Ziv, A., and Z. Levin (1974~. Thundercloud electrification cloud
growth and electrical development, J. Atmos. Sci. 31, 1652-1661.
OCR for page 146
OCR for page 147
III
GLOBAL AND REGIONAL
ELECTRICAL PROCESSES
OCR for page 148
Representative terms from entire chapter:
inductive process
