Met Office College - Course Notes
Basic Cloud Physics
Contents
1. Introduction
2. Atmospheric aerosol
2.1 Aerosol sizes
2.2 Aerosol properties and condensation
2.3 Aerosol sources
2.4 Aerosol and visibility
3. Condensation and the growth of cloud droplets
3.1 Curvature effects
3.2 The Kelvin effect
3.3 The solute effect
3.4 The Köhler curve
4. The formation of precipitation
4.1 Water clouds
4.2 Growth by condensation
4.2.1 Growth by coalescence
4.3 Ice and mixed phase clouds
4.3.1 Growth by deposition
4.3.2 Growth by accretion (riming)
4.3.3 Growth by aggregation
4.4 Summary of precipitation formation
5. Artificial cloud modification
6. References
 Crown Copyright. Permission to quote from this document must be obtained from The
Principal, Met Office College
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1. Introduction
To a synoptic meteorologist such as a forecaster on the bench, the
smallest atmospheric features of interest are probably individual
convective clouds with horizontal scales of tens or hundreds of metres.
However, there are many processes which take place within such clouds
which occur on much smaller scales than this. These small scale
processes contribute to the form that a cloud will take and, of particular
interest to the forecaster, they also determine whether the cloud will
produce any precipitation.
It is the study of these processes which forms the specialised branch of
meteorology known as cloud physics. The scales of such processes are
often of the order of microns (10-6m) and so are frequently referred to as
microphysical processes. Although the forecaster does not need a detailed
knowledge of this subject, a basic understanding of the processes which
lead to the formation of clouds and precipitation, combined with a
knowledge of the larger scale physical and dynamical processes in the
atmosphere, should lead to improved forecasts.
A good understanding of cloud physics is also required for the
development of NWP models. The current representation of
microphysical processes in most NWP models is rather crude or nonexistent, but it is thought that more sophisticated parametrizations
should lead to better precipitation forecasts by models. A lot of research
effort and money is therefore invested in studying this subject both in
the laboratory and using data from aircraft flying through clouds
carrying highly sophisticated measuring equipment.
The aim of this note is to give a basic introduction to cloud physics,
outlining the processes important in the formation of clouds and
precipitation, and how conditions in the larger scale environment affect
these processes.
2. Atmospheric aerosol
The basic ingredient required to form clouds and precipitation is water
vapour in the atmosphere. However, although water vapour will
readily condense onto the surface of the earth when the air becomes
saturated (forming dew), in the free atmosphere away from the surface,
the air can become highly supersaturated but the vapour will not
condense unless it has a surface onto which it can do so. In fact, relative
humidities of about 800% are required for water vapour to
spontaneously condense and form droplets without a surface to form
on. Since we rarely observe supersaturations of more than 1% in the
atmosphere (i.e. a relative humidity of 101%), yet frequently observe
clouds and rain, there must be something present in the atmosphere
onto which the vapour can condense. In fact the air is full of microscopic
particles which provide the very surfaces required for condensation.
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These particles are known as atmospheric aerosol and are composed of
tiny solid or liquid particles which have a small fall speed in air and
therefore appear to be suspended in the atmosphere on short timescales.
The sources of these aerosols, and their concentrations within the
atmosphere vary widely in time and location, but without their presence
in the atmosphere, clouds would never form. The size and chemical
constitution of these aerosols determines how readily water vapour will
condense onto them and we shall see later that certain types of aerosol
are much more likely to lead to cloud formation than others.
2.1 Aerosol sizes
Having said that aerosol is composed of microscopic particles, there is
actually a huge range of sizes of aerosol in the atmosphere. The smallest
particles are of the order of 10-10m (or 0.0001m) in radius and the
largest can have radii of several tens of microns. Particles larger than
this will have appreciable fall velocities and so are not classed as
aerosols as they do not appear to be suspended in the atmosphere.
Aerosols are classified by size into three types;
 Aitken nuclei are the smallest aerosols, with radii of less than 0.1m.
They are also the most numerous aerosol in the atmosphere.
 Large aerosols have a radius of between 0.1 and 1m and are less
numerous than Aitken nuclei although they constitute a larger
proportion of the total aerosol mass in the atmosphere due to their
larger size.
 Finally, giant aerosols have a radius greater than 1m and are less
numerous than large aerosols.
The actual concentrations of these three different sizes of aerosol varies
greatly depending on the nature of the airmass. Polluted urban air
contains many more Aitken nuclei than maritime air, but the numbers
of giant aerosol vary very little between different airmasses.
2.2 Aerosol properties and condensation
Aerosols can also be classified by how readily water vapour will
condense onto them (i.e. how suitable they are as cloud condensation
nuclei or CCN);
 Hygroscopic aerosol begin to dissolve when water forms around them.
This solute effect gives them an affinity for water and allows
condensation to occur at relative humidities well below 100%. This
makes hygroscopic aerosol the most efficient form of condensation
nuclei. Section 3.3 will describe this process in more detail.
 Wettable aerosols do not dissolve in water but allow it to spread out
into a film on their surface. They also serve as cloud condensation
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nuclei but require the air to be saturated for net condensation to
occur.
 Hydrophobic (or unwettable) aerosols are not suitable as condensation
nuclei as water does not spread out over their surfaces but instead
forms spherical drops. This effect is similar to what happens when
rain falls on a recently polished car or when water droplets run off a
duck’s feathers.
2.3 Aerosol sources
The source of most aerosols in the atmosphere is the earth’s surface, and
as a consequence, aerosol concentrations reduce with height, as shown
in figure 1 (note the logarithmic scale on the x axis).
Figure 1. Measurements of Aitken nuclei concentration against altitude
over western Germany on October 5th 1973. [adapted from Pure and
Appl. Geophys. 112]
The major sources of Aitken nuclei are combustion processes and so the
Aitken nucleus count tends to be particularly high around urban and
industrialised areas. However, natural sources such as forest fires and
volcanoes also generate appreciable quantities of these small particles.
As stated in section 2.1, the Aitken nucleus count in maritime air is
lower than that for continental airmasses. This means that there are less
aerosol particles competing for the available water vapour in maritime
air and so each individual cloud droplet will grow larger. One
consequence of this is that maritime clouds can produce rain more
quickly than continental clouds. This effect is actually parameterised in
the Unified Model, with maritime cumulus clouds able to produce rain
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when 1.5km deep, whereas clouds which form over land have to be 4km
deep before rain can be produced.
The fact that some Aitken nuclei are also found in unpolluted maritime
air means that there must be other sources apart from combustion. It is
thought that gas-to-particle conversion is one such source. This occurs
when certain gases in the atmosphere react chemically with each other
(often due to absorption of solar radiation) and leave behind tiny solid
particles. These reactions are enhanced by high relative humidities. This
process is thought to be a major source of sulphate aerosols in the
atmosphere. A number of complex chemical and mechanical processes
also occur within low level clouds which can alter the distribution of
aerosol sizes and increase the availability of effective cloud
condensation nuclei.
Windblown dust and pollen is a major source of large and giant aerosol,
particularly in arid regions. The sea surface is also a source of larger
aerosols in the form of salt particles. Bubbles bursting on the sea surface
eject a fine spray of droplets into the air. When these drops evaporate
they leave behind salt crystals which will act as hygroscopic nuclei.
Despite the rapid increase in man-made pollution during recent times, it
is estimated that only about 5% of the aerosol in the atmosphere comes
from human sources. However, the nature of much of this
anthropogenically generated aerosol is thought to interact significantly with
solar radiation thus affecting the energy balance of the earthatmosphere system.
2.4 Aerosol and visibility
Aerosols with radii between 0.1m and 1m (large aerosols) scatter
visible radiation very efficiently. This is because their diameters are very
similar to the wavelengths of visible light. Although much of the
scattering of light occurs in the forward direction, removal of light from
the direct beam results in distant objects becoming indistinct to the
observer, and the contrast between an object and its background is
reduced. In some cases all the light from an object may be scattered out
of the direct beam before it reaches the observer and so the object will be
invisible. High relative humidity will increase the size of some smaller
hygroscopic nuclei so that they come into the size range which scatters
visible light efficiently, forming haze and reducing the visibility.
3. Condensation and the growth of cloud droplets
The usual mechanism for producing condensation of water vapour in the free
atmosphere is adiabatic cooling of moist air due to vertical motion. As has
already been mentioned, condensation will not occur unless sufficient cloud
condensation nuclei are present. However, it is a property of the atmosphere
that there are always sufficient quantities of these CCN available for cloud
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droplets to form and so supersaturations greater than about 1% are almost
never observed. In this section, some of the mechanisms that allow these
cloud droplets to grow or dissipate will be examined.
3.1 Curvature effects
When examining the relationship between a surface of water and the
adjacent moist air, it is usual to consider a plane (i.e. flat) water surface.
An equilibrium state is reached between the surface and the air when
the number of water molecules leaving the surface (i.e. evaporating) is
equal to the number entering the surface from the atmosphere (i.e.
condensing). The equilibrium state is reached when the air is just
saturated (RH = 100%). If the relative humidity is less than this, more
molecules will evaporate than condense and so the RH will increase
until it reaches 100% again. If the humidity is greater than this, the
opposite will be the case.
If the water surface is curved, as it clearly is on a cloud droplet, the
equilibrium state will be reached at a different point. This is because the
water molecules on a curved surface are less tightly bound than those
on a flat surface as shown by figure 2. This means that is easier for water
molecules to escape from a curved surface (i.e. evaporate) than it is for
them to escape from a flat surface. So even at a relative humidity of
100%, more molecules will be evaporating from a spherical water
droplet than will be condensing onto it. The greater the curvature, the
higher the value of relative humidity required to maintain equilibrium.
A droplet of radius 0.01m would require a relative humidity of 112% to
remain in equilibrium, a value which is never observed in the
atmosphere. A droplet of radius 0.1m requires an RH of 101% for
equilibrium, a value which is observed in some clouds. Thus a wettable
aerosol particle needs to have a radius of at least 0.1m to act as a CCN.
Hygroscopic nuclei which smaller radii than this can still act as CCN for
reasons which will be discussed in section 3.3.
Figure 2. Water molecules in (a) a plane water surface and (b) a small
water droplet. The molecules in the curved surface expose a greater
surface area to the surrounding air and so are less tightly bound.
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3.2 The Kelvin effect
The greater the curvature of a droplet (and therefore the smaller the
radius), the higher the supersaturation required for it to remain in
equilibrium. However, if the radius of the droplet should increase (if for
instance it collides and joins with another droplet), then the
environment will be supersaturated with respect to the droplet. This
will initiate further condensation onto the droplet and it will thus grow
even bigger - a positive feedback. The radius of the drop will always
remain larger than its equilibrium radius and so it will continue to
grow. This growth is known as the Kelvin effect which is an unstable
process since a small increase in the radius of the drop results in rapid
growth. If the droplet were to reduce in size for some reason, the Kelvin
effect will mean that the environment is now subsaturated with respect
to the drop and so evaporation will occur resulting in a rapid
dissipation of the droplet.
This effect is illustrated in figure 3. The curve shows the equilibrium
relative humidity against droplet radius. If a small change to the droplet
size occurs to move it off this equilibrium curve then the drop will either
grow or dissipate rapidly. Since relative humidity rarely exceeds 101%
in the atmosphere, it is clear from this graph that a droplet must reach a
radius of at least 0.1m before it can grow rapidly by the Kelvin effect.
Figure 3. The equilibrium curve for a water droplet illustrating the
Kelvin Effect. If a droplet on the curve is displaced to the right of the
curve it will grow rapidly. Similarly, if a droplet is displaced to the left
of the curve, it will dissipate rapidly.
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3.3 The solute effect
The solute effect is a mechanism that will allow smaller cloud droplets to
reach a size which allows them to grow by the Kelvin effect. In section
2.2 it was stated that hygroscopic aerosols begin to dissolve when water
forms around them, allowing net condensation onto the droplet at
relative humidities of less than 100%. This will be examined in more
detail here.
When a hygroscopic aerosol begins to dissolve, some of the molecules in
the droplet will not be water molecules but molecules of the substance
of the nucleus (salt for instance). Some of these molecules may occupy
positions at the surface of the droplet thus reducing the number of
water molecules available for evaporation as shown in figure 4. Because
of this, the evaporation of water will be reduced even if the RH is less
than 100% and the droplet will grow as it is not losing as many water
molecules as it is gaining from its environment.
As the droplet size increases, the solution becomes more dilute and the
effect decreases so the drop starts to behave more like a pure water
droplet. Similarly, if the drop were to suddenly increase in size (once
again due to colliding with another droplet) it will become more diluted
and so will evaporate back towards its equilibrium size. Because of this
negative feedback, the solute effect is known as a stable process.
Figure 4. A droplet with a hygroscopic nucleus is a mixture of water
molecules and dissolved molecules of the nucleus. As the droplet grows
by condensation, the number of solute molecules remains the same but
the number of water molecules increases so the droplet behaves more
like pure water as it grows.
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The solute effect means that hygroscopic aerosol as small as 0.01m can
still serve as condensation nuclei, and that condensation can start at
relative humidities of as low as 60%.
3.4 The Köhler curve
For a small cloud droplet to grow large, a combination of the solute and
Kelvin effects is required. A droplet needs to grow by the solute effect to
a size at which the Kelvin effect will lead to rapid growth. If the droplet
should become too dilute before it reaches this critical size, it will
remain in equilibrium as a haze particle if the relative humidity is 100%,
or start to evaporate if the RH is less than this value.
This growth mechanism can be expressed graphically on a plot of droplet
radius against relative humidity known as a Köhler curve. An example of
several such curves is shown in figure 5 (note that the RH scale has been
exaggerated at values greater than 100% since we are particularly interested
in what happens when the air is supersaturated). The different curves
represent the behaviour of droplets with different chemical constituents.
The curves on the left hand side of the diagram represent growth by the
solute effect where droplets will grow and shrink in response to changes in
RH. If however a droplet radius increases beyond the turning point of the
curves, the Kelvin effect takes over and the drop is said to be activated. It can
now grow rapidly at the expense of the smaller droplets since as water
vapour condenses from the environment onto such a droplet, the RH will
fall and so the haze droplets will shrink.
Figure 5. Köhler curves for water drops with different concentrations of
solute. The bold curve is that for a pure water droplet. Drop (1) contains
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10-19 kg of ammonium sulphate, (2) contains 10-19 kg of salt, (3) contains
10-18 kg of ammonium sulphate and (4) contains 10-17 kg of salt.
4. The formation of precipitation
4.1 Water clouds
Figure 6 shows the relative sizes of typical cloud and rain droplets. If a
typically sized cloud droplet (with a radius of 10m ) fell out of the base
of a cloud into air with 90% relative humidity, it would evaporate by the
time it was 3cm below the cloud base. Clearly then, cloud droplets must
grow considerably before they are able to form precipitation which will
actually reach the ground before evaporating.
The conventional borderline between a cloud droplet and a raindrop is
usually considered to occur at a radius of about 100m. A drop of this
size would fall about 150m below the cloud base before evaporating in
air with 90% RH. So if the cloud base is low enough, such a droplet may
reach the ground before it evaporates completely, giving drizzle at the
surface.
Typical raindrops have a radius of about 1000m (1mm) although much
larger drops can form in convective clouds. So to become a raindrop, a
cloud droplet must increase its radius by a factor of 100, and in this
section, the main mechanisms for this growth will be examined.
Figure 6. Relative sizes of cloud and precipitation droplets, showing
radius in microns and fallspeed in cm.s-1.
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4.2 Growth by condensation
Once a cloud droplet has become activated it grows quickly at first,
reaching a radius of 10m within a few minutes. However, the rate of
growth is inversely proportional to the radius of the drop, so the growth
slows down as the drop gets bigger. This means that a cloud droplet
would take about 8 hours to reach drizzle size by condensation alone,
and would probably evaporate before it reached the ground unless the
cloud was very low. Since precipitation is sometimes observed to fall
within half an hour of a cumulus cloud forming, there must be other
processes that accelerate the growth of cloud droplets into precipitation.
4.2.1 Growth by coalescence
Within a water cloud, droplets sometimes collide with each other and
join together to form a larger drop. This is known as coalescence. Larger
droplets have faster fall speeds than smaller droplets and it is this
difference in fall speeds that allows the collisions to take place. If all the
droplets within the cloud were the same size they would all be falling at
the same speed and so collisions would be rare. The turbulent motions
of air within clouds also lead to collisions between different sized drops
as small drops are carried upwards within rising air currents more
quickly than large droplets. In both cases it is the relative velocities of
the colliding drops that is important rather than their absolute fall
speeds.
If, however the collecting drop is very much larger than the small drops
around it, coalescence becomes less efficient. This is because the large
drop forces air to flow around it as it falls, and very much smaller
droplets will be swept around the large drop instead of colliding and
joining with it, as shown diagrammatically in figure 7.
Figure 7. A large precipitation droplet falling through much smaller
drops may sweep them to the side instead of coalescing.
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Cloud droplets need to have a radius of at least 18m before they will
begin to grow by coalescence. Once a droplet reaches a radius of about
25m it will grow rapidly by this process. Figure 8 shows the radius of a
cloud droplet as a function of time as it grows by (a) pure condensation
and (b) pure coalescence. Statistical models of droplet growth suggest
that light rain may be formed by coalescence alone within 20 minutes of
a droplet reaching 25m radius in a maritime cumulus cloud. Including
the effects of the continued growth of the smaller droplets by
condensation can reduce this time to 10 minutes.
Figure 8. Curves of droplet size against time for growth by (a) pure
condensation and (b) pure coalescence.
4.3 Ice and mixed phase clouds
Water droplets can occur in clouds at temperatures well below 0°C, and
are referred to as supercooled droplets. A pure water droplet will actually
only freeze at temperatures of between -35°C and -40°C. This is known
as homogeneous nucleation.
If a water droplet contains a foreign particle known as a freezing
nucleus it can freeze by heterogeneous nucleation at temperatures much
closer to 0°C. This process occurs when water droplets collect on the
surface of a particle and bond together to form an ice-like structure. The
chances of freezing occurring are enhanced if the crystal structure of the
nucleus is similar to that of ice (i.e. hexagonal). Some small soil and ash
particles can nucleate ice at temperatures of between 0°C and -15°C, and
many organic substances such as tiny particles of decayed plant matter
also nucleate ice well. However, only a tiny proportion of the total
atmospheric aerosol content acts as ice nuclei.
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Clouds with tops of between 0°C and -4°C are likely to consist entirely
of water droplets. These are the conditions in which aircraft are most
likely to experience icing problems. With cloud top temperatures of 10°C there is a 50% probability of ice being present, and this increases to
95% if the cloud top temperature is below -20°C. Older clouds tend to
have higher concentrations of ice particles whereas newly formed
cumulus clouds tend to consist entirely of water droplets.
It is possible for ice particles within clouds to multiply without the
necessity for a nucleus. As water droplets freeze they release heat to
their environment so that a shell of ice forms first around the surface of
the drop, trapping liquid water inside. As this liquid core then freezes it
expands, setting up large stresses in the outer shell. This may cause it to
shatter, throwing off tiny ice splinters which can then act as ice nuclei
themselves. This process occurs most efficiently at temperatures of
between -3°C and -8°C. The fragile arms of dendritic (branchlike) snow
crystals may also break off as the crystal falls, and these too can act as
nuclei for further crystal formation.
4.3.1 Growth by deposition
In a mixed phase cloud consisting of both water droplets and ice particles,
the air can be close to saturation with respect to the water droplets but
supersaturated with respect to the ice. This is a consequence of the
saturated vapour pressure at a given temperature being lower for ice
than for water (i.e. water evaporates more readily than ice), as shown by
the es versus T curve in figure 9. At a temperature of -10°C if the air is
just saturated with respect to water then it will by supersaturated with
respect to ice by 10%. As we have already seen, this is a far greater
degree of supersaturation than ever occurs in the atmosphere with
respect to water.
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Figure 9. The vapour pressure versus temperature curves for saturation
with respect to water and ice.
A consequence of this is that in a mixed phase cloud, the ice crystals will
grow rapidly at the expense of the water droplets. This can be
understood by looking at a sequence of steps illustrated in figure 10.
1. In the initial state, water droplets and ice crystals exist together at
temperatures below 0°C. The air is just saturated with respect to the
water droplets, but supersaturated with respect to the ice.
2. Because the air is supersaturated with respect to the ice crystals,
water vapour will be deposited onto them, freezing on contact. The
deposition of vapour onto the ice crystals lowers the relative
humidity of the air.
3. Because the RH is reduced, the air is no longer saturated with respect
to water and so the water droplets begin to evaporate.
4. Further deposition of water vapour onto the ice crystals occurs so the
crystals continue to grow.
The continuation of this process means that eventually all the water
droplets will evaporate and the ice crystals will grow rapidly.
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Figure 10. An illustration of the steps in the process of growth by
deposition with allows ice crystals (hexagons) to grow at the expense of
supercooled water droplets (circles).
This process occurs most efficiently at temperatures of around -12°C, the
temperature at which the saturation vapour pressures with respect to ice
and water are most different. An ice crystal can attain a radius of 100m
within 2.5 minutes of its formation by this mechanism, and so
precipitation can form very rapidly in mixed phase clouds. This process
of ice crystal growth is often referred to as the Bergeron-Findeisen
process after the Norwegian and German meteorologists who first
described it.
4.3.2 Growth by accretion (riming)
Once an ice crystal has acquired a finite fall speed it can grow by
colliding with supercooled water droplets which freeze on contact with
the ice. These droplets form a coating of rime ice. If the freezing occurs
rapidly then air bubbles may be trapped within the ice and the rime
takes on an opaque appearance. However, if the water droplets
accumulate on the ice crystal at too great a rate to freeze rapidly, the
water has a chance to spread evenly over the surface and forms clear ice.
Ice crystals which become rimed to a state where their original form is
no longer clear are known as graupel or soft hail.
Hailstones are an extreme case of growth by accretion. They form in
convective clouds with strong updraughts and high water contents, but
a significant portion of the cloud has to be above the freezing level. The
way in which hailstones are formed is still the subject of some
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controversy. One theory is that they grow to a large size by repeated
recirculation within the cloud and where updraughts are strong enough
to support them. As ice crystals move up and down within the
updraughts and downdraughts they grow by riming water droplets.
Depending on their vertical velocity within the cloud and the water
content, they form alternate layers of clear and opaque ice.
4.3.3 Growth by aggregation
Ice particles in clouds can also grow by colliding and joining with other
ice crystals. As with the coalescence of water droplets, this will only
occur if the fall speeds of the crystals are significantly different.
Aggregation is also influenced by the shape of the crystals and the
temperature. Dendritic crystals such as snowflakes will tend to stick to
each other when they collide as their structures will become
intertwined. However, crystals with smooth surfaces will tend to
bounce off each other. Warmer temperatures also increase the
possibility of two crystals sticking.
4.4 Summary of precipitation formation
In the tropics where rain bearing clouds tend to be convective with high
water contents, the collision-coalescence mechanism is very important
and rain may form in a period of 10 minutes from the appearance of a
cloud by this process. Coalescence of water droplets can also generate
precipitation in mid and high latitudes, and the seeder-feeder mechanism
of enhanced precipitation as raindrops from mid level clouds fall
through orographically induced low level clouds is a good example of
growth by coalescence.
In mid and high latitudes, ice particles become important in the
formation of precipitation. Rapid initial growth of ice at the expense of
supercooled water by deposition in mixed phase clouds can lead to
precipitation sized droplets. Further growth by accretion and
aggregation can lead to large ice particles forming very quickly. These
may melt as they fall through the freezing level giving rain at the
surface, or stay frozen depending on the temperature of the air below
the cloud and their size, leading to hail, snow, sleet or soft hail.
5. Artificial cloud modification
Since the 1940’s many experiments have been carried out to modify the
formation of clouds, either in an attempt to increase rainfall, or to
dissipate clouds and fog and suppress the development of heavy
precipitation.
The introduction of solid carbon dioxide particles into a cloud can cause
supercooled water droplets to freeze spontaneously. This creates many
small ice crystals which are all competing for the available moisture in
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the cloud and so there is insufficient liquid water left in the cloud for
growth by the deposition process. This means that the cloud or fog
dissipates.
Silver iodide has a similar crystalline structure to that of ice and so can
act as a very efficient ice nucleus. Introducing silver iodide into a
cumulus cloud can induce explosive development of the cloud, but only
if the large scale condition of the atmosphere is unstable enough to
support such growth.
Most cloud seeding experiments have proved inconclusive, or at best
have only resulted in very localised modifications of clouds.
6. References
Further and more detailed information can be found in the following
sources.
J.M. Wallace and P.V. Hobbs. Atmospheric science - an introductory
survey. Chapter 4.
R.R. Rogers and M.K. Yau. A short course in cloud physics.
B.J. Mason. The physics of clouds and Clouds, rain and rainmaking.
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