At 40o C, the maximum amount of water that can occur in vapour form = 40 g kg-1, whereas at 0o C, the maximum possible mixing ratio = 4 g kg-1.
Clouds are among the most fascinating phenomena in atmosphere: clouds
make visible the movement of the air, and can reveal much about the state
of the atmosphere. To understand them, and larger-scale weather systems,
we need to examine the behaviour of water in the atmosphere.
Q: How much vapour can there be in a mass of air?
A: A useful measure of the amount of water vapour in the air is the mixing ratio, r:
r = mv/md
(mv = mass of vapour; md = mass of dry air).
The mixing ratio can be expressed as a percentage or in terms of grams per kilogram. A typical value in the low troposphere is ten grams per kilogram, (10 g kg-1 or 1 %). An alternative measure is the vapour pressure, or the pressure exerted by the water vapour component of the atmospheric mix. In Lecture 2, we saw that air exerts a pressure. We can subdivide this pressure into components exerted by the different constituents of the atmosphere, known as partial pressures. There are therefore partial pressures exerted by nitrogen, oxygen, and carbon dioxide. The vapour pressure is the partial pressure exerted by water vapour.
The existence of vapour pressure can be dramatically demonstrated by the Beer can experiment. First, drink the beer. Then, fill the can with hot water vapour by boiling a little water in it. The can is open to the atmosphere, so the internal pressure rapidly equilibriates with atmospheric pressure. Part of this pressure is exerted by water vapour. Plunging the can upside down onto a tray with a shallow layer of cold water causes condensation and loss of water pressure inside the can, allowing atmospheric pressure to crush the can. Reference for the experiment: Bohren, C.F. 1987. Clouds in a Glass of Beer: simple experiments in atmospheric physics, chapter 6.
The maximum mixing ratio ( and vapour pressure) is determined
by temperature alone, as shown in the temperature/vapour pressure graph.
At 40o C, the maximum amount of water that can occur in
vapour form = 40 g kg-1, whereas at 0o C, the maximum
possible mixing ratio = 4 g kg-1.
The relationship is non-linear, so warm air can contain very much more vapour than cold. This maximum amount is termed the saturation mixing ratio or saturation vapour pressure, and air is said to be saturated at this value. Saturation is defined as the mixing ratio which is at equilibrium with a flat water surface. At this value, rates of evaporation from the water to the air, and condensation from the air to the water are equal. Note that the condensation and evaporation of water reflect the energy of the water molecules and are NOT the result of some property of the air. Warm air does not 'hold' more water vapour than cold air: rather, warm (i.e. more energetic) water molecules are more likely to remain in the gas form that cold ones.
Saturation mixing ratios are less over ice surfaces, because the energy required to turn water from ice to vapour is greater (recall the discussion of latent heat in Lecture 1). When the amount of water present in the air exceeds the saturation mixing ratio, it condenses out, thus restoring equilibrium. The formation of water droplets on a cold bottle of coke can is an example of this. The cool drink chills the surrounding air, forcing the water vapour contained in it to condense out. Below 0o C, we can also define a saturation mixing ratio for air over a plane surface of ice. For temperatures down to about -50o C, the saturation mixing raio is less over ice than water, meaning that air will become saturated (i.e. clouds will form) more readily over ice than water, for a constant temperature. Thus, the curve of saturation vapour pressure for ice will plot below the curve for water, between 0o C and c. -50o C.
The actual amount of vapour in air can be much less than saturation value, and can be measured by the actual mixing ratio. However, it is most useful to define it in terms of the saturation value at the temperature of the air. This gives rise to the idea of Relative humidity:
Relative humidity (RH) = r / rs
that is: actual mixing ratio (r) divided by the saturation mixing ratio (rs). The relative humidity is usually expressed as a percentage, i.e. r / rs x 100%.
Relative humidity therefore depends on the actual mixing ratio and temperature, so RH will change with temperature: RH may decrease by up to 50% between morning and noon as temperatures rise, and increase again as temperatures cool in the afternoon.
(1) The Curvature Effect. Saturation was defined above in terms of equilibrium with a plane surface of water. However, for small water droplets, saturation values are very much higher, because of the effects of curvature. On curved surfaces, water molecules have fewer neighbours than on a plane surface, so bonding forces are weaker. Thus, evaporation occurs more easily from a small, curved water droplet than from a flat surface, and greater amounts of condensation are necessary to maintain equilibrium. Newly forming droplets are by definition very small, with tightly curved surfaces, and saturation mixing ratios may need to be as high as 400% for net condensation to occur. Air with RH values > 100% is said to be supersaturated.
(2) The Solute Effect. The presence of particles in the air provides
less tightly curved surfaces for droplet growth, reducing the amount of
supersaturation required for condensation. These particles are known as
cloud
condensation nuclei, or CCNs. Some CCNs attract water molecules: particles
with this property are known as hygroscopic particles. Examples
of hygroscopic materials are salt, plaster of paris, and the silica gel
sachets used to keep biscuits crunchy and electrical equipment dry. Hygroscopic
CCNs in the atmosphere include salt crystals, and dust coated with sulphur
dioxide. Hygroscopic CCNs actively draw in vapour, forming droplets of
solution, and condensation can be initiated at subsaturation mixing ratios.
The behaviour of a vapour droplet mix as condensation proceeds is displayed
on Kohler curves. On such curves, the point at which growth becomes
self sustaining can be identified: this marks a critical droplet radius,
beyond which droplet is said to be activated.
At temps > -10oC, almost no ice will form;
-10oC to -20oC : increasing minority of ice crystals;
-20oC to -30oC : increasing majority of ice crystals;
< -30oC : mostly ice crystals.
Cold air (< 0o C) which contains liquid water droplets
is referred to as supercooled. The water will tend to freeze as
soon as it finds a suitable surface where ice crystals can grow. An example
of this process is the formation of rime ice on fenceposts, clothing,
hair and beards when cold, misty air blows past.
From the above, we can see that clouds can be composed of water droplets,
ice crystals, or a mixture of the two. Water- and ice-clouds have distinctive
appearances, so we can tell the difference from the ground. Ice clouds(such
as cirrus) are fibrous in appearance, whereas water clouds (such as cumulus
or ground fog) may vary in appearance from 'puffy' to 'misty'.
Air mass cooling in situ
Cloud will form if a mass of air is chilled so that it can no longer
support the water present as vapour. The most familiar cloud of this type
is fog forming near the ground on a cold night. Because the mechanism
of cooling is the loss of energy by longwave emission, this type of fog
is termed radiative fog.
Vertical or horizontal motions
Similarly, cloud will form if an air mass is uplifted to higher altitudes
where the pressure drop causes cooling. Uplift may be due to winds blowing
over high ground (orographic cloud), or by vertical motions in the
free atmosphere (convection).
Mixing clouds
Cloud may also form by the mixing of two unsaturated air masses in
some circumstances. This may occur because of the non-linear form of the
saturation vapour pressure/ temperature curve.
On this diagram, points A and B represent unsaturated air masses. When
they mix, the resulting air (C) is saturated, indicating that cloud has
formed as a result of the mixing. Clouds formed in this way are called
mixing clouds. Common examples include breath on a cold day (when warm,
moist unsaturated air - your breath - mixes with cool unsaturated air -
the ambient air - to form a cloud) and aircraft contrails (when hot unsaturated
air - aircraft exhaust gas - mixes with cold, unsaturated air - the ambient
air - to form a condensation trail, or contrail). Contrails usually consist
of ice crystals. If you observe them closely, you will see cascades of
these crystals falling to earth before sublimating away into the cold,
high air.
Two main mechanisms have been identified to explain the growth of water droplets to form precipitation:
(1) Activated nuclei, or the growth of droplets by condensation
from surrounding vapour;
(2) Collision, or the growth of droplets by the combination
of two colliding particles.
For water droplets, both of these mechanisms are very slow: too slow to account for observed rates of cloud development and precipitation formation. Thus most precipitation is thought to develop as ice crystals at low temperatures, which may then thaw to form rain. This is known as the Bergeron-Findeisen mechanism, after two Norwegian meteorologists who first proposed the mechanism. Ice crystals grow more rapidly than water droplets, due to the lower saturation vapour pressure of air over ice, compared to water, but require very low temperatures. The formation of ice crystals in clouds is known as glaciation (not to be confused with terrestrial glaciation!). This is probably the most important mechanism of precipitation formation in many parts of the world, even in the tropics (where low temperatures occur in high cumulus clouds). Ice crystal clouds have wispy, fibrous shapes, and allows us to see glaciation occurring in high clouds. An important type of ice clouds is known as cirrus, after the Latin word for hair.
Types of precipitation include rain; snow (branching ice crystals
or aggregates of crystals); sleet; hail, and graupel (conical pellets of
spongy hail). The type that falls is dependent on the processes operating
within clouds and the air temperature profile between there and ground
(i.e. whether precipitation thaws or freezes en route to ground).
A good discussion of the false idea that warm air can "hold" more
water vapour than cold air can be found at the Bad
Meteorology website. This is a great website that examines all kinds
of false notions that are commonly passed on by unwitting teachers to trusting
students. We'll revisit this site when we look at the Coriolis effect in
a later lecture, but in the meantime, take a look around the site: it's
full of interesting gems.
Cloudman: a website devoted to
clouds, with nice galleries of photographs plus lots of links to interesting
sites