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Formation of Clouds
Cloud Lifetime
Saturation, Supersaturation and Initial Condensation
Initial Condensation
Processes that Produce Changes in Stability
Radiative heating and cooling at the surface:
Radiative heating and cooling aloft:
Lightning Hazards
Squall Line
CHAPTER 4 Thermodynamics

Formation of Rain

Formation of Clouds

Clouds are suspensions of liquid water drops that arise from the condensation of gaseous water vapor and subsequently disappear as they evaporate and the water is returned to the gaseous phase. As much of the liquid water that comprise the cloud has its origin from evaporation of water from the surface of the earth, the heat released to the air during condensation warms the cloud layer of the atmosphere. Were this process of transferring energy from the surface to the atmosphere at cloud level not present sensible heating of the layer of air near the ground would result in desert like heat everywhere. Because the water drops form and evaporate their life and the life of clouds is limited.

Cloud Lifetime

Clouds (particularly Cumulus clouds [Cu]) are dynamic phenomena - they are borne, reach maturity, go into old age and die. Small Cu may last only 5 minutes (birth to death). Large Cumulonimbus [Cb], while appearing to exist for hours, have individual cell lifetimes of only 10's of minutes (up to about 30 min). The ensemble of growing, mature and drying cells, all representing different stages in the life cycle of a cell, give clouds the appearance of longevity:

Wordsworth's lines: (The Daffodils)

"I wandered lonely as a cloud that floats on high o`er vales and hills"

is uncharacteristically inaccurate. Most clouds that produce rain live only for a short time (< 30 min). This fact is important when we consider how a raindrop is formed: where a raindrop must start with condensation and end with a mass large enough to fall to the ground.

Saturation, Supersaturation and Initial Condensation

Air becomes saturated when it cannot hold any additional water vapor at that temperature, i.e., the maximum number of water vapor molecules are contained in the volume of air at that temperature. The temperature at which the air is saturated with water vapor is the dew point temperature (Td)which is also the wet bulb temperature (Tw) (see
page 120). Another means of expressing the condition at which condensation begins is when the actual water vapor mixing ratio (w) equals the saturation mixing ratio (ws).

(EQ 204)

where rv is the density of water vapor and rd is the density of dry air.

FIGURE 57 Definition of Cloud Base and LCL

Clouds are almost exactly saturated with respect to liquid water, i.e., RH = 100 to 101%, i.e. there is a supersaturated by 0.1%. At saturation the rate at which water molecules leave a flat water surface equals the number of gaseous water molecules that condense onto the flat water surface. If you change the temperature of the water surface you will change the rate at which water molecules leave the water surface for the atmosphere. If temperatures increase water molecules will leave at a higher rate.

Initial condensation gives rise to drop sizes around 1m (1/1000 mm). The typical radius of a cloud drop is 10m (range = 0.5 to 100m) and number about 106 per liter of air. The speed at which such drops fall, i.e. their terminal velocity is about 1 cm/s.

FIGURE 58 Consider a Cylindrical Cloud

A typical thunderstorm (cumulonimbus cloud) is about 10,000 m in height and 2,500 meters in diameter. The liquid water content of such clouds is about 1 g of water for each m3. This cylindrical cloud would have a volume of pr2h or 18.75 x 1010 m3, and with 1 g/m3 water content it also has 18.75 x 107 kg or about 187,500 metric tons of water. Why then does not such large mass come crashing down? Within clouds there are vertical motions. Rain only falls out when the terminal velocity of the raindrop is greater than the upward motions within the clouds (updrafts).

In order to fall out as rain it must grow from their minute size at formation to ~ 500m or 0.5 mm (border between raindrop and cloud drop ~ 100m).

To grow from initial condensation drizzle size (0.2-0.5 mm) by condensation alone takes too long. In fact it takes longer to grow by condensation along than the average life span of a cloud. Even when the air is supersaturated it takes nearly 1 hour 15 min to grow from 2 mm to 30 mm.Cannot form raindrop by condensation process alone simply because the cloud element does not last that long.

Initial Condensation

The condensation of cloud drops and the subsequent growth of cloud drops is helped by the presence of particulate matter in the atmosphere called: condensation and freezing nuclei.

No condensation (or freezing) will occur in the natural environment without the presence of condensation nuclei (Vonnegut and Schaefer). Spontaneous nucleation of cloud drops or cloud ice particles at around T ~ -40xf8 C. Spontaneous nucleation could occur at high supersaturations of up to 700% but such conditions do not occur outside of the laboratory.

Condensation nuclei play three roles:

Solute Effect --Saturation vapor pressure, es (partial pressures - Dalton's Law ---- pO2 + pc02 + pN2 + es +... + pn = Ptotal)

Saturation vapor pressure is inversely proportional to the concentration of the solute: drops which form on large soluble condensation nuclei are more concentrated than drops forming on small condensation nuclei. Concentrated drops grow at the expense of the more dilute drops, and as drops grow they in turn become dilute (drop size distribution).

Curvature Effect -- Saturation vapor pressure is inversely proportional to the radius i.e., es a 1/r. The saturation vapor pressure (es) over large drops is low while over small drops is high. Larger drops grow at expense of smaller drops. This happens when there is a distribution of drop.

Collision and coalescence -- Large drops fall at a higher speed than small drops (1 m s-1 to 10 m s-1) [upward and downward motions - hail] (seeFigure 61)

FIGURE 59 : Size Range of Elements Involved in Cloud Physics

FIGURE 60 : Precipitation Particles and Drops

FIGURE 61 : Raindrop Growth by Collision and Coalescence

Fall velocities for various forms of precipitation are summarized in Table 10.

Fracturing -- Drops larger than 1 cm become unstable and can break apart forming several smaller drops. This occurs when the surface tension on the drop becomes less than the frictional drag and the drop is torn apart.

Role of Ice -- Bergeron Findersen - 3 Phase Process

Summary of Key Points

Sequence of processes in precipitation

Role of Ice in Precipitation

Processes that Produce Changes in Stability

There are three processes, each with two types, which destabilize a column of air. Up to now we have talked largely in terms of a "parcel" or "bubble" - we will still call upon this analogy but must now ask questions about the stability of a deeper column of air (or slice or slab). Three processes are of specific interest:

We will consider each of these in turn.

Radiative heating and cooling at the surface:

FIGURE 62 Dry and Moist Convection

Some examples of dry convection with and without clouds: In relatively weak wind fields, vertical motion is cellular: soaring of saccules (woodcock in circles, more recently studies of vultures (metabolism - energy intake to expenditure. They fly tremendous distances: how do they do it in terms of (food) energy supply.

FIGURE 63 Thermals

Benard Cells: usually on a scale larger than the individual cloud: hexagonal cells (8 sides)

FIGURE 64 Benard Cells

Rolls, lenticular vortices: when wind exceeds a critical value (about 6 m s-1) lenticular vortices or rolls form (usually with some change in vertical stability - capping inversions).

FIGURE 65 Lenticular Rolls (plan view and cross section)

Radiative heating and cooling aloft:

Destabilization of the top of the cloud (over warm ocean) - at night, cloud looses heat from to cloud top (Ll), gains at bottom (Ll)which gives rise to a more unstable atmosphere and nocturnal thunderstorms early evening over land, late night over sea - frequently very early morning.

FIGURE 66 : Day-Night Differences in Marine Cloud Dynamics

Advection over warmer/colder surface:

FIGURE 67 : Land-Sea and Sea-Land Advection

Advection: relative air motion:

FIGURE 68 : Warm and Cold Air Advections Giving Rise to Atmospheric Instability

Horizontal movement of air with its properties at different levels. Reverse if warm air is brought over cold air.

Forced convection: convergence/divergence

FIGURE 69 : Convergence and Forced Convection Effect on Lapse Rates

In Figure 69 convergence of air is indicated as wind speed slows (U1 to U2).

FIGURE 70 : Horizontal Divergence and Subsidence.

In Figure 70, divergence in the lowest layer of the atmosphere (ABCD to A'B'C'D') gives rise to a sinking of the layer of air aloft (ABEF to A'B'E'F'). Since this sinking is a dry adiabatic process the observed lapse rate at the start (open circles) changes to the form shown in filled circles on the illustration above. The resulting profile of temperatures with height contains an inversion in the surface layer (surface to A')

FIGURE 71 : Forced Convection During Upslope Flow

(Absolutely) Stable: g < Gs < Gd

Neutral: g = Gd for dry g = Gs for moist

(Absolutely) Unstable: g > Gd

Conditional Inversion: Gs < g < Gd

Convective (or potential)

Instability: occurs when lifting to saturation throughout

a layer (column) - will establish a lapse rate

(for the layer) > Gs


If the rising air did not mix or interact with its surroundings in any way, then from the thermodynamic diagrams we could determine the onset of convective clouds (time), the height of convective cloud base (LCL), and the depth or height of the cloud. In fact only time and the height of the cloud base are done accurately by the diagram, then the height of the cloud is done imprecisely. This is because we now deal with a pseudo-adiabatic process, i.e., heat can be released into the rising bubble by

but not all of the water vapor necessarily condenses (as is assumed by the saturated adiabatic process) and not all of the water freezes (supercooled). If we assume no addition or loss of heat then real cloud mix withtheir environment.



FIGURE 72 : Windshear and Thunderstorms

FIGURE 73 : Freezing, Condensation and Release of Heat


Impact: Four affects that can impact people


Fine weather, Earth carries a negative charge, positive charge in upper atmosphere (ionosphere). Potential difference of several hundred thousand volts can exist between surface and ionosphere. As charge builds up in atmosphere due to atmospheric motions, discharges (lightning) must occur to maintain a steady state. Discharges occur along ionized channels where ionization is the process by which atmospheric molecules (small ions) or other suspended particles (large ions) are electrically charged. Water drops in a field of drops in a cloud become charged and elongated.

FIGURE 74 : Charges on Cloud Droplets

Point discharges can coalescence into large, discharge channels forming channels along which charges can flow.

FIGURE 75 : Electric Field and Point Discharge

FIGURE 76 : Electric Field Associated with a Thunderstorm

When a cloud approaches given point on the Earth's surface and/or given stage in development, charge in cloud reverses - negative charge at cloud base replaced first by pockets of + charge and then by + charge reversing the original polarity of the cloud. Now have a thunderstorm. A reversal of charge used as a predictor. Gradients may reach 20,000V/m and may be 5000V/m at a distance of 5 km from cloud center.

The lightning sequence starts as a Stepped leader with discrete steps in the vertical of ~ 20 m (Figure 78). Return stroke of lightning from the ground upward follows after leader stroke reaches ground and is a brighter flash that returns to cloud. This flash is a faster lightning flash as it follows the path formed by the downstroke. Subsequent strokes follow initial sequence of stepped leader, leader stroke and return stroke - follows the dart leader same path but no branching, is faster than original sequence (0.01) A form of lightning called ribbon lightning occurs when there are high winds that shift each stroke into several parallel luminous ribbons and can strike different points (highest - 26 strokes).

FIGURE 77 : Thunderstorms, Electric Fields and Lightning Strokes

FIGURE 78 : Lightning Stroke Sequence

Lightning Hazards

Effects of lightning strikes on people are well studied but the specific mechanism of death due lightning is not all that clear. People are usually struck in one of three ways: direct strike (most dangerous), side flash (off a tree for example), and by step voltage where you are subject to a high voltage gradient but not the lightning leader (most survive this). Strikes to head and brain are most serious and are usually accompanied by a failure of the respiratory system to function. arrest. Restarting breathing is essential and artificial respiration should be tried. Lightning may cause a nerve block or could cause heart ventricular fribulation or asphyxia. Loss of consciousness following a lightning strike is common and may last few minutes or hours and may relapse at a later time. Burns also arise from the lightning strike and may take the form of a Lichtenberg Figure which is a tree like disfigurement but usually disappears in a few hours as it is not true burn. In the case of true lightning burn, tissue damage is greatest at the point of current entry which is often associated with metal objects such as chains, necklaces, or keys.

Personal protection against lightning varies with your position in the landscape. If you are standing in open field, your are the main lightning conductor on the landscape. Probability of being struck depends on your height above ground. Accordingly you should not increase your height. Being perched on a bicycle, tractor, back of truck, horse, open boat is not a good idea. Nor is it recommended that you point skyward your umbrella, fishing pole, golf clubs. Sit, squat or lie down. Dense woods are reasonably safe as is being under a power line but you should stay away from power line pylons. Buildings or all metal containers, e.g. cars or trucks, are safe places. Don't run for nearest large tree. Keep away from fences, pipes, railings, etc. and don't crowd as there is danger of side flashes from objects nearby. Swimmers not likely to be struck but are subject to flow of current through body if water is (especially if the water is saline, i.e. sea water) struck. Small tents at camp sites in the open are a danger and if you must camp, do so on high ground in thunderstorm weather and put out conductors lightning rods for protection.

Squall Line

A squall line is an aggregation of thunderstorm cells in line formation. Why? Most efficient way to maintain system - contrast against cloud area, not moving. Squall lines form ahead of cold front (
Figure 79) on a dry line where there is a large horizontal atmospheric density difference. Squall lines form abruptly -- temperature and humidity fall, the winds strengthen and then change direction. Wind speeds of 30-45 km/hr. are common and precautions should be taken as wind damage is likely. Ten to fifteen minutes after the temperature falls heavy rain and thunderstorm activity are expected. Squall lines are maintained by outflow from the tops of the thunderstorm cells and new growing cells are formed as older cells decay.The propagation of new cells (as much as 100 to 200 km distance) at one end of the squall line and decay at the other gives the appearance of motion in the direction of the line where in fact the line as a whole moves with the prevailing wind field in the region. The individual thunderstorms in the squall line and the entire line itself dissipate when the supply of heat and moisture is inadequate.

FIGURE 79 : Squall Line

FIGURE 80 : Conditions Favorable for Hail Development in the Mid-West


Formation of hail stone - successive freezing onto an ice nucleus to produce large enough mass to fall requires winds ~ 20 m s-1, supercooled water (-20 oC), and a water vapor density > 1 g/m3. Hail mitigation can be accomplished by providing nuclei to remove supercooled water Silver iodide yields 1012 nuclei per gram of the iodide.


Tornados are very intense (most intense), small vortices (rotating - either anti-clockwise or clockwise) with a great concentration of angular momentum. They are formed with in thunderstorms characterized as having intense instability and very cold cloud temperatures. There are 500-100 tornado per year in North America with the maximum frequency in early spring. Most occur in the afternoon -- 82% noon/midnight. The funnel of a tornado with air flow paths is shown in
Figure 81. Tornadoes have a ground speed of about 20 m/s or 50 m.p.h. (range = 30 to 66 m.p.h.). Wind speeds within a tornado at ground level varies from 120 m/s to 200 m/s (250 to 400 m.p.h.).

The Showalter Index is a measure of the local static stability of the atmosphere expressed as a numerical index. This index is determined by lifting an air parcel from 850 mb dry-adiabatically to the point of saturation, then saturation-adiabatically to 500 mb. At the 500 mb level, the temperature of the parcel is compared to that of the environment; the magnitude of the index is the difference between the two temperatures. If the parcel is colder than its new environment, the index is positive; if warmer, the index is negative (see Figure 82). If the (temperature environment - parcel temperature at 500 mb) is +3 or less, severe thunderstorm is indicated, if -6 then tornadoes are possible.

The conditions necessary for tornado development include extreme instability (Showalter Index <-6), pre-existing Cb thunderstorms and squall line, b. pre-existing rotation of cloud with a typical hook echo evident on radar.

FIGURE 81 : Flow Structure in a Tornado

FIGURE 82 : Tornado Indicator

Climate Dynamics - 05 FEB 96
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