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CloudsConsider a clean atmosphere with water vapor in it.

Dry AtmosphereWater Vapor

Given a long enough time, some water vapor molecules willrun in to one another. Typically they won’t stay together. Evenif the atmosphere was saturated, the likelihood that watervapor molecules will form a droplet is small.

If more water is added such that the atmosphere is supersaturated(RH~300-400 %), then water molecules can form a stable droplet.

This process is called homogeneous nucleation.

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CloudsWe can measure the amount of moisture in the air and find that the cloud droplets form when the air just reaches saturation……………………………..Why?

Nearly a century ago it was discovered that the atmosphere contains particles that have an affinity for water ---

These serve as centers for condensation

Cloud Condensation Nuclei (CCN)

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CloudsWith CCN, we need much smaller supersaturations. In naturewe find supersaturations on the order of 1.5%.

The atmosphere has plenty of CCNDust Salt Spray from OceansVolcanoes Sulfate Particles from PhytoplanktonForest Fires TreesAnthropogenic Origins

CCN are more plentiful near the surface of the earth.CCN are more plentiful over land rather than the ocean.

The formation of cloud droplets using CCN is called:

Heterogeneous Nucleation.

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The Precipitation Process

How can a very small droplet grow to the size of a rain drop?– Typical Sizes (Radius)

» CCN - 0.2 m» Typical Cloud Droplet - 20 m» Typical Rain Drop - 2000 m (0.08)

How fast can this process occur?– In the tropics, a cloud can form, grow, and

produce rain in as little as 30 minutes.

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Droplet Growth by Condensation

A droplet can grow only if the number of water molecules entering the drop exceeds the number of water molecules leaving the drop.

Supersaturation!

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Saturation Vapor Pressure

The saturation vapor pressure is defined over a plane (flat)surface of water.

Liquid H2O

Each water molecule attracts it’sneighbor. The combined attractiveforces on the molecules at thesurface make up the surface tension.

Consider the forces on the red molecule:

There are attractive forces fromall the surrounding molecules.These forces must be overcomefor the molecule to escape intothe vapor phase.

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Each water molecule attracts it’sneighbor. The combined attractiveforces on the molecules at thesurface make up the surface tension.

Consider the forces on the red molecule:

Saturation Vapor Pressure

The saturation vapor pressure is defined over a plane (flat)surface of water. Let us now consider a droplet.

Liquid H2O

The forces on the red molecule are lessthan that for a plane surface of water. Tomaintain equilibrium, the vapor pressureabove the drop must be greater in order tokeep the drop from evaporating.

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Curvature EffectThis reduced surface tension and the larger saturationvapor pressure required for the drop to remain inequilibrium with its surroundings is called thecurvature effect.

This effect is enhanced for smaller drops. In otherwords, the smaller the drop radius, the larger the curvature of the drop, and the larger the vaporpressure required to keep the drop in equilibriumat a given temperature.

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Curvature Effect

The figure at the right showsthe relationship between thesupersaturation (the RH above100 %) and the droplet radius.

The supersaturation increasesexponentially as the dropletradius gets smaller.

Note: If the supersaturation is greater than the equilibrium curvefor a given radius, then the drop will grow. If the RH is less thanthe the equilibrium curve, the drop will evaporate.

Droplet will grow

Droplet will evaporate Equilibrium Curve

RH

100 %

Droplet Radius

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Curvature Effect

For droplets less than 1 m, which is larger than for homogeneous nucleation, the supersaturations must be very high, well above what we see in the atmosphere, for the droplet to grow.

This is a problem!!!

CCN to the rescue!

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CCN to the Rescue!

CCN give the water molecules a place to gather together. This “instantly” gives them a much larger size than without the CCN.

Some CCN are hygroscopic. Some salts begin to collect water at RH’s as low as 75%. A solution is formed when water condenses onto a salt particle.

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Solute Effect

The saturation vapor pressure is defined over a plane (flat)surface of water.

Liquid H2OLiquid H2O

AddSalt

There are fewer water molecules at the surface. So not as manywater molecules can escape at a given temperature. Inequilibrium, the saturation vapor pressure over the salt water isless than that over the pure water. This is called the soluteeffect.

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Solute Effect

The saturation vapor pressure is defined over a plane (flat)surface of water. Let us now consider a droplet.

Liquid H2O Salty H2O

The solution (salty) drop has a lower saturation vapor pressurethan does the pure water drop. The solution drop can remainin equilibrium at relative humidities less than 100%.

AddSalt

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Solute Effect

The dashed line representsthe saturation vapor pressurecurve for a solution drop.

The vapor pressure for asolution drop is less than thatfor a plane of pure water.

The vapor pressure requiredto maintain equilibriumdecreases as the drop radiusdecreases.

This is opposite of the effect for curvature.

RH

100 %

Droplet Radius

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Köhler CurveWe can combine the effectsof curvature and solution.This curve, represented bythe thick line at the right, isthe Köhler curve.

Initially the solution effectdominates, but as the dropgets bigger, the curvatureeffect takes over.

When the drop is very large,neither effect dominates and the surface of the drop, to thewater molecules, appears as a flat surface.

Shrink

Grow

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Köhler Curve

Shrink

Grow

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Köhler Curve -- Critical Values

r*RH*

Grow

The critical values (r* -- radius, RH* -- Relative Humidity) representthe point of the peak on the Köhler curve.

For constant r* an increase in the RH will allow the drop to grow, a decrease in RH will cause the drop to shrink.

For a constant RH* either an increase or decrease in radius will allow the drop to grow

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Growth by Condensation Given:

– CCN with an initial mass of 10-12 g– RH greater than RH* (The critical RH)

How long will it take for a droplet to grow to the size of a cloud droplet (20 m)?– 5900 sec– ~98 Minutes!

» This is too slow for what we often observe!

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Collision-Coalescense Process

To increase the volume of a single drop to the size of a rain drop, it must grow for a very long time.

A faster way is to get several small drops together to form a single large drop.

Larger drops fall faster than small drops.

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Terminal Velocity

In the absence of anywind, the drop will begin to fall.

As soon as the drop falls,the air resists the fall of thedrop.

The air resistance is dependent on the size of the drop andthe velocity of the drop. So the larger the drop will have alarger air resistance.

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Terminal VelocityEventually, there will be a balance between gravity, which wants to pull the drop down toward the ground, and the airresistance, which wants to retard the fall of the drop to theground.

From Newton, when there is a balance of forces, the dropwill continue in a straight line at constant speed. Thisspeed is called the Terminal Velocity.

The larger drops will have a larger terminal velocity thansmall drops so the large drops will fall faster.

In calm air, a typical rain drop will fall nearly 600 timesfaster than a typical cloud droplet.

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Collision-Coalescense Process

If the larger drops fall faster, they can catch up to and run intothe smaller drops.

If the large drops collide with the smaller drops and merge withthem, this process is called coalescense.

Not all small drops willmerge with the largerones!

FlyAround Join then

Split

Merge

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Collision-Coalescense Process

Coalescense Depends On:– Cloud Water Content– Large Droplet Size– Small Droplet Size– Updrafts (Relative speed of the large drop

to the small drop.)– Cloud Electricity

A drop will grow quickly by this process.

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Rain Drops Keep Falling On My Head

The drops can make it to the ground if:– The drop is large enough– The cloud base is low enough– The air between the cloud base and the

ground is not too dry.

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Are Rain Drops Tear Shaped?

From this picture, it seems that somethingis pulling at the top of the drop!

Is this realistic?

Consider a small drop that is not falling.

The forces on each molecule areinward. The total force wants to pullthe molecule toward the center of the drop. This results in aspherical droplet.

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Are Rain Drops Tear Shaped?

As the drops fall, the air resistance force is applied at thebottom of the drop.

Air Resistance

The air resistance force pushes on the bottom of the drop.As the drop falls faster, the air resistance force increases.Surface tension will try to keep the drop a sphere. Thecombination of the two gives the resulting drop a“hamburger bun” shape.

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Are Rain Drops Tear Shaped?

Air Resistance

No drops fall in the shapeof a tear drop. They usuallyhave a flat bottom and a slightly oval shape.

If the drop is large enough, the air resistance forces canactually “inflate” the drop. The drop then breaks up intomany smaller drops. This is called “bag breakup.”

This sets an upper limit on the size of raindrops.