chapter 8: precipitation ats 572. “precipitation” can be: 1.rain 2.snow 3.hail 4.etc. however,...

Chapter 8: Precipitation

ATS 572

“Precipitation”

• Can be:1. Rain2. Snow3. Hail4. Etc.

• However, it MUST reach the ground.– Otherwise, it is called “virga”—hydrometeors

that are heavy enough to fall out of the base of the cloud be evaporate before hitting the ground,

“Virga”

“Fall Streaks”

• Same as “virga”, except virga is liquid water whereas fall streaks are made of ice crystals.

• Can be very hard to tell from virga.

“Fall Streaks”

Sizes of Hydrometeors

As you can see, cloud droplets are many millions of times smaller than a typical raindrop. Therefore, a cloud droplet is going to have to GROW in order to fall out of the cloud!

Three Processes That Control The Growth of Hydrometeors:

1. NucleationCondensation or deposition of water vapor onto a cloud

condensation nucleus (CCN)

2. DiffusionTransport of water vapor toward a growing droplet

3. Collision

Growth by sticking together smaller droplets

Each will be discussed at length!

“Nucleation”

• Involves the condensation or deposition of water vapor.

• Can be either “homogeneous” or “heterogeneous”.

• HOMOGENEOUS NUCLEATION:– Occurs in perflectly clear air.– Is practically impossible in the atmosphere.

“Heterogeneous Nucleation”

• Involves the use of impurities in the air to facilitate condensation or deposition.

• Impurities: Cloud Condensation Nuclei (CCNs), which are very abundant in the atmosphere.

• Their abundance is described by the Junge Distribution, which is equation 8.1 in Stuhl.

Condensation versus Evaporation

• Two processes are at work on every hydrometeor:

1. Water vapor molecules are continually condensing onto the drop.

2. Water molecules are continually evaporating from the drop.

• To grow, the condensation is going to have to be significantly faster than evaporation!

Two Effects Control the Rate of Evaporation:

1. The Curvature Effect

2. The Solute Effect

Let’s examine each effect in detail!

“The Curvature Effect”

• Small droplets have a small radius, or “radius of curvature”.• Larger droplets have a larger “radius of curvature”.• Flat surfaces have an INFINITE “radius of curvature”.


• Small droplets have a small radius, or “radius of curvature”.• Larger droplets have a larger “radius of curvature”.• Flat surfaces have an INFINITE “radius of curvature”.

Evaporation rate INCREASES as radius of curvature

DECREASES!


• Therefore, this makes it harder of droplets to grow, since the smallest droplets have the fastest evaporation rates!

The Solute Effect will tend to partially compensate for this problem.

“The Solute Effect”

• Solutions tend to evaporate more slowly than pure water does.

• Many CCNs dissolve into the cloud droplet that they are forming, making a solution.

“The Solute Effect”

• Smaller droplets will be STRONGER solutions, whereas bigger droplets are more DILUTED.

• Therefore, smaller droplets will tend to evaporate more slowly than bigger droplets, depending on the balance between the Curvature and Solute Effects.

The Kohler Equation

• Combines the Curvature Effect and the Solute Effect into one equation.

3

1-312

*

)gm x103.4(1

mK 3335.0exp

RM

mi

RT

e

e

s

ss

s

This is equation 8.2 in Stuhl.

The Kohler Equation

• The Left Hand Side of the equation is a number that represents relative humidity, where 1 = 100%.

3

1-312

*

)gm x103.4(1

mK 3335.0exp

RMmi

RTe

e

s

ss

s


The Kohler Equation

• The numerator of the Right Hand Side is the Curvature effect:

3

1-312

*

)gm x103.4(1

mK 3335.0exp

RMmi

RTe

e

s

ss

s


T = Temperature in K

R = Radius of the droplet, in micrometers

The Kohler Equation

• The denominator of the Right Hand Side is the Solute effect:

3

1-312

*

)gm x103.4(1

mK 3335.0exp

RMmi

RTe

e

s

ss

s


i = “van’t Hoff factor (always given to you)

ms = mass of the solute in g

Ms = molecular weight of the solute (given)

R = Radius of the droplet, in micrometers

The Kohler Curves

• Graphs of the Kohler equation are called “the Kohler Curves”.

• We’ll discuss plenty of examples now.

The Kohler Curve for Pure WaterKohler Curve for Pure Water

99

99.5

100

100.5

101

101.5

102

0.075 0.275 0.475 0.675 0.875

Droplet Radius (microns)

Rel

ativ

e H

um

idit

y (%

)

Mass of the solute was set to 0, so the denominator of the Kohler equation went to 1.


99

99.5

100

100.5

101

101.5

102

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

Regions above the curve are supersaturated: a droplet with that size will GROW at that relative humidity.


99

99.5

100

100.5

101

101.5

102

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

Regions below the curve are subsaturated: a droplet with that size will SHRINK at that relative humidity.


99

99.5

100

100.5

101

101.5

102

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

For very large PURE WATER DROPLETS, a relative humidity of only SLIGHTLY ABOVE 100% is enough for the droplet to

grow.


99

99.5

100

100.5

101

101.5

102

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

For very small droplets, the relative humidity has to be MUCH MORE THAN 100% for the droplet to grow—homogeneous

nucleation in nearly impossible for small droplets!

The Kohler Curve for Salt CCNsKohler Curve for NaCl

99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

100.6

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

The Kohler Curves for most CCNs look something like this—there is a “hump” in the curve.


99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

100.6

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

Above the “hump”, the droplet will ALWAYS grow, regardless of its size. This is the “critical supersaturation”, S*.

R*

S*


99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

100.6

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

Suppose that we have a droplet and the relative humidity is greater than the critical supersaturation. The droplet will

grow.

R*

S*


99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

100.6

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

As the droplet grows, notice that it is still supersaturated and will continue to grow without limit. The droplet has become

“activated”.

R*

S*

Let’s zoom in on part of the graph…

Kohler Curve for NaCl

99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

100.6

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

R*

S*

Very small droplets can grow, even at relative humidities less than 100%!


99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

100.6

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

R*

S*

However, these droplets soon will be BELOW the curve and are now SUBSATURATED, meaning that they will shrink.


99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

100.6

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

R*

S*

Before long, these droplets will be exactly ON the Kohler curve, and they will neither grow nor shrink.


99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

100.6

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

R*

S*

This is how HAZE happens! Haze is composed of very small droplets of water at relative humidities LESS THAN 100% (as low as 70%). The haze droplets neither grow nor shrink, so

they don’t fall out as precipitation!


99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

100.6

0.075 0.275 0.475 0.675 0.875


Rel

ativ

e H

um

idit

y (%

)

R*

S*

Droplets that are bigger than the “hump” of the curve (that is, the “critical radius”, will always be supersaturated and will

grow without limit.

Something to think about…

• Look back at the Kohler Equation.

• Consider how the mass of the solute influences the solute effect.

• An important question: which nuclei activate first—large nuclei or small nuclei?

The Bad News About Nucleation

• Nucleation is much too slow to ever produce a rain drop.

• Rather, nucleation produces large numbers of very small droplets, which can then grow by other processes.

A Second Process For Growth of Droplets: DIFFUSION!

Diffusion

• What is diffusion?• Motion of water vapor molecules…• By random, “brownian” motions…• Which transport water DOWN THE GRADIENT.

Diffusion

• It can be shown that the rate of transport of water TOWARDS the droplet by diffusion is given by:

x

rDF

Rate of Transport

Diffusivity (constant)

Water vapor gradient

VERY NEAR THE

DROPLET

Droplets Create A Moisture Gradient!

drier

drier

drier

drier

Small droplets make a very STRONG gradient

drier

drier

drier

drier

Large droplets make a very WEAK gradient!

drier

drier

drier

drier

Diffusion

• So SMALL DROPLETS GROW QUICKLY by diffusion…

• And LARGE DROPLETS GROW SLOWLY by diffusion…

• So you can see that the small droplets are going to “catch up” in size with the big droplets!

“Monodisperse”

• A cloud has become “monodisperse” when all of the droplets in the cloud are about the same size.

• Clouds become monodisperse through the process of diffusion.

Limit to Diffusion

• There is a limit to how big a droplet can grow by diffusion.

• Given by equation 8.9 in Stuhl.

• This limit is MUCH smaller than a raindrop.

• THEREFORE, diffusion cannot explain how rain forms!

Diffusion and Ice Crystals

• Ice Crystals can grow by diffusion, too.

• Two competing processes:1. Water molecules want to freeze into hexagonal

grids with as many molecules near them as possible.

2. Condensation scavenges water vapor from the air, so to grow the parts of the ice crystal need to be as far apart as possible.

As Near As Possible…

The molecules tend to form PLATES of ice.

As Far As Possible…

The molecules tend to form BRANCHES of ice.

• The final form of the ice crystal depends very sensitively on which process dominates.

• Ice crystals tend to be made of some combination of these shapes.

Dendrites

Needles

Plates

Columns

A Final Way For Droplets To Grow:

Falling at the “terminal velocity”

• Peak terminal velocity is about 11 m/s

• Faster than that, the droplets just break up into smaller droplets that will fall slowly.

Coalescence

Aggregation

Riming

Collision is not too effective…

• …when the cloud droplets are “monodisperse”.

Bergeron Process

• …That’s why we need the Bergeron Process!

Claussius-Clapeyron EquationS

atur

atio

n V

apor

Pre

ssur

e

Temperature

supersaturated

unsaturated

Claussius-Clapeyron EquationS

atur

atio

n V

apor

Pre

ssur

e

Temperature

water

ice

Sat

urat

ion

Vap

or P

ress

ure

Temperature

water

ice

A water droplet at this temperature and pressure will be subsaturated and shrink.

Sat

urat

ion

Vap

or P

ress

ure

Temperature

water

ice

An ice crystal at this temperature and pressure will be supersaturated and GROW.

x

The Bergeron Process

The Bergeron Process

The cloud is no longer monodisperse, so the process of collision and riming becomes very efficient!

chapter 8: precipitation ats 572. “precipitation” can be: 1.rain 2.snow 3.hail 4.etc. however,...

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