Upload
rosamund-rogers
View
218
Download
2
Embed Size (px)
Citation preview
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”.
“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”.
Evaporation rate INCREASES as radius of curvature
DECREASES!
“The Curvature Effect”
• 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
This is equation 8.2 in Stuhl.
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
This is equation 8.2 in Stuhl.
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
This is equation 8.2 in Stuhl.
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.
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 (%
)
Regions above the curve are supersaturated: a droplet with that size will GROW at that relative humidity.
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 (%
)
Regions below the curve are subsaturated: a droplet with that size will SHRINK at that relative humidity.
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 (%
)
For very large PURE WATER DROPLETS, a relative humidity of only SLIGHTLY ABOVE 100% is enough for the droplet to
grow.
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 (%
)
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
Droplet Radius (microns)
Rel
ativ
e H
um
idit
y (%
)
The Kohler Curves for most CCNs look something like this—there is a “hump” in the curve.
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
Droplet Radius (microns)
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*
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
Droplet Radius (microns)
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*
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
Droplet Radius (microns)
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
Droplet Radius (microns)
Rel
ativ
e H
um
idit
y (%
)
R*
S*
Very small droplets can grow, even at relative humidities less than 100%!
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
Droplet Radius (microns)
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.
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
Droplet Radius (microns)
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.
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
Droplet Radius (microns)
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!
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
Droplet Radius (microns)
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
Riming
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 Bergeron Process
The cloud is no longer monodisperse, so the process of collision and riming becomes very efficient!