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GEU 0047: Meteorology
Lecture 7
Precipitation
Precipitation Types
• Precipitation: The deposit of water (solid or liquid) falling
from the clouds and reaching the ground. It includes the
following types:
– drizzle
– rain
– snow
– sleet (雨夾雪)
– hail (冰雹)
– Glaze (also verglas; 雨淞)
Water Droplet Sizes
Rates of
condensation
and evaporation
control the
increase and
decrease in
water droplet
sizes.
Why “droplet” ? Why not “balls” ?
• Saturation (equilibrium) vapor pressure varies with surface area
because the evaporation does also.
• Water molecules are less attached to a curved surface and therefore
evaporate more readily.
• More water vapor is needed to reach equilibrium over a curved
surface.
• The Curvature effect lessens when the diameter is larger than 10 μm.
Curvature Effect
Greater curvature means a higher Relative Humidity (R.H.) is
needed to achieve equilibrium over the larger surface area.
Smaller
droplets
evaporate more
easily.
Only large
droplets
can survive at
lower R.H.
Condensation Droplets
• Typical scenario: adiabatic cooling of ascending air parcel.
• It passes the condensation level and water begins to
condense on condensation nuclei, especially hydroscopic.
• Soon, all of the condensation nuclei have seeded tiny water
droplets and condensation slows down. (Wet Haze)
• Condensation alone can produce water droplets on the order
of ~ 20 mm in radius. Further growth requires dropletdroplet interactions.
Solute Effect of Condensation Nuclei
Hydroscopic condensation nuclei allow droplet formation and
growth with less than 100% R.H. (as low as 75% R.H.)
They increase the likelihood of encounters between water
vapor and liquid droplets.
A solution (water and nuclei) also keeps water vapor from
evaporating so easily as it lowers the saturation vapor
pressure (i.e., solute effect).
Condensation Radius
• Supersaturation versus condensation nuclei radius
Concept of Air Friction
• Friction is dependent upon droplet surface area and velocity.
• Frictional force ~ r2v2
Ff = 4 p r2 k v 2
As the velocity increases, so does the frictional force.
When the acceleration due to the frictional force is
equal to the gravity, no acceleration takes place.
When velocity stops changing, this is terminal velocity.
Physics of Terminal Velocity
FORCE = Weight - Air resistance
ma = mg - Ff
Ff = 4pr2kv2
a = g - Ff/m
Acceleration occurs as long as the acceleration due to
gravity is greater than the acceleration due to the
frictional force.
Droplet weight (gravity) must overcome drag (air resistance).
The droplet mass must grow.
Terminal Velocity
• Gravity increases faster than drag with radius. WHY?
• Weight = r 4/3 p r3
depends on volume
• Drag = 4 p r2 kv2
depends on area
Vterminal = r1/2
weight = drag
• The terminal velocity increases as drop radius increases.
• Both gravity and drag increase with radius, one because of
mass the other because of surface area. Weight is faster.
• This is even ignoring updrafts. So size does matter!
Drop Size
• For a drop to fall, weight (r3) must overcome drag (r2).
• Therefore, it has to grow to a large enough size.
• Cloud drops are 1 million times smaller in total volume than
rain drops.
How Fast
A typical raindrop (2000 mm, 6.5 m/s) falls 600x faster than
a typical cloud droplet (20 mm, 0.01 m/s).
Using an average cloud height of 6500 meters and D = v t,
the time required for a drop to fall to the ground,
train = 6500 m/6.5 m/s
tdroplet = 6500 m/0.01m/s
= 1000 s
~ 16 minutes
= 160 hours
in CALM air, ignoring wind or updrafts.
Collision/Coalescence
With a random distribution of sizes, droplets interact because
of their differences in terminal velocities.
N
Size
Clouds
Most clouds do not produce precipitation as condensation and
evaporation continue to work at similar rates on small droplets
within the clouds.
Condensation nuclei and condensation working alone would
take days to form large enough drops to fall to the ground.
Warm Clouds
Warm clouds: Clouds that
do not have ice crystal
formation.
Collision/Coalescence
is the ONLY
droplet growth
mechanism.
Largest rain
drops hit the
ground first.
Stratus
Stratus: cloud droplets can be small
Very little vertical motions (updrafts), so small droplets
with small terminal velocities may reach the ground.
There is less time for collision and coalescence in the thin
stratus layer, so small drops are numerous. Drizzle and/or
misty rain is common.
Cumulus
Cumulus: cloud droplets can be very large.
Very large vertical motions (updrafts), so only large enough
heavy drops can make it to the ground.
There is more time for collision and coalescence in the
thick cumulus cloud with large vertical development, so
large drops are numerous.
Towering cumulus can produce heavy rain and even hail.
Ice Nuclei
In order for non-homogeneous freezing to take place at higher
temperatures, ice nuclei that are structurally similar must be
present to initiate freezing.
Silver and lead iodide, cupric sulfide (硫酸銅), kaolinite (高嶺
土) are examples.
Natural sources include clay soils, plant material, bacteria and
of course ice. Without these ice nuclei, saturated air will be
supercooled (often to ~ -40oC) before freezing would actually
take place.
Cloud Seeding
a form of weather modification (often refer to increase
rainfall.)
Providing ice nuclei with the right geometry to facilitate
condensation, growth and precipitation. (CO2 drop; i.e., dry
ice)
Cloud Seeding
• Static mode: add ice crystals (silver iodide or dry
ice) to cold clouds.
• Dynamic mode: enhance vertical air currents in
clouds and thereby vertically process more water
through the clouds. Usually a much larger number
of ice crystals is added to the cloud than in the
static mode.
• Hygroscopic mode: salt crystals are released into
a cloud. These particles grow until large enough to
cause precipitation. Clouds can be seeded from
above with the help of airplanes or from the
ground using rockets
Cool Clouds
Colder clouds have ice nuclei which allow faster growth rates
for cloud droplets.
Water Versus Ice
es = eo exp{L/Rv (1/To-1/T)}
Saturation Vapor Pressure
Saturation Vapor Pressure
For equilibrium between condensation and evaporation, more
water vapor is needed over water than over ice.
(Curvature and Temperature are the difference)
Maximum SVP Difference
Supercooled water vs. Ice
occurs when T ~ - 12 oC
Ice Crystals
Some water vapor
sublimates onto ice.
This removes water vapor
from the air and then causes
more evaporation of water
in order to establish
equilibrium.
BUT adding more water
vapor to the air, increases
ice crystal growth.
Bergeron Process
Evaporation is larger near
droplet, condensation is
larger around ice nuclei.
Water diffuses from drop
to ice.
Removing water vapor
increases evaporation
around droplet.
Ice crystals grow at the
expense of water droplets.
Ice Crystal Growth
• Two mechanisms facilitate the growth of ice crystals.
– Accretion: the growth of ice crystals as supercooled water
freezes onto them.
– Aggregation: the coalescense of ice crystals through adhesion
(falling ice crystals collide and stick to other ice crystals).
Accretion
Most precipitation begins with
falling ice crystals as they have
much higher growth rates than
water droplets acting under
condensation alone.
The physical conditions those ice
crystals encounter as they fall
ultimately determines the type
of precipitation that reaches the
ground.
Aggregation
Growth of dendrite ice crystal
otherwise known as snow
through aggregation and
adhesion.
Dendrite (snow) is favored
because its growth rate is the
highest at the maximum
difference in S.V.P. between
water and ice near -12oC.
Snow Flakes
• Dendrite Ice Crystals
Fracturing
Collision and fracturing provide
more ice nuclei.
Ratios of ice nuclei to droplets
1:100,000
precipitation
1:1
nothing
100,000:1
nothing
Even ice needs to get heavy
to fall.
Ice Crystal Habits
Ice crystal growth
is dependent upon
pressure and
temperature.
Growth rates are
highly dependent
upon the S.V.P.
difference between
water and ice.
Precipitations
• LIQUID
– Virga (wispy rain)
– Mist
– Drizzle
– Rain
virga
• ICE (Graupel:雪丸)
– Freezing Drizzle
– Freezing (Icy) Rain (Glaze)
– Sleet (雨夾雪)
– Snow
– Hail
sea mist
Rain or Snow?
Melting Level is a function of season, higher up in summer.
Rain Profile
• A deep warming layer always results in rain.
Rain
Rain Intensities (inch/hour)
Light
0.01- 0.10
Moderate
0.11- 0.30
Heavy
> 0.30
Rain Gauges
• All official rain gauge instruments have 8-inch diameter
openings.
Simple
Standard
Advanced
Rain Radar Intensity
dBZ = 10 log Z
log Z =
log (power)
+2 log(range)
+ constant
Rain Radar Intensity
• dBZ stands for decibels of Z, a
meteorological measure of equivalent
reflectivity (Z) of a radar signal reflected off
a remote object.
• The common reference level for Z is 1 mm6
m-3, which is equal to 1 μm3. It is related to
the number of drops per unit volume and
the sixth power of drop diameter.
Difference
between
dBZ(67,116)
and
vector(73,122)
estimations for
the center of
typhoon Nari is
about 7.8km
Precipitation Frequency
Virga
• Precipitation that evaporates before reaching the ground
Snow Profile
• Temperatures well below freezing allow snow to reach the
ground.
Snowfall Intensity
• Snowfall intensity is not measured by accumulation as in
the case of rainfall, usually.
• Intensity is measured by visibility (or lack thereof).
Heavy
Moderate
Light
< 0.25 mile
0.25 - 0.50 mile
> 0.50 mile
(~ 6 inch/day)
Snowfall Frequency
Sleet Profile
• A very deep freezing layer causes supercooled water
droplets to freeze into tiny ice pellets before reaching the
ground.
Sleet Formation
• The formation of sleet along a warm front.
Glaze Profile
• A shallow freezing layer allows supercooled water droplets
to freeze upon contact creating an ice coating.
Glaze
Very beautiful,
very heavy,
very dangerous,
very damaging.
Glaze
Glaze
Glaze
Graupel
• The tiny ice pellets that collect from ice crystals, can form
very large raindrops (upon melting), very clumpy snow, and
is the source for hail.
Hail Storm Frequency
Hail
Graupel ice that is allowed to
accumulate by accretion
and/or aggregation.
Associated with strong
updrafts.
The larger the hail, the stronger
and more severe the storms
associated with the strongest
updrafts.
Hail Formation
The tiny ice pellets
(graupel) can make
many trips up and
down in a large
cumulonimbus
cloud.
Each trip adds another
layer, like rings on a
tree for each season.
Rime
• Supercooled water droplets (freezing fog or drizzle) can
create a winter wonderland when deposition takes place.
Summary