Transcript No Slide Title

Precipitation
Hydrometer: Any product of condensation or
sublimation of atmospheric water vapor, whether
formed in the free atmosphere or at the earth’s
surface, or blown by wind from the earth’s surface:
cloud, haze, fog, mist, drizzle, rain, ice pellets,
hail, snow, snow grains, ice crystals, virga,
blowing spray, dew, frost, glaze, etc.
Precipitation: Liquid water or ice that falls to the
earth’s surface.
Virga: Liquid water or ice that falls
towards but does not reach the earth’s
surface.
Aerosols: Small, suspended particles in the
atmosphere. Haze, smoke, fogs, dust,
pollen grains, etc. Note: Clouds are usually
not considered aerosols.
Processes that control the growth of
precipitation.
1. Nucleation: Any process by which the phase
change of a substance to a more condensed state
(such as condensation, deposition, and freezing)
is initiated about a particle (nucleus) or at a
certain locus, or place.

Condensation nuclei, freezing nuclei.
2. Diffusion: Transport of a property through a
medium. For precipitation growth, it is the
movement of water vapor molecules toward an
existing hydrometer.
3. Collision: Two hydrometers striking
each other and combining to form a larger
hydrometer.
Nucleation
Of liquid droplets.



Homogeneous: Occurring in clean air, no
impurities. Practically impossible.
Heterogeneous: Involves impurities in air.
Cloud Condensation Nuclei (CCN): A
particle, either liquid or solid, upon which
condensation of water vapor begins in the
atmosphere.
Number of CCNs of various sizes in the
atmosphere.
The smaller the size of the CCN, the greater
the typical number found in the air. The
number per unit volume, for nuclei greater
than 0.2 mm, can be related to the radius of
the CCN by:
4
n(R)  cwhere,
R
n = number
per volume,
R = radius
of particle,
c=a
constant dependant on total concentration of
particles.
Curvature Effect
A curved liquid water surface (pure water
droplet) requires more water molecules in vapor
state around it to achieve saturation (balance)
than a flat water surface.
If the air were saturated (with respect to a flat
water surface), it would be unsaturated with
respect to a curved surface and the droplet would
evaporate until a saturated state (with respect to
its curved surface) existed.
The smaller the droplet, the greater the
supersaturation (with respect to a flat surface) is
required to keep the droplet from evaporating.
Solute Effect
Once an impurity, such as a salt particle,
replaces a water molecule in the lattice
structure of the droplet, the equilibrium
vapor pressure (number of water vapor
molecules required to surround the droplet
to maintain equilibrium) decreases.
Therefore, the water droplet can maintain
itself at a lower vapor pressure and grow
when the vapor pressure increases.
Assume an unsaturated volume of air contains cloud
condensation nuclei of varying sizes.
The volume begins to cool and the relative humidity
increases.
When the RH reaches near 78%, condensation
begins on the majority of nuclei.
As the air cools further, RH increases. The CCNs
containing the most salts grow fastest. They require
the lowest vapor pressure to maintain equilibrium.
As RH approaches 100%, the curvature effect
becomes negligible for the larger nuclei but remains
appreciable for smaller droplets.
As droplets grow, they remove water vapor from the
air, which decreases RH.
But, continued cooling increases RH.
When particles are small, the cannot condense water
vapor very rapidly.
As they grow larger, they become more efficient in
removing water vapor.
Eventually, water vapor is removed at the same rate
it is being produced.
The smaller droplets are less efficient at removing
vapor, due to curvature effect, and may actually
decrease.
The larger droplets will continue to grow to become
cloud droplets because the curvature effect is
negligible.
Kohler Equation
Combination of Curvature and Solute Effect.
Ratio of actual saturation vapor pressure (in
equilibrium over a solution with a curved surface),
to vapor pressure over a flat pure water surface.
 c1 
exp

*
es
T  R 

es 1 c2 i  ms
3
Ms  R
Where,
T = absolute temperature (oK),
R = drop radius (mm),
i = number of ions per molecule in solution,
ms = mass of solute in the droplet,
Ms = molecular weight of solute,
c1 = 0.3335 oK mm,
c2 = 4.3 X 1012 mm3 g-1
Critical Radius, pg. 161
Peak of the Kohler curve for a particular CCN.
For a particular RH,



at larger radii, droplet
will grow;
at smaller radii, droplet
will shrink.
If RH becomes greater
than the peak of the
Kohler curve, the
droplets can grow unimpeded.
Location of peak changes
with solute mass changes.

For larger droplets,
critical radius peak is at
lower RH.
Left of the peak on Kohler curve:




Small CNN grow into small droplets that stop growing
at equilibrium state of humidity, temperature and solute.
Called haze droplets.
Can exist at RH < 100%
Aerosol swelling - e.g.,
wet haze droplets and
smog.
Right of the peak on Kohler curve:



CNNs are activated.
Continue to grow as
long as water vapor
is available.
Become cloud
droplets.
The radius of the droplet where the critical point
occurs (i.e., whether it will grow- be activated or
reach equilibrium and remain small) is given by:
c3 i  ms T
R 
Ms
2
m
m
13
where:
c3  3.868x10 o
K g
*
from
i (number of ions per molecule in
solution)
Ms (molecular weight of solute)
table 8-1
T in oK
The supersaturation fraction at this critical peak
*
e
c 4  Ms
is given by:
*
s
S 
where:
es 1

c4  1.278x1015
i  ms T
o 3
K
g
3
i (number of ions per molecule in
solution)
Ms (molecular weight of solute) from
table 8-1
T in oK
ms = mass of solute in the droplet
Activated Nuclei
Those nuclei to the right of the Kohler peak can
continue to grow as long as there is water vapor
to condense onto the droplet.
The number density (number of activated cloud
condensation nuclei per cubic meter) is
k
approximately: N
 c  100 S
CNN
8 3
c

1x10
m and k  0.7 for marit im e air
where:
c  6x108 m 3 and k  0.5 for continent al air
S is the supersaturation (eq. 8.3a)
The number is small compared to the total
number of particles in the air.
The distance between cloud droplets is given by:
1
3
CCN
xN
Nucleation of Ice Crystals
Processes that aid in freezing of liquid water
droplets:



Homogeneous freezing: When temperatures
approach -40oC, liquid water spontaneously freezes.
Deposition nucleation: Water vapor deposits directly
on ice crystals. Unlikely on particles of 0.1 mm or
less.
Immersion nucleation: Occurs for liquid droplets
which contain an ice nucleus. Freezes when reaches a
critical temperature below 0oC, dependent on the size
of the drop. See equation 8.8
Condensation freezing: Occurs when the nuclei
is more attractive as a condensation nuclei than as
a deposition nuclei. Water condenses on the
nucleus and immediately freezes.
Contact freezing: Supercooled liquid water
droplet strikes an ice crystal and freezes on the
ice crystal.
Ice Nuclei are substances with molecular
structures similar to ice. Notice Table 8.2 and the
temperatures at which certain ice nucleation
processes can begin with various ice nuclei.
Droplet Growth by Diffusion
(condensation and deposition)
3
 3 

rL
ai r


Using eq. 8.9, R 



4  wate r nCCN 

1
the typical
droplet size would have a radius of 2 - 50 mm;
typical cloud droplet sizes. Typical precipitation
drops range from 500 mm to 2000 mm.
Some other process rather than just diffusion
must be occurring to cause them to grow to
precipitation size.
For Ice Crystal Growth by
Diffusion
The type of ice crystal produced (habit) is
dependant on the temperature and supersaturation
existing at the time of formation. See figure 8.6
1-D crystals tend to gain mass faster than 2-D or
3-D
Wegener-Bergeron-Findeisen Process
At temperatures below 0oC, the equilibrium vapor
pressure over liquid water is greater than over an ice
crystal.
Therefore, in a cloud of mixed liquid droplets and
ice crystals, the ice crystal will tend to gain water
molecules at the expense of the liquid droplet.
If relatively few ice crystals are present, they can
grow large enough to precipitate by this process.
If they pass through air warmer than 0oC, they can
melt and arrive at the ground as rain.
Collision and Collection (Coalescence)
Only process for making precipitation size droplets
in warm clouds.
As droplets fall, those with greater mass fall fastest
and can collide with slower falling droplets. The
droplet can thus grow by this method.
Droplets blown upward by updrafts can also collide
and coalesce.
Not all colliding droplets coalesce. Apparently a
charge difference on the droplets aids in
coalescence.
Fall rate of droplets
Cloud droplets, aerosols R<40 mm: w  k1  R
where: k1 = -1.19x108 /m•s
 

0

w

k

 R
Droplets R = 500 to 1000mm:
2 

ai r 

1/2
where: k2 = -220 m /s

R  R 
0

Drops R = 20 to 2,500mm: w  c  w0  exp





R




1
where the density correction
1
1
2


factor, c, is:  70kP a
70kPa  2

c  


  
 P 
  ai r 
Ro = 2500mm, R1 = 1000mm, w0 = 12
m/s
2
Precipitable Water
Depth of water resulting from all water (vapor,
liquid, solid) precipitating from a column of unit
cross-sectional area extending between two levels.
Total precipitable water extends the column from
the surface to the “top of the atmosphere”.
rT
dW 
 PB  PT 
g  li q
g = -9.8 m/s2
 liq = 1000 kg/m3
Rainfall amounts at any particular location can be
much greater than indicated because airflow
advects moisture into the column during the
precipitation process.
Pressure must be converted to base units.
rT must be in kg/kg.
Rainfall estimates by Radar
Z = radar reflectivity factor = the measure of the
efficiency of a radar target in intercepting and
returning radar energy.
Z is dependant on the size, shape, aspect, and the
dielectric properties of the surface of the target.
It includes not only reflection, but also scattering
and diffraction.
For hydrometers, it is dependant on drop-size
distribution, number of particles per unit volume,
physical state of hydrometers (ice or water),
shapes of the individual elements of the group, if
asymmetrical, their aspect to the radar.
6
D

One simplified expression is:
Z
V
where: D = droplet diameter, V = volume.
This is a meteorologically defined expression
relating to droplet sizes.
A more complex, but accurate expression

is:
6
Z   D  N(D)dD
where, 0
N(D) = number concentration of size D
droplets per volume interval:
 D
where:
N(D)  N 0e
  is mean droplet size
No is number of particles per unit volume.
A radar expression is given as:
10
2
2




2 ln 2 

r
P
r
  2 
Z

3
2
2
  c 
Pt    G   3dB 
 
 K 

The radar reflectivity factor, Z, is
usually expressed in terms of decibels
where: dBZ  10log(Z )
Z-RR (rainfall rate)
A unique relationship between Z and RR does not
actually exist (has not been determined).
 0.0625dBZ 
Stull uses: RR  c 10
where, c = 0.036 mm/hr
National Weather Service Doppler radars use the
following as an average expression for various
forms of expected precipitation:
Z  300 R
1.4
R is in mm/hr
For drizzle: Z  140 R
1.5
For thunderstorms:Z  500R
For snow: Z  2000 R2
For hail: varies from:
1.5
Z  84000 R
1.29
to Z  22500 R
1.17
Problems:
N1 (b, d, f), N2(b, d, f), N5 (c, h), N7 (c, h),
N9 (d, e), N10, N11 (d, f, h), N16, N18 ( a,
c, d, f), N21 (a), N23.
SHOW ALL EQUATIONS USED AND
CALCULATIONS