AOSC 620 Formation and Growth of Ice Crystals
A hailstone found in Vivian, SD by Les Scott July 23, 2010 was the record largest
U.S. hailstone by weight and diameter. Previous record 2003. This 8-inch
diameter stone, pictured above, weighed in at an incredible 1.94 lbs. Updraft
estimated at 75 m/s. BAMS 91(10), 2010.
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AOSC 620
Formation and Growth of Snow and Ice
(Cold Cloud Microphysics)
(Rogers and Yau Chapt. 9; Wallace and Hobbs, Chapt. 6)
Russell Dickerson
<http://www.courseevalum.umd.edu/>
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“Now, if you haven't heard this, the ice at the North
Pole, arctic ice, is at a record amount this early in the
post-summer season.”
http://www.rushlimbaugh.com/daily/2014/09/08/satell
ite_images_prove_algore_s_melting_ice_cap_predictio
n_wrong
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AOSC 620 Formation and Growth of Ice Crysta
Background Ideas
•Direct observations show that supercooled liquid
cloud water is common at temperatures well below
0°C (i.e., -20°C)
•Small droplets of pure H2O freeze only below
temperatures of -40°C, the spontaneous freezing
level.
•At higher temperatures, pure water droplets freeze
only if injected with tiny foreign particles called ice
nuclei.
•The equilibrium vapor pressure over ice is lower
than that over liquid water.
March 2, 2009
Getty Images / Win McNamee
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Water favors ice.
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High LWP
Low LWP
Air pollution aerosols inhibit precipitation from
relative thin clouds associated with gentle, warm rain
but invigorate deep, icy clouds related to heavy rain
lightning, and severe weather. ARM site in Oklahoma;
Feng Niu (2010)
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Mixed-phase
Liquid
Mixed-phase
Liquid
Impact of aerosols on tropical clouds. Precipitation rate (left)
and corresponding cloud top temperature (right) as functions of
AI (OMI Aerosol Index) for mixed-phase (blue dots) and liquid
clouds (red dots) over ocean. Please note only clouds with the
precipitation rate higher that 1 mm/h are included here. The far
right axis is oC is for liquid clouds. From Feng Niu, 2010.
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Common Ice Crystal Shapes
Hexagonal Plates
Stellar Crystal/
Dendrites
Hexagonal Prisms
Ice needles
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Goal: To shed light on the origin of the myriad of sizes and shapes
of ice and snow. These shape categories are called “habits”.
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http://www.its.caltech.edu/~atomic/sno
wcrystals/class/snowtypes4.jpg
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Molecular Structure of Ice
X-Ray and neutron diffraction experiments have shown
the basic crystal structure of ice at atmospheric
temperatures to consist of six oxygen atoms arranged
in a hexagon. Each oxygen atom is bonded to two
hydrogen atoms and (if you count H-bonding) each
hydrogen is bonded to two oxygen atoms.
O H O
O
O
O
H
O
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Ice in the hexagonal
crystalline structure.
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Ice Formation
Generally considered to be of two types
1. Deposition - transformation from vapor to solid
(the reverse is sublimation) Note that
homogeneous deposition does not
occur in the atmosphere.
2. Freezing - transformation from liquid to solid.
Includes riming, the freezing of
supercooled water droplets.
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Qualitative Description of Freezing
(homogeneous)
• Consider a volume of air with T < 0°C in which
water droplets are suspended.
• The H2O molecules in a drop at a given instant
may come into temporary alignment similar to that
of an ice crystal. This lower entropy increases the
free energy of the transition.
• Such molecular aggregates may grow but they may
also be destroyed by random molecular motions.
• If an aggregate happens to grow to such a size that
it is no longer affected by these thermal agitations,
the entire droplet quickly freezes. The probability
of growth of an aggregate to this critical size
increases as T decreases. (Fleagle and Bussinger)
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H 2O l ↔ H 2O s
DG = DH –T Df = 0 at 273 K
DH = – 6008 J/mole (334 J/g)
Df = DH/T = 334/273 = – 1.22 J/gK (22.0 J/moleK)
• As the temperature drops, the free energy becomes
more negative.
• Liquid cloud water at temperatures below – 40°C
is rare, but supercooled water is common, and a
hazard to aviation.
• Bottom line: Homogeneous nucleation doesn’t
happen in real clouds.
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Qualitative Description of Freezing
(heterogeneous)
• Add a foreign particle to droplet
• The particle makes the initial growth more
probable by attracting a surface layer of H2O
molecules on which the ice crystal lattice can form
more readily than in the interior of the liquid.
• Freezing of a droplet requires that only one
aggregate reach critical size.
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Ice Nucleation Mechanisms
• Heterogeneous Deposition - vapor is
transformed to ice on a nucleus.
• Condensation Followed by Freezing - droplet
forms on a nuclei which then freezes.
• Contact - nuclei makes contact with a droplet
which then freezes (airplane wing).
• Immersion- nuclei becomes immersed in a droplet
which then freezes about the nuclei.
The relative importance of the different modes has not
been established. It is difficult to distinguish between
deposition and freezing mechanisms. Usually refer to
the process as ice nucleation and the nuclei as ice nuclei.
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Ice Forming
Nuclei
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Important Features of Ice Nuclei
• Temperature
• Lattice structure - many of the most active
natural nuclei have crystal structures similar to
ice.
• Molecular binding • Low interfacial energy
Theory not yet able to explain which is most
important but, the most common natural nuclei
appear to be surface clays such as kaolinite.
However, it has been discovered that bacteria in
decaying plant leaf material can be effective nuclei,
but its importance has not yet been established.
(Russ Schnell & Gabor Vali)
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Ice in the hexagonal
crystalline structure.
Silver iodide (AgI) in the
hexagonal crystalline
structure.
Solubility is low ~3 × 10−7 g/100mL, at 20
°C.
[Bernard Vonnegut, the older brother of the late
novelist Kurt, uncovered silver iodide's weathermodifying properties as a researcher for General
Electric in 1946. He later taught atmospheric
science at the State University of New York at
Albany before passing away in 1997. See Cat’s
Cradle by K. Vonnegut]
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Kaolinite (Al2Si2O5(OH)4) Clay Particles
Ca2+ Mg2+ K+
Electron micrograph.
Acids can replace nutrient
cations with H+ for
efficient nucleation, but in
soils, acids reduce fertility.
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Ice Nuclei Concentration
Typical concentration is one nucleus per liter of air at a
temperature of -20°C, increasing by a factor of ten for each
additional 4°C of cooling. However, the count on any given
day may be greater or less than the typical values by an
order of magnitude!
Taking 104 cm-3 as the typical concentration of atmospheric
aerosols, one nucleus per liter is only one aerosol particle in
107. That is, ice forming nuclei are a very rare component of
atmospheric aerosols.
The concentration of active ice nuclei is a strong function of
temperature.
ln(N) = a(T1 – T)
Where N is the number of ice nuclei, 0.3 < a <0.8, and T1 is
the temp for one active ice nucleus per liter.
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N (m-3)
Number of active ice nuclei as a
function of supersaturation.
S (or –DT)
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If Nuclei Are So Rare, Why Are There
So Many Crystals?
Once freezing of supercooled droplets starts, it
progresses rapidly through a cloud.
Drop + nucleus
Thin film of transparent
ice on outside
As interior freezes and expands
the outer shell may rupture through
which a jet of water emerges and
freezes to form a spike
Also,
collisions between crystals
The entire shell
may explode to
produce hundreds of
splinters, each of
which can act as a
freezing nucleus
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Diffusional Growth of Ice Crystals
Basic Assumptions
• The surface of the crystal has uniform temperature;
therefore, it has uniform vapor pressure.
• The vapor pressure at an infinite distance is
assumed uniform as is the temperature.
• The vapor pressure and vapor density in the
neighborhood of the crystal may be represented by
surfaces that follow the contour of the crystal.
• Beyond a certain neighborhood of the crystal these
surfaces approach a spherical shape.
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Vapor Diffusion
Contours of
vapor density
The flux of water vapor to the crystal by diffusion occurs
in the direction normal to the surfaces of constant vapor
density. Therefore, near a sharp point vapor diffuses
toward the point from all directions. Ice may accumulate
more rapidly there than on flat surfaces.
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Ice Crystal Growth Equations
(similar to eq’s for liquid water)
dM
= 4CD(  v   vc )  Diffusion Eq.
dt
dM
Ls
= 4CK (Tc  T )  Conduction Eq.
dt
 Ls  1 1  
esi = esi (T ) exp       CC Eq.
 Rv T Tc  
where Tc and T are the temperatures of the crystal
and environment (), respectively, K is the thermal
conductivity of air, and C is the crystal shape factor.
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Shape Factor
The shape factor is nothing but the capacitance of an object. It depends on the
geometrical shape of the crystal. It has units of length. Examples:
Sphere C = r
Prolate spheroid (football) of major
and minor semi-axes a and b
Circular disk
C =
2r
C=

a 2  b2
a 
ln 



a 2  b 2 
b
 

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Crystal Growth Rate Estimate
Let
e
e
Si =
=
esi
ei
Si denotes saturation ratio w.r.t. ice
Following the procedure used for a water
droplet (S is the saturation w.r.t. liquid
water) we obtain:
dM
=
dt
Note that
( S i  1)
2
s
RvT
L

4DCesi RvT2 4KC
= M 'ice
 e es 
es 
Si =  
= S


es esi 
esi 
Supersaturation wrt ice (Si) grows linearly as cloud temps drop below 273 K.
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Comparison of Droplet and Crystal Growth
For a liquid water droplet of radius r
dM
4r ( S  1)
=
= M 'w
2
RvT
Lv
dt

Des RvT2 KC
For an ice crystal
4C ( Si  1)
dM
=
= M 'ice
2
RvT
Ls
dt

2
Desi RvT K
At T = -15°C and
for S = 1.001
M 'ice
C
 120
M 'w
r
R&Y Figure 9.4
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Saturation Vapor Pressure Relative
to Ice and Liquid Water
7
4
e s (T)
3
e (T)
2
si
0.2
0.1
e s (T) - e si (T)
s
e (T) (mb)
s
5
Saturation Vapor Pressures
at Different Temperatures
e (T) - e si (T) (mb)
6
0.3
1
0
-40
-35
-30
-25
-20
-15
Temperature (°C)
-10
-5
0
0
-40
-35
-30
-25
-20
-15
-10
-5
0
Temperature (°C)
Absolute value of es – ei peaks ~ – 12oC, but
relative difference grows at lowest temps.
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From Eq. 9.4 we see that the ice growth rate due to diffusion
varies inversely with pressure (faster diffusion) and reaches a
max near – 15oC at tropospheric pressures.
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Why so many forms and shapes of ice?
Growth of
different
shapes is
temperature
dependent
A molecular kinetic approach is required to explain
different habits/shapes.
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Growth by Accretion
Definitions (following Rogers and Yau, 1989;
Glossary of Meteorology, 2000)
Accretion is the capture of supercooled droplets by an
ice-phase precipitation particle. If the droplets freeze
immediately on contact, this forms a rimed crystal or
graupel. Slow freezing creates a denser structure;
e.g., hail (dia. hail > 5 mm).
Coalescence is the capture of small cloud droplets by
larger cloud drops.
Agglomeration is the collection of smaller ice
particles.
Aggregation is the clumping together of ice crystals to
form snowflakes
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Growth by Accretion - cont.,
or how do we get rain and snow?
The derivation of an equation for the continuous growth of ice
crystals by capture of other crystals or cloud droplets would
follow the same procedures as for liquid drops. Complications
arise due to difficulties in prescribing the dependence of crystal
fall speeds and their collection efficiencies.
Snowflake sizes indicate that significant aggregation occurs only
for T > -10°C.
dM
= Ew l R 2 V (Rogers and Yau , eq. 9.8)
Accretional growth
dt
dM
= Ew i R 2 (V  v) (eq. 9.9)
Aggregational growth
dt
E – collection Efficiency; wl liquid water mass; M condensed water
mass (R&Y use m for mass of particle); R – radius; V – fall speed.
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Crystal Fall Speeds
Fig. 9.7 from Rogers and Yau, 1989
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Snowflake Growth - Qualitative
• Must have an appropriate number of ice nuclei to
initiate freezing - 0.1 to 1 per liter at -20°C.
• Crystals form around nuclei and grow by diffusion.
• A few crystals grow faster and larger than their
neighbors by either enhanced diffusion or by
chance collisions with other crystals or droplets.
• These crystals fall faster than their neighbors and
grow by diffusion and by collisions with other
crystals or cloud droplets until they reach a size
where they can fall against an updraft and reach
the ground. A snowflake of 1 cm diameter requires
a cloud depth of about 1500 m.
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Both coalescence and aggregation can happen in a Cb.
Times Required for Growth is different.
Droplet collision - coalescence
crystal - diffusional
growth
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Precipitation Growth - Summary
•Condensation-diffusion is more effective for ice clouds
than for water clouds.
•In warm clouds, coalescence is the major scheme for
precipitation to occur.
•In cold clouds, both diffusion and aggregation are
important.
•Ice nuclei remain mysterious.
•Loss is glaciers and sea ice is a major environmental
threat.
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Some papers on clouds and ice.
•
Herman J. R., G. Labow, N. C. Hsu, D. Larko (2009), Changes in cloud and
aerosol cover (1980–2006) from reflectivity time series using SeaWiFS, N7-TOMS,
EP-TOMS, SBUV-2, and OMI radiance data, J. Geophys. Res., 114, D01201,
doi:10.1029/2007JD009508.
•
Weigelt A., M. Hermann, P. F. J. van Velthoven, C. A. M. Brenninkmeijer, G.
Schlaf, A. Zahn, A. Wiedensohler (2009), Influence of clouds on aerosol particle
number concentrations in the upper troposphere, J. Geophys. Res., 114, D01204,
doi:10.1029/2008JD009805. Waliser D., et al. (2009),
Cloud ice: A climate model challenge with signs and expectations of progress, J.
Geophys. Res., 114, D00A21, doi:10.1029/2008JD010015.
20 July 2009 | Nature | doi:10.1038/news.2009.705, How raindrops fall
Exploding drops produce miniature showers. By Fiona Tomkinson concerning
Villermaux, E. & Bossa, B. Nature Phys. doi:10.1038/NPHYS1340 (2009).
•
•
•
•
Climate Effects of Aerosol-Cloud Interactions By: Rosenfeld, Daniel; Sherwood,
Steven; Wood, Robert; et al., SCIENCE Volume: 343 Issue: 6169 Pages: 379380, JAN 24 2014
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Stopping By Woods On A Snowy Evening
Robert Frost
Whose woods these are I think I know.
His house is in the village though;
He will not see me stopping here
To watch his woods fill up with snow.
He gives his harness bells a shake
To ask if there is some mistake.
The only other sound's the sweep
Of easy wind and downy flake.
My little horse must think it queer
To stop without a farmhouse near
Between the woods and frozen lake
The darkest evening of the year.
The woods are lovely, dark and deep.
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.
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