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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(Cold Cloud Microphysics)
(Rogers and Yau Chapt. 9; Wallace and Hobbs, Chapt. 6)
Russell Dickerson
<http://www.courseevalum.umd.edu/>
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http://arctic.atmos.uiuc.edu/cryosphere/multiyear.ice.quikscat.mov
3

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 H
2
O 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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5

Low LWP
High 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)
6

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 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 o C is for liquid clouds. From Feng Niu, 2010.
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Hexagonal Plates Hexagonal Prisms
Stellar Crystal/
Dendrites
Ice needles
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Goal: To shed light on the origin of the myriad of sizes and shapes of ice and snow.
9

http://www.its.caltech.edu/~atomic/sno wcrystals/class/snowtypes4.jpg
10

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.
12

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.
13

• Consider a volume of air with T < 0 ° C in which water droplets are suspended.
• The H
2
O 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)
14

H
2
O l
↔ H
2
O s
D G = D H –T D f = 0 at 273 K
D H = – 6008 J/mole (334 J/g)
D f = D H/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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• Add a foreign particle to droplet
• The particle makes the initial growth more probable by attracting a surface layer of H
2
O 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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• 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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• 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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Al
2
Si
2
O
5
(OH)
4
Ca 2+ Mg 2+ K +
Electron micrograph.
Acids can replace nutrient cations with H + for efficient nucleation, but in soils, acids reduce fertility.
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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 10 4 cm -3 as the typical concentration of atmospheric aerosols, one nucleus per liter is only one aerosol particle in
10 7 ! 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(T
1
– T)
Where N is the number of ice nuclei, 0.3 < a <0.8, and T
1 the temp for one active ice nucleus per liter.
is
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S (or – D T)
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Once freezing of supercooled droplets starts, it progresses rapidly through a cloud.
Drop + nucleus
As interior freezes and expands the outer shell may rupture through which a jet of water emerges and freezes to form a spike
Also
Thin film of transparent ice on outside
, 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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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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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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(similar to eq ’ s for liquid water
) dM dt
=
4

CD (
 v 
  vc
)

Diffusion Eq .
L s dM
=
4

CK ( T c

T

)

Conduction Eq .
dt e si
= e si
( T

) exp
L s
R v



1
T


1
T c




CC Eq .
where T c 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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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 Circular disk
C
=
2 r

Prolate spheroid of major and minor semi-axes a and b
C
= a
2 ln
 
 a

a
 b
2
2  b
2

 b

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Let S i
= e
 e si 
= e e i
S i
Following the procedure used for a water droplet (S is the saturation w.r.t. liquid water) we obtain:
Note that dM
= dt R v
T

4

DCe si 
( S i

1 )

R v
T

2
L s
2
4

KC
= 
' ice
S i
=

 e  e s




 e s
 e si



=
S
 e s
 e si



Supersaturation wrt ice (S i
) grows linearly as cloud temps drop below 273 K.
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For a liquid water droplet of radius r dM
= dt
4
 r ( S

1 )
R v
T

De s 

L
2 v
R v
T

2
KC
=
M ' w
For an ice crystal dM
= dt
4

C ( S i

1 )
R v
T

De si 

L
2 s
R v
T

2
K
=
M ' ice
At T = -15 ° C and for S = 1.001
M
M
' ice

120
' w
C r
R&Y Figure 9.4
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5
4
3
2
7
6
Saturation Vapor Pressures at Different Temperatures e e s si
(T)
(T)
1
0
-40 -35 -30 -25 -20 -15 -10 -5 0
Temp erature (°C)
0.3
0.2
0.1
e s
(T) - e si
(T)
0
-40 -35 -30 -25 -20 -15 -10 -5 0
Temperature (°C)
Absolute value of e s
– e i peaks ~ – 12 o C, 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 and reaches a max near – 15 o C at tropospheric pressures.
32

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.
33

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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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.
Accretional growth dM
=
Ew dt l

R
2
V (Rogers and Yau , eq. 9.8)
Aggregational growth dM
=
Ew i

R
2
(V

v) (eq. 9.9) dt
E – collection Efficiency; M condensed water mass
(R&Y use m); R – radius; V – fall speed.
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Fig. 9.7 from Rogers and Yau, 1989
36

• 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.
37

Both coalescence and aggregation can happen in a Cb.
Times Required for Growth is different.
Droplet collision - coalescence crystal - diffusional growth
38

•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.
39

• 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).
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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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