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AOSC 620 Formation and Growth of Ice Crystals

Lecture 24

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. BAMS91(10), 2010.


AOSC 620Formation and Growth of Snow and Ice(Cold Cloud Microphysics)(Rogers and Yau Chapt. 9; Wallace and Hobbs, Chapt. 6)Russell Dickerson



“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.”



AOSC 620 Formation and Growth of Ice Crystals

Lecture 24

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


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)







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 oC is for liquid clouds. From Feng Niu, 2010.

common ice crystal shapes
Common Ice Crystal Shapes

Hexagonal Plates

Hexagonal Prisms

Stellar Crystal/


Ice needles


molecular structure of ice













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.

ice formation
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.

qualitative description of freezing homogeneous
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)
H2Ol ↔ H2Os

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.

qualitative description of freezing heterogeneous
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.
ice nucleation mechanisms
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.

important features of ice nuclei
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)


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 weather-modifying 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]

Ice in the hexagonal crystalline structure.

kaolinite al 2 si 2 o 5 oh 4 clay particles
Kaolinite (Al2Si2O5(OH)4) Clay Particles




Acids can replace nutrient cations with H+ for efficient nucleation, but in soils, acids reduce fertility.

Electron micrograph.

ice nuclei concentration
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.

number of active ice nuclei as a function of supersaturation
Number of active ice nuclei as a function of supersaturation.

N (m-3)

S (or –DT)

if nuclei are so rare why are there so many crystals

Thin film of transparent ice on outside

Drop + nucleus

If Nuclei Are So Rare, Why Are There So Many Crystals?

Once freezing of supercooled droplets starts, it progresses rapidly through a cloud.

The entire shell may explode to produce hundreds of splinters, each of which can act as a freezing 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, collisions between crystals

diffusional growth of ice crystals
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.
vapor diffusion
Vapor Diffusion

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.

Contours of

vapor density

ice crystal growth equations similar to eq s for liquid water
Ice Crystal Growth Equations(similar to eq’s for liquid water)

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.

shape factor

Sphere C = r

Circular disk

Prolate spheroid of majorand minor semi-axes a and b

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:

crystal growth rate estimate

Note that

Crystal Growth Rate Estimate


Following the procedure used for a water droplet (S is the saturation w.r.t. liquid water) we obtain:

Supersaturation wrt ice (Si) grows linearly as cloud temps drop below 273 K.

comparison of droplet and crystal growth

At T = -15°C andfor S = 1.001

Comparison of Droplet and Crystal Growth

For a liquid water droplet of radius r

For an ice crystal

R&Y Figure 9.4

saturation vapor pressure relative to ice and liquid water
Saturation Vapor Pressure Relativeto Ice and Liquid Water

Absolute value of es – ei peaks ~ – 12oC, but relative difference grows at lowest temps.


From Eq. 9.4 we see that the ice growth rate due to diffusion varies inversely with pressure and reaches a max near – 15oC at tropospheric pressures.

growth of different shapes is temperature dependent
Growth of different shapes is temperature dependent

Why so many forms and shapes of ice?

A molecular kinetic approach is required to explain different habits/shapes.

growth by accretion
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

growth by accretion cont or how do we get rain and snow

Accretional growth

Aggregational growth

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.

E – collection Efficiency; M condensed water mass (R&Y use m); R – radius; V – fall speed.

crystal fall speeds
Crystal Fall Speeds

Fig. 9.7 from Rogers and Yau, 1989

snowflake growth qualitative
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.
both coalescence and aggregation can happen in a cb times required for growth is different
Both coalescence and aggregation can happen in a Cb.Times Required for Growth is different.

Droplet collision - coalescence

crystal - diffusional


precipitation growth summary
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.
some papers on clouds and ice
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).

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.

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.

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.

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.