1. Primary and Secondary Ice Formation
Primary ice is the first ice formed, either from supersaturated vapor (as with deposition nucleation) or from supercooled liquid (homogeneous or heterogeneous freezing nucleation).
By contrast, “secondary ice” forms only once some ice is already present.
Evidence for the distinction between primary and secondary ice came initially from field observations. When the concentrations of ice particles in the mixed-phase region of cold clouds (−38◦ <T < 0 ◦C) agree with the measured concentrations of ice nuclei (IN), we suspect that the ice particles had primary origins, meaning that each ice particle likely formed by the activity of one ice nucleus.
By contrast, when the ice concentrations exceed the IN concentrations by several orders of magnitude, we are left with the conclusion that secondary ice processes must have been active.

2. Glaciation Mass conversion and ice multiplication (active processes)
Glaciation is the conversion of supercooled cloud water into ice. The mechanisms of glaciation invariably involve primary nucleation, but secondary ice formation, when active, can rapidly propagate the ice phase throughout a cloud.
Mass conversion
and
ice multiplication
(active processes)
Primary nucleation serves mainly as the trigger for explosive growth of the secondary ice population.

3. Mass conversion
Mass conversion of liquid to ice is stimulated by the inherent difference in the equilibrium vapor pressures of liquid and ice at any temperature below 0 ◦C.
maximum
Plot is for subsaturated conditions
Growth rates peak at lower temperatures because of latent heating effects
Diffusion coefficients are larger at lower pressure, so growth rates increase with altitude
Note for
3600 sec of growth will produce a droplet approximately 1mm in diameter -- a small raindrop! Compare this to the time required to produce this size drop by condensation growth.

4. Aside: the Bergeron-Findeisen process (AMS glossary)
Bergeron–Findeisen process—(Commonly called the ice process of precipitation, and formerly, ice-crystal theory; also Bergeron–Findeisen–Wegener process or theory, and with the names in a different order.)
A theoretical explanation of the process by which precipitation particles may form within a mixed cloud (composed of both ice crystals and liquid water drops).
The basis of this theory is the fact that the equilibrium vapor pressure of water vapor with respect to ice is less than that with respect to liquid water at the same subfreezing temperature. Thus, within an admixture of these particles, and provided that the total water content were sufficiently high, the ice crystals would gain mass by vapor deposition at the expense of the liquid drops that would lose mass by evaporation.
Upon attaining sufficient weight, the ice crystals would fall as snow and very likely become further modified by accretion, melting, and/or evaporation before reaching the ground.
Operation of this process requires numerous small water drops that are supercooled, which is a common feature in clouds between about 0° and −20°C or below, along with a small number of ice crystals. The crystals grow by vapor deposition at a rate (maximum at about −12°C) to give individual snow crystals in some 10 to 20 minutes. Much cloud seeding is based upon the introduction of artificial ice nuclei to supply more of the ice particles.
This theory was first proposed by T. Bergeron in 1933, and further developed by W. Findeisen. Certain of its features related to nucleation had been suggested by A. Wegener as early as 1911.

5. Thermal conductivity difference with T
Normalized growth rate, dm/dt divided by 4πC
Pruppacher &Klett (1978)
Normalized growth rates indicate that maximum growth rates occur at temperatures less than in a water-saturated environment.
1000mb
500mb
Maximum growth rates are shifted to lower temperatures due to latent heat release at surface of growing crystal. This in turn raises vapor pressure adjacent to crystal which slows growth rate.
Thermal conductivity difference with T
Note for ,
3600 sec of growth will produce a droplet approximately 1mm in diameter- a small raindrop! Compare this to the time required to produce this size drop by condensation growth.

6. (Cloud T above homogeneous freezing limit)
Ice Multiplication
(Cloud T above homogeneous freezing limit)
Over the years it has become apparent from observations that concentrations of ice crystals in clouds cannot always be explained by the concentrations of ice nuclei (IN) measured or expected to be activated
At temperatures warmer than -10 C, the concentrations of crystals can be times the concentrations of IN activated at cloud top temperature
Effect greatest in clouds with broad drop-size distributions
Hypotheses:
Fragmentation of large drops during freezing
Mechanical fracture of fragile ice crystals (dendrites and needles) by collision with graupel and other ice particles
Splinter formation during riming of ice crystals
Enhanced ice nucleation in regions of spuriously high supersaturations in the presence of high number concentrations of supercooled raindrops or in a turbulent cloud environment
Ice particle generation during evaporation of ice particles

7. Consider various hypotheses:
Fragmentation of large drops during freezing
Early lab experiments (1960’s) suggested that supercooled drops shattered and produced numerous splinters during freezing
Later studies showed that each drop-freezing event produces, on the average, less than 2 splinters
Even considering that these estimates are low by an order of magnitude – cannot explain the large observed enhancements
Mechanical fracture of fragile ice crystals (dendrites and needles) by collision with graupel and other ice particles
The rate of collision between ice particles is proportional to [concentration of ice crystals] × [concentration of other hydrometeors]
Thus process grows exponentially
However, if initial [IN] is low, then it takes a while to “spin up” and is unlikely to account for large enhancements
Splinter formation during riming of ice crystals
Bursting of supercooled droplets as they freeze onto a riming ice particle
Graupel undergoing wet accretion of supercooled cloud droplets grows whisker-like ice crystals

8. Consider various hypotheses (continued):
(continued) Hallett–Mossop process (also called rime splintering) – requires very specific conditions:
Temperature in the range of -3 to -8 ˚C
A substantial concentration of large cloud droplets (D > 25 µm), NL
Large droplets coexisting with small cloud droplets (D < 12 µm), NS
A maximum average splinter production rate of 1 secondary ice particle per 250 large droplet collisions occurs near -4 ˚C
Large supercooled drops capture small ice crystals formed on IN  freeze  rapidly rime cloud drops to produce splinters
About 50 splinters are produced per milligram of accreted ice
Splinters are captured by more of the supercooled drops, accelerating the process
Mossop (1978): number of ice particles per second, A:
Operates in maritime conditions (large drops present)
Need low updrafts so crystals can settle into T zone
Hallett and Mossop (1974), Mossop and Hallett (1974),Mossop (1976)

9. Consider various hypotheses (continued):
Enhanced ice nucleation in regions of spuriously high supersaturations in the presence of high number concentrations of supercooled raindrops or in a turbulent cloud environment
It is generally agreed that, in the absence of precipitation, peak supersaturations in convective clouds are below ~1%
But if precipitation drops accrete a large proportion of cloud drops, this may overly deplete the sink for generated supersaturation in rapidly rising convective towers  supersaturation rises (up to 5 – 10% ?)
This could enhance ice nucleation (if occurring at the right Ts)
Similar mechanism may occur in turbulent regions
May not be able to explain large enhancements on its own, but could initiate enough ice formation to kick off ice multiplication processes
Ice particle generation during evaporation of ice particles
Oraltay and Hallett (1989) and Dong et al. (1994) observed as many as 30 pieces per crystal formed when evaporating at RH < 70%
Fits with observed enhancements in evaporating cloud regions and in heavily mixed regions
Do pieces survive long enough in entrainment regions to serve as embryos for further crystal growth?

10. Timescale estimates from a simple model
Rapid glaciation almost always requires an active warm-cloud process to provide the large supercooled raindrops that capture the small secondary ice particles generated by rime splintering.
Exponential rise, consume raindrops
Note scale
From primary nucleation

11. Ice crystal growth mechanisms
Growth from the vapor phase, by deposition
Growth by aggregation
Growth by accretion of supercooled water, known as riming
In growth from the vapor phase, crystal growth spreads outwards from the nucleating site (Wikipedia.com):
In this faster process, the elements which form the motif add to the growing crystal in a prearranged system, the crystal lattice, started in crystal nucleation
As first pointed out by Frank, perfect crystals would only grow exceedingly slowly
Real crystals grow comparatively rapidly because they contain dislocations (and other defects), which provide the necessary growth points, thus providing the necessary catalyst for structural transformation and long-range order formation.

12. ICE CRYSTAL GROWTH MECHANISMS: Growth by deposition
Here ice particles continue to take up water vapor provided the ice crystal remains in an environment with
For ice crystal growth, growth rate is determined by balance between vapor supply to the surface of the growing crystal and heat conduction to the surrounding environment. This is analogous to condensation growth of a small droplet – the basic physics anyway.
Now latent heat of sublimation

13. Depositional growth theory is slightly more complicated than condensation growth since ice particles are non-spherical
- strike an analogy between an ice particle immersed in a field of water vapor and an electrical conductor immersed within an electric field.
- accumulation of vapor on the ice crystal is like accumulation of charge on the conductor.
Problem in electrostatics is to compute the electric field flux lines that terminate on a conductor that is placed within a potential gradient (Gauss’s Law):
The electric flux through any closed surface is proportional to the enclosed electric charge.
Gauss’s Law
Ice crystal
conductor
POTENTIAL
(steady state)
WATER VAPOR DENSITY
(Electric potential satisfies Laplace’s equation)

14. potential well removed from conductor’s surface
We can use Gauss’s Law to compute the total flux on the conductor, or the accumulation of charge on the surface of the conductor. Accumulation of charge on the conductor is the same as accumulation of vapor on the surface of the ice crystal.
Gauss’s Law ds
The electric field is the gradient of the potential
charge
potential at surface
voltage differential
potential well removed from conductor’s surface
For ice crystal analogy, so
is like for the conductor analogy.
Therefore
“C” has units of length. Note C = r for spherical geometry, as expected.

15. From electrostatics,
Where i is current (charge/ second) flowing to surface of conductor.
C= capacitance
= conductivity of medium over which a voltage gradient is applied
Coulombs/ second i
Hence i, current is analogous to ; the crystal growth rate. so
diffusivity
conductivity

16. Including the effects of latent heat release Ls, we can eventually arrive at the final form,
(analogous to condensation growth)
For a stationary ice crystal (1)
Mw= molecular weight of water
es,i(T) is the saturation vapor pressure over a plane surface of ice
saturation ratio
To use (1) we must know the “capacitance” of the ice crystal, C  function of geometry. Past work has resorted to metal analogs of ice crystal shapes!
Hence determining C requires knowing ice particle “habits”.

17. Pruppacher & Klett(1978)

18. This is in your Snowflake Manual
Pruppacher & Klett(1978)
This is in your Snowflake Manual

19. Pruppacher & Klett(1978)

20. Westbrook et al, JAS, 2008: modeling of capacitances (“random walks”)
“…the the capacitance of a sphere (C/Dmax = 0.5), which is commonly used in numerical models, overestimates the evaporation rate of snowflakes by a factor of 2”

21. bullet-rosette
bullet
stellar-dendrite
aggregate snowflakes

22. Understanding the origins of different crystal “habits” and sizes
Even for crystals that grow by diffusion processes, we see from observations that a wide range of different crystal shapes are possible
What controls the shape?
What controls the rate of growth? Only the driving force (vapor supersaturation)?
What happens in a liquid water cloud that cools below 0 ˚C? Can liquid and ice coexist?
Important points made in the following slides:
Typically, supersaturations over ice are very high (we will look at reasons for this)
The “crystal lattice” of ice is hexagonal in its symmetry under most atmospheric conditions
Varying conditions of temperature and vapor pressure can lead to growth of crystalline forms in which the simple hexagonal pattern is present in widely different habits (a thin hexagonal plate or a long thin hexagonal column)
trigonal symmetry can sometimes be observed, suggesting an influence of a cubic symmetry
Growth rates depend on supersaturations and on the crystal structure itself (i.e., they are not diffusion-limited, as modeled for drop condensational growth)

23. supersaturation LARGE SUPERSATURATIONS OVER ICE TYPICAL
~15% supersaturation with respect to ice (for water saturated cloud)
x100% for Si (%)
supersaturation
Expect in water saturated clouds that ice crystals have their largest growth rates
Most complex crystal geometries also occur near

24. Note Bailey & Hallett (2009) suggest that these commonly-accepted forms below -20 are in error: should be platelike down to -40 C
Pruppacher & Klett (1978)

25. Ice crystal habits
Ice crystals have one of two basic habits (shapes)
Plate-like (a-axis growth)
Prism-like (c-axis growth)
Prism face
a- axis
basal face
c- axis
Temperature controls basic growth habit, that is whether growth is primarily in c-axis or a-axis direction
As water saturation is approached, the crystal begins to take on complex geometrical forms

26. platelike (a-axis growth dominates)
Pruppacher & Klett (1978)
platelike (a-axis growth dominates)
As S increases, sector plates, stellar and dendritic crystals form
prismlike (c-axis growth dominates)
columns, needles
Here, prismlike said to dominate, but Bailey & Hallett (2009) suggest that these commonly-accepted forms below -20 are in error: should be platelike down to -40 C

27. INCREASING SKELETAL FEATURES
Pruppacher & Klett(1978)
INCREASING SKELETAL FEATURES
WATER SATURATION
ICE SATURATION
SOLID COLUMN
HOLLOW COLUMN- INCOMPLETE BASAL FACES AT HIGHER VAPOR DENSITIES
NEEDLES REPRESENT SHEATHS WHOSE PRISM FACES ARE INCOMPLETE.

28. Controlled Lab Experiment
Hobbs, Ice Physics
1cm

29. Updated diagram suggested by Bailey & Hallett, JAS, 2009

30. Updated diagram suggested by Bailey & Hallett, JAS, 2009

31. Updated diagram suggested by Bailey & Hallett, JAS, 2009

32. Wallace and Hobbs, Second Edition
Equiaxed means the crystal has similar dimensions along the c- and a-axis.

33. Change of habit occurs at -4, -10, and -22°C.
We see that ice crystal shapes are rather complicated, which leads us to suspect that heat and vapor exchange alone can’t adequately explain crystal growth/ habits. Must examine surface forces at surface of ice crystal and their ability to control incorporation of vapor molecules into the ice lattice.
Surface processes
T basic habit; vapor excess degree of skeletal growth