5. Formation and Growth of Ice Crystals

5.1 Effects of freezing in a cloud

5.2 Formation (nucleation) of ice crystals

5.3 Atmospheric ice nuclei

5.4 Ice crystal growth by diffusion

5.5 Ice crystal growth by aggregation & accretion

5.6 Shape of ice crystals

5.7 Models of liquid and ice clouds

5.1 Effects of freezing in a cloud

What is a typical temperature change associated with freezing?

How important is the release of latent heat when cloud liquid is changed to cloud ice?

- Consider freezing to occur at constant pressure and initial temperature is between 0 and -40 degrees- Assume the process is adiabatic

- As the water freezes, latent heat is released

- Air initially saturated with respect to water will be supersaturated with respect to the frozen droplets

- Deposition will occur, releasing an additional amount of latent heat

- Entire system is warmed, saturation vapor pressure with respect to ice will increase- Sublimation will occur and the system is in the equilibrium state

Three steps:

1. Water freezes at constant temperature T;

2. Vapor condenses on the ice at constant T, until the water vapor pressure reaches the saturation value over ice at T’;

3. The entire system is heated from T to T’.

• Cloud tops reach to heights where the temperature is colder than 0º c.

• Ice crystals may form.

• Freezing and deposition

• Homogeneous and heterogeneous nucleation.– Nucleation: to begin to form.

5.2 Formation (nucleation) of ice crystals

Why?

How?

• Growth is similar to that of a droplet.– Diffusion– Coagulation (collision and coalescence)

• What is the difference?

• Equilibrium vapor pressure– Vapor saturated with respect to liquid water is super-

saturated with respect to ice.• Diffusional growth is more significant.

Observations

• Droplets with r < 5 m will freeze spontaneously at a temperature of about -40º c.– Do drops exist near this temperature in the

atmosphere?• Observations from aircraft icing in clouds at

temperatures near -40º c indicate some drops don’t freeze until reaching this threshold.

• Not uncommon to find liquid water in clouds as cold as -20º c.– super-cooled

Liquid Water

• Water mass continuous, large drops, and close together.

• Single nucleation event causes the entire mass to freeze.

• Water mass distributed over a large number of very small drops

• Each drop must undergo its own nucleation event.

Bulk Water Cloud Water

Homogeneous• More than a factor of 20 in super-saturation

required to induce homogeneous nucleation at 0º c.– Even higher S-1 required for colder temps.

• Does not occur in the atmosphere due to the high super-saturation required.

• Observation: Ice crystals usually appear in appreciable numbers when the temperature drops below about -15º C.

Heterogeneous

• Formation of ice crystal in presence of foreign particles.– Foreign particles are important in the formation of ice

crystals, just as in the formation of water droplets.

• Water in contact with most materials freezes before temperatures reach -40ºC.

• Nucleation is aided by the presence of foreign surfaces or suspended particles.

Factors• Size

– The larger the aggregate, the more likely it will be stable and continue to exist.

• Material of substrate– The more tightly bound the water molecules to the

substrate, the greater the probability of ice nucleation.• Crystal structure of substrate

– The closer it resembles that of an ice crystal plane, the larger the chances of nucleation.

• When the binding and crystal lattice are favorable, the super-saturation and super-cooling required are much lower than for homogeneous nucleation.

Activation of Nuclei

Ice Nuclei

Which one would be mostlikely to activate as an icenuclei?

- Lattice most closely resembles ice.- Relatively warm nucleation temperature.

-Silver Iodide

5.3 Atmospheric ice nuclei

Ice Nuclei• Atmosphere has relative scarcity of freezing nuclei.• Fletcher (1962)

– 1 nucleus per liter of air at -20º C.– Increases by a factor of 10 for each 4º C. – Aerosol concentration: 107 nuclei per liter.

• Observation: There are more ice crystals than ice nuclei,– How can this be?

- Fracture of ice crystals

- Shattering or splintering of freezing drops

• Secondary processes

Studies• Vonnegut (1947): Material should have crystal properties

similar to ice.– AgI (Silver iodide)– PbI2 (Lead iodide)

• Experiment: Introduce AgI and PbI2 into super-cooled clouds.– PbI2 worked well, AgI not so well.– Soluble salt fouled up AgI, cleaner sample better.– Making AgI smoke did better yet!

• Fukuta (1958): Found 78 inorganic materials effective at temperatures > -20º C.

AgI• AgI widely used in cloud seeding

– Studied extensively

• Reynolds (1951): AgI less effective after surface changes caused by photo-decomposition in sunlight.

• Corrin, et al. (1967): Pure AgI less efficient than AgI containing hygroscopic impurities.

• Edwards and Evans (1960, 1968):– AgI works better as freezing nuclei than deposition nuclei.

Observations• Organic nuclei can be ice nuclei.

– Large number found that work at temps near 0º C.

• Kaolinite - most common atmospheric ice nuclei – mineral– found in many soil types

• Remark: Ice crystals that have been evaporated (sublimated) can grow into another crystal at higher temperatures than original.– Trained nuclei– Present with evaporation of cirrus clouds.

• A water saturated cloud has high super-saturation relative to ice. – Favorable for rapid growth by

diffusion and deposition.• Liquid drops available to

evaporate?– Conditions will remain favorable.– Equilibrium maintained with

respect to water.• If drops completely evaporate or

freeze, the equilibrium vapor pressure will decrease to the relative to ice value.

5.4 Ice crystal growth by diffusion

Growth Equation

• Ice crystal growth rate depends on temperature and pressure.– Inversely with pressure.

• Maximum growth occurs at -15ºc over a wide range of pressure.

• Kinetic and ventilation effects are neglected.

• Large particle overtakes small particle.

• Accretion: Capture of super-cooled droplets by an ice-phase precipitation particle.– Freeze on immediate contact Rimed crystals or

graupel– Freezing not immediate denser structures, hail.

• Aggregation: Clumping of ice crystals to form snowflakes.

5.5 Ice crystal growth by aggregation & accretion

Terminal Velocity

Wu et al. (1999, J. Atmos. Sci.)

Snowflake Formation

• Crystals form and grow by diffusion.

• Some of these crystals become larger than their neighbors– Enhanced diffusional growth– Chance collisions

• Crystals or small aggregates continue to grow by sweep out process.

Precipitation• For particles of appreciable size to develop:

– ice phase: aggregation or accretion– Water phase: coalescence.

• Warm Clouds– Condensation by diffusion alone cannot explain formation of particles

the size of a medium raindrop (1 mg or r0.62mm).– Coalescence must occur.

• Cold Clouds– Observation: Light precipitation has been observed in the form of

individual ice crystals.– Aggregation or accretion never occurred!– Drizzle or very light rain could have originated from melted ice crystals.

Process• Cumulus clouds develop at temperatures warmer than 0C.

– OR, at least warm enough to keep drops from freezing.

• Vertical Growth occurs to altitudes higher than 0C level.– Ice crystal formation likely to occur.

• Both coalescence (initially) and ice-processes occur.• Which dominates?

• Temperature at cloud top, cloud liquid water content, and droplet concentration.– Coalescence - warm clouds, high liquid water content, low drop

concentrations.

How Fast?

Precipitation:

Initiated when particles having mass of 4g areformed.

Meteorology 342 Homework (5)

1. Problem 9.1

2. A cloud which is cylindrical in shape has a cross-sectional area of 10 square kilometers and a height of 3 kilometers. The whole volume of the cloud is initially supercooled and the liquid water content is 2 grams per cubic meter. If all of the water in the cloud is transferred onto ice nuclei present in a uniform concentration of 1 nuclei per liter, calculate the mass of each ice crystal produced and the total number of ice crystals in the cloud. If all the ice crystals produce precipitate and melt before they reach the ground, what will be the total rainfall produced?

3. Calculate the time required for the diameter of a spherical snowflake to increase from 1 mm to 1 cm if it grows by aggregation as it falls through a cloud of small ice crystals present in an amount of 1 gram per cubic meter. You may assume that the collection efficiency is unity, that the density of the snowflake is 100 kilograms per cubic meter, and that the difference in the fall speeds of the snowflake and the ice crystals is constant and equal to 1 meter per second.

General Shapes

Basic Habits

5.6 Shape of ice crystals

Shapes

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Aggregates

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Flow Charts

5.7 Models of liquid and ice clouds

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