SNOW HYDROLOGY (GEOG 4321): SNOW FORMATION IN THE ATMOSPHERE

Instuctor: Mark Williams
Telephone: 492-4794 or 492-8830

Readings

• P. Hobbs, Ice in the Atmosphere
• Avalanche Handbook, pp 37-44
• Lind, Physics of Skiing, pp 17-20
• Handbook of Snow, Chapter 4.

Questions

• Can there be identical snowflakes?
• Are snowflakes in mountains prettier than other places?
• Why is snow white?
• Why are holes in a snowpack blue?

History

(from "In Praise of Snow, by Cullen Murphy"). The symmetry of ice crystals was commented upon by the Chinese in the second century B.C. Europeans had recorded the same observation at least by the Middle Ages. The intellectual pedigree of snow scholarship in the West is distinguished. The Dominican scholastic Albertus Magnus wrote about snow crystals in the thirteenth century. At the beginning of the seventeenth century the same subject beguiled Johannes Kepler. "There must be some definite cause," he wrote in 1609, shortly after making the discovery that the planets travel not in circles but in ellipses, "why, whenever snow begins to fall, its initial formation invariably displays the shape of a six-cornered starlet. For if it happens by chance, why do they not fall just as well with five corners or with seven?" In his pamphlet Kepler drew parallels with honeycombs and the pattern of seeds inside pomegranates, but was unable to explain the flakes' hexagonal form. Somewhat later Rene Descartes discerned that branches sprout off each side of the stems of hexagonal snowflakes at an angle of 60 degrees, with an angle of 120 degrees thus separating the branches themselves. The process is complex, but the hexagonal shape of snowflakes essentially reflects the underlying atomic structure of water. One suspects that even the skeptic Descartes would have offered up a Te Deum had he known that the two hydrogen atoms in a molecule of water branch off the oxygen atom with about 120 degrees of separation.

For all the scientific awareness of the symmetrical character of snow crystals, the ubiquity of their popular image--the one we see in children's paper cutouts and on bags of ice and signs for motels that have air-conditioning--is a relatively recent phenomenon. What snowflakes actually looked like was not widely known until the middle of the nineteenth century, when the book Cloud Crystals, with sketches by "A Lady," was published in the United States. The lady had caught snowflakes on a black surface and then observed them with a magnifying glass. In 1885 Wilson Alwyn ("Snowflake") Bentley, of Jericho, Vermont, began taking photographs of snowflakes through a microscope. Thousands of Bentley's photomicrographs were eventually collected in his book Snow Crystals (1931). The fact that not one of the snowflakes photographed by Bentley was identical to another is probably the basis for the idea that no two snowflakes are ever exactly the same--an idea that is in fact unverifiable.

Conditions for Precipitation

(from Hornberger et al., 1998): There are three primary steps in the generation of precipitable water in the atmosphere: (1) creation of saturated conditions in the atmosphere; (2) condensation of water vapor into liquid water; and (3) growth of small droplets by collision and coalescence until they become large enough to precipitate.

Saturated conditions typically arise in the atmosphere when an air mass is cooled by being lifted vertically. The vapor pressure e is a measure of how much water vapor is in the air. The saturation vapor pressure is the value of e for saturated conditions. This value is strongly dependent on the air temperature; that is, warm air can hold more water vapor, or, conversely, cool air cannot hold as much water vapor as warm air. Thus, cooling an air mass tends to produce saturated conditions, because e_sat is reduced. Cooling can happen in a number of ways, such as when air masses rise over mountains or other topographic features (referred to as orographic cooling), or warm air masses rise above cooler air masses at fronts.Heating of the Earth's surface (especially during the summer) can make air near the surface less dense so that it rises and cools, often producing thunderstorms.

Condensation is simply the phase change whereby water vapor becomes liquid water. It requires not only the creation of saturated conditions within the air, but also the presence of condensation nuclei, small particles such as dust or previously formed water or ice particles. Condensation may produce such small particles that they remain stable in the atmosphere. The white clouds observed on a fair day, for example, are composed of water droplets that are too small to precipitate. It is the coalescence of small droplets into larger drops, through collision of small droplets with each other or with larger drops, that gives rise to precipitable raindrops that are large enough to overcome gravity and fall to the ground as rain.

Snow differs from rain in a very important manner. Particules in the atmosphere must meet very specific requirements to act as ice nuclei. The reason for these exacting requirements is that it is very difficult to "make" water molecules line up correctly to form a crystalline, 3-dimensional shape. The limiting ingredient to form snow in the atmosphere is often nucleating agents. That's why cloud seeding works.

Thus, for snow to form in the atmosphere, we need:

• Water present in the vapor phase
• RH => to 100%
• Tair <= to 0 degree C
• Nucleating agents.

What happens if we meet all the requirements except the presence of nucleating agents? Is the amount of water vapor capped at a RH of 100%? The answer is no, the amount of water vapor in the atmosphere can continue to increase above a RH of 100%. When that occurs, we say the atmosphere is supersatured, that is, the amount of water vapor in the atmosphere exceeds 100%. The amount of supersaturation is often expressed as the actual relative humidty minus 100%. Thus, if the actual RH equals 112%, the amount of supersaturation is 12%.

You'll often see diagrams of crystal shape and size with axes of air temperature and vapor density rather than vapor pressure. Remember, vapor density and vapor pressure are interchangeable through the Ideal Gas Law. Vapor density is the preferred unit because our real interest is the mass of water that moves from the gas phase to become snow.

Nucleation

1. Homogeneous Nucleation
   • Spontaneous process.
   • No nuclei necessary.
   • formation of ice crystals from supercooled water droplets occurs at -40 deg C (also -40 deg F).
2. Heterogeneous Nucleation
   1. Deposition Nucleus
      • Growth by deposition from vapor phase onto existing ice nucleus.
      • Radius > 1000 angstroms
   2. Immersion-Freezing Nucleation
      • Ice nucleus imbedded within a super-cooled water droplet.
      • Radius > 100 angstroms.
   3. Contact Nucleation
      • Collosion contact between ice nucleus and supercooled water droplets.
      • More efficient than freezing nucleation.
      • Same particle nucleates at temperature that are 5-10 deg C warming than in freezing nucleation.
      • No good explanation as to why.

      Definition

      Deposition of gaseous or liquid water onto an ice nuclei.

      Size

      0.5 to 8.0 micrometers in diameter.

      Can be advected thousands of miles.

      dust storms, volcanic eruptions good sources.

      Ice nuclei

      Number of ice nuclei in the atmosphere, on average, is:

      ln N = A(T₁ - T) where T₁ is the temperature for a concentration of 1 active ice nucleus per liter and A varies from about 0.3 to 0.8. Typically, T₁ is about -20degC. Since the total number of particles in a liter of air is about 10⁸, only about 1 in 10⁸ airborne particles is effective as an ice nucleus at -20degC. Consequently, as a result of the low concentration of ice nuclei in the atmosphere, many clouds consist entirely, or partially, of supercooled water droplets. If we take A=0.6, the above equation predicts that the concentration of ice nuclei increases by about an order of magnitude for every 4degC fall in temperature.

      The surface of the earth appears to be the primary source of ice nuclei in the atmosphere.

      • Silicate minerals an important source
        • Clays such as kaolinite and illite
        • In Greenland, 85% of ice crystals had clay particle in their center, with
        • more than half the clay particles identified as kaolinite.
        • Sizes of ice nuclei ranged from 0.5 to 8 um in diameter.
      • Sea salt is a poor nucleating agent. Cloud drops must be cooled to at least -35degC before sea salt aerosols will act as ice nuclei.

      Organic Ice Nuclei (from LTER CED newsnotes)

      • Decomposing leaf matter appears to make excellent ice nuclei.
      • Microbial decomposition substantially increases the effectiveness of the ice nuclei.
      • Aerobic decomposition is much better than anaerobic decomposition in making ice nuclei.
      • Humus matter more than one year old nuclei that worked at temperatures of -5 deg C.
      • Newer organic matter had ice nuclei that worked at temperatures of -15 to -20 deg C, much older and hence much less efficient than more decomposed and older humus.
      • Decaying leaf material makes about 10¹⁰ ice nuclei per gram of decaying leaf material, about 0.1% of the mass of the orginal material.
      • Particle size ranged from 0.1 to 0.05 micrometers.
      • Fluxes of ice nuclei from 10 to 1,000 ice nuclei per square centimeter per day have been reported.
      • Fluxes of ice nuclei from organic matter go to near zero as when snow covers the ground.
      • Composition of organic ice nuclei:
        • Insoluble in water.
        • Stable in all common organic solvents.
        • Temperatures above 60 deg C deactivates the ice nuclei.

      References

      • Mason, BJ, The shapes of snow crystals---fitness for a purpose?, QJRMS, V 120, pp 849-860, 1994.
      • Schnell, R. C. and G. Vali, Atmospheric ice nuclei from decomposing vegetation, Nature, V 236, pp 163-165, 1972.
      • Schnell, R. C. and G. Vali, World-wide source of of leaf-derived freezing nuclei, Nature, V 246, pp 212-213, 1973.
      • Schnell, Bul of Am. Metero. Soc, V 55(6), pp 670, 1974.
      • Schnell, R. C. and G. Vali, Biogenic ice nuclei: part I. Terrestrial and Marine Sources, J. Atm. Sci., V33, pp 1554-1564.
      • Schnell, R. C. and G. Vali, Biogenic ice nuclei: part II. Bacterial Sources, J. Atm. Sci., V33, pp 1565-1570.
      • Fall, R., and P.K. Wolber, Biochemistry of bacterial ice nuclei, in Biologilcal Ice Nucleation and Its Applications, ed by R.E. Lee, Jr., G. J. Warren, and L. V. Gusta, pp 63-83, APS Press, St Paul, MN, 1995.
      • Chen, J. and V. Kevorkian, Heat and Mass Transfer in Making Artificial Snow, Ind. Eng. Chem. Process Des. Develop. V 10, p 75, 1971.

      Growth of ice particles

      Growth from the vapor phase

      Driving Mechanism

      Supersaturation is always greater over ice than over water at the same temperature. Supersaturation in cloudy air with respect to liquid water is generally less than 1%. However, this corresponds to supersaturation with respect to ice of about 10% at -10degC and 21% at -20degC.

      Net Result

      • Flux of water vapor liquid phase to ice phase
      • Flux of heat from ice to liquid phase produced by latent heat of fusion.

      Growth Rate

      • Maximum at -12 to -15 deg C.
      • Grows rapidly for about 1/2 hour, then relatively slowly.

      Maximum Size

      • Maximum mass is tens of micrograms.
      • Maximum diameter is tenths of millimeters.
      • Cannot produce large snowflake.
      • Produces only drizzle-size raindrops.
      • Large snowflakes must be grown by aggregration and riming.

      Aggregation

      Definition

      Snowflakes formed by the collosion and adhesion or sticking of ice and snow crystals.

      Growth Rate

      Fast compared to vapor diffusion.

      Can grow from 1 millimeter to 10 millimeters in about 20 minutes in a cloud with high ice content.

      Maximum Size.

      At -1 to -4 degC there is a substantial psuedo-liquid film on the ice surface. This promotes formation of an ice-neck connection between crystals. Crystals freeze together and are mechanically locked.

      Mass is sufficient for snowflakes to fall from the atmosphere to the ground, or to undergo sedimentation.

      Riming

      Definition

      Adhesion of a super-cooled water droplet to an ice particle or snow crystal.

      Size of Supercooled Water Droplets

      2-50 micrometers in diameter.

      Adhesion Efficiency

      Very high, approximately one, eg every super-cooled water droplet adheres or sticks to every ice particle or snow crystal it comes in contact with.

      Growth Rate

      Relatively fast. A single snow or ice crystal can grow from a 250 micrometer radius to 1-2 millimeter radius in 10-20 minutes.

      Formula for Calculatin Growth Rate.

      dm/dt = pie r² a b w W

      • r = radius of crystal;
      • a = adhesion efficiency, usually 1;
      • b = collosion rate between water droplets and ice crystals;
      • w = crystal fall velocity relative to water droplets;
      • W = liquid water content of cloud.

      Types of Riming

      Rimed

      Initial form of crystal is apparent.

      Graupel

      Original crystal shape obliterated, usually a round ball. Also called soft hail, snow pellet.

      Hail

      More advanced riming.

      Sleet

      sleet: partially melted and refrozen snow crystals or hard and transparent ice particles of frozen drops.

      Artificial Snow

      Kelly Doyle put together a nice powerpoint on snowmaking. Please download and read this powerpoint presentation on making snow

      Problem

      1. Water droplets have a "hang-time of about 15 seconds".
      2. Air temperatures relatively warm, close to 0 deg C.
      3. Natural air humidity low, less than 100% RH.

      Process

      1. Inject mixture of air and water from "snow-gun" into the atmosphere.
      2. Produces liquid water droplets 100-700 microns in diameter.
      3. Cooling of air mass by adiabatic expansion. The temperature of air and water shot out of the snowgun will be lower than the ambient temperature by several degrees.
      4. Add nucleating agents that are efficient at warm temperatures near 0 deg C.
      5. Makes good ski base.
         • Produces rounded ski grains that pack efficiently.
         • High density snow, 400-450 kg/m^3.

      Bacterial Ice Nuclei

      1. Pseduomonas syringae is commercial bacteria.
         • Bacteria.
         • Isolated from corn plant.
         • Cultivated and then freeze-dried, preserving cellular structure intact.
      2. Protein in cell wall the active nucleating agent.
         • Hexagonal platelets formed from proteins in cell wall.
         • Bond length between or nitrogen atoms comparable to bond length between oxygen atoms in ice.
         • Hydrogen bonds hold tertiary shape of proteins.
         • Exact mechanism of nucleating process unknown.
      3. P. syringae very efficient nucleating agent
         • 2.5 x 10^5 nucleation sites per mL of water from with 0 to 100 naturally occurring nucleations.
         • High fidelity of protein chains helps.
         • Helical structure of protein also helps.
         • Raises freezing temperature of super-cooled water droplets about 6 deg C.

      References

      • Dave Lind's book, pp 17-20.

      Types of Snow Crystals

      Factors that determine shape of snow crystals.

      • Temperature
      • Percent supersaturation
      • Ice nuclei type

      Growth directions

      • Basal Plane
        • three a axes;
        • each 120 deg apart;
        • hexagonal symmetry;
        • produces plate-like and star-like structures.
      • Optic Axis
        • c axis;
        • 90 deg to basal plane;
        • produces needle or columnlike structures.
      • High supersaturation
        • Growth occurs where excess vapor density is highest.
        • Growth occurs at edges and corners.
        • Complicated crystals such as dendrites.
      • Low supersaturation
        • Produces solid structures.
      • Atmospheric history after deposition.
        • Ice crystals and snowflakes often pass through different temperature and water vapor regimes as they pass through the atmosphere. Crystal type can change after initial formation.
        • Capped columns are an example. Solid column is formed in cold air with low supersaturation. As the solid column enters warmer air, plates may grow on end to make a "capped column".

      Overview of crystal types and growth patterns.

      Examples of snow crystal types.

      • Capped Column
      • Stellar
      • Stellar (SEM)
      • Plate (SEM)
      • Column (SEM)
      • Needle (SEM)
      • Riming and Aggregation (SEM)
      • Japanese Tsuzumi (SEM)
      • Abnormal and broken (SEM)
      • Heavily rimed (SEM)
      • Ice pellets, sleet (SEM)
      • Hail x-section (SEM)

      Impurities in Snow

      Incorporation in the ice lattice.

      • Ice is a poor solvent (in constrast to liquid water).
      • Impurities which are dissolved in water which freezes in the atmosphere generally:
        • are rejected, or;
        • precipitate.
      • Incorporation of impurities into snow involves:
        • vacancy substitution, the replacement of a water molecule with one that has a similar ionic radius and charge, such as ammonia (NH₃ for H₂O, or florine (F) for oxygen (O).
        • interstitial fit, accomodation in the open lattice space among water molecules, such as KOH.
      • Certain ions are more easily incorporated into solid water: F, NH3, K
      • Certain ions are not easily incorporated and rarely found inside the crystalline lattice, including sulfate and nitrate.

      Incorporation on outside of snow and ice crystals.

      • Snow and ice crystals have a very high surface to volume ratio relative to rain.
      • Snow and ice crystals generally have a much lower settling rate than rain.
      • Hence snow and ice crystals are much better at scavenging impurities out of the atmosphere than rain.
      • Snow and ice crystals thus have many of the impurities located on the outside of the particle rather than incorporated into the interior of the crystalline lattice structure.

      Storm Types

      

      

      

      

      

      References

      • CRREL 94-4 .

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      Here's a nice simple description of snow formation in the atmosphere, from the Teel family: Simple description of snow formation in the atmosphere

      Here's another nice simple description of snow formation in the atmosphere, this one from USA Today: Simple description of snow formation in the atmosphere

      Here's a slightly more detailed description of snow formation in the atmosphere, this one from NCAR/UCAR: Snow formation in the atmosphere: Science Now article from UCAR/NCAR

      Another nice description of snow formation in the atmosphere: Jerry Dennis on Snowflakes and Crystals

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