Snow Formation in the Atmosphere: Properties of Snow and Ice Crystals

1
Snow Formation in the Atmosphere Properties of
Snow and Ice Crystals
2
Snow Formation and Snowfall

• Clouds and Cloud Formation
• Crystal Formation
• Crystal Properties
• Precipitation Formation

3
Clouds

• Presence of water in the atmosphere from
• evaporation (of liquid water)
• transpiration (of liquid water)
• sublimation (of ice, i.e., snow)
• Presence of cloud condensation nuclei
• Cooling and cloud formation

4
Layering of the Atmosphere

• Estimated 126 x 1011 tonnes of water vapour in
  the atmosphere at any one time
• or 0.001 of all the water in the entire
  earth-atmosphere system
• 4 layers of the atmosphere

5
Layering of the Atmosphere (contd)

• Troposphere (lowest layer)
• contains 75 of gaseous mass of the atmosphere
• contains almost all water vapour and aerosols in
  the atmosphere
• capped by a temperature inversion layer of
  relatively warm air
• ceiling is called the TROPOPAUSE
• 16 km high at the equator due to the greatest
  heating and vertical convection turbulence
• 8 km high at the poles

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Layering of the Atmosphere (contd)

• Stratosphere - up to 50 km high
• Mesosphere - 50 km to 80 km high
• Thermosphere - above 80 km (up to 250 km)

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Temperature Variation in the Troposphere

• lapse rate with height in the Troposphere is an
  average decrease of 6.25 oC /km
• spatial and temporal variation

Temperature lapse rate in lowest 1000 - 1500 m
(after Lautensach Boegel, 1956)
Season of Rate Season of Rate Climate maximum (oC
/km) minimum (oC/km) Tropical rainy dry season gt
5 rainy season gt 4.5 Tropical and summer gt
8 winter gt 5 subtropical deserts Mediterranean
winter gt 5 summer lt 5 Mid-latitudes summer gt
6 winter 0 - 5 (cold winter) Boreal
continental summer gt 5 winter lt
0 Arctic summer lt 0 winter lt 0
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Temperature Variation in the Troposphere (contd)
Annual variation of lapse rate in five climatic
zones (after Hastenrath, 1968) 1 Tropical rainy
climate (Togo) 2 Tropical desert (Arizona) 3
Mediterranean (Sicily) 4 Mid-latitude, cold
winter (North Germany) 5 Boreal continental
(Eastern Siberia)
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Cloud Parameters

• Macro Scale
• Cloud type
• Cloud amount or cover fraction
• Height and thickness
• Micro scale
• Water content
• Droplet/Crystal size
• Phase

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Four main cloud groups (after Strahler, 1965)
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Cloud Formation

• There are three requirements for cloud formation
• sufficient moisture in the air to condense
• presence of cloud condensation nuclei
• cooling to cause condensation

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Humidity

• vapour pressure is the partial pressure exerted
  by water vapour
• saturated vapour pressure is the maximum vapour
  pressure that is thermodynamically achievable
• where esat is the saturated vapour pressure in mb
  and T is temperature in oC (based on
  Goff-Gratch equation)
• esat is the maximum amount of water that can be
  held by the atmosphere at T before condensation
  occurs
• absolute humidity is the total mass of water in a
  given volume of air

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Vapour Pressure
Vapour pressure
saturated vapour pressure
temperature
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Humidity (contd)

• relative humidity is the ratio of the actual
  vapour pressure to the saturated vapour pressure
  in percent
• where Wa is the relative humidity in percent and
  ea is the actual vapour pressure (in mb)
• dew point is the at which saturation occurs if
  air is cooled at constant pressure without a
  change in the quantity of water vapour available
• where Td(ea) is the dew point in oC
• specific humidity is the ratio of the mass of
  water vapour per unit mass of moist air
• where qv is the specific humidity in kg/kg and
  pa is the total pressure of moist air (in mb)

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Humidity (contd)

• precipitable water content (Wp ) is the amount of
  moisture in an atmospheric column, expressed as a
  depth
• considering an atmospheric element of height dz
  with a horizontal cross-sectional of A,
• the mass of the air is ra Adz,
• the mass of the water is qv ra Adz,
• the total mass of precipitable water between
  elevations z1 and z2 is
• the precipitable water content can be expressed
  empirically in terms of the surface dew point
  temperature
• Wp1.12 exp (0.0614 Td )

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Cloud Condesation Nuclei (CCN)

• CCN are particles around which water vapour in
  the atmosphere will condense
• smaller particles are held in suspension by air
  currents induced by friction between the ground
  and the wind or by thermals
• larger particles, such as sand or dust, have very
  short atmospheric residence time
• aerosols are small particles (solid or liquid)
• Aitken nuclei ( Dlt0.2 mm)
• large aerosols ( 0.2ltDlt 2 mm)
• giant aerosols ( 2 mmltD )
• size distribution and concentration vary
  temporally and spatially (horizontally and with
  height)

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Cloud Condesation Nuclei (contd)

• CCN concentrations are typically in the order of
  1012 m-3
• sources of CCN may be natural or anthropogenic
• concentrations may increase by up to 2 orders of
  magnitude over and downwind of industrial areas
  (eg. St Louis, MO generates CCN at a rate of 10-2
  m-3.s-1)

Worldwide aerosol production in tonnes per annum
(after Wallace Hobbs, 1971)
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Formation of Cloud Droplets

• presence of CCN in the atmosphere provides a
  potential for water to condense out of the vapour
  phase, given saturated conditions
• 2 factors regarding CCN ability to condense out
  vapour
• water condenses easier on larger aerosols due to
  vapour pressure
• saturated vapour pressures are larger over more
  curved surfaces
• if only very small aerosols exist, a greater
  degree of supersaturation is required for
  condensation to occur
• many aerosols are hygroscopic - this is the
  ability to attract water onto a surface
• condensation can thus occur even if air is not
  fully saturated with water
• water droplet density in the order of 109 m-3 (3
  to 4 orders of magnitude less than CCN
  concentration)

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Growth of Cloud Droplets

• as droplets grow initial increase in radius is
  rapid
• for larger particles, the increase in radius
  (with increasing surface area) is much less
• as clouds age, drop size decreases since larger
  droplets break due to air motion
• all droplets are subject to the force of gravity
• in a stable, undisturbed environment all droplets
  fall
• fall rate increases until the frictional force
  (FaV) and the gravity force are equal - terminal
  velocity is reached
• in real clouds
• uplift causes smaller particles to remain in
  suspension
• larger particles still fall against upcurrents
• small particles falling into an unsaturated
  environment often dissipate due to large
  evaporation surfaces
• clouds are often well defined and level

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Comparative sizes, concentrations and terminal
fall velocities of cloud droplets and rain drops
(after McDonald, 1958)
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Growth of Cloud Droplets (contd)

• 2 growth mechanisms condensation, collision and
  coalescence
• CONDENSATION (see Mason, 1962 Appendix A)
• assume an isolated water drop of mass m, radius
  r, and density rw growing by diffusion of water
  vapour according to Ficks Law of Diffusion
• where R is the radius of a spherical surface and
  D is the diffusion coefficient of water
• this equation can be reduced to yield a rate of
  increase in droplet radius as a function of the
  supersaturation (S), the latent heat of
  condensation (L), the molecular weight of water
  (M), the universal gas constant (R), the thermal
  conductivity of air (K), and temperature (T)

Mason, B.J., 1962. Clouds, Rain and Rainmaking.
Cambridge University Press.
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Growth of Cloud Droplets (contd)

• COLLISION AND COALESCENCE (Mason, 1971 Appendix
  A)
• a larger drop will fall at a greater velocity
  than a smaller particle
• the larger particle will overtake, possibly
  collide with, and potentially coalesce (fuse)
  with the smaller droplet
• Hocking (1959) showed that a drop must have a
  minimum radius of 19 mm (via condensation) such
  that collisions with smaller droplets may occur
• assuming that the large drop (of radius R falling
  at velocity V) and the small droplet (of radius r
  at velocity v) are spheroids, the rate of drop
  growth is
• where E is the collision efficiency

Mason, B.J., 1971. The Physics of Clouds, 2nd
edition. Oxford University Press.
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Growth of Cloud Droplets (contd)

• COLLISION AND COALESCENCE (contd)
• the collision efficiency has been defined as a
  function of the two radii and the initial
  distance between the centre of the two particles
  a larger drop will fall at a greater velocity
  than a smaller particle

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Ice Crystal Growth in Clouds

• supercooled water can exist in a liquid state
  between -40 and 0oC
• cloud type based on temperature
• WARM clouds contain only water droplets (T gt 0oC)
• MIXED clouds contain supercooled water and ice
  (above -12oC supercooled water dominates due to
  hostility of cloud environment to the freezing
  process)
• COLD clouds contain only ice particles
• 4 processes of ice particle formation are not
  well understood
• spontaneous or homogeneous formation below -40oC
• heterogeneous nucleation
• ice nucleus existing within a water droplet
  encourages freezing
• water droplets aggregate around ice nucleus
• temperature may be greater than -40oC

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Ice Crystal Growth in Clouds (contd)

• 4 ice particle formation processes (continued)
• contact nucleation
• supercooled water comes in contact with ice
  nucleus and freezing occurs instantly
• concentration of ice crystals within slightly
  supercooled convectional clouds exceed ice nuclei
  concentration by several orders of magnitude
• ice nucleation (saturated vapour pressure
  differences)
• requires the pre-existence of ice in the cloud
• divergence between saturation vapour pressure
  over ice and water at temperatures below 0oC
• if air is supersaturated with ice, water vapour
  will deposit directly unto existing ice particles
• air surrounding supercooled water droplets may
  become unsaturated and ice particles will grow

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Ice Crystal Growth in Clouds (contd)

• dominance of an ice-crystal formation process in
  mixed clouds depends on the temperature, and the
  size and morphology of pre-existing water
  droplets or nuclei
• clay and some decaying organic particulates do
  not absorb water and are sources of ice nuclei
• cloud type (and temperature) are dependent on
  cloud height and location, i.e., latitude

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Chemical-Physical Relationships in Clouds

• cloud reflectance (albedo) is partially dependent
  on drop size
• cloud droplet concentrations (N) are related to
  pollution (due to increases in CCN)
• as pollution emissions increase, cloud droplet
  concentrations increase, albedo increases, and
  temperature decreases
• pH, N, droplet size (in terms of mean particle
  diameter D), and atmospheric acidic
  concentrations ( ) have been shown to be
  related
• Hindman et al. (1994) found the following
• low pH, high N, low D, high
• specifically,
• pH 3.4, N 329 cm-3, D 6.4 mm, SO42-
  5.7mg.L-1
• pH 5.1, N 189 cm-3, D 8.0 mm, SO42-
  3.9mg.L-1

Hindman, E.A., M.A. Campbell, R.D. Borys, 1994.
A ten-winter record of cloud-droplet physical and
chemical properties at a mountaintop site in
Colorado. Journal of Applied Meteorology 33(7)
797-807.
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Water Molecules
Hydrogen bonding in water (after Webber et al.,
1970)
Charge separation in the water molecule (after
Webber et al., 1970)
The hexagonal crystalline matrix framework of ice
(from Webber et al., 1970)
Webber, H.D., G.R. Billings, and R.A. Hill, 1970.
Chemistry A Search for Understanding. Holt,
Rinehart and Winston of Canada, Limited, Toronto.
29
Snow Crystal Growth Patterns
from Ono, 1970 J. Atmos. Sci., 27 649-658.
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Snow Crystal shape is temperature dependent
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Snow Crystal Growth Patterns
a-axis
a-axis
c-axis
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3-D growth rate for T lt 0 oC
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Particle Shape
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Crystal Classification

• National Research Council, 1954. The
  International Classification of Solid
  Precipitation. IASH, Technical Memo 31, NRC,
  Ottawa, Canada.
• Others include
• Nakaya, U., 1954. Snow Crystals Natural and
  Artificial. Harvard University Press, 510pp.
• Magono, C., and C. Lee, 1966. Meteorological
  classification of natural snow crystals. J. Fac.
  of Science, Hokkaido University, Series VII(2)
  321-335.

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Fall Mechanics

• m is the particle mass,
• force of gravity (Fg),
• drag force (FD),
• buoyancy (FB),
• updrafts (-Fu) or downdrafts (Fu)
• acting on the particle
• If the net acceleration is initially positive,
  the particle will fall, until either the particle
  evaporates or a force balance is reached, at
  which time a terminal velocity is achieved.

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Terminal Velocities
 
 
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Winter Precipitation Mechanisms

• Convergence
• Frontal Forcing
• Orographic Forcing
• Convection (minimal)

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Convergence
ANTICYCLONIC SINKING
CYCLONIC LIFTING
Convergence around a low-pressure area (diameter
of about 1,000 km) causes widespread
precipitation. Divergence (sinking) around a
high causes clearing skies.
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Frontal Effects
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Orographic Effects
Orographic lifting is the most important winter
precipitation mechanism maximum effect is
produced when the wind is perpendicular to the
mountain barrier (left).