Download Snow formation in the atmosphere: properties of snow and ice crystals

Snow Formation in the
Atmosphere: Properties of Snow
and Ice Crystals
Snow Formation and Snowfall
•
•
•
•
Clouds and Cloud Formation
Crystal Formation
Crystal Properties
Precipitation Formation
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
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 earthatmosphere system
• 4 layers of the atmosphere
Layering of the Atmosphere
(cont’d)
• 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
Layering of the Atmosphere
(cont’d)
• Stratosphere - up to 50 km high
• Mesosphere - 50 km to 80 km high
• Thermosphere - above 80 km (up to 250 km)
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 > 5
rainy season > 4.5
Tropical and
summer
>8
winter
>5
subtropical deserts
Mediterranean
winter
>5
summer
<5
Mid-latitudes
summer
>6
winter
0-5
(cold winter)
Boreal continental summer
>5
winter
<0
Arctic
summer
<0
winter
<0
Temperature Variation in the
Troposphere (cont’d)
Annual variation of lapse rate
in five climatic zones
(after Hastenrath, 1968)
1
2
3
4
Tropical rainy climate (Togo)
Tropical desert (Arizona)
Mediterranean (Sicily)
Mid-latitude, cold winter
(North Germany)
5 Boreal continental
(Eastern Siberia)
Cloud Parameters
• Macro Scale
– Cloud type
– Cloud amount or cover fraction
– Height and thickness
• Micro scale
– Water content
– Droplet/Crystal size
– Phase
Four main cloud groups
(after Strahler, 1965)
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
Humidity
• vapour pressure is the partial pressure exerted by water
vapour
• saturated vapour pressure is the maximum vapour pressure
that is thermodynamically achievable
( )
17.3 T
esat(T)=6.11 exp
(T+237.3)
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
Vapour Pressure
Vapour pressure
saturated
vapour
pressure
( )
17.3 T
esat(T)=6.11 exp
(T+237.3)
temperature
Humidity (cont’d)
• relative humidity is the ratio of the actual vapour pressure to
the saturated vapour pressure in percent
Wa 
ea
e sat ( T )
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
Td ( e a ) 
ln ( e a )  1. 810
0. 0805  0. 00421 ln ( e a )
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
q v  0. 622
ea
pa
where qv is the specific humidity in kg/kg and pa is
the total pressure of moist air (in mb)
Humidity (cont’d)
• 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
z2
Wp =
qv a Adz

z1
• the precipitable water content can be expressed empirically
in terms of the surface dew point temperature
Wp=1.12 exp (0.0614 Td )
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 ( D<0.2 mm)
– large aerosols ( 0.2<D< 2 mm)
– giant aerosols ( 2 mm<D )
• size distribution and concentration vary temporally and
spatially (horizontally and with height)
Cloud Condesation Nuclei (cont’d)
• 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)
Natural sources
106 tpa
Human activities
106 tpa
Sea salt
Gas-to-particle conversion
Windblown dust
Forest fires
Meteoric debris
Volcanoes (highly variable)
TOTAL
1000
570
500
35
20
25
>2150
Gas-to-particle conversion
Industrial processes
Fuel combustion
(stationary sources)
Solid waste disposal
Transportation
Miscellaneous
TOTAL
275
56
44
2.5
2.5
28
410
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)
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
Comparative sizes, concentrations and terminal fall velocities
of cloud droplets and rain drops (after McDonald, 1958)
Growth of Cloud Droplets (cont’d)
• 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 Fick’s Law
of Diffusion:
dm
dr
2
F
 4 R v D
 a constant (B)
dt
dR
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.
Growth of Cloud Droplets (cont’d)
• 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:
dR EW

( V  v)
dt 4rw
where E is the collision efficiency
Mason, B.J., 1971. The Physics of Clouds, 2nd edition. Oxford University Press.
Growth of Cloud Droplets (cont’d)
• COLLISION AND COALESCENCE (cont’d)
– 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
E  y2c / (R  r )2
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 > 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
Ice Crystal Growth in Clouds
(cont’d)
• 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
Ice Crystal Growth in Clouds
(cont’d)
• 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
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.
Water Molecules
Hydrogen bonding in water
(after Webber et al., 1970)
Charge separation in the water
molecule (after 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.
The hexagonal crystalline matrix
framework of ice (from Webber
et al., 1970)
Snow Crystal Growth Patterns
1000
100
growth rate (x 10
-10
g/s)
maximum rate
minimum rate
10
1
-20
-15
-10
-5
0
temperature (degrees C)
from Ono, 1970: J. Atmos. Sci., 27: 649-658.
Snow Crystal shape is
temperature dependent
Snow Crystal Growth Patterns
a-axis
prism
face
a-axis
100% planar
basal
plane
-20
c-axis
100% columnar
-15
-10
-5
temperature (degrees C)
0
3-D growth rate for T < 0 oC
prism face
100
growth rate
basal plane
1000
2-3
1-2
0-1
-1-0
10
1
0.1
0
-2
-4
-6
-8
-10
-12
basal plane
-14
-16
temperature (degrees C)
-18
-20
-22
growth direction
-24
-26
-28
-30
-32
prism face
Particle Shape
symbolic
representation
Crystal
Classification
•
•
National Research Council,
1954. The International
Classification of Solid
Precipitation. IASH, Technical
Memo 31, NRC, Ottawa,
Canada.
EXAMPLES
NAME
SYMBOL
plate
F1
stellar crystal
F2
column
F3
needle
F4
spatial dendrite F5
capped column F6
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.
irregular crystal F7
graupel
F8
ice pellet
F9
hailstone
F0
Fall Mechanics
dv
m  Fg  FD  FB  Fu
dt
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.
Terminal Velocities
dimension/diameter (mm)
Needle
Plane dendrite
Spatial dendrite
Powder snow
Crystals with graupel
Graupel
Rain drops
1.53
3.26
4.15
2.15
2.45
2.13
0.2
0.4
0.6
0.8
1.0
2.0
3.0
4.0
5.0
2.50
terminal velocity (m/s)
0.50
0.31
0.57
0.50
1.00
1.80
0.71
1.6
2.46
3.25
4.03
6.49
8.06
8.83
9.09
6
2.00
Falling velocity (Vt in m/s)
crystal type
1
2
3
4
5
6
1.50
x
needle
plane dendrite
spatial dendrite
powder snow
crystal with droplets
graupel
5
1.00
1
x
0.50
x
x
x x
x
x
x
x
3
4
2
0
1
2
3
4
5
6
7
dimension of crystal (D in mm)
8
Winter Precipitation Mechanisms
•
•
•
•
Convergence
Frontal Forcing
Orographic Forcing
Convection (minimal)
Convergence
CYCLONIC LIFTING
ANTICYCLONIC SINKING
Convergence around a low-pressure area (diameter of about 1,000 km) causes
widespread precipitation. Divergence (sinking) around a high causes clearing skies.
Frontal Effects
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).