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 earth-atmosphere 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

Season of Rate Season of RateClimate maximum (oC/km) minimum (oC/km)Tropical rainy dry season > 5 rainy season > 4.5Tropical and summer > 8 winter > 5subtropical desertsMediterranean winter > 5 summer < 5Mid-latitudes summer > 6 winter 0 - 5(cold winter)Boreal continental summer > 5 winter < 0Arctic summer < 0 winter < 0

Temperature lapse rate in lowest 1000 - 1500 m (after Lautensach & Boegel, 1956)

Temperature Variation in the Troposphere (cont’d)

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)

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

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

17.3 T

(T+237.3)esat(T)=6.11 exp )(

Vapour Pressure

temperature

Vapour pressuresaturated

vapourpressure

17.3 T

(T+237.3)esat(T)=6.11 exp )(

Humidity (cont’d)

• 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)

We

e Taa

sat

( )

T ee

ed aa

a

( )ln( ) .

. . ln( )

1 810

0 0805 0 00421

qe

pva

a

0 622.

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 a Adz,

the mass of the water is qv a 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

Wp=1.12 exp (0.0614 Td )

2

1

z

z avp AdzqW =

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 m)

– large aerosols ( 0.2<D< 2 m)

– giant aerosols ( 2 m<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)

Human activities 106 tpa

Gas-to-particle conversion 275Industrial processes 56Fuel combustion (stationary sources) 44Solid waste disposal 2.5Transportation 2.5Miscellaneous 28TOTAL 410

Natural sources 106 tpa

Sea salt 1000Gas-to-particle conversion 570Windblown dust 500Forest fires 35Meteoric debris 20Volcanoes (highly variable) 25TOTAL >2150

Worldwide aerosol production in tonnes per annum (after Wallace & Hobbs, 1971)

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 (FV) 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 w growing by diffusion of water vapour according to Fick’s 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)

Fdm

dtR D

d

dRv

4 2 a constant (B)

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 m (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 efficiencydR

dt

EWV v

w

4

( )

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 y R rc 2 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 m, [SO42-] = 5.7mgL-1

» pH = 5.1, N = 189 cm-3, D = 8.0 m, [SO42-] = 3.9mgL-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)

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.

Snow Crystal Growth Patterns

from Ono, 1970: J. Atmos. Sci., 27: 649‑658.

1

10

100

1000

-20 -15 -10 -5 0

temperature (degrees C)

gro

wth

ra

te (

x 1

0-10 g

/s)

maximum rate

minimum rate

Snow Crystal shape is temperature dependent

Snow Crystal Growth Patterns

-20 -15 -10 -5 0temperature (degrees C)

100% planar

100% columnar

prismface

basalplane

a-axisa-axis c-axis

3-D growth rate for T < 0 oC

0-2

-4-6

-8-10

-12-14

-16-18

-20-22

-24-26

-28-30

-32

prism face

basal plane

0.1

1

10

100

1000

gro

wth

rat

e

temperature (degrees C)growth direction

2-3

1-2

0-1

-1-0

prism face

basa

l pla

ne

Particle Shape

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.

plate F1

ste llar crysta l F2

colum n F3

needle F4

spatia l dendrite F5

capped colum n F6

irregular crysta l F7

ice pellet F9

graupel F8

hailstone F0

NAM E SYM BO Lsym bolicrepresentation EX AM PLES

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.

uBDg FFFFdt

dvm

Terminal Velocities 

 

crystal type dimension/diameter (mm) terminal velocity (m/s)

Needle 1.53 0.50Plane dendrite 3.26 0.31Spatial dendrite 4.15 0.57Powder snow 2.15 0.50Crystals with graupel 2.45 1.00Graupel 2.13 1.80Rain drops 0.2 0.71

0.4 1.60.6 2.460.8 3.251.0 4.032.0 6.493.0 8.064.0 8.835.0 9.09

x

xx

xx x

xx

x x

2.50

2.00

1.50

1.00

0.50

0

Fal

ling

velo

city

(V

t in

m/s

)

1 2 3 4 5 6 7 8 dim ension of crysta l (D in m m)

2

4

1

5

3

6

1 needle2 plane dendrite3 spatial dendrite4 pow der snow5 crystal w ith droplets6 graupel

Winter Precipitation Mechanisms

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

Convergence

ANTICYCLONIC SINKINGCYCLONIC LIFTING

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).