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Distinct properties of snow

• High reflectivity or albedo • Low thermal conductivity & heat

capacity • Limited by 0oC (low energy status)• Reservoir for water & heat• Porous and translucent• Mobile & smooth surface• Varies greatly in space & time

So

urce: O

ke (19

87)

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Features that characterize a snowpack

• Snow depth• Snow water equivalent (swe)• Snow density• Grain size distribution• Albedo• Heat content (“cold content”)• Temperature

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Other features that characterize a snowpack

• Porosity• Liquid water content (“wet

snowpack”)• Texture• Layered structure• …

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Surface Radiation, Energy and Water Budgets

• Conservation of energy requires that radiation be either absorbed, transmitted or reflected.

• In other words: aλ + tλ+ αλ = 1

• where these are the fraction of absorbed (aλ), transmitted (tλ), or reflected (αλ) radiation at a given wavelength (λ).

• The reflectivity for shortwave radiation is called ``albedo''.

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• From Kirchoff's Law, it can be shown that ελ = aλ (i.e. emissivity = absorptivity).

• Thus good absorbers are also good emitters at a given wavelength.

• The albedo is an important surface property for shortwave (solar) radiation, the emissivity for longwave (terrestrial) radiation.

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Oke (1987)

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• Over one year, the energy input must equal the energy output of the earth-atmosphere system.

• Thus the incoming solar radiation K↓ is balanced by reflected shortwave radiation K↑ (i.e. from clouds, snow, etc.), and a balance between incoming L↓ and outgoing L↑ longwave radiation.

• The net all-wave radiation (Q*) is the most important energy exchange because for most systems it represents the limit of the available energy source or sink.

• The daytime surface radiation budget is the sum of the individual short- and long-wave components:

8Source: http://science.larc.nasa.gov

Earth’s Radiation Budget

9

Oke (1987)

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Earth’s energy balance

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• Q* = K* + L* = K↓ + K↑ + L↓ + L↑ • Such that: Q* = K↓ (1 - α) + L ↓ + εσT4 + (1

– ε)L↓

Where the albedo α = K↑/ K↓ and ranges from 0-1, averaging 0.3 for the entire globe.

• Stefan-Boltzmann Law provides information on the amount of radiation emitted by a body: E = εσT4 where T is in Kelvins and where σ = 5.67 × 10-8 W m-2 K-4

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• Q* is the net energy “left over” from radiation.

• The surface energy balance describes how this excess is distributed (deficit made up):

• Q* = QH + QE + QG

• Where QH is the sensible heat flux, QE is the latent heat flux, and QG is the ground heat flux, all in units of W m-2.

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• In some systems there can be storage of heat - the volume can gain heat:

• Q* = QH + QE + QG + ΔQS

• On an annual basis, storage of water remains small such that the water balance is given by:

• P = E + R,• where P is precipitation, E is evapo-

transpiration, and R denotes runoff.

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• Water exists in all states at normal earth temperatures.

• In changing between phases, latent heat is exchanged, thus linking the water and energy balances, i.e.

• QE = Lv E

• where Lv (= 2.5 MJ kg-1) is the latent heat of vapourization and E is in kg m-2 s-1.

• A phase change from snow and ice to water vapour is called sublimation whereas the reverse process is termed deposition.

• About 2.8 MJ kg-1 (latent heat of sublimation, Ls) is exchanged during this phase change. Thus the fusion of snow or ice requires 0.3 MJ kg-1 of energy.

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• Over shorter time scales, a change in storage (ΔS ) can become significant such that:

• P = E + R + ΔS

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Properties of Snow and Ice

• Snow and ice reflect incoming solar radiation K↓ very well - in fact, up to 95% of K↓ can be reflected back to space.

• Typical values of the surface albedo, defined as α = K↑/ K↓ , vary from 40% (old snow) to 95% (fresh snow).

• The albedo varies with the age of the snow, the amount of exposed vegetation, and the patchiness of the snowpack.

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• Snow and ice behave almost like “black bodies”, i.e. their emissivities (ε) approach unity.

• Hence the longwave radiation incident upon these surfaces is absorbed and then re-radiated back as thermal radiation.

• Following the Stefan-Boltzmann law, the amount depends on the surface temperature and has a maximum value of 316 W m-2 owing to the temperature constraint of the snowpack T = 0oC = 273.15 K.

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• Snow and ice are translucent such that they allow partial transmission of solar radiation according to Beer's Law:

• K↓(z) = K↓ (0) exp(-az)

• where a is an extinction coefficient.• Although solar radiation decreases

exponentially with depth, its penetration can reach 1 m in snow and 10 m in ice.

19Oke (1987)

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• In part because of their high albedo values, snow and ice have low energy status.

• L↑ and QE are often small owing to cold surface temperatures (limited by 0oC).

• Melting uses much of the energy when snowpack reaches 0oC, i.e. surface energy balance is given by:

• Q* = QH + QE + QG + ΔQS + QM

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Oke (1987)

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• A typical snowpack has a porosity of about 5% per volume.

• This implies that rainfall and/or meltwater can infiltrate the snowpack and refreeze lower down or even reach the surface and run off.

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• The thermal conductivity of snow is low compared with other soil surfaces and varies with the density and liquid water content of the snow cover.

• A typical thermal conductivity for dry snow with a density of 100 kg m-3 is 0.045 W m-1 K-1, over six times less than that for soil.

• This implies that snow can insulate over six times more efficiently than soil for equivalent depths.

• The total insulation provided by snow strongly depends on its depth.

24Oke (1987)

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• Snow and ice are aerodynamically smooth surfaces compared with most land surfaces, with roughness lengths (z0) of 0.01 mm to 1 mm.

• As such, wind speeds over snow tend

to increase compared to vegetated surfaces.

26Oke (1987)

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• The snow surface can move both vertically and horizontally.

• Snowfall adds depth to the snowpack whereas snowmelt or compaction can lead to a decrease in snow depth.

• Wind transport of snow can transport mass horizontally over large distances, decreasing snow depth in erosion zones and increasing snow depth in deposition areas.