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 Source: Oke (1987)

Features that characterize a snowpack Snow depth Snow water equivalent (swe) Snow density Grain size distribution Albedo Heat content (“cold content”) Temperature

Other features that characterize a snowpack Porosity Liquid water content (“wet snowpack”) Texture Layered structure …

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''.

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

Oke (1987)

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:

Earth’s Radiation Budget Source: http://science.larc.nasa.gov

Oke (1987)

Earth’s energy balance

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

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.

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.

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. 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.

Over shorter time scales, a change in storage (ΔS ) can become significant such that: P = E + R + ΔS

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.

Snow and ice behave almost like “black bodies”, i. e 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.

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.

Oke (1987)

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

Oke (1987)

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.

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.

Oke (1987)

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.

Oke (1987)

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.