The albedo of snow

As outlined by Nolin and Liang (2000), snow can be considered as a layered particulate medium composed of ice spheres in air. Scattering by the spheres is primarily through refraction. Using the refractive indices of ice and an optically equivalent ice sphere radius, Mie theory (appropriate when the effective particle radius is much larger than the wavelength of the interacting radiation) can be used to calculate single-particle scattering and absorption (i.e., the scattering and absorption of a single snow grain). In turn, the single-particle scattering properties can be transformed into multiple-scattering properties using radiative transfer approaches such as the delta-Eddington approximation that characterizes the strong forward scattering of snow (Mie scattering) in the solar wavelengths (Wiscombe and Warren, 1980). Although snow grains are usually not spherical, considering the grains as optically equivalent spheres can approximate their optical properties. Scattering and absorption is a function of the snow optical depth. Optical depth, which is wavelength dependent, is in turn affected by physical snowpack depth, snow density and grain size. Typical snow water equivalent depths for an optically thick snowpack at a wavelength of 0.46 ^m are 20 mm for a particle radius of 50 ^m and 200 mm for a particle radius of 1000 ^m. Smaller ice grains increase the number of scattering events. Hence, the smaller the grains, the thinner the snowpack can be and still appear optically thick.

An aggregation of ice particles will scatter nearly all energy in visible wavelengths. In the visible spectrum, ice particles scatter very strongly in the forward directions.

Figure 5.2 Direct-beam spectral reflectance for a semi-infinite snowpack as a function of wavelength for grain radii from 50 to 1000 ^m and for a solar zenith angle of 60° (from Wis-combe and Warren, 1980, by permission of AMS).

0.2 0,40.6 0.8 1.01.2 1.41.6 1.3 2.0 2,2 2.4 2,6 2,8 Wavelength (^m)

Figure 5.2 Direct-beam spectral reflectance for a semi-infinite snowpack as a function of wavelength for grain radii from 50 to 1000 ^m and for a solar zenith angle of 60° (from Wis-combe and Warren, 1980, by permission of AMS).

0.2 0,40.6 0.8 1.01.2 1.41.6 1.3 2.0 2,2 2.4 2,6 2,8 Wavelength (^m)

If absorbing particulates (e.g., dust and soot) are mixed with the snow, scattering decreases and becomes more isotropic. In the near infrared region (0.7-4.0 ^m) ice is still forward scattering but the property controlling the magnitude of scattering is the particle size. As snow ages, snow grains increase in size, which increases the probability of a photon being absorbed and reduces the effective volume scattering. The modeled direct-beam spectral reflectance of a snowpack of semi-infinite depth for different grain radii for a zenith angle of 60° is provided in Figure 5.2.

The liquid water content of snow rarely exceeds 5%. As the refractive indices of ice and liquid water are nearly identical, liquid water has little direct effect on the scattering. However, there is an indirect effect as water enables the growth of clusters of snow grains, which respond optically as individual grains. As a significant portion of the solar spectrum lies in the near infrared, changes in snow grain size significantly affect the albedo.

Building on previous discussion, the albedo of a snow cover tends to increase with an increasing solar zenith angle. This is understood from the forward scattering of snow particles. For a large zenith angle, there is a high likelihood that a photon will be scattered upwards and out of the snowpack. For a small zenith angle, there will be more interactions between a photon and snow grains, and a greater likelihood of absorption.

As mentioned previously, clouds preferentially absorb the longer solar wavelengths and cause more of the radiation to be diffuse. This shift in the spectral characteristics of the incident flux is augmented by multiple scattering between the surface and cloud base (Wiscombe and Warren, 1980). These processes increase the proportion of visible-band radiation for which scattering is greatest, hence increasing the albedo. Multiple scattering between a stratiform overcast sky and a snow surface can cause a 7-20% increase in snow albedo compared to clear skies (Petzold, 1977; Choudhury and Chang, 1981). The effect of increasing the diffuse component is to change the effective solar zenith angle (Warren, 1982). The effective solar zenith angle for overcast conditions is about 50°. Hence, if the true solar zenith angle is >50°, the effect of clouds is to decrease the effective solar zenith angle and reduce the albedo. By contrast, if the true solar zenith angle is <50°, the effect of clouds is to increase the effective solar zenith angle and increase the albedo. According to Warren (1982) the effect of the spectral shift in the incident flux (enrichment of the visible-band portion) is normally greater than the effect of the changed zenith angle, such that cloud cover increases the albedo. The snow albedo can also be influenced by the surface morphology. Carroll and Fitch (1981) found a reduction in albedo of 4% during periods when the solar zenith angle is normal to sastrugi in the surface snow cover (resulting in shadowing) compared to periods when it is parallel to sastrugi.

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