Shortwave radiation is the main driver of snow and ice melt in most environments. Incoming solar radiation is absorbed and scattered as it traverses the gauntlet of atmospheric gases and aerosols (suspended particles such as water droplets, ice crystals, and dust). The processes of absorption and scattering depend on the wavelength of the electromagnetic radiation and the size of the obstacle (gas or aerosol). Similarly, backscatter (reflection) from ice crystals is also wavelength dependent, as discussed in chapter 2. This complexity is commonly neglected in cryosphere studies, however, and the shortwave radiation and albedo in (3.1) are defined based on an integrated broadband spectrum, from about 0.2 to 2.5 mm. Alternatively, shortwave radiation can be modeled in two or three wavelength bands, for instance ultraviolet, visible, and near-infrared frequencies. This is becoming more common in energy balance studies as it permits a separate treatment of visible and near-infrared albedos, which differ markedly for snow (figure 2.5).
The average top-of-atmosphere solar irradiance is the solar constant, I0, which is approximately equal to 1366 W m-2. The solar constant is not really constant; daily and decadal variations of up to a few watts per square meter are common, as a result of variable solar convec-tive activity. The instantaneous top-of-atmosphere solar irradiance also differs from the solar constant as a function of the Earth-Sun distance. This instantaneous distance is denoted R. Top-of-atmosphere irradiance, QS0, is calculated from where R0 = 1.5 x 108 km is the mean Earth-Sun distance. Peak top-of-atmosphere solar irradiance occurs when the Earth is at its closest approach to the Sun, a time known as the perihelion. Perihelion currently occurs on January 3, although its timing varies on timescales of 104 years as part of the Milankovitch cycles (see chapter 9).
Incoming shortwave radiation at the surface, also known as insolation, is made up of two main components: direct and diffuse solar radiation. A third contribution, direct light that is reflected from the surrounding terrain, can also add to the surface insolation. Direct solar radiation is the radiative flux from the solar beam, which comes in at a zenith angle Z, measured from the normal to the geoid surface. The zenith angle is a function
of latitude, time of year, and time of day. Potential direct (clear-sky) solar radiation on a horizontal surface can be estimated from
where y is the atmospheric transmissivity at sea level, P is the air pressure at the site, and P0 = 101.325 kPa is the mean air pressure at sea level. P/P0cos(Z) in (3.9) account for the effects of atmospheric attenuation due to the amount of atmosphere that the direct beam must traverse, a function of both elevation (atmospheric pressure) and slant path.
It is common to use the clear-sky atmospheric transmissivity in (3.9), y0 . 0.84. The effects of cloud cover or varying atmospheric absorption (e.g., associated with dust or aerosols) can also be incorporated in y. In thick haze or smog, y . 0.6, and under heavy cloud cover, y " 0. The actual direct solar radiation at a site only equals the potential direct solar radiation under clear-sky conditions.
In mountain topography, the effects of surface slope, aspect, and shading also need to be incorporated in estimates of potential direct solar radiation. This can be approximated from digital elevation models, and the solar geometry can be modeled for a particular location, time of year, and time of day, allowing detailed calculations of potential direct solar radiation at any point in space.
In addition to the direct solar beam, diffuse radiation reaches a site from all directions in the sky hemisphere. Diffuse atmospheric radiation arises due to Rayleigh scattering off of atmospheric gases and Mie scattering off of aerosols, water droplets, and ice crystals. Illumination from diffuse light is the reason that there is not complete darkness when the Sun is obscured. Diffuse atmospheric radiation is close to isotropic (derived equally from all points in the sky vault) when it is overcast, but it is generally anisotropic, with more radiation in proximity to the direct beam. Total incoming solar radiation at the surface, QS', is equal to the sum of the direct, diffuse, and terrain contributions. This is often called the global radiation, although this is unfortunate terminology as it is not global in the true sense of the word.
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