An energy-balance model has been developed by Oerlemans (1988, 1991, 1992). This model calculates the components of the surface energy balance. It takes meteorological data, the area distribution with altitude of ice mass, and parameters defining the global radiation as input values. This model has also been used to calculate mass balance for glaciers in the Austrian Alps (Oerlemans and Hoogendoorn, 1989), southern Norway (Oerlemans, 1992), the Greenland ice sheet (Oerlemans, 1991) and NW Spitzbergen (Fleming et ah, 1997). The input data for the model are the annual mass balance, the fraction of meltwater that refreezes instead of running off, the energy balance at the surface, the latent heat of melting, and the rate of precipitation in solid form. The energy exchange between the atmosphere and the glacier surface is found from:
where a is the surface albedo, Q is the shortwave radiation reaching the surface, Iin and
Iout are the incoming and outgoing long-wave radiation, and Fs and F| are the sensible and latent heat fluxes. The energy budget is divided into several components: solar radiation, long-wave radiation, turbulent energy fluxes and the refreezing of meltwater. The solar radiation reaching the top of the atmosphere is attenuated by absorption and scattering. Cloudiness, solar zenith angle and surface elevation are accounted for. However, the geometry of the glacier surface is not normally accounted for. Surface albedo is dependent on the presence of snow, the distance to the equilibrium line, and the total area of glacier ice exposed during the ablation season. The long-wave component of the energy equation is divided between the outgoing radiation from the glacier surface and the incoming radiation from the atmosphere. The atmospheric long-wave radiation is in two parts: the contribution from a clear sky and that from the clouds. Turbulent fluxes are proportional to the difference between the air and surface temperatures and humidity. There are three approaches by which the required meteorological parameters are made available to the model: (1) the use of long-term climate data; (2) annual fits to measured data; and (3) daily inputs. The annual method has been used most commonly (Oerlemans, 1991, 1992) because daily meteorological data are either lacking or are only available from meteorological stations remote from the glaciers being modelled. This requires the annual temperature to be expressed as a sinusoidal function. Precipitation is defined as constant through the year. Precipitation is assumed to fall as snow when the daily average temperature is below 2°C. All rainfall is assumed to run off. Humidity and cloudiness are constant throughout the year, and set to the mean annual value.
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