Physical Basis for the Temperature-Based Melt-Index Method

The close relationship between air temperature measured at standard screen level and the rate of melt on snow and ice has been widely used to estimate the rate of melt. The parameterization of the melt rate using air temperature usually takes a simple form as a function of either the mean temperature for the relevant period or positive degree-day statistics. The computation provides the melt rate with sufficient accuracy for most practical purposes. Because of its simplicity, it is often called a crude method and is rated as inferior to other more sophisticated methods such as the energy balance method. The method is often used with the justification that temperature data are easily available or that obtaining energy balance fluxes is difficult. The physical process responsible for the temperature effect on the melt rate is often attributed to the sensible heat conduction from the atmosphere. The simulation capacity of the temperature-based melt-index method, however, is too good to be called crude and inferior. The author investigated physical processes that make the air temperature so effective a parameter for melt rate. Air temperature has a more profound influence on melt than previously has been acknowledged. The influence of air temperature through the turbulent sensible heat flux is limited, however. The air temperature information is transferred to the surface mainly through longwave atmospheric radiation, which is by far the most important heat source for melt. Under cloudless-sky conditions, as much as 60% of the atmospheric emission is derived from within the first 100 m and 90% from the first 1 km of the atmosphere. When the sky is overcast with the cloud bottom within the first 1 km, more than 90% originates within this layer between the surface and the bottom of the cloud. When the sky is overcast with the cloud bottom higher than 1 km, the first 1 km of the atmosphere still makes up about 70% of the longwave irradiance at the surface, for which the air temperature measured at standard screen level is the single most influential factor. Wind speed is only weakly correlated with melt rate, because the main energy source for melting is longwave atmospheric radiation, followed by the absorbed global radiation, both of which are independent of the movement of the atmosphere.