Climate on the equilibrium line altitudes of glaciers: theoretical background behind Ahlmann's P/T diagram

The climatic condition that prevails at a glacier equilibrium line altitude (ELA) is often parameterized in terms of summer air temperature (T) and annual precipitation (P). This simple parameterization was initially proposed by Hans W:son Ahlmann. The physical background of the relationship between P and T on the equilibrium line, however, has been left unexplained since Ahlmann first questioned the mathematical form of the relationship. This relationship can be explained when the thermal and hydrological processes of the ELA formation are investigated. The present authors studied the energy exchange processes that prevail on the ELA during the melt season. The inclusion of solar radiation brings Ahlmann's hypothesis closer to energy balance, and improves his P/T diagram. By comparing the observed fluxes from the polar through the mid-latitude to the equatorial glaciers, it was found that these glaciers in different climatic regions share important similarities at the ELA. Further, it was found that the classic P/T curve originally proposed by Ahlmann in the early 20th century is a concise expression of the conservation principle of energy and mass at the ELA of glaciers, and takes the form of a polynomial of the fourth order.