A semi-analytical solution for the positive degree-day model with stochastic temperature variations

A semi-analytical solution the positive degree-day model with stochastic temperature variationsThe degree-day model is a parameterization for the melt rate of snow and ice at the surface of an ice sheet or glacier.It is a simple, empirical relation which states that the melt rate is proportional to the surface-air temperature excess above 08C (e.g.Braithwaite and Olesen, 1989;Hock, 2003).The physical basis of this and related temperature-based meltindex methods was examined by Braithwaite (1995).It was suggested by Braithwaite (1984) that the number of positive degree-days, PDD, could be calculated from the normal probability distribution around the long-term monthly mean temperatures.A form, which is based on that and is widely used in current ice-dynamic models, was proposed by Reeh (1991).It