Runoff Parameterizations

The simplest parameterization, called here the linear model, relies on the observed correlation between the summer ablation, in meters, and the average summer temperature, T_avg, for T_avg > - 2^oC (Wild and Ohmura (1999)):

Runoff = 0.514 ^. T_avg + 0.93 (1)

The coefficients were obtained by performing a linear regression between the ablation and the summer temperature. This model has the advantage of simplicity, yet the drawback of neglecting the influence of a number of factors on melting. The non-linear evolution of the surface albedo for air temperatures near and above the melting point and the differences in albedo between snow and ice (Kang (1994)) can for example be expected to undermine the assumption of a linear behavior underlying this model.

A slightly more sophisticated temperature based parameterization is commonly referred to as a degree-day model (Braithwaite and Olesen (1989), Huybrechts et al. (1989)). It relies on the integral of the positive air temperatures over the summer, positive degree-days or PDD, as melting potential and introduces two different melting factors for snow and ice in an attempt to represent the differences in the albedos of these two surfaces. The snow accumulated during the winter is melted first at the rate m_snow = 0.03 m/PDD. A prescribed fraction of that meltwater, P_max = 0.6, refreezes to form superimposed ice layers. The remainder of the positive degree-days are used to melt ice at the rate m_ice = 0.08 m/PDD, this meltwater contributes to the runoff from the ice sheet. The melt rates, m_snow and m_ice, have been shown to vary with location on the ice sheet (Braithwaite (1995)), they will be kept constant in this study to test the universality of the parameterization and allow a comparison with previous model studies.