A new spatially and temporally variable sigma parameter in degree-day melt modelling of the Greenland Ice Sheet 1870–2013

Abstract. The degree-day based method of calculating ice-/snow-melt across the Greenland Ice Sheet (GrIS) commonly includes the temperature parameter sigma (σ) accounting for temperature variability on short (sub-monthly down to hourly) timescales, in order to capture melt in months where the mean temperature is below 0 °C. Sigma is typically assumed to be constant in space and time, with values ranging from ~ 2.5 to 5.5 °C. It is unclear in many cases how these values were derived and little sensitivity analysis or validation has been conducted. Here we determine spatially and temporally varying monthly values of σ for the unique, extended 1870–2013 timescale based on downscaled, corrected European Centre for Medium-Range Weather Forecasts (ECMWF) Interim (ERA-I) and Twentieth Century Reanalysis (20CR) meteorological reanalysis 2 m air temperatures on a 5 km × 5 km polar stereographic grid for the GrIS. The resulting monthly σ values reveal a distinct seasonal cycle. The mean summer σ value for the study period is ~ 3.2 °C, around 1 °C lower than the value of 4.2 °C commonly used in the literature. Sigma values for individual summers range from 1.7 to 5.9 °C. Since the summer months dominate the melt calculation, use of the new variable σ parameter would lead to a smaller melt area and a more positive surface mass balance for the GrIS. Validation of our new variable σ dataset shows good agreement with standard deviations calculated from automatic weather station observations across the ice sheet. Trend analysis shows large areas of the ice sheet exhibit statistically significant increasing temperature variability from 1870–2013 in all seasons, with notable exceptions around Summit in spring, and Summit and South Dome in winter. More recently, since 1990, σ has been decreasing, significantly so in the north-west during July. These interannual σ trends reflect climate change and variability processes operating across the ice sheet, several mechanisms of which are briefly discussed.