We propose a surface melt scheme for glaciated land surfaces, which only requires monthly mean short wave radiation and temperature as inputs, yet implicitly accounts for the diurnal cycle of short wave radiation. The scheme is deduced from the energy balance of a daily melt period which is defined by a minimum solar elevation angle. The scheme yields a better spatial representation of melting than common empirical schemes when applied to the Greenland Ice Sheet, using a 1948–2016 regional climate and snow pack simulation as a reference. The scheme is physically constrained and can be adapted to other regions or time periods.