The disintegration of Larsen A and B ice shelves in 1995 and 2002, respectively, was preceded by intense surface melting during the summer of ice-shelf collapse and previous summers. To understand the transition of the ice-shelf surface from dry to wet conditions, we developed a one-dimensional model, describing the mass, heat and force balances of water and firn within the ice-shelf surface layer. The model is run using atmospheric data from an automatic weather station on Larsen C ice shelf (World Meteorological Organization station ‘Larsen Ice Site’) located south of Larsen A and B. The model’s derived melting rate is greater than melting predicted by the positive degree-day (PDD) approach, common in studies of ablating ice sheets, such as Greenland. The model shows that the years of ice-shelf break-up (1995 and 2002) are distinguished from previous years by local maxima in the number of melting days. When the PDD approach is considered, however, a maximum in the number of positive degree-days appears in the 2002 break-up year, but not in 1995.