The supraglacial hydrological system of the Greenland Ice Sheet (GrIS) delivers ~60% of total mass loss from the ice sheet to the ocean (van den Broeke et al., 2016), making a thorough understanding crucial for sea level rise predictions. Supraglacial lakes play a crucial role in the evolution of this system and have been implicated in initiating rapid ice-sheet acceleration (Das et al., 2008), the formation of inland surface-bed meltwater pathways (Christoffersen et al., 2018; Hoffman et al., 2018) and cryo-hydrologic warming (Phillips et al., 2010, 2013). No model currently exists to reproduce the full evolution of these lakes in the ablation zone, including the effect of snow cover. Here, the IceLake model is presented which effectively replicates recorded supraglacial lake depth data to within 0.7 m after a 165-day, over-winter, run. IceLake is computationally efficient, taking <30 seconds for a one-year run using a 3.2 GHz processor. The parameter space of IceLake is comprehensively tested and the model output is found to be relatively insensitive to the variation of most parameters, with the exception of changes to the I0 term, which controls the amount of incoming shortwave radiation that can enter a lake’s water column. IceLake is applied to a 100–2200 m a.s.l. elevation transect of Upernavik Isstrøm Glacier (72.8°N) in West Greenland to investigate the dependence of lake evolution on elevation. When only basal ice melt is accounted for and no water input is included, it is found that lake depth decreases at ~0.004 m m-1, that the time the lake has a frozen cover increases at ~0.06 days m-1, and that maximum lid thickness exhibits little variation, with a range of 1.15-1.95 m, although a clear increase and thicker average lids are seen if snow is excluded. The latter result has the important implication that even shallow (1.9 m) lakes at high elevation can effectively retard the cooling of the underlying ice overwinter and provide latent heat stores for the following spring, expediting the melt season evolution of supraglacial hydrology. Lake bottom freeze-up rate was found to be low (0.15 m year-1) and controlled primarily by ice temperature at depth.