Recent studies suggest that the Greenland Ice Sheet (GrIS) is thinning rapidly and contains sufficient water equivalent to raise global sea levels by ~7m. The dynamic response of ice sheets to rising air temperatures has been well documented, whereby increased surface meltwater accessing the ice sheet bed results in high subglacial water pressures that lubricate the bed and enhance basal motion. This could in turn drastically amplify the contribution of GrIS to sea-level rise (SLR). However, the inadequate formulation of ice dynamics in current ice-sheet models was identified as the largest source of uncertainty in SLR projections in the latest IPCC AR4 report. This thesis focuses on the supraglacial and subglacial hydrology of the Paakitsoq region in western Greenland to provide an insight into present-day dynamic behaviour of the ice sheet, and its potential response to climatic warming over the 21st century. Surface meltwater production and routing for 2005 are simulated using a surface mass balance model and a positive-degree day model, which in turn provides the input to a distributed, physically based model of subglacial drainage applied to Paakitsoq. The drainage model is then forced with future climate scenarios based on the IPCC’s new framework of Representative Concentration Pathways (RCPs). The simulations produce a distinctive split in “marginal” and “inland” drainage behaviour at Paakitsoq, whereby the inland system is typified by low discharge magnitudes, high water pressures and small conduit CSAs, and the marginal system displays high discharge, mid to low pressures and higher conduit CSAs. Comparisons between measured and modelled proglacial discharge suggest that the appropriate k factor (the ratio of water pressure to ice overburden pressure) for modelling the study system is between 0.925 and 0.95. The most extreme climate scenario predicts a ~7oC rise from 2010 to 2100, which will result in proglacial discharge increasing by the end of the 21st century to levels four times greater than today. However, significant inter-annual variability in melt production at Paakitsoq will probably lead to high-melt years whose peak subglacial discharges may be even more intense. This could cause considerable inland migration of channelised behaviour. The implications for future ice dynamics in the Paakitsoq region are considered.