Rising global air temperatures are causing increased melting across the surfaces of large ice masses such as the Greenland Ice Sheet and the ice caps of Arctic Canada. The fraction of this melt that refreezes within the snow and firn has a large spatial variability across the surfaces of these ice masses. This spatial variability is an important control on the surface mass balance, and has important implications for the interpretation of satellite radar altimetry data sets. The sensitivity of large ice masses to climate change depends on changes in the melt-runoff relationship, and changes in the spatial extents of surface snow zones within the accumulation zone. Therefore, this thesis develops a model used to calculate melt, near-surface refreezing and surface runoff across the surface of a large ice mass. The model is used to predict both stratigraphic changes and bulk snow and firn properties over a melt season across a transect of points. A high-resolution snow and firn data set from Devon Ice Cap is used to calibrate and validate the model. It is then run across a transect covering the entire altitude range of the ice cap for the summers of 2004 and 2006. The model matches measured trends in bulk snowpack variables across the transect in both years. Calculated fraction of melt running off is similar in both years at ~44%, though is sensitive to change in air temperature. Surface mass balance (including internal accumulation), found to be +0.26 Gt in 2004 and +0.18 Gt in 2006, changes in a parabolic way for a linear air temperature change. The model is then applied to the Greenland Ice Sheet without altering any of the calibrated parameters. It is run for two melt seasons, 2004 and 2005, over which model output compares well with measurements of snow depth, sub-surface density and altitudes of snow surface boundaries. The wet snow line responds in a linear way to change in air temperature, and the runoff line is sensitive to the specified depth within the firn of the impermeable layer. Over the next century, the model shows that the dry snow zone will disappear completely under moderate warming scenarios, and the percolation zone will also disappear under intense warming scenarios. Including a more complicated representation of vertical meltwater percolation through the snow and firn grid substantially alters modelled autumn density profiles, and produces more accurate values of meltwater percolation depth and ice fraction within the autumn snowpack. However, bulk snowpack properties are of similar accuracy to the un-modified model. Scaling up of the model, in both spatial and temporal terms, will make it useful for assistance in the interpretation of satellite radar altimetry data sets, as well as assessing future changes in the spatial variability of refreezing and runoff, reducing the uncertainty in long term surface mass balance predictions across large ice masses.