A new implementation of a calving model, using the finite-element code Elmer, is presented and used to investigate the effects of surface water within crevasses on calving rate. For this work, we use a two-dimensional flowline model of Columbia Glacier, Alaska. Using the glacier's 1993 geometry as a starting point, we apply a crevasse-depth calving criterion, which predicts calving at the location where surface crevasses cross the waterline. Crevasse depth is calculated using the Nye formulation. We find that calving rate in such a regime is highly dependent on the depth of water in surface crevasses, with a change of just a few meters in water depth causing the glacier to change from advancing at a rate of 3.5 km a-1 to retreating at a rate of 1.9 km a-1. These results highlight the potential for atmospheric warming and surface meltwater to trigger glacier retreat, but also the difficulty of modeling calving rates, as crevasse water depth is difficult to determine either by measurement in situ or surface mass-balance modelling.