We applied a glacier and hydrology model in the McMurdo Dry Valleys (MDV) to model the start and duration of melt over a summer in this extreme polar desert. To do so, we found it necessary to prevent the drainage of melt into ice and optimize the albedo scheme. We show that simulating albedo (for the first time in the MDV) is critical to modelling the feedbacks of albedo, snowfall and melt in the region. This paper is a first step towards more complex spatial modelling of melt and streamflow.