Snowmelt is an important source of runoff in high mountain catchments. Snowmelt modelling for alpine regions remains challenging with scarce gauges. This study simulates the snowmelt in the Karuxung River catchment in the south Tibetan Plateau using an altitude zone based temperature-index model, calibrates the snow cover area and runoff simulation during 2003–2005 and validates the model performance via snow cover area and runoff simulation in 2006. In the snowmelt and runoff modelling, temperature and precipitation are the two most important inputs. Relevant parameters, such as critical snow fall temperature, temperature lapse rate and precipitation gradient, determine the form and amount of precipitation and distribution of temperature and precipitation in hydrological modelling of the sparsely gauged catchment. Sensitivity analyses show that accurate estimation of these parameters would greatly help in improving the snowmelt simulation accuracy, better describing the snow-hydrological behaviours and dealing with the data scarcity at higher elevations. Specifically, correlation between the critical snow fall temperature and relative humidity and seasonal patterns of both the temperature lapse rate and the precipitation gradient should be considered in the modelling studies when precipitation form is not logged and meteorological observations are only available at low elevation. More accurate simulation of runoff involving snowmelt, glacier melt and rainfall runoff will improve our understanding of hydrological processes and help assess runoff impacts from a changing climate in high mountain catchments. Copyright © 2013 John Wiley & Sons, Ltd.