Snow and ice melt form significant contributions to river base flows throughout the Himalayas, but their contribution to seasonal and catastrophic flooding is unclear. As glaciers melt and winter accumulation and temperature patterns shift with climate change, this contribution will cause changes to flood risk. This paper applies a new physical model of streamflow to estimate the separate contributions of precipitation and melt to historical flows at the Bhakra Dam on the Sutlej river, in the Indus River Basin. At the Bhakra dam, 26% of the flow volume of historical floods within our dataset is attributable to melt. A multivariate copula-based probability model produces a similar result for the 10-year flood. Using the model parameters calibrated for the Bhakra inflow, we find that the contribution of melt to flood flows varies over the basin, being higher at high elevation and in smaller basins, and is between 10 to 30% for the larger Indus river basin. We also perform sensitivity checks across a range of increases in temperature and precipitation.