Many mountain glaciers carry some amount of rocky debris on them, which modifies surface ablation rates. The debris is typically derived from erosion of the surrounding topography and its supraglacial extent is predominantly controlled by the relative accumulation rates of debris versus snow. Because Global Warming results in shrinking glaciers as well as thawing permafrost worldwide, changes in both rates will most likely affect the evolution of supraglacial debris cover and thus the response of glaciers to climate change. Here we report 10 Be concentrations measured in five amalgamated debris samples collected from the main medial moraine of the Chhota Shigri Glacier, India. Results suggest headwall erosion rates that are~0.5-1 mm year −1 , and apparently increasing (10 Be concentrations are decreasing) toward the present. We employed a numerical ice flow model that we combined with a new Lagrangian particle tracing routine to explore the impact of spatial and temporal variability in erosion rates and source areas on 10 Be concentrations in the medial moraine. Our modeling results show that neither changes in source areas, related to the transient response of the glacier to ongoing climate change, nor four different scenarios of spatial and temporal variability in erosion rates could explain the observed trend in 10 Be concentrations. Although not accounted for in our modeling explicitly, we suggest that the observed trend could be due to transiently enhanced erosion of recently deglaciated areas, or to greater spatial variability in erosion rates than explored in our models. Plain Language Summary High and steep mountain ranges are currently undergoing changes due to increasing temperatures. These changes include rapidly shrinking glaciers as well as thawing permafrost, which together destabilize rock walls that surround valley glaciers. In consequence, slope failures and thus erosion rates in these environments are expected to increase. However, quantifying rock wall erosion in alpine landscapes is difficult and estimates of background erosion rates that are unaffected by Global Warming are rare. Here we estimate rock wall erosion rates above the Chhota Shigri Glacier, Indian Himalaya, by studying rocky debris from the glacier surface. This debris is sourced from the surrounding topography and we use geochemical tools to measure its residence time at the Earth surface. We combine our geochemical observations with a computer model of the glacier that allows us to explore the effect of Global Warming on the evolution of the glacier and the debris on its surface. Our results suggest recent changes in rock wall erosion rates that may be related to glacier retreat and an increase in the erosion of rock walls that were previously ice covered.