The Response Time of Glacial Erosion

There has been recent progress in the understanding of the evolution of Quaternary climate. Simultaneously, there have been improvements in the understanding of glacial erosion processes, with better parameter constraints. Despite this, there remains much debate about whether or not the observed cooling over the Quaternary has driven an increase in glacial erosion rates. Most studies agree that the erosional response to climate change must be transient; therefore, the time scale of the climatic change and the response time of glacial erosion must be accounted for. Here we analyze the equations governing glacial erosion in a steadily uplifting landscape with variable climatic forcing and derive expressions for two fundamental response time scales. The first time scale describes the response of the glacier and the second one the glacial erosion response. We find that glaciers have characteristic time scales of the order of 10 to 10,000 years, while the characteristic time scale for glacial erosion is of the order of a few tens of thousands to a few million years. We then use a numerical model to validate the approximations made to derive the analytical solutions. The solutions show that short period forcing is dampened by the glacier response time, and long period forcing (>1 Myr) may be dampened by erosional response of glaciers when the rock uplift rates are high. In most tectonic and climatic conditions, we expect to see the strongest response of glacial erosion to periodic climatic forcing corresponding to Plio-Pleistocene climatic cycles. Finally, we use the numerical model to predict the response of glacial systems to the observed climatic forcing of the Quaternary, including, but not limited to, the Milankovich periods and the long-term secular cooling trend. We conclude that an increase of glacial erosion in response to Quaternary cooling is physically plausible, and we show that the magnitude of the increase depends on rock uplift and ice accumulation rates.