Statistical estimation and generalized additive modeling of rock glacier distribution in the San Juan Mountains, Colorado, United States

Abstract

Our goal is to quantify rock glacier abundance and analyze the topographic controls of rock glacier distribution patterns. For this purpose we use statistical estimation techniques and generalized additive models relating rock glacier occurrences to terrain attributes. Significant applied results include the ability to determine water equivalence and denudation rates. The statistical estimation of regional rock glacier abundance based on local interpretation of air photos is an efficient alternative to costly rock glacier inventories. These presence‐absence data (N = 2933) also allow us to analyze the partly nonlinear topographic controls on rock glacier distribution with generalized additive models. We apply these techniques in the San Juan Mountains (2874 km2 above 3400 m), Colorado, where we obtained a total rock glacier surface area of 70 km2 corresponding to a water equivalence in the order of 0.50–0.76 km3. Estimated rock glacier debris volumes imply postglacial denudation rates on the order of 0.5–1.1 mm yr−1 within the talus sheds of rock glaciers. The distribution model shows the nonlinear factors of local slope, slope of the contributing area, local curvature, and size of the contributing area controlling the probability of rock glacier occurrence. The model yields an area under the receiver‐operating characteristics curve of 0.91, which indicates an excellent fit. On the basis of the present results the integration of terrain attributes with remote‐sensing data will be the next step toward automatic mapping of rock glaciers in vast mountain areas.