## 1. Introduction

[2] Rock glaciers are mesoscalar geomorphological and geocryological features of high mountains (Figure 1). *Barsch* [1996] characterized them as the geomorphological expression of creeping mountain permafrost. Rock glaciers are particularly frequent and well-developed in dry, continental mountain areas, where they also constitute an important, but often unheralded store of water [*Gorbunov*, 1983; *Schrott*, 1996; *Trombotto et al.*, 1999; *Trombotto*, 2000; *Brenning*, 2005a, 2005b]. Their occurrence is related to local and regional climatic and topographic controls including thermal conditions, talus production and transport, and past glaciations [*White*, 1973, 1979a, 1979b; *Olyphant*, 1983; *Parson*, 1987; *Frauenfelder et al.*, 2003; *Brenning*, 2005a]. Quantitative information on their distribution can be used to infer denudation rates [*Barsch*, 1977a, 1977c; *Schrott*, 1996; *Barsch and Jakob*, 1998; *Brenning*, 2005a] and to provide a first-order approximation of the distribution of mountain permafrost [e.g., *Barsch*, 1978; *Schrott*, 1996; *Lieb*, 1998; *Urdea*, 1998; *Frauenfelder et al.*, 2001; *Janke*, 2005].

[3] The objective of the present work is to quantify and analyze the spatial distribution of rock glaciers in the San Juan Mountains of Colorado, USA, as related to local topography. For this purpose we perform a statistical sample survey and fit a generalized additive model. The sample survey for the quantification of the altitudinal distribution of rock glaciers is based on air photos and digital elevation models (DEMs). This approach has previously been applied by *Brenning* [2005b] and *Brenning et al.* [2005] in the dry Andes.

[4] We use a semiparametric regression technique to identify local topographic and topoclimatic controls on rock glacier distribution and describe the topographic niche of these landforms. Specifically, we apply generalized additive models with a logistic link function to discriminate between rock glaciers and other areas based on terrain attributes. This technique is an extension of the logistic (linear) regression approach applied by *Brenning and Trombotto* [2006] to model rock glacier distribution.

[5] Generalized additive models (GAMs) are an extension of generalized linear models in that they conveniently include nonlinear relationships between a response and multiple explanatory variables [*Hastie and Tibshirani*, 1990]. The additive structure of these models and the possibility of including both linear and nonlinear effects leads to a more flexible, yet still interpretable model structure. The risk of overfitting GAMs is however low compared to highly flexible machine-learning techniques such as artificial neural networks or classification trees [see, e.g., *Hand*, 1997].