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Remote sensing techniques are frequently applied for the surveying of remote areas, where the use of conventional surveying techniques remains difficult and impracticable. In this paper, we focus on one of the remote glacier areas, namely the Tyndall Glacier area in the Southern Patagonian Icefield in Chile. Based on optical remote sensing data in the form of multi-spectral Sentinel-2 imagery, we analyze the extent of different snow and ice classes on the surface of the glacier by means of pixel-wise classification. Our study comprises three main steps: (1) Labeled Sentinel-2 compliant data are obtained from theoretical spectral reflectance curves, as there are no training data available for the investigated area; (2) Four different classification approaches are used and compared in their ability to identify the defined five snow and ice types, thereof two unsupervised approaches (k-means clustering and rule-based classification via snow and ice indices) and two supervised approaches (Linear Discriminant Analysis and Random Forest classifier); (3) We first focus on the pixel-wise classification of Sentinel-2 imagery, and we then use the best-performing approach for a multi-temporal analysis of the Tyndall Glacier area. While the achieved classification results reveal that all of the used classification approaches are suitable for detecting different snow and ice classes on the glacier surface, the multi-temporal analysis clearly reveals the seasonal development of the glacier. The change of snow and ice types on the glacier surface is evident, especially between the end of ablation season (April) and the end of accumulation season (September) in Southern Chile. [ABSTRACT FROM AUTHOR]