Dynamical segmentation of avalanche debris from a time-series of Sentinel-1 SAR images

Mountain snow surfaces evolve through a combination of continuous processes, such as accumulation, melt, and redistribution, as well as abrupt, impulse-driven events, including snow avalanches. While C-band Synthetic Aperture Radar (SAR) time series have proven effective for avalanche mapping, most existing approaches rely on bi-temporal change detection or data-driven classification, treating avalanches as isolated events and neglecting the underlying temporal persistence and terrain-controlled spatial distribution of avalanche debris. In this study, we present a modified dynamical algorithm (m-DYN) for avalanche debris detection, which builds upon earlier applications of dynamical systems for mapping wet snow. The algorithm takes a SAR backscatter intensity ratio (BSR) image as an initial condition and iteratively evolves it toward a segmented image following a bistable dynamic.  This dynamics incorporates both a thresholding effect that tends to classify large BSR as avalanche debris and small BSR as background snow, and a physically consistent (topography-constrained) exchange of information between pixels at each iteration. Pixel coupling decreases with distance and is modulated by elevation differences, slope, and aspect, guiding the propagation of information along realistic avalanche flow paths and deposition zones. 

The methodology was evaluated over a study region of approximately 180 km² in the vicinity of Davos, Switzerland, within the Swiss Alps, an area of high relevance for avalanche research. Two periods of pronounced avalanche activity were analysed: 20–24 January 2018 and 13–16 January 2019. During both intervals, high-resolution SPOT-6 imagery was acquired by the WSL Institute for Snow and Avalanche Research (SLF), and precise avalanche boundaries were mapped and are publicly available. These independently mapped avalanche outlines, together with associated ground-truth coverage information, serve as validation datasets. Sentinel-1 Level-1 Ground Range Detected (GRD) imagery at 20 m spatial resolution and a nominal 6-day revisit interval was used for the SAR time-series analysis.

Initial results demonstrate that the m-DYN algorithm generates spatially coherent and terrain-consistent avalanche debris maps, effectively suppressing noise and seasonal variability while preserving fragmented and low-contrast deposits. Compared to traditional threshold-based approaches, which produce patchy detections, the dynamical segmentation approach substantially improves the reconstruction of continuous avalanche flow paths while maintaining robust precision values. The method converges reliably within a limited number of iterations and shows strong agreement with independent validation datasets across both study periods, underscoring the potential of topography-aware dynamical algorithms for avalanche mapping using a SAR time series.