Debris-Flow Erosion Volume Estimation Using a Single High-Resolution Optical Satellite Image

Debris flows pose significant risks to mountainous regions, and quick, accurate volume estimation is crucial for hazard assessment and post-disaster response. Traditional volume estimation methods, such as ground surveys and aerial photogrammetry, are often limited by cost, accessibility, and timeliness. While remote sensing offers wide coverage, existing optical and Synthetic Aperture Radar (SAR)-based techniques face challenges in direct volume estimation due to resolution constraints and rapid terrain changes. This study proposes a Super-Resolution Shape from Shading (SRSFS) approach enhanced by a Non-local Piecewise-smooth albedo Constraint (NPC), hereafter referred to as NPC SRSFS, to estimate debris-flow erosion volume using single high-resolution optical satellite imagery. By integrating publicly available global Digital Elevation Model (DEM) data as prior terrain reference, the method enables accurate post-disaster topography reconstruction from a single optical image, thereby reducing reliance on stereo imagery. The NPC constraint improves the robustness of albedo estimation under heterogeneous surface conditions, enhancing depth recovery accuracy. The methodology is evaluated using Gaofen-6 satellite imagery, with quantitative comparisons to aerial Light Detection and Ranging (LiDAR) data. Results show that the proposed method achieves reliable terrain reconstruction and erosion volume estimates, with accuracy comparable to airborne LiDAR. This study demonstrates the potential of NPC SRSFS as a rapid, cost-effective alternative for post-disaster debris-flow assessment.