Estimating Original Topography of Zones Affected by Debris-flows Using Geometric Continuity

Quantifying debris-flow damage requires an estimation of the pre-event topography. However, acquisition of pre-event topographic data is often limited by the spatiotemporal uncertainty of such events. To address the limitation, this study proposes a topography estimation method based on geometric continuity and compares its performance with those of a Gaussian mixture model (GMM)-based approach and ordinary kriging. Using a pre-event LiDAR digital elevation model (DEM) as a reference, the proposed model yielded the lowest global mean absolute error of approximately 0.943 m across the entire extent of the debris-flow. Statistical errors (MAE and RMSE) were evaluated, and shape similarity was assessed using dynamic time warping (DTW) for 30 randomly extracted cross sections. The proposed model achieved the lowest average MAE of 0.544 m, RMSE of 0.685 m, and DTW distance of 5.078 m. Although the GMM-based model and kriging showed locally superior accuracy in some sections, the proposed model exhibited a higher estimation capability at the global scale. This implies that topography estimation accuracy is not determined solely by the algorithmic characteristics of a single model, and that model performance may vary depending on geomorphic conditions. Nevertheless, the proposed model provides a structurally stable estimation of the debris-flow-impacted topography and has potential applicability to similar disaster-induced landforms.