SCaLS: A two-stage scale correction framework for improving slope length and steepness factor estimation from coarse-resolution DEMs

The slope length and steepness factor (LS factor) is a key parameter in soil erosion modeling, and its accuracy directly affects the reliability of soil erosion predictions. However, LS factor estimates derived from coarse-resolution digital elevation models (DEMs) often deviate from high-resolution reference values, as low-resolution data fail to capture fine-scale terrain variability. Existing scale correction methods (e.g., histogram matching, fractal-based approaches and geographically weighted regression method) partially alleviate this issue but remain limited in preserving spatial patterns and ensuring cross-regional applicability. To address these limitations, we propose SCaLS (Scale Correction and Adjustment for LS factor), a two-stage framework designed to enhance LS factor estimation from coarse-resolution DEMs. The SCaLS framework comprises two components: (i) spatial correction, which reduces terrain-induced distortions in the spatial distribution of LS factor, and (ii) statistical adjustment, which refines the statistical properties of the LS factor using high-resolution references. SCaLS was evaluated across 20 watersheds with diverse topographic conditions using multi-resolution datasets (10 m and 30 m DEMs). Results demonstrated that SCaLS markedly improved LS factor accuracy, with a coefficient of determination (R²) of 0.81, a root mean square error (RMSE) of 2.99, and a structural similarity index (SSIM) of 0.90, outperforming the fractal-based method (R²=0.19, RMSE=9.48, SSIM=0.48), the histogram matching method (R²=0.19, RMSE=7.30, SSIM=0.51), and the geographically weighted regression method (R²=0.68, RMSE=3.54, SSIM=0.77). Moreover, SCaLS also demonstrated effective applicability at a provincial scale, further confirming its robustness. Overall, SCaLS effectively reduces both statistical bias and spatial distortion from coarse DEMs, providing a robust and transferable scale-correction framework. This framework offers valuable support for regional soil erosion modeling, land degradation assessment, soil conservation, and ecological management.