Predictive performance and uncertainty analysis of ensemble models in gully erosion susceptibility assessment

Abstract

Gully erosion, as a significant natural process in geomorphological evolution, poses serious threats to natural environments and socio-economic stability. In response, Gully Erosion Susceptibility Maps (GESMs) have become essential references for effective watershed management. This study aims to identify the optimal feature datasets and to quantify the uncertainty associated with gully erosion prediction models by developing a novel methodological framework based on ensembles of the three machine learning models: Random Forest (RF), Convolutional Neural Network (CNN), and Transformer models. This study area is the Tuquan watershed in Inner Mongolia, China. A total of 25 Geo-Environmental Factors (GEFs) were selected to build datasets, supplemented by a gully inventory map comprising 823 gullies, resulting in 12,946 samples of both gully and non-gully occurrences. 3 ensemble methods including probability mean (PM), Probability Weighted Mean (PWM), and Probability Empirical Weighted Mean (PEWM) were used. Subsequently, the datasets underwent multi-collinearity testing before model computations. The optimal feature datasets S₇ included factors such as the Convergence Index (CI), Topographic Wetness Index (TWI), Terrain Ruggedness Index (TRI), distance from river, annual rainfall, distance from road, drainage density, elevation, Normalized Difference Vegetation Index NDVI, slope, and Slope Length (LS). The ensemble model Transformer-RF-CNN employing PEWM demonstrated superior performance, validated by 10-fold cross-validation and 8 metrics: Efficiency (E), True Positive Rate (TPR), False Positive Rate (FPR), True Skill Statistics (TSS), Kappa coefficient (K), Area Under the receiver operating characteristic Curve (AUC), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). The uncertainty associated with GESMs was quantified using the Coefficient of Variation (CV) map, resulting in a confidence map that classified 20 zones, with 75.976% of gullies located in high-susceptibility and low-uncertainty areas. This study provides critical insights for regulators and decision-makers, facilitating more informed planning for gully erosion prevention and control.