Assessing the potential of complex artificial neural networks for modelling small-scale soil erosion by water

Abstract. Accurately modelling soil erosion by water is essential for developing effective mitigation strategies and preventing on- and off-site damages in agricultural areas. So far, complex artificial neural networks have rarely been applied in small-scale soil erosion modelling, and their potential still remains unclear. This study compares the performance of different neural network architectures for modelling soil erosion by water at a small spatial scale in agricultural cropland. The analysis is based on erosion rate data at a 5 m × 5 m resolution, derived from a 20-year monitoring programme, and covers 458 hectares of cropland across six investigation areas in northern Germany. Nineteen predictor variables related to topography, climate, management and soil properties were selected as inputs to assess their interrelationships with observed erosion patterns and to predict continuous soil erosion rates. A single-layer neural network (SNN), a deep neural network (DNN), and a convolutional neural network (CNN) were applied and evaluated against a random forest (RF) model used as a benchmark. All machine learning models have successfully captured spatial patterns of soil erosion, with the CNN consistently outperforming the others across all evaluation metrics. The CNN achieves the lowest root mean squared error (RMSE: 1.05) and mean absolute error (MAE: 0.41), outperforming the RF (RMSE: 1.31, MAE: 0.58) and the SNN (RMSE: 1.48, MAE: 0.63), while the DNN performs similarly to the CNN with a slightly higher RMSE (1.1) and MAE (0.45). The CNN notably outperforms the other three approaches when evaluating their capability to accurately predict soil erosion within given classes, achieving a weighted mean F1 score of 0.7. A permutation importance analysis identified the digital elevation model as the most influential predictor variable across all models, contributing between 15 % and 18.3 %, while USLE C and R factors also had significant importance. Overall, these findings highlight the potential of complex neural networks for predicting spatially explicit rates of soil erosion by water.