Evaluating the effect of the actual eroded badland area on the estimate of eroded volume in Italian calanchi areas

According to the available literature, the morphometric characteristics of badland basins (e.g., area of the badland drainage basin, A, and actual eroded badland area, AE) can be used for deducing an empirical model able to predict the eroded volume, V. The main aim of this investigation is to implement a model to estimate the volume of eroded sediments, which uses widely applied morphological indices. This model, deduced by applying dimensional analysis and self-similarity theory, was calibrated and verified using the badland morphometric characteristics of five datasets (four available in the literature and one presented in this investigation). The results showed that the estimate of the eroded volume is reliable only for the data characterized by V/A values higher than a threshold (0.1 m) corresponding to the vertical resolution of the investigated digital terrain models (DTMs). For considering that the actual eroded badland area AE can be different from the respective drainage area A, as badland erosion induces a headward extension, the model for estimating the eroded volume was calibrated by differentiating between partially (AE/A < 1) and totally (AE/A = 1) eroded badland basins. The analysis highlighted that the actual eroded badland area, which is the area that more contributes to the active erosion process, remarkably influences the estimate of V, and the inclusion of the ratio AE/A in the model is useful to improve this estimate. The estimate of the eroded sediment volume from calanchi areas has a scientific and practical relevance as the high erosion rates of small badland areas can disproportionately contribute to the basin-scale sediment budget.