A new empirical model for estimating calanchi Erosion in Sicily, Italy

•A model is introduced to predict eroded volume from calanchi landforms.•Dimensional analysis and self-similarity theory are used to deduce the model.•The model is validated in four different calanchi sites in Italy.•The goodness of the model is measured by calculating the MSE and NSE.•The model is considered complete due to the normal distribution of the residuals.

Calanchi (plural of calanco) are typical badland landforms of the Italian landscape. They consist of dense networks of V-shaped valleys, with a sparse or absent vegetation cover, which frequently develop on unconsolidated or poorly consolidated clayey deposits. In this paper, the dimensional analysis and the incomplete self-similarity theory were used to deduce a model relating the volume of sediments eroded from the calanchi area to a set of geometric attributes of their tributary areas. The morphometric characteristics of 209 calanchi basins were used to calibrate and validate the model. The predictive skill of the model was assessed by calculating the mean square error and the Nash–Sutcliffe model efficiency coefficient. The model was found to provide a reliable prediction of eroded volume from basins entirely covered by calanchi landforms as well as from basins only partially affected by badland erosion processes. Furthermore, as the residuals between the calculated and the measured volume of the eroded material are normally distributed, the deterministic model may be considered complete, meaning that no other variables are necessary to explain the studied physical process. In other words, the model is able to predict erosion volume in calanchi landforms from a deterministic point of view.