Gully erosion is considered to be one of the main causes of land degradation in arid and semi-arid territories around the world. In this research, gully erosion susceptibility mapping was carried out in Semnan province (Iran) as a case study in which we tested the efficiency of the index of entropy (IoE), the Vlse Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method, and their combination. Remote sensing and geographic information system (GIS) were used to reduce the time and costs needed for rapid assessment of gully erosion. Firstly, a gully erosion inventory map (GEIM) with 206 gully locations was obtained from various sources and randomly divided into two groups: A training dataset (70% of the data) and a validation dataset (30% of the data). Fifteen gully-related conditioning factors (GRCFs) including elevation, slope, aspect, plan curvature, stream power index, topographical wetness index, rainfall, soil type, drainage density, distance to river, distance to road, distance to fault, lithology, land use/land cover, and soil type, were used for modeling. The advanced land observing satellite (ALOS) digital elevation model with a spatial resolution of 30 m was used for the extraction of the above-mentioned topographic factors. The tolerance (TOL) and variance inflation factor (VIF) were also included for checking the multicollinearity among the GRCFs. Based on IoE, we concluded that soil type, lithology, and elevation were the most significant in terms of gully formation. Validation results using the area under the receiver operating characteristic curve (AUROC) showed that IoE (0.941) reached a higher prediction accuracy than VIKOR (0.857) and VIKOR-IoE (0.868). Based on our results, the combination of statistical (IoE) models along with remote sensing and GIS can convert the multi-criteria decision-making (MCDM) models into efficient and powerful tools for gully erosion prediction. We strongly suggest that decision-makers and managers should use these kinds of results to develop more consistent solutions to achieve sustainable development on degraded lands such as in the Semnan province.
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