Novel ensembles of COPRAS multi-criteria decision-making with logistic regression, boosted regression tree, and random forest for spatial prediction of gully erosion susceptibility

Gully erosion is considered as a severe environmental problem in many areas of the world which causes huge damages to agricultural lands and infrastructures (i.e. roads, buildings, and bridges); however, gully erosion modeling and prediction with high accuracy are still difficult due to the complex interactions of various factors. The objective of this research was to develop and introduce three new ensemble models, which were based on Complex Proportional Assessment of Alternatives (COPRAS), Logistic Regression (LR), Boosted Regression Tree (BRT), Random Forest (RF), and Frequency Ratio (FR) for spatial prediction of gully erosion with a case study at the Najafabad watershed (Iran). For this purpose, a total of 290 head-cut of gullies and 17 conditioning factors were collected and used to establish a geospatial database. Subsequently, FR was used to determine the spatial relationship between the conditioning factors and the head-cut of gullies, whereas RF, BRT, and LR were used to quantify the relative importance of these factors. In the next step, three ensemble gully erosion models, named COPRAS-FR-RF, COPRAS-FR-BRT, and COPRAS-FR-LR were developed and verified. The Success Rate Curve (SRC), and the Prediction Rate Curve (PRC) and their areas under the curves (AUC) were used to check the performance of the three proposed models. The result showed that Soil group, geomorphology, and drainage density factors played the key role on the occurrence of the gully erosion. All the three models have very high degree-of-fit and the prediction performance, the COPRAS-FR-RF model (AUC-SRC = 0.974 and AUC-PRC = 0.929), the COPRAS-FR-BRT model (AUC-SRC = 0.973 and AUC-PRC = 0.928), and the COPRAS-FR-LR model (AUC-SRC = 0.972 and AUC-PRC = 0.926); therefore, it is concluded that they are efficient and new powerful tools which could be used for predicting gully erosion in prone-areas.