Prediction of Gully Erosion Susceptibility and Its Hazards in Kloche Bijar Watershed Using Spatial Predictive Models

Introduction
Soil erosion by water is one of the most important processes of land degradation, especially in semi-arid regions. Among the different types of water erosion, gully erosion is one of the most important events affecting soil destruction, changing the landscape and water resources, and land regression [1]. Gully erosion is the most obvious form of soil erosion, which leads to a decrease in soil production capacity and restrictions on land use, and can be a serious danger to roads, fences, and various structures, and also causes significant soil losses and the production of large amounts of sediment [2]. This erosion is also called gully erosion. A gully is a relatively permanent waterway that temporary streams of water pass through during rainfall and carry a large amount of sediment [11]. The formation of gullies is always accompanied by erosion and changes in the appearance of the land and causes the production of a significant amount of sediment, destruction of lands, roads, irrigation networks and filling of dams [9]. Gullies, which are considered major indicators of environmental changes in most cases, are not considered normal forms of erosion due to their rapid growth [8].
In the studies conducted both inside the country and abroad, various methods have been used to evaluate the potential of gully erosion, which are mentioned below. Among the methods used to determine the potential of gully erosion are regression models [17, 10, 4, 15, 23, 22], knowledge-based model of hierarchical analysis [6, 21, 22, 3, 29], fuzzy logic. [12 and 13], Dempster-Shafer model [14], artificial neural network and support vector machine [33], etc. pointed out that, based on this, the watershed of Klocheh Bijar in Kurdistan province has been severely affected by this type of erosion and caused the loss of many agricultural lands in the studied basin have been eroded. Therefore, the gully erosion susceptibility mapping of the studied basin was studied and investigated using Logistic Regression and Fuzzy Logic models, and finally mapping of gully erosion in the studied area and the validity of both used models were verified.
Material and Methods
Gully erosion inventory map
In this study, 950 points at the top of gullies (head cuts) were recorded as a distribution map of gully erosion using Google Earth images and field survey. Then, they were divided into two parts of training data (70%) and validation (30 percent) were divided. The training data were used in the model learning section with the logistic regression method and the validation data were used to determine the validity/prediction power of the models.
Logistic regression model
Multiple logistic regression is a multivariate technique that considers several physical parameters that may affect the probability. In this method, the values of the independent variable can be expressed in binary form (0 and 1) and as a numerical quantity.
Fuzzy logic model
In classical set theory, an element is either a member of the set or not (zero and one). Fuzzy set theory extends this concept and introduces graded membership. So that an element can be a member of a set to some degree and not completely. In other words, a fuzzy set is a set of elements with similar characteristics, where the set has a certain degree from zero to one. Zero means no membership and one mean full membership [24]; Therefore, before implementing the fuzzy model, it is necessary to determine the membership functions for each of the layers mentioned above and set the value of the layers in a range between (zero and one) and then enter the layers into the fuzzy model. To implement the fuzzy technique, a gamma operator is needed, the value of the modulating gamma is between zero and one, zero gamma is equivalent to fuzzy multiplication and one gamma is equivalent to fuzzy addition.
Results and Discussion
Gully erosion susceptibility map
logistic regression
Table. 1 shows TOL and VIF values of factors affecting the occurrence of gully erosion. Viewing this table shows that all effective factors have a TOL value greater than 0.1 and a VIF less than 10, which indicates the absence of multiple collinearities between them, and all of them are used as input for the model. They were branched with appropriate logistic regression.
Fuzzy Logic
Figure 5 shows the prediction map of gully erosion using fuzzy logic. Although the pattern of distribution of different areas from the map obtained with the fuzzy logic model follows the logistic regression model, but it seems that an exponential exaggeration in the area of the area with the probability of gully erosion is very high is seen, which is probably related to choose the numbers for the gamma value during modeling with this method. However, the areas with high and very high probability of occurrence correspond to the top of gullies (head cuts).
Conclusion
Gully erosion is one of the most important natural hazards and the main cause of land degradation in the Klocheh Bijar watershed in Kurdistan province. Recognizing the most important factors affecting the occurrence of this phenomenon as well as predicting areas prone to its occurrence is one of the management and preventive measures to better understand the area before any engineering/structural and biological measures (land management) or a combination of both. Reduction of possible damages. Preparing a gully erosion susceptibility map can be a useful guide for planners, managers, organizations and decision makers regarding the management of these areas. In this research, 950 points at the top of gullies (head cuts) were recorded as a distribution map of gully erosion using Google Earth images and field survey and were divided in the ratio of 70 to 30. Multilinear correlation test was used to check the internal correlation of 20 effective factors, as well as two models of logistic regression and fuzzy logic were used to prepare prediction maps of gully erosion in the study area.