تعیین مناطق مستعد فرسایش خندقی با استفاده از تابع عضویت فازی(مطالعه موردی:شهر مهر در جنوب استان فارس)

Introduction
Among the various types of water erosion, gully erosion is one of the most important events affecting soil destruction, landscape change, loss of water resources and land regression (Poison et al., 2003) that occurs under certain environmental conditions. This type of erosion is an evolved form of furrow erosion that forms at the beginning of valleys or on slopes and plains and cut sections (roads and canals) (Tucker, 2005). This type of erosion occurs widely in arid and semi-arid regions (Frankl, 2012). There are various methods for determining areas prone to gully erosion, that the Multiple-criteria decision-making (MCDM) method is one of the most recently used methods. Arabameri et al. (2020) used MCEM to determine areas prone to gully erosion in the Dasjard River watershed in Iran. The results showed that machine learning (ML) method in GIS environment is a suitable method for determining erosion sensitive areas. Hembram and Saha (2020) used the fuzzy-AHP and compound factor (CF) methods to determine areas prone to gully erosion in the Jainti River basin in India. The results showed that both methods have good accuracy for predicting erosion. Choubin et al. (2019) used the fuzzy analytical network process (Fuzzy ANP) method to determine areas prone to gully erosion in Kashkan-Poldokhtar Basin, Iran. The results showed that drainage density, soil texture and lithology are the most important factors of watershed erosion in the study area. Couple hybrid algorithms of a commonly used base classifier (reduced pruning error tree, REPTree) with AdaBoost (AB), bagging (Bag), and random subspace (RS) were used to determine areas prone to ditch erosion by Nhu et al. (2020). The results showed that the RS-REPTree hybrid model has high accuracy in determining erosion in Shoor River watershed in Iran. One of the areas in Iran that has undergone land use changes in recent decades is the city of Mohr in the south of Fars province.This area is located on erosion-sensitive soils, which has recently led to large gully in the area. Due to the importance of the subject in this study, areas prone to erosion have been identified using the fuzzy method and AHP and the necessary solutions to prevent the progression of this erosion have been presented.

Methodology
In order to prepare the areas prone map to gully erosion were used aspect data, CL, Dd, elevation, TPI, geology, land use, LS, curvature plan, TRI, profile curvature, rainfall, distance to river, distance to road, TWI, slope, soil , SPI, NDVI as input data. After preparing zoning maps for each of the parameters, the fuzzy membership function was used to prepare fuzzy maps for each of the parameters. In this study to prepare a fuzzy map of slope, distance to road, TRI, soil, altitude, TWI, LU, SPI, LS, direction, distance to river from incremental linear membership function. For other parameters, the decremental linear membership function was used (Arabamari et al., 2020). Then, to prepare the final map of areas prone to gully erosion, using AHP method, a two-by-two comparison of each parameter was performed based on the degree of importance of each of them.
Then, using Expert choices software, the qualitative results became quantitative and finally the weight of each parameter was determined.

Results and Discussion
The results of AHP method showed that lithology has the highest impact (weight 0.2) and LS has the lowest impact (weight .002) in mapping areas prone to gully erosion. The results of fuzzy and AHP methods showed that the areas located in the center (about 15%) of the study area are more sensitive to erosion. The results also showed that large gully erosion have been seen in the areas that are prone to gully erosion. Therefore, the AUC values were close to 85%, which indicates the high accuracy of the model for predicting areas prone to gully erosion.
Gully erosion created in the region is a serious threat to rural and agricultural lands in this region. In fact, with human interventions in erosion-sensitive areas, it leads to the progression of erosion and loss of satisfaction (Arabameri et al., 2019). Land use as a variable is very effective in spreading gully erosion. Rijsdijk et al. (2006) in a study of Java ditches in Indonesia concluded that changes in land use and improper plowing were the cause of the increase in ditches in this area.

Conclusion
The results showed that the areas located in the center of the study area are more prone to gully erosion than other sections. In this study, it was found that land use changes have led to intensification of erosion in the region. So that with the increase of agricultural and residential lands in the study area, the rate of gully erosion has increased. Therefore, it is important to use soil protection operations to control and prevent the progression of gully erosion in this area.