Badland erosion susceptibility mapping using machine learning data mining techniques, Firozkuh watershed, Iran

Badlands are landforms related to runoff, with dissected V-shaped valleys, short steep slopes, and high drainage density, and results from a very important type of erosion that develops due to a complex interaction of conditioning factors, including climatic, hydrologic, geologic and soil properties, topographic characteristics, and land use. The main goals of this study were (1) create badland susceptibility maps of the Firozkuh watershed and five machine learning algorithms (models)—functional discriminant analysis (FDA), generalized linear model (GLM), mixture discriminant analysis (MDA), multivariate adaptive regression spline (MARS), and support vector machine (SVM); and (2) compare the accuracy of these models. Sixteen conditioning factors were chosen to model and classify badland susceptibility based on a literature review, data availability, and field surveys. Model accuracy was assessed using ROC curve and AUC analyses. The analyses showed that SVM was “excellent,” MARS was “very good,” MDA was “good,” and GLM and FDA were “moderate” in classification accuracy. The land area of the very high and high classes ranged from 31 to 51% of the Firozkuh watershed for the GLM and SVM models, respectively. This indicates that badland erosion is a very important problem in the study area. Climatic, hydrologic, geologic, topographic, and soil conditions as well as land use changes render the Firozkuh watershed prone to badland formation and soil erosion which results in substantial socioeconomic losses. Badland susceptibility mapping is an important tool that can be used to improve managing future badland erosion in the Firozkuh watershed and other areas affected by badland erosion.


Introduction
Soil, as a valuable natural resource, provides a large number of services and has an important effect on the environment and world economy (Sepuru and Dube 2018). Soil erosion and degradation is a natural phenomenon altering the relief of the landscape.

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Erosion is influenced by weather extremes and environmental factors. Badlands are dryterrain landforms with little vegetation cover where relatively soft sedimentary rocks and clayey soils have been broadly eroded. Badlands develop due to a complex interaction of conditioning factors, such as climatic (intense rainfall events followed by dry periods), hydrologic, geologic and soil properties, topographic characteristics, and land use/land cover (Bosino et al. 2019). Water erosion including surficial erosion processes and subsurface piping erosion are the main causes for the development of badlands (Hosseinalizadeh et al. 2018). Depending on the conditions of the region (e.g., soil type and humidity), the type of badlands may be different. Based on Moretti and Rodolfi (2000) report, badlands can be classified into different types, which include: Type "A" that usually develops because of the action of concentrated runoff on clayey substrata with very high silt and sand content and channels with V-shaped form. Type B is often caused by surface landslides or regoliths that are placed on a non-weathered substratum. In this type, slopes are gentler and the drainage pattern less dense. Soil degradation and erosion (removal, transport, and deposition of soil) reduce the quality and quantity of the soil and are important natural and anthropogenic processes that affect many countries. Water erosion is a common kind of soil degradation and erosion and is a significant and dangerous phenomenon in arid and semiarid areas in terms of soil loss and land degradation (BouKheir et al. 2007). Soil erosion can cause on-site and off-site hazards. A principal on-site hazard is the reduction of topsoil thickness, which can result in reduced crop yields. Off-site hazards include enhanced air and water pollution, sedimentation, and silting of surface-water bodies (Noor et al. 2016). Approximately 60% of the land area in Iran is arid or semiarid, and about 1 trillion square meters of this area is prone to desertification (Chen et al. 2022). The major factors affecting the occurrence and development of erosion are population increase, destruction of rangeland, overgrazing, reduction of vegetation cover, heavy and short-duration rainfall, unsuitable land use management, cultivation on high slopes, inappropriate irrigation design, and the presence of susceptible geologic and soil conditions (Jahantigh and Pessarakli 2011). Erosion in badland areas is an important contributor to sediment production (Ranga et al. 2016;Maerker et al. 2020) and the paucity of vegetation facilitates it (Bryan and Yair 1982). Badland could be employed as a small laboratory for modeling erosion processes and is known as an upscaling instrument (Caraballo-Arias and Ferro 2017). Badlands are much dissected, and not suitable for agriculture. These regions have V-shaped valleys, short steep slopes, and high drainage density (Sinha and Joshi 2012). Bryan and Yair (1982) explained that geomorphic processes in these settings are primarily related to seasonal climatic variations. Badlands are usually sites of heavy erosion and patterned development of drainage networks (Deshmukh et al. 2011). In Italy, badland erosion was divided into two different categories including Calanchi and Biancane. In this regard, Calanchi badlands are rapidly developing phenomenon, characterized by rill and gully landforms with a dense dendritic drainage network, whereas Biancane appear as clay domes and dissected by rills (Vergari 2015). The badland erosion develops rapidly in time and space and has a variety of geomorphic processes (Alexander 1980;Bryan and Yair 1982;Buccolini et al. 2010;Torri et al. 2013). Badland erosion can reduce the amount of fertile soil, destroy farmland, destabilize slopes, weaken infrastructure, and alter transportation routes. In some countries, erosion directly affects the economy. For example, in India 4.32 million ha of land is affected by severe gully erosion. Being an agriculture dependent economy, India suffers great economic loss to badlands (Ranga et al. 2016). Of course, in some countries, erosion zones were employed in a proper way. There are some regions covered by intense gully that have been designated as geoparks and protected areas, for education and tourism, especially in North America and Europe (Güney 2020). As such, it is beneficial to develop and apply a sustainable watershed management approach in these affected regions.
Due to the importance of gully erosion and badlands, various reports have been presented in this regard. Azareh et al. (2019) used certainty factor and maximum entropy methods to model gully erosion susceptibility in Ilam province, west of Iran. Based on theirs results, aspect and distance to river the most important factors for gully occurrence. Lei et al. (2020) applied four data mining techniques (i.e., random forest, credal decision trees, kernel logistic regression, and best-first decision tree) for gully erosion susceptibility assessment in Robat Turk watershed, Iran. Theirs findings showed that the random forest model is the most accurate model in the study area. Nhu et al. (2020) prepared a gully erosion susceptibility maps for Shoor River watershed in northwestern Iran. Results of the study showed that rainfall and elevation were the most important conditioning factors of gully erosion. Tien  used RF-ADTree to spatially predict gully erosion in the part of Kurdistan province, Iran. Distance to river was the main conditioning factor and most gullies were located beside the river. Cama et al. (2020) applied entropy model to map susceptibility of sheet, gully, and badland erosions in the Meskay watershed located in the central part of Ethiopia. Results showed that elevation and land use highly influence the badland erosion.
Despite badland erosion damages to the inhabitants and farmlands in the Firozkuh watershed, only one research has been done in this area and drainage density, elevation, and rainfall were introduced as the most important conditioning factors of the badlands (Mohammady et al. 2022). Because of the rapid development of infrastructure in the watershed, the suitability of lands for development needs to be determined. Erosion susceptibility assessment demands an interdisciplinary geomorphic, hydrologic, geologic, and pedologic approach, one that emphasizes predominantly a quantitative approach, incorporating mathematical and statistical methods to assess erosion phenomena (Ghosh and Bhattacharya 2012). The Firozkuh watershed is susceptible to severe erosion because of its geomorphologic conditions and lithologic properties. Different statistical methods have been used to assess the susceptibility of landforms and investigate their relationships with respect to geo-environmental factors (Botero-Acosta et al. 2017). Selection of methods to susceptibility mapping often depends on the availability of independent geo-environmental data particularly information on past phenomenological events.
The two main goals of this study were (1) create badland susceptibility maps of the Firozkuh watershed using data mining techniques and five machine learning algorithms (models)-functional discriminant analysis (FDA), mixture discriminant analysis (MDA), generalized linear model (GLM), support vector machine (SVM) and multivariate adaptive regression spline (MARS); and (2) compare the accuracy of these models.
Machine learning algorithms have been used to analyze many environmental phenomena. Mosavi et al. (2022) and Mohammady et al. (2021b) used FDA to map and predict flood, erosion, and habitat Suitability. Rösch et al. (2006), Lu et al. (2012), and Kalantar et al. (2019) applied MDA model to monitor bioaerosols, predict the habitat degradation status, and map groundwater potential, respectively. GLM model was used by Torabi Haghighi et al. (2021), Thuiller et al. (2003), and Ravindra et al. (2019) to map land degradation risk, predict spatial distributions of plant and assess the air pollution. Some researchers also used SVM model for flood susceptibility mapping (Tehrany et al. 2014), and landslides (Zhou et al. 2018). MARS model was also used in many cases such as earthquake (Zheng et al. 2019), estimation of solar radiation (Li et al. 2019), temperature forecast within active mines (Krzemień, 2019), and rock slope damage level prediction (Erdik and Pektas 2019). In many studies, machine learning algorithms were introduced as suitable methods. For this reason, they were considered in this research.

Study area
Firozkuh watershed is in eastern Tehran Province, Iran. The watershed with an area of 1.450 billion square meters lies between 35°40′ and 35°57′ N latitudes, and 52°19′ and 53°07′ E longitudes ( Figure 1). The Firozkuh watershed is characterized by hilly landforms at altitudes between 1712 and 3941 meters above sea level. The climate in this region is semiarid and is known as the Turani climate (Mohammadzadeh et al. 2007). Land use in the watershed is characterized by forest, rangeland, agricultural, residential, and bare land, with rangeland being the major land use. The geologic formations of the watershed include 18 different units, among which the tuffaceous shale and green tuff (Ek), thin-bedded to massive limestone (Jl), orbitolina bearing limestone (Ktzl), and high-level piedmont fan (Qft1), in the study area, are the main formations. In the Firozkuh watershed, badlands are the most important contributors to soil erosion because the condition of climatic, hydrologic, topographic, and reduced vegetation conditions, and as well as presence of susceptible soil and geology formations In this region, typical badland areas comprise sharp ridges, pyramidal hills, and deeply incised streams with steep slopes (Mohammady et al. 2022).

Materials and methods
In general, the research process applied to determining and assessing badland susceptibility in the Firozkuh watershed is shown in Fig. 2 and summarized in the following steps: • Badland distribution mapping using satellite imagery and field surveys; • Selection of conditioning factors using literature review and data availability; • Badland susceptibility mapping using machine learning data mining techniques; • Accuracy assessment of applied machine learning algorithms (models) and selection of the best algorithm.

Badlands distribution map
Badlands in the Firozkuh watershed were identified and mapped ( Figure 1) using Google Earth imagery and field surveys. The exact position of the badlands was recorded following identify (on the Google Earth) and field survey (using a GPS device). In this regard, 115 locations of badland erosion were identified and about 70 percent of the badlands were chosen for modeling and about 30 percent were chosen to validate the applied algorithms.

Conditioning factors
Sixteen conditioning factors (five topographic factors, four hydrologic factors, and seven environmental factors) were chosen to map badland susceptibility in the Firozkuh watershed based on a literature review, data availability, and field surveys. Topographic characteristics are important factors that affect soil degradation and erosion (Arabameri et al. . A digital elevation model (DEM) of ASTER 1 with 30 m resolution was used to create the GIS topographic layers of slope, aspect, topographical wetness index (TWI), and plan curvature attributes. These layers were extracted using the DEM in SAGA GIS and ArcGIS software. Slope is a very important factor affecting soil erosion and degradation (Pal 2016). The range of slope is 0 to 69.9° in the Firozkuh watershed. The aspect map of the watershed was classified using nine aspects: flat, north, south, west, east, northeast, southeast, northwest, and southwest ( Figure 3). TWI is a wetness index that explains the effect of topography on hydrologic conditions. The following equation introduced by Moore et al. (1991) was used to compute TWI:

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where As is watershed area (m 2 ) and θ is slope in degrees. Plan curvature explains the geometry of the land surface and changes of slope (Nefeslioglu et al. 2008). Positive values of plan curvature indicate convexity, zero values define a flat surface, and negative values indicate concavity (Meliho et al. 2018). The plan curvature ranged from 0 to 20 for the watershed. The distance from river conditioning factor has been selected as an effective (1) TWI = ln( As tanθ ) factor of badland erosion, assuming that the areas near existing streams are more sensitive to badland erosion. Hydrologic characteristics important to water erosion were represented using four conditioning factors. Distance from river was calculated using the Euclidian distance measurement technique in ArcGIS and ranged from 0 to 6600 m for the watershed. Drainage network map of the study area was extracted from map produced by the Iranian National Cartographic Center (INCC). Drainage density was computed using the mapped drainage network and area, and ranged from 0.1 to 2.5 km/km 2 in the watershed. A soil permeability map was developed using five classifications: very high, high, moderate, low, and very low. An average annual rainfall map was developed using rainfall data from meteorological stations and the inverse distance weighting (IDW) technique. We had limitations to use some geostatistical methods (due to the insufficient number of stations and sampling points). The use of IDW method has been found suitable for these conditions (Chen et al. 2022). Environmental factors related to erosion included four soil conditioning factors, land use, and geology related to erosion. To map soil characteristics, about 30 samples were taken in depths of 0.3 meters and analyzed in the laboratory. Usually, sampling of topsoil (0-30 cm) is acceptable to investigate soil erosion (Ranga et al. 2015;Azareh et al. 2019). The clay percent, silt percent, pH, and soil hydrologic groups were determined in the laboratory, and then, their maps were created using the IDW method in GIS. The ranges of clay percent, silt percent, and pH are 14-33, 27-52, and 6-8.1, respectively. Soil hydrologic groups also included three groups B, C, and D.
The soil depth map was received from Natural Resources and Watershed Management Organization of Tehran province. Land use is a very important conditioning factor of soil erosion (Bajocco et al. 2012). The land use of Firozkuh watershed was created from LANDSAT 8 images of year 2020 (30-meter resolution) using a synthetic method in the ENVI software (Mohammady et al. 2015). Five land use types including agriculture, bare land, forest, rangeland, and residential were classified in this Firozkuh watershed. The surficial geology of the watershed was extracted from the geologic map of Iran with the scale of 1:100000. The geologic map of the watershed consists of 18 units including CZL (micaceous siltstone and sandstone), E1m (marl, and limestone), Db-sh (limestone, marl and shale), Ek (tuffaceous shale and green tuff), Jd (argillaceous limestone with intercalations of calcareous shale), Jl (thin-bedded to massive limestone), K (Cretaceous rocks), Kbv (basaltic volcanic), Ktzl (orbitolina bearing limestone), Ku (Upper Cretaceous rocks), Murm (gypsiferous marl and brown marl), PeEz (reef-type limestone and gypsiferous marl), Pgkc (polygenic conglomerate, coarse grained), Pr (dark gray limestone), Qft1 (high-level piedmont fan), Qft2 (low-level piedmont fan), TRe (shaly limestone, gray oolitic limestone, dolomite and dolomitic limestone), and TRJs (dark gray shale and sandstone). Figure 3 shows the conditioning factor maps of the study area. All conditioning factor maps as well as the modeling were based on a pixel size of 30 meters. The literature reviews (e.g., Mohammady et al. 2021a;Torabi Haghighi et al. 2021) also explained that 30 m resolution is suitable to use machine learning techniques.

Badland susceptibility mapping
To create the badland susceptibility maps for Firozkuh watershed selected data mining techniques FDA, MDA, GLM, MARS, and SVM were used. The FDA algorithm is a nonparametric model, so it can be effective in various fields (Epifanio and Ventura-Campos 2011;Mohammady et al. 2021b). Like many other statistical approaches, discriminant analysis has been generalized to the functional items in the FDA algorithm. The GLM algorithm is defined based on regression, and can show differences between the factors (Ozdemir and Altural 2013). The GLM algorithm can be applied to analyze different types of data, including Bernoulli success/failure data, normal data, and others (Torabi Haghighi et al. 2021). The GLM algorithm applies multiple regressions, to increase the accuracy and quality and to establish a proper relationship between dependent and independent variables (Wang et al. 2011). The MDA is a supervised classification algorithm with the mixture of Gaussian distributions and is applied to obtain a probability estimation for each class. The MDA is a useful technique to model the variables with non-normality and nonlinear relationships to increase the classification accuracy (Kalantar et al. 2019). The MARS model (algorithm) has been observed to be a flexible, accurate, and quick method to forecast binary output and continuous variables. The main benefit of the MARS model is that it is interactive, additive, and includes fewer variable interactions (Kisi and Parmar 2016). The MARS model has been applied in different fields, including natural resources, geophysics, geomorphology, and climatology (Luoto and Hjort 2008;Mohammady et al. 2021b).
The SVM algorithm, which is characterized by its suitability to nonlinear and high dimension processes, has become popular because of development of artificial intelligence and the use of GIS and remote sensing (Huang and Zhao 2018). High-dimensional and nonlinear classification problems are easier to solve using the SVM method using the kernel function and the introduction of slack variables (Huang and Zhao 2018).
To run these models, various special packages in the "R 3.5.3" software were used. The R packages used in this research were "fda" (Ramsay et al. 2018), "glm" (Gill and Torres 2019), "mda" (Hastie 2017), "MARS" (Holmes et al. 2012), and "SVM" (Ratkovic 2015). Finally, the weights computed in the R 3.5.3 packages were entered into ArcGIS software, and susceptibility maps were created and classified.

Validation of the models
In this research, the validation of the badland susceptibility maps was performed through the success and prediction rate curves method. About thirty percent of badland sites (unused in modeling) were applied to validate the models. The ROC 2 curve and the AUC 3 values were used to validate and assess accuracy of the models. The AUC identifies the model performance using prediction of the occurrence and non-occurrence of badlands. The AUC is classified as follows: poor (0.5-0.6), moderate (0.6-0.7), good (0.7-0.8), very good (0.8-0.9), and excellent (0.9-1) (Rasyid et al. 2016).

Results
A multicollinearity test was used to determine the correlation between each of the conditioning factors on badland susceptibility modeling. The test uses two indices, tolerance (T) and the variance inflation factor (VIF). If the amount of tolerance is lower than 0.1, and VIF is higher than or equal to five, it can be considered that the factors have no correlation (O' Brien, 2007). The computed multicollinearity statistics for each of the conditioning factors are presented in Table 1. In this study, there is no correlation between conditioning factors.
The calculated weights from the FDA, GLM, MDA, MARS, and SVM algorithms were entered into ArcGIS 10.3 to produce the badland susceptibility maps (Figures 4,  5, 6, 7, 8). These maps were classified into very high, high, moderate, and low classes  (Table 2). The ROC curve and AUC values were used to validate the susceptibility maps and range of each class (poor, moderate, good, very good, and excellent) was explained in "validation of the models" section. Table 3 and figure 9 show results of model validation. The AUC values show that SVM is "excellent," MARS is "very good," MDA is "good," and GLM and FDA are "moderate" in accuracy classification.

Discussion
As shown in Figs. 4, 5, 6, 7, 8 and Table 2, a large part of the Firozkuh watershed has a high to very high badland susceptibility. The land area of the high and very high classes is 31% to 51% of the Firozkuh watershed for the GLM and SVM models (computed using Table 2 and the land area of the Firozkuh watershed of 1450 km 2 ). This indicates that badland erosion is a potentially very important problem in the study area. Climatic, geologic, hydrologic, soil, and topographic conditions as well as land use changes in this area have created conditions for the occurrence and development of badland landforms. Geologic materials related to the badland erosion are usually fine-grained sediments such clay, shale, and marl that can lead to erosion when exposed to alternate drying-rewetting cycles (Cerda` 2002).
In the study area, many badlands were occurred in marl, limestone, marl, and shale, which shows the importance of the geologic characteristics. In this regard, Azareh et al. (2019) pointed that lithology is a very important conditioning factor of erosion and can be related to the fine and coarse fractions of the particle size distribution in the soil.
Overgrazing is one of the most important factors of natural resources destruction especially in reducing the vegetation cover of rangelands. Most of the current badlands in the watershed have occurred in rangelands and agricultural areas. Previous research has also emphasized the effect of land use on erosion. Mosavi et al. (2022) explained that land use is a very important factor affecting soil erosion in Talar watershed, Iran. Leh et al. (2013), Mekonnen et al. (2016), Abdulkareem et al. (2019), and Arabameri et al. (2019) showed that land use is one of the key variables affecting the soil erosion. Castaldi and Chiocchini (2012) studied the impacts of land use change on badland erosion, concluding that land reclamation has an important role in reduction of erosion of the clayey substrate. Azareh et al. (2019) claimed that agricultural land (which can be subject to tillage practices) have the highest susceptibility to gully erosion among different land uses located in in the part of Iram province, Iran. Soil properties especially medium-texture soils also have a direct effect on soil erosion. Other research has also pointed to the importance of soil properties on erosion. Sinha and Joshi (2012) explained that very fine texture and coarse texture soils can be resistant to erosion. The results indicated that silt and fine sand are more susceptible to erosion. Bierbaß et al. (2014) studied the effects of soil properties and vegetation on badlands and showed that vegetated areas can improve water infiltration, organic matter accumulation, and sodium leaching, and demonstrated that vegetation plays an important role in terrain stability. Azareh et al. (2019) stated that clay and sandy clay loam soils were positively associated with gully erosion susceptibility in a semiarid region, Iran. Lei et al. (2020) also emphasized the role of soil properties on the creation of erosion in Robat Turk watershed, Iran. Topographic factors such as altitude and slope were also identified as important factors in the study area. Steep slopes are very susceptible to badland erosion. In fact, badlands are characterized with highly dissected topography with steep slopes (Ranga et al. 2016). This topographic factor can control drainage intensity, surface runoff, and detachment of soil particles (Hembram et al. 2018). Clarke and Rendell (2006) used erosion pins in Basilicata, Italy, to determine the mean annual erosion rates. Results of their research showed that the maximum erosion rates coincided with high slopes. As the same, Azareh et al. (2019) introduced slope aspect as the most important factor of gully erosion occurrence. Rainfall is an important effective factor of badland erosion in the Firozkuh watershed. Due to heavy rainfall and low vegetation cover in arid and semiarid regions such as the Firozkuh watershed, the effect of rainfall on erosion is very substantial. In fact, badland occurrence and development can be the result of climatic conditions, such as the Mediterranean rainfall regime (Moretti and Rodolfi 2000). Lei et al. (2020) explained that rainfall is the most conditioning factor of gull erosion in the part of semiarid region of Iran. Based on the results of Nhu et al. (2020), the rainfall and elevation are the most important conditioning factors to create gully erosion susceptibility maps for the region between Markazi and Isfahan provinces, Iran. Drainage network including distance from river and drainage density are very important conditioning factors of erosion. Tien  used data mining methods to spatially predict gully erosion in the part of Kurdistan province, Iran. Distance to river was introduced as the main factor affecting gully erosion. Parallel to our findings, Azareh et al. (2019) explained that higher drainage density can be indicator of the region with low infiltration, greater runoff, more surface flow, and can be a powerful predictor of gully erosion susceptibility. Accuracy assessment of the models showed that the SVM (excellent) and MARS (very good) models have the highest AUC values (Table 3). The SVM model is more accurate, because SVM is based on the principle of structural risk minimization, instead of traditional experience risk minimization (Zhou et al. 2018). One of the chief advantages of the SVM model is that it can use and manage complicated, nonlinear interactions among the dependent and independent variables (Yu and Kim 2012). According to the results of previous research, the SVM model had accurate prediction in many cases, which indicated that the performance of SVM model has a strong robustness (Tehrany et al. 2014;Pham et al. 2017;Lee et al. 2017;Mohammady et al. 2021b).
Among the five models used in this research, the MARS model ranks second in terms of accuracy (Table 3). One advantage of the MARS algorithm is that it explains the complex nonlinear relation between response variables and predictor. Also, the MARS model can be applied in a forward and backward stepwise procedure (Kisi and Parmar 2016). Other research that used the MARS model confirmed its accuracy. Erdik and Pektas (2019), Chu et al. (2018), and Mohammady et al. (2021a) used the MARS model to assess rock slope damage, landslide susceptibility, and land subsidence susceptibility. Results of these studies showed the acceptable accuracy of the MARS models. Although the SVM and MARS models are most accurate for badland susceptibility mapping in the Firozkuh watershed (Table 3), it cannot be said with certainty that these models will always be more accurate when applied to different processes and (or) in different places. For example, the FDA and GLM models in this study had the lowest accuracy, but may have been selected as appropriate models in other studies. James and Hastie (2001), Albanese et al. (1980), Chamroukhi et al. (2010), and Burfield et al. (2015) applied FDA in their research and found the model very accurate. There are also some studies that have applied the GLM model as a suitable model in other areas (Guisan et al. 2000;Thuiller et al. 2003;Marmion et al. 2009).
Based on a literature review of data mining techniques, it can be said that the selection of a suitable model for an area is complicated and that model-comparison studies are needed before a suitable model can be selected for a particular study area. The complexity of the badland erosion process and its spatiotemporal variability suggest that more research is needed to determine an applicable badland susceptibility model for a particular study area. Therefore, various models have been proposed and applied to investigate the hazard and susceptibility of geo-environmental phenomena. Data mining techniques and machine learning algorithms are among the most widely used models in this field. The main advantage of machine learning methods is that various types of conditioning factors can be incorporated into the modeling process and that missing data can be easily accommodated. Moreover, machine learning algorithms can be used to model different phenomena, including landslide and land subsidence susceptibility mapping, erosion, ecology, and groundwater spring potential mapping (Mohammady et al. 2019;Mohammady et al. 2022). Climatic, hydrologic, geologic, topographic, and soil conditions as well as land use changes have rendered the Firozkuh watershed prone to badland formation and soil erosion which has resulted in substantial realized and potential economic and social losses. Badland susceptibility mapping is an important tool for managing badland erosion in this watershed and can be used to improve natural resources management plans.

Conclusion
The Firozkuh watershed is susceptible to severe erosion and because of its geomorphic conditions and lithologic properties badland erosion is an important phenomenon in this watershed. The main objective of this study was to assess badland susceptibility using five machine learning algorithms (models) including FDA, GLM, MDA, MARS, and SVM. ROC curve and AUC analyses were applied for accuracy assessment of the mentioned models. Results showed that the SVM and MARS models have the highest accuracies (highest values of AUC [excellent and very good, respectively]) and are suitable models to map badland susceptibility in the Firozkuh watershed. Results showed that about 31-51 percent of the watershed has high to very high susceptibility to the badland erosion, so susceptibility assessment and management of badland erosion is essential in Firozkuh watershed. Badland susceptibility assessment, including classification into susceptibility categories and mapping, facilitates understanding and managing vulnerability to badland erosion.