Exploring topographic variables in gully erosion susceptibility mapping in Central Brazil
Explorando variables topográficas en el mapeo de susceptibilidad a la erosión en cárcavas en el centro de Brasil
Laudier Lopes Abreu1, Alessandra Cristina Pereira1, Fabio Corrêa Alves2, Max Well de Oliveira Rabelo1, Elizon Dias Nunes3, Édipo Henrique Cremon1,4,*
1 Instituto Federal de Goiás, Campus Goiânia. Rua 75, 46 Centro, 74055-110, Goiânia, Brazil.
2 Universidade Federal do Oeste da Bahia, Centro das Humanidades. Rua da Prainha 1326, Morada Nobre, CEP 47810-047, Barreiras, Brazil.
3 Universidade Federal de Goiás, Instituto de Estudos Socioambientais. Av. Esperança, s/n Samambaia, 74001-970, Goiânia, Brazil.
4 Instituto Nacional de Pesquisas Espaciais, Divisão de Observação da Terra e Geoinformatica. Avenida dos Astronautas, 1.758, 12227-010, São José dos Campos, Brazil.
* Corresponding author: (E.H. Cremon) This email address is being protected from spambots. You need JavaScript enabled to view it.
How to cite this article:
Abreu, L.L., Pereira, A.C., Alves, F.C., Oliveira-Rabelo de, M., Dias-Nunes, E., Cremon, E.H., 2025, Exploring topographic variables in gully erosion susceptibility mapping in Central Brazil: Boletín de la Sociedad Geológica Mexicana, 77(3), A121025. http://dx.doi.org/10.18268/BSGM2025v77n3a121025
Manuscript received: December 6, 2024. Corrected manuscript received: May 21, 2025. Manuscript accepted: August 1, 2025.
ABSTRACT
This study investigates gully erosion susceptibility in southwestern Goiás State, Central Brazil, where extensive gully erosion affects the landscape. The primary objective was to evaluate the predictive power of less commonly analyzed topographic variables, derived from Digital Elevation Models, in comparison with traditional predictors. A total of 5 660 gully samples were mapped, with gully heads selected as the main modeling target due to their geomorphological relevance. The methodology integrated topographic, hydrological, lithological, pedological, and anthropogenic factors. Advanced variable selection methods, including the Recursive Feature Elimination (RFE) algorithm and Variance Inflation Factor (VIF), were employed to enhance model accuracy and eliminate multicollinearity. The Random Forest algorithm was implemented for modeling, calibrated through cross-validation and tested independently using the Area Under the Curve (AUC) metric. Results demonstrated that incorporating unconventional topographic variables, such as multiscale roughness and terrain surface texture, significantly improved predictive performance. The RFE-based model achieved the highest AUC value (0.9459), underscoring the effectiveness of this approach in identifying critical predictors. Gully erosion susceptibility mapping was primarily associated with land use, drainage density, and specific terrain characteristics. The findings emphasize the value of integrating advanced geomorphometric analyses with machine learning to better understand and predict gully erosion processes, such as gullies in southwestern Goiás, Central Brazil.
Keywords: soil erosion modeling, digital elevation models, machine learning applications.
RESUMEN
Este estudio investiga la susceptibilidad a la erosión en cárcavas en el suroeste del estado de Goiás, Brasil Central, una región significativamente afectada por este fenómeno. El objetivo principal es evaluar la capacidad predictiva de variables topográficas menos analizadas, derivadas de Modelos Digitales de Elevación (MDE), en comparación con variables tradicionales. Se cartografiaron 5 660 cárcavas; sus cabezas se identificaron como el foco principal del modelado debido a su relevancia geomorfológica. La metodología integró factores topográficos, hidrológicos, litológicos, pedológicos y antropogénicos. Se aplicaron métodos avanzados de selección de variables, como el algoritmo de Eliminación Recursiva de Características (RFE) y el Factor de Inflación de Varianza (VIF), para optimizar la precisión del modelo y eliminar la multicolinealidad. Se implementó el algoritmo Random Forest para el modelado, calibrado mediante validación cruzada y evaluado independientemente con la métrica de Área Bajo la Curva (AUC). Los resultados demostraron que la inclusión de variables topográficas no convencionales, como la rugosidad multiescala y la textura de la superficie del terreno, mejoró considerablemente el rendimiento predictivo. El modelo basado en RFE obtuvo el valor más alto de AUC (0.9459), lo que resalta la eficacia de este enfoque para identificar predictores clave. La cartografía de la susceptibilidad a la erosión en cárcavas se asoció principalmente con el uso del suelo, la densidad de drenaje y características específicas del terreno. Los resultados subrayan la importancia de integrar análisis geomorfométricos avanzados con aprendizaje automático para comprender y predecir los procesos de erosión, como las cárcavas, en el suroeste del estado de Goiás, Brasil Central.
Palabras clave: modelado de erosión del suelo, modelos digitales de elevación, aplicaciones de aprendizaje automático.
1. Introduction
Gully erosion is a significant cause of soil degradation, reducing the quality and availability of arable land in both developed and developing countries (Valentin et al., 2005; Boardman et al., 2003). According to FAO (2015), soil erosion results in the annual loss of 25 to 40 billion tons of soil, diminishing agricultural productivity, compromises food security, and reduces the soil’s capacity to retain water and nutrients.
In this study, gully erosion refers to channels exceeding the dimensions of rills (depth >0.3 m), including both ephemeral gullies (temporary features erased by tillage) and permanent gullies (deep, persistent incisions into subsoil). The latter represent the most severe form of linear erosion, requiring distinct mitigation strategies due to their irreversibilityunderconventionallandmanagement (Poesen et al., 2003; Valentin et al., 2005).
This phenomenon negatively affects several United Nations (UN) Sustainable Development Goals (SDGs), including Zero Hunger and Sustainable Agriculture, Life on Land, and Sustainable Cities and Communities. In this context, gully erosion susceptibility mapping is a valuable tool for identifying vulnerable areas, guiding conservation strategies, controlling erosion, and supporting sustainable soil management. These maps help mitigate erosion impacts and contribute to achieving sustainable development objectives.
Recent advances in machine learning have enabled algorithms to identify patterns in large datasets (Zhang and Tsai, 2006). In gully erosion susceptibility mapping, methods such as Random Forest (RF), Support Vector Machine (SVM), Logistic Regression (LR), Multilayer Perceptron (MLP) and Extreme Gradient Boosting (XGBoost) have been increasingly employed. These models effectively capture complex environmental relationships and process large geospatial datasets. RF, in particular, has been widely utilized due to its high predictive accuracy (Mohebzadeh et al., 2022).
In South America, particularly in Brazil, regional-scale studies have tested multiple algorithms, with RF typically achieving superior performance (Lana et al., 2022; Bouramtane et al., 2022; Marques Filho et al., 2024; Pereira et al., 2025). Globally, recent research confirms the efficacy of RF and XGBoost across diverse environments, including highly dissected terrains (Yang et al., 2021), semi-arid basins (Hasanuzzaman and Shit, 2025), and regions under land-use pressure (Arabameri et al., 2020b). These findings highlight their adaptability for erosion modeling under varying conditions.
The integration of machine learning with remote sensing, geographic data, and Geographic Information System (GIS) enables researchers to evaluate multiple conditioning factors simultaneously, improving the accuracy of gully erosion predictions (Arabameri et al., 2019; Arabameri et al., 2020a). Key geo-environmental factors affecting gully erosion encompass geomorphological (topographic), hydrological, lithological, pedological, and anthropogenic characteristics (Arabameri et al., 2020a). These variables influence water-flow dynamics and erosive processes, underscoring their importance in developing effective soil and water conservation strategies (Shit et al., 2015).
Geomorphological factors, derived from Digital Elevation Models (DEMs) using GIS software, are represented by topographic variables such as slope, aspect, curvature, and the topographic position index. These variables, also referred to as topographic attributes, terrain attributes, or geomorphometric attributes (Pike et al., 2009; Florinsky, 2016), provide quantitative information about the Earth’s surface.
Although commonly used topographic variables are frequently applied in erosion studies, exploring less commonly analyzed variables may reveal additional patterns and enhance model performance. Evaluating these lesser-known topographic variables and comparing their predictive value with established ones addresses an important gap in the literature. Expanding the range of conditioning factors can improve predictive accuracy and deepen understanding of gully erosion processes.
This study investigates the role of less-conventional topographic variables derived from DEMs in gully erosion susceptibility mapping. It compares their predictive value to that of widely used variables to determine their contribution to improving model outcomes and understanding erosion dynamics.
2. Study area
The study area is located in the southwestern region of Goiás State, Central Brazil, covering 12 002.35 km² and including the municipalities of Mineiros, Santa Rita do Araguaia, Perolândia, and Portelândia (Figure 1). This region exhibits a high density of gullies, previously examined from multiple perspectives (Marinho et al., 2006; Nunes and Castro, 2015; Nunes and Castro, 2023; Carvalho and Castro, 2023; Pereira et al., 2025). However, the relative contribution of variables commonly used in gully erosion susceptibility models has not yet been systematically evaluated. This area was selected due to the detailed mapping of soils and erosion features by Nunes and Castro (2015, 2023), who classified soils at the third hierarchical level of the Brazilian Soil Classification System (SiBCS; Santos et al., 2018) at a 1:50,000 scale. Dominant soil types include Oxisols (Latossolos), Ultisols (Argissolos), and Quartzarenic Neosols (Neossolos Quartzarênicos), with smaller areas of Litholic Neosols (Neossolos Litólicos), Cambisols (Cambissolos), and Gleysols (Gleissolos).
The terrain is mostly flat, with slopes ranging from 3.45% to 8.84%, although isolated areas exceed 45%. The geology is composed of sedimentary rocks (IBGE, 2023), mainly sandstones and basic intrusives, creating a stepped relief.
In the north, Phanerozoic sedimentary deposits prevail, including sandstones, shales, and siltstones from the Aquidauana Formation, with elevations reaching up to 590 m. Narrow sandstone and siltstone bands from the Corumbataí Formation occur near watercourses, where Neosols are present. Red Ultisols occupy middle slopes, and Red-Yellow Oxisols occur near drainage divides. In the south, basaltic rocks of the Serra Geral Formation and shales from the Irati Formation are associated with steeper, rugged terrain dominated by Litholic Neosols. Interspersed areas contain sandstones and siltstones of the Corumbataí Formation.
The central region features eolian sandstones of the Botucatu Formation, with elevations between 500 and 1 000 m. Quartzarenic Neosols are widespread, and Red and Red-Yellow Oxisols dominate the western portion. In the central-eastern and southern zones, Phanerozoic deposits from the Cachoeirinha Formation, composed of clays, sandstones, and sandy materials, are prevalent. These gently sloping areas are mainly covered by Red Oxisols, with Haplic Gleysols near drainage lines (Cremon et al., 2021).
3. Methodology
3.1. ACQUISITION OF GULLY EROSION SAMPLES
A total of 5 660 gully erosion features were mapped as polygons through visual interpretation of high-resolution remote sensing imagery from 2018 (Nunes and Castro, 2023), representing areas affected by erosion in the study region.
In susceptibility mapping, gully heads are emphasized due to their geomorphological and hydrological relevance, marking the initiation of erosion (Valentin et al., 2005). These points concentrate key triggering factors—soil properties, topography, and runoff—and reflect the interaction between land use and natural conditions, making them highly sensitive to environmental and anthropogenic changes.
Although gullies often exhibit multiple active incision points, including lateral branches, the uppermost head cut with the greatest up slope contributing area generally represents the primary zone of initiation. Using this point as a proxy for gully occurrence is supported by geomorphological and hydrological principles, particularly the well-established relationship between slope (S) and drainage area (A) as a threshold for gully initiation (Torri and Poesen, 2014). This strategy allows for consistent extraction of key conditioning factors and has been widely adopted in recent susceptibility studies using statistical and machine learning approaches (e.g., Hosseinalizadeh et al., 2019; Arabameri et al., 2021; De Geeter et al., 2023).
To identify gully heads, mapped polygons were geometrically corrected, and their vertices extracted. The vertex with the highest elevation and flow accumulation was designated as the gully head (Figure 2). This was determined using the D8 algorithm, which assigns flow direction based on the steepest downslope path in the DEM (O’Callaghan and Mark, 1984).
Based on the gully presence points, absence points were defined as areas assumed to be non-gullied. To ensure spatial independence and minimize environmental overlap, absence points were randomly selected under the condition that they were located at least 1 000 meters away from any gully presence point. This minimum distance was defined through preliminary sensitivity tests to balance representativeness and spatial separation. A total of 5 660 absence points were generated—matching the number of gully presence points—to maintain a balanced dataset for binary classification. Presence and absence points were labeled as ‘1’ and ‘0’, respectively, and used for binary classification modeling.
3.2. ACQUISITION AND PROCESSING OF VARIABLES
The study employed a broad set of topographic variables as independent predictors to identify areas susceptible to gully formation. These variables were derived from the Forest and Building Removed Copernicus Digital Elevation Model (FABDEM) (Hawker et al., 2022), a Digital Terrain Model (DTM) in geographic coordinates, based on the Copernicus DSM, with WGS-84 datum and 1 arc-second resolution. FABDEM provides the most accurate freely available elevation data for the study area (Cremon et al., 2022; Bielski et al., 2024).
The dataset was reprojected to UTM Zone 22 South, SIRGAS2000 datum, with 30-meter resolution. Cubic spline resampling was applied using QGIS (QGIS Development Team, 2024), following the recommendations of Purinton and Bookhagen (2021).
Hydrological correction of the DTM was performed using the TerraHidro package (Rosim et al., 2011), which applies flat-carving algorithms and the Priority-First Search (PFS) method ( Jones, 2002), preserving terrain features and ensuring drainage continuity in flat or depressed areas.
A total of 64 topographic variables were derived using GRASS GIS (GRASS Development Team, 2024), SAGA-GIS (Conrad et al., 2015), QGIS (QGIS Development Team, 2024), and Whitebox (Lindsay, 2016), as well as the TAK toolbox for MATLAB (Forte and Whipple, 2019), Surf Rough (Trevisani et al., 2023), and the terra package for R (Hijmans, 2024).
For interpretability, variables were grouped into categories based on primary characteristics: morphology (geometric terrain properties), roughness (surface complexity), relative topographic position (elevation relative to surroundings), and hydrological/combined variables, which integrate terrain attributes with hydrological processes. Some variables span multiple categories due to overlapping functions (Figure 3).
Given the large number of variables tested for gully erosion susceptibility mapping, two selection methods were used: Variance Inflation Factor (VIF) and Recursive Feature Elimination (RFE). VIF was initially applied to identify and remove highly collinear variables. Variables with VIF values above 10 were iteratively removed to retain only independent predictors, enhancing model reliability and interpretability. Logistic regression was used to fit the initial model, and VIF values were recalculated at each step until all retained variables had VIF values below 10, eliminating multicollinearity.
In parallel, RFE was used to identify the most relevant predictors. This backward selection algorithm determines the optimal subset of variables for regression or classification tasks (Kuhn and Johnson, 2013). In this study, RFE was implemented with Random Forest, iteratively removing less informative variables and retaining those with higher predictive power. Using 10-fold cross-validation, the final subset of predictors was defined. The combined use of VIF and RFE reduced redundancy while improving model relevance.
For variables requiring a defined filter size, a 21-pixel window (630 m) was applied, based on the 30 m DEM resolution. This value reflects the average spatial dependency range of the topographic data (Figure 4), as determined by variogram analysis (Cremon et al., 2021).
Mohebzadeh et al. (2022) reviewed the most frequently used variables in gully erosion susceptibility studies. Among topographic predictors, 14 key variables were identified, including elevation and aspect. Other key variables were slope and the LS Factor, defined as the product of slope and contributing area, commonly used in the Universal Soil Loss Equation (USLE). Additional variables included flow accumulation, curvature, plan curvature (horizontal), profile curvature (vertical), and convergence index, which aid in assessing flow paths and water accumulation. Topographic indices such as the stream power index and topographic wetness index (TWI) were also emphasized for their relevance to erosion and flow concentration. Terrain roughness index and topographic position index (TPI) contribute to understanding surface complexity and erosion potential, making them widely applied in susceptibility modeling (Mohebzadeh et al., 2022). Beyond topography, the study incorporated hydrological, lithological, pedological, environmental, and anthropogenic factors:
Hydrological variables: Rainfall erosivity (R Factor in USLE; Panagos et al., 2017) and drainage density were included. Drainage density was derived from IBGE’s hydrographic network, refined at 1:50 000 scale, and calculated within a 1 km radius.
Lithological variables: Based on the 1:250,000 geological map (IBGE, 2023), lithology was treated as a categorical variable. Euclidean distance rasters were generated for lithological boundaries and morphostructural lineaments.
Pedological variables: A 1:50,000 scale soil map (Nunes and Castro, 2015; Cremon et al., 2021) was used, with erodibility values (K Factor in USLE) assigned to each class (Nunes and Castro, 2023).
Environmental and anthropogenic variables: Land use and land cover (LULC) data were obtained from the 2018 mapping of MapBiomas Collection 9. NDVI and road proximity rasters were also included. NDVI was calculated using a temporal median of Landsat-8 OLI images from 2018, matching the gully inventory year, and processed via Google Earth Engine. Road data were sourced from IBGE and OpenStreetMap (OSM).
All datasets were standardized to the same grid size and reference coordinate system. The methodological flowchart is presented in Figure 5.
For this study, three scenarios were analyzed (Figure 5). In the first scenario, the analysis included the most commonly used topographic and environmental variables for gully erosion susceptibility studies, as identified by Mohebzadeh et al. (2022). The following variables were considered: Aspect, Catchment area, Convergence Index, Drainage density, K Factor, Rainfall erosivity (R Factor), LS Factor, Distance to the road network, Plan Curvature, Profile Curvature, Slope, Stream Power Index (SPI), Topographic Position Index (TPI), Topographic Wetness Index (TWI), Terrain Ruggedness Index (TRI), Lithology map, LULC, and NDVI.
In the second scenario, less commonly used topographic variables were evaluated, and variable selection was performed using the Variance Inflation Factor (VIF) method. In the third scenario, the same set of less conventional variables was analyzed using the Recursive Feature Elimination (RFE) method. For both scenarios 2 and 3, conventional variables were included in the selection process to ensure a comprehensive evaluation of predictors.
Gully erosion susceptibility was modeled using the RF algorithm implemented via the caret package (Kuhn and Johnson, 2013) in R, using the RStudio interface. RF was chosen for its efficiency and strong performance in this modeling context (Mohebzadeh et al., 2022).
Model training and calibration were performed using 10-fold cross-validation, with evaluation based on the Receiver Operating Characteristic (ROC) curve. Hyperparameters were tuned by testing 10 values to identify optimal settings. 70% of samples were used for training, and the remaining 30% for independent testing, with model performance assessed by the Area Under the ROC Curve (AUC; Kuhn and Johnson, 2013). Variable importance was evaluated using the varImp function, based on the Gini importance metric (Breiman, 2001). Results were presented graphically for the 20 most influential variables in predicting gully occurrence.
4. Results
4.1. VARIABLE SELECTION PERFORMANCE
The analysis of RF models was conducted across three scenarios, each applying different strategies for variable selection and hyperparameter tuning. In scenario 1, which included traditional variables, the optimal number of predictors per tree split was set to 10. In scenario 2, where variable selection was based on the VIF method, the optimal number of predictors per tree split was adjusted to 13. In scenario 3, where variables were selected using the RFE method, the optimal number of predictors per tree split was reduced to 6.
The models were validated using an independent test dataset, and the AUC values obtained were 0.9344 for scenario 1, 0.9396 for scenario 2, and 0.9459 for scenario 3. The results indicate an improvement in model performance as variable selection and hyperparameter tuning were refined, with scenario 3 achieving the highest predictive accuracy, as demonstrated by the highest AUC value (Figure 6).
The findings suggest that incorporating less conventional topographic variables improved the predictive capacity of the models for gully erosion susceptibility. The scenario utilizing variables selected through the RFE method achieved the highest AUC, indicating superior predictive performance compared to the scenarios with traditional variables and those selected using the VIF method. These results highlight that, in addition to exploring less commonly used variables, the RFE approach was more effective in identifying the most relevant predictors for modeling gully erosion susceptibility.
Following the evaluation of validation metrics, the best-performing model was applied to generate a susceptibility map for gully formation in the study area. The resulting raster dataset ranges from 0 to 1, indicating areas with the lowest and highest susceptibility to gully formation, respectively (Figure 7).
Regions with lower susceptibility to gully erosion are typically associated with flat terrain and the presence of vegetation, which mitigates the impact of rainfall and reduces surface runoff.
In some agricultural areas, such as those used for soybean cultivation under appropriate management practices, the occurrence of gullies is also minimized. In contrast, areas with higher susceptibility to gully formation are predominantly located near drainage headwaters. These regions are characterized by factors such as high terrain roughness, erosion-prone soils, water flow convergence, proximity to the water table, and insufficient implementation of conservation practices. Pasturelands, in particular, often lack effective management strategies, contributing to the development of intense erosive processes (Figure 7).
4.2. VARIABLE IMPORTANCE
The most relevant variables for predicting gully erosion susceptibility were evaluated for all three scenarios using the RF algorithm. In scenario 1, all traditional variables were included, regardless of potential informational redundancy. In scenario 2, variables with VIF values exceeding 10 were excluded, resulting in a more independent set of predictors. In scenario 3, the RFE algorithm combined with cross-validation was used to iteratively select the most informative variables, producing a subset with greater predictive power and improved model efficiency (Figure 8).
4.2.1. SCENARIO 1
In modeling gully erosion susceptibility in southwestern Goiás, the most relevant traditional variables were associated with physical characteristics and land use or land cover. Pasture emerged as the most important variable, followed by drainage density. The K Factor, representing soil erodibility, was also highly influential, along with the TWI and NDVI, which are proxies for soil moisture and vegetation cover, both critical for mitigating erosion. Other significant topographic variables, such as slope and the TRI, were also notable due to their impact on water flow dynamics and erosion potential.
Variables like the convergence index, profile curvature, plan curvature, and TPI, reflect terrain characteristics that influence surface runoff and water concentration; these variables ranked moderately important. The R Factor, which accounts for rainfall erosivity, contributed significantly to estimating erosion intensity.
Less influential variables included lithological classes such as the Botucatu Formation and the Neogene Detrital-Lateritic Cover. Proximity to the road network, though relevant, was less impactful than variables related to topography and land use or land cover. These results indicate that the interplay between physical factors, land use, and rainfall erosivity is a key determinant in modeling gully erosion susceptibility in the region.
4.2.2. SCENARIO 2
In the scenario using less conventional topographic variables selected via the VIF method, pasture remained the most significant variable, reaffirming its influence on gully erosion susceptibility. Drainage density was the second most significant variable, followed by multiscale roughness and terrain surface texture, which describe surface irregularity and variability, capturing interactions between terrain characteristics and erosive processes.
Other important variables included maximum downslope elevation change and average normal vector angular deviation, both of which influence water flow direction and velocity, contributing to erosion-prone areas. Variables such as valley depth and NDVI, representing valley morphology and vegetation cover, respectively, were also significant in reducing erosion susceptibility.
The roughness concentration index (RCI), linked to slope variability, and the vertical distance to channel network (VDCN), representing vertical proximity to drainage channels, were among the critical predictors. Variables derived from the TAK toolbox, such as ksn and χ (chi), ranked moderately in importance. Ksn quantifies the erosive power of fluvial systems based on slope and contributing area, while χ (chi) measures the relative position of a point within the fluvial network, weighted by drainage area and erosion potential, offering valuable perspectives on geomorphic processes.
Additional variables, including topographic coherence, elevation entropy, and average normal vector angular deviation, captured terrain variability and played a significant role in modeling erosion processes. Proximity to the road network, convergence index, and profile curvature, derived from the Topodata method (Valeriano and Albuquerque, 2010), provided further insight into water flow direction and concentration, influencing susceptibility to erosion.
4.2.3. SCENARIO 3
In the scenario with less conventional topographic variables selected using the RFE method, pasture again emerged as the most important variable, highlighting its consistent role in determining erosion susceptibility. Similarly, drainage density was ranked as the second most significant variable, aligning with findings from the other scenarios.
Other significant variables included multiscale roughness and terrain surface texture, which describe terrain irregularity and variability. The K Factor, representing soil erodibility, emphasized the role of soil types in gully formation. Additionally, maximum downslope elevation change and average normal vector angular deviation underscored the influence of slope and surface orientation on water dynamics and erosion.
Variables such as NDVI and valley depth captured vegetation cover and valley morphology, which are key factors in reducing erosion risk. The VDCN and geomorphic variables derived from the Topotoolbox, such as χ (chi) and ksn, ranked moderately in importance, reflecting the interactions between terrain features and the erosive capacity of fluvial systems.
Less impactful variables included the SAGA TWI and convergence index, which provide information on water concentration and slope saturation. Other variables, such as the terrain classification index for lowlands (TCI low) from SAGA GIS and edge density, represented surface morphology and roughness. Proximity to the road network and lithology, including savanna formations and the Neogene Detrital-Lateritic Cover, also contributed to the model, though their influence was relatively minor compared to topography and vegetation-related variables.
5. Discussion
Gully formation is a complex process influenced by various environmental, topographic, and hydrological factors that directly affect erosive potential. Conditioning variables such as topographic characteristics, hydrological features, climatic factors, land use and land cover, and soil properties are important for modeling susceptibility effectively. However, the selection of the most suitable variables lacks universal agreement, necessitating an evaluation of their relative importance within the specific context of the study area (Azareh et al., 2019). Machine learning models, including RF, have proven effective in identifying key variables and their interactions, enhancing the accuracy of susceptibility assessments.
Across the three evaluated scenarios—traditional variables in scenario 1, VIF-based variable selection in scenario 2, and RFE-based variable selection in scenario 3—the land use and land cover class “pasture” consistently ranked as the most significant predictor. This result likely reflects the impact of soil compaction and inadequate management practices, which increase erosion susceptibility (Galdino et al., 2016; Nunes and Castro, 2023; Pereira et al., 2025). In the study area, converted pastures often feature cattle trails and boundary fences that exacerbate erosive processes (Santana et al., 2007; Nunes and Castro, 2015; Pereira et al., 2025). Additionally, NDVI showed moderate importance in all scenarios, highlighting the role of vegetation cover in mitigating erosion. Dense and healthy vegetation reduces soil exposure to rainfall and surface runoff, limiting erosion.
Drainage density, defined as the ratio of total stream length to unit area, reflects the interplay between erosive forces and surface material resistance. Influenced by climate, vegetation, lithology, and soils (Huggett and Shuttleworth, 2022), this metric correlates with runoff capacity and directly impacts rock and soil erodibility (Gournellos et al., 2004). In the study area, drainage density was consistently ranked as a key predictor, being the second in the list (Figure 8). Regions with higher drainage density are often more susceptible to gully formation, especially in areas with poor soil management, such as degraded pastures.
The inclusion of less conventional topographic variables in scenarios 2 and 3 highlighted the significance of roughness-related metrics. In scenario 1, only one roughness variable was among the top 20 predictors, compared to seven in scenario 2 and four in scenario 3. Notable variables included multiscale roughness and terrain surface texture, which were highly predictive in both VIF-and RFE-based selection methods. Multiscale roughness adapts the level of detail based on the local topographic context of each DEM cell, enabling a nuanced understanding of roughness and its relationship with specific erosion patterns (Lindsay, 2023). Terrain surface texture, in contrast, uses a fixed filter radius to quantify the relative frequency of pits and peaks, delineating valleys and ridges. High-frequency cells indicate rougher terrain, while low-frequency cells suggest smoother surfaces (Iwahashi and Pike, 2007).
Additional roughness metrics, such as average normal vector angular deviation and edge density, provided additional perspectives under RFE selection. Average normal vector angular deviation quantifies angular variation in surface normal vectors, emphasizing topographic complexity (Ko et al., 2016; Lindsay, 2023). Edge density measures the concentration of slope breaks, capturing abrupt changes in terrain (Lindsay, 2023). These variables enhance gully susceptibility modeling by identifying localized terrain variations that influence erosion processes. Among relative topographic position variables, max downslope elevation change, valley depth, and VDCN were highly significant. Max downslope elevation change identifies abrupt elevation variations, indicating areas with accelerated water flow and heightened erosion potential (Lindsay, 2023). Valley depth measures dissection relative to ridge cells, where concentrated water flow intensifies erosion. VDCN, widely used in gully susceptibility modeling, captures the relationship between groundwater emergence and surface processes. In areas where the water table is near the surface, exfiltration intensifies erosion, promoting gully development (Marinho et al., 2006).
Combined topographic variables, such as the SAGA TWI and TCI low, were moderately significant in low-slope areas. SAGA TWI indicates moisture retention and saturation potential, with high values linked to soil instability and deep erosive processes (Valipour et al., 2022; Wang et al., 2021). TCI low integrates SAGA TWI and VDCN to identify low-slope, high-moisture areas conducive to gully formation (Bock et al., 2007). The convergence index, which measures water flow concentration, was also important, amplifying erosion in susceptible areas (Chaplot, 2013).
Variables such as ksn, χ, and proximity to lithological boundaries exhibited intermediate importance. The ksn index reflects the erosive power of water, influenced by slope and contributing area, with higher values indicating greater susceptibility (Whipple et al., 2022). The χ variable, used to analyze drainage divide mobility, highlighted areas with contrasting erosion rates, corresponding to boundaries of gully-prone regions (Willett et al., 2014; Forte and Whipple, 2018). Proximity to lithological boundaries influences subsurface processes like piping, which destabilizes soil and promotes gully formation (Marinho et al., 2006).
Proximity to road networks moderately influenced susceptibility, as poorly planned roads alter water dynamics and fragment landscapes, creating localized erosion conditions (Santana et al., 2007). Lithological classes, such as the Neogene Detrital-Lateritic Cover, exhibited resistance to erosion due to their consolidated structures. Among land cover classes, savanna formations ranked within the top 20 variables, reflecting their ability to reduce runoff velocity and protect against direct rainfall impacts, mitigating initial erosive processes.
The consistent prominence of “pasture” as a predictor suggests the need for variable refinement. Current classifications may obscure internal variability, such as pasture age, degradation, and management practices, which affect soil structure and erosion. Incorporating descriptors like degradation indices or vegetation dynamics could improve model sensitivity.
Anthropogenic and microtopographic features—such as cattle paths, fences, and roadside ditches—can create preferential flow paths that influence gully initiation. However, the 30-meter DEM resolution used here precluded their explicit inclusion. Future studies should integrate high-resolution spatial data, including models derived from Unmanned Aerial Vehicles (UAVs) or manually mapped features, to better capture fine-scale flow dynamics critical to gully formation.
6. Conclusions
The results of this study confirm that incorporating less commonly explored topographic variables can enhance predictive models for gully erosion susceptibility. Variables such as multiscale roughness and terrain surface texture emerged as significant predictors, demonstrating the value of including more complex topographic characteristics in modeling erosive processes.
Among the variable selection methods evaluated, the RFE algorithm outperformed the VIF method. This is reflected in the relatively higher AUC values achieved and the identification of more relevant predictors. The RFE approach effectively captured interactions between variables while reducing redundancies, improving the efficiency and reliability of the generated models.
Surface roughness and terrain structure variables made substantial contributions to the models, highlighting the importance of surface variability in shaping erosive dynamics. The integration of data derived from DEMs with advanced machine learning methods was shown to be an effective strategy for mapping areas susceptible to gully formation.
This study emphasizes the importance of incorporating less conventional topographic variables in future research, particularly in tropical and subtropical regions where terrain and hydrological processes are highly heterogeneous. This approach enhances the accuracy of susceptibility predictions and contributes to a more in-depth understanding of the mechanisms underlying gully initiation and development.
Contributions of authors
(1) Conceptualization: LLA, ÉHC; (2) Analysis or data acquisition: LLA, FCA, ÉHC, EDN, ACP; (3) Methodologic/technical development: LLA, ACP, ÉHC; (4) Writing of the original manuscript: LLA, ÉHC, FCA; (5) Writing of the corrected and edited manuscript: LLA, ÉHC, FCA; (6) Financing: ÉHC; (7) Software: LLA, ÉHC, ACP; (8) Supervision and resources, EDN, ÉHC.
Financing
This research has not received any external funding.
Acknowledgements
ÉHC is research fellow of Brazilian National Council for Scientific and Technological Development -CNPq/Brazil (#310198/2022-4).
Conflicts of interest
The authors declare not having any conflict of interest.
Handling editor
Grace Bungenstab Alves.
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