Integrated assessment of landslide susceptibility in the Kalaleh Basin, Golestan Province, Iran using novel SVR-GOA ensemble validated with BRT, ANN, and elastic net models

doi:10.21203/rs.3.rs-2458371/v1

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Integrated assessment of landslide susceptibility in the Kalaleh Basin, Golestan Province, Iran using novel SVR-GOA ensemble validated with BRT, ANN, and elastic net models

https://doi.org/10.21203/rs.3.rs-2458371/v1

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Landslides cause severe environmental problems, such as severe damages to infrastructures (i.e., bridges, roads, network masts, and buildings) and agricultural lands, across many parts of the world. Unfortunately, a high degree of accuracy in landslide mapping and prediction is still challenging due to the complicated interactions of many factors. The goal of this study was to create and introduce a new ensemble model (support vector regression–grasshopper optimization algorithm (SVR–GOA)) validated alongside artificial neural network (ANN), boosted regression tree (BRT), and elastic net models for landslide susceptibility modeling taking the Kalaleh Basin in Iran as a case study. For this objective, a total of 140 landslides were considered and 16 conditioning factors used to construct a geographic database. Subsequently, variance inflation factor and tolerance indices were used to test the multicollinearity of the hazard conditioning variables. The relative significance of these factors and their connections to the locations of the landslides were determined using random forest. The development and validation of the four landslide models, SVR-GOA, ANN, BRT, and elastic net, were then performed. This study is the first to implement the SVR-GOA in landslide mapping. The effectiveness of the models was evaluated using area under the curve (AUC), kappa, and root mean squared error values. The outcome indicated that the lithology, slope degree, rainfall, topography position index, topography wetness index, surface area, and landuse/landcover were the most influential conditioning factors. All of the models provided predictions with good degree of fit, with the SVR-GOA performing better than others. The models performed in the order, at validation phase: SVR-GOA (AUC = 0.930) > ANN (AUC = 0.833) > BRT (AUC = 0.822) > elastic net (AUC = 0.726). Our novel approach employing the SVR-GOA ensemble in landslide mapping would help advance landslide research on regional, national, and global scales.

Artificial neural network (ANN)

Boosted regression tree (BRT)

Elastic net model

Ensemble model

Landslide susceptibility

Support vector regression–Grasshopper optimization algorithm (SVR–GOA)

Natural catastrophes have occurred more frequently and had more severe effects recently as a result of declining environmental quality, climate change, fast population growth, and intensive and unsuitable land-use planning (Saha et al. 2021). Landslides, soil erosion, floods, earthquakes, and tsunamis, among others, have an influence on human populations, resulting in serious injuries and fatalities, damage to residences and infrastructure, financial loss, and social unrest (Nwazelibe et al. 2023; Saha et al. 2021; Lee 2018). Soil erosion frequently occurs in conjunction with landslides, and vice versa. The two most significant land degradation processes are water erosion and landslides, particularly in semi-arid areas (Dotterweich et al. 2012). They are geomorphologic processes that cause environmental degradation, the loss of livelihoods and ecosystem services, disturbance of the social and economic conditions of human communities, and degradation of the environment. Water erosion and landslides cause issues far outside the area by lowering the quality of the soil and causing sedimentation (Diyabalanage et al. 2017; Poesen 2011).

Several studies have employed different techniques in the past to evaluate a region's sensitivity and likelihood of experiencing landslides. The creation of susceptibility maps using various methods frequently involves landslide susceptibility zonation or mapping. The methods used can be broadly divided into qualitative and quantitative approaches. The quantitative method uses deterministic, statistical, and artificial intelligence approaches, whereas the qualitative approach uses descriptions and heuristic techniques (Shano et al. 2020; Ayalew and Yamagishi 2005; Vakhshoori and Zare 2016; Aleotti and Chowdhury 1999). Over time, it has been found that the quantitative methods seem to be more objective and realistic than the qualitative methods, which are more subjective and frequently lead to interpretation bias. However, because they are adaptable and take into account a particular area's unique characteristics, qualitative approaches are thought to be preferable. Indeed, each strategy has benefits and drawbacks. Many landslide studies have recently combined geographic information systems (GIS) and remote sensing (RS) to improve the analysis and visualization of landslide data.

Geophysical, geotechnical, indexical, geostatistical, artificial intelligence, and geospatial techniques are some of the methods that have been often used in recent years (Shano et al. 2020). In order to estimate the spatial susceptibility of landslides, landslide studies frequently combine some of the methodologies mentioned above with geoinformatics technology. Van Western et al. (2006) classified two methods in the geographic modeling of landslides. The first is dynamic and deterministic modeling that is fundamentally concerned with the geotechnical characteristics of rocks and soils and is strongly related to the physical process of landslides. This approach offers insights that are essential for stabilizing destabilized or fragile slopes. According to Van Western et al. (2006), the geographic mapping of prior landslides and the prediction of landslide-prone regions based on some conditioning elements constitute the second modeling technique, which uses a variety of landslide conditioning factors, including earthquakes, rainfall, hydrologic conditions, elevation, geology and lithology, slope properties, land use/land cover (LU/LC) type, soil properties, distance to surface water body, distance to road networks, and human activities, etc. (Shit et al. 2016; Ayalew and Yamagishi 2005; Shano et al. 2020). Through the use of artificial intelligence or machine learning algorithms and multivariate statistical techniques, this mapping strategy also pinpoints locations that are susceptible to landslides. However, a survey of previous literature also demonstrates that this modeling approach only foresees regions that may be at risk from landslides rather than definitely predicting when they will happen (Shano et al. 2020). The size of landslides is not also predictable with these models.

Fortunately, data-driven and intelligent computational techniques have many advantages. Undoubtedly, there is a significant gap in the use of artificial intelligence (data-driven learning algorithms) for modeling geohazards in environments with little data (Saha et al. 2021). However, using machine learning (ML) tools in both data-rich and data-poor environments has produced promising outcomes. For instance, several ML methods have been successfully utilized in the modeling of different geohazards such as landslide susceptibility (Turan et al. 2020), gully erosion susceptibility (Debanshi and Pal 2020), flood susceptibility (Falah et al. 2019; Termeh et al. 2018; Saha et al. 2021), and soil erosion investigation (Efthimiou et al. 2020; Sholagberu et al. 2017), etc. Because they are the consequence of intricate processes, landslides and soil erosion are still challenging to predict with high accuracy. Thus, the applicability of several ML models has been explored for the geohazards: support vector machine (SVM) (Pourghasemi et al. 2017), classification and regression trees (Gutiérrez et al. 2009), artificial neural network (ANN) (Garosi et al. 2018; Pourghasemi et al. 2017), decision tree (Geissen et al. 2007), multivariate adaptive regression splines (Conoscenti et al. 2018; Gutiérrez et al. 2009), random forest (RF), boosted regression tree (BRT), Stochastic Gradient Treeboost (SGT) (Angileri et al. 2016), etc. Overall, geohazard models powered by ML algorithms can provide predictions that are more accurate than those made using statistical methods. The scientific community has accepted ML models because of their robustness and accuracy.

Through a suitable and accurate susceptibility study, the effects of landslides can be reduced. Therefore, one of the main objectives of researchers and policymakers/decisionmakers is to produce accurate landslide modeling. Numerous geoscientific techniques have been employed in the literature. Although for a thorough investigation of possible landslide occurrences, traditional methodologies like physical models and data-driven strategies have limitations. The primary reason is that most traditional methods use a one-dimensional approach when there are several conditioning factors that are not stable but have dynamic characteristics to jointly induce high landslide susceptibility and soil erosive potential. Additionally, the traditional approaches demand a significant amount of fieldwork and funding for data collection. The aforementioned shortcomings led geoscientists to adopt more sophisticated empirical and data-driven methodologies, often coupled with RS and GIS technologies. Modeling natural hazards using machine-based ensemble prediction is another emerging development (Barzegar et al. 2018; Hong et al. 2020). Due to its capacity to increase the predictive capability of existing predictive models, ensemble approaches have gained significant interest in model development and prediction of geohazards in more recent years (Pourghasemi et al. 2017; Chen et al. 2018; Hosseinalizadeh et al. 2019). Several studies around the world have successfully used various ensemble ML approaches for modeling landslide-prone areas and have determined the optimal ensemble ML strategies for their studies. The application has gained popularity since it allows users to choose the best model through a series of trial-and-error procedures. Based on the better results and insights drawn from the application of ensemble models, investigation of geohazards like landslides benefit from adopting newer hybrid and ensemble models.

Through the creation of a new support vector regression–grasshopper optimization algorithm (SVR–GOA) ensemble landslide model, this study seeks to increase the body of knowledge on landslide prediction. The SVR-GOA is a hybridization of SVM and GOA for spatial landslide prediction with a case study of Kalaleh Basin, Golestan Province, Iran. The current study is focused on the development and application of novel SVR-GOA ensemble for landslide modeling. The SVR-GOA model is an efficient and new computational technique which has been very recently implemented in flood modeling (Panahi et al. 2021; Ruidas et al. 2022). This is the first time that this ensemble model is used for spatial landslide modeling, to the best of our knowledge. Additionally, this study took into account sixteen landslide conditioning elements altogether. The present study also used 3 other models (BRT, ANN, and elastic net) as benchmarks for the development of the novel SVR-GOA. The integration of a multi-model strategy based on ML computing for spatial landslide prediction is targeted at improving the performance and the state-of-the-art in Iran and other regions of the world. Testing the applicability of the ensemble SVR-GOA model alongside the three other models in landslide susceptibility mapping (LSM) offers the main novelty in this research. Great advancements in landslide mapping literature would be made from the insights that could be drawn from this study. The landslide models could successfully identify the hazard-prone areas, the information from which will aid rural and urban development policymakers to ensure nature-friendly hazard mitigation and risk management.

2.1 Brief description of the study area

The Kalaleh basin is located in the northeastern Golestan Province near the city of Kalaleh. The basin is delineated by a box drawn between 36°53′12″ and 37°43′25″ N, and between 55°14′26″ to 55°54′34″ E (Fig. 1). The study region covers about 2917.5 km. Elevation in the study area ranges from 60 to 2348 m.a.s.l. The slopes in the study area range from 0 to 73˚. Most of the basin, a portion of the Alborz Mountain range, is mountainous with gentle slopes. The lowest and highest temperatures in this area are 11 C° and 19 C° (IRIMO 2012). Diverse lithologies cover the area. The largest are swamp (58.7%) and swamp and marsh (12.9%), and grey to block shale with thin layers of siltstone and sandstone (7.8%), The remaining area is accounted by other formations (GSI 1997) (Table 1). Average annual precipitation of this region ranges from 236 to 1005 mm, with more rainfall in the southeast. There are four climates in the study area: humid, semi-humid, semi-arid, and Mediterranean (IRIMO 2012). This is the source region of the main branch of the Gorganrood River. Land use and land cover (LULC) is classified as forest (21.99%), agriculture (19.18%), orchards (0.022%) dryland farming (52.41%), water (1.31%), agri-orchard (22.37%), rock (0.16%) and urban (0.46%).

Table 1

Lithological units and their descriptions in the study area
Unit	Description
DCkh	Yellowish, thin to thick-bedded, fossiliferous argillaceous limestone, dark grey limestone, greenish marl and shale, locally including gypsum
Sn	Greenish grey, shale, sandstone, sandy lime, coral limestone and dolomite (NIUR FORMATION)
Ekh	Olive-green shale and sandstone (KHANGIRAN FORMATION)
Murm	Light-red to brown marl and gypsiferous marl with sandstone intercalations
Jd	Well-bedded to thin-bedded, greenish-grey argillaceous limestone with intercalations of calcareous shale (DALICHAI FORMATION)
Jl	Light grey, thin - bedded to massive limestone (LAR FORMATION)
Jmz	Grey thick - bedded limestone and dolomite (MOZDURAN FORMATION)
Kat	Olive green glauconitic sandstone and shale (AITAMIR FORMATION)
Ksn	Grey to black shale and thin layers of siltstone and sandstone (SANGANEH FORMATION)
Ksr	Ammonite bearing shale with intercation of orbitolin limestone (SARCHESHMEH FORMATION)
Pz	Undifferentiated lower Palaeozoic rocks
PlQc	Red sandstone and shale with subordinate sandy limestone (DORUD FORMATION)
Qsw	Swamp
Qft2	Low level piedmont fan and valley terrace deposits
Qm	Swamp and marsh
Qft1	High level piedmont fan and valley terrace deposits
Qs,d	Unconsolidated wind-blown sand deposits including sand dunes

2.2 Landslide inventories

The current study illustrates how machine learning ensemble strategies can be used in LSM. The flowchart of our research approach is shown in Fig. 2. Accuracy of the landslide occurrence data is very important for landslide susceptibility, hazard, and risk assessments. Accordingly, the first step in these analyses is landslide inventory mapping. The landslide inventory map displays characteristics and locations of landslides associated with past movements. Landslides are controlled by geological, topographical and climatic factors. Therefore, location and condition of future landslides can be predicted based on these factors. For this purpose, determination of accurate location and areal extent of landslides is prominent for preparation of landslide susceptibility maps (Yalcin 2008). A variety of sources, instruments and methods have been suggested for landslide mapping (van Westen et al. 2008) and the landslide susceptibility assessment is carried out in various phases as well.

Identification and evaluation of landslide prone areas is an initial phase for preparation of an inventory landslide map. Various approaches such as field studies, interpretation of aerial photographs/satellite images, and also historical landslide records are used for landslide inventory mapping. Widespread mass movements occurred in the study area play a significant role in the landslide assessment. A total of 140 landslides were identified and analyzed by field surveys, aerial photographs, and satellite images and divided into two groups: 70% for training and 30% for validation. Landslide types of the study area include 42 (30%) transitional slides, 39 (28%) rotational slides, 28 (20%) complex, 18 (13%) debris flows, and 13 (9%) surface landslide with a total areal extent of 7,287,187 m². Transitional and rotational landslides are very common in the study area. The analysis on sizes of landslides shows that areal extents of the smallest and largest landslides are about 68.22 and 981,814 m², respectively, with an average about 21,287.5 m². Most of the landslides are shallow-seated (Fig. 3).

2.3 Landslide conditioning factors

In the Kalaleh Basin of Golestan Province in Iran, landslides are severely disrupting daily life. The lack of adequate criteria in the construction of homes, roads, and other infrastructures in potentially endangered regions is to blame for the study area's vulnerability to landslides and the losses that come from them. To ensure effective and secure operations in the area, it is vital to identify and map landslide-prone locations. Decision-makers should avoid building inappropriate structures there, avoiding the area completely, or using efficient technological solutions to mitigate the potential hazard by being informed about potentially sensitive places. To achieve these, the combination of landslide conditioning factors that are peculiar to the area under study is required. Therefore, the present study integrated sixteen (16) conditioning factors in mapping the landslide-prone areas. The 16 factors are elevation, slope aspect, slope degree (angle), plan curvature (PC), topography position index (TPI); topography wetness index (TWI), surface area (SA), terrain ruggedness index (TRI), normalized difference vegetation index (NDVI), rainfall; distance to stream (DtS), distance to road (DtR), soil type, terrain surface texture (TST), lithology/geology, and landuse/landcover (LU/LC). The initial step taken in the mapping of landslides in the research area was to ascertain the most efficient landslide predisposing elements. Without a grasp of the peculiar and potent landslide conditioning elements, the susceptibility map produced would not be accurate/dependable. The 16 landslide conditioning factors were classified into four main categories, namely the topographical/geomorphological factors (elevation, slope degree, slope aspect, TWI, PC, TPI, TRI, SA, and TST), the hydrological factors (rainfall and DtS), the geological factors (lithology), and the environmental factors (DtR, LU/LC, NDVI, and soil type) (Fig. 2). The topographical factors, the hydrological factors, the geological factors, and the environmental factors were integrated and considered in this study based on the peculiarities of the area and some existing landslide literatures in Iran (Pham et al. 2017). Also, the investigation of multicollinearity for predicting the risk zones in the Kalaleh Basin influenced the selection of the conditioning factors.

The data sources, resolutions, techniques, and classification methods for the landslide conditioning factors are presented in Table 2. Studies have shown that Phased Array-type L-band Synthetic Aperture Radar (PALSAR) Digital Elevation Model (DEM) is more accurate and trustworthy than the SRTM DEM and ASTER. The PALSAR DEM with a resolution of 12.5 m x 12.5 m was used in this study. Using appropriate methodologies, the topographical elements were retrieved from the PALSAR DEM in ArcGIS and are shown and described in Table 2. A 1:100,000 geologic map of Iran was used to produce the geological map of the study region. The major geological units in the Kalaleh Basin were identified Table 1). A total of 30 years’ average rainfall data of different stations in the study area, obtained from the Islamic Republic of Iran Meteorological Organization, were utilized. Kriging interpolation method was used to process the data. Distances to streams and roads were extracted from ALOS DEM (12.5 m x 12.5 m resolution) and topographical map (scale 1: 25000) plus Google earth image, respectively (Table 2). The Euclidian distance buffering tool in ArcGIS software was utilized for the preparation of the DtS map. However, digitization method was used for the DtR. The NDVI and LU/LC maps were created using Sentinal-2 photos with a resolution of 30 m x 30 m and the supervised maximum likelihood classification option. Numerous controls in reality were employed to assess the categorization accuracy of the LU/LC map. and high overall accuracy was obtained. A projected soil map (scale 1:25,000) that was accessed from the Iranian Agricultural and Natural Resources Center and used to create the soil map was digitized after being imported into the ArcGIS.

Table 2

The conditioning factors, their data sources, resolutions, techniques, and classification methods
Factor	Data used/ resolution/ scales	Data sources	Techniques	Classification methods
Elevation (m)	ALOS DEM (12.5m*12.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	12.5 m*12.5m DEM	Natural break (Jenks)
Slope (⁰)	ALOS DEM (12.5m*15.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	$\operatorname{Tan} \theta =\frac{{N \times i}}{{636.6}}$ N = No. of Contour Cutting; i = Contour Interval (12.5m*15.5m resolution)	Natural break (Jenks)
Aspect	ALOS DEM (12.5m*15.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	$Aspect=57.29578 \times a\tan 2(\left[ {dz/dy} \right], - \left[ {dz/dx} \right])$ Where,$dz/dx=((c+2f+i) - (a+2d+g))/8$$dz/dy=((g+2h+i) - (a+2b+c))/8$ Here, a to i indicates the cell value of 3*3 window	-
Plan curvature (PC)	ALOS DEM (12.5m*12.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	12.5 m*12.5m DEM	Natural break (Jenks)
TRI	ALOS DEM (12.5m*12.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	$TRI=\sqrt{\left\|X\right\|}\left({max}^{2}-{min}^{2}\right)$ where X represents the altitude of every neighbor cell to a definite cell, and max and min are the highest and smallest altitude among different neighboring cells	Natural break (Jenks)
TPI	ALOS DEM (12.5m*12.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	${\text{TPI=}}{{\text{Z}}_{\text{0}}}{\text{-}}\overline {{\text{Z}}}$$\overline {Z} =\frac{1}{{{n_R}}}\sum\nolimits_{{i \in R}} {{Z_i}}$ Center point elevation (Z₀) and the average elevation ($\overline {Z}$) around it within a predetermined radius (R	Natural break (Jenks)
TWI	ALOS DEM (12.5m*12.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	${\text{TWI=In}}\left( {{{\text{A}}_{\text{s}}}{\text{/tanθ}}} \right)$ α is a total upslope area that drains through a point (per unit ontour length), β is a gradient of the slope (in degree).	Natural break (Jenks)
Terrain surface texture (TST)	ALOS DEM (12.5m*12.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	TST is calculated by input elevation through a median filter over a neighbourhood specified by the pixel size. TST is calculated in the SAGA-GIS platform	Natural break (Jenks)
Surface area (SA)	ALOS DEM (12.5m*12.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	SA is calculated in the SAGA-GIS platform -	Natural break (Jenks)
Distance to road (m)	Topographical map ( scale 1: 25000) and Google earth image	Cartography department of Iran	Digitization process	Natural break (Jenks)
Distance to stream (m)	ALOS DEM (12.5m*12.5m resolution)	https//vertex.daac.asf.alaska.edu (Alaska Satellite Facility)	Euclidian Distance Buffering	Natural break (Jenks)
Rainfall (mm)	30 years average rainfall data of different stations	Islamic Republic of Iran Metrological Organization	Kriging Interpolation method	Natural break (Jenks)
Lithology	Projected geological map (scale 1:100,000)	Geological Survey of Iran	Digitization process	Equal interval
LU/LC	Landsat 8 OLI/TIRS (Path 162/Row 34) ( 30m*30m resolution)	U.S Geological Survey	Supervised classification (Maximum likelihood)	Maximum likelihood
NDVI	Landsat 8 OLI/TIRS (Path 162/Row 34) ( 30m*30m resolution)	U.S Geological Survey	$NDVI=\frac{{NIR - IR}}{{NIR+IR}}$ Where, NIR is near inferred band or band 4 and IR is the Inferred band or band 3.	Natural break (Jenks)
Soil type	Projected soil map (Scale 1: 25,000)	Agricultural and Natural Resources Research Center in Iran	Digitization process	Equal interval

2.4 Testing the multicollinearity of the conditioning factors

By assisting in the selection of the best parameters for hazard mapping, the multicollinearity test improves the outcomes of spatial models (Pradhan et al. 2017). Multicollinearity is a type of linear dependency that suggests that a dataset has two or more linked variables. Susceptibility maps of groundwater potentiality, soil/gully erosion, and landslides have all been done using the multicollinearity test (Cama et al. 2016; Hong et al. 2017; Gayen et al. 2019). The multicollinearity test was employed by Roy and Saha (2018) to examine several factors for LSM. The multicollinearity of the conditioning factors was tested in the present study by using the VIF (variance inflation factor) and tolerance indices. Using Eqs. 1 and 2, the VIF is determined as the reciprocal of the tolerance values.

$$\text{T}\text{o}\text{l}\text{e}\text{r}\text{a}\text{n}\text{c}\text{e} =1- {\text{R}}_{j}^{2}$$

$$\text{V}\text{I}\text{F} =\left[\frac{1}{\text{T}\text{o}\text{l}\text{e}\text{r}\text{a}\text{n}\text{c}\text{e}}\right]$$

where, the R²_j represents the regression determination coefficient factor j on all the other factors.

2.5 Applied modeling techniques

2.5.1 SVR-GOA ensemble

The SVR is a supervised machine learning method created by Cortes and Vapnik (1995) that employs the same concepts for classification as the support vector machine, with a few small variations (Vapnik et al. 1997). SVR may be used to tackle linear and nonlinear problems, particularly when the number of data points and their characteristics is minimal. The structural risk minimization (SRM) parameter, which specifies the connection between input and output variables, is one of the fundamental parameters in SVR models (Rastogi and Sharma 2021). As a result, SRM should be estimated in an SVR model, and this can be done using the following equations:

$$y=k\left(z\right)=v\text{\varnothing }\left(z\right)+c \left(3\right)$$

$$\text{Minimize : }\left[\frac{1}{2}\parallel v{\parallel }^{2}+P\sum _{b=1}^{n} \left({\vartheta }_{b}+{\vartheta }_{b}^{*}\right)\right] \left(4\right)$$

$$\text{Subject to : }\left\{\begin{array}{c}{y}_{b}-\left(v\text{\varnothing }\left({z}_{b}\right)+{c}_{b}\right)\le \epsilon +{\vartheta }_{b}\\ \left(v\text{\varnothing }\left({z}_{b}\right)+{c}_{b}\right)-{y}_{b}\le \epsilon +{\vartheta }_{b}^{*}\\ {\vartheta }_{b},{\vartheta }_{b}^{*}\ge 0\end{array}\right. \left(5\right)$$

where P = the penalty factor, ${\vartheta }_{b}$ and ${\vartheta }_{b}^{*}$ = the loose variables, and $\epsilon$ = the optimized performance of the model (Su et al. 2018; Wang et al. 2012). The optimization problem is resolved using the equations below.

$$\begin{array}{c}L\left(v,c,{\vartheta }_{b},{\vartheta }_{b}^{*},{B}_{b},{B}_{b}^{*},{\delta }_{b},{\delta }_{b}^{*}\right)=\frac{1}{2}|v{|}^{2}\\ +P\sum _{b=1}^{1} \left({\vartheta }_{b}+{\vartheta }_{b}^{*}-\sum _{b=1}^{1} {B}_{b}\left({\vartheta }_{b}+\epsilon -{y}_{b}+v\text{\varnothing }\left(z{z}_{b}\right)+c\right)\right.\\ -\sum _{b=1}^{1} {B}_{b}^{*}\left({\vartheta }_{b}^{*}+\epsilon +{y}_{b}-v\text{\varnothing }\left({z}_{b}z\right)-c\right)\\ \left.-\sum _{b=1}^{1} \left({\delta }_{b}{\vartheta }_{b}+{\delta }_{b}^{*}{\vartheta }_{b}^{*}\right)\right) \left(6\right)\end{array}$$

where ${B}_{b}$, ${B}_{b}^{*}$, ${\delta }_{b}$, and ${\delta }_{b}^{*}$ = the Lagrange multipliers, and L = the Lagrangian function.

SVR can be computed using the following equations.

$$k\left(z\right)=\sum _{b=1}^{1} \left({B}_{b}-{B}_{b}^{*}\right)m\left(z.{z}_{b}\right)+c \left(7\right)$$

The mathematical expression of the kernel function is represented in Eq. 8.

$$m\left(z,{z}_{b}\right)=⟨\text{θ}\left(z\right)\cdot \text{θ}\left({z}_{b}\right)⟩ \left(8\right)$$

The process of determining the best value for a variable in order to minimize and maximize an objective function of a specific problem is known as optimization. Nature-inspired population-based algorithms and stochastic optimization approaches have recently surpassed mathematical optimization methods in popularity (Ruidas et al. 2022). Multiple nature-inspired meta-heuristic approaches were employed in various studies in recent years, including grasshopper optimization algorithms (GOA), ant colony optimization, particle swarm optimization, and genetic algorithms (Ruidas et al. 2022). Among these optimization methods, GOA has stood out as an important meta-heuristic, multiple objective-based, and multi-solution technique (Saremi et al. 2017). The GOA was created by Saremi et al. (2017) and is completely based on the swarm trait of grasshoppers. Grasshoppers have three life stages: egg, nymph, and adult. The nymph phase is distinguished by modest, slow movements, whereas the adult phase is distinguished by lengthy, rapid movements. GOA intensification and diversification are determined by mobility during the nymphal and adult stages (Ewees et al. 2020; Meraihi et al. 2021). One key assumption of the GOA is that gravity has no effect on grasshopper movement, resulting in a higher rate of result convergence (Qin et al. 2021). GOA has been used in a variety of disciplines because of its efficiency and ease of use (Haji Seyed Asadollah et al. 2022; Ruidas et al. 2022; Panahi et al. 2021; Tharwat et al. 2018; Łukasik et al. 2017). According to Luo et al. (2018), In comparison to other nature-inspired optimization methods, the GOA has provided the most precise and competitive outcomes. The procedures used for the application of the GOA were extracted from Haji Seyed Asadollah et al. (2022) and are described below.

The position of the i-th grasshopper ${Y}_{i}$ is expressed in Eq. 9.

$${Y}_{i}= {So}_{i}+ {Gr}_{i}+ {Aw}_{i} \left(9\right)$$

For the computation of random swarm behavior, Eq. 10 is utilized.

$${Y}_{i}= {r}_{1}*{So}_{i}+ {r}_{2}*{Gr}_{i}+ {r}_{3}*{Aw}_{i} \left(10\right)$$

where ${Gr}_{i}$ stands for the gravitational force on the i-th grasshopper; ${Aw}_{i}$ stands for the advection of wind; ${r}_{1}$, ${r}_{2}$, and ${r}_{3}$ represents random numbers between 0 and 1.

The ${So}_{i}$ is calculated using Eq. 11.

$$\begin{array}{c}S{o}_{i}=\sum _{\begin{array}{c}j=1\\ i\ne j\end{array}}^{n} sf\left({D}_{ij}\right)\widehat{{D}_{ij}}\end{array} \left(11\right)$$

Where $sf$ represents a mathematical expression used to calculate the power of social organizations, ${D}_{ij}$ stands for the distance value between the j-th and i-th grasshopper, and $\widehat{{D}_{ij}}$ represents a unity vector from the i-th to j-th grasshopper.

The $sf$ is calculated using Eq. 12.

$$sf\left(r\right)= {Ie}^{-r/In}- {e}^{-r} \left(12\right)$$

where I = the attraction intensity, r = a random number between 0 and 1, and ln = the preferred length scale.

The mathematical functions of ${Gr}_{i}$ and ${Aw}_{i}$ are expressed in Eq. 13 and Eq. 14, respectively.

$${Gr}_{i}= \widehat{{-ge}_{gr}} \left(13\right)$$

$${Aw}_{i}= \widehat{{de}_{w}} \left(14\right)$$

where g = the gravitational constant, $\widehat{{e}_{gr}}$= the unit vector toward the center of the earth, d = a constant value and $\widehat{{e}_{w}}$= the unit vector in the direction of the wind.

Therefore, ${Y}_{i}$ can be fully expressed using Eqs. 15 and 16.

$$\begin{array}{c}{Y}_{i}=\sum _{j=1}^{n} sf\left(\left|{Y}_{j}-{Y}_{i}\right|\right)\left(\left|{Y}_{j}-{Y}_{i}\right|/{D}_{ij}\right)-gr\widehat{{e}_{gr}}+d\widehat{{e}_{w}}\\ i\ne j\\ \end{array} \left(15\right)$$

$${Y}_{i}^{d}=cz*\left\{\sum _{j=1}^{n} cz\left(\frac{\left|u{l}_{d}-l{l}_{d}\right|}{2}\right)sf\left(\left|{Y}_{j}^{d}-{Y}_{i}^{d}\right|\right)\left(\frac{\left|{Y}_{j}-{Y}_{i}\right|}{{D}_{ij}}\right)\right\}+\widehat{{T}_{d}} \left(16\right)$$

where n = the number of grasshoppers, $l{l}_{d}$ and $u{l}_{d}$ are the lower and upper limits in the D-th dimension, $\widehat{{T}_{d}}$= the value of the target in the D-th dimension, and $cz$ = a coefficient which decreases the comfort zone proportional to the number of iterations.

The $cz$is computed using Eq. 17.

$$cz= {cz}_{max}-t*\frac{{cz}_{max}- {cz}_{min}}{{t}_{max}} \left(17\right)$$

where ${cz}_{max}$ = the upper limit value, ${cz}_{min}$ = the lower limit value, t = the current iteration, and ${t}_{max}$ = the maximum number of iterations.

2.5.2 BRT model

As the name implies, boosted regression tree (BRT) is a nonparametric data mining model composed of regression trees with node networks and boosting functions (Elith et al. 2008). BRT modeling is an important tool for determining the significance of individual variables as well as addressing grouping and forecasting issues (Aertsen et al. 2011). Instead of employing a single ideal prediction, BRT iteratively fits decision trees to enhance outcomes accuracy (Chen 2014). For LS modeling, BRT employs a random subset of the whole dataset of controlling factors and landslide data, with each iteration substituting the previously used subset. The stochastic method of randomly selecting subsets increases the model's predictive performance (Friedman 2002). After that, the subset is returned to the full dataset for the next iteration and successive trees. Aside from the dataset partitioning, the landslide inventory is partitioned probabilistically but without replacement relying on a ratio known as the bag fraction (Youssef et al. 2016). BRT is distinguished by its intrinsic boosting approach, in which each consecutive stepwise operation is utilized to scale previously used subsets for reuse (Pourghasemi et al. 2020; Lombardo et al. 2015; Elith et al. 2008). BRT has been confirmed as a reliable model for LS mapping in a number of studies (Pourghasemi et al. 2020; Park and Kim 2019).

In the BRT modeling, the divisor variable is initially utilized to split the target variable. The data is then divided into two groups in order to find the optimal divisor variable (Breiman 1998). The recursive aspect point segmentation divides each node into two and then separates these divided nodes. This distinction comes to an end when nodes become homogenous (Aertsen et al. 2011). The purpose of regression analysis in BRT modeling is to make a choice regarding the divisions. The tree method divides all of the data, which might result in overfitting if the divisions do not end (Therneau et al. 2014). BRT is calculated using Eq. 18.

$$F\left(X;{\left[{\beta }_{m}{\alpha }_{m}\right]}^{{m}_{0}}\right)=\sum _{m=0}^{m} {\beta }_{m}h\left(x;{\alpha }_{m}\right) \left(18\right)$$

2.5.3 ANN model

ANN is a commonly used machine learning approach that relies on human brain concepts. The capacity of ANN is derived from training and learning procedures that simulate nonlinear numerical model components. ANN has been confirmed as a reliable model for landslide susceptibility mapping by a number of studies (Tekin and Çan 2022; Daviran et al. 2022; Gorsevski et al. 2016; Arnone et al. 2013; Ermini et al. 2005). In the current work, landslide susceptibility (LS) maps were constructed by processing collected data with GIS, and then training the processed information with ANN. The steps employed for LS mapping was derived from Shahri et al. (2019).

An image is a digital depiction of reality that is portrayed as an mn matrix, M, with pixel information included in each member of the array (Shahri et al. 2019). A grid cell (pixel) may depict unique environmental variables crucial to evaluating landslide susceptibility, or it may be the product of mapping mistakes unrelated to landslide susceptibility. Thus, a landslide may be regarded as a spatial specificity with a disturbance of the stability state based on the causal factors in the form of a vector (Tsangaratos and Benardos 2014).

The physical environment of the ith grid cell of the region is produced using ${Cell}_{i}=\left[{a}^{\left\{i\right\}}, S \right]$, since the combination of the superimposed layers can reveal the relative landslide susceptibility of the grid cells. The causal variables ${a}^{\left\{i\right\}}= \left[{{a}_{1}}^{\left\{i\right\}} , {{a}_{2}}^{\left\{i\right\}} ,\dots , {{a}_{n}}^{\left\{i\right\}}\right]$ define the location, and S is a bivariate parameter derived from the superimposed layers that equals 0 in stable areas and 1 in unstable areas.

The predicted ${Cell}_{i}$ in the ANN indicates the expected degree of landslide hazard for each terrain pixel, and higher cell values represent more susceptibility.

In the ANN, the predicted, ${Cell}_{i}$ value reflects the estimated degree of landslide hazard for each terrain pixel, with larger cell values representing more susceptibility. The mathematical expressions of hidden (y_j), input (x_i), and output (Z_k) layers of the ANN are represented in Eqs. 19 and 20.

$${y}_{j}=f\left({X}_{j}\right)=f\left({w}_{oj}+\sum _{i=1}^{I} {w}_{ij}{x}_{i}\right) \left(19\right)$$

$$\begin{array}{c}{Z}_{k}=f\left({Y}_{k}\right)=f\left({w}_{ok}+\sum _{j=1}^{J} {w}_{jk}{y}_{j}\right)\stackrel{\text{ for layer }l\text{ in the }{t}^{th}\text{ iteration }}{\to }{y}_{j}^{\left(l\right)}\\ =\sum _{i=0}^{p} \left({y}_{i}^{(l-1)}\left(t\right){w}_{ji}^{l}\left(t\right)\right)\end{array} \left(20\right)$$

where, ${w}_{oj}$ and ${w}_{ok}$ = the bias weights for setting the threshold values. ${X}_{j}$ and ${Y}_{k}$ = temporary outcomes before utilizing the activation function, f, which should be employed in the output and hidden layers. The error (E) between the produced output (${d}_{k}$) and real values (${O}_{k}$) is calculated at the output level using Eq. 21.

$$E=\frac{1}{2}\sum _{k} {\left({d}_{k}-{O}_{k}\right)}^{2} \left(21\right)$$

The error between layers is then minimized by back-propagating E across the network and updating the weights.

$${w}_{ji}^{\left(l\right)}={w}_{ji}^{\left(l\right)}\left(t\right)+\alpha \left[{w}_{ji}^{\left(l\right)}\left(t\right)-{w}_{ji}^{\left(l\right)}\left(t-1\right)\right]+\eta {\delta }_{j}^{\left(l\right)}\left(t\right){O}_{i}^{\left(l-1\right)}\left(t\right) \left(22\right)$$

where, $\eta$ represents the learning rate parameter with a value between 0 and 1, ${\delta }_{j}$ denotes the rate of error change, and $\alpha$ represents the momentum parameter. To adjust the weight, the error between the input–hidden and hidden–output layers is derived by applying a gradient-descent strategy:

$$\frac{\partial E}{\partial {w}_{lj}}=\left[\sum _{k=1}^{k} \frac{\partial E}{\partial {Z}_{k}}\frac{\partial Z}{\partial {Y}_{k}}\frac{\partial {Y}_{k}}{\partial {y}_{j}}\right]\times \left(\frac{\partial {y}_{j}}{\partial {X}_{j}}\right)\times \left(\frac{\partial {X}_{j}}{\partial {w}_{lj}}\right)={f}^{{\prime }}\left({X}_{j}\right)\sum _{k=1}^{K} {\delta }_{k}{w}_{jk} \left(23\right)$$

$$\frac{\partial E}{\partial {w}_{jk}}=-E\frac{\partial F\left({Y}_{k}\right)}{{Y}_{k}}{y}_{j}=-{\delta }_{k}{y}_{j} \left(24\right)$$

The LS of each cell is then determined using n neurons in the hidden layers as described in Eq. 25.

$$\left.LS=f\left(\sum _{r=1}^{n} {w}_{\text{i}r}f\left(\sum _{j=1}^{m} {v}_{rj}{u}_{j}+{b}_{r}\right)\right)+{c}_{y}\right) \left(25\right)$$

Where, ${w}_{\text{i}r}$ and ${v}_{rj}$ represents adjusted weights, ${u}_{j}$ and y denotes m × 1 input and output vector layers, and ${b}_{r}$ and ${c}_{y}$ represents neuron biases in the hidden layers and output layer. For all neurons except those in the input layer, the biases may be viewed of as the constant weight, with value 1.

2.5.4 Elastic net model

The elastic net, which is based on the linear regression regularization method, has been frequently utilized for variable selection (Zou and Hastie 2005). Elastic net model is a lasso extension that can determine the best correlation between variables (Friedman et al. 2010). According to Zou and Hastie (2005), when variables were highly correlated, an elastic net and the lasso solution route were employed for high-dimensional data analysis and to avoid instability, respectively. The elastic net is essentially a mix of $\mathcal{l}1\text{ (}\text{ridge expression}\text{) }$penalties and $\mathcal{l}1\text{ (}\text{lasso}\text{) }$(Ogutu et al. 2012). The mathematical functions used for the computation of the elastic model are provided below.

l1 (lasso) and l1 (ridge expression) penalties (Ogutu et al. 2012).

$$\beta \left(\text{ enet }\right)=\left(1+\frac{{\lambda }_{2}}{n}\right)\left\{\beta \text{a}\text{r}\text{g}\text{m}\text{i}\text{n}\parallel y-X\beta {\parallel }_{2}^{2}+{\lambda }_{2}\parallel \beta {\parallel }_{2}^{2}+{\lambda }_{1}\parallel \beta {\parallel }_{1}\right\} \left(26\right)$$

The elastic net estimator is shown to be identical to the minimize of $\beta \left(\text{ enet }2\right)=\beta \text{a}\text{r}\text{g}\text{m}\text{i}\text{n}\parallel y-X\beta {\parallel }_{2}^{2}$, on the setting of $\alpha ={\lambda }_{2}/\left({\lambda }_{1}+{\lambda }_{2}\right)$.

Depending on,

$${\rho }_{\alpha }\left(\beta \right)=(1-\alpha )\parallel \beta {\parallel }_{1}+\alpha \parallel \beta {\parallel }_{2}^{2}\le \text{ sforsomes}\text{ (27)}$$

where ${\rho }_{\alpha }\left(\beta \right)$ = the elastic net penalty. When $\alpha =1$, the elastic net reduces to a simple ridge regression, and when $\alpha =0$, it simplifies to the lasso (Zou and Hastie 2005).

2.5.5 Validation of landslide models

The rationale of the LSMs produced using various models requires validation. The produced landslide vulnerability maps have no use or value in the absence of validation (Pradhan 2011). The various models were evaluated using AUROC (area under receiver operating characteristics) curve. The AUROC curve is a method for measuring predictive performance that is independent of thresholds. The model's predicted accuracy is shown by the AUROC. The frequency of values for predictions is how the AUROC is calculated (Yesilnacar and Topal 2005). Typically, AUROC values fall between 0.5 and 1. The model performs better when the AUROC value is closer to 1 (Pradhan and Kim 2014). Yesilnacar and Topal (2005) divided the AUROC values into five categories: low (0.5–0.6), moderate (0.6–0.7), good (0.7–0.8), very good (0.8–0.9), and outstanding (0.9–1). This method was used to build a curve using the testing and learning datasets, and then it was used to determine the model's accuracy and goodness of fit (Bui et al. 2012). When evaluating the prediction effectiveness of models using training and test datasets, focus on goodness of fit is preferred (Yin et al. 2006). In this study, the testing and training datasets were used to generate the AUROC curve. The sensitivity and specificity, also known as TPR (true positive rate) and false positive rate (FPR), are the two variables that make up the AUROC curve graphic (Oh and Lee 2010). The TPR displays the proportion of pixels correctly classified as landslide events, while the FPR displays the proportion of pixels incorrectly classified as landslide events (Corsini et al. 2009). The study’s TPR and FPR were calculated using Equations 28 and 29, respectively.

$$\text{T}\text{P}\text{R} = \frac{\text{T}\text{P}}{\text{T}\text{P} + \text{F}\text{N} }$$

$$\text{F}\text{P}\text{R} = \frac{\text{F}\text{P}}{\text{F}\text{P} + \text{T}\text{N}}$$

where, TN (representing true negative) and TP (representing true positive) are properly categorized pixel numbers, whereas FN (representing false negative) and FP (representing false positive) are erroneously categorized pixel numbers. The accuracy of models in foretelling whether or not landslides will occur is shown by the AUROC. Root mean square error (RMSE; Eq. 30) and Kappa validation techniques were also used in this research to test the validity and reliability of the spatial landslide prediction models. The RMSE is often used to checkmate the statistical errors observed in prediction models. The Kappa coefficients also provided insights for the evaluation of the models’ performances. The Kappa values were determined by comparing the classifications that were correctly classified to those that were predicted to be correctly classified (Avand et al. 2022; Allouche et al. 2006).

$$\text{R}\text{M}\text{S}\text{E}= \sqrt{\sum _{i=1}^{n}\frac{\left({X}_{measured value} - {X}_{predicted value}\right)}{n}}$$

where, n is the number of inputs.

3.1 Multicollinearity testing on the conditioning factors

A test for multicollinearity was run on all the landslide precondition variables. The linearity existing between the parameters, according to Chen et al. (2018), would reduce the predictive power of the models. The multicollinearity was tested using the tolerance and VIF. Values of tolerance and VIF < 0.1 and > 10 signify multicollinearity issues (Du et al. 2017). It is interesting to note that the threshold values for tolerance and VIF were discovered to be, respectively, > 0.1 and 10. (Table 3). To choose appropriate parameters for LSMs. Various landslide precondition elements, include the topographical/geomorphological factors (elevation, slope degree, slope aspect, TWI, PC, TPI, TRI, SA, and TST), the hydrological factors (rainfall and DtS), the geological factors (lithology), and the environmental factors (DtR, LU/LC, NDVI, and soil type) were chosen for the LSMs based on the various models utilizing the multicollinearity test. Because all of the landslide conditioning factors have Tolerance and VIF values that are lower than threshold values, the outcomes of this study's multicollinearity analysis listed in Table 3, reveal that the effective factors of landslides have no multicollinearity problem. The highest Tolerance value was shown on DtR (0.995), with the minimum value seen on lithology (0.344). On the other hand, the VIF value of lithology (2.907) was identified as the highest amongst the sixteen conditioning factors whereas the least VIF value was recorded on DtR (1.005) (Table 3). These results suggest that all the input predisposing factors were suitable for the production of the landslide maps based on the SVR-GOA, BRT, ANN, and elastic net models in Kalaleh basin.

Table 3

Result of multicollinearity analysis among landslide conditioning factors
Factor	Collinearity Statistics
Factor	VIF	Tolerance
Elevation	0.912	1.096
Aspect	0.943	1.060
Slope	0.740	1.351
Plan curvature (PC)	0.522	1.916
Topography position index (TPI)	0.705	1.418
Topography wetness index (TWI)	0.897	1.115
Surface area (SA)	0.369	2.710
Terrain ruggedness index (TRI)	0.444	2.252
NDVI	0.504	1.984
Rainfall	0.823	1.215
Distance to stream (DtS)	0.878	1.139
Distance to road (DtR)	0.995	1.005
Soil	0.436	2.294
Terrain surface texture (TST)	0.936	1.068
Lithology	0.344	2.907
LU/LC	0.779	1.284

3.2 Spatial distribution and effects of the landslide conditioning factors

Landslides are caused by a number of hydrological, geological, environmental, geomorphological, and topographical variables. Selecting pertinent factors is crucial in LSM because only a small number of parameters in a given area have a major impact on landslide events. Sixteen landslide predisposing factors were chosen in this study (Fig. 4). Random forest (RF) modeling was used to depict the mutual links between landslide sites and conditioning factors, with the management of landslide mitigation as the study’s goal. The RF-based pixel-based investigation is more precise and suitable for landslide susceptibility mapping. As shown in Table 4, it is indicated that the geology (lithology), slope degree, rainfall, TPI, TWI, SA, and LU/LC are the most influential conditioning factors of landslide in the Kalaleh basin.

Table 4

Relative influence of landslide conditioning factors in the LSM based on RF
Factor	Weight
Elevation	3.9
Aspect	3.6
Slope	17.9
Plan curvature (PC)	0.3
Topography position index (TPI)	8.9
Topography wetness index (TWI)	7.9
Surface area (SA)	6.1
Terrain ruggedness index (TRI)	1.3
NDVI	2.8
Rainfall	11.3
Distance to stream (DtS)	4.9
Distance to road (DtR)	4.2
Soil	0.7
Terrain surface texture (TST)	3.8
Lithology	19.3
LU/LC	5.5

The topographical/geomorphological factors adopted in this study were classified using the Jenk’s natural break method and the results of the factors are spatially distributed as presented in Fig. 4. Elevation ranged from 60–2348 m (Fig. 4a), slope aspect ranged from − 1–359.7 (Fig. 4b), slope degree ranged between 0° and 73.1° (Fig. 4c), PC was found between − 72.7 and 93 (Fig. 4d), and TPI ranged from 5.4–6.9 (Fig. 4e). Further, other topographical/geomorphological factors such as TWI, SA, TRI, and TST were found to range from 12–22.5 (Fig. 4f), 900–3013 (Fig. 4g), 0–62.1 (Fig. 4h), and 0.05–67.6 (Fig. 4n), respectively, across the study area. The lithology (representing the geology) was categorized into various classes (as shown in Fig. 4o) in line with the geologic units presented in Table 1. The hydrological factors, which include rainfall and DtS, are found to range from 236–1005 mm (Fig. 4j) and 0–1800 m (Fig. 4k), respectively. The NDVI, DtR, soil type, and LU/LC were also classified spatially into various groups. The NDVI sublayers, classed using the Jenk’s natural break method, were found to range from − 0.18 to 0.68 (Fig. 4i). The DtR in the study area ranged between 0–12,472 m (Fig. 4l). The different soil types in the area are altisols, inceptisols, mollisols, and entisols (Fig. 4m). The different types of LU/LC characterizing in the in Kalaleh basin are forest, agriculture, dry farming, orchard, water bodies, rock bodies, agriculture-orchard, and urbanized areas (Fig. 4p). It is worthy to mention that the lithology, soil type, and LU/LC are regarded as categorical conditioning parameters.

When preparing LSM, topographic variables have significant importance (Rahmati et al. 2016). There is a direct correlation between elevation and the likelihood of landslides. The different zones of susceptibility have been shown by the sub-classes of the elevation dataset. In most places, precipitation or rainfall is the main reason landslides occur. Due to soil loosening, quicker rate of sediment transmission, and increased surface runoff velocity, prolonged periods of heavy precipitation have a direct impact on landslides. It is projected that areas in the research region with the most rainfall will be most susceptible. When it comes to the slope, steeply sloping parts are more prone to landslides than gently sloping areas (Nwazelibe et al. 2023). The study's classes with the highest likelihood of landslides occurring are those with slopes greater than 30°. One of the elements that affects the likelihood of landslides is the TPI. The TPI sublayers were greater than 2 and thus suggesting that they indicate high landslide susceptibility. However, lower TPI values could have indicated lesser susceptibility to landslide occurrences.

The relationship between road distance and landslide locations may point to areas with extremely high landslide risks. In this area, landslides commonly happen near roadways (Fig. 3). With higher distance from nearby roadways, the DtR subclasses > 1000 m show a decreased link to landslide occurrence. In terms of the distance to streams, being close to a stream has a significant influence on the likelihood of landslides. A result of the streams' rapidity and discharge, the shortest distance from one (DtS) directly affects the likelihood of landslides. In other words, the closer soil or rock slopes are to streams, the higher their susceptibility to slides. In contrast, a higher DtS has no direct influence on landslide occurrences. The DtS sublayers > 200 m would have low implications on the landslide susceptibility. The SA often directly affects the susceptibility of landslide. Maximum surface area exposure can create a favourable situation for landslides. The SA subclasses obtained in this study indicate high possibility of landslide event and disaster.

Geologically, the research area is dominated by sedimentary formations that are often more susceptible to slides than hard rocks. The most vulnerable, brittle, and soft soils in the area have the largest risk of landslides when it comes to the soil type factor. Thus, compared to entisols and mollisols, alfisols and inceptisols have a larger impact on the occurrence of landslides. Landslides are also significantly influenced by LU/LC. Eight LU/LC classes in total were found. According to field observations and Fig. 4p, most of the landslides in the region happen in urbanized, agricultural-orchard, and mountain rock sectors. In the agricultural areas, dry farming areas, and forested areas, very few are seen. While great concentrations of landslides may characterize a low vegetation area, which is more prone to the occurrence of landslides and erosion, a high vegetation density can minimize the landslide risk and also delay the soil transmission and erosion (Nwazelibe 2023).

3.3 Landslide susceptibility models and their implementation

The dependent parameters were written as binary variables in this study of landslide susceptibility. Using the R programming application, the categorical and numerical values of the landslide conditioning elements were retrieved in order to build the final landslide maps based on the four computational ML models. The 4 LSM models are presented in Fig. 5. The results, as given in Fig. 5, which show that the landslide susceptibility of the area can be classified into five, such as very low susceptibility, low susceptibility, moderate susceptibility, high susceptibility, and very high susceptibility zones. A closer look at the maps produced using the four models suggest that the area is predominantly characterized by moderate to very high landslide susceptible zones. Generally, across the area, the southern, central, and northern portions are more characterized by high and very high susceptibility zones (Fig. 5). The eastern and western portions of the study area, on the other hand, are characterized by very low, low, and moderate susceptibility zones (Fig. 5). However, it was also noticed that the elastic net and SVR-GOA models look much alike (Figs. 5a and 5c) while some spatial similarities were noticed between the BRT and ANN models (Figs. 5b and 5d).

Furthermore, the results obtained from this study indicate that the portions that are faced with moderate, high and very high hazard risks are greater than the portions known for very low and low hazard risks (Fig. 5). This is quite critical for the area and the inhabitants. The specific percentages of areal coverage of each susceptibility class in the different models have been broken down in Fig. 6. The ANN LSM covered about 27.69%, 25.46%, 18.71%, 15.72%, and 12.42% of very low, low, moderate, high, and very high landslide susceptibility zones in the Kalaleh basin, respectively. The ANN model demonstrates the predominance of combined very low and low susceptibility zones over the combinations of the moderate, high, and very high susceptibility zones (Fig. 6). The LSM result based on the SVR-GOA model indicate that 19.30% and 18.49% of the area are, respectively, characterized by high and very high susceptibilities whereas 20.28%, 21.31%, and 20.62% of the study area have moderate, low, and very low susceptibilities. The SVR-GOA identified that there the portions of the area known for moderate, high and very high risks predominated.

The BRT LSM was also classified into the 5 classes of very high, high, moderate, low, and very low hazard zones. About 26.67% of the total landmass of the study area has very low landslide susceptibility, 26.48% has low risk, 19.00% has medium risk, 15.49% has high risk, and 12.36% has very high susceptibility. The combinations of the susceptibility zones seem to agree more with that of the ANN model (Fig. 6). Lastly, the elastic net model agrees more with the SVR-GOA. Based on the elastic net model, it is indicated that 20.23%, 20.03%, and 14.59% of the Kalaleh basin are, respectively, characterized by moderate, high, and very high hazard susceptibilities whereas 20.09% and 20.05% of the basin have low and very low landslide susceptibilities (Fig. 6).

3.4 Validation and comparison of the models’ performances

The success and reliability of the landslide models were tested using prediction AUROC curves (Fig. 7), which were obtained using the testing and training landslide datasets. Also, Kappa and RMSE values were used for the model validation (Fig. 8). For the training datasets, the AUROC values were 0.992 (99.2%), 0.901 (90.1%), 0.900 (90.0%), and 0.757 (75.7%) for the SVR-GOA, ANN, BRT, and elastic net models, respectively. This reveals that the SVR-GOA learnt better and performed better than the other models in the order: SVR-GOA > ANN > BRT > elastic net. The same performance trend was obtained in the training according to the Kappa and RMSE values (Figs. 8). Interestingly, the same performance trend was also seen in the testing stage. However, the AUROC and Kappa values decreased while RMSE values increased for the testing datasets. The AUROC values for the model testing were 0.930 (93.0%), 0.833 (83.3%), 0.822 (82.2%), and 0.726 (72.6%) for the SVR-GOA, ANN, BRT, and elastic net landslide models, respectively. Comparing the training and testing performances of the models, the Kappa values dropped from 0.945 to 0.872, 0.812 to 0.790, 0.804 to 0.783, and 0.698 to 0.672 for the SVR-GOA, ANN, BRT, and elastic net, respectively. Meanwhile, the RMSE increased from 0.280, 0.320, 0.330, and 0.410 in the training to 0.300, 0.350, 0.370, and 0.430 in the testing for the SVR-GOA, ANN, BRT, and elastic net landslide models, respectively.

The outcomes of the validations obtained in this study also indicated that strong relationships exist between the reality and the currently identified landslide sites and the machine learning model-predicted landslide locations. Although discrepancies have been noticed in the performances of the models, it is interesting to also note that the novel SVR-GOA, which has now been tested in landslide mapping, performed much better with the lowest modeling errors than the ANN, BRT, and elastic net models. This implies that the LSM model by SVR-GOA promises to match more with the reality in the Kalaleh basin than other models. However, it is realized that ANN, BRT, and elastic net models performed well too, as their AUROC and Kappa values for the training and testing datasets were much above the benchmark value of 0.500 for model acceptability. Moreover, their RMSE values in training and testing stages were found to be much lower than 1, indicating high model acceptability. Thus, as recognized in this study, all the four models performed well but the novel SVR-GOA was exceptionally excellent in producing a more accurate landslide mapping. Nevertheless, the agreement or correlation between the landslide models is significant. It is also pertinent to note that the variations noticed in the performances of the four models could be attributed to the structural variations in their algorithmic makeup.

3.5 Performance of the present SVR-GOA ensemble and previous studies

Numerous studies have used ensemble models to do spatial modeling (Ruidas et al. 2022). Due to its excellent predicted accuracy and capacity for working with huge, less expensive datasets, ML or AI algorithms have recently gained a lot of attention, especially for analyzing environmental dangers (Fu et al. 2020; Band et al. 2020). Based on the proper conditioning elements in a certain area, all of these strategies have produced the best outcomes. Even if LSM approaches have undergone significant progress, new developments are surely needed to boost performance. The SVR-GOA ensemble has been recently utilized in the modeling of flood susceptibility in the Qazvin Plain, Iran (Panahi et al. 2021) and in the Gandheswari River basin, India (Ruidas et al. 2022). However, we are not aware of any study that implemented this ensemble in LSM. Hence, its application in this study is considered novel.

The comparison of the results of this study with those on flooding is necessary. As several factors influence flooding, so are several factors affecting landslide occurrence. Moreover, some of the factors are the same for both geohazards. Validation of the developed models was attained by using three statistical techniques – AUROC, Kappa value, and RMSE. In this comparison, reference will only be made to AUROC of the studies. The study conducted by Panahi et al. (2021) utilized SVR-GOA and reported a validation AUROC value of 0.959 (95.9%). Also, the study by Ruidas et al. (2022) implemented SVR-GOA and obtained a validation AUROC = 0.938 (93.8%). However, the AUROC value for the validation of the SVR-GOA ensemble in this study is 0.930 (93.0%). These show high predictive performance of the SVR-GOA as a modeling technique. Also, this study has demonstrated a high-level consistency, in terms of performance, with the previous modeling studies that have applied the SVR-GOA ensemble model. The SVR-GOA ensemble exhibits a very little variation in the testing and training stages compared to the three other models (ANN, BRT, and elastic net), according to all of the adopted validation methods. This, additionally, suggests that Due to the combination of several models, overfitting issues can be greatly overcome. This validated SVR-GOA ensemble model created in this work fits the LSM of the Kalaleh basin, hence it is a good fit.

3.6 Implications of the present prediction modeling

The results of this study indicate that all of the conditioning elements are significant factors influencing the landslide risk of the different areas in the Kalaleh basin. As a result, priority areas with high landslide hazards must be carefully taken into account for prompt and efficient soil management and conservation. The results and insights from the present investigation have shown that the applied SVR-GOA ensemble was effective alongside the ANN, BRT, and elastic net models. Therefore, we suggest that the design of this study can be applied effectively in other settings and regions of the world. The following are possible practical implications of this study.

The use of multiple data-driven models in this study convincingly minimized the bias that could arise from the implementation of standalone SVR-GOA model. Accordingly, the problem of overfitting has been eliminated. Thus, the SVR-GOA can be applied with these other models elsewhere or can also be integrated with other types of data-driven algorithms.
The performance of the SVR-GOA could be due to lesser computational time required to implement it. The validated SVR-GOA ensemble required less computation time and had lower error. The other standard models, on the other hand, seemed to require more memory, a large dataset, and more processing time in order to enhance their performances. In a similar way, standard statistical methods need a lot of effort, vast datasets, and additional input factors that are inappropriate for areas with low data. In contrast to the other three models, the SVR-GOA method demonstrated more accuracy with the provided datasets.
The application of SVR-GOA ensemble in LSM would certainly advance landslide research on regional, national, and global scales. As have been cited earlier, there are no previous literatures on the application of SVR–GOA algorithm in LSM. This algorithm showed good performance in this case study, as can be observed. As a result, it is highly good at predicting landslide susceptibility. This research paper's content provides baseline data on SVR-GOA landslide mapping, which may be highly helpful in future studies in many parts of the world.
The SVR-GOA ensemble could improve the Kalaleh basin's pixel detection of vulnerable spots that require rapid reclamation and upkeep as well as the prioritization of landslide risk. This study identified the local characteristics that affect the likelihood of landslides. When the proper area-specific conditioning factors and model input variables are taken into account, the innovative method suggested in our study can effectively estimate landslide susceptibility in various basins.
Other natural hazards can potentially be modelled to the SVR-GOA ensemble model to increase accuracy.

By identifying the regions that are most vulnerable, landslide susceptibility modeling enhances the feasibility of landslide mitigation techniques. The present work constructed four models and combined the robust ML (SVR) model with the metaheuristic GOA to predict landslide susceptibility with greater accuracy. The study's findings supported the effectiveness of the models suggested for spatial landslide vulnerability prediction in Kalaleh basin, northeastern Golestan Province, Iran. Previous landslide analyses had not looked into the efficacy of SVR-GOA ensemble. All of the models created in this study performed well, with the SVR-GOA model performing best. The SVR-GOA model performed better in both training and testing phases than the other standalone (ANN, BRT, and elastic net) models implemented in this study. The SVR-GOA ensemble can automatically manage the complexity in LSM and has high generalization capabilities. The ANN, BRT, and elastic net models for landslide susceptibility modeling were used to validate its results. This study revealed that the SVR-GOA learnt better and performed better than the other models in the order: SVR-GOA > ANN > BRT > elastic net. The same performance trend was obtained in the training according to the Kappa and RMSE values. Interestingly, the same performance trend was also seen in the testing stage. A close-range of performance was seen with previous studies that have implemented the SVR-GOA in flood susceptibility studies, indicating that the SVR-GOA ensemble is a high-performance predictive modeling technique. Furthermore, this research indicated that the geology (lithology), slope degree, rainfall, TPI, TWI, SA, and LU/LC are the most influential conditioning factors of landslide in the Kalaleh basin. The maps produced using the four models suggest that the study area is predominantly characterized by moderate to very high landslide susceptible zones, with varied percentages of coverage. Generally, across the area, the southern, central, and northern portions are characterized by high and very high susceptibility zones. The eastern and western portions of the study area, on the other hand, are characterized by very low, low, and moderate susceptibility zones. The results of this study could give decision-makers important information to help them create more thorough land use policies and management plans for ecological and soil restoration in the Kalaleh basin.

Funding: The authors did not receive support from any organization for the submitted work.

Author Contributions: Conceptualization, A.A., Q.Z..; methodology, A.A., Q.Z.; software, A.A.; validation, A.A. and Q.Z.; formal analysis, A.A.; investigation, A.A. and Q.Z.; resources, A.A. and M.S.; data curation, A.A.; writing—original draft preparation, Q.Z., A.A., M.S., J.C.E., and J.C.A.; writing—review and editing, Q.Z., A.A., M.S., J.C.E., and J.C.A. All authors have read and agreed to the published version of the manuscript.

Availability of Data and Materials: The data used in this research are available by the corresponding author upon reasonable request.

Ethics Approval: The authors confirm that this article is original research and has not been published or presented previously in any journal or conference in any language (in whole or in part).

Consent to Participate and Consent to Publish: Not applicable.

Competing Interests: The authors have no conflict of interest.

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Editorial decision: Major Revision
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Integrated assessment of landslide susceptibility in the Kalaleh Basin, Golestan Province, Iran using novel SVR-GOA ensemble validated with BRT, ANN, and elastic net models

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Abstract

Figures

1 Introduction

2 Materials And Methods

2.1 Brief description of the study area

2.2 Landslide inventories

2.3 Landslide conditioning factors

2.4 Testing the multicollinearity of the conditioning factors

2.5 Applied modeling techniques

2.5.1 SVR-GOA ensemble

2.5.2 BRT model

2.5.3 ANN model

2.5.4 Elastic net model

2.5.5 Validation of landslide models

3 Results And Discussion

3.1 Multicollinearity testing on the conditioning factors

3.2 Spatial distribution and effects of the landslide conditioning factors

3.3 Landslide susceptibility models and their implementation

3.4 Validation and comparison of the models’ performances

3.5 Performance of the present SVR-GOA ensemble and previous studies

3.6 Implications of the present prediction modeling

4 Conclusions

Declarations

References

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