Uncertainties of landslide susceptibility prediction: Influences of random errors in landslide conditioning factors and errors reduction by low pass filter method

Fming Hung ,Zuokui Tng ,Chi Yo,* ,Shui-Hu Jing ,Filippo Ctni ,Wi Chn ,Jinsong Hung

a School of Infrastructure Engineering,Nanchang University,Nanchang,330031,China

b State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,Chengdu University of Technology,Chengdu,610059,China

c Department of Geosciences,University of Padova,Padova,Italy

d College of Geology and Environment,Xi’an University of Science and Technology,Xi’an,710054,China

e Discipline of Civil,Surveying and Conditioning Engineering,Priority Research Centre for Geotechnical Science and Engineering,University of Newcastle,Newcastle,NSW,Australia

Keywords: Landslide susceptibility prediction Conditioning factor errors Low-pass filter method Machine learning models Interpretability analysis

ABSTRACT In the existing landslide susceptibility prediction (LSP) models,the influences of random errors in landslide conditioning factors on LSP are not considered,instead the original conditioning factors are directly taken as the model inputs,which brings uncertainties to LSP results.This study aims to reveal the influence rules of the different proportional random errors in conditioning factors on the LSP uncertainties,and further explore a method which can effectively reduce the random errors in conditioning factors.The original conditioning factors are firstly used to construct original factors-based LSP models,and then different random errors of 5%,10%,15% and 20% are added to these original factors for constructing relevant errors-based LSP models.Secondly,low-pass filter-based LSP models are constructed by eliminating the random errors using low-pass filter method.Thirdly,the Ruijin County of China with 370 landslides and 16 conditioning factors are used as study case.Three typical machine learning models,i.e.multilayer perceptron (MLP),support vector machine (SVM) and random forest (RF),are selected as LSP models.Finally,the LSP uncertainties are discussed and results show that:(1)The low-pass filter can effectively reduce the random errors in conditioning factors to decrease the LSP uncertainties.(2) With the proportions of random errors increasing from 5% to 20%,the LSP uncertainty increases continuously.(3) The original factors-based models are feasible for LSP in the absence of more accurate conditioning factors.(4) The influence degrees of two uncertainty issues,machine learning models and different proportions of random errors,on the LSP modeling are large and basically the same.(5) The Shapley values effectively explain the internal mechanism of machine learning model predicting landslide susceptibility.In conclusion,greater proportion of random errors in conditioning factors results in higher LSP uncertainty,and low-pass filter can effectively reduce these random errors.

1.Introduction

Landslides seriously endanger people’s life and property safety worldwide (Ko and Lo,2018).The accurate and reliable landslide susceptibility prediction (LSP) modeling is in urgent need to effectively predict the spatial probability distribution of landslide occurrence.The LSP modeling is also the focus of regional landslide risk assessment and prevention at present(Huang et al.,2023a).

In the LSP modeling,the known landslides and related conditioning factors in the region are taken as input variables,to predict the possible spatial probability of landslides in future.The LSP modeling process includes: (1) obtaining the landslide inventory and conditioning factors in the study area;(2) establishing the nonlinear correlations between the landslides and conditioning factors;(3) determining the input variables of the LSP models;(4)dividing the training and testing datasets of LSP models;and (5)evaluating the LSP results(Wang et al.,2014;Li et al.,2017).In the LSP modeling processes,the uncertainties generated by errors in the data sources,such as the conditioning factors,landslide inventory and other spatial datasets,will interfere with the LSP results.Specially,the errors in the original conditioning factors including the terrain,hydrology,land cover and remote sensing data are inevitable for the data sources,due to the limitations in mapping technologies,spatial resolution of conditioning factors,parameters uncertainty of spatial analysis in GIS and professional cognitive level.These errors directly affect the accuracies of model input and output variables,and they are considered to be one of the most important reasons for the reduction of LSP performance(Panahi et al.,2020).

Accurate landslide conditioning factors are the premise for reasonable LSP modeling (Chang et al.,2023a).In most relevant literature,the obtained original conditioning factors are generally assumed to be determined values which are directly used for LSP modeling,while ignoring the different proportions of errors existed(Bunn et al.,2020).Unfortunately,these errors in fact restrict the practicability and reliability of LSP results in engineering(Van Den Eeckhaut et al.,2012).In an effort to solve this problem,this study intends to analyze the error sources of conditioning factors,discuss the influence of the random errors on the LSP modeling,and further explore reliable methods to reduce the errors existed in the original conditioning factors.

For various types of continuous conditioning factors,such as digital elevation model data,remote sensing images(rock types can be regarded as discrete factors),the errors in these data can be classified as systematic errors and random errors (Moayedi et al.,2018).The systematic errors are caused by unavoidable factors such as instrumentation or manual labor in the process of managing the original factors (Yang et al.,2023).By contrast,the random errors are influenced by the earth’s magnetic field,topography,vegetation characteristics,weather,etc.(Yang et al.,2016;Zhang et al.,2021).In this study,we plan to add different proportional random errors into the original conditioning factors,so as to reveal the influences of the random errors on the uncertainty of LSP modeling.In general,the systematic errors can be reduced by calibrating the instrument accuracy and adjusting the mapping data.On the other hand,the low-pass filter,wavelet analysis and Kalman filter methods are often used to estimate the random errors and reduce their influences on various prediction models (Zhang et al.,2006;Jiang et al.,2023;Wang et al.,2023).Among them,the low-pass filter method is adopted in this study to smooth the original continuous conditioning factors because it can filter out the random errors of spatial images which are often regarded as high-frequency random signals (Lakomy et al.,2022).Furthermore,the low-pass filter method can improve the texture and contrast of the image and reduce the distortion of the spectral information of the fused image.The low-pass filter method can also eliminate extreme values in the data,making the data more stable.As a result,this method has been well applied for the processing of various types of spatial image data (Gao and Xu,2012;Yang et al.,2015;Sofwan et al.,2018).We believe that,the original conditioning factor data will be smoother after being preprocessed by the low-pass filter method,which will reduce the random errors in the input variables of LSP model and help to improve the LSP performance.Hence,the low-pass filter method is adopted in this study,and then comparative experiments by integrating the original data,5%-20% error data and low-pass filtered data are conducted to validate the use of low-pass filter in reducing the LSP uncertainty caused by the random errors in conditioning factors.

When discussing the influence of random errors in the conditioning factors on LSP uncertainty,how to choose an appropriate LSP model is also a essential issue.At present,many machine learning models have been successfully used for LSP modeling,including the multi-layer perceptron (MLP) (Luo et al.,2019),logistic regression,random forest(RF)(Huang et al.,2023b),support vector machine (SVM) (Chang et al.,2023b),and deep learning models.These machine learning models can predict the landslide susceptibility indices (LSIs) accurately in a large area with limit landslide samples(Merghadi et al.,2020).However,there is still no unified conclusion on which machine learning model can achieve a better LSP performance,and thus the common idea of avoiding the uncertainties caused by different models is to compare the LSP accuracies of various models (Dou et al.,2019).In this study,the MLP,SVM and RF are selected to avoid the LSP uncertainties caused by different models,because these models have the advantages of easy to implement with fast training speed,efficient application to large-scale datasets and high ability of nonlinear fitting(Huang and Zhao,2018;Fh et al.,2021;He et al.,2021a).

From the LSP modeling process,both the uncertainty issues of random errors in the conditioning factors and selection of machine learning models have influences on the LSP results.Researchers have explored the uncertainty characteristics of LSP modeling under a given uncertainty issue (Qin et al.,2013;Jacobs et al.,2020).However,there are few studies on exploring the influence degrees of various uncertainty issues on LSP modeling,i.e.the sensitivities of uncertainty issues (Ilia and Tsangaratos,2016;Segoni et al.,2020).Therefore,in this study,the “average correlation coefficient method” is proposed to calculate the correlation coefficients between the uncertainty issues and the LSP accuracies according to the dumb variables and correlation analysis,so as to quantify the sensitivity of each uncertainty issue to LSP modeling(Steger et al.,2016).

Although machine learning model is essential for LSP modeling,lack of modeling interpretability leads to questionable engineering applications.Many engineers think that the machine learning model is just like “black box operation”.After giving an input into the machine learning model,a decision result such as landslides susceptibility and hazard index will be fed back (Roscher et al.,2020).However,it cannot know exactly the physical mechanism and decision basis behind its distinguishing landslide susceptibility characteristics,in addition to the reliability of the decision(Murdoch et al.,2019).The lack of interpretability may pose serious threats to practical projects,especially the machine learning-based engineering applications for landslide risk diagnosis.Therefore,this problem has become one of the main obstacles to the effective application of machine learning in engineering practices such as regional LSP modeling (Zhou et al.,2022).

To sum up,the original factors,low-pass filter,5%-20% errorsbased MLP,SVM and RF models are constructed in this study,to explore the LSP uncertainties under different random errors in conditioning factors and various machine learning models.At last,the area under receiver operating characteristic curve (AUC),distribution characteristics of LSIs,interpretability of machine learning,etc.are respectively adopted to quantitatively analyze the LSP uncertainties (Shirzadi et al.,2019).

2.Methodology

2.1.LSP modeling processes

The LSP modeling processes include the following five steps as shown in Fig.1.Firstly,the landslide inventory and related conditioning factors in the study area are obtained through remote sensing and ArcGIS 10.2 software,and then the nonlinear correlations between the landslides and conditioning factors are established by the frequency ratio method.Secondly,these original continuous conditioning factors are processed by the low-pass filter,and some random errors are also added to these original factors,respectively.These simulation processes are carried out independently for five times,and the average values of the five simulation results are finally taken to avoid the uncertainty generated when random error are added to the continuous conditioning factors.Then,the frequency ratios of conditioning factors under low-pass filter and different proportional random errors are calculated.Thirdly,these calculated frequency ratios are taken as the input variables of MLP,SVM and RF models with LSIs as output.Fourthly,machine learning models based on the original factors,low-pass filter and 5%,10%,15%,20% random errors are established for LSP modeling.Finally,the influences of random errors on the uncertainty of LSP modeling are discussed by several uncertainty analysis methods,and the relative contributions of conditioning factors under the same machine learning model or the same random errors condition are discussed(Wang et al.,2014;Samia et al.,2018).In the LSP,relevant conditioning factors such as terrain and landforms,land cover,hydrological and lithology are mainly obtained through remote sensing images and the ArcGIS platform.This paper employs ArcGIS 10.2 software for spatial analysis and data management.The original data,which refers to data that have not been subjected to any other processing,serve as the input variables for the original-based model in machine learning.The low-pass filter data are obtained by applying low-pass filter using the ArcGIS 10.2 software.Similarly,the low-pass filter-based model is created by inputting the filtered data into the machine learning model.

Fig.1.Processes of LSP modeling.

2.2.Methods of adding random errors to conditioning factors

In this study,the random errors are added to original continuous conditioning factors using theRV.Uniformfunction in SPSS 25 software,and four proportions are set to 5%,10%,15% and 20%,respectively(Qin et al.,2013).TheRV.Uniformfunction is written as

whereSis the original conditioning factor,is the conditioning factor after adding random errors,andnis the proportion of adding random errors.Generally,the random errors in the discrete conditioning factors are ignored,and only the random errors in the continuous conditioning factors,such as elevation and slope,are considered.Therefore,in the present work,it is only necessary to add random errors to the continuous conditioning factors.Then the frequency ratio values of original conditioning factors and conditioning factors with different proportional random errors are calculated as the input variables of machine learning models.Taking the elevation factor as an example,the elevation maps under different treatment measures are shown in Fig.2.

Fig.2.Three types of elevations: (a) Original elevation,(b) Elevation with low pass filter,and (c) Elevation added with 20% random errors.

2.3.Low-pass filter method

The filter method is generally used to improve the image quality through the means of elimination of high-frequency noise and interference,image edge enhancement,linear enhancement and deblurring (Xiong et al.,2017).Based on operation difference for functionality,the filter methods can be classified as low-pass filter with smoothing functionality and high-pass filter with sharpening functionality.In this study,the low-pass filter is used to smooth the original continuous conditioning factors and reduce its importance of abnormal values.The low-pass filter is calculated as

whereais the filtering coefficient,X（n）is the sampling value,Y（n-1）is the output variable of the last filter,andY（n）is the output variable of this filtering.By comparing the LSP results of original factors and low-pass filter-based machine learning models,the feasibility of the low-pass filter for reducing the random errors in conditioning factors is verified,and the possibility of low-pass filter method for improving the LSP accuracy is further explored (Rabus and Pichierri,2018).

2.4.Frequency ratio method

The frequency ratio method is widely used in the process of LSP modeling (Luo et al.,2019;Chen et al.,2020).Continuous conditioning factors can be divided into different intervals through natural break method,equal interval,geometric interval and other methods.Then the corresponding frequency ratios of different intervals of conditioning factors are calculated(Huang et al.,2020).If the frequency ratio value is greater than 1,it indicates that the subinterval corresponding to this conditioning factor is more conducive to the landslide evolution;if the frequency ratio value is less than 1,it means that this subinterval is not conducive to the landslide evolution,which are expressed as

whereFRis the frequency ratio value,Nijis the area of landslide occurring in classjinterval of theiconditioning factor,Aijis the number of grid units occupied by the classjinterval of theiconditioning factor,Nris the total area of the landslide area in the study area,andAris the total grid unit in the study area.

2.5.Machine learning models

Numerous studies have demonstrated that the MLP,SVM and RF models can effectively predict landslide susceptibility and achieve high accuracies (Chang et al.,2023b).This paper uses three different machine learning models with the aim of exploring the impact of conditioning factor errors on LSP results under multiple machine learning models,in order to obtain more widely applicable results.The modeling results based on the MLP,SVM and RF models show that the impact of conditioning factor errors on LSP results is consistent,which proves the rationality of the research results.

2.5.1.Multi-layer perceptron

MLP model is a type of neural network that includes input,hidden and output layers.It is useful for solving nonlinear problems and has high stability and modeling efficiency.The weight and deviation values can be adjusted to change the relationship between the input and output (Wang et al.,2020).By training and testing the weight values of neuronal connections,the MLP can form a stable network structure with decision-making ability.During the modeling process,the weight values between the input and hidden layers are randomly initialized.The activation function in the hidden layer is used to adjust the weight values and minimize the error between the output and expected values.The connection weight is updated iteratively using the error back propagation method to obtain a result with minimum error.

2.5.2.Support vector machine

SVM is a type of generalized linear classifier for binary classification of data according to supervised learning.Its decision boundary is the maximum margin hyperplane for solving learning samples,which can transform the problem into a convex quadratic programming problem (Moosavi and Niazi,2016).SVM provide a clearer and more powerful way to learn complex nonlinear equations.Specifically,it is to find the optimal classification hyperplane of two types of samples in the original space in the case of linear scalability.When linearity is not separable,relaxation variables are added and the samples in the low-dimensional input space are mapped to the high-dimensional space by using nonlinear mapping to make it linearly separable.In this way,the optimal classification hyperplane can be found in the feature space.

2.5.3.Random forest model

RF is a classification model made up of multiple decision trees.Each decision tree votes to select the best classification for a given independent variableX.To create the model,the original training set is sampled using bagging,with each sample having the same number of features as the initial training set(Di Traglia et al.,2018).A decision tree is built usingKsamples,resulting inKdifferent classification results.In each sampling,a featuren(n≤m) is randomly selected,and the best feature expansion node is selected.Whenn＜m,there are differences among decision trees (Youssef et al.,2016).The final classification is determined by voting among theKspecies.RF synthesizes the results of various trees to avoid discontinuity of predicted values,prevent overfitting,and improve model stability.

2.6.Uncertainty analysis methods

In the present study,the frequency ratios calculated under different conditions are taken as the input variables of machine learning models.After carrying out the LSP modeling,the AUC accuracy assessment,distribution characteristics of LSIs,significance of difference,relative contributions of conditioning factors and sensitivity assessment are calculated to quantitatively analyze the uncertainty characteristics of LSP modeling.Meanwhile,the relative contributions of conditioning factors under different proportions of random errors are calculated,and the measures to reduce the errors in conditioning factors are further discussed(Kamran et al.,2023).

2.6.1.LSP results assessed by AUC values

The AUC value is equal to the probability that the ranking of randomly selected positive samples is higher than that of randomly selected negative samples.The AUC value is between 0 and 1,and the closer to 1,the higher the accuracy of LSP by this model is,and vice versa(Chen et al.,2020).The calculation formula is expressed as

wheren0represents the number of negative samples,n1represents the number of positive samples,andrirepresents the position order of theinegative sample in the whole test sample.

2.6.2.Distribution characteristics of LSIs

The mean value and standard deviation can be used to reflect the average level and dispersion degree of LSIs,thus they can be used to compare the LSP uncertainties under original factors-,lowpass filter-and/or random errors-based machine learning models(Chang et al.,2023a).

2.6.3.Difference significance of LSIs under different conditions

The Wilcoxon signed rank test and the Kendall consistency coefficient test are commonly used to study the significance of differences,by comparing the comparative distribution and quantitative correlation of LSIs,which provides reliable support for the analysis of LSP modeling uncertainty.The significance levelais the probability value of the test statistic falling in an extreme area when the null hypothesis is true.Usually,a=0.05 ora=0.01,indicating a 95% or 99% probability that the decision to accept the null hypothesis is correct (Sahin et al.,2020).

2.6.4.Interpretability of machine learning by Shapley method

The predicted value of a single sample can be interpreted by calculating its Shapley value(Zhou et al.,2022).The interpretation principle of Shapley method can be summarized as follows: the predicted value of a specific sample minus the contribution value of all features of the sample to the prediction is equal to the average predicted value of the data set.The Shapley value of each feature(conditioning factor) in the grid and the average predicted value(baseline value) of the dataset are calculated using a sample grid.The Shapley value can be calculated as

whereSis a subset of the features used in the model,x is the vector of feature values of instance to be explained,pthe number of features,and val（S）is the prediction for feature values in setSmarginalized over features that are not included in setS.

2.6.5.Relative contributions of conditioning factors

The contribution of conditioning factors in LSP modeling is determined by multiple factors,including the characteristics of conditioning factors themselves,combination mode of conditioning factors,machine learning model types and different scale of the study area,which lead to great uncertainty in the relative contribution of the conditioning factors(Pourghasemi et al.,2020;Wang et al.,2021).In this study,the“weighted mean method”is proposed to determine the relative contributions of conditioning factors.The basic steps are as follows: (1) Obtain the conditioning factors and construct the spatial data set,and then establish the machine learning model to LSP under each condition;(2) Compare the contribution of conditioning factors under different proportional random errors in the same machine learning model;(3) Compare the changes in the contribution of conditioning factors after lowpass filter in different machine learning models;(4) Assign weight on each conditioning factor according to the AUC accuracy of the model,and the higher the accuracy is,the greater the corresponding weight value will be.The final relative contributions can be calculated by multiplying the weight values by the standardized contribution of each factor and summing them up together.The final relative contribution is calculated by

wherefiis the contribution of a conditioning factor,wiis the weight ratio of the accuracy of LSP,andWiis the contribution of a weighted factor.

2.6.6.Sensitivity assessment of different uncertainty issues

The sensitivity assessment is used to characterize the influence degree of different uncertainty issues on LSP modeling.Each uncertainty issue can be represented by discrete data variables,and there is a one-to-one correspondence between a certain value of uncertainty issue and its LSP modeling performance.Therefore,“dumb variable” can be used to represent a certain value of uncertainty issue.Then,the Pearson correlation coefficient is used to calculate the correlation between the uncertainty issue and the LSP accuracy (Chen et al.,2018),with the range of [-1,1].After calculating an average value for the absolute values of correlation coefficients under all dumb variable conditions of a given uncertainty issue,the average value can reflect the sensitivity of this uncertainty issue to LSP accuracy.The larger average value of the correlation coefficient indicates that the LSP results are more sensitive to this factor,i.e.the sensitivity of this uncertainty issue is higher,otherwise the sensitivity is smaller.

3.Study area and materials

3.1.Brief introduction to Ruijin County

Ruijin County in Jiangxi Province of China is located between 115°42′-116°22′E and 25°30′-26°20′N.This county covers an area of 2441.40 km2,of which the built-up area covers an area of 29.3 km2and the forest coverage rate is about 75.6%.This region is located in the transitional zone between the climate zone of central China and southern China,and it belongs to the humid subtropical monsoon climate.The average annual temperature is 18.9°C.The average annual rainfall is 1710 mm,and the average annual rainfall days are 163.7 days.Ruijin County is located in the Nanling complex structural belt,where fold structures and fault structures are developed,and its territory is dominated by the low mountains,magmatic,metamorphic,clastic and carbonate rocks.The northern mountainous area is a dense area of rivers and also an area where landslides occur frequently.

The main data sources of this study include: (1) landslide data investigated by Ruijin Natural Resources Department;(2) 30 m resolution DEM data,used to extract topography and hydrological factors (Freely downloaded from http://www.91weitu.com);(3)Extract geological information by using 1:100,000 scale geological map mapped by Jiangxi Geological Survey;(4) a single scene of Landsat TM8 remote sensing image with a resolution of 15 m,used to extract land cover factors (http://glovis.usgs.gov/).

3.2.Landslide inventory

The main geological disasters in Ruijin County include landslide,collapse,debris flow and ground subsidence.According to the information provided by the Bureau of Land and Resources,as of July 2014,there have been 414 disasters in Ruijin County,370 of which are landslides (Fig.3).These landslides are mainly in small scale,with a total of 369 landslides ranging from 125 m2to 7300 m2.There is only one medium landslide,with an area of about 7300 m2,and the landslide body is mainly composed of Quaternary silty clay interspersed fragments.The thickness of the landslide body is about 1-4 m,and the movement mode is mainly downward sliding of the slope body.Since disasters occur in populated areas of villages and towns and are induced by heavy rainfall,slope cutting,slope erosion and weathering,they are easy to cause major disaster accidents,which restricts the local economic development and threatens the safety of people’s life and property(Gong et al.,2021).

Fig.3.Landslide distribution in Ruijin County.

3.3.Landslide conditioning factors

The occurrence of landslides is the result of the combined action of conditioning factors of the slope itself and external inducing factors.The attributes of the slope itself include landform,land cover,hydrology and lithology,while the external inducing factors include earthquake,heavy rainfall et al.,Generally,in the LSP modeling,only the conditioning factors of the slope itself are considered and the external inducing factors are not considered(Chen et al.,2020).According to the formation conditions of landslides in the study area and related literature,16 conditioning factors are selected in the present study,including:(1)terrain factors(elevation,aspect,slope,plan curvature,profile curvature and relief amplitude);(2) land cover factors (normalized difference building index(NDBI),normalized difference vegetation index(NDVI),total radiation index and population density index);(3) hydrological factors (modified normalized difference water index (MNDWI),topographic wetness index (TWI),annual rainfall and distance to river);and (4) lithology (rock types and fault density) (Dou et al.,2019;Huang et al.,2021a;Chang et al.,2023c).Each continuous conditioning factor is divided into 8 subsections by natural break method.The original conditioning factors,the conditioning factors after low-pass filter,and those added by 5%-20% random errors are classified into 6 building conditions.Then the part of corresponding frequency ratio of each sub-interval is calculated,as shown in Table 1,so as to analyze the influence degrees of different attribute intervals of conditioning factors under each condition on landslide evolution.

Table 1Frequency ratio values of part of conditioning factors under various conditions.

3.3.1.Terrain factors

From the digital elevation model data,the terrain factors can be extracted,including elevation,aspect,slope,plan curvature,profile curvature and relief amplitude.Elevation reflects the influence of the difference in the distribution of rock and soil mass,water system and vegetation on the landslide evolution.As shown in Table 1,the frequency ratio of elevation is greater than 1 in the range of 129-308 m under various conditions,indicating that the elevation in a lower range is more conducive to the landslide evolution.Different aspect and slopes are exposed to different intensities of sunlight,and the inclination angle and stability of slope are also different,-1 represents the plane,which indicates that the difference in frequency ratio value between different aspect is small,while the middle and low slope intervals are more suitable for landslide evolution.The plan and profile curvatures reflect the complexity of the terrain from different angles.Meanwhile,the relief amplitude reflects the variation of the surface elevation in the study area (Samia et al.,2018).

3.3.2.Land cover factors

Land cover factors include NDVI,NDBI,total radiation index and population density index.The NDVI is used to reflect the vegetation coverage rate.According to Table 1,the frequency ratio of the NDVI is high at the range of 0.56-0.79.Combining the landslides distribution in the study area,relatively low vegetation coverage is beneficial to the occurrence of landslide.In addition,The NDBI reflects the degree of human engineering activities,of which the frequency ratio presents a normal distribution,indicating that relatively low or high building indices are not conducive to the landslide evolution(Hua et al.,2021).Total radiation index refers to the sum of direct solar radiation and sky radiation received by the horizontal surface,which affects the surface vegetation coverage and soil moisture.Population density index reflects the aggregation of population and affects the probability of landslide through human engineering activities.

3.3.3.Hydrological and lithology factors

The evolution of landslide is highly affected by river and groundwater erosion,and the closer to the river,the higher the soil water content and the worse the relative slope stability(Tong et al.,2023).Hydrological factors include MNDWI,TWI,annual rainfall and distance to river.It can be seen from the landslides distribution in the study area(Fig.3) and their distances to river(Fig.4n) that,the areas with dense rivers and surrounding reservoirs are the areas with high frequency of landslides,while the farther away from the river,the lower the frequency of landslides.Under all the six conditions,the frequency ratio of the distance to river less than 150 m is the highest,and with the increase of the distance to river,its frequency ratio decreases gradually.

Fig.4.Landslide conditioning factors:(a)Elevation,(b)Aspect,(c)Slope,(d)Plan curvature,(e)Profile curvature,(f)Relief amplitude,(g)NDVI,(h)NDBI,(i)Total radiation index,(j)Population density index,(k) MNDWI,(l) TWI,(m) Annual rainfall,(n) Distance to river,(o) Rock types,and (p) Fault density.

Lithology factors include rock types and fault density.The lithology is an important factor affecting the occurrence of landslides in the areas of physical and mechanical properties of rock and soil and accumulation body,making lithology an important factor in the occurrence of landslides (Yang et al.,2023).The rock type distribution in the study area mainly includes metamorphic rock,magmatic rock,clastic rock and carbonate (Fig.4o).It can be seen from Fig.1 that the relatively low rock and soil strength of carbonate is conducive to slope stability and has a great influence on the landslide evolution,with frequency ratio greater than 1.On the contrary,the magmatic rock has the least influence on the landslide evolution (Wu et al.,2023).

4.LSP modeling under random errors-and low-pass filterbased factors

4.1.Preparation of spatial datasets

In this study,the grid unit with 30 m resolution is used as landslide prediction unit.The frequency ratios calculated under 16 conditioning factors with different proportional random errors and low-pass filter and other conditions are re-assigned to each conditioning factor as the input variables of the machine learning models.Three hundred and seventy landslides in Ruijin County are divided into 5482 gird units(assigned to 1),and the same number of non-landslide grid units (assigned to 0) are randomly selected from non-landslide area.The landslide and non-landslide grid units are combined into a spatial dataset.70% and 30% grid units of this spatial dataset are used for model training and testing,respectively.Then the LSIs of 2,750,691 grid units in the whole area are predicted by these machine learning models.The Ruijin County are divided into five susceptibility levels,i.e.very high,high,medium,low and very low using the natural break method.

4.2.LSP using MLP model under various conditions

In this study,the MLP model is established in SPSS 25 software for LSP,and the optimal solution is obtained by adjusting the relevant parameters using the cross-validation method(Chen et al.,2020).Through this method,the optimal parameters of original factors,low-pass filter and 5% errors-based MLP models are obtained.Results show that the learning rate,momentum and iteration time are 0.01,0.25 and 500,respectively,the hiding layer is two layers and the activation function is hyperbolic tangent.Moreover,the optimal parameters setting of learning rate,momentum,iteration time,number of hidden layer and the activation function under 10%,15% and 20% errors-based MLP models are 0.015,0.3,600,1 and hyperbolic tangent,respectively.Actually,the parameters of MLP models under different conditions do not change significantly,thus those under a typical condition are listed here.

After completing the training and testing of the original factors and low-pass filter-based MLP model using the above parameters,the LSP modeling in Ruijin County is performed and the results are shown in Fig.5.It can be seen from Fig.5 that,very high and highsusceptible areas are mainly distributed in the densely fluvial areas in the northwest of the study area,and in the mountain areas with higher elevation and slope in the southeast.Meanwhile,the moderately susceptible areas are distributed in the relatively flat terrain area on the east and west sides of the main urban area,while the very low and low susceptible areas are distributed in the areas with dense buildings and relatively high vegetation coverage.

Fig.5.LSP under different conditions: (a)Original factors-based MLP,(b)Low-pass filter-based MLP,(c)5% errors-based MLP,(d)10% errors-based MLP,(e)15% errors-based MLP,and (f) 20% errors-based MLP models.

Fig.6.LSP under different conditions:(a)Original factors-based SVM,(b)Low-pass filter-based SVM,(c)5% errors-based SVM,(d)10% errors-based SVM,(e)15% errors-based SVM,and (f) 20% errors-based SVM models.

4.3.LSP using SVM model under various conditions

Various SVM models are established by importing the training and testing data into SPSS Modeler 18 software,under the conditions of original factors,low-pass filter and different proportional random errors.After cross validation method,the parameters of original factors and low-pass filter-based SVM models are determined asC0=8,ε=0.1 and γ=0.6,respectively;the parameters of 5% and 10% errors-based SVM models areC0=8,ε=0.2 and γ=0.5,respectively.Meanwhile,the parameters of 15% and 20% errorsbased SVM models areC0=9,ε=0.1 and γ=0.6,respectively.The patterns of susceptibility maps predicted by SVM models are similar to those predicted by the MLP and RF models,and the distribution range of high and low susceptibility areas is also close to each other.

4.4.LSP using RF model under various conditions

The function library inRStudio software is used to build RF model,and the bag-outside errors of different random forests are calculated by the cyclic iteration.Generally,the smaller the bagoutside errors are,the higher the LSP accuracy will be (He et al.,2021b).The optimal feature numbers of original factors-,lowpass filter-,5% errors-,10% errors-,15% errors-and 20% errorsbased RF models are 4,4,3,3,5 and 5,respectively;and the corresponding numbers of decision trees of random forest are 500,500,500,500,600 and 600,respectively,by the cross-validation method.Finally,the frequency ratios of conditioning factors calculated under these six conditions are taken as the model input variables to train and test the RF models,and then the predicted LSIs of the whole study area are output.The same as in the MLP model,we find that the parameters of RF models under different conditions do not change much,thus only the parameters under a typical condition are listed here.

After completing the training and testing of the original factors and low-pass filter-based RF models,the LSP modeling of Ruijin County is carried out and the results are shown in Fig.7.It can be seen from Fig.7 that,the general rule of landslide susceptibility map produced by the RF model is similar to the MLP model and SVM model,but the proportion of each susceptible area is different.In addition,it can be seen that the proportion of very high and high susceptible areas in RF model is less than that in the MLP model and SVM model,while the proportions of very low and low susceptible areas are relatively larger.

Fig.7.LSP under different conditions:(a)Original factors-based RF,(b)Low-pass filter-based RF,(c)5% errors-based RF,(d)10% errors-based RF,(e)15% errors-based RF,and(f)20% errors-based RF models.

4.5.Analysis of the difference between the results

Figs.5-7 show the results obtained by three different machine learning models.Due to the different nonlinear fitting capabilities and sample training methods of the three models,although they generally present similar patterns,there are significant differences in the results presented in the landslide susceptibility map.Specifically,RF shows a clear transition from extremely high to extremely low susceptibility,resulting in a more reasonable distribution of the landslide susceptibility map.SVM shows less transition,but high and extremely high susceptibility areas are more distinct.This is because RF effectively reduces the risk of overfitting by averaging decision trees,resulting in more stable landslide susceptibility prediction results.The distribution characteristics of the landslide susceptibility index are different for RF and MLP,with the highest number of extremely low susceptibility areas and the fewest extremely high susceptibility areas.However,SVM shows a sudden increase in the number of extremely high susceptibility areas,which is due to the fact that SVM uses a fixed penalty coefficientC,but the losses caused by errors in positive and negative samples are different.The three machine learning models have different ROC accuracies,with RF having the highest accuracy,followed by SVM and MLP.

5.Uncertainties of LSP results under different modeling conditions

5.1.Comparative analysis of AUC accuracy

In the above analysis,original factors,low-pass filter and different proportional random errors-based MLP,SVM and RF models are used for LSP.Here,the AUC values are used as an index to evaluate the LSP accuracies of these models.The results are shown in Fig.8,and it can be seen that the AUC values under the original factors-based MLP,SVM and RF models are 0.833,0.838 and 0.902,respectively.Correspondingly,the landslide sample data processed by low pass filter have been improved in the LSP,with the AUC values of 0.839,0.844 and 0.931,respectively.However,the AUC values of all of them decrease gradually along with the increase of the added random errors.The overall results show that the MLP,SVM and RF models have good prediction accuracy in the LSP modeling,and the overall prediction ability of RF model is better than those of MLP and SVM models.

Fig.8.AUC values under different LSP modeling conditions.

5.2.Distribution pattern in LSIs under different conditions

The mean value and the standard deviation are proposed to measure LSP uncertainties under different conditions.In the same machine learning model,the smaller the mean value,the greater the standard deviation,indicating that more grid units of the study area can be predicted with smaller LSIs.Taking the MLP model for example,the distribution characteristics of LSIs are shown in Fig.9.The mean values of the predicted LSIs from large to small are as follow: 20% errors ＞15% errors ＞10% errors ＞5% errors ＞original factors ＞low-pass filter.The mean value of the LSIs under the six conditions is distributed in the middle and low susceptibility levels,while it is less distributed in the very high susceptibility levels.In addition,the standard deviation values of the LSIs are in the opposite order to the mean values.We found that the higher the AUC value is,the smaller the mean value is and the larger the standard deviation is.These results indicate that the LSIs have a good differentiation under the low-pass filter-based models,which can better reflect the differences of the LSIs in different grid units and has a lower uncertainty.

Fig.9.Distribution characteristics of LSIs using MLP model under different proportional random errors.

Fig.10.Distribution characteristics of LSIs using SVM model under different proportional random errors.

Fig.11.Distribution characteristics of LSIs using RF model under different proportional random errors.

The LSP results of various MLP,SVM and RF models(Figs.10 and 11)show that,the AUC values decrease continuously along with the increase of added random errors.However,the AUC value after low-pass filter is improved significantly.By comparing the average level and dispersion degree of the LSIs among the above three models,it is also shown that smoothing the original factors can reduce the uncertainty of the LSP and improve the accuracy.

5.3.Statistical differences under different conditions

Kendall cooperative coefficient correlation test method is used to conduct non-parametric test on the LSIs,in order to compare the significance of difference of the LSP results under the original factors,low-pass filter and different proportional random errorsbased MLP,SVM and RF models.The significance level and the confidence interval are set to 0.01 and 99%,respectively.If the significance level of the test results is smaller than 0.01,it means that the LSP results under different models are significantly different.The comparison results of three models show that the significance of LSIs under different proportional random errors is close to 0,indicating that the difference is significant.Therefore,it is necessary to make a comparative analysis between the LSIs of different proportional random errors and the original factors.

5.4.Interpretability analysis of RF model for LSP modeling

In this section,the Shapley’s interpretation of a typical sample,the Shapley’s analysis of conditioning factors and the contributions of various conditioning factors are explored and discussed.

5.4.1.Shapley’s interpretation of a typical sample

A grid unit with susceptibility index of 0.963 calculated by RF model is selected as a sample,to interpret the internal mathematical relationship between this calculated LSI and the related 16 conditioning factors.The Shapley values are calculated and the decision graph of conditioning factors is shown in Fig.12.The arrows in Fig.12 show the effect of each factor on the prediction of LSI with the blue arrow representing a negative influence and the red arrow representing a positive influence.For the individual conditioning factor shown in Fig.12,it is found that distance to river have the largest positive contribution on susceptibility index with a Shapley value of 0.16,followed by the elevation with a Shapley value of 0.12,and so forth.On the contrary,the aspect has the largest negative contribution to the predicted LSI with a Shapley value of-0.02,followed by the annual rainfall with a Shapley value of-0.02.The seven other factors with a Shapley value of 0.02.Next,the sum of these calculated Shapley values of all 16 conditioning factors is considered as the difference between the LSI of this sample and the average of all LSIs,i.e.the basic value of the study area,which is calculated to be 0.46.Finally,the sum of final Shapley value and the basic value can be considered as the final LSI of this sample,which is 0.963.

Fig.12.Decision graph of a typical sample.

5.4.2.Shapley’s analysis of conditioning factors

Shapley value is used to represent the importance of features and evaluate the feature behaviors of samples.The Shapley values of 16 conditioning factors in all samples are calculated and plotted in Fig.13.In Fig.13,each row represents a conditioning factor,and each point means a Shapley value of a sample (grid unit).The red and blue points of these samples respectively mean large and small frequency ratios of this conditioning factor,and the abscissa represents Shapley values.It can be seen from Fig.13 that except for profile curvature,the Shapley values of most conditioning factors increase along with the increase of frequency ratios,i.e.the landslide probability increases.This result is consistent with the prior knowledge and the definition of frequency ratio.Through the independent analysis of profile curvature,it is found that after the frequency ratio values of profile curvature significantly change,its Shapley values vary within a small range,indicating that the frequency ratio of profile curvature has little influence on LSP modeling.In this condition,the feature of profile curvature is not considered for prediction,as its importance is not high.

Fig.13.Shapley value of all sample features.

5.4.3.Contributions of conditioning factors under different proportional errors-based models

The discussions in Sections 5.1-5.3 show that,there present different LSP results under different proportional errors-based machine learning models.Similarly,the relative contributions of conditioning factors,i.e.the effect degrees of different conditioning factors on LSP results,under different proportional errors-based MLP,SVM and RF models varies significantly as well.

For the contributions of conditioning factors with different proportional errors-based MLP models shown in Table 2,we can find that with the increase of the error proportional of conditioning factors,the relative contributions of rock type,slope and aspect factors in MLP model change significantly.Among them,the contribution of rock type factor becomes much larger,and its contribution has been exaggerated.By contrast,the contributions of slope and aspect are greatly reduced,especially the slope which can be almost ignored.Therefore,different proportional random errors in conditioning factors have an important negative influence on MLP modeling.The contributions of other conditioning factors have also changed,with a less extent and a certain randomness,which is closely related to the principle of random determination of initial weights of neural networks in the MLP model.Meanwhile,the factor contributions of the SVM model and MLP model under different proportional errors show similar rules in general,as shown in Table 2.

Table 2Relative contributions of part of typical factors under different proportional errors-based models.

For the contributions of conditioning factors of different proportional errors-based RF models in Table 2,their relative contributions change somewhat with the increase of the error proportion,but their change range is far smaller than the errorsbased MLP and SVM models.This is because the RF model has a higher tolerance for random errors in conditioning factors.As a result,the relative weights of its conditioning factors still change little in the case of 5%-15% errors added to the conditioning factors,and only when the errors proportion in the conditioning factors reaches 20% can the contributions show a greater fluctuation rule on LSP.In addition,the results of relative contributions of conditioning factors calculated by MLP and SVM models are relatively consistent.While results calculated by the RF model are significantly different from those by the MLP and SVM models,indicating that the modeling rules of the RF differ from those of the MLP and SVM models.

It can be seen from the discussions in Sections 5.1-5.3 and the factor contributions analysis in the present section that,there is a great difference between the RF model and the MLP,SVM models.In general,the LSP accuracy of the RF model is better than the other two models,which is in consistence with the finding in various literature(Dou et al.,2019;Chen et al.,2020;Merghadi et al.,2020;Sun et al.,2020).This is because,firstly,the RF is a model integrating the prediction results of multiple decision trees,and the final output is the average value of the majority of classification or regression problems (Youssef et al.,2016).Secondly,the RF model can reduce the high variance of flexible model such as decision tree and conventional artificial neural network,and the RF model can remember the training test data set and overcome the error interference.In a word,the RF model has a clear and easy explained structure,and it has relatively low requirements on data quality without the appearance of serious over-fitting (Krka? et al.,2017).

5.4.4.Contributions of conditioning factors under low-pass filterbased machine learning

The effects of low-pass filter method on the relative contributions of the original conditioning factors are further discussed,as shown in Table 3.Results of MLP model show that,the contributions of rock type and slope factors processed by the low-pass filter show a slight increase,while those of the factors such as NDVI have few changes.Results of SVM model show that,the contributions of slope and aspect decrease greatly after low-pass filter,while those of distance to river are amplified.Meanwhile,the results of RF model show that,the low-pass filter has relatively few influences on the contributions of original conditioning factors,and the change of the contribution of each factor remains in a stable and reasonable range.Also,we can find that the low-pass filter method not only reduces the errors in the original factors and improves the LSP accuracy,but also maintains the stability of the contributions of conditioning factors on the whole.Hence,the relative contributions of conditioning factors calculated by the low-pass filter-based machine learning models are more accurate and more reliable than the other models.Finally,the contributions of conditioning factors to LSP in Ruijin County are calculated by the mean values of factors contributions calculated by the low-pass filter-based MLP,SVM and RF models (Table 3),indicating that the main control conditioning factors of this study area are distance to river,rock type,slope,etc.

Table 3Relative contributions of part of typical conditioning factors under different machine learning models.

5.5.Sensitivity assessment of uncertain factors

In this section,“dumb variable”(Table 4)is used to represent the results calculated under different machine learning models and different proportional random errors.Then,the correlation coefficients between the variables of different machine learning,proportional random errors and the corresponding LSP accuracies are calculated.A mean value is calculated by the absolute values of these correlation coefficients for a given uncertainty issue,and the mean value can reflect the sensitivity of uncertainty issues.That is,the average correlation coefficient is proportional to the sensitivity of uncertainty issues.

Table 4Correlation coefficients between uncertainty issues and AUC accuracies.

The correlation coefficients between AUC values and MLP,SVM and RF models are respectively-0.236,-0.256 and 0.493,with absolute average value of 0.328.Meanwhile,the correlation coefficients between AUC values and original factors,factors filtered by low pass,factors with 5% errors,factors with 10% errors,factors with 15% errors and factors with 20% errors are respectively 0.4,0.527,-0.018,-0.056,-0.379 and-0.474,with absolute average value of 0.309.Hence,we can find that both uncertainty issues have significant influences on LSP,however,the influences of different machine learning models are greater than those of different proportional random errors in conditioning factors.

6.Discussion

6.1.Comprehensive discussion of LSP results

The uncertainties existed in the LSP modeling are analyzed through adding different proportional random errors to the original conditioning factors,as well as reducing random errors in the original conditioning factors by low-pass filter method.Results in Sections 5.1-5.4 show that,the LSP accuracy is reduced and the uncertainty is gradually increased with the increase of proportional random errors added.The low-pass filter-based MLP,SVM and RF models can produce more accurate LSP results than the original conditioning (Qin et al.,2013).After adding random errors,the associated frequency ratio values of landslide original conditioning factors will change,and there is no significant variation rule for the frequency ratio with different attribute intervals.However,combined with the LSP results and the comprehensive analysis of the LSIs,it is found that the LSIs of a certain grid unit after adding proportional random errors may not conform to the actual landslide evolutions.With the increase of the proportion of adding random errors,the LSIs deviates more from the real landslide inventory information in the study area,and the AUC value decreases continuously (Li et al.,2017).

It is not easy to acquire satisfied conditioning factors with enough quality.At present,these factors are mainly extracted through remote sensing images and related investigation maps.The main factors affecting the quality of landslide conditioning factors are as follows: (1) the spatial resolutions of basic topographic maps and remote sensing images;(2) the complexity of topography and geology in the study area,as well as the status of conditioning factors surrounding the landslide;(3) the interpretation methods of remote sensing images,professional quality and research depth of interpreters.In general,the quality of conditioning factors mainly depends on whether the selected basic geology images and remote sensing image interpretation methods and the professional level of practitioners are appropriate for the local geographical conditions (Samodra et al.,2017;Ghiasi et al.,2021).In addition,one weakness of this study is that although the LSP modeling results are repeated five times when adding random errors into conditioning factors,the LSP modeling times are still not enough,which induces that the randomness and contingency still exist.Next,the errors of the landslide spatial locations and the hidden landslide data in the study area are not considered,meaning that the hidden landslide data might be introduced into the non-landslide samples.These errors will also bring some uncertainties to the LSP modeling(Fell et al.,2008;Wang et al.,2014).

6.2.Advantages of low-pass filter compared to other methods

In this study,the LSP results of low-pass filter-based RF model are superior to those of original factors based-RF model.For example,the distribution of the landslide susceptibility indices predicted by the low-pass filter-based RF model is more reasonable and smooth than that of other models,with the AUC accuracy,mean value and standard deviation reaching 0.931,0.264 and 0.255,respectively.The same LSP patterns are also observed in the SVM and MLP models.Additionally,some literature has found that errors in conditioning factors have a serious impact on LSP modeling,and a few tools and methods have also been developed to solve this uncertainty issue(Zhao and Chen,2023).For example,Qin et al.(2013)chose to focus on the most important conditioning factors for error analysis and used Monte Carlo simulation of DEM errors to analyze the uncertainties in LSP modeling.Similarly,Saleem et al.(2019) improved the accuracy and resolution of DEM to reduce the errors in terrain factors,which is also an effective idea for reliable LSP modeling.Chang et al.(2016) employed the certainty factors method to optimize the selection and combination of conditioning factors,where positive certainty factor values were specifically chosen to minimize the LSP uncertainty associated with conditioning factors.Huang et al.(2022)investigated the errors and suitability of discrete linear conditioning factors on LSP,suggesting that continuous density factors are more feasible than discrete linear factors with more explicit physical significance.

The comparisons between this study and other related literature suggest that,this study presents remarkable advantages: (1) A more comprehensive and thorough simulation of random errors in continuous conditioning factors involved in this LSP modeling process;(2)An innovative exploration of low-pass filter method to reduce the LSP uncertainties caused by random errors in conditioning factor;(3)The systematical use of various models,i.e.MLP,SVM and RF,to mitigate the impacts of different types of machine learning models on the LSP uncertainties (Ma et al.,2023);(4)Machine learning interpretability is introduced to avoid the uncertainties effect on the reliability of these LSP results caused by the“black box operation”of traditional machine learning models in LSP modeling (Roscher et al.,2020).To sum up,the low-pass filterbased RF model constructed in this study is superior to original factors based-and errors based-RF for LSP.In theory,the low-pass filter method minimizes the impact of random errors on the accurate distribution of conditioning factors,making the conditioning factors more statistical significance and improving the smoothness of spatial data distribution (Yang et al.,2015).This successful application of low-pass filter method offers a valuable reference for further optimizing other uncertainty issues in LSP modeling.

6.3.Measures to improve the quality of conditioning factors

High-resolution visible and thermal infrared images,space borne interferometric radar measurements,laser radar and airborne laser altimetry can be adopted to improve the landslides identification and monitoring (Li et al.,2019).These advanced remote sensing interpretation methods can be combined with local geological field survey data to improve the landslide inventory information (Del Ventisette et al.,2014).Moreover,the manual mapping can be introduced to improve the professional level of interpreters according to the GIS spatial analysis,and then the obtained landslide inventory can be comprehensively verified to further improve the LSP accuracy (Zhong et al.,2019).

In terms of GIS spatial data layer generation,different methods are adopted to draw the landslide boundary,conditioning factors,and some other spatial data,which usually lead to unpredictable errors.For example,in the process of MapGIS data conversion to ArcGIS format,500 points of automatic interruption is preprocessed in MapGIS 6.7 software and then the topology relationship is rebuilt in ArcGIS 10.2 software after conversion.In order to promote the reliability analysis of practical engineering problems,some scholars put forward the inverse FORM method (Ji et al.,2019),and then combined with GIS to further form the GIS-form landslide prediction toolbox,which can quickly map the regional landslide caused by earthquake (Ji et al.,2022).

It is necessary to increase the types of original conditioning factors.At present,the conditioning factors used for LSP can be mainly divided into four categories,i.e.the landform,surface cover,lithology and hydrological environment (Youssef et al.,2016).In fact,it can be considered to increase other data sources such as gully density,road density,and surface roughness.Through numerical simulation of the complete process of failure of rock slopes,the rules of crack propagation can be understood,thus increasing the data source (Yang et al.,2020).The influence weights of conditioning factor errors on the LSP modeling can be reduced by adding data sources (Liu et al.,2016;Long et al.,2023).

Most of data sources used for LSP are mainly grid units with 30 m resolution.Perhaps improving the spatial resolution of original conditioning factors to 15 m or even 8 m can improve the accuracy of LSP modeling.Existed studies show that improving the spatial resolution of data source is beneficial to improve the ability of LSP (Mahalingam and Olsen,2015;Bueechi et al.,2019).

The classification method and number of the attribute interval of conditioning factors should be appropriately adjusted.On this basis,the connection method between the landslides and their conditioning factors should be improved,as the errors between landslides and conditioning factors can be finally reflected in the connection values,such as frequency ratio values (Huang et al.,2021b).The present studies show that appropriately increasing the classification number of the attribute interval of conditioning factors,as well as choosing the weight of evidence method or index of entropy as the connection method,can effectively reduce the influences of the errors in conditioning factors on the LSP uncertainties(Razavizadeh et al.,2017).

7.Conclusions

In this paper,different proportional random errors are added to the original conditioning factors.Meanwhile,the low-pass filter is also adopted to smooth the original conditioning factors.Hence,the original factors-,low pass filter-,as well as 5%-20% errors-based MLP,SVM and RF models are built to reveal the uncertainties that the errors in conditioning factors affect the LSP modeling.Some valuable conclusions are drawn as follows:

(1) The uncertainties of LSP modeling increase continuously with the proportions of random errors in conditioning factors increasing from 5% to 20%,indicating that the LSP modeling is negatively affected by the increasing random errors.

(2) The low-pass filter-based machine learning models have significantly higher accuracy and lower uncertainties than those of the original factors-based and different proportional random errors-based machine learning models,suggesting that the low-pass filter can effectively reduce the random errors in conditioning factors.

(3) Generally,the LSP results of original factors-based and errors-based machine learning models both reflect the spatial distribution of landslide susceptibility correctly,indicating that the original factors-based LSP models are feasible as a whole and the random errors of landslide conditioning factors are within acceptable range.

(4) The sensitivity assessment results show that,the influence degrees of both uncertainty issues of different machine learning models and different proportional random errors in conditioning factors on the LSP modeling are significant.Furthermore,the machine learning models have slightly higher sensitivity than that of different proportional random errors.

(5) The Shapley values efficiently reflect the mechanism of machine learning model built for LSP.The contributions of rock type,distance to river and other factors are moderately increased by low-pass filter method.However,these contributions are abnormally amplified with the increase of random errors in conditioning factors.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is funded by the National Natural Science Foundation of China (Grant Nos.42377164 and 52079062),and the National Science Fund for Distinguished Young Scholars of China(Grant No.52222905).