Comparing predictive capability of statistical and deterministic methods for landslide susceptibility mapping: a case study in the northern Apennines (Reggio Emilia Province, Italy)

Statistical and deterministic methods are widely used in geographic information system based landslide susceptibility mapping. This paper compares the predictive capability of three different models, namely the Weight of Evidence, the Fuzzy Logic and SHALSTAB, for producing shallow earth slide susceptibility maps, to be included as informative layers in land use planning at a local level. The test site is an area of about 450 km² in the northern Apennines of Italy where, in April 2004, rainfall combined with snowmelt triggered hundreds of shallow earth slides that damaged roads and other infrastructure. An inventory of the landslides triggered by the event was obtained from interpretation of aerial photos dating back to May 2004. The pre-existence of mapped landslides was then checked using earlier aerial photo coverage. All the predictive models were run on the same set of geo-environmental causal factors: soil type, soil thickness, land cover, possibility of deep drainage through the bedrock, slope angle, and upslope contributing area. Model performance was assessed using a threshold-independent approach (the ROC plot). Results show that global accuracy is as high as 0.77 for both statistical models, while it is only 0.56 for SHALSTAB. Besides the limited quality of input data over large areas, the relatively poorer performance of the deterministic model maybe also due to the simplified assumptions behind the hydrological component (steady-state slope parallel flow), which can be considered unsuitable for describing the hydrologic behavior of clay slopes, that are widespread in the study area.     

Use of GIS-based fuzzy logic relations and its cross application to produce landslide susceptibility maps in three test areas in Malaysia

Landslides are one of the most frequent and common natural hazards in Malaysia. Preparation of landslide susceptibility maps is one of the first and most important steps in the landslide hazard mitigation. However, due to complex nature of landslides, producing a reliable susceptibility map is not easy. For this reason, a number of different approaches have been used, including direct and indirect heuristic approaches, deterministic, probabilistic, statistical, and data mining approaches. Moreover, these landslides can be systematically assessed and mapped through a traditional mapping framework using geoinformation technologies. Since the early 1990s, several mathematical models have been developed and applied to landslide hazard mapping using geographic information system (GIS). Among various approaches, fuzzy logic relation for mapping landslide susceptibility is one of the techniques that allows to describe the role of each predisposing factor (landslide-conditioning parameters) and their optimal combination. This paper presents a new attempt at landslide susceptibility mapping using fuzzy logic relations and their cross application of membership values to three study areas in Malaysia using a GIS. The possibility of capturing the judgment and the modeling of conditioning factors are the main advantages of using fuzzy logic. These models are capable to capture the conditioning factors directly affecting the landslides and also the inter-relationship among them. In the first stage of the study, a landslide inventory was complied for each of the three study areas using both field surveys and airphoto studies. Using total 12 topographic and lithological variables, landslide susceptibility models were developed using the fuzzy logic approach. Then the landslide inventory and the parameter maps were analyzed together using the fuzzy relations and the landslide susceptibility maps produced. Finally, the prediction performance of the susceptibility maps was checked by considering field-verified landslide locations in the studied areas. Further, the susceptibility maps were validated using the receiver-operating characteristics (ROC) success rate curves. The ROC curve technique is based on plotting model sensitivity—true positive fraction values calculated for different threshold values versus model specificity—true negative fraction values on a graph. The ROC curves were calculated for the landslide susceptibility maps obtained from the application and cross application of fuzzy logic relations. Qualitatively, the produced landslide susceptibility maps showed greater than 82% landslide susceptibility in all nine cases. The results indicated that, when compared with the landslide susceptibility maps, the landslides identified in the study areas were found to be located in the very high and high susceptibility zones. This shows that as far as the performance of the fuzzy logic relation approach is concerned, the results appeared to be quite satisfactory, the zones determined on the map being zones of relative susceptibility.     

Spatial prediction of urban landslide susceptibility based on topographic factors using boosted trees

As global warming accelerates, abnormal weather events are occurring more frequently. In the twenty-first century in particular, hydrological disruption has increased as water flows have changed globally, causing the strength and frequency of hydrological disasters to increase. The damage caused by such disasters in urban areas can be extreme, and the creation of landslide susceptibility maps to predict and analyze the extent of future damage is an urgent necessity. Therefore, in this study, probabilistic and data mining approaches were utilized to identify landslide-susceptible areas using aerial photographs and geographic information systems. Areas where landslides have occurred were located through interpretation of aerial photographs and field survey data. In addition, topographic maps generated from aerial photographs were used to determine the values of topographic factors. A frequency ratio (FR) model was utilized to examine the influences of topographic, soil and vegetation factors on the occurrence of landslides. A total of 23 variables that affect landslide frequency were selected through FR analysis, and a spatial database was constructed. Finally, a boosted tree model was applied to determine the correlations between various factors and landslide occurrence. Correlations among related input variables were calculated as predictor importance values, and sensitivity analysis was performed to quantitatively analyze the impact of each variable. The boosted tree model showed validation accuracies of 77.68 and 78.70% for the classification and regression algorithms using receiver operating characteristic curve, respectively. Reliable accuracy can provide a scientific basis to urban municipalities for policy recommendations in the management of urban landslides.     

A comparison of logistic regression-based models of susceptibility to landslides in western Colorado,USA

The Paonia-McClure Pass area of Colorado has been recognized as a region highly susceptible to mass movement. Because of the dynamic nature of this landscape, accurate methods are needed to predict susceptibility to movement of these slopes. The area was evaluated by coupling a geographic information system (GIS) with logistic regression methods to assess susceptibility to landslides. We mapped 735 shallow landslides in the area. Seventeen factors, as predictor variables of landslides, were mapped from aerial photographs, available public data archives, ETM + satellite data, published literature, and frequent field surveys. A logistic regression model was run using landslides as the dependent factor and landslide-causing factors as independent factors (covariates). Landslide data were sampled from the landslide masses, landslide scarps, center of mass of the landslides, and center of scarp of the landslides, and an equal amount of data were collected from areas void of discernible mass movement. Models of susceptibility to landslides for each sampling technique were developed first. Second, landslides were classified as debris flows, debris slides, rock slides, and soil slides and then models of susceptibility to landslides were created for each type of landslide. The prediction accuracies of each model were compared using the Receiver Operating Characteristic (ROC) curve technique. The model, using samples from landslide scarps, has the highest prediction accuracy (85 %), and the model, using samples from landslide mass centers, has the lowest prediction accuracy (83 %) among the models developed from the four techniques of data sampling. Likewise, the model developed for debris slides has the highest prediction accuracy (92 %), and the model developed for soil slides has the lowest prediction accuracy (83 %) among the four types of landslides. Furthermore, prediction from a model developed by combining the four models of the four types of landslides (86 %) is better than the prediction from a model developed by using all landslides together (85 %).     

A distributed hydrological–geotechnical model using satellite-derived rainfall estimates for shallow landslide prediction system at a catchment scale

This paper describes the potential applicability of a hydrological–geotechnical modeling system using satellite-based rainfall estimates for a shallow landslide prediction system. The physically based distributed model has been developed by integrating a grid-based distributed kinematic wave rainfall-runoff model with an infinite slope stability approach. The model was forced by the satellite-based near real-time half-hourly CMORPH global rainfall product prepared by NOAA-CPC. The method combines the following two model outputs necessary for identifying where and when shallow landslides may potentially occur in the catchment: (1) the time-invariant spatial distribution of areas susceptible to slope instability map, for which the river catchment is divided into stability classes according to the critical relative soil saturation; this output is designed to portray the effect of quasi-static land surface variables and soil strength properties on slope instability and (2) a produced map linked with spatiotemporally varying hydrologic properties to provide a time-varying estimate of susceptibility to slope movement in response to rainfall. The proposed hydrological model predicts the dynamic of soil saturation in each grid element. The stored water in each grid element is then used for updating the relative soil saturation and analyzing the slope stability. A grid of slope is defined to be unstable when the relative soil saturation becomes higher than the critical level and is the basis for issuing a shallow landslide warning. The method was applied to past landslides in the upper Citarum River catchment (2,310 km²), Indonesia; the resulting time-invariant landslide susceptibility map shows good agreement with the spatial patterns of documented historical landslides (1985–2008). Application of the model to two recent shallow landslides shows that the model can successfully predict the effect of rainfall movement and intensity on the spatiotemporal dynamic of hydrological variables that trigger shallow landslides. Several hours before the landslides, the model predicted unstable conditions in some grids over and near the grids at which the actual shallow landslides occurred. Overall, the results demonstrate the potential applicability of the modeling system for shallow landslide disaster predictions and warnings.     

Application of fuzzy logic and analytical hierarchy process (AHP) to landslide susceptibility mapping at Haraz watershed, Iran

The main goal of this study is to produce landslide susceptibility maps of a landslide-prone area (Haraz) in Iran by using both fuzzy logic and analytical hierarchy process (AHP) models. At first, landslide locations were identified by aerial photographs and field surveys, and a total of 78 landslides were mapped from various sources. Then, the landslide inventory was randomly split into a training dataset 70?% (55 landslides) for training the models and the remaining 30?% (23 landslides) was used for validation purpose. Twelve data layers, as the landslide conditioning factors, are exploited to detect the most susceptible areas. These factors are slope degree, aspect, plan curvature, altitude, lithology, land use, distance from rivers, distance from roads, distance from faults, stream power index, slope length, and topographic wetness index. Subsequently, landslide susceptibility maps were produced using fuzzy logic and AHP models. For verification, receiver operating characteristics curve and area under the curve approaches were used. The verification results showed that the fuzzy logic model (89.7?%) performed better than AHP (81.1?%) model for the study area. The produced susceptibility maps can be used for general land use planning and hazard mitigation purpose.     

不同环境因子联接和预测模型的滑坡易发性建模不确定性

拟深入探讨滑坡与其环境因子间的非线性联接计算以及不同数据驱动模型等因素,对滑坡易发性预测建模不确定性的影响规律.以江西省瑞金市为例共获取370处滑坡和10种环境因子,通过概率统计（probability statistics,PS）、频率比（frequency ratio,FR）、信息量（information value,Ⅳ）、熵指数（index of entropy,IOE）和证据权（weight of evidence,WOE）等5种联接方法分别耦合逻辑回归（logistic regression,LR）、BP神经网络（BP neural networks,BPNN）、支持向量机（support vector machines,SVM）和随机森林（random forest,RF）模型共构建出20种耦合模型,同时构建无联接方法直接将原始数据作为输入变量的4种单独LR、BPNN、SVM和RF模型,预测出总计24种工况下的滑坡易发性;最后分别使用ROC曲线、均值、标准差和差异显著性等指标分析上述24种工况下易发性结果的不确定性.结果表明:（1）基于WOE的耦合模型预测滑坡易发性的平均精度最高且不确定性较低,基于PS的耦合模型预测精度最低且不确定性最高,基于FR、Ⅳ和IOE的耦合模型介于两者之间;（2）单独数据驱动模型易发性预测精度略低于耦合模型,且未能计算出环境因子各子区间对滑坡发育的影响规律,但其建模效率高于耦合模型;（3）RF模型预测精度最高且不确定性较低,其次分别为SVM、BPNN和LR模型.总之WOE是更优秀的联接法且RF模型预测性能最优,WOE-RF模型预测的滑坡易发性不确定性较低且更符合实际滑坡概率分布特征.      

基于不同模型的赣南地区小型削方滑坡易发性评价对比分析

赣南地区滑坡灾害点多、面广、规模小,具有群发性和突发性的特点,90%以上的滑坡是因人工切坡导致的。为研究赣南地区小型削方滑坡对易发性评价模型的适用性,以赣州市于都县银坑镇为例,基于野外地质调查成果,并利用地理探测器,选取坡度、坡体结构、岩组、断层、道路、植被等6个评价指标,分别选用信息量模型、人工神经网络模型、决策树模型和逻辑回归模型开展易发性评价。结果表明：信息量、人工神经网络、决策树和逻辑回归等模型得到的AUC值分别为0.800、0.708、0.672和0.586,信息量模型所得的易发性结果与研究区滑坡实际分布情况较吻合,高易发区和中易发区滑坡占比近80%。信息量模型较其他三个模型,更适合于赣南地区小型削方滑坡易发性评价,评价结果对该地区地质灾害易发性评价模型选取提供了参考与借鉴。     

Landslide susceptibility mapping using rough sets and back-propagation neural networks in the Three Gorges, China

In the Three Gorges of China, there are frequent landslides, and the potential risk of landslides is tremendous. An efficient and accurate method of generating landslide susceptibility maps is very important to mitigate the loss of lives and properties caused by these landslides. This paper presents landslide susceptibility mapping on the Zigui-Badong of the Three Gorges, using rough sets and back-propagation neural networks (BPNNs). Landslide locations were obtained from a landslide inventory map, supported by field surveys. Twenty-two landslide-related factors were extracted from the 1:10,000-scale topographic maps, 1:50,000-scale geological maps, Landsat ETM + satellite images with a spatial resolution of 28.5 m, and HJ-A satellite images with a spatial resolution of 30 m. Twelve key environmental factors were selected as independent variables using the rough set and correlation coefficient analysis, including elevation, slope, profile curvature, catchment aspect, catchment height, distance from drainage, engineering rock group, distance from faults, slope structure, land cover, topographic wetness index, and normalized difference vegetation index. The initial, three-layered, and four-layered BPNN were trained and then used to map landslide susceptibility, respectively. To evaluate the models, the susceptibility maps were validated by comparing with the existing landslide locations according to the area under the curve. The four-layered BPNN outperforms the other two models with the best accuracy of 91.53 %. Approximately 91.37 % of landslides were classified as high and very high landslide-prone areas. The validation results show sufficient agreement between the obtained susceptibility maps and the existing landslide locations.     

贵州省都匀市滑坡易发性评价研究

都匀市是贵州省城镇滑坡地质灾害多发频发区。文章以都匀市沙包堡镇为研究区,采用栅格单元提取高程、坡度、岩性、水系等9项致灾因子,分别使用都基于数学统计模型的定量分析方法（二元逻辑回归模型、信息量模型）和定性分析方法（层次分析模型）对都匀市研究区滑坡地质灾害易发性进行评价。结果表明:二元逻辑回归模型预测精度与预测效果均为最优,其ROC曲线下面积AUC值为0.873,易发性分区中高易发区和中易发区内预测发生滑坡面积比占95.41%,且最符合野外实地调查验证情况。评价方法与结果可为贵州城镇地区滑坡地质灾害评价和防治提供借鉴。     

Application of logistic regression model for slope instability prediction in Cuyahoga River Watershed,Ohio, USA

High incidences of slope movement are observed throughout Cuyahoga River watershed in northeast Ohio, USA. The major type of slope failure involves rotational movement in steep stream walls where erosion of the banks creates over-steepened slopes. The occurrence of landslides in the area depends on a complex interaction of natural as well as human induced factors, including: rock and soil strength, slope geometry, permeability, precipitation, presence of old landslides, proximity to streams and flood-prone areas, land use patterns, excavation of lower slopes and/or increasing the load on upper slopes, alteration of surface and subsurface drainage. These factors were used to evaluate the landslide-induced hazard in Cuyahoga River watershed using logistic regression analysis, and a landslide susceptibility map was produced in ArcGIS. The map classified land into four categories of landslide susceptibility: low, moderate, high, and very high. The susceptibility map was validated using known landslide locations within the watershed area. The landslide susceptibility map produced by the logistic regression model can be efficiently used to monitor potential landslide-related problems, and, in turn, can help to reduce hazards associated with landslides.     

Landslide susceptibility mapping using GIS and weighted overlay method: a case study from North Jordan

Road instability along the Jerash–Amman highway was assessed using the weighted overlay method in Geographic Information System environment. The landslide susceptibility map was developed from nine contributing parameters. The map of landslide susceptibility was classified into five zones: very low (very stable), low (stable), moderate (moderately stable), high (unstable), and very high (highly unstable). The very high susceptibility and high susceptibility zones covered 15.14% and 31.81% of the study area, respectively. The main factors that made most parts of study area prone to landslides include excessive drainage channels, road cuts, and unfavorable rock strata such as marl and friable sandstone intercalated with clay and highly fractured limestone. Fracture zones are a major player in land instability. The moderate and high susceptibility zones are the most common in urban (e.g., Salhoub and Gaza camp) and agricultural areas. About 34% of the urban areas and 28.82% of the agricultural areas are characterized by the high susceptibility zone. Twenty percent of the Jerash–Amman highway length and 58% of the overall highway length are located in the very high susceptibility zone. The landslide susceptibility map was validated by the recorded landslides. More than 80 of the inventoried landslides are in unstable zones, which indicate that the selected causative factors are relevant and the model performs properly.     

Effects of strong ground motion on the susceptibility of gully type debris flows

Typhoon Herb in 1996 caused widespread debris flows in central Taiwan. The 7.3 Chi-Chi earthquake on September 21, 1999, which also took place in central Taiwan, induced many landslides in the region. These landslides turned into debris flows when Typhoon Toraji struck Taiwan in 2001. This research selects three regions which suffered a ground motion class of 5, 6, and 7 on the Richter scale during the Chi-Chi earthquake as study areas. Air photos from 1997 and 2001 of these regions are used to map the gully-type debris flows that took place after Typhoons Herb and Toraji, respectively. The gullies adjacent to the debris flow, but without a trace of debris flows, are also mapped as the non-debris flow data. The topography, hydrogeology, and rainfall factors – where debris flow occurred and in which there was no occurrence of debris flows in these gullies were retrieved from DTM, geological maps, and iso-countour maps, and of rainfall through GIS processing. These characteristic are introduced into a probabilistic neural network to build a predicting model for the probability of the occurrence of debris flows. Three series of cross analyses are conducted to compare the probability of the occurrence of debris flows of the same dataset predicted by different prediction models. The results reveal that the susceptibility of debris flows was elevated after the Chi-Chi earthquake struck. The upsurge of susceptibility was more obvious for the regions that received a higher class of ground motion.     

Mapping of micro topography using airborne laser scanning

Intense rainfall conditions and seismic activity commonly trigger fluidised landslides which are characterized by rapid movement and long run-out. They are potentially a very dangerous form of landslide phenomena and may result in extensive damage due to their sudden movement. Until now, photogrammetry has been used to produce maps and investigate such landslides in areas where these disasters occur. Recently, however, airborne laser scanning technology has become a promising technique for making topographical maps and investigating the micro topographic details of these landslide disasters, particularly on slopes around urban areas where the potential risk is high. In this study, airborne laser scanning was carried out in the Tama Hills, near Tokyo, Japan, which is extensively affected by this type of landsliding. The effectiveness of this technique was tested and compared with a laser contour map and aerial photograph interpretations.     

Quality assessment of the Italian Landslide Inventory using GIS processing

Landslides constitute one of the most important natural hazards in Italy as they are widespread and result in considerable damage and fatalities every year. The Italian Landslide Inventory (IFFI) Project was launched in 1999 with the aim of identifying and mapping landslides over the entire Italian territory. The inventory currently holds over 480,000 landslides and has been available by means of Web services since 2005. The aim of this study is to define quality indices for evaluation of the homogeneity and completeness of the IFFI database. In order to estimate the completeness of the landslide attribute information, a heuristic approach has been used to assign weighting values to significant parameters selected from the landslide data sheet. The completeness and homogeneity of the landslide mapping has been evaluated by means of three different methods: an area-frequency distribution analysis; the proximity of the landslides surveyed to urban areas; variation of the landslide index within the same lithology. The quality indices have allowed identification of areas with a high level of completeness and critical areas in which the data collected have been underestimated or are not very accurate. The quality assessment of collected and stored data is essential in order to use the IFFI database for definition and implementation of landslide susceptibility models and for land use planning and management.     

基于多模型的滑坡易发性评价以甘肃岷县地震滑坡为例

2013年7月22日,甘肃省岷县漳县交界处发生了MS6.6级地震(岷县地震),本文以这次地震烈度Ⅷ度区为研究区,根据地震前后遥感影像解译出来的2330个地震滑坡数据,以坡度、坡向、水系、岩性和断层为因子图层,分别应用模糊逻辑法,信息量模型及Shannon熵改进的信息量模型,对研究区的地震滑坡易发性进行评价。结果表明: 1滑坡的高易发性地区位于研究区的中间部分,以及水系0～50m这一缓冲区范围内,离水系越近滑坡易发性等级越高; 2应用ROC曲线对3个模型的易发性评价结果进行比较,信息量模型和Shannon熵改进的信息量模型的AUC值分别为0.8488, 0.8502; 模糊逻辑模型的AUC值为0.7640,表明前两个模型的表现较好,而模糊逻辑模型相对来说表现一般; 3通过对比3个模型中各等级易发性所占的面积比例和各等级易发性中滑坡数目占总数比例,表明Shannon熵改进后的模型更适用于灾害风险评价以及应急风险管理等实际应用。     

基于随机森林的滑坡空间易发性评价:以三峡库区湖北段为例

滑坡空间易发性分析有助于开展滑坡防灾减灾工作,训练有效的滑坡预测模型在其中扮演重要角色.以三峡库区湖北段为研究区,选取高程、坡度、斜坡结构、土地利用类型、岩土体类型、断裂距离、路网距离、河网距离、以及归一化植被指数这9个影响因子建立滑坡空间数据库,采用集成学习中的随机森林算法进行滑坡易发性评价.结果显示,随机森林抽样训练的方式有利于确定较优的训练参数,保证随机森林在不过拟合的情况下取得满意的拟合能力和泛化能力.随机森林绘制的滑坡易发性分级图显示出合理的空间分布,其中73.35%的滑坡分布在较高和极高级别区域.而巴东县北部、秭归县中部以及夷陵区南部等区域显示出较高的易发性级别.性能评估及易发性统计结果均表明随机森林是一种出色的算法,在滑坡空间预测领域具有较好的适用性.      

Assessing shallow landslide hazards using the TRIGRS and SHALSTAB models,Serra do Mar,Brazil

The hillslopes of the Serra do Mar, a system of escarpments and mountains that extend more than 1500 km along the southern and southeastern Brazilian coast, are regularly affected by heavy rainfall that generates widespread mass movements, causing large numbers of casualties and economic losses. This paper evaluates the efficiency of susceptibility mapping for shallow translational landslides in one basin in the Serra do Mar, using the physically based landslide susceptibility models SHALSTAB and TRIGRS. Two groups of scenarios were simulated using different geotechnical and hydrological soil parameters, and for each group of scenarios (A and B), three subgroups were created using soil thickness values of 1, 2, and 3 m. Simulation results were compared to the locations of 356 landslide scars from the 1985 event. The susceptibility maps for scenarios A1, A2, and A3 were similar between the models regarding the spatial distribution of susceptibility classes. Changes in soil cohesion and specific weight parameters caused changes in the area of predicted instability in the B scenarios. Both models were effective in predicting areas susceptible to shallow landslides through comparison of areas predicted to be unstable and locations of mapped landslides. Such models can be used to reduce costs or to define potentially unstable areas in regions like the Serra do Mar where field data are costly and difficult to obtain.     

Inclusion of earthquake strong ground motion in a geographic information system-based landslide susceptibility zonation in Garhwal Himalayas

Garhwal Himalayas are seismically very active and simultaneously suffering from landslide hazards. Landslides are one of the most frequent natural hazards in Himalayas causing damages worth more than one billion US$ and around 200 deaths every year. Thus, it is of paramount importance to identify the landslide causative factors to study them carefully and rank them as per their influence on the occurrence of landslides. The difference image of GIS-derived landslide susceptibility zonation maps prepared for pre- and post-Chamoli earthquake shows the effect of seismic shaking on the occurrence of landslides in the Garhwal Himalaya. An attempt has been made to incorporate seismic shaking parameters in terms of peak ground acceleration with other static landslide causative factors to produce landslide susceptibility zonation map in geographic information system environment. In this paper, probabilistic seismic hazard analysis has been carried out to calculate peak ground acceleration values at different time periods for estimating seismic shaking conditions in the study area. Further, these values are used as one of the causative factors of landslides in the study area and it is observed that it refines the preparation of landslide susceptibility zonation map in seismically active areas like Garhwal Himalayas.     

National-scale data-driven rainfall induced landslide susceptibility mapping for China by accounting for incomplete landslide data

China is one of the countries where landslides caused the most fatalities in the last decades.The threat that landslide disasters pose to people might even be greater in the future,due to climate change and the increasing urbanization of mountainous areas.A reliable national-scale rainfall induced landslide suscep-tibility model is therefore of great relevance in order to identify regions more and less prone to landslid-ing as well as to develop suitable risk mitigating strategies.However,relying on imperfect landslide data is inevitable when modelling landslide susceptibility for such a large research area.The purpose of this study is to investigate the influence of incomplete landslide data on national scale statistical landslide susceptibility modeling for China.In this context,it is aimed to explore the benefit of mixed effects mod-elling to counterbalance associated bias propagations.Six influencing factors including lithology,slope,soil moisture index,mean annual precipitation,land use and geological environment regions were selected based on an initial exploratory data analysis.Three sets of influencing variables were designed to represent different solutions to deal with spatially incomplete landslide information:Set 1(disregards the presence of incomplete landslide information),Set 2(excludes factors related to the incompleteness of landslide data),Set 3(accounts for factors related to the incompleteness via random effects).The vari-able sets were then introduced in a generalized additive model(GAM:Set 1 and Set 2)and a generalized additive mixed effect model(GAMM:Set 3)to establish three national-scale statistical landslide suscep-tibility models:models 1,2 and 3.The models were evaluated using the area under the receiver operating characteristics curve(AUROC)given by spatially explicit and non-spatial cross-validation.The spatial pre-diction pattern produced by the models were also investigated.The results show that the landslide inven-tory incompleteness had a substantial impact on the outcomes of the statistical landslide susceptibility models.The cross-validation results provided evidence that the three established models performed well to predict model-independent landslide information with median AUROCs ranging from 0.8 to 0.9.However,although Model 1 reached the highest AUROCs within non-spatial cross-validation(median of 0.9),it was not associated with the most plausible representation of landslide susceptibility.The Model 1 modelling results were inconsistent with geomorphological process knowledge and reflected a large extent the underlying data bias.The Model 2 susceptibility maps provided a less biased picture of landslide susceptibility.However,a lower predicted likelihood of landslide occurrence still existed in areas known to be underrepresented in terms of landslide data(e.g.,the Kuenlun Mountains in the northern Tibetan Plateau).The non-linear mixed-effects model(Model 3)reduced the impact of these biases best by introducing bias-describing variables as random effects.Among the three models,Model 3 was selected as the best national-scale susceptibility model for China as it produced the most plausible portray of rainfall induced landslide susceptibility and the highest spatially explicit predictive perfor-mance(median AUROC of spatial cross validation 0.84)compared to the other two models(median AUROCs of 0.81 and 0.79,respectively).We conclude that ignoring landslide inventory-based incomplete-ness can entail misleading modelling results and that the application of non-linear mixed-effect models can reduce the propagation of such biases into the final results for very large areas.