Quantitative assessment of geological hazard risk with different hazard indexes in mountainous areas 山区地质灾害风险的不同危险指数定量评估
Fang Zou , Erzhuo Che , Meiqin Long 方走 ，二桌车 ，梅琴龙 School of Architecture, Changsha University of Science and Technology, Changsha, China 长沙理工大学建筑学院，中国长沙 School of Civil and Construction Engineering, Oregon State University, Oregon, USA 俄勒冈州立大学土木与建筑工程学院，美国俄勒冈
A R T I C L E I N F O 文章信息
Handling Editor: Maria Teresa Moreira 主编：Maria Teresa Moreira
Keywords: 关键词：
Geological hazard risk assessment 地质灾害风险评估
Hazard indexes 危险指数
Mountainous areas 山区地区
Abstract 摘要
A B S T R A C T To prevent and control geological hazards (geohazards), the intensity of geohazards compared to the frequency is more important in geohazard risk assessment. This has mostly been overlooked in previous studies. To address this deficiency, this study established different hazard indexes to comprehensively and quantitatively express the risks of geohazards. Moreover, human factors and anthropogenic activities characteristic of mountainous areas have been introduced into geohazard evaluation by different spatial autoregression models through a case study. The case is reported as follows: (1) Different hazard indexes can fully express the location, frequency and intensity of geohazards. (2) Areas with high incidence and high intensity of geohazards can be accurately identified in the case study area with an accuracy of 0.829 and 0.730 , respectively. (3) Regions with the highest-risk and high-risk intensity and the highest-risk and high-risk frequency are not spatially consistent, accounting for and of the case areas, respectively. The hazard indexes developed in this work have the potential to increase comprehensive geohazard risk identification while also providing scientific support for hazard prevention and mitigation. 摘要 为了预防和控制地质灾害（地灾），在地灾风险评估中，与频率相比，地灾的强度更为重要。这在以往的研究中大多被忽视。为了解决这一不足，本研究建立了不同的灾害指数，全面、定量地表达地灾风险。此外，通过一个案例研究，将山区的人为因素和人类活动引入地灾评估中，采用不同的空间自回归模型。案例报告如下：（1）不同的灾害指数可以充分表达地灾的位置、频率和强度。（2）在案例研究区域，高发生率和高强度地灾的区域可以准确识别，准确率分别为 0.829 和 0.730。（3）最高风险和高风险强度区域与最高风险和高风险频率区域并不空间一致，分别占案例区域的 和 。 本工作中开发的危险指数有潜力提高综合地质灾害风险识别，同时为灾害预防和减灾提供科学支持。
1. Introduction 1. 引言
Geological hazards (geohazards) are events caused by geological features and processes that present severe threats to humans, property, nature and the eco-environment (Muco et al., 2012). Data released by the Emergency Events Database (EMDAT) appear to underline this trend from 2001 to 2021 (Fig. 1). Landslides, collapses, debris flows, earthquakes and mixed-type geological disasters are typical examples of such events (Peng and Wang, 2015; Anbalagan, 1992). With the development of the economy and population, geohazards pose a great threat to world security and China is no exception (Fig. 1). 地质灾害是由地质特征和过程引起的事件，对人类、财产、自然和生态环境构成严重威胁（Muco 等，2012 年）。应急事件数据库（EMDAT）发布的数据似乎强调了 2001 年至 2021 年间的这一趋势（图 1）。滑坡、崩塌、泥石流、地震和混合型地质灾害是这类事件的典型例子（Peng 和 Wang，2015 年；Anbalagan，1992 年）。随着经济和人口的发展，地质灾害对世界安全构成巨大威胁，中国也不例外（图 1）。
Geohazards are the result of two interacting sets of forces: the precondition factors, generally naturally induced, and the preparatory and triggering factors, induced either by natural factors or by human intervention (Hufschmidt et al., 2005; Zou et al., 2018; Zou et al., 2022). A mountainous area is a typical region that can satisfy the two interacting sets of forces of geohazard formation. First, the precondition factors of geohazards are common in mountainous areas where there is steep terrain, complicated geology and active earthquakes. In addition, the preparatory and triggering factors specifically refer to the rapid growth of human activities, such as road construction, mining and construction, mountain tourism, etc., so that construction projects and the population increase, resulting in the change of landform and the destruction of geological structure, thus increasing the construction of geological disasters in mountainous areas and the increase of population. Therefore, it is very important and urgent for mountainous areas to pay attention to the prevention and control of natural and manmade geohazards. 地质灾害是两组相互作用的力量的结果：预备因素通常是自然引起的，而准备和触发因素则是由自然因素或人为干预引起的（Hufschmidt 等，2005 年；邹等，2018 年；邹等，2022 年）。山区是一个典型的地区，可以满足地质灾害形成的这两组相互作用的力量。首先，地质灾害的预备因素在山区很常见，那里地形陡峭，地质复杂，地震活跃。此外，准备和触发因素特指人类活动的迅速增长，如道路建设、矿业和建筑、山地旅游等，使得建设项目和人口增加，导致地貌变化和地质结构破坏，从而增加山区地质灾害的发生和人口增加。因此，山区重视自然和人为地质灾害的预防和控制非常重要和紧迫。
Scientific and accurate geohazard risk assessment is the key to geohazard prevention and control research. A large number of scholars have conducted in-depth research and practice on this topic. From the content of geohazard risk studies, the existing research has mainly concerned hazard vulnerability, hazard sensitivity, hazard susceptibility, and so on. Although these studies focused on geohazards in varied contexts, the core of those studies was to infer the risk of geohazards from the hazard formation mechanism. In most cases, the relationship between geohazard frequency and hazard factors was investigated qualitatively or quantitatively to assess hazard risk and in an attempt to produce maps portraying their spatial distribution (Guzzetti et al., 1999; Mândrescu, 1984; Huo et al., 2012; Cigna et al., 2014; Joyce et al., 2014; Peng and Wang, 2015; Zhuang et al., 2016). Therefore, the researchers placed more emphasis on the location and frequency of geohazards, while the intensity of geohazards was inadequate in previous research. The intensity of geohazards refers to the ground destruction degree, which is often used to express the size of the disaster itself, such as the volume of rock or soil displacement after geohazard. The intensity of geohazards, an important attribute of disasters, should not be missing in the expression disaster characteristics. Conversely, the intensity of geohazards is important in describing the actual risk of geohazards, which should not be ignored in geohazard risk evaluations. 科学准确的地质灾害风险评估是地质灾害防治研究的关键。许多学者对这一主题进行了深入研究和实践。从地质灾害风险研究的内容来看，现有研究主要涉及灾害脆弱性、灾害敏感性、灾害易感性等。尽管这些研究关注了不同背景下的地质灾害，但这些研究的核心是从灾害形成机制推断地质灾害风险。在大多数情况下，研究人员定性或定量地调查了地质灾害频率与灾害因素之间的关系，以评估灾害风险，并试图制作描绘其空间分布的地图（Guzzetti 等，1999 年；Mândrescu，1984 年；Huo 等，2012 年；Cigna 等，2014 年；Joyce 等，2014 年；Peng 和 Wang，2015 年；Zhuang 等，2016 年）。因此，研究人员更加强调地质灾害的位置和频率，而先前的研究中地质灾害的强度不足。 地质灾害的强度指的是地面破坏程度，通常用来表达灾害本身的大小，比如地质灾害发生后岩石或土壤位移的体积。地质灾害的强度是灾害的重要属性，在表达灾害特征时不应缺失。相反，地质灾害的强度在描述地质灾害的实际风险时至关重要，地质灾害风险评估中不应忽视。
From the study methods of geohazard risk evaluation, a number of different methods have been utilised and suggested. The trend of geohazard risk evaluation methods ranges from qualitative approaches to quantitative approaches. Early attempts at geohazard risk evaluation pay more attention to qualitative methods, which depend on expert opinions. Some qualitative approaches, however, incorporate the concept of rank and weight and may evolve into being semiquantitative (Yalcin, 2008; Ayalew et al., 2005). The best examples of qualitative or semiquantitative methods are the Delphi method, analytic hierarchy process and so on (Komac, 2006; Yalcin et al., 2011; Kumar and Anbalagan, 2016; Fan et al., 2004; Wu, 2004). More sophisticated assessments are involved in quantitative methods, such as bivariate, multivariate, logistics regression frequency ratio and artificial neural network analysis (Erener and Duzgun, 2010; Pradhan, 2010; Yalcin et al., 2011; Hadji et al., 2013; Jiang et al., 2017). These quantitative methods can more accurately and scientifically analyze geohazard risk compared with qualitative methods, and their essence is to analyze the role of disaster-causing factors in the formation of geohazards. However, the scientificity and accuracy of geohazard risk assessment are dependent not only on the analysis of the factors causing hazards but also on the analysis of the geohazards themselves. The spatial autoregressive model is effective at examining the interconnected features of geographical events, and this technology is not widely used in current geohazard risk research. 从地质灾害风险评估的研究方法来看，已经采用和建议了许多不同的方法。地质灾害风险评估方法的趋势从定性方法到定量方法。早期的地质灾害风险评估尝试更多地关注定性方法，这些方法依赖于专家意见。然而，一些定性方法融入了等级和权重的概念，可能演变为半定量方法（Yalcin，2008 年；Ayalew 等，2005 年）。定性或半定量方法的最佳示例是德尔菲法、层次分析法等（Komac，2006 年；Yalcin 等，2011 年；Kumar 和 Anbalagan，2016 年；Fan 等，2004 年；吴，2004 年）。定量方法涉及更复杂的评估，如双变量、多变量、逻辑回归频率比和人工神经网络分析（Erener 和 Duzgun，2010 年；Pradhan，2010 年；Yalcin 等，2011 年；Hadji 等，2013 年；Jiang 等，2017 年）。 这些定量方法与定性方法相比，可以更准确、科学地分析地质灾害风险，其本质是分析灾害因素在地质灾害形成中的作用。然而，地质灾害风险评估的科学性和准确性不仅取决于对引发灾害因素的分析，还取决于对地质灾害本身的分析。空间自回归模型能有效地检验地理事件的相互关联特征，而这项技术在当前地质灾害风险研究中并不广泛应用。
This study aimed to solve these two above problems by further exploring quantitative geological hazard risk assessment. A new research framework was designed to improve the comprehensiveness and scientificity of geohazard risk assessment. The central tenet of the new research hypothesis was that both the spatial autoregressive model of hazard features in mountainous locations and the attribute of hazard intensity should be taken into consideration. The specific research content is as follows. First, a typical mountainous area was chosen as a case study in China. Then, two types of hazard indexes were defined and compared to describe the risk of hazards. Utilising SAG, geohazard risk evaluations were conducted on coupling natural and human factors. Finally, cross validation (CV) and receiver operating characteristic curve (ROC) were used to test the accuracy of geohazard risk assessment results through different hazard indexes under different models. The results of this case study can fully identify the geohazard risk to guide government's disaster prevention and mitigation work, so as to ensure environmental safety and ultimately improve the regional sustainable development. 本研究旨在通过进一步探索定量地质灾害风险评估来解决上述两个问题。设计了一个新的研究框架，以提高地质灾害风险评估的全面性和科学性。新研究假设的核心观点是，应考虑山地地区灾害特征的空间自回归模型和灾害强度属性。具体研究内容如下。首先，在中国选择了一个典型的山地地区作为案例研究。然后，定义并比较了两种灾害指数，以描述灾害风险。利用 SAG，对自然因素和人为因素的耦合进行了地质灾害风险评估。最后，使用交叉验证（CV）和接收器操作特性曲线（ROC）来测试不同模型下不同灾害指数的地质灾害风险评估结果的准确性。本案例研究的结果可以充分识别地质灾害风险，指导政府的灾害防范和减灾工作，以确保环境安全，最终提高区域可持续发展。
2. Study area 2. 研究区域
2.1. Basic situation 2.1. 基本情况
Shennongjia is a county located in the eastern part of China (Fig. 2). It is administered by five towns and three townships, where about 78,900 people lived until 2019. The geographical location of Shennongjia is between and east longitude, to north latitude (Fig. 2). This area contains 3253 square kilometres, which extends over from north to south. Shennongiia is typically a mountainous area with significant differences in topography and geology. The main mountain range of Shennongjia is part of the Daba Mountains, with the highest peak at above sea level. With its steep mountains and complex geology, Shennongjia belongs to a region prone to geological hazards. In the past 15 years (from 2005 to 2019 [2016 data are missing]), there were 317 geohazards in this area, which mainly included collapses, debris flows and landslides. The hazards in Shennongjia are characteristically small-scale, but high-frequency and wide-spread. 神农架是中国东部的一个县（图 2）。它由五个镇和三个乡组成，直到 2019 年大约有 78,900 人口。神农架的地理位置位于东经 和 ，北纬 到 之间（图 2）。该地区面积为 3253 平方公里，南北延伸 。神农架通常是一个地势崎岖、地质差异显著的山区。神农架的主要山脉是大巴山脉，最高峰海拔 。由于陡峭的山脉和复杂的地质构造，神农架属于一个容易发生地质灾害的地区。在过去的 15 年（从 2005 年到 2019 年[2016 年数据缺失]），该地区发生了 317 起地质灾害，主要包括崩塌、泥石流和滑坡。神农架的灾害特点是规模小、频率高且范围广。
Due to its location in a remote mountainous area, Shennongjia's economic development is relatively backward compared to other Chinese counties. However, due to its unique location, Shennongjia, with its superior natural resources and landscape, has been added to the World Heritage List. During this century, Shennongjia will still face a number of challenges due to the rapid growth of tourism and the continued increase in geohazards. 由于位于偏远山区，神农架的经济发展相对落后于其他中国县。然而，由于其独特的地理位置，神农架以其优越的自然资源和景观被列入世界遗产名录。在本世纪，神农架仍将面临旅游业快速增长和地质灾害持续增加等诸多挑战。
Some of the major issues now confronting Shennongjia include: 目前神农架面临的一些主要问题包括：
(1) Tourism is bringing population growth, land expansion and intensified human construction activity. （1）旅游业带来人口增长、土地扩张和人类建设活动加剧。
(2) Land is always lacking due to its topographic limitations. (2) 由于地形限制，土地总是短缺。
(3) Geohazards are aggravated by human activities, which have brought huge economic losses and life risk. (3) 地质灾害受人类活动的影响而加剧，给经济和生命带来巨大风险。
2.2. Study data 2.2. 研究数据
Knowledge of the behaviour of natural and man-made environments in the recent past can be used as a basis for hazard assessment in the near future. It is reasonable to assume that an analysis of a period covering the last few decades will provide useful keys to forecasting behaviour during the next few decades (with conditions presumably being quite 在最近的自然和人为环境行为知识可以作为未来近期危险评估的基础。合理地假设，对涵盖过去几十年的时期进行分析将为预测未来几十年的行为提供有用的线索（条件可能会相当
Fig. 1. Total worldwide number of geological hazards between 1951 and 2019 (Source: Emergency Events Database). 图 1. 1951 年至 2019 年全球地质灾害总数（来源：紧急事件数据库）。
Fig. 2. Geographical location and geohazard distribution of the study area until 2019. 图 2. 研究区域的地理位置和地质灾害分布情况直至 2019 年。
similar) (Remondo et al., 2005). Thus, case study data is fundamental for the successful evaluation of geohazard risk and processing data is the first steps in the research. 因此，案例研究数据对于成功评估地质灾害风险至关重要，处理数据是研究的第一步。
Data for the case regions were collected by the relevant local departments through provision and on-the-spot investigations (Table 1). The data required for this study comprised mainly two categories: geohazards and hazard formation factors. Geohazard data summarise basic information, such as time, location, frequency and size. The hazard formation factor data contains natural and human influence factors, which can comprehensively reflect the underlying conditions of mountain area. For example, three factors (Lithology, Fracture and Physiognomy) are used to represent the geological conditions of the case area based on data availability, all of which have a significant impact on mountain geological hazards. In the meantime, this study also explains the types of data sources and then emphasizes how the selected data were obtained from different institutions and at different scales (Table 1). Due to the differences in resolution and accuracy of the data from multiple sources, methods such as interpolation, reclassification, and data cleaning have been employed to reconcile the data appropriately. The data was then processed and organized in a geographic database using the Geographic Information System (GIS). This geographic database was used to define a unified geographic coordinate system for CGCS2000 and a projected coordinate system for CGCS2000 3D GK CM 111E. 案例区域的数据是通过相关地方部门通过提供和现场调查收集的（表 1）。本研究所需的数据主要包括两类：地质灾害和灾害形成因素。地质灾害数据总结了基本信息，如时间、地点、频率和规模。灾害形成因素数据包含自然和人为影响因素，可以全面反映山区的基本情况。例如，三个因素（岩性、裂缝和地貌）用于根据数据可用性代表案例区域的地质条件，所有这些因素都对山地地质灾害产生重要影响。同时，本研究还解释了数据来源的类型，然后强调了所选数据是如何从不同机构和不同尺度获得的（表 1）。由于多个来源的数据分辨率和准确性存在差异，因此采用插值、重分类和数据清理等方法来适当调和数据。 然后使用地理信息系统（GIS）将数据进行处理和组织，存储在地理数据库中。该地理数据库用于为 CGCS2000 定义统一的地理坐标系统和为 CGCS2000 3D GK CM 111E 定义投影坐标系统。
Table 1 表 1
Classification, data type and scale of study data. 研究数据的分类、数据类型和比例尺。
Classification
Sub-classification
Data type
Data
accuracy
Geohazards data 地质灾害数据
Geological hazards 地质灾害
inventory
Vector
data
1:10,000
Hazard factors data 危险因素数据
Nature influencing 自然影响
factors
NDVI
Raster
data
Slope-aspect
Raster
Slope
data
Curvature
Elevation
Water distribution 水分配
Vector
data
1:10,000
Lithology
Vector
data
1:10,000
Precipitation
Vector
data
1:10,000
Fracture
Vector
data
Physiognomy
Vector
data
1:10,000
Human influencing 人类影响
factors
Building activities 建筑活动
AutoCAD
Road activities 道路活动
AutoCAD
Farming activities 农业活动
AutoCAD
Mining activities 采矿活动
AutoCAD
3. Methodology 3. 方法论
An overview of the research methodology that was applied to quantify geohazard risks with respect to size is shown in Fig. 3. The main stream of research can be divided into four phases. The first phase is data processing and classification, which is the data preparation phase for follow-up studies. In addition to the processing of data, data classification is prepared for the following cross validation (CV), which divides geological hazards inventory into validating samples or training samples. The second phase was the innovation of this study. Two methods of geodesic indexing were defined and completed. The difference between the two metrics is that one takes into account the intensity of geohazards, while the other only takes into account the location and frequency of geohazards. The construction and comparison of multiple models for the two types of geodesic indices in the third stage form the main part of this paper. In this phase, two types of models (the spatial lag model and the spatial error model) were built and used to quantify the relationship between geohazards and hazard-forming factors considering the coupling effect of different factors. The validation method of Receiver Operating Characteristic was then used not only to verify the effectiveness of the model but also to test the reliability of the predictions for different hazard metrics. The fourth phase, based on the selected best model, comprehensively assessed the risk of hazards in the case region based on different hazard indicators, including the frequency, location and intensity of geohazards. 应用于量化地质灾害风险的研究方法概述如图 3 所示。研究的主要流程可分为四个阶段。第一阶段是数据处理和分类，这是后续研究的数据准备阶段。除了数据处理外，数据分类还为接下来的交叉验证（CV）做准备，将地质灾害清单分为验证样本或训练样本。第二阶段是本研究的创新。定义并完成了两种大地测量指数方法。这两种指标之间的差异在于一种考虑了地质灾害的强度，而另一种仅考虑了地质灾害的位置和频率。第三阶段的主要部分是构建和比较两种类型大地测量指数的多模型。在这个阶段，建立并使用了两种模型（空间滞后模型和空间误差模型）来量化地质灾害与形成因素之间的关系，考虑了不同因素的耦合效应。 接收者操作特征验证方法不仅用于验证模型的有效性，还用于测试不同危险指标的预测可靠性。基于选定的最佳模型，第四阶段全面评估了基于不同危险指标（包括地质灾害的频率、位置和强度）的案例区域的危险风险。
3.1. Definition of hazard index: hazard frequency index (HFI) and hazard intensity index (HII) 3.1. 危险指数的定义：危险频率指数（HFI）和危险强度指数（HII）
Quantitative geohazard risk is used to calculate the relationship between geohazards and influence factors to represent the possibility of geohazards with a specific value (Dou et al., 2015). The definition of a hazard index, which refers to how to scientifically quantify hazards, is important in hazard risk assessment in geology. In geographical events, each geological hazard has specific indicators such as time, location, frequency and size. Therefore, scientifically and efficiently quantifying geohazards is a complex process. 量化地质灾害风险用于计算地质灾害与影响因素之间的关系，以表示具有特定值的地质灾害的可能性（Dou 等，2015）。危险指数的定义，即如何科学量化危险，在地质灾害风险评估中至关重要。在地理事件中，每种地质灾害都有特定的指标，如时间、位置、频率和规模。因此，科学而高效地量化地质灾害是一个复杂的过程。
Many studies have used the frequency of disasters to quantify geohazards, while ignoring the intensity of the hazard. However, different size of geohazards indicate different levels of risk and damage in different regions. Therefore, the hazard intensity is an important indicator of hazard indicators and should be considered in the hazard risk assessment of geohazards. In this study, two hazard index definitions were used for the evolution of geohazards, as well as a comprehensive description of hazard features compared with the single index. The index of hazard frequency (HFI) concerns location and frequency, while the index of hazard intensity (HII) concerns size and location. The exact definition is as follows. 许多研究已经使用灾害频率来量化地质灾害，而忽略了灾害的强度。然而，不同规模的地质灾害表明不同地区的风险和损害水平不同。因此，灾害强度是灾害指标的重要指标，应该在地质灾害的灾害风险评估中予以考虑。在本研究中，使用了两种灾害指数定义来描述地质灾害的演变，以及与单一指数相比的灾害特征的综合描述。灾害频率指数（HFI）涉及位置和频率，而灾害强度指数（HII）涉及规模和位置。确切的定义如下。
Fig. 3. Flow diagram of this study. 图 3. 本研究的流程图。
In Equation (1), represents the incidence rate (occurrence) of geohazard in the map unit , where means the total number of geohazards in the case area, and means the number of geohazards in map unit . In Equation (2), represents the intensity of geohazard in the map unit means the size of the disaster which is calculated by disaster volume, and means the volume of the disaster . After computation, the value of HFI or HII is between 0 and 1 , and the higher the value, the higher the risk of disaster frequency or intensity. 在方程（1）中， 代表地质灾害在地图单元 中的发生率（发生次数），其中 表示案例区域中地质灾害的总数， 表示地图单元 中地质灾害的数量。在方程（2）中， 代表地图单元 中地质灾害的强度，表示灾害体积计算的灾害大小， 表示灾害 的体积。计算后，HFI 或 HII 的值介于 0 和 1 之间，数值越高，灾害频率或强度风险越高。
3.2. Methods of geohazard risk assessment 3.2. 地质灾害风险评估方法
The geohazard risk assessment model uses a mathematical model to calculate the quantitative relationship between geohazards and geohazard formation factors and then speculates on the likelihood of geohazards occurring. The choice of a model is crucial in geohazard risk quantification, as it can lead to different results in the same region. Therefore, we needed to construct different models to find the best model using the scientific model comparison method. 地质灾害风险评估模型利用数学模型计算地质灾害与地质灾害形成因素之间的定量关系，然后推测地质灾害发生的可能性。模型的选择在地质灾害风险量化中至关重要，因为它可能导致同一地区的不同结果。因此，我们需要构建不同的模型，通过科学的模型比较方法找到最佳模型。
The multiple regression model is a classical model used to quantify a relationship between a variable and another variable, which depends on the specific calculation method and theory (Dai and Lee, 2003; Song et al., 2014). In the study of geohazards, a regression model can predict the possibility of geohazard occurrence through the analysis of existing hazard cases. This paper used the spatial autoregressive model (SAR). The spatial lag model (SLM) and the spatial error model (SEM) were chosen for the spatial autoregressive model (SAR). Therefore, two models (SLM and SEM) were used for multiple models to build and compare in this study. These models were built as follows in equations and (4). 多元回归模型是一种经典模型，用于量化一个变量与另一个变量之间的关系，这取决于特定的计算方法和理论（Dai 和 Lee，2003 年；Song 等，2014 年）。在地质灾害研究中，回归模型可以通过分析现有的灾害案例来预测地质灾害发生的可能性。本文采用了空间自回归模型（SAR）。空间滞后模型（SLM）和空间误差模型（SEM）被选择为空间自回归模型（SAR）。因此，在本研究中建立和比较了两个模型（SLM 和 SEM）。这些模型如方程 和（4）所示建立。
SEM : SEM：
While the hazard index is interpreted as variable , natural and artificial factors are interpreted as variable in all models. In all equation, is the coefficient of the independent variables, is subject to the same normal distribution of random variables. In equations (3) and (4), and are the parameters of spatial autocorrelation, is the spatial weight matrix, and are the error terms. SLM and SEM are typical spatial autoregressive models that are more suitable for the spatial interdependence of dependent variables. The basic assumptions of SLM and SEM take into account the autocorrelation effect. In contrast to general regression models, SLM and SEM pay more attention to the nature of mutual influence and constraints, and can consider the coupling effect between different factors at the same time. The difference between SLM and SEM is that the former describes the real correlation, while the latter describes the effects of autocorrelation of random errors (Anselin, 1988; Anselin et al., 2006; Zhang et al., 2009; Song et al., 2014). 尽管危险指数被解释为变量 ，但所有模型中自然和人为因素被解释为变量 。在所有方程中， 是自变量的系数， 服从相同的随机变量正态分布。在方程（3）和（4）中， 和 是空间自相关的参数， 是空间权重矩阵， 和 是误差项。SLM 和 SEM 是更适合于因变量的空间相互依赖性的典型空间自回归模型。SLM 和 SEM 的基本假设考虑了自相关效应。与一般回归模型相比，SLM 和 SEM 更关注相互影响和约束的性质，并可以同时考虑不同因素之间的耦合效应。SLM 和 SEM 之间的区别在于前者描述了真实的相关性，而后者描述了随机误差的自相关效应（Anselin，1988；Anselin 等，2006；Zhang 等，2009；Song 等，2014）。
3.2.2. Multicollinearity diagnosis 3.2.2. 多重共线性诊断
Multicollinearity is a common problem in multivariate regression analysis. The reason why collinearity occurs is due to the existence of an exact correlation or a high degree of correlation between explanatory variables. Collinearity is divided into fully sharp and approximate collinearity. Complete collinearity is rare, and it is often the case that there is some degree of collinearity. There are a number of collinearity diagnostics, such as stepwise regression methods and the analysis of correlations between explanatory variables. The variance inflation factor (VIF) was used in this study (Eq. (5)), which was based on the correlation coefficient ( ) calculation and judgment. 多重共线性是多元回归分析中常见的问题。共线性发生的原因是解释变量之间存在精确相关或高度相关。共线性分为完全尖锐和近似共线性。完全共线性很少见，通常存在一定程度的共线性。有许多共线性诊断方法，如逐步回归方法和解释变量之间的相关性分析。本研究中使用了方差膨胀因子（VIF）（方程（5）），该因子基于相关系数（ ）的计算和判断。
The VIF is the inverse of tolerance and can be used as an indicator of multilinearity, with a larger VIF indicating more collinearity. Specific diagnostic methods are as follows: checking for multicollinearity, linear regression models using the same dependent and explanatory variables should be computed using the SPSS software platform. Collinearity diagnostics can then be generated along with the model operation. Large VIF values are redundant, implying the presence of collinearity. Remove redundant variables from the model. Statistically speaking, there is no multicollinearity when ; when , there is strong multicollinearity; and when the VIF is larger than 100, there is severe multilinearity. VIF 是容忍度的倒数，可用作多重共线性的指标，较大的 VIF 表示更多的共线性。具体的诊断方法如下：检查多重共线性，使用相同的因变量和自变量的线性回归模型应使用 SPSS 软件平台进行计算。然后可以生成共线性诊断以及模型操作。大的 VIF 值是多余的，意味着存在共线性。从模型中删除多余的变量。从统计学角度来看，当 时，不存在多重共线性；当 时，存在强烈的多重共线性；当 VIF 大于 100 时，存在严重的多重共线性。
There are a variety of factors that affect geohazards in this study. It is necessary to eliminate the effect of redundant variables arising from collinearity on the evaluation results. 本研究中有许多因素影响地质灾害。有必要消除由共线性产生的多余变量对评估结果的影响。
3.3. Validation methods for geological hazard risk assessment 地质灾害风险评估的验证方法
3.3.1. Cross validation 3.3.1. 交叉验证
Cross validation (CV) is a statistical analysis method used to verify the performance of classifiers, which is usually used for geohazard susceptibility evolution (Dou et al., 2015; Carrara et al., 1991; Lee, 2005; Erener and Duzgun, 2012). First, the basic idea of CV is to group the data (hazards), which was done in phase 1. Part of the data was regarded as training samples (training set), and the other part of the data was regarded as validation samples (validation set or test set). Then, in learning phase 2, the training set was used to build a multi-model with different hazard metrics, which can quantify the relationship between 交叉验证（CV）是一种用于验证分类器性能的统计分析方法，通常用于地质灾害易感性评估（Dou 等，2015 年；Carrara 等，1991 年；Lee，2005 年；Erener 和 Duzgun，2012 年）。首先，CV 的基本思想是将数据（危险）分组，这是在第 1 阶段完成的。数据的一部分被视为训练样本（训练集），另一部分数据被视为验证样本（验证集或测试集）。然后，在学习第 2 阶段，使用训练集构建具有不同危险度量标准的多模型，可以量化危险和危险形式因素之间的关系
hazard and hazard form factors. 危险和危险形式因素。
The final test set was used to predict geohazards risk with a multimodel approach, which can compare the accuracy of the geohazards susceptibility assessment in the third stage of the study. Common CV methods are the hold-out method, K-fold CV and leave-one-out CV. In this study, the hold-out method was used because the data were not reused or cross-used. However, in this geohazard inventory, of the samples were used as the training set and the remaining were used as the test set. Then, in learning phase 2 , the training set was used to build a multi-model with different hazard metrics to quantify the relationship between hazards and hazard form factors. 最终测试集用于采用多模型方法预测地质灾害风险，可以比较研究第三阶段中地质灾害易感性评估的准确性。常见的 CV 方法有留出法、K 折交叉验证和留一法。在本研究中，采用了留出法，因为数据没有被重复使用或交叉使用。然而，在这个地质灾害清单中， 的样本被用作训练集，剩余的 被用作测试集。然后，在学习阶段 2 中，训练集被用来构建一个多模型，其中包含不同的危险度指标，以量化危险和危险形成因素之间的关系。
3.3.2. Receiver operating characteristic (ROC) and area under curve 3.3.2. 接收者操作特征曲线（ROC）和曲线下面积（AUC）
(AUC) （AUC）
The ROC and AUC are the most commonly used methods for checking the validity of model prediction, and thus are widely used in the evaluation of geological hazards (Oh et al., 2010, Pradhan, 2010; Erener and Duzgun, 2012; Hadji et al., 2013; Ahmed, 2014; Dou et al., 2015; Legorreta Paulin et al., 2016). ROC 和 AUC 是检验模型预测有效性最常用的方法，因此在地质灾害评估中被广泛使用（Oh 等，2010 年；Pradhan，2010 年；Erener 和 Duzgun，2012 年；Hadji 等，2013 年；Ahmed，2014 年；Dou 等，2015 年；Legorreta Paulin 等，2016 年）。
The ROC's main analysis tool is a curve drawn on the twodimensional plane. The abscissa is the false positive rate (FPR), and the ordinate is the true positive rate (TPR). The experimental data of the sample were used to draw points with the predicted value as the coordinates and the actual value as the coordinates. These points can then form a curve that passes through and . The curve was used to determine the degree of consistency between the evaluation results and the true value. Although the ROC curve can intuitively express the model prediction results, no specific indicators are quantified. However, the AUC is often combined with the ROC curves, which are the quantitative indicators of the results of the models' performance. The AUC is the size of the area under the ROC curve. Theoretically, the AUC values ranged from 0.5 to 1 . The size of the AUC value can be the criterion for validity validation. The specific AUC classification and diagnosis results are shown in Table 2. ROC 的主要分析工具是在二维平面上绘制的曲线。横坐标是假阳性率（FPR），纵坐标是真阳性率（TPR）。使用样本的实验数据绘制点，预测值作为 坐标，实际值作为 坐标。这些点可以形成一条曲线，经过 和 。该曲线用于确定评估结果与真实值之间的一致性程度。虽然 ROC 曲线可以直观地表达模型预测结果，但没有具体的量化指标。然而，AUC 常常与 ROC 曲线结合使用，是模型性能结果的定量指标。AUC 是 ROC 曲线下面积的大小。理论上，AUC 值范围从 0.5 到 1。AUC 值的大小可以作为有效性验证的标准。具体的 AUC 分类和诊断结果显示在表 2 中。
In this study, the ROC and AUC were used to compare the accuracy of disaster sensitivity prediction under different geohazard indexes. In the ROC and AUC of this study, the true positive rate was the cumulative percentage of actual geohazards, and the false positive rate was the cumulative percentage of geohazard susceptibility. The SPSS program was used to complete the ROC and AUC in this study. 在这项研究中，ROC 和 AUC 被用来比较不同地质灾害指数下灾害敏感性预测的准确性。在本研究的 ROC 和 AUC 中，真阳性率是实际地质灾害的累积百分比，假阳性率是地质灾害易感性的累积百分比。本研究使用 SPSS 程序完成了 ROC 和 AUC。
4. Results 4. 结果
4.1. Results of hazard index: hazard frequency index (HFI) and hazard intensity index (HII) 4.1. 危险指数的结果：危险频率指数（HFI）和危险强度指数（HII）
The HFI and HII were computed in the case region according to the construction method for different hazard indices. In order to visually compare the HFI and HII results, the original calculated values were normalised. The same manual classification method was also used to display the classification at the same level. The final results are shown in Fig. 4. Comparing the red circles at the same positions in Fig. 4 shows that the location of the HFI high value is not necessarily the location of the HII high value. This indicates that regions with high geohazard frequency are not necessarily regions with high geohazard intensity. There is no one-to-one correspondence between HFI and HII at present. 根据不同的危险指数计算方法，在案例区域计算了 HFI 和 HII。为了直观比较 HFI 和 HII 的结果，对原始计算值进行了归一化处理。相同的手动分类方法也用于显示相同级别的分类。最终结果显示在图 4 中。比较图 4 中相同位置的红色圆圈表明，HFI 高值的位置不一定是 HII 高值的位置。这表明高地质灾害频率区域不一定是高地质灾害强度区域。目前 HFI 和 HII 之间没有一一对应关系。
Table 2 表 2
AUC for validity validation. 用于有效性验证的 AUC。
AUC value
Diagnostics
Low
Medium
0.9
High
4.2. Results of multicollinearity diagnosis 4.2. 多重共线性诊断结果
Fourteen factors were selected for this study to be considered as the elements involved in the assessment of hazard risk from geohazards. The analysis of multicollinearity diagnostics was done using SPSS software. Specific diagnostic results appear in Fig. 5. The value of VIF varies among factors, with a maximum of 2.276 , a minimum of 1.016 and an average of 1.435 . However, the VIF of all factors is below 10 and there is no multicollinearity in the theory. This means that all factors can be included in the subsequent model assessment of the susceptibility of the geohazards and cannot affect the results of the model calculation. 本研究选取了十四个因素作为评估地质灾害危险风险的元素。使用 SPSS 软件进行了多重共线性诊断分析。具体诊断结果见图 5。VIF 的值在各因素之间变化，最大值为 2.276，最小值为 1.016，平均值为 1.435。然而，所有因素的 VIF 均低于 10，在理论上不存在多重共线性。这意味着所有因素可以纳入地质灾害易感性后续模型评估中，并且不会影响模型计算结果。
4.3. Results of multiple regression model construction and operation 4.3. 多元回归模型构建和运行结果
According to the grouping ratio of 7:3 in , there were 222 geohazards (2323 analysis units) in the final training group and 95 geohazards (1123 analysis units) in the test group. The training group has been used to build and run multiple regression models, which is located in the south of the case area. Based on the results of the training group, data from the test group were then applied for geological hazard risk assessment validation. Fig. 6 shows the results of the multiple regression models based on the HFI in the test group. The SLM model is on the left and the SEM is on the right. Also depicted in Fig. 7 are the results of multiple regression models on the HII for geohazards, while the SLM model run results appear on the left and the SEM results appear on the right. In order to better compare the differences between different geological hazard risk assessment models, the results of multiple regression model construction and operation are shown in the same classification. The results show that not only the HFI- and HII-based evaluation models significant differences, but also the SLM and SEM models are completely different. 根据 中 7:3 的分组比例，最终训练组中有 222 个地质灾害（2323 个分析单元），测试组中有 95 个地质灾害（1123 个分析单元）。训练组已用于构建和运行多元回归模型，该模型位于案例区域的南部。根据训练组的结果，随后应用了来自测试组的数据进行地质灾害风险评估验证。图 6 显示了基于测试组 HFI 的多元回归模型的结果。SLM 模型位于左侧，SEM 模型位于右侧。图 7 还显示了基于地质灾害 HII 的多元回归模型的结果，SLM 模型运行结果显示在左侧，SEM 模型结果显示在右侧。为了更好地比较不同地质灾害风险评估模型之间的差异，展示了多元回归模型构建和运行结果的相同分类。结果表明，不仅基于 HFI 和 HII 的评估模型存在显著差异，而且 SLM 和 SEM 模型也完全不同。
4.4. Results of validation 4.4. 验证结果
To compare the accuracy of different hazard metrics and the effectiveness of different hazard assessment models, the ROC and AUC results were calculated as follows. Fig. 8 and Table 3 show the validation results of the geohazard evaluation results for different hazard indices. In the left panel of Fig. 8, the ROC curve of the SLM simulation is closer to the Y-axis than to the SEM curve under the HFI. The same happens for the HII-based ROC in the right panel of Fig. 8. The front row of Table 3 shows the AUC values for the SLM and SEM simulations with HFI at 0.829 and 0.789 , respectively. The behind row of Table 3 also depicts the AUC values for the SLM and SEM simulations, with HII at 0.730 and 0.714 , respectively. 为了比较不同危险指标的准确性和不同危险评估模型的有效性，计算了 ROC 和 AUC 结果如下。图 8 和表 3 显示了不同危险指标的地质灾害评估结果的验证结果。在图 8 的左侧面板中，SLM 模拟的 ROC 曲线比 HFI 下的 SEM 曲线更靠近 Y 轴。在图 8 的右侧面板中，基于 HII 的 ROC 也是如此。表 3 的前排显示了 HFI 下 SLM 和 SEM 模拟的 AUC 值分别为 0.829 和 0.789。表 3 的后排还显示了 HII 下 SLM 和 SEM 模拟的 AUC 值分别为 0.730 和 0.714。
These results point to two conclusions. First, regardless of HFI or HII, the results of the hazard assessment are relatively accurate from a statistical point of view, with the AUC values greater than 0.700 . Second, the operation results of the SLM model were stronger than those of the SEM model in the validation of the geological hazard sensitivity assessment results. It was demonstrated that the validation value of the AUC in the SLM model was larger than the SEM under HFI and HII. 这些结果得出两个结论。首先，无论是 HFI 还是 HII，从统计角度来看，危险评估的结果相对准确，AUC 值大于 0.700。其次，在地质灾害敏感性评估结果验证中，SLM 模型的操作结果比 SEM 模型强。结果表明，在 HFI 和 HII 下，SLM 模型的 AUC 验证值大于 SEM。
4.5. Results of the geohazard risk assessment under HFI and HII 4.5. HFI 和 HII 下地质灾害风险评估结果
To accurately compare the geohazard risk of the two types of indexes, the risk assessment values of HFI and HII were normalised and divided into the same classification. Figs. 9 and 10 show the final five geohazard risk zones in the case region, and there are obvious spatial differences between the high-frequency area and high-intensity area of geohazards. 为了准确比较两种指数的地质灾害风险，HFI 和 HII 的风险评估值被归一化并划分为相同的分类。图 9 和图 10 显示了案例区域最终的五个地质灾害风险区，高频区和高强度区的地质灾害之间存在明显的空间差异。
The left panel of Figs. 9 and 10, based on HFI, depicts the possibility of geohazards in the case region in terms of the hazard frequency. Specifically, the highest- and high-risk areas are concentrated in the east-west trend of Songbai Town, the north-south trend of Songluo Town, the north-south trend of Honghuoping Town and parts of Muyu 根据 HFI，图 9 和图 10 的左侧面板描述了在危险频率方面可能发生地质灾害的可能性。具体来说，最高风险和高风险区域集中在松柏镇的东西走向、松罗镇的南北走向、红火坪镇的南北走向以及木鱼的部分地区
Fig. 4. Display image of different hazard index, (left) HFI, (right) HII. 图 4. 显示不同危险指数的图像，（左）HFI，（右）HII。
Fig. 5. The expansion coefficient results of the evaluation factors. 图 5. 评价因素的扩展系数结果。
Fig. 6. The results of the regression model in the test group based on HFI, (left) SLM, (right) SEM. 图 6. 基于 HFI 的测试组回归模型结果，（左）SLM，（右）SEM。
Fig. 7. The results of the regression model in the test group based on HII, (left) SLM, (right) SEM. 图 7. 基于 HII 的测试组回归模型结果，（左）SLM，（右）SEM。
Fig. 8. The results of the ROC based on different hazard sensitivity indexes, (left) HFI, (right) HII. 图 8. 基于不同危险敏感性指数的 ROC 结果，（左）HFI，（右）HII。
Table 3 表 3
The results of the AUC based on different hazard sensitivity indexes. 基于不同危险敏感性指数的 AUC 结果。
Test Result
Variable(s)
Area
Std.
Error
Asymptotic
Sig.
Asymptotic 95% 渐近 95%
Confidence Interval 置信区间
Lower
Bound
Upper
Bound
HFI SLM1
0.829
0.022
0.000
0.786
0.872
HFI SEM1
0.789
0.026
0.000
0.738
0.841
HII SLM2
0.775
0.027
0.000
0.721
0.828
HII SEM2
0.600
0.037
0.001
0.528
0.671
Under the nonparametric assumption. 在非参数假设下 。
Null hypothesis: True area . 零假设：真实面积为 。
Town and Dajiu Lake Town, which account for and , respectively. The areas dominated by moderate risk are distributed along the highest-and high-risk areas, which account for . Meanwhile, the areas with low and the lowest risk across the entire region accounted for of the total. Moreover, the geohazard risk assessment of the HFI shows obvious spatial agglomeration and spatial autocorrelation.
The HII-based geohazard risk prediction results appear in the right panel of Figs. 9 and 10. This reflects the possibility of geohazards in the case region in terms of the hazard intensity. Specifically, the highest-risk and high-risk areas are mainly concentrated in the town of Songbai, while the remaining areas are scattered in the towns of Muyu, Dajiu Lake and Songluo. The areas dominated by moderate, low and lowest risk are distributed across all regions, which also show some spatial agglomeration and spatial autocorrelation. Of the study region as a whole, the areas from highest risk to lowest risk account for , and , respectively. Therefore, the high-intensity and high-frequency of the hazard risk area are not in complete agreement.
5. Discussion
5.1. Implications of the hazard index 5.1. 危险指数的含义
The hazard index is a quantitative description and expression of the likelihood of a hazard in a region, which is an important ingredient for hazard prediction. In previous studies, the frequency of geohazards has been the focus of attention, and its intensity is also critical information for a disaster. Therefore, the construction of various hazard indexes is helpful in identifying comprehensive geohazard risk characteristics. In this study, two types of hazard indices were proposed. The HFI was constructed from the hazard frequency at different spatial locations based on existing studies, while the HII focused on the intensity of the hazards. The results show that both HFI and HII can be accurately and efficiently predicted, with significant differences between highfrequency and high-intensity regions. 危险指数是对某一地区危险发生可能性的定量描述和表达，是灾害预测的重要组成部分。在先前的研究中，地质灾害的频率一直是关注的焦点，其强度也是灾害的关键信息。因此，构建各种危险指数有助于识别综合地质灾害风险特征。在本研究中，提出了两种类型的危险指数。HFI 是根据现有研究基于不同空间位置的危险频率构建的，而 HII 侧重于危险的强度。结果表明，HFI 和 HII 都可以被准确高效地预测，高频率和高强度地区之间存在显著差异。
We then took different disaster prevention measures in highfrequency risk areas and high-intensity risk areas. The construction of different disaster indexes can improve the accuracy and effectiveness of disaster prevention and control. Therefore, it is of great interest to construct different hazard indices that can help identify the different hazard properties of the area. At the same time, the two index construction methods (HFI and HII) have universal applicability and are also effective outside the case area. However, it is difficult to collect accurate hazard size data in reality, and data reliability is difficult to guarantee. The construction of a hazard index still motivates the study of geohazard risk assessment in mountainous areas. 然后，我们在高频风险区和高强度风险区采取了不同的灾害预防措施。不同灾害指数的构建可以提高灾害预防和控制的准确性和有效性。因此，构建不同的危险指数对帮助识别该地区的不同危险特性具有极大的意义。同时，两种指数构建方法（HFI 和 HII）具有普适性，也在案例区域之外具有有效性。然而，在现实中收集准确的危险规模数据是困难的，数据可靠性也难以保证。危险指数的构建仍然推动了山地地区地质灾害风险评估的研究。
5.2. Implications of the regression model comparison and the evaluation factor 5.2.回归模型比较和评估因素的含义
In the existing research, the general regression model pays more attention to the analysis of disaster-causing factors, and the coupling effect of diversified natural elements on geohazards. However, the evaluation model of this study also emphasizes the spatial autocorrelation characteristics of geohazards compare with the general regression model, and explores the coupling effect of human factors and natural factors in the geohazard mechanism. Therefore, additional discussion on the generalizability of the geohazard risk assessment model and the evaluation factors in the case region is required. 在现有研究中，一般回归模型更加关注灾害因素的分析，以及多样化自然要素对地质灾害的耦合效应。然而，本研究的评估模型也强调了与一般回归模型相比地质灾害的空间自相关特征，并探讨了人为因素和自然因素在地质灾害机制中的耦合效应。因此，需要进一步讨论地质灾害风险评估模型的普适性以及案例区域中的评估因素。
First, it can be confirmed that the overall procedure for constructing and comparing logical hazard assessment models in this paper is general and applicable to regions beyond the case region. Moreover the SAR model in this study is highly effective in risk prediction for geohazards, whether the prediction of geohazards frequency or the geohazards intensity. Additionally, in existing studies, some scholars use other methods, logistic regression model and spatial regression model to draw similar conclusions in the same case area, which could also support the reliability of this research findings (Zou, F. et al., 2022, Q. M. Zhan W et al., 2016). However, whether SLM or SEM can explain geohazards more strongly needs to be scientifically addressed. For example, SLM may be more appropriate than SEM in areas similar to the case region in terms of physical geography and economic development levels. The final conclusions need to be determined based on the actual findings. 首先，可以确认本文中构建和比较逻辑危险评估模型的整体程序是通用的，并适用于超出案例区域的地区。此外，本研究中的 SAR 模型在地质灾害风险预测方面非常有效，无论是地质灾害频率的预测还是地质灾害强度。此外，在现有研究中，一些学者使用其他方法，如逻辑回归模型和空间回归模型，在同一案例区域得出类似结论，这也可以支持本研究结果的可靠性（邹 F.等，2022 年，詹 W.等，2016 年）。然而，SLM 或 SEM 是否能更强有力地解释地质灾害需要进行科学论证。例如，在地理和经济发展水平类似于案例区域的地区，SLM 可能比 SEM 更合适。最终结论需要根据实际发现来确定。
Second, human activities should be included in the selection of 其次，人类活动应纳入选择中
Fig. 10. Cartogram of geohazard risk assessment with different hazard risk indexes. 图 10. 不同危险风险指数的地质灾害风险评估分级图。
Fig. 9. Zoning map of geohazard risk assessment, (left) HFI, (right) HII. 图 9. 地质灾害风险评估分区图，（左）HFI，（右）HII。
geohazard impact factors. This conclusion is equally general and scientific. However, the factors specific to Human should take into account the actual situation of the region, such as the progress of urbanisation and the characteristics of the construction of the project. The four human factor indicators selected in this study are not necessarily applicable in all regions. Overall, the flow of methods established in the study has a high degree of generality, but specific conclusions need to be treated differently in different regions. 地质灾害影响因素。这个结论同样具有普遍性和科学性。然而，应考虑到人类特定的因素，如城市化进程和项目建设特点等，这些因素应考虑到该地区的实际情况。本研究选取的四个人类因素指标并不一定适用于所有地区。总体而言，研究中建立的方法流程具有很高的普适性，但具体结论在不同地区需要有所区别对待。
5.3. Implications of the geohazard risk assessment results 5.3. 地质灾害风险评估结果的意义
It is worth discussing and explaining the aspects of frequency and intensity of the final geohazard risk evaluation results under HFI and HII in the case region. On one hand, the display of hazard risk assessment maps is different due to different cartographic classifications and grading methods. Therefore, when hazard assessment results are presented in the form of a partition map, the number and mode of classification should be determined according to the needs of different management departments for practical guidance. However, the evaluation results for geodesic hazards are specific values that belong to a continuous variable. These can reflect the actual situation of hazard assessment in this area, which is significant. In addition, the scale of analysis unit of risk assessment will also have an impact on the evaluation results. The size of the map unit in this study is determined by considering the autocorrelation characteristics of the factors and the accuracy of the existing data. This has also been confirmed by similar research of some scholars (Zou et al., 2018, Zou, F. et al., 2022). 值得讨论和解释在案例区域中，在 HFI 和 HII 下最终地质灾害风险评估结果的频率和强度方面。一方面，由于不同的制图分类和分级方法，灾害风险评估图的显示是不同的。因此，当灾害评估结果以分区图的形式呈现时，分类的数量和模式应根据不同管理部门的需求确定，以提供实际指导。然而，地质灾害的评估结果是属于连续变量的具体数值。这些数值可以反映该地区灾害评估的实际情况，具有重要意义。此外，风险评估的分析单元的规模也会影响评估结果。本研究中的地图单元大小是通过考虑因素的自相关特性和现有数据的准确性来确定的。这也得到了一些学者类似研究的证实（邹等，2018 年，邹等，2022 年）。
On the other hand, hazard assessment zoning maps for HFI and HII were generated by studying historical cases to predict future development laws. The degree of accuracy of "case historical data" directly determines the degree of accuracy of "prediction". In other words, regardless of the method of display, geohazard evaluation results and case data are highly correlated. Therefore, geohazard evaluation results are affected by the accuracy of the case data and the equilibration of the case sampling. 另一方面，通过研究历史案例来预测未来发展规律，生成了 HFI 和 HII 的危险评估分区图。"案例历史数据"的准确度直接决定了"预测"的准确度。换句话说，无论显示方法如何，地质灾害评估结果和案例数据高度相关。因此，地质灾害评估结果受案例数据的准确性和案例采样的均衡性影响。
6. Conclusions 6. 结论
In this study, two types of hazard indices play an important role in this study, which not only scientifically described the location of the frequency of geohazards, but also included the intensity of geohazards. Moreover the geohazard risk assessment results show that the spatial distribution of these two types of disaster attributes is obviously inconsistent and cannot replace each other. Therefore, the most important contribution of this study is to quantitatively describe the intensity of geohazards, which improves the comprehensiveness of geohazard risk assessment. On the other hand, the model validation results again suggest that the spatial autocorrelation characteristics of geohazards and the coupling effect of human factors based natural factors should not been overlooked in the interpretation of geohazards in this case. 在这项研究中，两种类型的危险指数在研究中起着重要作用，不仅科学描述了地质灾害频率的位置，还包括地质灾害的强度。此外，地质灾害风险评估结果显示，这两种灾害属性的空间分布明显不一致，不能相互替代。因此，这项研究最重要的贡献是定量描述地质灾害的强度，提高了地质灾害风险评估的全面性。另一方面，模型验证结果再次表明，在解释本案例中的地质灾害时，不应忽视地质灾害的空间自相关特征和基于自然因素的人为因素的耦合效应。
Nonetheless, this study has the following limitations. First, limitations in the accuracy and completeness of the data may affect the accuracy of the hazard risk assessment results. The implications are clear. For example, for the intensity attribute of geohazards in HII, the determination of its size is different in different recording periods, and there will be some error in its absolute value. Therefore, more methods should be used to improve the accuracy of the data and to reduce errors in the future.Second, this study focused on the spatial distribution of hazard formation, and only a basic statistical analysis was performed for the temporal part. However, the formation of geohazards has distinct temporal and spatial features. Therefore, follow-up studies should focus more on spatiotemporal-dynamic research methods. For example, a spatiotemporal series model was chosen and applied to geohazard evaluation. 然而，这项研究存在以下局限性。首先，数据的准确性和完整性方面的限制可能会影响灾害风险评估结果的准确性。这带来的影响是明显的。例如，在 HII 中的地质灾害强度属性，其大小在不同记录期间的确定是不同的，其绝对值会存在一定误差。因此，应该采用更多方法来提高数据的准确性，并在未来减少错误。其次，这项研究侧重于灾害形成的空间分布，对于时间部分只进行了基本的统计分析。然而，地质灾害的形成具有明显的时间和空间特征。因此，后续研究应更多关注时空动态研究方法。例如，选择并应用时空序列模型进行地质灾害评估。
Although this study has some shortcomings, it is still able to enrich the existing literature. It not only considers the intensity characteristics of geohazards to improve our comprehensive understanding of hazard risk but also considers the spatial autocorrelation characteristics of hazards to improve the accuracy of hazard risk assessment. In general, these new research frameworks and findings of this study are devoted to the environmental safety and improvement of regional sustainable development via the comprehensive geohazard risk management. 尽管这项研究存在一些缺点，但仍能丰富现有文献。它不仅考虑了地质灾害的强度特征，以提高我们对灾害风险的综合理解，还考虑了灾害的空间自相关特征，以提高灾害风险评估的准确性。总的来说，这项研究的新研究框架和发现致力于通过综合地质灾害风险管理来促进环境安全和区域可持续发展的改善。
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. 作者声明他们没有已知的竞争性财务利益或个人关系，可能会影响本文报告的工作。
Data availability 数据可用性
The data that has been used is confidential. 使用的数据是机密的。
Acknowledgements and Funding 致谢和资助
We would like to express our respects and gratitude to the anonymous reviewers and editors for their professional comments and suggestions. The work was supported by the Hunan Social Science Research Project [grant number 22YBA093], the Research project of Hunan Natural Resources Department [grant number 20230116DZ]. 我们要向匿名审稿人和编辑表示敬意和感激，感谢他们的专业意见和建议。该工作得到了湖南社会科学研究项目的支持[资助号 22YBA093]，湖南自然资源厅研究项目的支持[资助号 20230116DZ]。
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