Global warming has led to increased compound hazards, and an accurate risk assessment of such hazards is of great importance to urban emergency management. Due to the interrelations between multiple hazards, the risk assessment of a compound hazard faces several challenges: (1) the evaluation of hazard level needs to consider the correlations between compound hazard drivers, (2) usually only a small number of data samples are available for estimating the joint probability distribution of the compound hazard drivers and the loss caused by the hazards, and (3) the risk assessment process often ignores the temporal dynamics of compound hazard occurrences. This paper aims to address the mentioned challenges and develop an integrated risk assessment model VFS–IEM–IDM to quantify the dynamic risk of compound hazards based on variable fuzzy set theory (VFS), information entropy method (IEM), and information diffusion method (IDM). For the first challenge, VFS–IEM–IDM measures the effect of the compound hazard drivers via the use of relative membership degree and analyses the correlation between drivers with the entropy weight method, which is combined to evaluate compound hazard level. To address the second challenge, VFS–IEM–IDM applies the normal diffusion function to estimate the probability distribution of the compound hazard and the corresponding loss vulnerability curve. To deal with the third challenge, VFS–IEM–IDM assesses the risk of a compound hazard in different months based on the definition of probabilistic risk. In the end, this paper takes the typhoon–rainstorm disaster in Shenzhen, China, as an example to evaluate the effectiveness of the proposed VFS–IEM–IDM model. The results show that VFS–IEM–IDM effectively estimates the typhoon–rainstorm compound hazard level and assesses the dynamic risk of the compound hazards.

With global climate change, many cities have suffered extreme natural hazards more frequently

The risk of a hazard is defined as the potential consequences brought by the disaster and can be quantified by the probability of losses

There are many research works discussing the risk assessment of multi-hazards. They classify the relationship between the individual hazards in the scenarios of multi-hazards into three categories: mutually amplified hazards, mutually exclusive hazards, and non-influential stakes

Compound hazards, a sub-group of “multi-hazards”, are considered as the combination of multiple hazard drivers that contribute to societal or environmental risks. The characteristics of compound hazards include (1) two or more extreme events occurring simultaneously or successively, (2) combinations of extreme events with underlying conditions that amplify the impact, and (3) combinations of events that are not themselves extreme but lead to an extreme event or impact when combined

While there have been many attempts to assess the risk of multi-hazards, most of the existing methods have limitations in dealing with compound hazards

To address the first limitation, researchers have applied variable fuzzy set (VFS) methods to deal with the multi-factor problem. Some researchers have shown that the relative membership function can be used to evaluate the relations between multiple indicators in risk assessment

To deal with the second limitation, the information diffusion method (IDM) is commonly used to model the physical relationship between different attributes. In many cases, it is challenging to collect compound hazard data, and the historical data are often sparse. To this end, many fuzzy probabilistic models have been proposed to enhance the accuracy of the risk assessment results

As for the third limitation, preliminary attempts have been made to develop quantitative multi-hazard risk assessment frameworks

The main contributions of this paper are summarized as follows.

We propose a model named variable fuzzy set and information diffusion (VFS–IEM–IDM) to assess the dynamic risk of compound hazards, which takes into account the interrelations between the hazard drivers, deals with the problem of data sparsity, and considers the temporal dynamics of the occurrences of the compound hazards.

We simplify the procedures of calculating relative membership degree to improve the efficiency of compound hazard level evaluation, and we also use a predictive cumulative logistic model to verify the evaluation results.

To examine the efficacy of the proposed model VFS–IEM–IDM, a case study of the typhoon–rainstorm hazards in Shenzhen, China, is presented.

From the previous studies, risks could be classified into four categories: pseudo-risk, probability risk, fuzzy risk, and uncertainty risk

Though these four types of risks have been investigated by many researchers, there are few studies on dynamic compound hazard risk. In this paper,

Workflow of the VFS–IEM–IDM dynamic compound hazard risk assessment model for typhoon–rainstorm hazards. Based on the historical records of typhoon–rainstorm hazards, our proposal provides two-part procedures: firstly, an enhanced implementation of the compound hazard level evaluation is proposed to assess the typhoon–rainstorm hazard level; and then the probability distribution and the corresponding loss vulnerability curve of typhoon–rainstorm are estimated to calculate the dynamic hazard risk. We use the black rectangle to denote different calculation modules and use the blue one to represent the results obtained by the VFS–IEM–IDM model.

Risk assessment of compound hazards should consider the correlation between the compound hazard drivers, the problem of data sparsity, and the dynamic property of hazard occurrences. This section proposes VFS–IEM–IDM, a risk assessment model for compound hazards, which combines the variable fuzzy set theory with the information diffusion method to assess the dynamic risk of compound hazards when only a small set of data samples is available. Our proposal mainly consists of two components: with individual hazard level and historical records of hazard drivers as inputs, the first component VFS–IEM combines variable fuzzy set methods with information entropy methods to provide a comprehensive evaluation of the compound hazard level (Sect. 3.1). Based on the compound hazard levels and historical records of risk assessment attributes, the second component IDM adapts normal information diffusion methods to quantify the dynamic risk of the compound hazards in terms of the direct economic losses (Sect. 3.2). Figure

For the compound hazard risk assessment, the correlation between the compound hazard drivers should be considered. Fortunately, the variable fuzzy set (VFS) theory which considers the contributions of multiple related drivers and decreases the fuzziness by using membership functions

Lowest case: the position between

Based on VFS, the fuzzy set intervals given by the individual hazard level classification can be used to assess the compound hazard level. For example, suppose we have two fuzzy set intervals

It can be seen that RMD is influenced by the hyper-parameter

Highest case: the position between

Middle case: the position between

VFS–IEM compound hazard level evaluation.

The compound hazard driver fuzzy set

Individual hazard level assessment matrix,

Comprehensive value of compound hazard level.

Identification of interval

Define the balance boundaries matrix

Calculate the weight of each driver

Calculate RMD

Calculate RMD

Calculate RMD

The relative membership matrix of each sample is denoted as

Combine

Following the previous works by

To assess the dynamic risk of compound hazards, especially when the data sets are sparse, the information diffusion method (IDM) which belongs to the fuzzy theory can be used to extract useful underlying information from the limited data samples to estimate the probability function

Similarly, we can calculate the three-dimensional diffusion function for the compound hazard attributes set

Based on the VFS–IEM–IDM risk assessment model, the dynamic compound hazard risk (direct economic losses) can be obtained via Eq. (

In this section, we evaluate VFS–IEM–IDM with a case study of typhoon–rainstorm compound hazards that occurred in Shenzhen, China. Shenzhen is located on the east bank of the Zhujiang River (also known as the Pearl River) and is surrounded by Daya Bay and Dapeng Bay, where the climate is subtropical and maritime. Typhoons and rainstorms are the most frequently occurring hazards in Shenzhen. According to the collected data, as shown in Table

Classification standards of individual hazard level.

IDM dynamic risk assessment model.

Compound hazard data samples

Coefficients of diffusion function

Dynamic compound hazard risk.

Compound hazard level evaluation by Algorithm

Monitor space of different attributes

Construct normal information diffusion functions based on the universes of monitor space and Eq. (

Estimate the joint and conditional probability distribution based on Eqs. (

Determine the fuzzy cause relationship based on Eq. (

Derive the dynamic risk (direct economic loss) of compound hazards by Eq. (

The typhoon–rainstorm compound hazards are usually characterized by three drivers, i.e., maximum daily precipitation (MDP), extreme wind intensity (EWI), and landing location. To better measure the impact of typhoon landing on the typhoon–rainstorm compound hazard level, the landing location is converted into transformed location number (TLN) via circle distance calculation, where the large value represents that the typhoon landing in Shenzhen is closer. Based on the data provided by the Meteorological Bureau of Shenzhen Municipality (

Based on the segmentation of the four individual hazard levels, we also classify the typhoon–rainstorm compound hazards into four levels, i.e., I, II, III, and IV, where a higher compound hazard level indicates the corresponding compound hazard is of greater severity. As described in Sect. 3.1, the VFS–IEM compound hazard level evaluation model (Algorithm

The relative membership degree is determined by the individual hazard level classifications. According to the value segmentation shown in Table

To derive the compound hazard level, the information entropy method is used to obtain the weight of each hazard driver. We have the weight

Based on the VFS–IEM compound hazard level evaluation model (Algorithm

Transformed typhoon–rainstorm hazard data sets in Shenzhen.

Based on the data in Table

Following Algorithm

From the results above, it can be seen that the typhoon and rainstorm with hazard level III occur more frequently, and they are most likely to occur in August and September. Furthermore, the vulnerability distribution

It can be seen that most of the economic losses caused by the typhoon–rainstorm hazards are concentrated in August and September. Dynamic compound hazard risks can be quantified as the expected value of the damages caused by the compound hazards, and the result is

The proposed VFS–IEM–IDM model provides a comprehensive evaluation of the compound hazard level, but the relationship between the hazard level and the hazard drivers is unclear. To find more information from the results of the compound hazard level evaluation model, we build a predictive model (shown in Eq.

Since the compound hazard level

One advantage of using the information diffusion method to assess the risk of compound hazards is that it does not need to know the type of distribution from which the given samples are drawn and the function form of the causal relationship, which are constructed by the joint probability distribution and the vulnerability distribution. More importantly, it can provide a more accurate evaluation when the compound hazard data set is sparse. The performance of the IDM estimation procedure has been well studied in the literature. For example,

For the dynamic risk assessment of typhoon–rainstorm hazards, this paper proposes a hybrid model VFS–IEM–IDM and provides extensive assessment results based on a case study. The results of the VFS–IEM evaluation model show that the probability of type II and III hazard levels is the highest in Shenzhen, so the emergency management department should prepare more effective emergency plans to reduce secondary hazards. The dynamic risk assessment model IDM shows that the hazard occurrence probability of different hazard levels is different, and hazard level II and III are most likely to occur in August and September. Furthermore, considering the occurrence of the hazards with different hazard levels for each month, the probability of hazard level I occurring in June and July is the highest. Hazard level II mainly happens in August and October, and hazard level III is most likely to occur in September. From the perspective of hazard losses, the difference between the direct economic losses caused by the typhoons and rainstorms of the same hazard level each month indicates that the impacts of the typhoon–rainstorm hazards on the economy are not the same. Besides, the influence of economic losses decreases when the compound hazard level rises, which indicates that the capacity of typhoon–rainstorm hazard resistance in Shenzhen is reliable, and the ability to cope with sudden compound hazards is relatively strong under the existing emergency management system. The dynamic compound hazard risk of the typhoon–rainstorm hazards in Shenzhen shows that the compound hazard risk in each month is different, and the highest risk appears in August and September. On average, the typhoon–rainstorm hazards brought Shenzhen RMB 114 million and RMB 167 million in losses in these two months, respectively, which is in line with the actual situation.

Compound hazard risk assessment is a complex multi-criteria problem and is crucial to the success of strategic decision-making in emergency management. Traditional statistical methods are often inaccurate when only a small set of data samples is available. Few studies discuss the correlations of compound hazard drivers and consider the dynamics of the occurrences of the compound hazards. In this paper, we first present the definition of dynamic compound hazard risk and then propose the variable fuzzy set (VFS) and information entropy method (IEM) model to evaluate the compound hazard level by considering the correlations of different hazard drivers. Based on the results obtained by VFS–IEM, we apply the information diffusion method (IDM) to estimate the compound hazard probability and vulnerability distribution with the hazard occurrence time and the corresponding losses. Then the dynamic risk is calculated by the probabilistic model.

There are mainly three aspects of innovations in this paper. Firstly, based on the definition of compound hazard risk, we consider the temporal dynamics and introduce the concept of dynamic compound hazard risk. Secondly, considering that compound hazards have many drivers for the hazard level evaluation, a hybrid model of variable fuzzy sets and the information entropy method has been proposed to improve the accuracy of compound hazard level evaluation. Thirdly, according to the concept of dynamic compound hazard risk, we apply the information diffusion method to estimate the hazard probability and the vulnerability distribution. The proposed model VFS–IEM–IDM can be used to deal with the problem of data sparsity in dynamic compound hazard risk assessment. We quantify the dynamic typhoon–rainstorm risk by evaluating the expected value of the conditional probability distribution and the vulnerability distribution. Furthermore, VFS–IEM–IDM can be extended to other compound hazards in urban cities, such as flooding. As a case study, we show that the occurrences of the typhoon–rainstorm risks bring Shenzhen RMB 114 million and RMB 167 million in losses in August and September, respectively.

Dynamic risk assessment is a relatively new topic, and many issues need further improvement. In this paper, the weights of different hazard drivers are subjective, and the results of the vulnerability curve have not considered the development of the affected areas. There are also some subjective issues regarding the processing of the data sets. We will explore techniques to deal with these issues and improve assessment accuracy in future work.

For the typhoon–rainstorm dynamic compound hazard risk assessment, the useful data sets were collected from the Meteorological Bureau of Shenzhen Municipality (

Data sets of typhoon–rainstorm hazards in Shenzhen.

Based on the VFS–IEM model, this paper takes the average of

Comprehensive compound hazard level in Shenzhen.

The data and code used in the study are available at

WG and LY conceived the research framework and developed the methodology. WG was responsible for the code compilation, data analysis, and graphic visualization. WG and JJ wrote the first draft. LY managed the implementation of the research activities and revised the manuscript. All the authors discussed the results and contributed to the final version of the paper.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the special issue “Advances in flood forecasting and early warning”. It is not associated with a conference.

This work was mainly supported by the National Key Research and Development Program of China (grant nos. 2019YFC0810705 and 2018YFC0807000) and the National Natural Science Foundation of China (grant no. 71771113). The authors would like to acknowledge Shuanghua Yang and Manyu Meng of the Southern University of Science and Technology for providing useful information.

This research has been supported by the National Key Research and Development Program of China (grant nos. 2019YFC0810705 and 2018YFC0807000) and the National Natural Science Foundation of China (grant no. 71771113).

This paper was edited by Jie Yin and reviewed by three anonymous referees.