1 Introduction

Climate change is causing more frequent and intense natural disasters such as storms, heat waves, and wildfires, and economic losses are also growing as more people build in disaster-prone areas. According to the disaster database of the centre for research on the epidemiology of disasters (CRED), which offers essential core data on the occurrence and effects of disasters worldwide, 16,513 natural disasters occurred from 1900 to 2022, resulting in 8.5 billion victims and economic damage of up to USD 66.96 trillion. While there have been lot of natural disaster research (Kwak et al. 2014; Kim et al. 2015, 2019; Parinussa et al. 2016; Choi et al. 2018; Ran et al. 2018; Dissanayaka et al. 2022; Han et al. 2022; Marengo et al. 2022), most studies assume that each natural disaster is independent of others. This assumption is problematic as it underestimates natural disaster risk by ignoring the interaction between them (Zscheischler et al. 2018).

To solve this problem, the concept of compound natural disaster (CND) was proposed by the report of the IPCC (Field et al. 2012). The report defined CNDs as follows: (1) two or more extreme events occurring simultaneously or successively, (2) combinations of extreme events with underlying conditions that amplify the impact of events, or (3) combinations of events that are not themselves extremes but lead to extreme events or impact when combined. Thereafter, many scholars have also sought to define CND (Minquan and Michael 2014; Leonard et al. 2014; Kumasaki et al. 2016; Pescaroli and Alexander 2018; Zscheischler et al. 2018, 2020; Gissing et al. 2022). The definitions of CND have three common features: (1) a combination of two or more drivers or natural disasters (ex, rainfall, typhoon, and so on), (2) natural disasters occurring simultaneously or successively, and (3) an interaction or combination between drivers, and natural disasters. A representative case is the Great East Japan (Tohoku) earthquake, the strongest earthquake of magnitude 9.0 in its recorded history that struck the eastern coastal area of Japan on 11 March 2011, resulting in 38 m tsunami waves, and widespread damage and destruction. The tsunami waves caused massive destruction along 450 km of coastline, which had 19,846 deaths, with economic losses of approximately USD 210 billion (World Bank 2012). Other examples of CNDs include three consecutive hurricanes named Harvey, Maria, and Ima of 2017 in the United States, and the 2019–2020 Australian bushfires.

Many studies on CND have attempted to define the CND and its elements and to identify actual cases of CNDs (Eisner 2014; Pescaroli, and Alexander, 2018; Cutter 2018; Catto and Dowdy 2021). Minquan and Michael (2014) proposed a typological framework for defining compounding processes that shows how the first event directly causes or impacts the second event. Zscheischler et al. (2018) suggested four elements of modulator, driver, hazard, and impact for CND and analyzed cases based on them. They expressed each case of a CND using these elements and classified them into four categories: preconditioned, multivariate, temporally compounding, and spatially compounding events. However, the problem with these approaches is that they are greatly influenced by the researcher’s judgment. To solve this problem, Gissing et al. (2022) suggested a method for identifying CNDs based on the time window between natural disasters. They defined CND as two or more natural disaster events that took place within a 3-month window. 3 months was chosen as a pragmatic compromise with given data availability because the end dates of events are not recorded in the underlying datasets. However, the time window does not consider any characteristics of the natural disaster. Unfortunately, no standard method for defining CNDs quantitatively has emerged.

This study applies a method for estimating the ınter-event time definition (IETD), which is commonly used for the characterization of independent rainfall events, to define CNDs with a time window that we define the natural disaster ınter-event time definition (NIETD). The NIETD proposed in this study is used to define CNDs that occurred in South Korea. Also, this study used bootstrapping to explore the question of whether natural disasters are or are not random and frequency analysis was conducted to check which CND is dominant in South Korea.

The remainder of this paper is organized as follows: Section 2 describes the data used, the inter-event time definition, and the bootstrapping method; Section 3 presents the NIETD for defining the CNDs and discussions; and Section 4 presents the conclusions.

2 Material and methods

2.1 Previous definition of compound natural disaster

Gissing et al. (2022) defined CNDs based on a time window, using Australian natural disaster data (start date, peril type, location, and event size in the form of insured losses) from the ınsurance council of Australia (ICA) disaster list for the period from 1966 to 2020, and classified natural disasters into six types: tropical cyclones, floods, storms, bushfires, heatwaves, and landslides. When two or more natural disasters occur within a 3-month window, they are defined as CNDs. Gissing et al. (2022) suggested that communities impacted by natural disasters within a 3-month period would likely still be in recovery. Figure 1 shows CNDs in Australia from 1966 to 2020. During this time, 36 CNDs occurred, mostly in December, January, and February, which is consistent with bushfires, tropical cyclones, and severe storm seasons.

Fig. 1
figure 1

CNDs within a three-month window in the Australia (Gissing et al. 2022)

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The 3-month window for defining compound disasters based on the availability of data in the ICA database raises questions about the appropriateness of the time window for studying CNDs in Australia. While data availability is an important consideration in research, it is also crucial to consider characteristics of the natural disasters. About this problem, IETD can be a solution.

2.2 Inter-event time definition

The IETD has been widely used to distinguish between independent rainfall events (Balistrocchi and Bacchi 2011; Raimondi et al. 2023). If the non-rainfall period between two consecutive rainfall events is shorter than the IETD, these two events can be considered as independent rainfall events. Conversely, if the non-rainfall period between two consecutive rainfall events is longer than the IETD, two events can be considered as two separate independent rainfall events. Therefore, by comparing the non-rainfall period between rainfall events with the IETD, we can examine the independence of two rainfall events as shown in Fig. 2 (Kim 2018). Using the concept of IETD, we define a Natural disaster ınter-event time definition (NIETD) and examine the independence of natural disasters.

Fig. 2
figure 2

Identification of independent rainfall events using IETD (Kim 2018); If non-rainfall period between consecutive rainfall events is longer than the IETD, two events can be considered as two separate independent rainfall events (event A); Conversely, two events can be considered as an independent rainfall event (event B)

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Numerous methodologies have been developed to estimate IETD (Joo et al. 2014; Medina-Cobo et al. 2016; Lee and Kim 2018). Of them, three estimation methods are widely used: autocorrelation function (ACF), coefficient of variation (CV), and average annual number of events (Fig. 3). The ACF method calculates the IETD based on the autocorrelation between rainfall events. This method assumes that rainfall events are autocorrelated, and the IETD is identified as the lag time at which the autocorrelation coefficient of rainfall events converges to zero. This indicates that independent rainfall events have no correlation (Adams and Papa 2000).

$${R}_{k}=\frac{\sum ({y}_{t}-\overline{y })({y}_{t-k}-\overline{y })}{\sum {({y}_{t}-\overline{y })}^{2}}$$
(1)

where \({y}_{t}\) is a rainfall time series, \(\overline{y }\) is the average of rainfall events, and \(k\) is the lag time.

Fig. 3
figure 3

IETD estimation methods: a ACF method; b CV method; c average annual number of events method; Three figure show the results of IETD estimation methods on rainfall; In ACF method, IETD is the lag time at which autocorrelation coefficient of events converges to zero; In CV method, IETD is the lag time where coefficient of variation is equal to one; In average annual number of events method, IETD is the lag time at which the average annual of events become constant

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The CV method assumes that the probability density function of non-rainfall periods follows an exponential distribution. The lag time is determined based on where the coefficient of variation is equal to one (Bedient and Huber 1988). This is because the exponential distribution has the same mean and standard deviation values.

$$CV=\frac{\sigma }{\mu }$$
(2)

where, \(\mu\) and \(\sigma\) are the mean and standard deviation of the non-rainfall periods between rainfall events, respectively.

In the method of average annual number of events, the number of independent rainfall events is identified based on lag times, and the average annual number of rainfall events is then calculated. The IETD is determined as the lag time at which the average annual of events become constant, regardless of the increase in lag time. This method utilizes the relationship between IETD and the average annual number of events and demonstrates better results compared to other methods by reflecting the rainfall characteristics (Lee and Kim 2018). This study examines estimation methods for IETD to be applied in natural disasters and attempts to calculate the NIETD.

2.3 Bootstrap method

The bootstrap method, proposed by Efron (1979), is a resampling technique used to identify statistical characteristics of a population by sampling a dataset with replacement. Efron’s bootstrap is defined as follows (Kim et al. 2004): Given a samples N independent and identically distributed random vectors \({X}_{1}, {X}_{2}, {X}_{3}, \cdots , {X}_{N}\) and a real-valued estimator \(\Theta ({X}_{1}, {X}_{2}, {X}_{3}, \cdots , {X}_{N})\) (denoted by Θ*) of the distribution parameter Θ, a procedure of the bootstrap to assess the accuracy of Θ* is defined in terms of the empirical distribution function \({F}_{n}\). This empirical distribution function assigns probability mass \(1/N\) to each observed value of random vectors \({X}_{i}\) for \({\text{i}}=\mathrm{1,2},\cdots ,{\text{N}}\).

$${\text{P}}\left({X}_{i}^{*}={x}_{j}\right)=1/N$$
(3)

The bootstrap method allows researchers to calculate standard errors, construct confidence intervals, and perform hypothesis testing for various types of sample statistics (Lim et al. 2019). This method is also widely used to check the randomness of data by comparing the statistics of the samples with those of the original data (Davidson and MacKinnon 2007; Dolnicar and Leisch 2010; Cavaliere and Georgiev 2020; Gissing et al. 2022). This study employed Monte Carlo simulation to simulate 100 event sets in which events retained the probability of occurrence of CNDs and did the same procedure with a random probability.

2.4 Study data

To define CNDs in South Korea, we utilized data from the statistical yearbook of natural disaster (SYND), which is published by the Ministry of the Interior and Safety, South Korea. The SYND includes information on natural disasters as well as their damage, and recovery cost. It has been published since 1979, with the most recent edition being published in 2020. We constructed a natural disaster dataset using the SYND data from 2010 to 2019. This dataset includes information on the start and end dates, administrative divisions (si(city), gun(country), and gu(district)), economic damage, number of victims, and deaths. We excluded data from the SYND 2020 because it has a different resolution for administrative divisions (do(province), si(city)).

Between 2010 and 2019, a total of 223 natural disasters occurred in South Korea, consisting of ten different types of disasters that are recorded in the SYND (Fig. 4). On average, there were approximately 22 natural disaster events per year. The highest number of disasters occurred in 2013 (28 occurrences), while the lowest number occurred in 2011 (13 occurrences). More than 50% (112) of all-natural disasters were caused by rainfall, while 16% were caused by heavy snowfall, and 12% were caused by wind waves and strong winds. These three types of natural disasters occur every year. Of all the disasters, typhoons caused the most damage, with a total of around USD 1.314 billion and an average of approximately USD 0.654 billion per year.

Fig. 4
figure 4

Number of natural disasters in South Korea (2010–2019)

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3 Applications and discussions

3.1 Calculation of NIETD

The three IETD estimation methods introduced in Sect. 2.2 were examined for their applicability in natural disasters, to calculate the NIETD. The ACF method has difficulty in application, as it estimates autocorrelation coefficients based on lag times. Although the autocorrelation coefficient for rainfall data, which is a time series, can be calculated, natural disasters are events rather than continuous time series. Therefore, it was not possible to estimate the coefficient for natural disasters. However, the other two methods can be applied to natural disasters.

When the two methods were applied, the maximum lag time was fixed at 15 days (28 July 2002–11 August 2002), which was the longest duration of natural disasters from 2010 to 2019. Prior to applying the two methods, we defined CNDs according to each lag time by comparing the lag time and intervals between the disasters (Fig. 5). After definition, we estimated intervals between each CND to calculate the coefficient of variation and counted the number of CNDs for each lag time to calculate the average annual number of events.

Fig. 5
figure 5

CND definition method based on the NIETD; If the period between natural disasters is longer than the NETD, each event is classified as a separate independent natural disaster event; Conversely, two events are considered to be part of the CND event

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Based on the estimated intervals for each lag, we calculated the coefficient of variation and attempted to identify the lag time at which the value is one (Fig. 6a). However, all the coefficients were larger than one with increasing pattern as lag time increased. Therefore, it was impossible to select the NIETD using the CV method. In the average annual number of events method, we calculated the annual number of CNDs by summing up the number of CNDs for each lag time. We then attempted to identify the lag time at which the average annual events converge. However, it is difficult to clearly determine the lag time at which convergence begins in a figure (Fig. 6b). Therefore, the rates of change in the average for lag times were calculated by dividing the difference between the average at lag time t and t + 1 with the average in lag time t + 1(rate of change = \(\frac{{Average}_{t+1}-{Average}_{t}}{{Average}_{t+1}}\)). To determine the convergence point, we defined that if the rates are less than 5%, the annual average has converged. We then concluded that the NIETD is 8 days (Table 1).

Fig. 6
figure 6

NIETD calculation using the IETD estimation methods: a CV method; b average annual number of events method; In the CV method, all coefficients of variation are larger than one. Therefore, it is impossible to choose the NIETD; In the average annual number of events method, average annual numbers of CNDs for each lag time are calculated, and the convergence point is found by comparing the rates of change with the 5% convergence criteria

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Table 1 Annual average of CND and ratio of change for lag times; Starting from 8 days, the rates of change are less than 5% which is the convergence criteria
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3.2 Compound natural disasters in the South Korea

We defined CNDs based on the NIETD calculated in Sect. 3.1, then examined the interval of natural disasters and NIETD as well as the matching locations of natural disasters. In addition, if the durations of many natural disaster events are less than NIETD, the events can be considered as a single event. For example, when we checked natural disaster events in the period of 10 July 2010 to 18 August 2010, there were many occurrences of natural disasters (4 rainfalls → 1 typhoon → 1 rainfall). This is classified as a CND caused by the combination of rainfall and typhoon. After the above procedure to define CNDs, we also checked the elements of each CND, because some cases contain natural disasters that do not affect each other.

A total of 89 CNDs of 14 different types occurred from 2010 to 2019 in South Korea (Fig. 7). First, when looking at the number of CNDs by year, 2010 had the highest rate (24 times, 27%) and 2016 had the lowest (2 times, 2%). In 2010, a total of 22 natural disasters, which have impacts on many regions, occurred. Moreover, the average interval between natural disasters in 2010 was 14 days, which was the shortest compared to other years. On the other hand, in 2016, the total number of natural disasters (18 times) was less than the average annual number of natural disasters (22.3 times) and the disaster interval (19.3 days) was the longest. When comparing the types of CNDs in each year, consecutive rainfall disasters are a common type that occurs every year in rainy season, summer.

Fig. 7
figure 7

Number of CNDs in South Korea (2010–2019); Every year contains CND of rainfall + rainfall disasters (red bar)

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The East Asian monsoon brings heavy rainfall during a short rainy season called Jangma from the end of June to the end of July. Jangma is a stationary front caused by an encounter between the cold air mass of Okhotsk Sea from the north, and a hot and humid air mass of North Pacific high-pressure developed in the south. More than 30% of the annual average rainfall in South Korea occurs in Jangma season. The heavy rain damage mostly occurred in the Jangma season of 1 month and the interval between rainfall disaster events is shorter than in other seasons. This characteristic shows a high probability of being identified as a CND in the time-window-based method.

We identified 14 different types of CNDs in Fig. 8. When we looked at the frequency of occurrence of the CNDs, we found that two types (rainfall + rainfall, and rainfall + typhoon) occurred far more frequently than the others (Fig. 8). Typhoon is one of the natural disasters that receives significant attention on CND research due to its ability to bring out several different types of natural disasters such as rainfall, storm surge, high wind speed, and more. These disasters occur simultaneously and interact with one another under the influence of a typhoon.

Fig. 8
figure 8

Number of CNDs in terms of types; Two types (rainfall + rainfall, and rainfall + typhoon) of CNDs are lager than the other types

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CNDs composed of rainfall and typhoon showed the biggest amount of damage (approximately USD 0.26 billion) (Fig. 9). This is because the average amount of damage caused by typhoons (approximately USD 63,891 per a case) is significantly larger than that caused by other natural disasters.

Fig. 9
figure 9

Total amount of damage according to CND type

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The statistics of the CNDs based on year and type revealed that rainfall and typhoon disasters have the most significant impact on the CNDs in South Korea.

Regarding the total number of victims and deaths, CNDs composed of consecutive rainfall disasters incurred significant casualties (Fig. 10).

Fig. 10
figure 10

Number of victims according to CND type

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3.3 Randomness test using bootstrapping and frequency analysis

To test the randomness of the occurrence of CNDs using the bootstrap method, sampling weights, which are probabilities based on both single disasters and CNDs, were first calculated. We calculated the probability of occurrence for seven natural disaster types (heavy snowfall, wind wave, rainfall, typhoon, strong wind, wind wave/strong wind, and earthquake) and then estimated the conditional probability of their combination into a CND. In each trial, 1,000 cases of CNDs were extracted and classified according to their types. Then, occurrence rates were calculated. This process was repeated 100 times and then average the rates for comparing with the actual rates of CNDs in the South Korea. We also repeated the same process using randomness weights (Fig. 11).

Fig. 11
figure 11

Occurrence likelihood according to CND type: the blue bars represent the actual cases; the red bars indicate simulated cases with calculated weights; green bars show the cases with randomness weights; the blue and red bars have a similar percent of CNDs occurrence while green bars have different percent

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When comparing real and sample cases based on the calculated probabilities, there was an average difference of approximately 2.23%. Specifically, CNDs composed of consecutive rainfall disasters had the largest difference, which was 9.86%, while those composed of consecutive wind wave∙strong wind disasters had the smallest difference, which was 0.19%. In cases where the sampling had a lower percentage of occurrence than the identified cases, CNDs with the same consecutive type were less likely to occur. This is because the probability of the same natural disasters occurring consecutively is lower than that of different ones occurring in the same way. Based on random probability, the occurrence percentages of CNDs were approximately the same. Upon comparing the results, we found that the occurrence of CNDs in South Korea was not random.

We then conducted a frequency analysis based on the estimated probability of occurrence and conditional probability (Table 2). According to the frequency analysis, CND consisting of rainfall and typhoon occurred every 7.6 years, while consecutive rainfall disasters occurred every 9.4 years. These two types of CNDs were found to overwhelmingly more frequent than others, which had a return period of over 100 years.

Table 2 Return period of CNDs
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3.4 Discussion

To define CNDs, this study used the IETD estimation method (average annual number of events) to calculate the NIETD, which is a criterion for determining the independence of each natural disaster. The proposed methodology addresses the problem of the previous methods, but there are points that can be further improved.

After identification of CNDs using the NIETD, we further checked the natural disasters of each CND, because some cases consisted of unrelated natural disasters. However, if natural disasters are categorized into groups based on their cause and characteristics, the CNDs with unrelated natural disastsers cannot be identified. Natural disasters within the same group share common causes and characteristics, therefore, they influence each other. Therefore, if CNDs consist of natural disasters in the same group, it is not necessary to conduct the above procedure. In addition, if we can define relationships between the natural disaster groups, the identifiaction of CNDs can be easily carried out using the relationships. The study by Kim et al. (2019) is one of similar examples. Kim et al. (2019) classified structural flood defense measures into groups according to the installable area and functions and defined relationships between the measures as independent and dependent (contingent and exclusive) proposals. The independent proposal refers to the relationship between flood prevention measures that do not have any impact on the other measures. The dependent proposal includes an exclusive proposal, where flood measures are in an exclusionary relationship, and a contingent proposal, where one measure is in a relationship with the other supportive measures. Through the above relationship, Kim et al. (2019) excluded impracticable combinations of measures and increased the efficiency of the analysis. For CND, if the same method as Kim et al. (2019) is applied, it is possible to determine CNDs easily. However there are special cases in the CNDs. For example, if a rainfall disaster occurs after a forest fire, people usually focus on mitigating the damage of the forest fire. However, the forest fire exacerbates the impact of the rainfall disaster. The vegetation is removed by the fire, which leads to increased surface exposure to rainfall. The soil layer can quickly become saturated, and it leads to increase of direct-runoff discharge and subsequent flood damage (Nalbantis and Lymperopoulos 2012). Therefore, we need more CND related to categorize natural disasters and define the relationship of groups of natural disasters. Among the four types of CNDs (see Sect. 1. Introduction) proposed by Zscheischler et al. (2020), CNDs based on the NIETD can be defined as temporally compounding events. A temporally compounding event is a succession of natural disasters that affect a geographical region and cause significant damage due to vulnerability from the prior one. A CND composed of consecutive rainfall disasters is a representative example of temporally compounding events. However, CNDs can occur through various mechanisms. Therefore, the proposed method can be further developed by adding methods to identify diverse types of CNDs. The proposed method has another improvement point with considering physical characteristics. A temporally compounding event refers to a situation where a second natural disaster occurs while the physical factors related to the first disaster are still present. The state of physical factors related to disasters can be used to identify whether there is an interaction between natural disasters that have occurred in succession. The physical factors need to be identified to determine the interaction between natural disasters and can vary depending on the type of natural disasters interacted. For example, in CNDs where rainfall disasters occur consecutively, the interaction between the rainfall events can be checked by soil moisture. Soil moisture can indicate how much water the soil is holding and how much runoff there may be. When the first rainfall occurs, soil moisture becomes saturated. As time passes, soil moisture decreases due to evaporation or infiltration. However, if a second rainfall occurs while the soil moisture level is still above average, the ground quickly becomes saturated, leading to increased flooding and potentially more damage (Kim 2018). However, further research is still needed on what physical factors should be considered for each combination of CNDs. This study suggested NIETD for identifying CNDs by statistical concept. If we consider physical factors, understanding CNDs would be very complicated because we need to find various factors involved in disasters. Therefore, instead of the use of physical factors in the identification of CNDs, the physical factors could be used for analyzing detailed studies on each type of CND after defining CNDs.

In Sect. 3.2, it is observed that a CND consisting of consecutive rainfall disasters occurs every year. Apart from these, we identified independent rainfall disasters that caused damage equivalent to that of CNDs. These events had two common elements: they were caused by heavy rainfall and had a precedent rainfall event. A representative case is a heavy rainfall in the central area of the Korean peninsula in July 2011. Jangma began on the 22nd of June, dumping a large amount of rainfall in the central area for a month, which kept the ground saturated. Under these conditions, heavy rainfall occurred from July 25th to 28th, causing severe flooding and enormous damage, including flood damage, road collapse, and ground failure. In this case, wet conditions had already been created, increasing the scale of the flood prior to the heavy rainfall. Thus, it is difficult to describe this as a single natural disaster, being closer to a preconditioned event, which is a type of CNDs defined by Zscheischler et al. (2020). In preconditioned events, one or more climate events or natural disasters can have an impact or can lead to an amplified impact. Because of the limitations of SYND, preconditioned events were not identified in the proposed methodology. The SYND only provides information on climatic phenomena that directly cause natural disasters, and there is no information about other climatic factors affecting the disasters. Nonetheless, these factors can be used as important information in understanding the case of natural disasters and identifying CNDs. Thus, it is necessary to include such factors in the SYND. To address this limitation, we will incorporate observation data related to weather, climate, and ocean to identify preconditioning events.

CND often results in greater damage than single natural disasters due to preceding factors that affect the scale and size of the damage. Preceding natural disasters or triggers create conditions that amplify the influence of the following natural disasters. Thus, it becomes crucial to minimize the influence of the preceding factors to prevent the scale of damage caused by CNDs. Here, resilience can be a crucial factor to consider. Resilience, derived from the Latin word “resiliere” meaning “to jump back”, is often used synonymously with “bouncing back” (Kim 2016). First proposed by Holling (1973), he defined resilience as the ability to absorb shocks, avoid transitioning to an irrecoverable state, and rebuild quickly after a system disturbance. When a disaster occurs, a society with high resilience can quickly identify the damage and recover to a normal condition, which means minimizing the impact of the disaster. Throughout history, societies have sought various means of predicting and warning against natural disasters, as well as defense alternatives. However, due to the increase in CNDs, there are limitations to these measures. Therefore, society needs to find a new way to reduce the damage, and resilience can be a solution.

4 Conclusions

This study proposed a method for defining CNDs based on IETD. We calculated the NIETD, which is the criterion for identifying CNDs, for natural disasters that occurred in South Korea from 2010 to 2019. We then compared the NIETD with the intervals between natural disasters. As a result, we defined 89 CNDs of 14 different types, with rainfall and typhoon disasters having the greatest impact. To evaluate the randomness of the occurrence of CNDs, we used a bootstrapping method and conducted frequency analysis. Based on the analysis results, we identified improvement points in the proposed method as well as limitations of the natural disaster data from the SYND. Moreover, we suggested that increasing resilience is a way to minimize the damage caused by CNDs. The influence of CNDs on society will be more and more increased; therefore, more research on the CND should be conducted. In this regard, the proposed method could be a useful tool for defining CNDs and for further research.