Copula-Based Joint Probability Analysis of Compound Floods from Rainstorm and Typhoon Surge: a Case Study of Jiangsu Coastal Areas, China

sustainability

Article Copula-Based Joint Probability Analysis of Compound Floods from Rainstorm and Typhoon Surge: A Case Study of Jiangsu Coastal Areas, China

Ping Ai 1,2, Dingbo Yuan 1 and Chuansheng Xiong 1,* ID

1 College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China; [email protected] (P.A.); [email protected] (D.Y.) 2 College of Computer and Information, Hohai University, Nanjing 211100, China * Correspondence: [email protected]

Received: 13 May 2018; Accepted: 24 June 2018; Published: 28 June 2018

Abstract: Coastal areas are vulnerable to floods caused by rainstorms and typhoons. It is necessary to ascertain the risk of floods caused by both of these extreme weather events. A conceptual risk model is proposed to evaluate the rainstorm risk, typhoon surge risk, and the compound risk in the coastal areas of Jiangsu Province during the period of 1960–2012. The results of the model show that the typhoon surge risk in the study region is greater than the rainstorm risk. Three Archimedean copulas were used to fit the joint probability distributions of the compound events. The Frank copula and the Gumbel copula proved to be the best-fitting joint distribution function for the Huaibei plain district and the Lixiahe district, respectively. The probability of the extreme compound events not happening is less than 90% in the study region. This means that the flood risk is mainly subject to the encounter of a low-level rainstorm and a low-level typhoon surge. The study shows that the northern region of Jiangsu Province is more vulnerable to the compound risk, and that we should pay more attention to the floods caused by the compound events of rainstorm and typhoon surge.

Keywords: rainstorm; typhoon surge; joint probability analysis; copula; return period; coastal areas

1. Introduction Violent tropical cyclones that develop in the western of North Pacific Ocean and move towards the west or northwest, landing in Japan, Korea, and the southwestern coast of China, are usually called typhoons. A strong typhoon often generates winds and rainfall [1]. The coastal areas are more vulnerable to specific hazards due to the development of the national economy [2], as an overwhelming part of the population is concentrated along or near the coasts, facing a high risk of coastal floods [3]. China is a country subject to frequent natural hazards and their impacts, including lives lost and property damaged. Among such hazards, floods are the most serious disasters [4]. Typhoon-related coastal floods are mainly caused by heavy rainfall and high sea levels due to a combination of rainstorms and typhoon surges [5]. When a typhoon approaches China, its strong winds and low atmospheric pressure often generate rainfalls and typhoon surges, which can lead to floods in coastal areas [6]. According to the typhoon track data from the China Meteorological Administration (CMA), China suffers an average of seven or eight typhoons annually. Most typhoons hit China between June and October every year. During the period of 1983–2006, seven typhoons made landfall over mainland China and Hainan Island, leading to a direct economic loss of 28.7 billion yuan (CNY) and killing 472 people annually based on the Department of Civil Affairs of China’s statistical data [7]. Consequently, it is important to analyze the flood risk in coastal areas to reduce the damage, especially when a typhoon encounters a rainstorm.

Sustainability 2018, 10, 2232; doi:10.3390/su10072232 www.mdpi.com/journal/sustainability Sustainability 2018, 10, 2232 2 of 18

As widely studied hydrological extreme events, floods are characterized by flood peak flow, flood volume, and flood duration. For most flood frequency analyses, considering one variable provides limited information [8,9] because univariate probability analysis cannot provide a perfect evaluation of the occurrence of extreme events, which are characterized by a series of associated random variables [10]. In fact, the correlation between environmental variables of extreme weather is usually important, considering that the characteristics of variables and their possible interdependence are the foundation of the design and safety assessment of coastal flood control projects [11]. Therefore, the analysis and evaluation of flood risk in the coastal area has become a very important topic nowadays. Rainstorms and typhoons are the main disaster-causing factors of floods in the coastal areas. It is meaningful work to determine the correlation between rainstorms and typhoons in flood risk, especially for floods caused by compound events of rainstorms and typhoons. The copula theory, first introduced by Sklar [12], provides an ideal function to represent the multivariate joint distribution from univariate margins based on the random variables’ multivariate dependence structures [13], and it has been extensively used in insurance and finance. A detailed and comprehensive copula theory was introduced by Nelsen [14]. The Archimedean copulas, which include Clayton, Frank, and Gumbel copula, are widely used in hydrology analysis, and they have been applied to model the dependence when the hydrologic variables have positive or negative correlations [15]. Hu et al. [16] used the Gumbel copula function to analyze the encounter frequency of typhoon and plum rain in Taihu Lake Basin. Shiau et al. [17] used the copula function to describe the joint distribution of depth and duration of rainfall, ultimately deriving a depth-duration-frequency model. Tao et al. [18] selected the Poisson bivariate compound maximum entropy distribution to establish the joint distribution of extreme water level and wave height in a typhoon period. Wahl et al. [19] ascertained the likelihood of compound events of storm surge and heavy precipitation for the coastal areas of the United States (US), and the results showed that the flood risk from compound events was higher in the Atlantic/Gulf coast. Kwon et al. [20] analyzed the correlation between annual maximum wind speed and rainfall by using the copula function in the typhoon danger zone. A new bivariate compound extreme value distribution was proposed by Dong [21] to describe the probability distribution of annual extreme wind speed and maximum rainfall intensity in the coastal areas that are affected by typhoons. The simultaneous encounter of rainstorm and typhoon is more likely to cause severe floods in the coastal areas and often leads to huge catastrophic consequences [22]. In particular, the rise in sea level caused by typhoon surge has gradually become the main factor for the amplification of flood risk [23]. During the period of a rainstorm, the sluice gates need to open to drain floodwater, but during the period of a typhoon, the sluice gates need to close to prevent seawater intrusion. The main purpose of this work is to implement a copula-based methodology to analyze the frequency of the simultaneous encounter of rainstorms and typhoon surges. The primary objectives of this research can be summarized as follows: (1) to understand the causes and the implications of statistical features between rainstorms and typhoon surges in the research areas; (2) to identify the key risk factors of the compound events; (3) to investigate the relationship between rainstorms and typhoon surges, and to build a proper bivariate copula function for the simultaneous encounter of rainstorms and typhoon surges. The rest of this paper is structured as follows: Section2 provides the foundation of the case study, introducing the theory of copulas used in this study. Section3 analyzes the characteristics of rainstorms, typhoons, and typhoon surges in the research areas. Section4 discusses the marginal distribution and the return period of compound events of rainstorms and typhoon surges. Finally, Section5 concludes the paper. Sustainability 2018, 10, x FOR PEER REVIEW 3 of 18 Sustainability 2018, 10, 2232 3 of 18

2. Materials Materials and Methods

2.1. Study Study Area Area and Data The studystudy areaarea (as (as shown shown in in Figure Figure1) for 1) thisfor researchthis research is located is located in the in east the coastal east coastal areas of areas Jiangsu of JiangsuProvince, Province, China, from China, 116 from◦180 E 116°18′ to 121◦ E57 to0 E 12 and1°57′ from E and 30◦ 45from0 N to30°45′ 35◦20 N0 N.to 35°20′ It has aN. coastline It has a ofcoastline 954 km ofalong 954 thekm Yellow along Sea. the TheYellow Yangtze Sea. River The Yangtze passes through River passes the southern through part the of southern Jiangsu Province, part of Jiangsu and the Province,Huaihe River and the passes Huaihe through River the passes northern through part. the Accordingnorthern part. to the According geographical to the andgeographical hydrological and hydroconditions,logical the conditions, coastal areas the of coastal Jiangsu areas are of usually Jiangsu divided are usually into four divided districts: into the four Ganyu districts: district, the Ganyuthe Huaibei district, plain the district, Huaibei the plain Lixiahe district, district, the Lixiahe and the district Tongnan, and district. the Tongnan district.

Figure 1. LocationLocation of of the the research research areas.

The Huaihe River basin has always been a key area of flood risk research in China [24]. The The Huaihe River basin has always been a key area of ﬂood risk research in China [24]. Huaibei plain district, with fewer interfering factors, and the Lixiahe district, with a long coastline, The Huaibei plain district, with fewer interfering factors, and the Lixiahe district, with a long coastline, are the two main research areas in this study. The total drainage area of the two regions is 4150 km2 are the two main research areas in this study. The total drainage area of the two regions is 4150 km2 and 21,497 km2; the Yanwei station is located at the main coastal port of the Huaibei plain district, and 21,497 km2; the Yanwei station is located at the main coastal port of the Huaibei plain district, and the Xinyang station is the main tidal station of the Lixiahe district. Both stations are strongly and the Xinyang station is the main tidal station of the Lixiahe district. Both stations are strongly representative of these research areas due to their location, which are at the mouths of the main representative of these research areas due to their location, which are at the mouths of the main rivers. rivers. The rainfall data and the typhoon track data [25] were provided by the National Meteorological The rainfall data and the typhoon track data [25] were provided by the National Meteorological Information Center of China Meteorological Administration (http://data.cma.cn,tcdata.typhoon.org.cn); Information Center of China Meteorological Administration (http://data.cma.cn, tcdata.typhoon.org.cn); The duration of the rainfall data is from the establishment of the station until 2012. The tidal data, The duration of the rainfall data is from the establishment of the station until 2012. The tidal data, provided by the State Oceanic Administration (http://ocean.cnss.com.cn/), has a time span from provided by the State Oceanic Administration (http://ocean.cnss.com.cn/), has a time span from 1960 1960 to 2012. In order to maintain the consistency of data with respect to time scale, the study period to 2012. In order to maintain the consistency of data with respect to time scale, the study period was was established as 1960–2012. There are 191 rainfall stations that fall into the study period, and the established as 1960–2012. There are 191 rainfall stations that fall into the study period, and the area area rainfall (average precipitation) of each research region was calculated with the Thiessen polygon rainfall (average precipitation) of each research region was calculated with the Thiessen polygon method based on the selected stations. The intensity of typhoon surges depends on the level of typhoon, method based on the selected stations. The intensity of typhoon surges depends on the level of different from astronomical tides which have a periodic character of rising and falling. The typhoon typhoon, different from astronomical tides which have a periodic character of rising and falling. The surge deviation H(t) at time t can be expressed as the difference between the measured sea water level typhoon surge deviation Ht() at time t can be expressed as the difference between the measured y(t) and the estimated astronomical tide level Y(t) [26], i.e.: sea water level yt() and the estimated astronomical tide level Yt() [26], i.e.: H(t) = y(t) − Y(t) (1) H()()() t y t Y t (1) Sustainability 2018, 10, 2232 4 of 18

2.2. Marginal Distribution The Pearson distribution is a family of continuous probability distributions, first published by Karl Pearson in 1895. The log–Pearson type III distribution curve method is recommended by the Water Resources Council of the United States, and it was fitted to the sample hydrological data by using the mean, standard deviation, and skewness coefficient of the logarithms [27,28]. This method is also widely used in the frequency analysis of extreme hydrology events in China [29,30]. In this study, we chose the Pearson type III (P-III) distribution curve to model the marginal distribution of rainstorms and typhoon surges, using Simpson’s Rule to reduce the error. The P-III probability density function can be expressed as:

α β − f (x) = (x − α )α 1e−β(x−α0) α > 0, β > 0 (2) Γ(α) 0 where Γ(α) is the Gamma distribution of α, α is the shape parameter, β is the scale parameter, and α0 is the minimum value of the α.

2.3. Copula Functions The copulas link the univariate distribution functions of random variables to construct multivariate distribution functions, in which the domain is [0,1]. However, when two random variables are considered, based on Sklar’s theorem, if there is a two-dimensional joint cumulative distribution function FX,Y(x, y), and FX(x) and FY(y) are the marginal distribution functions of X and Y, then there exists a bivariate copula C, which can be written as the formula:

FX,Y(x, y) = C(FX(x), FY(y)) x, y ∈ R (3)

The mapping function C : |0, 1|2 → |0, 1| is the copula function for two independent uniform distributions u, v in the domain of [0,1], and c is the density function of C, which can be deﬁned as:

∂2C(u, v) c(u, v) = (4) ∂u∂v

In this study, we selected three widely used Archimedean copulas (Clayton, Frank, and Gumbel–Hougaard) as the candidate functions for modeling the joint probability distribution of compound events. The three Archimedean copula functions are deﬁned in Table1.

Table 1. Function expressions of Archimedean copulas.

Family Expression Generator ϕ (t) Parameter Space Relationship between τ and α −α −α −1/α 1 −α ≥ = ( + ) Clayton (u + v − 1) α (t − 1) α 0 τ α/ α 2 − − − − 1 (e αu 1)(e αv 1) exp(−αt)−1 4 1 R α t Frank − ( + ) − ln( ) α ≥ 0 τ = 1 − (1 − t dt) α ln 1 e−α−1 exp(−α)−1 α α 0 e −1 1/α α Gumbel exp(−(− ln u)α + (− ln v)α ) (− ln t) α ≥ 1 τ = 1 − 1/α

2.4. Parameter Estimations The optimal copula function is determined by the appropriate parameters. Sadegh et al. [31] put forward a newly invented Multivariate Copula Analysis Toolbox, which employs the Bayesian framework to describe dependence and uncertainty of fitted copulas; it has been proved that it can be used to find the best copula family among 26 families. In addition, there are many methods to confirm the correlation between random variables: Pearson correlation coefficient ρ, Kendall rank correlation coefficient τ, Spearman rank correlation coefficient ρs, and tail correlation coefficient λ. Other optimal criteria of the copula function, such as the least root-mean-square error (RMSE), Kolmogorov–Smirnov (K–S) test [32], Anderson–Darling (A–D) test [33], Jarque–Bera (J–B) test [34], Sustainability 2018, 10, 2232 5 of 18

Cramer–von Mises tests [35], Akaike information criterion (AIC) [36], ordinary least squares (OLS), and Bayesian information criterion (BIC), are usually used to estimate the goodness-of-ﬁt (GOF) of copula families. The nonparametric estimation method used to estimate the copula parameters in this study was put forward by Genest and Rivest [37]. It mainly depends on the relationships between the Kendall rank correlation τ and the corresponding copula parameter α. Kendall’s tau τ, which is used to determine the relevance of random variables, can be expressed as:

2(n − n ) τ = c d (5) n(n − 1) where nc is the number of concordant pairs, nd is the number of discordant pairs (concordant: ordered in the same way; discordant: ordered differently). The goodness-of-ﬁt tests were mainly used to calculate the “distance” between data and distribution and compare the “distance” to the threshold value [38]. Various ﬁtness tests are available for copula functions, and there was little difference between the results of different GOF tests due to the limited number of samples that were considered in this study. The fundamental purpose of this study is to determine whether the copula function can be used to describe the distribution of compound events of rainstorm and typhoon surge in these study areas. Therefore, several commonly used evaluation criteria met the needs of this study for selecting the optimal copula functions, such as the K–S test (Equation (6)), RMSE (Equation (7)), and AIC (Equation (8)). mi − 1 mi D = max F (x , y ) − , F (x , y ) − (1 ≤ i ≤ n) (6) 0 i i n 0 i i n where (xi, yi)(i = 1, 2, ··· , n) is the observation sample, F0(xi, yi) is the joint distribution of sample estimates, mi is the number of observed samples that satisfy the conditions of x ≤ xi, y ≤ yi, n is the total number of observed samples.

s n 1 2 RMSE = ∑ (Pei − Pi) (7) n 1 1 n AIC = n ln( (Pe − P )2) + 2m (8) − ∑ i i n m 1 where Pei and Pi are empirical frequency and theoretical frequency of the i-th compound sample, respectively, m is the number of the joint distribution function parameters, n is the number of samples.

3. Statistical Features of Historical Typical Hydrological Events in the Study Areas during the Period of 1960–2012

3.1. Rainstorms The rainstorms in the coastal areas of Jiangsu Province mainly consist of three types: plum rain, heavy convective rainfall, and typhoon rain. The research regions are located in the lower-middle research area of the Yangtze River. Plum rain easily forms in late June and early July. Figure2 shows a signiﬁcantly positive correlation between precipitation level and duration of the plum rain season. With the annual plum rain statistical calendar from 1960 to 2012, it is shown that the season’s earliest plum rain started on 2 June (1972, 1995, 2000) and the season’s latest plum rain ended on 27 July (1987). The shortest plum rain only lasted 3 days in 1978, while the longest plum rain lasted 48 days in 1996. The average duration of the plum rain season was 24 days. Sustainability 2018, 10, x FOR PEER REVIEW 6 of 18

Sustainability 2018, 10, x FOR PEER REVIEW 6 of 18 Sustainability 2018, 10, 2232 6 of 18 800 80 Rainfall Duration 700 70 800 80 Rainfall 600 Duration 60 700 70

500 50 600 60

400 40 500 50

300 30

Rainfall (mm) Rainfall

Duration (day) Duration

400 40

200 20 300 30

Rainfall (mm) Rainfall

Duration (day) Duration

100 10 200 20

0 0 100 10 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

0 Year 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Figure 2. Plum rain in the coastal areas of Jiangsu Province.

Figure 2. Plum rain in the coastal areas of Jiangsu Province. In addition to theFigure rainy 2.season Plum rainof the in theJiangsu coastal coastal areas of areas, Jiangsu convective Province. weather systems, shear line weather regimes, and strong convective weather systems can cause heavy rainstorms. The In addition to the rainy season of the Jiangsu coastal areas, convective weather systems, shear line heavyIn convectiveaddition to rainfall the rainy pattern season is usuof theally Jiangsu more intense coastal withareas, a shconvectiveorter duration weather compared systems, to shear plum weather regimes, and strong convective weather systems can cause heavy rainstorms. The heavy linerain. weather The average regimes, duration and strongof the convective convective rainfall weather every systems year canwas cause1–2 days heavy for the rainstorms. study period The convective rainfall pattern is usually more intense with a shorter duration compared to plum rain. heavy(Figure convective 3). The average rainfall value pattern of maximum is usually 1more-day intensearea rainfall with ina sh theorter coastal duration areas comparedof Jiangsu towas plum 54.8 The average duration of the convective rainfall every year was 1–2 days for the study period (Figure3). rain.mm Thefor the average period duration of 1960– of2012. the convective rainfall every year was 1–2 days for the study period The average value of maximum 1-day area rainfall in the coastal areas of Jiangsu was 54.8 mm for the (Figure 3). The average value of maximum 1-day area rainfall in the coastal areas of Jiangsu was 54.8 period of 1960–2012. mm for the period of 1960–2012.

4 Maximum one-day area rainfall Average duration 120 4 Maximum one-day area rainfall Average duration 3 120100

3 10080 2

8060 2

Average duration (day) duration Average

1 6040

Average duration (day) duration Average

Maximum one-day area rainfall (mm) rainfall area one-day Maximum

4020 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Maximum one-day area rainfall (mm) rainfall area one-day Maximum Year 20 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Figure 3. Heavy convective rainfall in the coastal areas of Jiangsu Province. Figure 3. Heavy convective rainfall Yearin the coastal areas of Jiangsu Province.

Monthly distribution of convective rainfall shows that it mainly concentrates in the ﬂood season, Monthly distribution of convective rainfall shows that it mainly concentrates in the flood which is betweenFigure May 3. andHeavy September. convective Convectiverainfall in the raincoastal is mostareas of likely Jiangsu to occurProvince in. August, after the season, which is between May and September. Convective rain is most likely to occur in August, plum rain season. Convective rainfall occurred in August 32 times during the study period (Figure4). Monthly distribution of convective rainfall shows that it mainly concentrates in the flood season, which is between May and September. Convective rain is most likely to occur in August, Sustainability 2018, 10, x FOR PEER REVIEW 7 of 18

after the plum rain season. Convective rainfall occurred in August 32 times during the study period (Figure 4). Sustainability 2018, 10, 2232 7 of 18

40 Convective rainfall 35

total number total 15

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure 4. The total numbers for monthly convective rainfall in the coastal areas of Jiangsu from 1960 toFigure 2012. 4. The total numbers for monthly convective rainfall in the coastal areas of Jiangsu from 1960 to 2012. Typhoons can also bring heavy rain to the coastal areas of Jiangsu, but the duration of typhoon rain is usuallyTyphoons short due can to also the bring rapid heavy movement rain ofto athe typhoon. coastal Accordingareas of Jiangsu, to the schedulebut the duration of when of typhoons typhoon maderain landfall,is usually there short was due atotal to the of 22rapid occurrences movement of typhoonof a typhoon. rain in According the two districts to the (Figureschedule5). Dueof when to thetyphoon geographicals made speciﬁcity landfall, there of the was research a total areas,of 22 mostoccurrences typhoons of typhoon landed in rain south-central in the two Jiangsu districts coastal(Figure areas; 5). Due therefore, to the the geographical area rainfall of specificity typhoon rainof the in theresearch Lixiahe areas, district most was typhoons greater than land ined the in Huaibeisouth-central plain district, Jiangsu in coastal most cases.areas; therefore, the area rainfall of typhoon rain in the Lixiahe district wasThere greater are than three in types the Huaibei of rainstorms plain district that occur, in atmost different cases.times and are closely related to different meteorologicalThere are conditions. three types Plum of rainstorms rain occurs that in late occur June at and different early July, times typhoon and are rain closely tends related to occur to indifferent August meteorological and September conditions. of the typhoon Plum period,rain occurs and in convective late June and rainfall early occurs July, typhoon when the rain earth’s tends surfaceto occur is withinin August a conditionally and September unstable of the or typhoon humid atmosphereperiod, and thatconvective is hotter rainfall than the occurs surrounding when the environment.earth’s surface Because is within of the a different conditionally mechanisms unstable of the or three humid types atmosphere of rainstorms, that their is hotter durations than are the dissimilar.surrounding Plum environment. rain has the Because longest duration—up of the different to mechanisms 20–30 days—nevertheless, of the three types the average of rainstorms, daily rainfalltheir durations caused by are the dissimilar. typhoon is Plum the highest rain has (Table the longest2). duration—up to 20–30 days—nevertheless, the average daily rainfall caused by the typhoon is the highest (Table 2). Table 2. Statistical results of the three types of rainstorms in the coastal areas of Jiangsu Province from 1960Table to 2012.2. Statistical results of the three types of rainstorms in the coastal areas of Jiangsu Province from 1960 to 2012.

TypeType PlumPlum Rain Rain TyphoonTyphoon Rain Rain ConvectiveConvective Rain Rain NumberNumber ofof occurrences occurrences 6262 2222 105105 Duration (days) 20–30 1–4 1–2 Duration (days) 20–30 1–4 1–2 Average area rainfall (mm) 231.4 104.1 54.8 Average area rainfall (mm) 231.4 104.1 54.8

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300 Lixiahe District Huaibei plain District 250

200

150

100

area rainfall (mm) rainfall area

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Typhoon series

Figure 5. The typhoon rain series according to the order of occurrence over time. Figure 5. The typhoon rain series according to the order of occurrence over time. 3.2. Typhoons and Typhoon Surges 3.2. Typhoons and Typhoon Surges The study areas are affected by typhoons frequently, about three times per year (Figure6). The earliestThe study typhoon areas hits are Jiangsu affected in by May, typhoons the latest frequently hits in, November. about three Accordingtimes per year to the (Fig Besture Track6). The Datasetearliest of typhoon typhoons hits from Jiangsu 1949 to in 2012 May, [25 ], the there latest are hits mainly in November. two paths of According typhoons that to the occur Best in Track the studyDataset areas: of (1)typhoons the typhoon from 1949 that landsto 2012 at [ the25], Yangtzethere are River mainly mouth, two paths moving of typhoon to the northwest;s that occur (2) in the the typhoonSustainabstudy areas:ility that 2018 arrives (1), 10 the, x FOR attyphoon 35 PEER degrees REVIEW that north lands latitude at the Yangtze of the Jiangsu River mouth, coastline, moving then changesto the northwest its path to; (2)9 theof the18 northeast,typhoon andthat landsarrives at at North 35 degrees Korea. north The typhoonlatitude of following the Jiangsu the coastline, second path then occurs change thes its most path in to the the coastalnortheast, areas and of Jiangsu, lands at accounting North Korea for. aboutThe typhoon 62%. following the second path occurs the most in the coastal areas of Jiangsu, accounting for about 62%. 8 Typhoon events 7

Occurrence number Occurrence 2

0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year

Figure 6. The number of typhoons landing on the coastal areas of Jiangsu every year. Figure 6. The number of typhoons landing on the coastal areas of Jiangsu every year.

The coastal areas of Jiangsu are mainly controlled by two tidal wave systems: the East China Sea forward wave and the South Yellow Sea rotating wave. Observation of the tidal characteristics along the nearshore coast of the research areas reveals that the tides of the two tidal wave systems in the north and south basically intersect in the vicinity of Dongtai port. In order to distinguish the influence factors of tidal level change in these areas, we checked the typhoon track data and analyzed the tide levels of two stations. The results show that 148 typhoons affected the study areas: 88 were accompanied by rainfall in the Huaibei plain district, and 95 were accompanied by rainfall in the Lixiahe district. The minimum levels of typhoon surges at Yanwei station and Xinyang station were 32 cm and 31 cm, and the maximum typhoon surges at the two stations were 243 cm and 240 cm, respectively.

4. Results and Discussion

4.1. Marginal Distributions of Compound Events According to the design standard of flood control projects along Jiangsu coastal cities, it is typical that when the typhoon surge is higher than 200 cm in the absence of rain, the city river discharge is affected. Daily average rainfall over 50 mm is treated as a rainstorm in China. However, when the rainstorm encounters a typhoon surge, the coastal areas are more prone to flooding. Based on the rainstorm features and typhoon surge features of these geographically distinctive areas, the criteria used to select the samples from the compound events were an area rainfall of a rainstorm greater than 30 mm and a typhoon surge greater than 100 cm. The results show that 44 of 88 compound events conformed to the sample criteria in the Huaibei plain district, and 38 of 95 compound events conformed to the sample criteria in the Lixiahe district during the study period

(Figure 7). The rainstorm sample is recorded as xi , the typhoon surge sample is recorded as yi , and

the real-number pair (,)xyii is the i-th compound event that meets the sample criteria. Sustainability 2018, 10, 2232 9 of 18

The coastal areas of Jiangsu are mainly controlled by two tidal wave systems: the East China Sea forward wave and the South Yellow Sea rotating wave. Observation of the tidal characteristics along the nearshore coast of the research areas reveals that the tides of the two tidal wave systems in the north and south basically intersect in the vicinity of Dongtai port. In order to distinguish the inﬂuence factors of tidal level change in these areas, we checked the typhoon track data and analyzed the tide levels of two stations. The results show that 148 typhoons affected the study areas: 88 were accompanied by rainfall in the Huaibei plain district, and 95 were accompanied by rainfall in the Lixiahe district. The minimum levels of typhoon surges at Yanwei station and Xinyang station were 32 cm and 31 cm, and the maximum typhoon surges at the two stations were 243 cm and 240 cm, respectively.

4. Results and Discussion

4.1. Marginal Distributions of Compound Events According to the design standard of ﬂood control projects along Jiangsu coastal cities, it is typical that when the typhoon surge is higher than 200 cm in the absence of rain, the city river discharge is affected. Daily average rainfall over 50 mm is treated as a rainstorm in China. However, when the rainstorm encounters a typhoon surge, the coastal areas are more prone to ﬂooding. Based on the rainstorm features and typhoon surge features of these geographically distinctive areas, the criteria used to select the samples from the compound events were an area rainfall of a rainstorm greater than 30 mm and a typhoon surge greater than 100 cm. The results show that 44 of 88 compound events conformed to the sample criteria in the Huaibei plain district, and 38 of 95 compound events conformed to the sample criteria in the Lixiahe district during the study period (Figure7). The rainstorm sample isSustainab recordedility 2018 as x, 10i,, the x FOR typhoon PEER REVIEW surge sample is recorded as yi, and the real-number pair (xi, yi)10is of the 18 i-th compound event that meets the sample criteria.

300 300 Compound event Compound event Selected samples Selected samples

200 200

100 100

Typhoon surge (cm) surge Typhoon

0 0 50 100 150 200 250 0 0 50 100 150 200 250 300 Rainfall (mm) Rainfall (mm)

(a) (b)

FigureFigure 7. TheThe distribution distribution of of the the compound compound events events in in the the research research areas: areas: (a) (Huaibeia) Huaibei plain plain district; district; (b) (Lixiaheb) Lixiahe district district..

The P-III marginal distributions of rainstorms and typhoon surges with different Cs in the two The P-III marginal distributions of rainstorms and typhoon surges with different Cs in the two research areas are shown in Figures 8 and 9. The optimal parameters (Cv and Cs) of the P-III research areas are shown in Figures8 and9. The optimal parameters ( Cv and Cs) of the P-III marginal marginal distribution based on the joint samples (,)xyii in the Huaibei plain district and the distribution based on the joint samples (xi, yi) in the Huaibei plain district and the Lixiahe district are Lixiahe district are shown in Table 3. shown in Table3.

(a) (b)

Figure 8. The marginal distributions of rainstorms and typhoon surges in the Huaibei plain district: (a) the probability curve of rainstorms during the typhoon period; (b) the probability curve of typhoon surges at the Yanwei tidal station.

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300 300 Compound event Compound event Selected samples Selected samples

200 200

100 100

Typhoon surge (cm) surge Typhoon

0 0 50 100 150 200 250 0 0 50 100 150 200 250 300 Rainfall (mm) Rainfall (mm)

(a) (b)

Figure 7. The distribution of the compound events in the research areas: (a) Huaibei plain district; (b) Lixiahe district.

The P-III marginal distributions of rainstorms and typhoon surges with different Cs in the two research areas are shown in Figures 8 and 9. The optimal parameters (Cv and Cs) of the P-III marginal distribution based on the joint samples (,)xyii in the Huaibei plain district and the LixiaheSustainability district2018, are10, 2232shown in Table 3. 10 of 18

(a) (b)

FigureFigure 8. 8. TheThe marginal marginal distributions distributions of of rainst rainstormsorms and and typhoon typhoon surges surges in in the the Huaibei Huaibei plain plain district: district: ((aa)) t thehe probability probability curve curve of of rainstorms rainstorms during during the typhoonthe typhoon period; period; (b) the (b probability) the probability curve of curve typhoon of Sustainability 2018, 10, x FOR PEER REVIEW 11 of 18 typhoonsurges at surges the Yanwei at the tidalYanwei station. tidal station.

(a) (b)

Figure 9. The marginal distributions of rainstorms and typhoon surges in the Lixiahe district: (a) the Figure 9. The marginal distributions of rainstorms and typhoon surges in the Lixiahe district: (a) the probabilityprobability curve curve of of rainstorms during typhoon period;period; ((bb)) thethe probabilityprobability curve curve of of typhoon typhoon surges surges at atthe the Xinyang Xinyang tidal tidal station. station.

Table 3. The P-III parameters of rainstorms and typhoons in the research areas. Table 3. The P-III parameters of rainstorms and typhoons in the research areas. Coefficient of Areas Event Skew Factor C Mean Value R VariationCoefﬁcient C of s Areas Event Mean Value R v Skew Factor Cs Variation Cv Area rainfall 52.6 mm 0.41 3.0 Huaibei plain District Area rainfall 52.6 mm 0.41 3.0 Cv Huaibei plain District Typhoon surge 145.2 cm 0.28 2.0 Typhoon surge 145.2 cm 0.28 2.0 Cv Area rainfall 77.5 mm 0.67 3.0 Area rainfall 77.5 mm 0.67 3.0 Cv LixiaheLixiahe District District Typhoon surgesurge 153.8 cm 0.24 0.24 4.0 4.0 Cv

4.2.4.2. Determination Determination of of the the Disaster Disaster Risk Risk Model Model FloodFlood risk risk caused caused by by c compoundompound events events can can be be calculated calculated as as Risk Risk = = Severity Severity ×× FrequencyFrequency [39] [39,], wherewhere the the severity severity of of every every compound compound event event is is determined determined by by the the severity severity of of the the rainstorm rainstorm and and typhoontyphoon surge. surge. We hypothesizedhypothesized that that rainstorms rainstorms and and typhoon typhoon surges surges have have the the same same effect effect on the on ﬂood the flooddisaster. disaster. The distribution The distribution of the of red the selected red selected sample sample in Figure in Figure7 shows 7 shows that the that sample the sample criteria criteria are the areorigin the oforigin the risk of the evaluation risk evaluation model. Thismodel. differs This from differs the Euclideanfrom the Euclidean distance between distance the between compound the compound event and the origin point as a measure of severity. We use the area of r1 and r2 in Figure 10 to describe the severity of the compound event. This can better distinguish the degree of influence of rainstorms and typhoon surges for the severity of compound events. The calculation formula of (rainstorm risk r1 ) and r2 (typhoon surge r2 ) is as follows:

 xx arctan(i 0 )  yy 2 r()()() ii 0  x  x22  y  y  1360  ii 0 0  (9)   2  r()()()() i x  x22  y  y  r i  24  ii 0 0 1 Sustainability 2018, 10, 2232 11 of 18

event and the origin point as a measure of severity. We use the area of r1 and r2 in Figure 10 to describe the severity of the compound event. This can better distinguish the degree of inﬂuence of rainstorms and typhoon surges for the severity of compound events. The calculation formula of r1 (rainstorm risk r1) and r2 (typhoon surge r2) is as follows:

x −x  arctan( i 0 ) q 2  ( ) = yi−y0 ( − )2 + ( − )2  r1 i 360 π xi x0 yi y0 q 2 (9)  π 2 2  r2(i) = 4 (xi − x0) + (yi − y0) − r1(i) Sustainability 2018, 10, x FOR PEER REVIEW 12 of 18

FigureFigure 10. 10.The The damage damage evaluation evaluation model model of of compound compound events. events.

The frequency ( Pi()) of the compound events are derived from the calculation results in Section The frequency (P(i)) of the compound events are derived from the calculation results in Section 4.1 4.1 above. The disaster risk R for this study is shown below: above. The disaster risk Ri for thisi study is shown below:

Ri r1 ( i ) P 1 ( i ) r 2 ( i ) P 2 ( i ) (10) Ri = r1(i)P1(i) + r2(i)P2(i) (10) where Pi1 () is the frequency of rainstorm and Pi2 () is the frequency of typhoon surge. where P (i) is the frequency of rainstorm and P (i) is the frequency of typhoon surge. Due1 to the different extents of rainfall and2 typhoon, for a better comparative analysis, we used a Due to the different extents of rainfall and typhoon, for a better comparative analysis, we used a linear normalization method to convert the risk into the range of [0,1]. The risk maps of rainstorm linear normalization method to convert the risk into the range of [0,1]. The risk maps of rainstorm and and typhoon surge in the Huaibei plain district and the Lixiahe district are shown in Figure 11. The typhoon surge in the Huaibei plain district and the Lixiahe district are shown in Figure 11. The results results show that the risks of typhoon surge in the two research areas are greater than the rainstorm show that the risks of typhoon surge in the two research areas are greater than the rainstorm risks. risks. The compound risks of rainstorm and typhoon surge are shown in Figure 12. The results show The compound risks of rainstorm and typhoon surge are shown in Figure 12. The results show that the that the Huaibei plain district faces a higher average compound risk of rainstorm and typhoon surge Huaibei plain district faces a higher average compound risk of rainstorm and typhoon surge than the than the Lixiahe district. Lixiahe district.

(a) (b) Sustainability 2018, 10, x FOR PEER REVIEW 12 of 18

Figure 10. The damage evaluation model of compound events.

The frequency ( Pi()) of the compound events are derived from the calculation results in Section

4.1 above. The disaster risk Ri for this study is shown below:

Ri r1 ( i ) P 1 ( i ) r 2 ( i ) P 2 ( i ) (10)

where Pi1 () is the frequency of rainstorm and Pi2 () is the frequency of typhoon surge. Due to the different extents of rainfall and typhoon, for a better comparative analysis, we used a linear normalization method to convert the risk into the range of [0,1]. The risk maps of rainstorm and typhoon surge in the Huaibei plain district and the Lixiahe district are shown in Figure 11. The results show that the risks of typhoon surge in the two research areas are greater than the rainstorm risks. The compound risks of rainstorm and typhoon surge are shown in Figure 12. The results show that the Huaibei plain district faces a higher average compound risk of rainstorm and typhoon surge Sustainability 2018, 10, 2232 12 of 18 than the Lixiahe district.

SustainabSustainabilityility 2018 2018, 10, 10, x, xFOR FOR PEER PEER REVIEW REVIEW 1313 of of 18 18 (a) (b)

(c()c ) (d(d) )

FigureFigure 11 11. The. The risk risk map maps sof of rainstorm rainstorm and and typhoon typhoon surge surge in in the the two two research research areas: areas: (a ()a rainstorm) rainstorm risk risk Figure 11. The risk maps of rainstorm and typhoon surge in the two research areas: (a) rainstorm risk inin the the Huaibei Huaibei plain plain district; district; ( b(b) )t yphoontyphoon surge surge risk risk in in the the Huaibei Huaibei plain plain district; district; ( c()c )rainstorm rainstorm risk risk in in in the Huaibei plain district; (b) typhoon surge risk in the Huaibei plain district; (c) rainstorm risk in thethe Lixiahe Lixiahe district; district; ( d(d) typhoon) typhoon surge surge risk risk in in the the Lixiahe Lixiahe district district. . the Lixiahe district; (d) typhoon surge risk in the Lixiahe district.

(a()a ) (b(b) )

FigureFigureFigure 12. 12 12.The The. The compound compound compound risksrisk risks s of of rainstorm rainstorm and andand typhoon typhoontyphoon surge surge in in in the the the two two two research research research areas: areas: areas: (a ()a (Huaibei)a Huaibei) Huaibei plain district; (b) Lixiahe district. plainplain district; district; ( b(b)) Lixiahe Lixiahe district.district.

4.34.3. Selection. Selection of of Copula Copula Functions Functions TheThe marginal marginal distributions distributions of of two two hazard hazard contributing contributing factors factors were were calculated calculated with with the the P P-III-III methodmethod described described in in Section Section 4.1. 4.1. Kendall’s Kendall’s tau tau is is − 0.43−0.43 and and 0.75 0.75 in in Huaibei Huaibei plain plain and and Lixiahe, Lixiahe, respectively.respectively. The The critical critical value value of of the the K K–S–S statistic statistic in in the the Huaibei Huaibei plain plain district district and and the the Lixiahe Lixiahe districtdistrict is is 0.2120 0.2120 and and 0.2360 0.2360, respectively, respectively, with, with a astatistical statistical significance significance level level of of 0.05 0.05. I. nIn this this study, study, all all thethe K K–S–S value values sof of the the three three copulas copulas in in the the two two areas areas conformed conformed to to the the critical critical value. value. Based Based on on the the minimumminimum value value criterion criterion of of RMSE RMSE and and AIC, AIC, the the two two values values of of the the Frank Frank and and Gumbel Gumbel copula copulas shave have littlelittle difference, difference, but but the the Gumbel Gumbel copula copula can can only only be be used used to to des describecribe the the positive positive relationship relationship of of the the compoundcompound events. events. Therefore, Therefore, the the Frank Frank copula copula was was selected selected to to be be the the best best-fitting-fitting copula copula in in the the HuaibeiHuaibei plain plain district. district. With With the the same same criteria, criteria, the the Gumbel Gumbel copula copula is is the the best best one one for for the the Lixiahe Lixiahe districtdistrict (the (the detail detaileded p parametersarameters of of the the candidate candidate copulas copulas are are shown shown in in Table Table 4). 4). The The empirical empirical probabilitiesprobabilities and and the the theoretical theoretical probabilities probabilities (P (P-P)-P) of of the the rainstorms rainstorms and and typhoon typhoon surges surges in in the the two two areasareas are are shown shown in in Fig Figureure 13. 13. It It shows shows that that the the estimated estimated cumulative cumulative probability probability i si sconsistent consistent with with thethe empirical empirical results. results. Sustainability 2018, 10, 2232 13 of 18

4.3. Selection of Copula Functions The marginal distributions of two hazard contributing factors were calculated with the P-III method described in Section 4.1. Kendall’s tau is −0.43 and 0.75 in Huaibei plain and Lixiahe, respectively. The critical value of the K–S statistic in the Huaibei plain district and the Lixiahe district is 0.2120 and 0.2360, respectively, with a statistical signiﬁcance level of 0.05. In this study, all the K–S values of the three copulas in the two areas conformed to the critical value. Based on the minimum value criterion of RMSE and AIC, the two values of the Frank and Gumbel copulas have little difference, but the Gumbel copula can only be used to describe the positive relationship of the compound events. Therefore, the Frank copula was selected to be the best-ﬁtting copula in the Huaibei plain district. With the same criteria, the Gumbel copula is the best one for the Lixiahe district (the detailed parameters of the candidate copulas are shown in Table4). The empirical probabilities and theSustainab theoreticalility 2018, probabilities 10, x FOR PEER (P-P) REVIEW ofthe rainstorms and typhoon surges in the two areas are shown14 of in18 Figure 13. It shows that the estimated cumulative probability is consistent with the empirical results.

Table 4. The parameters of the candidate copulas. Table 4. The parameters of the candidate copulas. Areas Copula Parameter K–S RMSE AIC Areas CopulaClayton Parameter −0.362 K–S0.1065 0.0365 RMSE −322.65 AIC Huaibei plain DistrictClayton Frank −0.3622.263 0.10650.1454 0.0309 0.0365 −369.14−322.65 − Huaibei plain District FrankGumbel 2.2630.930 0.14540.1597 0.0321 0.0309 −365.06369.14 Gumbel 0.930 0.1597 0.0321 −365.06 Clayton 4.50 0.1935 0.0332 −323.40 − Lixiahe District ClaytonFrank 4.506.42 0.19350.1791 0.0354 0.0332 −338.73323.40 Lixiahe District Frank 6.42 0.1791 0.0354 −338.73 GumbelGumbel 3.313.31 0.12240.1224 0.0323 0.0323 −336.69−336.69

(a) (b)

FigureFigure 13. TheThe probability probability-probability-probability plot plot of of the the compound compound events events in inthe the two two research research areas: areas: (a) (Huaibeia) Huaibei plain plain district; district; (b) (Lixiaheb) Lixiahe district district..

4.4. Joint Probability Distribution of Compound Events and Their Return Period 4.4. Joint Probability Distribution of Compound Events and Their Return Period Through the disaster risk model that is proposed in this study, we know that the compound Through the disaster risk model that is proposed in this study, we know that the compound risk risk is positively correlated with rainstorm and typhoon surge. Based on the marginal distributions is positively correlated with rainstorm and typhoon surge. Based on the marginal distributions of of compound events and the parameters of the selected copula functions above, we constructed a compound events and the parameters of the selected copula functions above, we constructed a joint joint probability distribution for compound events. The X-axis indicates the value of typhoon surge, probability distribution for compound events. The X-axis indicates the value of typhoon surge, the the Y-axis indicates the value of area rainfall, and the Z-axis indicates the probability that the Y-axis indicates the value of area rainfall, and the Z-axis indicates the probability that the compound compound events do not happen. The results of the two copula functions are shown in Figure 14 as events do not happen. The results of the two copula functions are shown in Figure 14 as an intuitive an intuitive visual. The joint probability of a 200 mm level rainstorm and 200 cm level typhoon surge visual. The joint probability of a 200 mm level rainstorm and 200 cm level typhoon surge is 10% in the is 10% in the Huaibei plain district, and the probability of 200 mm level rainstorm and 200 cm level typhoon surge is 24% in the Lixiahe district.

(a) (b) Sustainability 2018, 10, x FOR PEER REVIEW 14 of 18

Table 4. The parameters of the candidate copulas.

Areas Copula Parameter K–S RMSE AIC Clayton −0.362 0.1065 0.0365 −322.65 Huaibei plain District Frank 2.263 0.1454 0.0309 −369.14 Gumbel 0.930 0.1597 0.0321 −365.06 Clayton 4.50 0.1935 0.0332 −323.40 Lixiahe District Frank 6.42 0.1791 0.0354 −338.73 Gumbel 3.31 0.1224 0.0323 −336.69

(a) (b)

Figure 13. The probability-probability plot of the compound events in the two research areas: (a) Huaibei plain district; (b) Lixiahe district.

4.4. Joint Probability Distribution of Compound Events and Their Return Period Through the disaster risk model that is proposed in this study, we know that the compound risk is positively correlated with rainstorm and typhoon surge. Based on the marginal distributions of compound events and the parameters of the selected copula functions above, we constructed a joint probability distribution for compound events. The X-axis indicates the value of typhoon surge, the Y-axis indicates the value of area rainfall, and the Z-axis indicates the probability that the compoundSustainability events2018, 10 ,do 2232 not happen. The results of the two copula functions are shown in Figure 1414 ofas 18 an intuitive visual. The joint probability of a 200 mm level rainstorm and 200 cm level typhoon surge is 10% in the Huaibei plain district, and the probability of 200 mm level rainstorm and 200 cm level Huaibei plain district, and the probability of 200 mm level rainstorm and 200 cm level typhoon surge typhoon surge is 24% in the Lixiahe district. is 24% in the Lixiahe district.

Sustainability 2018, 10, x FOR(a )PEER REVIEW (b) 15 of 18

FigureFigure 14. 14.The The joint joint probability probability distribution distribution ofof compoundcompound eventsevents notnot occurringoccurringin inthe the two two research research areas:areas: ( a(a)) Huaibei Huaibei plain plain district; district; ( b(b)) Lixiahe Lixiahe district. district.

TheThe return return periods periods of of the the compound compound events events in in thethe twotwo areas areas are are plotted plotted asas contour contour lines lines in in FigureFigure 15 15,, thethe intersectionintersection pointspoints ofof thethe curvecurve withwith thethe XX andand YY axesaxes areare the the surge surge value value (typhoon (typhoon

surge:surge: xxi)i ) and and rainfallrainfall valuevalue (rainfall: yyii)) ofof the compound compound events events,, and and the the value value of ofthe the curve curve is the is thereturn return period period of the of the compound compound event event.. For For instance, instance, thethe return return period period of compound of compound events events that that are arecharacterized characterized by bya 40 a 40mm mm rainfall rainfall and and a a112 112 cm cm typhoon typhoon surge surge is is 11.1.1 yearsyears inin thethe HuaibeiHuaibei plain plain district.district. WeWe used used the the copula copulamodel modelto toevaluate evaluate twotwo historichistoric floodsfloods (Dafeng(Dafeng floodflood onon 1919 AugustAugust 1965,1965, andand Huaibei Huaibei flood flood on on30 August30 August 2000) 2000) in Jiangsu in Jiangsu Province. Province The results. The are results consistent are consistent with the historical with the assessmenthistorical assessment of the two floods.of the two floods.

(a) (b)

FigureFigure 15. 15. JointJoint co-occurrence co-occurrence return return period period of of the the best-selected best-selected copula copula based based on on the the number number of of occurrences:occurrences: ( a(a)) Huaibei Huaibei plain plain district; district; ( b(b)) Lixiahe Lixiahe district. district.

The encounter probabilities of different levels of rainstorms and typhoon surges are listed in The encounter probabilities of different levels of rainstorms and typhoon surges are listed in Table 5; the results show that a 50 cm level typhoon surge encounter with a 50 cm level rainstorm Table5; the results show that a 50 cm level typhoon surge encounter with a 50 cm level rainstorm has a probability of 70% in the Huaibei plain district and a probability of 55% in the Lixiahe district, has a probability of 70% in the Huaibei plain district and a probability of 55% in the Lixiahe district, which means that the Huaibei plain district is more sensitive to rainstorms in the case of a 50 cm typhoon surge.

Table 5. The encounter probability of different levels of rainstorms and typhoon surges.

Surge 50 cm 100 cm 150 cm 200 cm 250 cm Rainstorm 50 mm 70% 60% 30% 20% 9% Huaibei 100 mm 35% 25% 25% 20% 8% Plain 150 mm 20% 15% 15% 10% 6% District 200 mm 10% 7% 7% 5% 3% 50 mm 55% 30% 15% 8% 100 mm 50% 30% 15% 8% Lixiahe 150 mm 40% 30% 15% 8% District 200 mm 30% 15% 10% 6% 250 mm 12% 10% 6% 5%

The results of the study confirm that the copula functions are feasible for coupling the risk of compound events in the east coastal areas of Jiangsu Province. Rainstorm and typhoon surge have a positive correlation with disaster risk. We used a conceptual model to evaluate the rainstorm risk, typhoon surge risk, and compound event risk in the two regions. However, the impacts of rainstorms and typhoon surges on compound risk are not consistent, so future research will focus on Sustainability 2018, 10, 2232 15 of 18 which means that the Huaibei plain district is more sensitive to rainstorms in the case of a 50 cm typhoon surge.

Table 5. The encounter probability of different levels of rainstorms and typhoon surges.

The results of the study confirm that the copula functions are feasible for coupling the risk of compound events in the east coastal areas of Jiangsu Province. Rainstorm and typhoon surge have a positive correlation with disaster risk. We used a conceptual model to evaluate the rainstorm risk, typhoon surge risk, and compound event risk in the two regions. However, the impacts of rainstorms and typhoon surges on compound risk are not consistent, so future research will focus on the impacts of rainstorms and surges on different degrees of risk. The risk maps show that the Huaibei plain district faces rainstorm risk, typhoon surge risk, and compound risk that are higher than these risks in the Lixiahe district due to the special geographical features of the Huaibei plain region. The joint probability distributions of the compound events show that high-risk compound events have a low joint co-occurrence probability, while low-risk compound events have a high joint co-occurrence probability in both areas. The Lixiahe district is more prone to heavy rainstorms than the Huaibei plain. On the other side, the encounter probability of different levels of rainstorms and typhoon surges shows that Huaibei plain is more easily faced with a high-level typhoon surge than the Lixiahe district. The different return periods for different levels of compound events mean that the Huaibei plain is more vulnerable to flooding caused by typhoon surges than southern Jiangsu, and we should use different methods to control the flood risk in these two areas.

5. Conclusions The flood hazards in coastal areas are mainly caused by rainstorms and typhoons, and any one of these extreme weather events may lead to massive damages. Rainstorms increase the amount of water in floods, while typhoon surges affect flood discharge. It is essential to analyze the frequency of compound events of rainstorms and typhoon surges in the coastal areas, and it is also important to assess the impact of compound events on flood risk. The joint probability distribution of the compound events can be used to deduce the characteristics of the flood hazards and to predict the flood risk in the future, which is very significant for the future development of flood control strategies. In order to study the risk of floods caused by the compound events of rainstorm and typhoon surge in Jiangsu Province, this study proposes a conceptual risk model for the floods caused by rainstorm and typhoon surge, which was successfully used to evaluate the rainstorm risk, typhoon surge risk, and compound event risk in the Huaibei plain district and the Lixiahe district. We carried out an encounter joint probability analysis of rainstorms and typhoon surges in the two research areas using copula functions. The main conclusions of this paper are as follows: (1) A conceptual disaster risk model for evaluating the risk of compound events of rainstorm and typhoon surge is proposed in the study, and it proved to be reasonable. We used the model to calculate the rainstorm risk, typhoon surge risk, and compound event risk. The results show that the Sustainability 2018, 10, 2232 16 of 18 risk of typhoon surge in the Huaibei plain district and the Lixiahe district is greater than the rainstorm risk, mainly because the coastal areas of Jiangsu are plain terrain and are prone to floods caused by typhoon surges. (2) The area rainfall of rainstorms and the water level deviation of typhoon surge were used as the risk factors of compound events; these factors were used as inputs to the copula functions to establish the joint probability distributions. Based on the optimal parameters and evaluation criteria, the Frank copula proved to be the best-fitting joint distribution function for the Huaibei plain district, and the Gumbel copula is the most suitable function for the Lixiahe district. (3) The joint probability distribution of compound events shows that the low risk of low-level rainfall and low-level surge compound events have a high frequency, while the high risk of high-level rainfall and high-level surge compound events have a low frequency in the two regions. For the same level of typhoon surge, lower intensity rainstorms happen more frequently in the Huaibei plain district than in the Lixiahe district. Under the same rainfall conditions, the Huaibei plain district is more likely to suffer from high-level typhoon surges. (4) The co-occurrence return period of high-level rainstorms and high-level typhoon surges is longer than low-level compound events. The results of this study are consistent with the disaster grade after analyzing two typical flood disasters in the research areas. It turns out that the copula functions that were used to analyze the joint probability distribution of encounter risk between rainstorms and typhoon surges in the Jiangsu coastal areas are feasible. Furthermore, we should pay more attention to floods caused by the low-level compound events.

Author Contributions: This research was carried out in collaboration with all authors. The study was designed and the data were prepared by C.X. The analysis method was provided by P.A., C.X., and D.Y. The research area map was provided by D.Y. The manuscript was prepared by D.Y. and revised by P.A. and C.X. Funding: This research is supported by ‘the Fundamental Research Funds for the Central Universities’ (Grant No. 2017B616X14) and ‘the National Natural Science Foundation of China’ (Grant No. 51420105014). Acknowledgments: We would like to give our greatest gratitude to the academic editors and two anonymous reviewers for their helpful and constructive suggestions used to improve the quality of the manuscript, the help of language editing offered by Tim Michigan is also greatly appreciated. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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