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.
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
] 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: Section 2
provides the foundation of the case study, introducing the theory of copulas used in this study. Section 3
analyzes the characteristics of rainstorms, typhoons, and typhoon surges in the research areas. Section 4
discusses the marginal distribution and the return period of compound events of rainstorms and typhoon surges. Finally, Section 5
concludes the paper.