Compound flooding from rainfall and storm tides is prone to occur in coastal cities. The identification of them is essential for controlling urban flooding. First, the dependence between rainfall and storm tides is quantified by Kendall's τ, Spearman's ρ, and tail dependence coefficient. Then, a bivariate copula-based probability distribution model is built to calculate the joint and conditional probability of rainfall and storm tides. Finally, MK and SQMK methods are employed to detect the trends of the dependence and joint probability. The results show that: (1) The dependence between strong rainfall and corresponding storm tides is much higher than that of small rainfall and storm tides, and the effect of tropical cyclones may be one of the reasons. (2) The dependence between rainfall and storm tides is the largest in October and the smallest in July. More attention should be paid to the compound flooding caused by rainfall and storm tides in October for Haikou. (3) The upper tail dependence coefficient of the rainfall and storm tides is significantly greater than the lower tail dependence coefficient and exhibits a significant positive trend. The results can provide additional insights into the effect of rainfall and storm tides for coastal flood management.

  • The compound effects of rainfall and storm tides were investigated from different perspectives.

  • Trends of the compound risk were analyzed by the copula and Mann–Kendall method.

  • Significant increasing trends of joint probability were detected after 1988–1992.

  • Compound event of rainfall and storm tides is more likely to occur when a high storm tide event has occurred.

With climate change and rapid urbanization, urban floods become more and more frequent, and flood risk presents an increasing trend (Xu et al. 2020). In China, coastal cities with high urbanization levels and rapid economic growth are vulnerable to floods caused by the compound effect of rainfall and storm tides, which are two main disaster-causing factors in coastal cities and are often driven by common meteorological conditions such as low atmospheric pressure and tropical cyclone (TC) (Zheng et al. 2014). In coastal cities, rainfall collected by drainage systems flows into the sea either directly, or it flows into tidal rivers first and is then pumped into the sea. High storm tide has an adverse influence on drainage capability and could directly cause coastal flooding. According to the report by the Intergovernmental Panel on Climate Change, extreme rainfall and sea level have rising trends in recent years. Thus, the compound effects of rainfall and storm tides will be more and more significant and it is necessary to investigate the trends of compounding rainfall and storm tide events in coastal cities.

There are numerous studies on the dependence between rainfall and storm tides. Svensson & Jones (2002) found that the dependence between precipitation and surge is strongest when precipitation preceded surge by 1 day in eastern Britain. However, in South and West Britain, they found the dependence between precipitation and daily maximum surge is strongest when they occurred on the same day, but is not particularly strong for any lag (Svensson & Jones 2004). Archetti et al. (2011) considered different rainfall and sea level conditions to estimate the threshold of flooding and proposed a simplified method to assess the urban flooding severity as a function of climate variables in Rimini (Italy). Zheng et al. (2013) employed a bivariate logistic threshold-excess model to quantify the dependence between extreme rainfall and storm surge. Statistically significant dependence is observed for the majority of locations along the Australian coastline and the strength of dependence varies with storm burst duration and the lag between extreme rainfall and storm surge events. More recently, Hurk et al. (2015) used an ensemble of regional climate model simulations to demonstrate that the combined occurrence of heavy precipitation and storm surge is physically related in a Dutch coastal polder area. They concluded that the role of the correlation between storm surge and heavy precipitation increases with inland storm tide up to a certain value, but its role decreases at the higher storm tides when tidal characteristics become increasingly important. Couasnon et al. (2018) proved that considering the compound effect through building a copula-based Bayesian network was crucial for flood risk assessment in coastal cities. Xu et al. (2022) investigated the amplification of flood Risks by the compound effects of precipitation and storm tides under the nonstationary scenario. The above analyses show that there is a certain dependence between rainfall and storm tides. Even though the dependence is often weak, it can have significant implications for flood risk estimation (Archetti et al. 2011; Zheng et al. 2014; Lian et al. 2017; Xu et al. 2023; Guan et al. 2023).

Overall, the above studies mainly focus on the dependence and joint probability between rainfall and storm tides. However, little attention has been paid to the trends and compound effects of rainfall and storm tides in different magnitudes, different years, and different months. The existence of trends is an indication of potential climate change and the identification of such trends in rainfall and storm tides is essential for planning and design of sustainable drainage measures in coastal cities. The aim of the study is to detect the trend of dependence between rainfall and storm tides in coastal cities. The main contributions include that (1) the compound effects of rainfall and storm tides were investigated from different perspectives (different magnitude, annual dependence, monthly dependence, tail dependence) and (2) trends of the compound risk were analyzed by a bivariate copula-based probability distribution (BCPD) model, Mann–Kendall (MK), and the sequential Mann–Kendall (SQMK) test method. The study area and used data are described in Section 2. Section 3 describes the method used in this study. In Section 4, the dependence between rainfall and storm tides is quantified by Kendall's τ, Spearman's ρ, and tail dependence coefficient first, and then the trends of the dependence are detected by the MK test method and the SQMK test method. Finally, a BCPD model is established to calculate the joint probability and conditional probability of rainfall and storm tides, and the trends of joint probability and conditional probability are also analyzed. The discussion and conclusions are summarized in Section 5.

In this study, the trend of compounding rainfall and storm tide events during the period from 1974 to 2012 are analyzed from the following three aspects. First, the annual dependence, monthly dependence and dependence between different magnitudes of rainfall and corresponding storm tides are investigated by Kendall's τ, Spearman's ρ, and their trends are detected by the MK and SQMK test methods. Secondly, tail dependence coefficients including upper and lower tail dependence coefficients are calculated by the BCPD model, and then the trends of upper and lower tail dependence coefficients are determined. Thirdly, the trends of the joint probability and conditional probability calculated by the BCPD model are also detected. The BCPD model and tail dependence coefficient are described as follows.

Study area and data

Haikou City is located in the northern part of Hainan Island, China and is adjacent to the Qiongzhou Strait (Figure 1). It is the capital city of Hainan Province, which was established in 1988. It is vulnerable to the joint impact of rainfall and storm tides due to its special geographical location and flat terrain. Haikou is one of the regions most frequently and seriously affected by TCs in China with an average of 4.2 TCs per year. Heavy rainfall and high storm tides caused by TCs often bring severe flood damage to Haikou. The flooding occurs from June to October. Among them, the 20081015, 20101003, 20111005, and 20120723 flooding events had a severe impact on the main urban area of Haikou City. The flooding caused many adverse effects such as waterlogging of roads, disruption of traffic, and damage to municipal drainage facilities in Haikou City. For example, typhoon Rammasun attacked Haikou in July 2014, which caused the death of eight people and a 13.627 billion Yuan (2.05 billion USD) loss.
Figure 1

Storm tide station and rainfall stations in the study area.

Figure 1

Storm tide station and rainfall stations in the study area.

Close modal

This paper presents an assessment of Haikou city center with an area of 150 km2 as the study area. Daily rainfall data and storm tide data from 1974 to 2012 provided by Haikou Municipal Water Authority are collected from six rainfall stations and a storm tide station in the city center of Haikou respectively. The daily rainfall data used in the following analysis take the average of six rainfall stations by Thiessen Polygon Method. The maximum distance between the storm tide station and the rainfall station is about 9.5 km, and the nearest distance is about 3 km. The continuity of the data has been checked. The TC data are available from the best-track dataset by the Shanghai Typhoon Institute of China Meteorological Administration (http://tcdata.typhoon.org.cn/zjljsjj_zlhq.html).

BCPD model of rainfall and storm tides

Copula functions have been widely applied to multivariate analysis of hydrologic events in recent years (Wang et al. 2017; Guo et al. 2018) because marginal properties and the dependence structure of random variables could be investigated separately. and are marginal distributions of X and Y, respectively. According to Sklar's theorem (Sklar 1959), if u and v are continuous, the copula function is unique. Commonly used copula functions are presented in Supplementary material, Table A1.

The joint distribution function of rainfall (H) and storm tides (Z) is defined as .
(1)

The marginal distribution is fitted using Lognorm, Gamma, Weibull and GEV distribution. Norm, Gamma, Weibull, and Generalized Extreme Value (GEV) distribution are employed to fit . The parameters of the above distributions are estimated by the maximum likelihood method. The best-fit marginal distribution and are selected by the Akaike information criterion (AIC) and ordinary least squares criteria (OLS).

The goodness of fit for a probability distribution is usually tested by Kolmogorov–Smirnov (K–S) test. K–S statistic D is defined as follows:
(2)
where is the theoretical distribution of the measured samples; i is the serial number of the measured samples in ascending order; and m is the number of samples. When the statistic D is less than the critical value , the test is accepted.
The formula of is defined as follows:
(3)
where N is the number of samples. RMSE is the root mean square error of samples; and k is the number of variables. A smaller AIC value indicates a better fit.
The formula of OLS is defined as follows:
(4)
where and are theoretic and empirical frequencies of the joint distribution, respectively. m is the number of samples.

After determining the optimal marginal distribution and , the copulas in Supplementary material, Table A1 are used to build a joint distribution of rainfall and storm tides. The maximum likelihood method is employed to estimate the parameters in copulas. The best-fit copula is selected by AIC and OLS.

The joint probability that at least one variable, rainfall H or storm tides Z, exceeds its extreme values, is denoted as . The expression of is as follows:
(5)
The conditional probability that H exceeds a certain extreme when Z is also high, is denoted as . The expression of is as follows:
(6)

Tail dependence coefficient

Common correlation coefficients like Kendall's τ and Spearman's ρ are not able to correctly describe the dependence of extremes. However, extreme events are of particular importance due to their severe impacts on the economy, environment and society (Aghakouchak et al. 2010). The degree of association between extreme values can be described by the tail dependence coefficient. Let X1 and X2 be two random variables and let and be their distribution functions, respectively. The upper tail dependence coefficient is defined as (Frahm et al. 2005):
(7)
where w is the extreme value threshold. Similarly, the lower tail dependence coefficient is defined as:
(8)
In this study, the tail dependence coefficient is calculated by the copula function (Frahm et al. 2005; Domino et al. 2014). The Gumbel copula function is sensitive to the changes in the variables at the upper tail of the distribution, while the Clayton copula function is sensitive to the changes in the variables at the lower tail. Thus, the tail dependence coefficient can be calculated by following formulas (Domino et al. 2014).
(9)
(10)
where is the parameter in the Gumbel copula function; is the parameter in the Clayton copula function.

Analysis on dependence between rainfall and storm tides

Dependence between different magnitudes of rainfall and corresponding storm tides

According to the rainfall classification of the China Meteorological Administration, different magnitudes of rainfall include rainfall >1, >10, >25, and >50 mm. The number of occurrences exceeding the different thresholds is 3,690; 1,624; 739; and 259, respectively. The dependence between different magnitudes of rainfall and corresponding storm tides are quantified by Kendall's τ and Spearman's ρ. As shown in Table 1, the Spearman's ρ would more than double (increases from 0.124 to 0.276) when rainfall increases from higher than 1 mm to higher than 50 mm. The Kendall's τ has similar trends. It indicates that the dependence between strong rainfall and corresponding storm tides is greater than that between small rainfall and corresponding storm tides. The reason may be related to rainfall patterns of different magnitudes of rainfall. Small rainfall such as 1–10 mm rainfall is more susceptible to local small-scale climate (e.g., air humidity), but it has a small impact on storm tides, which results in weak dependence between rainfall and storm tides. Moderate rainfall and heavy rainfall are more susceptible to mesoscale weather systems, such as TCs. TCs are often accompanied by strong winds and rainstorms, which both have a significant impact on rainfall and storm tides. As shown in Table 2, in TC conditions, the Spearman's ρ of TC rainfall and storm tides is 0.274 with the significant level at 0.01 when rainfall is higher than 25 mm, which is much higher than that of non-TC rainfall and storm tides with the value of 0.04. It indicates that the dependence between rainfall and storm tides is enhanced by TCs for moderate rainfall and heavy rainfall in Haikou City.

Table 1

Dependence between different magnitudes of rainfall and corresponding storm tides

Correlation CoefficientsDependence between different magnitudes of rainfall and corresponding storm tides
Rainfall >1 mmRainfall >10 mmRainfall >25 mmRainfall >50 mm
Kendall's τ 0.084*** 0.103*** 0.108*** 0.183*** 
Spearman's ρ 0.124*** 0.153*** 0.159*** 0.276*** 
Correlation CoefficientsDependence between different magnitudes of rainfall and corresponding storm tides
Rainfall >1 mmRainfall >10 mmRainfall >25 mmRainfall >50 mm
Kendall's τ 0.084*** 0.103*** 0.108*** 0.183*** 
Spearman's ρ 0.124*** 0.153*** 0.159*** 0.276*** 

***Significance at α = 0.01.

Table 2

Dependence between TC rainfall and storm tides and non-TC rainfall and storm tides

Correlation CoefficientsRainfall higher than 10 mm
Rainfall higher than 25 mm
TC rainfall and storm tidesNon-TC rainfall and storm tidesTC rainfall and storm tidesNon-TC rainfall and storm tides
Kendall's τ 0.171*** 0.051*** 0.189*** 0.027 
Spearman's ρ 0.249*** 0.076*** 0.274*** 0.04 
Correlation CoefficientsRainfall higher than 10 mm
Rainfall higher than 25 mm
TC rainfall and storm tidesNon-TC rainfall and storm tidesTC rainfall and storm tidesNon-TC rainfall and storm tides
Kendall's τ 0.171*** 0.051*** 0.189*** 0.027 
Spearman's ρ 0.249*** 0.076*** 0.274*** 0.04 

***Significance at α = 0.01.

Annual dependence analysis

The annual dependence between rainfall and storm tides is shown in Figure 2. In general, Kendall's τ and Spearman's ρ in each year increase with the increase of rainfall. For higher than 1 mm rainfall, the average value of Spearman's ρ is 0.11. When rainfall is higher than 25 mm, the maximum value of Spearman's ρ is 0.633 (occurred in the 1977 year) and the average value is 0.20 significance at α = 0.01.
Figure 2

Dependence between different magnitudes of rainfall and corresponding storm tides. The red bar diagram represents rainfall >1 mm. The black bar diagram represents rainfall >10 mm. The blue bar diagram represents rainfall >25 mm.

Figure 2

Dependence between different magnitudes of rainfall and corresponding storm tides. The red bar diagram represents rainfall >1 mm. The black bar diagram represents rainfall >10 mm. The blue bar diagram represents rainfall >25 mm.

Close modal
The graphical representation of the SQMK test statistics is shown in Figure 3. A similar trend is observed in Kendall's τ and Spearman's ρ. When rainfall is higher than 1 mm, UF and UB statistics of the SQMK test experience more than one non-significant change point and a decreasing trend is detected after 1989 (Figure 3(a) and 3(b)). When rainfall is higher than 10 mm, the UF statistics depict that, after a change in 1992, Kendall's τ and Spearman's ρ lean toward an increasing trend (Figure 3(c) and 3(d)). When the rainfall is higher than 25 mm, an increasing trend is detected after 1995 (Figure 3(e) and 3(f)). Results from the SQMK test reveal the approximate year of the start of a significant trend between 1989 and 1995, which is consistent with the urbanization time of Haikou.
Figure 3

The SQMK statistics for Kendall's τ and Spearman's ρ between different magnitudes of rainfall and corresponding storm tides: (a) rainfall >1 mm, Kendall's τ, (b) rainfall >1 mm, Spearman's ρ, (c) rainfall >10 mm, Kendall's τ, (d) rainfall >10 mm, Spearman's ρ, (e) rainfall >25 mm, Kendall's τ, (f) rainfall >25 mm, Spearman's ρ. The solid black line represents the UF value, and the blue dashed line represents the UB value.

Figure 3

The SQMK statistics for Kendall's τ and Spearman's ρ between different magnitudes of rainfall and corresponding storm tides: (a) rainfall >1 mm, Kendall's τ, (b) rainfall >1 mm, Spearman's ρ, (c) rainfall >10 mm, Kendall's τ, (d) rainfall >10 mm, Spearman's ρ, (e) rainfall >25 mm, Kendall's τ, (f) rainfall >25 mm, Spearman's ρ. The solid black line represents the UF value, and the blue dashed line represents the UB value.

Close modal

Monthly dependence analysis

The monthly characteristics of rainfall and storm tides are shown in Figure 4. Rainfall in Haikou occurs mainly from June to October, accounting for 72% of annual rainfall. Rainfall intensity increases gradually from May, and it reaches an extreme value in October. The variation of storm tides is consistent with that of rainfall. The storm tides increase from January to October, and it is the highest in October.
Figure 4

The monthly characteristic of rainfall and storm tides. Rainfall intensity is the average daily rainfall in every month during 1974–2012. Rainfall amount is the sum of daily rainfall in every month during 1974–2012.

Figure 4

The monthly characteristic of rainfall and storm tides. Rainfall intensity is the average daily rainfall in every month during 1974–2012. Rainfall amount is the sum of daily rainfall in every month during 1974–2012.

Close modal
Figure 5 shows the correlation coefficient between rainfall and storm tides in each month. It can be observed that the dependence between rainfall and storm tides is the largest in October and lowest in July. Thus, the urban disaster prevention strategy should consider the compound flooding from rainfall and storm tides in October. The reason for the different dependence between October and July may be related to the monthly rainfall structure. Compared with October, the number of rainy days in July (442 days) is higher than that in October (332 days), while the total rainfall amount in July (8,353.2 mm) is lower than that in October (9,149.6 mm). The proportion of rainfall lower than 10 mm in July is 76.46%, while it is 68% in October. This indicates that rainfall in July is mainly composed of small rainfall. Small rainfall is more susceptible to local small-scale climate (e.g., air humidity), but it has a small impact on storm tides, which would result in weak dependence between rainfall and storm tides. Moreover, the number of heavy rainfall (daily rainfall >25 mm) caused by TCs over the past decade is the highest in October and lowest in July (see Table 3). TCs are often accompanied by strong winds and rainstorms, which would enhance the dependence between rainfall and storm tides. Furthermore, the average wind speed of TCs is the strongest in October (see Table 3), which has the greatest influence on storm tides.
Table 3

The number of days of heavy rains caused by TCs and average wind speed of TCs during 2003–2012

MonthJun.Jul.Aug.Sep.Oct.
The number of days of heavy rains 12 
Average wind speed of TCs (m/s) 19.20 21.25 20.29 21.49 25.49 
MonthJun.Jul.Aug.Sep.Oct.
The number of days of heavy rains 12 
Average wind speed of TCs (m/s) 19.20 21.25 20.29 21.49 25.49 
Figure 5

Dependence of rainfall and storm tides for different months. The solid black line represents the Kendall's τ-value, and the blue dashed line represents the Spearman's ρ-value.

Figure 5

Dependence of rainfall and storm tides for different months. The solid black line represents the Kendall's τ-value, and the blue dashed line represents the Spearman's ρ-value.

Close modal

Analysis on tail dependence coefficient between rainfall and storm tides

The tail dependence coefficient between rainfall and storm tides is shown in Figure 6. The upper tail dependence coefficient of the rainfall and storm tides is significantly greater than the lower tail dependence coefficient, and the lower tail dependence coefficient is close to 0, that is, the upper tail is dependent and the lower tail is asymptotically independent. Furthermore, the upper tail dependence coefficient exhibits a significant positive trend with asignificant level equal to 0.01 (MK value = 0.266). This indicates that the relationship between extreme rainfall and high storm tides has shown a significantly increasing trend in recent years, which is consistent with the analysis in Section 3.1.2.
Figure 6

Tail dependence coefficient of rainfall and storm tides during 1974–2012. The solid black line represents the upper tail dependence coefficient value, and the blue dashed line represents the lower tail dependence coefficient value.

Figure 6

Tail dependence coefficient of rainfall and storm tides during 1974–2012. The solid black line represents the upper tail dependence coefficient value, and the blue dashed line represents the lower tail dependence coefficient value.

Close modal

In order to verify this conclusion, events that exceeded both the rainfall and storm tides marginal thresholds (90th percentile) in the different decades are shown in Supplementary material, Figure A1. The red points in the figure represent extreme rainfall observations co-occurring with extreme storm tides on the same day. As can be seen from the figure, joint extremes in the period of 2003–2012 occur more frequently than in other decades. It indicates that there is an increasing trend of dependence between extreme rainfall and extreme storm tides in recent years.

Analysis on joint probability distribution of rainfall and storm tides

Joint probability analysis

The joint probability of different combinations of H and Z is estimated through Equation (5). The MK test statistics of the joint probability for different return periods (RPs) of H and Z are shown in Supplementary material, Table A2. Supplementary material, Table A2 illustrates that there is a significantly increasing trend in the joint probability of different combinations of H and Z. The results of the SQMK test statistics in different combinations of H and Z are shown in Figure 7. A positive UF value indicates an increasing trend of H and Z, and a negative curve indicates a decreasing trend. When the UF value exceeds the critical value, it indicates a significant trend of change. The intersection of the curves UF and UB represents the change point of rainfall and storm tide events. From the figures a common characteristic can be seen: the joint probability shows a decreasing trend before 1988 and the changes are not significant, but a significantly increasing trend is observed after 1988–1992. This period is consistent with the analysis of Section 3.1.2.
Figure 7

The SQMK test statistics for the joint probability of different frequency rainfall and corresponding storm tides. 2% rainfall–2% storm tides means the combination of 50-year RP rainfall and 50-year RP storm tides.

Figure 7

The SQMK test statistics for the joint probability of different frequency rainfall and corresponding storm tides. 2% rainfall–2% storm tides means the combination of 50-year RP rainfall and 50-year RP storm tides.

Close modal

Conditional probability analysis

From the analysis of Section 3.1 and Section 3.2, the dependence between heavy rainfall and high storm tides is stronger than the dependence between small rainfall and low storm tides, and the joint impact of heavy rainfall and high storm tides is greater than that of small rainfall and low storm tides on urban flooding in the coastal cities. Thus, heavy rainfall events (50-year RP rainfall) and high storm tide events (50-year RP storm tides) are selected to analyze the conditional probability of rainfall and storm tides. Figure 8 shows the variability of and during 1974–2012. is the probability that Z exceeds (i.e., 50-year RP storm tides) when H exceeds (i.e., 50-year RP rainfall). is the probability that H exceeds when exceeds . Figure 8 illustrates that: (a) an increasing trend is observed in , but the change of is not obvious. (b) with the average value of 0.13 is significantly larger than with the average value of 0.05, that is, the occurrence probability of strong rainfall in high storm tide conditions is higher than that of high storm tide in strong rainfall conditions. Thus, compound flooding from rainfall and storm tides is more likely to occur when a high storm tide event has occurred.
Figure 8

The variability of and during 1974–2012.

Figure 8

The variability of and during 1974–2012.

Close modal

Limitation and future work

Similar to most research, some limitations also exist in this study. One is the limited record length and the quality of the observed data. The available record length of the observed data in this study lasted for 39 years. This record length is consistent with that of many studies (Yilmaz & Perera 2015; Zhang et al. 2018). Trend analysis on different temporal scales has attracted great concern over the past century. Long-term data covering more than 80 years (Haylock & Nicholls 2015; Bisht et al. 2017) and short-term data covering less than 30 years (Li et al. 2015; Naidu et al. 2015) have both been used in trend analysis on rainfall. It is noted that the trend analysis results are more reliable with a long time span and high-quality data. Another limitation of this investigation is the weak correlation between rainfall and storm tides when we establish the joint probability distribution between the two variables. The weak correlation between variables may have a potential influence on the joint probability analysis results. Even though the correlation between rainfall and storm tides is often weak, there are still many studies about their joint probability analysis (Zheng et al. 2014). For instance, Lian et al. (2013) used Gumbel copula and Zheng et al. (2013) proposed a bivariate logistic threshold-excess model to quantify the dependence between rainfall and storm surge. It is noted that a reasonable model which can reveal the weak correlation between the two variables should be selected to build the joint probability distribution.

In this paper, trends of compounding rainfall and storm tide events in a coastal city are investigated integrating Kendall's τ, Spearman's ρ, tail dependence coefficient, BCPD model, and the MK and SQMK test methods. From an annual variability point of view, statistically decreasing trends are observed when rainfall is higher than 1 mm. However, it is worth pointing out that increasing trends are detected when rainfall is higher than 10 and 25 mm. Furthermore, the upper tail dependence coefficient has a significantly positive trend. This indicates that the dependence between extreme rainfall and high storm tides has shown an increasing trend in recent years. For urban flood management, it is necessary to pay attention to the compound events from extreme rainfall and high storm tides. When any extreme event occurs, the compound effect of rainfall and storm tides on urban floods should be considered. From a monthly variability point of view, the dependence between rainfall and storm tides is the largest in October and the smallest in July. So, the urban disaster prevention strategy should consider the compound effect of rainfall and storm tides in October.

For joint probability, significant increasing trends are detected in different combinations of rainfall and storm tides after 1988–1992. This period is consistent with the result of annual dependence variability and the urbanization time of Haikou. Furthermore, flooding would occur when either rainfall or storm tides exceeds the design standard. Thus, it is necessary to consider the compound effect of rainfall and storm tides when urban flooding standards are developed in coastal cities. For coastal cities with two kinds of hazard factors (rainfall and storm tides), the traditional univariate analysis (e.g., rainfall analysis) cannot describe the dependence between the two hazard factors, and cannot fully reflect the factual flood mechanism of coastal flood disaster. Therefore, it is necessary to study the encounter probability of rainfall and storm tides based on the two-variable frequency analysis, so as to determine the flooding standard in coastal cities. For conditional probability, an increasing trend is observed in, and with the average value of 0.13 is significantly larger than with the average value of 0.05. Thus, compound flooding from rainfall and storm tides is more likely to occur when a high storm tide event has occurred.

The results contained herein will provide additional insights into the effect of climate change in Haikou City. The existence of the trends is essential for the planning and design of sustainable drainage measures in coastal cities. The impacts of the trends on urban drainage engineering need to be further explored.

This work was supported by the National Natural Science Foundation of China (Grant No. U20A20316), the Foundation for Innovative Research Groups of the Natural Science Foundation of Heibei Province (Grant No. E2020402074).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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