Haikou is located in the north of Hainan Island, China, where the geographical position is relatively independent (Fig. 1). The coastal area of Haikou is low and flat. In particular, the elevation of downstream plain and areas along Nandu River (in Fig. 1) is less than 3.0 m. Haikou is frequently affected by TCs and rainstorms from June to October. The annual rainfall is around 1660 mm. Storm tide flooding caused by TCs is one of the main natural hazards in Haikou, roughly three storm surges have occurred in Haikou every year in recent decades. The combination of storm tide and rainstorm will increase the probability of extreme compound flooding, posing a threat to social infrastructure and urban traffic in Haikou. For example, during Typhoon Kalmaegi (2014), a total of 219.8 mm (24 h) of precipitation was produced and the highest tide level reached 4.3 m in Haikou. The occurrence of heavy rainfall and strong storm tide caused serious compound flooding with an economic loss of USD 220 million. Under the changing environment, Haikou will face greater compound flooding risks and challenges from TCs, storm surges, and rainstorms in the future.

The geographic and meteorological data of the study area were systematically collected in this study (Table 1). The topographic map of the study area was provided by Hainan Emergency Management Department, and the bathymetry data of South China Sea and Beibu Bay were obtained from General Bathymetric Chart of the Oceans (GEBCO). The spatial resolution of the topographic map is 5 m, and the bathymetry data are 500 m. The meteorological data include historical TC track data and daily rainfall data from 1960 to 2017. The historical TC track data containing the TCs location (latitude and longitude), 2 min mean maximum sustained wind (MSW; m s-1), and minimum pressure (hPa) near the TC centre were provided by Shanghai Typhoon Institute of China Meteorological Administration. The daily rainfall data of Haikou were downloaded from the CMA website (http://data.cma.cn/, last access: 16 July 2020) and can be transferred to hourly rainfall by interpolation for inundation simulation (Ye et al., 2018; Yang et al., 2013). The annual river discharges at Longtang hydrological station from 1960 to 2020 were provided by Hainan Hydrology and Water Resources Survey Bureau.

Delft3D Flexible Mesh (DFM), developed by Deltares in 2011, is a practical unstructured shallow water flow calculation model (De Goede, 2020). It can be used for ocean hydrodynamic and surface runoff numerical simulations (Kumbier et al., 2018; Meijer and Hutten, 2018). In this study, the DFM model was established to calculate the hydraulic boundary conditions needed to estimate the overland flow boundary and simulate the overland inundation during the TC period (Gori et al., 2020b).

The TCs that pass through the region (18–22∘ N, 109–113∘ E) and stay over 24 h have an apparent effect on Haikou (Ding, 1999; Wang et al., 1998; He, 1988). According to this, we analyse historical TC tracks and give the priority to the TC passing between latitudes 18 and 22∘ N and longitudes 109 and 113∘ E. TC tracks lasting less than 24 h in this region are removed in this study. Therefore, 66 TCs from 1960 to 2017 are selected in this study (Fig. 2), and we construct typhoon wind fields and simulate the storm tide of these TCs. Each TC event has a code; for example, the ninth typhoon in 1963 is coded as TC6309.

In this study, we investigate the probability distribution of storm tides to assess compound flood hazards. Based on the storm surge model, the storm tide series of 66 TCs are simulated. The highest storm tides during TCs are used to calculate the probability distribution function at Xiuying tide gauge station.

Exploring the storm tide distribution can offer comprehension of the probability of compound flood hazards from storm surge. Extreme value distribution (EVD) is widely applied to investigate storm tide probability distribution (Yum et al., 2021). We assume that the storm tide fits either Gumbel or Weibull extreme value functions, then calculate their function fitting parameters. We compare the goodness of fit of two distribution functions (Gumbel, Weibull) with Kolmogorov–Smirnov (K–S) test. K–S test is an appropriate method to explore the distribution of continuous random variables and can be used to select the best fitting distribution function. According to the storm tide distribution, we can achieve tide levels at different probabilities (P). We replace P with storm tide return periods (T), which is equal to 1/P, to investigate the possibility of an extreme storm tide. The corresponding TC events in 5-, 10-, 25-, 50-, and 100-year return periods can be found to compare the compound flood hazards with different storm tides.

We use TC1415 to verify the astronomical tide and storm tide of the storm surge model. In the validation of astronomical tide, we use the predicted astronomical tide at two gauge stations: Naozhoudao (Zhanjiang, Guangdong) and Xiuying (Haikou, Hainan). The calculation results show that the RMSE is 0.18 and 0.14 m for Naozhoudao and Xiuying gauge station; the R2 values of both Naozhoudao and Xiuying gauge station are 0.91. Figure 3a and b depict simulated and predicted water level at Xiuying and Naozhoudao gauge station. The curves of simulated astronomical tide at the two stations fit observed tide level points well. Thus, this model has a good ability to simulate astronomical tides. In the validation of storm tide, we add the wind field of TC1415 in the model and only use the observed tide level at Xiuying gauge station for validation (Fig. 3c). The calculation of RMSE is 0.34 and R2 is 0.83. It can be seen from Fig. 3c that the curve of simulated storm tide is consistent with the observation, and the highest storm tide is well simulated.

Tide levels along the coastline extracted from the storm surge model serve as coastal boundary conditions for the overland flooding model. We utilize the TC1415 event also to validate the overland flooding model. Comparing the simulation of compound flooding with the measured inundation of roads during TC1415 (Kuang and Zhang, 2014), the main inundation area in the simulation is coincident with the flooded roads (Fig. 4). Furthermore, the distribution of simulated inundation area is also consistent with the actual flood distribution. Hence this overland flooding model has a good capacity for modelling and demonstrating TC flood hazards.

Xiuying gauge station is selected as a representative location to examine the probability exceedance of TC storm tide. Storm tide return period is calculated based on the maximum storm tide in the past 58 years simulated for 66 TCs. The results of K–S test show that the D value and P value of GUM are 0.0615 and 0.9995, while the D value and P value of WEI are 0.0769 and 0.9876. Thus, the Gumbel extreme value (GEV) distribution function can fit TC storm tide better. Figure 5 shows that GEV fits storm tide well, presenting the corresponding TCs under different return periods. Red circles represent the maximum storm tide from the 66 TCs in the past. The solid line represents estimation of the GEV fitting.

Table 2 shows the corresponding TC events and their highest storm tide and accumulated rainfall under different return periods. TC1415, with the highest storm tide, is considered a 100-year event. In order to investigate the compound effects of storm tide and rainstorm on the overland inundation, TCs with higher accumulated rainfall are selected. As a result, TC6311, TC8616, TC8007, and TC7109 are assigned to 50, 25, 10, and 5 years based on GEV fitting, respectively.

Figure 6 presents the compound flood inundation maps under 5-, 10-, 25-, 50-, and 100-year return period. For the 5-year inundation map, the major inundation area is distributed along the Jiangdong New Area and Xinbu Island on the northeast coast. The inundation area with sporadic distribution is caused by rainfall in the inland urban area. As return periods increase, Haidian Island, north Longhua district, and northwest Xiuying district begin to have serious flood extents, and the compound flooding severity of Jiangdong New Area and Xinbu Island increases. For 100-year return period, the inundation depth regions are above 1.0 m, and the floodplain depth is above 3.0 m in most of Jiangdong New Area. Regions with inundation depth below 0.05 m are not evaluated in this study due to their low risk.

Table 3 indicates the inundation depth and area under different return periods. In 100-year TC event, the total inundation area is 12613 ha, and the inundation area between 0–0.5 and 1.0–2.0 m accounts for 29.4 % and 31.1 %, respectively. The inundation area between 0.5–1.0 m and 2.0–3.0 m accounts for a total of 32.7 %. For the other TC events, the inundation depth at a range of 0–0.5 and 1.0–2.0 m has the most inundation area. For a 100-year TC event, the inundation area with a depth above 1.0 m increases by approximately 2.5 times compared with a 5-year TC event.

Figure 7 illustrates the maps of rainstorm inundation and storm tide flooding under different return periods. In each rainfall scenario, the overall inundation depth is below 1.0 m, while in each storm tide scenario, the overall inundation depth is above 1.0 m. When comparing the rainstorm inundation map and storm tide flooding map in the same TC event, it is obvious that the storm tide flooding is significantly worse than rainstorm inundation.

Figure 8 compares the overall inundation area of rainstorm, storm tide, and compound flooding under different return periods. The inundation area of compound flooding exceeds the inundation area of rainstorm inundation and storm tide flooding in each TC event. Thus, compound flood hazards can have more serious consequences than rainstorm and storm flooding (Bevacqua et al., 2019; Wahl et al., 2015; Zscheischler et al., 2018). Moreover, it can be seen from Fig. 8 that compound flooding has more inundation area than the accumulation of rainstorm and storm tide flooding under different return periods. For example, in the TC6311 scenario, the total inundation area of compound flooding is 11 462 ha, exceeding the sum of rainstorm inundation and storm tide flooding, which is 10 616 ha. Therefore, compound flood hazards are more destructive than the combination of single-driven flood hazards and have a certain amplification effect (Fang et al., 2021; Xu et al., 2019).

However, storm tide and rainstorm are the driving factors in a compound flood hazard (Hsiao et al., 2021; Fang et al., 2021; Bevacqua et al., 2019). This study investigates the compound effect of flood hazards by studying the probability distribution of highest storm tides during TCs. Many studies have confirmed that rainfall and storm surge have statistically positive dependence (Wu et al., 2018; Wahl et al., 2015; Xu et al., 2014; Zheng et al., 2014; Lian et al., 2013). Hence, it is of practical significance to reveal compound flood risk considering the statistical dependence of rainfall and storm surge. Copula is a kind of function connecting joint distributions and marginal distributions (Lin-Ye et al., 2016). Zhang et al. (2021) calculated the overtopping occurrence by determining the correlations between tidal levels and wave heights based on copula function. In recent years, the copula function has been confirmed to model and describe the dependence between flood variables and express compound flood risk (Zellou and Rahali, 2019). Xu et al. (2019) employed the copula function to investigate the bivariate return period of compounding rainfall and storm tide events, finding that the joint probability analysis can reveal more adequate and comprehensive risk about compound events than univariate analysis. Therefore, in future works, we will adopt the copula function to investigate the joint occurrence of rainfall and storm surge during TCs, further assessing extreme compound flooding severity.