Simulation of storm surge inundation under different typhoon intensity scenarios: Case study of Pingyang County, China

China is one of the countries that are most seriously affected by storm surges. In recent years, storm surges in coastal areas of China have caused huge economic losses and a large number of human casualties. Knowledge of the inundation range and water depth of storm surges under different typhoon intensities could assist pre-disaster risk assessment and making evacuation plans, as well as provide 15 decision support for responding to storm surges. Taking Pingyang County in Zhejiang Province as a case study area, parameters including typhoon tracks, radius of maximum wind speed, astronomical tide, and upstream flood runoff were determined for different typhoon intensities. Numerical simulations were conducted using these parameters to investigate the inundation range and water depth distribution of storm surges in Pingyang County considering the impact of seawall collapse under five different intensity 20 scenarios (corresponding to minimum central pressure values equal to 915, 925, 935, 945, and 965 hPa) . The inundated area ranged from 103.51233.16 km to 103.51233.16 km for the most intense typhoon. The proposed method could be easily adopted in various coastal counties and serves as an effective tool for the decision making in storm surge disaster risk reduction practices.

(1) ln 22 -"The inundated area ranged from 233.16 km to 103.51 km for the most intense typhoon. " -> " "The inundated area ranges from 103.51 km to a 233.16 km for the most intense typhoon. " (2) ln 389 -"the sea wall would be failed to prevent inundation" -> "the sea wall would fail to prevent inundation" (3) ln 379 -"Statistical results of maximum inundated area associated with different typhoon intensity scenarios" -> "Extension of inundated areas associated with different typhoon intensity scenarios for different water level thresholds " Response: Thanks for all of your suggestion and comments. we have modified it according to your advice in the revised manuscript.

Introduction
China is among the few countries affected seriously by storm surges. A storm surge can cause overflow of tide water and seawall destruction that can result in flooding in coastal areas, which can be extremely destructive and can have serious impact on surrounding areas (Sun et al. 2015). Storm surges have occurred along much of China's coast from south to north (Gao et al. 2014). On average, approximately 30 nine typhoons annually make landfall over China (Shi et al. 2015), most of which cause storm surges. In owing to global climate change and sea level rise, the occurrence of weather situations that trigger storm surges has become more frequent and the associated risk level of coastal storm surges has increased significantly (Fang et al., 2014;Yasser et al., 2018). Fortunately, the number of fatalities in China due to storm surges has decreased significantly because of improvements in the regional early warning capability (Shi et al. 2015). Thus, the focus on storm surge disasters has changed from reduction of 40 disaster losses to mitigation of disaster risks. Therefore, research on storm surge risk has been attracted more and more attention (Shi et al., 2019).
Storm surge risk assessment aims to estimate the risk level of storm surges in a certain region based on deterministic numerical simulation in combination with designed probabilistic storm surge scenarios (Shi et al. 2013;Wang et al. 2018). The calculation of storm surge under scenarios with storms of different 45 intensity is an important part of storm surge risk assessment. The calculation results could provide important decision-making support for the response to storm surges in coastal areas, and they could assist in both the pre-assessment of storm surge disasters and the preparation of storm surge emergency evacuation plans. Following the earthquake-induced "3.11" tsunami that occurred in Japan in 2011, scientific research on many aspects of marine disaster risk management became of great concern to 50 various governments. With consideration of storm surge disaster as the primary hazard, China commenced a project for marine disaster risk assessment and zoning, and it subsequently released its marine industry standard, the Technical Guidelines for Risk Assessment and Zoning of Marine Disaster Part 1: Storm Surge (Liu et al. 2018). Calculation of the inundation range and water depth of storm surges associated with typhoons of different intensity is one of the most important tasks in storm surge 55 risk assessment.
The core element of simulation of inundation by storm surge disaster under scenarios of different typhoon intensity is to set key parameters for both the typhoons and the storm tides (e.g., typhoon track, typhoon intensity, radius of maximum wind speed, and astronomical tide) under different conditions (Shi et al, 2020). Tomohiro et al. (2010) set key parameters for the largest possible 60 typhoon-induced storm surge in different regions of Japan by simulating typhoon track translation using indicators of the Ise Bay typhoon (the most serious typhoon event recorded in Japan's history) as reference typhoon parameters. To overcome the limitation of historical records , a stochastic modelling method has been developed for simulation of typhoon track and intensity. This method is to analyze the statistical probability characteristics of historical typhoons in terms of their annual 65 frequency, seasonal distribution, track distribution, intensity, and influence areas. Based on these features, the generation, development, and lysis of typhoons can be simulated to generate a large number of typhoon events (Powell et al., 2005;Lin et al., 2010). By selecting events with different typhoon intensity from the generated samples, the inundation extents and depths of the study area can be calculated using the storm surge numerical model (Wood et al. 2006;Wahl et al. 2015), and 70 these researches mainly focus on the coast of North Atlantic Ocean. Considering the typhoon landing and historical storm surge events happened in the coastal areas of China, how to set the parameters for performing the simulation of typhoon-induced storm surge under different typhoon intensity scenarios is an interesting and important topic towards the coast of China.
This study considered Pingyang County of Zhejiang Province (China) as a case study area. The objective 75 was to propose a deterministic method to calculate the inundation extents and depths caused by different typhoon intensity scenarios combined with the storm surge numerical model. The key parameters (e.g., typhoon intensity, typhoon track, maximum wind speed radius) corresponding to the characteristics of typhoons landing the coastal areas of China was set. The astronomical tide, upstream flood runoff and seawall collapse was taken into consideration as an important factor in the storm surge simulation. The 80 results aim to contribute to the methodology of quantitative assessment of storm surge hazards for coastal counties.

Case study area
Pingyang County is a coastal county belonging to the city of Wenzhou in Zhejiang Province, China (Fig. 85 1) and is affected most frequently by storm surge in coastal areas. It is located in the tropical storm zone of the western Pacific Ocean and is generally exposed to the risk of storm surges during July-October.
Pingyang County lies within the region 27°21ˊ-27°46ˊN, 120°24′-121°08′E, and it is bordered by Ruian, Wencheng, Taishun, and Cangnan counties. The county extends roughly 83 km from east to west and roughly 25.4 km from north to south, covering an area of approximately 1051 km2. It is a highly

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Multisource data (Table 1) were collected to perform a storm surge numerical modelling in Pingyang county. The digital elevation map (DEM) of Pingyang county and nearshore submarine topography data were collected to construct the numerical model, and tidal observational data were used to validate the model. Historical typhoon records, including time, location, and intensity, were collected to set the typhoon parameters driving the storm surge numerical model. A field survey was 105 carried out by Zhejiang Institute of Hydraulics and Estuary to investigate the inundation situation along the Ao Jiang river in Pingyang County. Researchers equipped with GPS-RTK (Global Positioning Systems, Real-Time Kinematic) and rangefinders worked in two groups to make measurements from Oct.2nd to Oct.7th in 2013. The extent of the inundation was estimated based on flooding marks, such as the accumulation of trash, signs of mud, and withered plants. In addition, 110 the extent of inundation was established through interviews with local residents.

Methods
This study proposed a framework for calculation of storm surge inundation simulation under different 115 typhoon intensity scenarios (Fig.2). The proposed framework was composed by four parts: model configuration, model validation, parameters setting and inundation simulation. The numerical model was used to simulate the storm surge inundated range and water depth, and the DEM and nearshore submarine topography data was used to construct the storm surge numerical model. The numerical model was validated by historical observational data of tidal station and field-surveying data of inundated areas.

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Based on the historical observational data, the key parameters (e.g., typhoon track, radius of maximum wind speed, astronomical tide, and upstream flood runoff) could be set to drive the storm surge numerical model. The proposed method could be easily adopted in various coastal counties and serves as an effective tool for the decision making in storm surge disaster risk reduction practices.

Model configuration
The typhoon-astronomical-flood-wave coupled numerical model used in this study, developed by the Zhejiang Institute of Hydraulics and Estuary, is based on the unstructured-grid finite volume method, 130 and more detailed model information could be found in Chen et al (2019). It has characteristics of high efficiency, accuracy, conservation, and automatic capture of intermittent flow. This model could be used to simulate conventional river channel flow and offshore water flow including flood evolution, astronomical tides, storm surges, and flooding. The storm surge simulations were performed in combination with the calculation of river runoff and consideration of typhoon wind and air pressure fields. Waves caused by typhoon are simulated by Simulating Waves Nearshore (SWAN) model in this study (Booij et al, 1999). The SWAN model is a third-generation numerical wave model, which is used to simulate wind-generated wave propagation in coastal regions. It can describe the evolution of wave fields 150 under specific wind, flow and underwater terrain conditions in shallow waters. The governing equation is as follows.
In the equation, N is wave action, is relative frequency of waves, is wave direction, and S is source item. and are wave propagation speed in and direction, respectively. is propagation speed 155 of wave action in frequency space, and is the propagation speed of wave action in wave direction space. Based on the wave elements and the structural parameters of the seawall, the overtopping discharge is calculated by the empirical formula. In the simulation of dike-breaching, the varying dike top elevation is applied according to overtopping discharge to simulate the process of dike-breaching.

External force
The storm surge numerical model was driven by wind stress and the atmospheric pressure gradient acting 165 on the surface. The Jelesnianski model was chosen to generate the wind and pressure fields (Jelesnianski, 1965), for which the calculation formulas are as follows: , (0< ≤ ) (2) and In the above equations, R is the radius of maximum wind speed, r is the distance from the calculated point to the center of the typhoon, ( 0 , 0 ) is the translation speed of the typhoon, ( , ) and ( , )are the coordinates of the calculated point and the typhoon center, respectively, is the inflow 175 angle, 0 is the central pressure of the typhoon, ∞ is the atmospheric pressure at infinite distance, and is the maximum wind speed of the typhoon.     Besides, a validation for the inundation simulation was performed based on the inundation ranges through field surveying. The model described above was used to perform a simulation of the area along the Aojiang river (Pingyang County) inundated by Typhoon Fitow. A field survey was undertaken by the Zhejiang Institute of Hydraulics and Estuary to investigate the inundation areas in Pingyang County during the storm surge disaster period caused by Fitow (Fig. 7b). The simulated and investigated 220 inundation areas were compared (Fig. 7). It can be seen that the surveyed and simulated inundated areas are similar. The extent of the surveyed inundated area was slightly larger than that simulated because typhoon precipitation during the period of influence of Fitow caused urban waterlogging in parts of Pingyang County.    (Fig.9). This track was then used for the inundation superposition calculation. Warning Center,2018), it can be seen that the radius of maximum wind speed is inversely proportional to the central pressure difference (Fig 10). The radius of maximum wind speed has a strong relationship with the typhoon intensity, and an empirical formula was used to calculate the radius of maximum wind 280 speed as below: R = R 0 − 0.4( 0 − 900) + 0.01( 0 − 900) 2

Model verification
where 0 is the central air pressure (hPa), R is the radius of maximum wind speed, and R 0 is an empirical constant. The recommended value is 40, although this can also be adjusted by the fitting accuracy of the air pressure or the wind speed. Thus, the radius of maximum wind speed can be calculated

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The upstream flood is a factor required for numerical simulation of storm surges in estuary areas.
Analysis of measured data and model studies indicate that the high-water level in an estuary area is controlled mainly by the astronomical tide and the typhoon-induced storm surge. The peak flow in an estuary has obvious influence on the high-water level during the passage of a typhoon (Sun et al., 2017).
The storm surge-runoff interaction in an estuary area increases the tidal level of a typhoon-induced storm 305 surge, resulting in a larger hazard (Zheng et al., 2013). The larger the volume of runoff is, the greater the tidal level in the estuary area will be (Hao et al. 2018). The Feiyun and Aojiang rivers, located on the northern and southern sides of Pingyang County, respectively, are the main rivers that affect the level of flooding in Pingyang County. In this study, the superimposed upstream flood in the numerical simulation of storm surge was the average peak flows in the estuary areas of these rivers in the period of the selected 310 historical typhoons during April-October, i.e., 1717 and 2348 m3/s for the Aojiang River and Feiyun River, respectively.

Seawall collapse scenario
The seawall is an important barrier against storm surges and excessive overtopping of waves is the main cause of seawall collapse. Overtopping waves flush the seawall or the landward slope, forming a scour 315 pit. As the scour pit grows, the upper structure of the seawall loses support and becomes unstable (Sun et al. 2015;Zhang et al. 2017). In the design of the majority of seawalls in China's coastal areas, the wave overtopping rate, which is determined based on tide level, wave height, and seawall structure, is used as a controlling indicator and as a parameter to judge whether a seawall will collapse. According to the results of physical model tests, seawall collapse will occur when the wave overtopping rate of the 320 coastal seawall in Pingyang County exceeds 0.05 m 3 /s (Zhejiang Institute of Hydraulics and Estuary 2018). Once seawall collapse is determined in the numerical simulation, it will occur instantaneously without consideration of its process. After seawall collapse occurs in the numerical simulation, the ground elevation within the seawall is taken as the shoreline elevation, and the width of seawall collapse is determined by the wave overtopping rate at the representative point on the seawall. Each representative 325 point represents a section of seawall.

Calculation results
To further analyze the accuracy of the calculation results derived from the simulations, 22 representative reference points were set along the Pingyang County coast to obtain the desired data (Fig. 11). The calculated maximum water level at each reference point for typhoons of different intensity is shown in 330     by storm surge. The obtained results could serve as a basis for developing a methodology for storm surge disaster risk assessment in coastal areas. The study provides an insight into the spatial distribution of the areas potentially endangered by the typhoon related flooding. It can be helpful for further hazard and risk assessments for urban planning, emergency procedures and insurance.
The inundation extent of a storm surge is related to many factors (Petroliagkis, 2018). In this study, the 395 process of inundation is independent on the duration of the storm surge event, and a simplified sudden collapse of the seawall is assumed, which could increase the inundation range of the simulated result.
The water level in the towns of Shuitou and Xiaojiang in Pingyang County is mainly caused by the upstream flood of the Ao Jiang River. Consequently, the inundation in these two areas is directly related to upstream flood runoff. The impact of the upstream flood was only considered as the average of the 400 flood peak flow during the storm surge in this study. The water level and inundation areas caused by the large astronomical tide due to the superposition of the extreme flood scenarios might be more unfavourable than the simulated storm surge with the superimposed average of the flood peak runoff, which might result in uncertainty in the calculation results. We will analyze the quantitative response relationship between typhoon intensity at landfall and upstream flood runoff, and propose a quantitive 405 method for setting flood runoff upstream of the estuary area in the further research.
This paper presents a deterministic method for setting key parameters under typhoon intensity scenarios assuming that these factors (e.g., typhoon track, radius of maximum wind speed, astronomical tide, and upstream flood runoff) are independent. However, any correlation between these parameters is ignored.
The occurrence probability of parameter combinations is difficult to evaluate. The joint probability 410 method is an efficient way to determine the base flood elevation due to storm surge (Yang et al. 2019), and the joint probability among these factors could be established (e.g., using the Copula method) to calculate the occurrence of extreme storm surge events.
Data availability: All data used during the study are available from the corresponding author by request.