Sensitivities of modelling storm surge to bottom friction, wind drag coefficient, and meteorological product in the East China Sea

Estuarine, Coastal and Shelf Science 231 (2019) 106460

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Sensitivities of modelling storm surge to bottom friction, wind drag coefficient, and meteorological product in the East China Sea Dongdong Chu a, b, Jicai Zhang a, c, *, Yongsheng Wu b, Xiaohui Jiao a, Suhui Qian a a

Institute of Physical Oceanography, Ocean College, Zhejiang University, Zhoushan, 316000, China Ocean Ecosystem Sciences Division, Fisheries and Oceans Canada, Bedford Institute of Oceanography, Dartmouth, Canada c Applied Ocean Physics and Engineering Department, Woods Hole Oceanographic Institution, Woods Hole, 02543, Massachusetts, USA b

A R T I C L E I N F O

A B S T R A C T

Keywords: Storm surge Wind fields Wind drag coefficient bulk formulae Bottom friction FVCOM

In this study, effects of meteorological product, wind drag coefficient, and the bottom drag coefficient on the modelling storm surge in the East China Sea were investigated by using a high-resolution model based on FVCOM (Finite Volume Community Ocean Model). The model was first evaluated against the observational storm surge caused by Typhoon Winnie; the sensitivities of modelling surge variations to different factors were then exam­ ined, including four different meteorological products (ERA-Interim, ERA5, CCMP, NCEP-CFSR), seven formulae of wind drag coefficient (Peng & Li, Large & Pond, Garratt, Wu, Large & Yeager, Edson, and Zijlema), and six cases of bottom drag coefficient. The results indicated that all the experiments could capture temporal variations of the surge elevations. However, NCEP-CFSR wind field performs the best among the four wind field products. The wind drag coefficient formulae of Large & Yeager produce better results than the other formulae. The formulae of Edson, Wu, and Garratt produce higher surge elevations than those of the Large & Pond and Zijlema at the time of peak surge. Decreasing the bottom friction has a greater impact on surge elevations and current velocities than increasing the bottom friction. The non-linear interaction between tides and surge was studied as well, and the results showed that the non-linear effect contributed by 37% to the peak surge. The best combi­ nation of wind field and parameters derived from the sensitivity studies was used for the other three different storms (Chan-Hom, Herb and Mireille), and the simulations indicated that the best combination of forcing and drag coefficient obtained in this study in general can improve the performance of storm surge models.

1. Introduction Surges, induced by storms, such as tropical cyclones, are able to cause extreme flooding in coastal areas (Xia et al., 2008; Feng et al., 2016; Mao and Xia, 2017), particularly when they coincide with high spring tides or low neap tides (Maspataud et al., 2013; Olbert et al., 2013). Storm surges are usually caused by the cumulative effect of multiple processes such as strong wind, atmospheric pressure distur­ bances, wind-driven wave setup and currents, geostrophic effect, and astronomical tides (Kerr et al., 2013). The combination of storm surge, tides and waves are able to cause flooding in coastal cities, severe erosion along beaches, and damage to marinas and ships in harbors (Lin et al., 2012; Haigh et al., 2014). The dynamics of surge, such as its propagation, nonlinear interaction with tides, topography, and waves are quite complex. Variations in surge are not only related to the properties of forcing, such as wind speeds,

storm sizes and transit speeds, but also the local topography and coastlines (Rego and Li, 2010). Storm surges can be aggravated by some of these features, and others attenuate it through surface and bottom friction (Bunya et al., 2010; Wamsley et al., 2010). It is, therefore, of practical as well as scientific interests to study surges caused by tropical cyclones and to understand how they change spatially. It is also neces­ sary to understand the variations of surges as a function of storm and tide characteristics, and the effect of bottom friction introduced by local seabed properties. In order to accurately predict storm surge, it is important to get a better understanding of the sensitivity of storm surges in response to different atmospheric forcing and drag coefficient formulations (Die­ trich et al., 2010; Akbar et al., 2017). In recent years, storm surge forecasting and hindcasting have achieved great progress. Wave-current coupled models have been widely used in storm surge simulations (Ferrarin et al., 2013; Xie et al., 2016). In addition, ocean models with

* Corresponding author. Institute of Physical Oceanography, Ocean College, Zhejiang University, Zhoushan, 316000, China. E-mail address: [email protected] (J. Zhang). https://doi.org/10.1016/j.ecss.2019.106460 Received 10 January 2019; Received in revised form 19 October 2019; Accepted 30 October 2019 Available online 5 November 2019 0272-7714/Crown Copyright © 2019 Published by Elsevier Ltd. All rights reserved.

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Fig. 1. (a) Bathymetry of numerical model and observed tidal gauge stations (red inverted triangle symbol) recorded during typhoon Winnie, (b) computational grid of study domain, and (c) observed tidal gauge stations (red solid circles for water level and red pentagrams for wind speed) recorded during typhoon Chan-Hom. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

unstructured grid are employed to perform coastal oceanographic research, and numerical models with higher resolution and complexity are adopted to improve the accuracy of simulations (Moon et al., 2009). Nevertheless, there are still areas to be improved in storm surge modeling, such as accuracy of the wind field, parameterization of sur­ face wind drag coefficient and bottom friction effect. Wind is the main driving force for storm surges. A variety of studies have been conducted to forecast and hindcast wind fields. Currently, several kinds of wind field sources are adopted in storm surge simula­ tions, for instance: (1) Reanalysis data generated by European Centre for

Medium-Range Weather Forecasts (ECMWF) (Dee et al., 2011), Cross-Calibrated Multi-Platform (CCMP) (Atlas et al., 2011), National Centers for Environmental Prediction’s Climate Forecast System Rean­ alysis (NCEP-CFSR) (Saha et al., 2014); (2) Analytical parametric models (Holland, 1980); (3) Full scale physics-based dynamics models, such as Weather Research and Forecasting model (WRF) (Skamarock et al., 2005), and the Fifth-generation Penn state/NCEP mesoscale model (MM5) (Grell et al., 1994). Wind drag coefficient and bottom friction coefficient are the key control parameters to parameterize the sea surface and bottom friction effects in storm surge models. 2

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Fig. 2. The wind intensity and path of typhoons Winnie and Chan-Hom during August 15–20, 1997 and July 07–12, 2015, respectively. The best track data for two typhoons was obtained from IBTrACS.

Historically, wind drag coefficient has commonly been set either as a constant value (Jones and Davies, 1998), or using an empirical formula that is linearly related to wind speed (Garratt, 1977; Smith, 1980; Large and Pond, 1981; Wu, 1982). In recent years, multiple nonlinear formulae have been proposed and applied to storm surge simulations (Jarosz et al., 2007; Large and Yeager, 2009; Zijlema et al., 2012; Edson

et al., 2013; Peng and Li, 2015). Previous studies concentrated on either parameterizations of multi­ ple processes for a single storm or parameterization of one process for multiple storms. Akbar et al. (2017) used SWANþ ADCIRC model to study the effect of bottom friction, wind drag coefficient, and meteo­ rological forcing in the hindcast of hurricane Rita. Mao and Xia (2017)

Fig. 3. The wind intensity and path of typhoons Herb and Mireille during July 30, 1996 to August 2, 1996 and September 25–28, 1991, respectively. The best track data for two typhoons was obtained from IBTrACS. 3

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Table 1 Locations, record time and observed variables at different tide-gauge stations during four wind events. ID

Station

Observed Variable

Record Time

Lon (� E)

Lat (� N)

DJS

Dajishan

Water Level (Winnie)

122.1667

30.8167

DH

Dinghai

Water Level (Winnie)

122.1000

30.0167

SS

Sansha

Water Level (Winnie/ Herb/ Mireille)

120.2167

26.9167

DS

Dongshan

Water Level (Winnie)

117.5333

23.7333

GT

Guantou

Water Level (Winnie)

119.5667

26.1333

CW

Chongwu

Water Level (Winnie)

118.9333

24.9833

PT

Pingtan

Water Level (Winnie/ Mireille)

00:00 August 16–18:00 August 19, 1997 00:00 August 16–18:00 August 19, 1997 00:00 August 16–18:00 August 19, 1997/00:00 July 30–18:00 August 02, 1996/ 00:00 September 25–07:00 September 28, 1991 00:00 August 16–18:00 August 19, 1997 00:00 August 16–18:00 August 19, 1997 00:00 August 16–18:00 August 19, 1997 00:00 August 16–18:00 August 19, 1997/00:00 September 25–07:00 September 28, 1991 00:00 August 16–18:00 August 19, 1997/00:00 July 30–18:00 August 02, 1996 00:00 July 01–18:00 July 11, 2015 00:00 July 01–18:00 July 11, 2015 00:00 July 01–18:00 July 11, 2015 00:00 July 01–18:00 July 11, 2015/00:00 July 09–18:00 July 11, 2015 00:00 July 09–18:00 July 11, 2015 00:00 July 09–18:00 July 11, 2015 00:00 July 09–18:00 July 11, 2015

119.8333

25.4667

SC

Shacheng

Water Level (Winnie/ Herb)

A

Dachen

Wind (ChanHom)

B

Nanji

Wind (ChanHom)

C

Zhoushan Sea

Wind (ChanHom)

D

Zhujiajian

Wind/Water level (ChanHom)

E

Daishan

Water level (Chan-Hom)

F

Liuheng

Water level (Chan-Hom)

G

Beilun

Water level (Chan-Hom)

120.2833

27.2833

121.9011

28.4531

121.0823

27.4589

123.9650

29.5000

122.4274

29.8935

122.2200

30.2800

122.0600

29.7700

122.1200

29.9300

Table 2 Model setups of sensitivity experiments in storm surge simulations. Case Name

Simulation Period

Wind Source

Bulk Formula

BDC

1a 1b 1c 1d 2a 2b 2c 2d 2e 2f 3a 3b 3c 3d 3e 4a 4b 4c 4d 4e 4f

1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 1997 July 10-August 30 2015 June 01-July 16 2015 June 01-July 16 1996 July 01-August 05 1996 July 01-August 05 1991 September 01–30 1991 September 01–30

NCEP-CFSR CCMP ERA-Interim ERA5 NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR NCEP-CFSR

LP81 LP81 LP81 LP81 Edson G77 LY Peng Wu Zijlema LY LY LY LY LY LP81 LY LY LY LY LY

default default default default default default default default default default Koutitas 0.0015 0.003 Cz/2 2Cz default Cz/2 default Cz/2 default Cz/2

Table 3 Evaluation of model performance of sensitivity experiments. Case Name 1a 1b 1c 1d 2a 2b 2c 2d 2e 2f 3a 3b 3c 3d 3e 4a 4b 4c 4d 4e 4f

Total elevation

Surge elevation

MS

RMSE

CC

RB

MS

RMSE

CC

0.98 0.99 0.99 0.99 0.98 0.98 0.99 0.96 0.98 0.98 0.99 0.98 0.98 0.98 0.98 0.95 0.97 0.99 0.99 0.99 0.99

0.35 m 0.32 m 0.32 m 0.32 m 0.40 m 0.40 m 0.35 m 0.56 m 0.40 m 0.36 m 0.35 m 0.43 m 0.36 m 0.49 m 0.37 m 0.42 m 0.29 m 0.37 m 0.33 m 0.23 m 0.36 m

0.98 0.98 0.99 0.98 0.98 0.98 0.98 0.97 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.94 0.96 0.99 0.99 0.99 0.99

13 7 8 7 16 15 13 21 15 13 13 13 13 13 13 / / / / / /

0.82 0.73 0.75 0.74 0.84 0.84 0.83 0.76 0.84 0.82 0.83 0.84 0.82 0.84 0.81 0.94 0.94 0.87 0.87 0.72 0.80

0.28 m 0.34 m 0.33 m 0.33 m 0.30 m 0.29 m 0.28 m 0.41 m 0.29 m 0.29 m 0.28 m 0.28 m 0.29 m 0.27 m 0.29 m 0.19 m 0.19 m 0.23 m 0.23 m 0.09 m 0.08 m

0.86 0.84 0.85 0.84 0.86 0.85 0.86 0.73 0.85 0.84 0.86 0.86 0.86 0.86 0.85 0.91 0.90 0.85 0.85 0.68 0.71

RB

/ / / / / / / / / / / / / / / / /

28 47 44 43

storm surges and the upper ocean response in coastal water have been studied in previous studies, the combination of wind forcing and parameterization of drag coefficient in storm surge modelling with an unstructured mesh is lacking in the East China Sea, which is charac­ terized by frequent and strong storm surges. Besides, the mechanisms by which the tide-surge interaction, wind stress and bottom friction influ­ ence the dynamics of storm surges are far from clear for the East China Sea. In this study, a high-resolution unstructured model is developed based on FVCOM and evaluated against field observations. The model is then used to investigate the sensitivity of wind fields, bottom drag for­ mulations, and wind drag formulations in storm surge modelling. The main research objectives are listed as follows: (1) To establish a 3-D high-resolution ocean model that can reasonably simulate storm surges; (2) To explore the above three processes in storm surge models in the East China Sea, as well as the tide-surge interaction of storm surges that caused by typhoon Winnie. (3) To examine the synergistic effect of the above three processes in other three typhoon induced storm surge simulations (typhoon Chan-Hom, Herb and Mireille).

explored the dynamics of wave-current-surge interactions while considering the effects of wind field sources, wind drag coefficient bulk formula, and parameterizations of the bottom friction term in Lake Michigan. Peng and Li (2015) compared eight wind drag coefficient formulas in eight typhoon-induced storm surges in the South China Sea. Jensen et al. (2012) adopted NCEP-CFSR wind field to hindcast seven storms passing over Lake Michigan. Different wind stress and bottom friction combinations may lead to the similar result in the storm surge simulation. Although the modelling studies of typhoon’s impacts on 4

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Fig. 4. The model results of Case 1a, (a) peak surge; (b) maximum current velocity.

Fig. 5. The model results of surge elevations by using NCEP-CFSR (Case 1a), CCMP (Case 1b), ERA-Interim (Case 1c), and ERA5 (Case 1d) winds versus observed values at various tidal gauge stations during typhoon Winnie. (a) Daijishan; (b) Dinghai; (c) Shacheng; (d) Sansha; (e) Guantou; (f) Pingtan; (g) Chongwu; (h) Dongshan.

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Fig. 6. Contour plots of peak surge elevation and velocity differences for the hindcast of typhoon Winnie storm surges. (a) Maximum elevation difference: Case 1bCase 1a; (b) maximum velocity difference: Case 1b-Case 1a; (c) maximum elevation difference: Case 1c-Case 1a; (d) maximum velocity difference: Case 1c-Case 1a; (e) maximum elevation difference: Case 1d-Case 1a; (f) maximum velocity difference: Case 1d-Case 1a.

The paper is organized as follows. Section 2 introduces the meth­ odology including the model and data. Section 3 describes the sensitivity analysis and model results. Three validation cases of typhoon ChanHom, Herb and Mireille are also included. Conclusions are shown in section 4.

2.2. Descriptions of finite-volume community ocean model (FVCOM) The model used in this study is FVCOM (Chen et al., 2003). It uses a non-overlapping unstructured triangular grid in the horizontal to resolve dynamics in complex regions, which is highly suitable for the present study with irregular complex coastlines. Wind stress is computed by using the conventional formulation with respect to the wind speed as follows:

2. Methodology 2.1. Study domain and model meshes

�! �! ! τs ¼ Cd ρa j VW j VW

The study domain covers the Bohai Sea, the Yellow Sea, and the East China Sea. The land boundaries are limited by the coastlines, and three open boundaries are set along the open seas. The high-resolution ba­ thymetry data for the coastal areas adjacent to Zhejiang province and Yangtze estuary were provided by the Ocean and Fisheries Bureau of Zhejiang Province, and data for the other areas were obtained from Etopo1 and interpolated to the computational cells. The unstructured triangular grid of computational domain consists of 29916 nodes and 57125 elements and has a resolution from 0.5 km for coastal zone to 20 km near open sea boundaries. In addition, 7 uniform σ layers are specified in the vertical profiles.

(1)

�! where ρa , Cd , and VW are the air density, wind drag coefficient, and wind velocity at 10 m above the sea surface, respectively. The wind drag co­ efficient formula proposed by Large &Pond (1981), hereafter referred to as LP81, is incorporated into the default FVCOM: 8 < 3

Cd � 10 ¼

6

:

1:2 �! 0:49 þ 0:065j VW j 0:49 þ 0:065 � 25

�! j VW j � 11:0 �! 11:0 � j VW j � 25:0 �! j VW j � 25:0 (2)

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Fig. 7. Time series of wind speed and wind direction from CCMP, NCEP-CFSR, ERA-Interim and ERA5 wind fields versus observations at Zhujiajian, Dachen, Nanji, Zhoushan Sea during July 01–12, 2015.

The bottom friction stress is calculated from a quadratic expression: qffiffiffiffiffiffiffiffiffiffiffiffiffiffi � τbx ; τby ¼ Cz ρw ðub ; vb Þ u2b þ v2b (3)

The four wind field sources include: (a) ERA-Interim: 6-hourly, 0.125� -resolution forcing is a global atmospheric reanalysis from 1979, continuously updated in real time; (b) CCMP: 6-hourly, 0.25� resolution forcing produced From satellite, moored buoy, and model wind data, using a Variational Analysis Method to produce four maps daily of 0.25� -resolution gridded vector winds; (c) NCEP-CFSR: 6-hour­ ly, 0.3� -resolution horizontal resolution, along with forecast 6 h; (d) ERA5: 1-hourly, 0.25� -resolution forcing that combines vast amounts of historical observations into global estimates using advanced modelling and data assimilation systems. In addition, NCEP-CFSR wind field is produced from the two-way atmosphere-ocean fully coupled modeling system (Mao and Xia, 2017). CCMP wind field is a reanalysis product which is produced using satellite data, moored buoy observations, and model wind data. ERA-Interim is a global atmospheric reanalysis prod­ uct which is generated by Variational Analysis Method, and ERA5 is a dataset using advanced modelling and data assimilation systems. The dataset of historical tropical cyclones was obtained from the International Best Track Archive for Climate Stewardship (IBTrACS). It provides central position, minimum pressure and maximum sustained wind speed every 6 h.

where ðub ; vb Þ is the x and y components of bottom current velocity; the drag coefficient Cz is determined by matching a logarithmic bottom layer to the model at a height Zab above the bottom, mathematically expressed as: � � � �2 � Zab Cz ¼ max k2 ln ; 0:0025 (4) Zo where k ¼ 0.4 is the von Karman constant and Zo is the bottom rough­ ness parameter. 2.3. Model input and observational data The external forcing for the present model includes water level, wind speed, air pressure, and river runoff. The model domain contains three oceanic open boundaries. As shown in Fig. 1a, the Northern, Eastern and Southern open boundaries are located in the Korea Strait, the shelf of the East China Sea, and the Taiwan Strait, respectively. The water levels prescribed along the open boundaries was derived from the TPXO 7.2 global model of ocean tides (available at http://volkov.oce.orst.edu/ tides/TPXO7.2.html). Hourly tidal elevations were predicted by four diurnal components (K1, O1, P1, Q1), four semidiurnal components (M2, S2, N2, K2), three shallow water components (M4, MS4, MN4), and two long-period components (Mf, Mm). The daily discharge of Yangtze River was employed in the present model. The data was obtained from the Datong hydrological station, available at http://yu-zhu.vicp.net/. Since daily discharge data before the year of 2000 were not available, the average multi-year daily discharge was used as the inflow condition of the typhoon Winnie, typhoon Herb and typhoon Mireille; however, typhoon Chan-Hom used daily discharge measured at Datong Station.

2.4. Design of numerical experiments Storm surge simulations were conducted for Typhoons Winnie, Chan-Hom, Herb, and Mireille, which caused combined damages of more than hundreds of million U.S. dollars. The tracks of four typhoon events are shown in Fig. 2 and Fig. 3. Besides, the detailed record in­ formation of four typhoon events are shown in Table 1. In order to simulate the storm surge event of Winnie, four different wind field sources, seven various wind drag coefficient formulae, and six different parameterizations of bottom drag coefficient formulae were employed to study the sensitivity of storm surge model in response to these physical processes. Detailed settings of sensitivity experiments including the formulae of bottom drag coefficient (BDC) and the bulk formula of the wind drag coefficient are listed in Table 2. In Table 3, the Model Skill 7

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Fig. 8. Wind fields (black arrows) and corresponding surge elevations (colored maps) using CFSR, ERA-Interim, CCMP and ERA5 wind fields 6 h prior to (left panel), during (middle panel), and 6 h after (right panel) the surge peak of the typhoon Winnie at 00:00 on August 18, 1997.

(MS), root-mean-square error (RMSD), correlation coefficient (CC) and relative error (RB) are calculated for total elevation and storm surge elevation. The numerical case 1a is used as the benchmark experiment; experiments of 1a-1d are used to analyze the effects of four different wind fields; 2a-2f are adopted to analyze the impacts of seven wind drag formulae; 3a-3e are employed to analyze the influence of six bottom drag coefficient on storm surge elevation; 4a-4f are used to examine the effect of the best combination of forcing and parameterization of drag coefficient in other three storm surge simulations.

where n is the number of the variable values; Xm and Xm are time-varying model results and time mean values, respectively; Xo and Xo are timevarying values of observed results and time mean values, respectively. (b) The root-mean-square deviation "

i¼1

i¼1

i¼1

ðXo

(6)

n

# 2

Xo Þ

(7)

i¼1

The performance of the model depends on the value of MS, and it is classified as excellent (MS > 0.65), very good (0.5 < MS < 0.65), good (0.2 < MS < 0.5), and poor(MS < 0.2), respectively (Mar�echal, 2004; Allen et al., 2007).

#1=2

n X

Xo Þ2

(c) The model skill " , n n X X 2 MS ¼ 1 ðXm Xo Þ ðXo

In order to evaluate the effectiveness of the model, four parameters are calculated to quantify the difference between observations and simulation results. The parameters are computed as follows.

X m Þ2

ðXm i¼1

2.5. Skill metrics

(a) The correlation coefficient " #," n n X X CC ¼ ðXm X m ÞðXo X o Þ ðXm

, #1=2

n X

RMSD ¼

X o Þ2

(d) The relative bias

i¼1

(5)

8

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D. Chu et al. n P

ðXm Xo Þ RB ¼ i¼1 P � 100% n jXo j

(8)

i¼1

3. Results of sensitivity experiments Different model setups are used to hindcast storm surge caused by typhoon Winnie. Fig. 4 shows the model results of the spatial distribu­ tion of peak surge and maximum current velocity during the period of typhoon Winnie, respectively. According to the model results, one can find that both the peak surge and the maximum current velocity increase from the open seas to the coastal zone and reach the maximum value at the Hangzhou Bay. 3.1. Sensitivity to various wind field sources Fig. 5 shows the comparisons of the time series of simulated storm surge elevations forced by four different meteorological forcing against observed data at eight stations recorded from August 16–20, 1997. Four skill metrics of total elevation and surge elevation are presented in Table 3. The calculated values of model skill forced by three wind fields are greater than 0.65. In addition, the correlation coefficients between model results and observed water levels reach above 0.94, relative percent error less than 20% (except in case 4d), and the model skill above 0.94, which indicates that the model is reasonable to simulate this storm surge. The smallest RMSD of 0.32 m and the smallest RB of 7% are both obtained in ERA5 wind field simulation case when evaluating the performance of total elevation. In the meanwhile, the smallest RMSD of 0.28 m, the largest CC of 0.86 and the smallest RB of 28% are all ob­ tained in NCEP-CFSR simulation case, while CCMP simulation case ob­ tained the largest RMSD value of 0.34 m and smallest CC of 0.84. Consequently, the model results of NCEP-CFSR wind field achieved the minimum bias compared with the other three wind fields in sue eleva­ tion simulations. On average, the model results of four wind fields show similar surge patterns and reproduce the variations of sea level anomaly reasonably. In addition, in four cases the predicted arrival time of surge peaks is the same, with different phase shift at different observed sta­ tions. Fig. 5g–h shows 3 h ahead of time compared with the observed data in Chongwu and Dongshan stations. Fig. 5a presents 2 h ahead of time compared with the observed data in Dajishan station, and Fig. 5b, c, 5e, and 5f show 1 h ahead of time at Dinghai, Shacheng, Guantou, and Pingtan stations, respectively. At Sansha station, however, the model results of surge elevation capture the arrival time of peak surge satis­ factorily. In addition, numerical simulations forced by four different meteorological forcing underestimated surge elevations in comparison to the observed ones with the default model settings, which can be

Fig. 9. Wind stress drag coefficient as a function of wind speed in different formulae. Peng and li (2015, black), Garratt (1977, green), Large and Pond (1981, blue), Wu (1982, peach), Large and Yeager (2009, black and dash line), Edson (2003, black and circle line), Zijlema (2012, red and circle line). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

improved by adjusting the models described in the following sections. Furthermore, the model results before storm surge peak are more consistent with the observed data than those after the peak. The effects of different wind fields in the peak surge and maximum water velocity are shown in Fig. 6. To assess the differences, both peak surge and maximum water velocity were subtracted from those of benchmark Case 1a. Fig. 6a, c and 6e show that Cases 1b, 1c and 1d obtain lower peak surge in comparison to Case 1a, especially in the Northern side of Yangtze Estuary and Southern side of Zhejiang prov­ ince. On the contrary, larger maximum water velocity was found at the mouth of Hangzhou Bay and Northern side of Yangtze Estuary. The time series of wind speed and wind direction obtained from the CCMP, NCEP-CFSR, ERA-Interim and ERA5 wind fields are compared with observations during July 01–12, 2015 (Fig. 7). The NCEP-CFSR wind speed predicts larger wind speed than the other three wind fields when the wind speed reaches the peak, while the trend of wind direction among four wind fields are similar. It is noted that the time of each wind field reaching the maximum wind speed magnitude is different and varies from station to station. Besides, the maximum wind speed magnitude of NCEP-CFSR is larger than the observed data at Zhujiajian station and Zhoushan station. At Dachen station and Nanji station, the

Table 4 Different wind drag coefficient formulae. Reference Peng and Li (2015) -Peng Large and Pond (1981) -LP81 Garratt (1977) -G77 Wujin (1982) -Wu Large and Yeager (2009) -LY Edson (2013) -Edson Zijlema (2012) -Zijlema

Bulk Formula �! aðjVW j

Cd ¼

Remark 2

33Þ þ c

8 <

1:2 �! 0:49 þ 0:065jVW j : 0:49 þ 0:065 � 25 �! Cd � 103 ¼ 0:75 þ 0:067jVW j

Cd � 103 ¼

�! jVW j � 11:0 �! 11:0 � jVW j � 25:0 �! jVW j � 25:0

a0 ¼ 2:0 � 10 6 c0 ¼ 2:34 � 10 3

�! Cd � 103 ¼ 0:80 þ 0:065jVW j � Cd ¼

�! �! �! a1 =jVW j þ a2 þ a3 jVW j þ a8 jVW j6 3 2:34 � 10

�! Cd ¼ ðCm þ u0 =jVW jÞ2 e Cd � 103 ¼ ð0:55 þ 2:97U

2

e Þ 1:49U

9

�! 0:0 < jVW j < 33:0 �! jVW j � 33:0

a1 ¼ 2:70 � 10 3 a2 ¼ 1:42 � 10 4 a3 ¼ 7:64 � 10 5 a8 ¼ 3:14807 � 10 cm ¼ 0:062 u0 ¼ 0:28 �! e ¼ jV U W j=Uref Uref ¼ 31:5m=s

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Fig. 10. The model results of time series of surge elevations produced from different wind drag coefficient formulae versus observed values at various tidal gauges during the time of typhoon Winnie (August 16–20, 1997). (a) Daijishan; (b) Dinghai; (c) Shacheng; (d) Sansha; (e) Guantou; (f) Pingtan; (g) Chongwu; (h) Dongshan.

Fig. 11. The wind drag coefficients as a function of wind speed with different formulae during the time of typhoon Winnie (00:00 08 Aug 1997–00:00 22 Aug 1997).

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Fig. 12. Contour plots of peak surge elevation and maximum velocity differences for hindcast of typhoon Winnie. a, c, e, g, i, k: maximum elevation differences of Case 2a-Case 1a, Case 2b-Case 1a, Case 2c-Case 1a, Case 2d-Case 1a, Case 2e-Case 1a, Case 2f-Case 1a,respectively; b, d, f, h, j, l: maximum velocity differences of Case 2a-Case 1a, Case 2b-Case 1a, Case 2c-Case 1a, Case 2d-Case 1a, Case 2e-Case 1a, Case 2f-Case 1a,respectively.

maximum wind speed of NCEP-CFSR is slightly smaller than the observed data. For example, the estimated peaks of wind speed pro­ duced from CCMP, NCEP-CFSR, ERA-Interim and ERA5 at Dachen sta­ tion are 25.8, 32.5, 20.9 and 26.7 m/s, respectively, and the observed wind speed at Dachen station is 33.0 m/s. The smallest underestimation of 1.5% is found in NCEP-CFSR, while 20.9%, 36.8% and 19.1% for the CCMP, ERA-Interim and ERA5, respectively. In addition, when the observed wind speed reached peak in Zhujiajian station, the estimated wind speed produced from CCMP, NCEP-CFSR, ERA-Interim and ERA5 are 9.0, 19.0, 9.7 and 23.4 m/s, respectively; and, the observed maximum wind speed is 20.9 m/s. As a result, the underestimation of 56.9%, 9.1%, 53.6% and overestimation of 12.0% are found for CCMP, NCEP-CFSR, ERA-Interim and ERA5, respectively. Partly, that’s a reason why the performance of NCEP-CFSR in the hindcast of the surge eleva­ tion performs best among these four wind fields. In order to assess the spatial variability of storm surge due to different wind fields, spatial wind speed distributions and corresponding water elevations using four wind fields 6 h prior to and 6 h after the surge peak are shown in Fig. 8. It can be found that the spatial distri­ butions of wind speed and corresponding water elevations are almost the same, while the NCEP-CFSR wind field leads to a slightly stronger wind speed and higher surge elevation. The physical explanation can be related to the description in section 2.3. In addition, the intensity of wind speed increased progressively from

deep water to coastal areas, which generated the maximum water level in the Hangzhou Bay. It can also be found that an anti-cyclone was formed. Wind velocity at the right side of typhoon Winnie is higher than that at the left side. As a conclusion of this section, CFSR performs the best among the four wind fields in storm surge simulations of typhoon Winnie. As a result, NCEP-CFSR wind product is employed as the default wind forcing for storm surge simulation in the following sections. 3.2. Effects of wind drag coefficient bulk formula This section is focused on the effects of wind drag coefficient formulae. Seven wind drag coefficient formulae are employed to study their sensitivity in the storm surge simulations. The wind drag coeffi­ cient formulas compared in the manuscript were following the previous studies that was used in simulating storm surges caused by typhoon. For example, Akbar et al. (2017) used SWANþ ADCIRC model to hindcast storm surges caused by hurricane Rita. In their study, two quadratic profiles from Zijlema and Peng & Li are used to calculate wind stresses; In addition, the G77 and Large & Pond are the default bulk formulas in ADCIRC model and FVCOM model, which are popular linearly varying drag coefficient formulas, and are often used to hindcast storm surges. Mao and Xia (2017) used these two models to hindcast two wind event induced by the storm surges. Moon et al. (2009) investigated the effect of surface wind stress parameterizations on the storm surge modelling, 11

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August 8 to 00:00 on August 22, 1997, which covers the period of typhoon Winnie. The calculated wind drag coefficients during the time in Fig. 10 are presented by two vertical black solid lines in Fig. 11. It can be found that G77, Wu, and Edson produce much bigger wind drag coefficients than LP81. LY and Peng produce slightly bigger values than LP81, and Zijlema produces a smaller value than LP81. Fig. 12 shows the differences produced by different wind drag co­ efficient formulae in comparison to the default case, Case 1a. Figs. 12e, 11f and 11k, and 11l show that the peak surge and maximum velocity produced by wind drag coefficients of LY and Zijlema are very similar to the default case, while the adoption of Edson, G77, Wu and Peng formulae overestimates the values of peak surge and maximum velocity than the default case, which produce relatively large difference compared with the default case. In addition, the model results of skill metrics show that LY produces similar simulation results when compared with LP81, but with a slightly better performance in model skill, RMSD, and CC. Besides, G77, Wu and Zijlema produce similar results. Compared with the results using LP81, the adoption of Peng and Edson produces higher surge elevations, with RMSD values of 12 cm using Peng formulation, 2 cm using Edson formulation, respectively. Therefore, the LY formulation was adopted as the wind drag coefficient formula in the following experiments.

Table 5 Settings of Bottom drag coefficient and bottom drag formulae. Reference Default Koutitas C1-0.0015 C2-0.003 Half Double

Bottom drag coefficient

Remark

�

� �2 � Zab Cz ¼ max k2 =ln ; 0:0025 Z o � � � �2 H Cz ¼ k2 = ln þ1 1 z0 0.0015 0.003 Cz/2 2Cz

H : Water Depth z0 ¼ 0:002mm Cz refers to default case (a) Cz refers to default case (a)

and they adopted Wu wind drag coefficient formula. The Edson and Large & Yeager drag coefficient formulas concentrated on the study of air-sea flux and the exchange of momentum over open ocean, which covers high wind speed situations. Peng and Li (2015) adopted these two wind drag coefficient formulas to simulate different typhoon-induced storm surge cases. In order to assess the performance of different wind drag options in the hindcast of typhoon Winnie, all the above wind drag coefficient formulas are employed. Table 4 lists the wind drag coefficient formulae proposed by previous studies and Fig. 9 shows the drag coefficient profiles as functions of wind speed. The wind drag coefficient formulae adopted here are the pre­ dominant wind speed-dependent empirical equations. Time series of surge elevations produced from seven wind drag co­ efficient bulk formulae versus the observed values at different tidal gauge stations are shown in Fig. 10. In general, all the sensitivity ex­ periments reproduced the temporal variations of surge elevation reasonably. The time phases of different wind drag coefficient formu­ lations are consistent with those produced from different wind fields when compared with observed surge data. Fig. 11 shows the calculated wind drag coefficients with different wind drag coefficient bulk formulae during the time from 00:00 on

3.3. Effects of bottom drag coefficient and bottom drag formula In coastal areas where the water depth is lower than 10 m, the bot­ tom friction plays an important role in the tidal energy dissipation (Xu et al., 2017), which indicates that increasing bottom friction may attenuate storm surge propagation in multi-islands waters, while leading to an opposite effect by decreasing bottom friction. In addition, a sys­ tematic study on the quantitative effect of low and high bottom friction on storm surges is not available in open literatures for the present study areas. As a result, it is necessary to conduct sensitivity experiments of

Fig. 13. The model results of surge elevations produced from different bottom friction versus observed values at various tidal gauges during the time of typhoon Winnie (August 16–20, 1997). (a) Daijishan; (b) Dinghai; (c) Shacheng; (d) Sansha; (e) Guantou; (f) Pingtan; (g) Chongwu; (h) Dongshan. 12

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Fig. 14. Contour plots of peak surge elevation and velocity differences for hindcast of typhoon Winnie storm surges. (a, c, e, g, i) maximum elevation difference: Case 3a-Case 2c, Case 3b-Case 2c, Case 3c-Case 2c, Case 3d-Case 2c, Case 3e-Case 2c, respectively; (b, d, f, h, j) maximum velocity difference: Case 3a-Case 2c, Case 3bCase 2c, Case 3c-Case 2c, Case 3d-Case 2c, Case 3e-Case 2c, respectively.

bottom friction in the multi-islands environment. The previous studies indicated that parameterization of bottom friction term plays an important role in storm surge simulation (Kerr et al., 2013a; Akbar et al., 2017). In this study, aside from the default bottom friction formula of FVCOM, sensitivity experiments using Cz/2, 2Cz, Koutitas and constant bottom drag coefficients of 0.003 and 0.0015 were conducted (Table 5). Fig. 13 shows the time series of surge elevations obtained from different bottom drag coefficient settings versus the observed values at eight tidal gauge stations. The results show that there is a slight differ­ ence among these experiments. In general, these experiments capture the similar temporal variations in comparison to previous experiments. The effects of parameterization of the bottom friction term are shown in the maximum peak surge and maximum velocity contour plots in Fig. 14. To assess the differences, both maximum peak surge and water velocity were subtracted from those of the default case, Case 2c. Fig. 14d and h shows that decreasing bottom drag coefficient (Case 3b and Case 3d) could lead to stronger velocity as expected. The maximum difference of current velocity can reach about 0.5 m/s, and was found at the mouth inside of the Hangzhou Bay and adjacent coastal waters along the Jiangsu Province. This may be due to the shallow water depth at these waters. In addition, a slight difference was found when adopting other parameterizations of bottom friction (Cases 3a, 3c and 3e), with an average of 5% and 8% difference comparing with the reference experi­ ment in surge elevation and current velocity, respectively. The model

results indicated that decreasing the bottom friction from the default value of Cz ¼ 0.0015 leads to a greater impact on surge elevation and current velocity than increasing the coefficient. The model results of skill metrics show that a bottom drag coefficient of Cz/2 produces the best performance in storm surge simulations, and a constant value of 0.0015 follows. Therefore, half of bottom drag coef­ ficient is recommended for the modeling of storm surge caused by typhoon Winnie in FVCOM-based storm surge model. 3.4. Sensitivity of tide-surge interaction Tide-surge interaction along the coast of China has been discussed during the past decades (Wang and Chai, 1989; Duan and Qin, 1997; Zhou et al., 2000; Zhang et al., 2010; Feng et al., 2015, 2018; Li et al., 2018). Wang and Chai (1989) showed that the periodic residual during storm surge periods was mainly caused by tide-surge interaction. Duan and Qin (1997) found a substantial improvement of water level accuracy when tide-surge interaction was considered in numerical simulation. In addition, significant tide-surge interaction was analyzed in the Taiwan Strait (Zhang et al., 2010). Feng et al. (2015) indicated that the tide-surge interaction played an important role in the variation of extreme sea levels. To understand the tide-surge nonlinear interactions, we carry out three different model simulations, which are tide forcing only, wind forcing only, and tide and wind forcing simultaneously, 13

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Fig. 15. Surge elevations produced from experiment forced by wind and tide and experiment forced by wind only versus observed values at various tidal gauges. (a) Daijishan; (b) Dinghai; (c) Shacheng; (d) Sansha; (e) Guantou; (f) Pingtan; (g) Chongwu; (h) Dongshan.

respectively. The non-tidal sea level anomaly was obtained by sub­ tracting the simulated tide elevations forced by tide only. Compared with tidal gauge data, the model results underestimate the surge elevation at eight stations (Fig. 15). Table 6 shows the height of peak surge with three different forcing, and the non-linear tide-surge inter­ action at eight stations. There are two apparent and important charac­ teristics in Table 6. One is that the relative time differences of peak surge between windþtide forcing case and the observed record are all positive at seven stations (except at Sansha station), which means that the peak surge in windþtide forcing case arrives earlier than the observed record. The other characteristic is that, in general, the farther the maximum radius of typhoon center is, the smaller the peak surge elevation and the larger relative time difference of peak surge between windþtide forcing case and the observed records will be. Take Sansha, Dajishan and Dongshan stations for example: among the three stations, Sansha is the closest station to the maximum radius of typhoon center, and the model captures the timing of peak surge well which is 1.14 m. Besides, the model hindcasts 2 h earlier timing of peak surge, and the peak storm surge elevation is 0.86 and 0.88 m at Dajishan and Dongshan stations, respectively. The contribution of non-linear interaction varies at different stations, with a range from 20% at Sansha station to 44% at Chongwu station. The larger value of tide-surge interaction is due to the larger relative time. Overall, station-averaged non-linear tide-surge interaction is 37%. Take

Table 6 The model results and the observations of non-linear interaction at eight stations. Station Name

1

2

3

4

5

Daijishan Dinghai Shacheng Sansha Guantou Pingtan Chongwu Dongshan

0.71 1.11 0.97 0.95 0.92 0.84 0.68 0.56

þ2 h (0.86) þ1 h (1.57) þ1 h (1.12) 0 h (1.14) þ1 h (1.22) þ1 h (1.07) þ2 h (0.89) þ2 h (0.88)

1.04 1.48 1.33 1.17 1.50 1.30 1.17 0.94

0.42 0.56 0.39 0.23 0.61 0.49 0.52 0.40

40% 38% 29% 20% 41% 38% 44% 43%

1: Height (m) of peak surge (wind forcing simulation). 2: Timea and height (m) of peak surge (windþtide forcing simulation), a: The time refers to the relative time of peak surge between windþtide forcing case and the observed record at each station. A positive value means that the peak surge in windþtide forcing case arrives earlier than the observed record, while a negative value has an opposite meaning. 3: Height (m) of peak surge (observed). 4: Height (m) of tide-surge interaction. 5: Percentage of tide-surge interaction contributes to the surge height.

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Fig. 16. The model results of surge elevations produced from LY-Cz/2 and default setting versus observed values at various tidal gauges during typhoon Chan-Hom (July 09–12, 2015) at (a) Daishan; (b) Zhujiajian; (c) Liuheng; (d) Beilun. During typhoon Herb (July 30–August 03, 1996) at (e) Shacheng; (g) Sansha. And during typhoon Mireille (September 25–28, 1991) at (f) Sansha; (h) Pingtan.

Pingtan station (Fig. 15f) for example: the peak surge in the wind forcing only scenario is 0.84 m and it arrives 2 h earlier. Besides, the peak surge in the windþtide forcing scenario is 1.07 m and it arrives 1 h earlier. Meanwhile, the peak surge of observed data is 1.30 m. At the time of peak storm surge, the wind effect contributes by 0.81 m, and the tidesurge interaction contributes by 0.49 m, which indicates that the nonlinear effect between storm surge and astronomical tides contributes to the peak storm surge by 38%. Li et al. (2018) showed that the tide-surge interaction contributed to the peak storm surge by 34% in Xiamen station. The distance between Pingtan and Xiamen is 217 km, our model results are comparable to their study.

Hom wind event slightly overpredict the surge, but the overall perfor­ mance is better. It is mainly due to that the NCEP-CFSR wind field overpredicts the wind speed during the passing by of typhoon ChanHom (Fig. 7). In addition, grid in this area has higher resolution and can better resolve the coastal bathymetry and topography, which in­ dicates that the grid resolution is of great importance in storm surge simulations. Moon et al. (2009) conducted sensitivity experiments to explore the effect of the surface wind stress parameterization on the storm surge modelling, and they drew a conclusion that higher resolu­ tion led to better surge simulation. In the other two typhoon-induced storm surges, the model results underpredict the surge elevation. For the experiments (Cases 4a-4f) in which independent storm surge event is modeled, the difference of surge elevation between modeling results and observed storm surge is small with good model skill metrics, which demonstrating that the selected options for wind drag and bottom drag are acceptable and applicable. In addition, the model results show that the synergistic effect has an improvement with 0.13 m and 0.04 m in total elevation in terms of RMSD based on the simulation of storm surges caused by Chan-Hom and Herb, (Table 3, Cases, 4a-4d). Besides, on the one hand, the model results show a difference of 0.13 m in RMSD of total elevation in typhoon Mireille, on the other hand, it also show improved model skill metrics in surge elevation (Table 3, Cases, 4e-4f). In this study, the simulations indicated that the best combination of forcing and drag coefficient in general improved the model performance

3.5. Application in the modelling of other typhoon induced storm surges In order to assess the above selections of wind source and formula­ tion of wind drag coefficient and bottom drag coefficient, other three storm surge events caused by typhoon Chan-Hom, Herb and Mireille were modeled to test the effectiveness. As analyzed above (Section 3.1, Fig. 7), we adopted NCEP-CFSR wind field as default wind forcing in this section. Time series of simulated surge elevations with different wind drag and bottom friction settings (Cases 4a-4f) are evaluated against observed data, as shown in Fig. 16. Compared with model results of surge simu­ lations caused by Winnie wind event, the model results caused by Chan15

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of surge compared to the observations. The mode results also indicated that it was hard to choose a single best combination of forcing and drag coefficient in different storm surge simulations. For example, different typhoon paths may correspond to different optimal combination of forcing and drag coefficient. It is noted that in all simulations there is a marked dissimilarity in predicted and observed simulations after the peak surge is reached. All models show a rapid decrease in surge elevation whereas the observa­ tions are higher (Figs. 5, 10, 13, 15 and 16). Based on the previous studies (Moon et al., 2009; Sun et al., 2013; Yu et al., 2017; Mao and Xia, 2018), the possible reasons for the rapid decrease are: (I) wave effects are not included in the model, and (II) the model resolution is not high enough at the locations of the tidal gauges. These two facts are inter­ esting to be verified in the future.

Declaration of competing interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements The bathymetry data near the coast of Zhejiang Province was pro­ vided by Zhejiang Province Ocean and Fisheries Bureau. The CCMP wind field was provided by Earth Science Enterprise of National Aero­ nautics and Space Administration (NASA). The ERA-Interim and ERA5 wind product was provided by European Centre for Medium-Range Weather Forecasts (ECMWF). The NCEP-CFSR wind product was pro­ vided by National Center for Atmospheric Research (NCAR). The typhoon data was provided by International Best Track Archive for Climate Stewardship (IBTrACS). The FVCOM source code was developed by C. Chen and MEDM research group.

4. Conclusions In this paper, FVCOM was employed to study the sensitivities of modelling storm surge to bottom friction, wind drag coefficient, and meteorological product in the East China Sea. The NCEP-CFSR wind field, Large & Pond wind drag formulation, default bottom friction formulation in FVCOM are used as the default settings in model setup. The results are evaluated against the observed data at eight tide-gauge stations, which demonstrate that the modeling results are reasonable. The model results driven by NCEP-CFSR wind field present better performance than the other three meteorological forcing (CCMP, ERAInterim and ERA5), with an improved RMSD value of 5 cm. CCMP, ERA-Interim and ERA5 wind fields produced similar model results. It is likely due to that NCEP-CFSR wind field is a two-way atmosphere-ocean fully coupled model product. In addition, the time series of wind speed and direction produced from NCEP-CFSR coincided with the wind ob­ servations more at the observations during typhoon Chan-Hom. Among the seven wind drag bulk formulae, LY produced better storm surge agreement with observed data. The formulae of Edson, Wu, and Garratt produce higher surge elevations than those of Large & Pond and Zijlema at the time of peak surge. Decreasing the bottom friction has a greater impact on surge elevation and current velocity than increasing the bottom friction. Half of the bottom friction produced better results in storm surge simulations. It indicates that the bottom friction in the simulation domain should have a smaller value. In order to examine the combined effect of wind drag formulation and bottom friction formu­ lation, other three typhoon induced storm surges (typhoon Chan-Hom, Herb and Mireille) were simulated. The model results showed that the synergistic effect of forcing and drag coefficient obtained in this study in general improve the model performance of surge compared to the observations. In this study, we also explore the interaction between tide and surge. In the hindcast of typhoon Winnie, the model results indicate that the nonlinear interaction effect contributes by 37% at the time of peak surge. In the future, we are going to consider the wave-current effect and baroclinicity on the simulation of storm surge simulations to improve the accuracy of the storm surge simulation. The underlying mechanisms of storm surges, such as tide-surge interaction and characteristics of storm surge propagation, will also be studied in the future work.

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Funding This work was supported by the National Key Research and Devel­ opment Plan [grant numbers 2017YFC1404000 and 2017YFA0604100]; the National Natural Science Foundation of China [grant number 41876086], and the Fundamental Research Funds for the Central Uni­ versities in China (grant number 2019QNA4052). J. Zhang thanks the support of China Scholarship Council for the visiting research in WHOI, and he also thanks the host of WHOI.

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