Jin-hai Zheng*,Jin-cheng WangChun-yan ZhouHong-jun ZhaoSang Sang

aKey Laboratory of Coastal Disaster and Defence(Hohai University),Ministry of Education,Nanjing 210098,China

bCollege of Harbor Coastal and Offshore Engineering,Hohai University,Nanjing 210098,China

Numerical simulation of typhoon-induced storm surge along Jiangsu coast, Part II:Calculation of storm surge

Jin-hai Zhenga,b,*,Jin-cheng Wanga,b,Chun-yan Zhoua,b,Hong-jun Zhaoa,b,Sang Sanga,b

aKey Laboratory of Coastal Disaster and Defence(Hohai University),Ministry of Education,Nanjing 210098,China

bCollege of Harbor Coastal and Offshore Engineering,Hohai University,Nanjing 210098,China

The Jiangsu coastal area is located in central-eastern China and is well known for complicated dynamics with large-scale radial sand ridge systems.It is therefore a challenge to simulate typhoon-induced storm surges in this area.In this study,a two-dimensional astronomical tide and storm surge coupling model was established to simulate three typical types of typhoons in the area.The Holland parameter model was used to simulate the wind field and wind pressure of the typhoon and the Japanese 55-year reanalysis data were added as the background wind field.The offshore boundary information was provided by an improved Northwest Paci fic Ocean Tide Model.Typhoon-induced storm surges along the Jiangsu coast were calculated based on analysis of wind data from 1949 to 2013 and the spatial distribution of the maximum storm surge levels with different types of typhoons,providing references for the design of sea dikes and planning for control of coastal disasters.

Jiangsu coast;Typhoon-induced storm surge;Numerical simulation;Holland parameter model;ADCIRC

1.Introduction

Storm surges induced by typhoons are among the most popular research topics in flood prevention and engineering design along coastal areas(Chen et al.,2009;Zhang et al., 2013).For example,according to the nuclear safety guide issued by the National Nuclear Safety Administration of China (1990),the probable maximum storm surge of the sea area around a nuclear power station is the essential element that determines the design basis of the flood.The design high tide level of nuclear power stations under construction or soon to be under construction is determined as the sum of the maximum astronomical tide level and the probable maximum storm surge level according to international standards(Liang and Zou,2004).

In terms of modeling storm surges along the Jiangsu coast, probable maximum storm surge levels of Haizhou Bay along the Jiangsu coast have been calculated by a numerical model of the storm surge,governed by a depth-averaged flow equation in spherical coordinates,and verified by five cases of remarkable extratropical storm surges with a maximum storm surge level of 3.36 m(Yu et al.,2002;Wu et al.,2002).A high-resolution storm surge model along the Jiangsu coast has been built using the explicit difference method(Zhang,2008), showing that the stability was low and the computation time was long.Several typhoons striking Jiangsu Province have been simulated using the weather research and forecasting (WRF)model and Delft 3D model in order to investigate the influence of storm surges on the radial sand ridges off the Jiangsu coast with the sea level rising(Yu et al.,2014).The hydrodynamics in the Jiangsu sea waters during Typhoon Damrey have been simulated and a good fit was generated between the simulated and measured values of the typhoondata(Wang et al.,2015),where the gradient wind field of Typhoon Damrey was computed by a Jele wind parameters model,and then combined with the ambient wind field from the United States National Centers for Environmental Prediction(NCEP).

In this study,hydrodynamic simulations were carried out to investigate the storm surge along the Jiangsu coast during different typhoons,based on the tracks and parameters of the hypothetical typhoons.The calculated surge levels show the spatial distribution of the maximum storm surge levels with different types of typhoons,providing valuable references for planning and control of coastal disasters.

2.Method

2.1.Model description

The water levels of tide gauges consist of the astronomical tide level and storm surge level during the typhoon period. This study built an astronomical tide and storm surge coupling model and validated the reasonability of the model topography,the boundary conditions,and the wind field.The surges caused by hypothetical typhoons along the Jiangsu coast were calculated using the storm surge model.

The numerical model included three sub-models,which were the wind field and wind pressure model,an improved Northwest Pacific Ocean Tide Model(a large model),and a two-dimensional(2D)typhoon storm surge model for the Jiangsu coast(a small model).The Holland parameter model was used to simulate the wind field and pressure field of the typhoon.The improved Northwest Pacific Ocean Tide Model (Zhang et al.,2012)provided the open boundary water levels for the 2D typhoon storm surge model,and the latter calculated the surge along the Jiangsu coast.

The improved Northwest Pacific Ocean Tide Model uses the 2D tidal propagation equation in spherical coordinates (Zhang et al.,2013),with a domain covering the East China Sea,South China Sea,Philippine Sea,Japan Sea,Sulu Sea,and nearby Pacific Ocean areas.The initial flow velocity is zero. When computing the coupled water level of the astronomical tide level and storm surge level,the open boundary condition for the large model was provided by a tidal prediction system (NOA.99b),developed by the National Astronomical Observatory of Japan,with 16 short-period tidal constituents(M2, S2,K1,O1,N2,P1,K2,Q1,M1,J1,OO1,2N2,Mu2,Nu2,L2,and T2)and 7 long-period tidal constituents(Mtm,Mf,MSf,Mm, MSm,Ssa,and Sa)(Matsumoto et al.,2000),and the boundary conditions for the small model are the coupled water level of the astronomical tide level and storm surge level derived from the large model.While the storm surge is simulated alone,the open boundary water level for the large model is set as zero,so that the large model only provides the storm surge level for the small model.The model was validated with four main constituents(M2,S2,K1,and O1)of 435 tide gauges listed in the Admiralty Tide Table and the strong agreement indicated that the model is capable of simulating the tidal system of the Bohai Sea,the Huanghai Sea,and the East China Sea.

2.1.1.Wind field and wind pressure model

The wind field and wind pressure model adopted the Holland parameter model,which is the most popular method used to simulate typhoon storm surges.The Tropical Cyclone Best Track Dataset issued by the Shanghai Typhoon Institute of the China Meteorological Administration was used as the input conditions for the model to simulate typhoons(Ying et al.,2014).

The Holland parameter model relies on the primary assumption of a radially symmetric pressure field,but with a modified rectangular hyperbola to give the pressure p at any radius(r)from the typhoon center as follows:

where p(r)is the surface pressure at a distance r from the typhoon center;pcis the central pressure;Δp is the difference between the ambient pressure(pn)and the central pressure (Δp=pn-pc),and the value of the first anti-cyclonically curved isobar is pnin practice;Rmaxis the radius to the maximum wind speed,referring to the distance from the typhoon center to the region of the maximum wind speed;and B is the so-called profile peakedness used to characterize the shape of the radial pressure profile.

Gradient winds in the upper atmosphere are derived from the balance between the centrifugal and Coriolis forces acting outwards and the pressure acting inwards:

where Vg(r)is the gradient wind speed(m/s)at a distance r from the typhoon center;f is the Coriolis parameter and f=2usinφ;u is the angular speed of the Earth's rotation,set to be 7.27×10-5rad/s;φ is the latitude;and ρa(bǔ)is the air density(assumed to be constant at 1.15 kg/m3in the Holland parameter model).

Substituting the pressure field equation(Eq.(1))into the force balance equation(Eq.(2))will yield the gradient wind field Vg(r):

In the region of the maximum wind speed,the Coriolis force is small compared to the pressure gradient and centrifugal forces,so the Coriolis force may be ignored and Eq.(3) can be simplified into

According to the distribution of typhoon wind speed,the maximum wind speed Vmaxoccurs at Rmax.Then,replacing r in Eq.(4)with Rmaxwill lead to

According to Eq.(5),the parameterBin the Holland parameter model can be calculated as follows:

The wind field derived from the Holland parameter model is symmetrical with respect to the center of the typhoon. Considering the asymmetry of the real wind field,the Holland parameter model should be amended,taking into account some additional effects.

The first is the amendment of the angle of inflow(+β for the southern hemisphere,and-β for the northern hemisphere).Surface friction and continuity demand that the wind flow inward across the isobars.The angle of inflow is considered to be approximately 25°in the outer region,but decreases to zero near the radius of the maximum wind speed. The β proposed by Harper et al.(2001)was used in this study.

Typhoon forward motion is another important factor producing complex changes to the surface wind field and asymmetric wind field of tropical cyclones.Thus,this asymmetry should be achieved by adding the forward velocity vector(Vt) to the surface wind speed.The effect of forward motion weakens with distance from the eye of the typhoon,so Vtshould multiply a weight coefficient,which decreases with distance from the cyclone center.The formula proposed by Miyazaki(1977)is employed as the forward wind field:

whereVxandVyare the components of forward speed of the typhoon center,withVxbeing positive eastward andVybeing positive northward;and i and j are the unit vectors in thexandydirections,respectively.

Combining Eqs.(3)and(8)yields the model's wind field:

wherec1andc2are the correction coefficients,set to be 0.8 and 1.0,respectively;α is the angle between the gradient wind and sea surface wind;and θ is the angle between thexaxis and the line connecting the computing point and typhoon center.

The input parameters other thanRmaxfor the Holland parameter model can be derived from the Tropical Cyclone Best Track Dataset.Rmaxcan be calculated as follows(Carr and Elsberr,1997):

The range of influence of typhoons is hundreds of kilometers in general.The Holland parameter model is good at describing the wind field and wind pressure within the range affected by typhoons,but the surrounding ambient wind field differs greatly from the Holland parameter model's result due to the influence of other meteorological systems.This difference can be eliminated by considering the background wind field(Zhao et al.,2010).The Japanese 55-year reanalysis(JRA-55),the second-generation reanalysis carried out by the Japan Meteorological Agency(Harada et al.,2016; Kobayashi and Iwasaki,2016),was employed as the background wind field.The JRA-55 includes reanalyzed meteorological data from the period of 1958-2012,and has 640 and 320 grid cells in the longitude and latitude directions, respectively,with a resolution of 0.5625°and a time interval of 6 h,providing the typhoon background wind field and pressure field.

The background wind field and typhoon model wind field can be combined as follows:

where VCis the combined wind field;VQis the background wind field;eis the weight coefficient used to smooth the two wind fields'connection;ande=c4/（1+c4）,wherec=r/（10Rmax）.

The model results were verified with wind speeds and wind directions of meteorological stations along the Jiangsu coast during typhoon No.9711,and the strong agreement indicated that parameters adopted by the model and the simulation method were appropriate.

2.1.2.Typhoon storm surge model(ADCIRC)along Jiangsu coast

The advanced circulation(ADCIRC)model,developed by the University of North Carolina in the United States,is a 2D finite-element hydrodynamic model and has very broad applications(Luettich et al.,1992).

Fig.1 shows the mesh of a typhoon storm surge model along the Jiangsu coast.The offshore boundary is basically parallel to the Jiangsu coastline.The mesh is finer near the coast with the minimum grid size of 600 m,and coarser in the open sea with a grid size of 10 km.Local mesh refinement was carried out in the radial sand ridge area,which has complex topography and many tidal channels,and the minimum grid distance was about 170 m(Fig.1).There were 45872 elements and 23485 nodes in the mesh.

The model time step was 3 s,the horizontal viscosity diffusion coefficient was 10 m2/s,and the bottom friction coefficient adopted the hybrid friction formulation(Luettich and Westerink,2015):

Fig.1.ADCIRC model mesh and local mesh refinement in radial sand ridge area.

whereCdb2dis the bottom friction coefficient,Cfminis the minimum friction coefficient(in deep waters),HBREAKis the control water depth,and θf(wàn)and γfare coefficients.The friction coefficient satisfies the Manning formula in shallow water (H＜HBREAK),close toCdb2d=Cfmin（HBREAK/H）γf,and satisfies the Chezy formula in deep water(H＞HBREAK),close toCfmin.In this study,Cfminwas set to be 0.0015,HBREAKwas set to be 1.0 m,andθf(wàn)andγfwere setto be 10 and 4/3,respectively.

The surface wind stress was calculated as follows:

where τsxand τsyare the surface wind stress in thexandydirections,respectively;ρ0isthe reference density ofwater;W10is the wind velocity at10 m above the watersurface;W10xandW10yare the componentsof W10in thexandydirections,respectively; andCdsis the surface wind drag coefficient,which was calculated as follows(Luettich and Westerink,2015):

The dry-wet boundary was determined by a node-element combination approach.When all the nodes of one element werewet,the element was included in the calculation.The dryness-wetness of a node was determined mainly by two parameters.First,the minimum wetness heightH0(between 0.01 and 0.10 m in general,set to be 0.1 m here),was used to determine wetness or dryness for a node.Second,the minimum wetting velocityUminwas set to be 0.05 m/s.When a node satisfied both the water level and wetting velocity conditions simultaneously,it turned into a wet node.The dry-wet elements information was first updated before each calculation, demanding that the time step of ADCIRC should not be too large.However,the matrix was solved with the finite element method,and the calculation still proceeded very quickly.

2.2.Model verification

The model coupling the astronomical tide and storm surge was verified with three typhoons,No.9711,No.0012,and No.1210.The improved Northwest Pacific Ocean Tide Model (the large model)provided the coupled water level at the open boundary of the small model.The verification with typhoon No.0012 in 2000(Fig.2)shows that the model results agree with the measured data at the Lianyungang and Lu¨si tide stations along the Jiangsu coast.The other verifications are described in Wang(2015).The strong agreement indicatedthat the boundary conditions,wind field data,and parameters adopted by the model were appropriate.

Fig.2.Tide level comparison for typhoon No.0012 in 2000.

2.3.Storm surge simulation along Jiangsu coast

The Holland parameter model calculated the wind field and pressure field of a hypothetical typhoon,providing the atmospheric driving force for the other two sub-models.By not including the astronomical tide at the open boundary,the large model calculated the pure storm surge under the effect of the wind field and pressure field of the hypothetical typhoon, which then provided the pure storm surge as the water level at open boundaries of the small model.Finally,the ADCIRC model computed the pure storm surge along the Jiangsu coast. Tide stations are shown in Fig.3,and the modeled surge levels at the tide stations induced by the three types of typhoons are shown in Fig.4,Fig.5,and Fig.6,respectively.

Fig.3.Tide stations along Jiangsu coast.

Fig.4.Time series of surge levels at coastal observation stations for typhoons making straight landfall.

During the hypothetical typhoon,there is no measured background wind field to be used to amend the ambient wind field.Thus,the surge process curve is different,to some extent,from the result considering the background wind field.

3.Results and discussion

The typhoons affecting the Jiangsu coast can be classified into three types:typhoons making straight landfall,typhoons active in the offshore area,and typhoons moving northward after landfall,corresponding to typhoons No.1210,No.0012, and No.9711,respectively(Fig.5 in Zheng et al.(2017)).The storm surge along the Jiangsu coast during these three types of typhoons was modeled and investigated as follows.

3.1.Typhoons making straight landfall

Typhoons making straight landfall can be divided into three types according to the path(Fig.6 in Zheng et al.(2017)).The typhoon with path A1 makes landfall near the Yanwei Station, and hits the Haizhou Bay area directly.The typhoon with path A2 makes landfall near the Chenjiawu,which is between Haizhou Bay and the radial sand ridge area.The typhoon with path A3 makes landfallatthe north bank ofthe Yangtze Estuary.

The model simulated the typhoons from 00:00 on August 1, 2012 to 00:00 on August 4,2012(Greenwich Mean Time).The time series of surge levels are shown in Fig.4.For the typhoon making straight landfall,the largest surge occurred at the right side of landfall point(the right side of the typhoon heading direction)when the typhoon was making landfall.The surge duration and length are listed in Table 1,in which the surge level induced by the three typhoons is higher than 1 m or 2 m.

In terms ofsurge area and duration,the surge area induced by the typhoon making landfall at Haizhou Bay was relatively larger,mainly due to the coastline and topography of Haizhou Bay.Based on the surge amplitude,with a probable surge level of3.4 m,the typhoon with path A3 caused the mostsevere threat to the Jiangsu coast ofall the typhoons making straight landfall.

Fig.5.Time series of surge levels at coastal observation stations for typhoons active in offshore area.

Fig.6.Time series of surge levels at coastal observation stations for typhoons moving northward after landfall.

Table 1 Surge duration and length caused by typhoon making straight landfall.

3.2.Typhoons active in offshore area

The occurrence frequency of typhoons active in the offshore area is in the middle of that of all the three types of typhoons.Based on typhoon No.0012,three hypothetical typhoons active in the offshore area with different paths were modeled(Fig.8 in Zheng et al.(2017)).

The simulation time was three days from 12:00 on August 29,2000 to 12:00 on September 1,2000(Greenwich Mean Time).The time series of surge levels during these three hypothetical typhoons are shown in Fig.5.

The surge curves of the coastal observation stations were different for the typhoons active in the offshore area.It is worthwhile to note that when the typhoon left the Jiangsu coast and arrived at the Korean Peninsula or Liaodong Peninsula,the surge that propagated from the Shandong Peninsula would arrive at the Jiangsu coast and would continue to propagate southward.This surge oscillation could reach 0.8 m sometimes,a fact that should be investigated and noted for the purpose of coastal disaster prevention and relief. In general,when the typhoons were active 170 km away from the Jiangsu coastline,the induced surge level along the Jiangsu coast was not very high,mostly less than 1 m.When the typhoons were closer to the Jiangsu coastline,the induced surge level was higher.When the typhoon was moving just along the coastline,the induced surge level was quite high,up to 3.47 m. Moreover,the surge caused by this type of typhoon was not large at the straight coastline section,but very large at Haizhou Bay and the radial sand ridge area.

3.3.Typhoons moving northward after landfall

The occurrence frequency of typhoons moving northward after landfall is the largest of the three types of typhoons.On the basis of typhoon No.9711,this type of typhoon is classified based on four paths(Fig.9 in Zheng et al.(2017)).The model run duration was seven days from 00:00 on August 15, 1997 to 00:00 on August 22,1997(Greenwich Mean Time). The time series of surge levels during these four theoretical typhoons are shown in Fig.6.

The range of influence of typhoons is generally hundreds of kilometers.Thus,the wind speed of a typhoon with path C1 along the Jiangsu coast diminished considerably without consideration of the background wind field,and the induced surge was almost zero.However,in the real process of typhoon No.9711,there was strong landward and northeast wind lasting a long time throughout the Jiangsu coastal area,which could not be reproduced in the hypothetical typhoon.

In terms of the surge area,the surge induced by a typhoon with path C2 mainly occurred at Haizhou Bay,and the coastline section of 120 km between the Rizhaogang and Yanwei stations had a surge level higher than 1 m.A surge induced by a typhoon with path C3 also mainly occurred at Haizhou Bay. The surge induced by a typhoon with path C4 mainly occurred at the coastline section between the Chenjiawu and Lu¨si stations,and the length of the coastline section was about 150 m.

In terms of the surge amplitude,the typhoon exiting the sea near the radial sand ridge area had the most significant influence on the Jiangsu coast of all the typhoons moving northward after landfall,and the typhoon with path C4 can cause a surge level up to 2.09 m in this area.

3.4.Spatial distribution of storm surge

In terms of the spatial distribution of storm surges caused by the hypothetical typhoons,the Jiangsu coastal area was divided into the radial sand ridge area,the middle straight coastline area,and the Haizhou Bay area from south to the north.The storm surge level caused by the typhoon making straight landfall can be high,up to 2.5 m in the Haizhou Bay area, 2.6 m in the middle straight coastline area,and 3.4 m in the south radial sand ridge area.The storm surge level induced by the typhoon active in the offshore area was high,up to 3.47 m, occurring at the radial sand ridge area.The storm surge levels caused by typhoons moving northward after landfall were as high as 1.32 m and 2.09 m in the Haizhou Bay area and the radial sand ridge area,respectively.Generally speaking,the storm surge level caused by each type of typhoon was highest in the radial sand ridge area and decreased northward.

4.Conclusions

A 2D astronomical tide and storm surge coupling model was established using the Holland parameter model,improved Northwest Pacific Ocean Tide Model,and ADCIRC model,in order to simulate the typhoon storm surges along the Jiangsu coast.Based on the 65-year Tropical Cyclone Best Track Dataset,the typhoons affecting Jiangsu Province were investigated and the parameters of various typical typhoons were obtained.The surge distribution of the Jiangsu coastal area under hypothetical typhoons was modeled in order to obtain the storm surge caused by the hypothetical typhoons along the Jiangsu coast.

The frequency of typhoons making straight landfall was lowest but the induced surge was relatively large.The surge caused by the typhoon active in the offshore area was lowest in general,but the extreme high storm surge could occur in the rare event that the typhoon moved just along the coastline.The frequency of typhoons moving northward after landfall was the highest,and the induced surge was relatively large.

In terms of spatial distribution,the radial sand ridge area was more seriously affected by the three types of typhoons and the storm surge was the largest.The storm surge levels caused by typhoons making straight landfall,by typhoons active in the offshore area,and by typhoons moving northward after landfall were high,up to 3.4 m,3.47 m,and 2.09 m,respectively,and all occurred in the radial sand ridge area.The storm surge level caused by each type of typhoon decreased northward.

The astronomical tide and storm surge are nonlinearly coupled.Their interaction is complicated,and thus it is necessary to study the nonlinear pattern in terms of coupled tide-storm surges along the Jiangsu coast in future research.

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Received 22 June 2016;accepted 15 December 2016

Available online 14 March 2017

This work was supported by the National Science Fund for Distinguished Young Scholars(Grant No.51425901)and the National Natural Science Foundation of China(Grant No.41606042).

*Corresponding author.

E-mail address:jhzheng@hhu.edu.cn(Jin-hai Zheng).

Peer review under responsibility of Hohai University.

http://dx.doi.org/10.1016/j.wse.2017.03.011

1674-2370/?2017 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).

?2017 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).