**Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China**

Jisheng Zhang1, Chi Zhang1, Xiuguang Wu2 and Yakun Guo<sup>3</sup> <sup>1</sup>*State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, 210098* <sup>2</sup>*Zhejiang Institute of Hydraulics and Estuary, Hangzhou, 310020* <sup>3</sup>*School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE* 1,2*China* <sup>3</sup>*United Kingdom*

#### **1. Introduction**

178 Hydrodynamics – Natural Water Bodies

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The Hangzhou Bay, located at the East of China, is widely known for having one of the world's largest tidal bores. It is connected with the Qiantang River and the Eastern China Sea, and contains lots of small islands collectively referred as Zhoushan Islands (see Figure 1). The estuary mouth of the Hangzhou Bay is about 100 km wide; however, the head of bay (Ganpu) which is 86 km away from estuary mouth is significantly narrowed to only 21 km wide. The tide in the Hangzhou Bay is an anomalistic semidiurnal tide due to the irregular geometrical shape and shallow depth and is mainly controlled by the M2 harmonic constituent. The M2 tidal constituent has a period about 12 hours and 25.2 minutes, exactly half a tidal lunar day. The Hangzhou Bay faces frequent threats from tropical cyclones and suffers a massive damage from its resulting strong wind, storm surge and inland flooding. According to the 1949-2008 statistics, about 3.5 typhoons occur in this area every year. When typhoon generated in tropic open sea moves towards the estuary mouth, lower atmospheric pressure in the typhoon center causes a relatively high water elevation in adjacent area and strong surface wind pushes huge volume of seawater into the estuary, making water elevation in the Hangzhou Bay significantly increase. As a result, the typhoon-induced external forces (wind stress and pressure deficit) above sea surface make the tidal hydrodynamics in the Hangzhou Bay further complicated.

In the recent years, some researches have been done to study the tidal hydrodynamics in the Hangzhou Bay and its adjacent areas. For example, Hu et al. (2000) simulated the current field in the Hangzhou Bay based on a 2D model, and their simulated surface elevation and current field preferably compared with the field observations. Su et al. (2001), Pan et al. (2007) and Wang (2009) numerically investigate the formulation, propagation and dissipation of the tidal bore at the head of Hangzhou Bay. Also, Cao & Zhu (2000), Xie et al. (2007), Hu et al. (2007) and Guo et al. (2009) performed numerical simulation to study the typhoon-induced

Fig. 2. A sketch of measurement stations and topography

no current velocity was measured.

given here for completeness and convenience.

*∂ζ <sup>∂</sup><sup>t</sup>* <sup>+</sup> *∂Du ∂x* + *∂Dv ∂y* + *∂ω*

**3. Numerical simulation**

**3.1 Governing equations**

(No.8114), which resulted in one of extremely recorded high water levels in the Hangzhou Bay, wind fields were observed every hour and storm tides were recorded every three hours at Daji station and Tanxu station (see Figure 1). Only the surge elevations were recorded and

Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 181

A 3D mathematical model based on FVCOM (an unstructured grid, Finite-Volume Coastal Ocean Model) (Chen et al., 2003) is developed for this study. The model uses an unstructured triangular grid in horizontal plane and a terrain-following *σ*-coordinate in vertical plane (see Figure 3), having a great ability to capture irregular shoreline and uneven seabed. The most sophisticated turbulence closure sub-model, Mellor-Yamada 2.5 turbulence model (Mellor & Yamada, 1982), is applied to compute the vertical mixing coefficients. More details of FVCOM can be found in Chen et al. (2003). Only the governing equations of the model are

*∂σ* <sup>=</sup> 0 (1)

Fig. 1. Global location and 2005's bathymetry of the Hangzhou Bay and its adjacent shelf region

storm surge. However, most of them mainly focused on the 2D mathematical model. The main objective of this study is to understand the characteristics of (i) astronomical tide and (ii) typhoon-induced storm surge in the Hangzhou Bay based on the field observation and 3D numerical simulation.

#### **2. Field observation**

To understand the astronomical tides in the Hangzhou Bay, a five-month in situ measurement was carried out by the Zhejiang Institute of Hydraulic and Estuary from 01 April 2005 to 31 August 2005. There were eight fixed stations (T1-T8) along the banks of the Hangzhou Bay, at which long-term tidal elevations were measured every 30 minutes using ship-mounted WSH meter with the accuracy of ±0.03 m. The tidal current velocity was recorded every 30 minutes at four stations H1-H4 using SLC9-2 meter, manufactured by Qiandao Guoke Ocean Environment and Technology Ltd, with precisions of ±4◦ in direction and ±1.5% in magnitude. The topography investigation in the Hangzhou Bay was also carried out in the early April 2005. Figure 2 shows the tidal gauge positions and velocity measurement points, together with the measured topography using different colors.

On 27/08/1981, a tropical depression named Agnes was initially formed about 600 km west-northwest of Guam in the early morning and it rapidly developed as a tropical storm moving west-northwestward (towards to Zhejiang Province) in the evening. Agnes became a typhoon in the morning of 29/08/1981, 165 km southwest of Okinawa next day. Agnes started to weaken after entering a region of hostile northerly vertical wind shear. The cyclonic center was almost completely disappeared by the morning of 02/09/1981. During Typhoon Agnes

Fig. 2. A sketch of measurement stations and topography

(No.8114), which resulted in one of extremely recorded high water levels in the Hangzhou Bay, wind fields were observed every hour and storm tides were recorded every three hours at Daji station and Tanxu station (see Figure 1). Only the surge elevations were recorded and no current velocity was measured.

#### **3. Numerical simulation**

2 Will-be-set-by-IN-TECH

Fig. 1. Global location and 2005's bathymetry of the Hangzhou Bay and its adjacent shelf

storm surge. However, most of them mainly focused on the 2D mathematical model. The main objective of this study is to understand the characteristics of (i) astronomical tide and (ii) typhoon-induced storm surge in the Hangzhou Bay based on the field observation and 3D

To understand the astronomical tides in the Hangzhou Bay, a five-month in situ measurement was carried out by the Zhejiang Institute of Hydraulic and Estuary from 01 April 2005 to 31 August 2005. There were eight fixed stations (T1-T8) along the banks of the Hangzhou Bay, at which long-term tidal elevations were measured every 30 minutes using ship-mounted WSH meter with the accuracy of ±0.03 m. The tidal current velocity was recorded every 30 minutes at four stations H1-H4 using SLC9-2 meter, manufactured by Qiandao Guoke Ocean Environment and Technology Ltd, with precisions of ±4◦ in direction and ±1.5% in magnitude. The topography investigation in the Hangzhou Bay was also carried out in the early April 2005. Figure 2 shows the tidal gauge positions and velocity measurement points,

On 27/08/1981, a tropical depression named Agnes was initially formed about 600 km west-northwest of Guam in the early morning and it rapidly developed as a tropical storm moving west-northwestward (towards to Zhejiang Province) in the evening. Agnes became a typhoon in the morning of 29/08/1981, 165 km southwest of Okinawa next day. Agnes started to weaken after entering a region of hostile northerly vertical wind shear. The cyclonic center was almost completely disappeared by the morning of 02/09/1981. During Typhoon Agnes

together with the measured topography using different colors.

region

numerical simulation.

**2. Field observation**

#### **3.1 Governing equations**

A 3D mathematical model based on FVCOM (an unstructured grid, Finite-Volume Coastal Ocean Model) (Chen et al., 2003) is developed for this study. The model uses an unstructured triangular grid in horizontal plane and a terrain-following *σ*-coordinate in vertical plane (see Figure 3), having a great ability to capture irregular shoreline and uneven seabed. The most sophisticated turbulence closure sub-model, Mellor-Yamada 2.5 turbulence model (Mellor & Yamada, 1982), is applied to compute the vertical mixing coefficients. More details of FVCOM can be found in Chen et al. (2003). Only the governing equations of the model are given here for completeness and convenience.

$$\frac{\partial \zeta}{\partial t} + \frac{\partial Du}{\partial x} + \frac{\partial Dv}{\partial y} + \frac{\partial \omega}{\partial \sigma} = 0 \tag{1}$$

where x, y and *σ* are the east, north and upward axes of the *σ*-coordinate system; u, v and w are the x, y and *σ* velocity components, respectively; t is the time; *ζ* is the water elevation; D is the total water depth (=H+*ζ*, in which H is the bottom depth); P*atm* is the atmospheric pressure; *ρ* is the seawater density being a polynomial function of temperature T and salinity S (Millero & Poisson, 1981); f is the local Coriolis parameter (dependent on local latitude and the angular speed of the Earth's rotation); g is the acceleration due to gravity (=9.81 m/s2); *ρ*<sup>0</sup> is the mean seawater density (=1025 kg/m3); K*<sup>m</sup>* and K*<sup>h</sup>* are the vertical eddy viscosity coefficient and thermal vertical eddy diffusion coefficient; F*u*, F*v*, F*<sup>T</sup>* and F*<sup>S</sup>* are the horizontal u-momentum, v-momentum, thermal and salt diffusion terms, respectively; q<sup>2</sup> is the turbulent kinetic energy; l is the turbulent macroscale; K*q*<sup>2</sup> is the vertical eddy diffusion

Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 183

coefficient of the turbulent kinetic energy; *<sup>W</sup>* is a wall proximity function (=1+E2( *<sup>l</sup>*

constants assigned as 16.6, 1.8 and 1.33, respectively.

Guo et al. (2009) for more information.

**3.2 Boundary conditions**

the parameter L−1=(*ζ*-z)−1+(H+z)−1); F*q*<sup>2</sup> and F*q*2*<sup>l</sup>* represent the horizontal diffusion terms of turbulent kinetic energy and turbulent macroscale; and B1, E1 and E2 are the empirical

Mode splitting technique is applied to permit the separation of 2D depth-averaged external mode and 3D internal mode, allowing the use of large time step. 3D internal mode is numerically integrated using a second-order Runge-Kutta time-stepping scheme, while 2D external mode is integrated using a modified fourth-order Runge-Kutta time-stepping scheme. A schematic solution procedure of this 3D model is illustrated in Figure 4. The point wetting/drying treatment technique is included to predict the water covering and uncovering process in the inter-tide zone. In the case of typhoon, the accuracies of the atmospheric pressure and wind fields are crucial to the simulation of storm surge. In this study, an analytical cyclone model developed by Jakobsen & Madsen (2004) is applied to predict pressure gradient and wind stress. The shape parameter and cyclonic regression parameter are determined by the formula suggested by Hubbert et al. (1991) and the available field observations in the Hangzhou Bay (Chang & Pon, 2001), respectively. Please refer to

The moisture flux and net heat flux can be imposed on the sea surface and bottom boundaries, but are not considered in this study. The method of Kou et al. (1996) is used to estimate the bottom shear stress induced by bottom boundary friction, accounting for the impact of flow acceleration and non-constant stress in tidal estuary. A river runoff (Q=1050 m3/s) from the Qiantang River according to long-term field observation is applied on the land side of the model domain. The elevation clamped open boundary condition and atmospheric force (wind stress and pressure gradient) above sea surface are the main driving forces of numerical simulation. In modeling astronomical tide, the time-dependent open-sea elevations are from field observation at stations T7-T8 and zero atmospheric force is given. In modeling typhoon-induced storm surge, the time-dependent open-sea elevations are from FES2004 model (Lyard et al., 2006) and typhoon-generated water surface variations and atmospheric force is estimated by the analytical cyclone model. In this study, the external time step is

Δ*tE*=2 sec and the ratio of internal time step to external time step is I*S*=5.

*<sup>κ</sup><sup>L</sup>* ) 2 , where

Fig. 3. Coordinate transformation of the vertical computational domain. Left: *z*-coordinate system; Right: *σ*-coordinate system

$$\begin{aligned} \frac{\partial u}{\partial t} + \frac{\partial u^2 D}{\partial x} + \frac{\partial u\sigma D}{\partial y} + \frac{\partial u\sigma}{\partial \sigma} &= f\nu D - \frac{D}{\rho\_o} \frac{\partial P\_{atm}}{\partial x} - gD\frac{\delta\tau}{\partial x} \\ &- \frac{\partial D}{\rho\_o} [\frac{\partial}{\partial x} (D\_f \int\_{\sigma}^{\rho} d\rho d\sigma) + \tau \rho \frac{\partial D}{\partial x}] + \frac{\partial}{\partial x} (C\_{\text{m}} \frac{\partial u}{\partial \sigma}) + DF\_u \end{aligned} \tag{2}$$
 
$$\begin{aligned} \frac{\partial vD}{\partial t} + \frac{\partial vD}{\partial x} + \frac{\partial v^2 D}{\partial y} + \frac{\partial v\sigma}{\partial \sigma} &= -fuD - \frac{D}{\rho\_o} \frac{\partial P\_{atm}}{\partial y} - gD \frac{\delta\xi}{\partial y} \\ &- \frac{gD}{\rho\_o} [\frac{\partial}{\partial y} (D \int\_{\sigma}^{\rho} d\rho d\sigma) + \tau \rho \frac{\partial D}{\partial y}] + \frac{\partial}{\partial \sigma} (K\_{\text{m}} \frac{\partial v}{\partial \sigma}) + DF\_{\text{v}} \end{aligned} \tag{3}$$
 
$$\frac{\partial TD}{\partial t} + \frac{\partial TuD}{\partial x} + \frac{\partial TvD}{\partial y} + \frac{\partial Tw}{\partial \sigma} = \frac{\partial}{\partial \sigma} (K\_{\text{h}} \frac{\partial T}{\partial \sigma}) + DF\_{\text{v}} \tag{4}$$
 
$$\frac{\partial SD}{\partial t} + \frac{\partial SuD}{\partial x} + \frac{\partial SvD}{\partial y} + \frac{\partial Sw}{\partial \sigma} = \frac{\partial}{\partial \sigma} (K\_{\text{h}}$$

$$\begin{aligned} \frac{\partial q^2 lD}{\partial t} + \frac{\partial uq^2 lD}{\partial x} + \frac{\partial vq^2 lD}{\partial y} + \frac{\partial \omega q^2 l}{\partial \sigma} &= \frac{lE\_1 K\_m}{D} [\left(\frac{\partial u}{\partial \sigma}\right)^2 + \left(\frac{\partial v}{\partial \sigma}\right)^2] + \frac{lE\_1 g}{\rho\_o} \mathcal{K}\_h \frac{\partial \rho}{\partial \sigma} \\ &- \frac{Dq^3}{B\_1} \tilde{W} + \frac{\partial}{\partial \sigma} (\frac{K\_q z}{D} \frac{\partial q^2 l}{\partial \sigma}) + DF\_{q^2 l} \end{aligned} (8)$$

where x, y and *σ* are the east, north and upward axes of the *σ*-coordinate system; u, v and w are the x, y and *σ* velocity components, respectively; t is the time; *ζ* is the water elevation; D is the total water depth (=H+*ζ*, in which H is the bottom depth); P*atm* is the atmospheric pressure; *ρ* is the seawater density being a polynomial function of temperature T and salinity S (Millero & Poisson, 1981); f is the local Coriolis parameter (dependent on local latitude and the angular speed of the Earth's rotation); g is the acceleration due to gravity (=9.81 m/s2); *ρ*<sup>0</sup> is the mean seawater density (=1025 kg/m3); K*<sup>m</sup>* and K*<sup>h</sup>* are the vertical eddy viscosity coefficient and thermal vertical eddy diffusion coefficient; F*u*, F*v*, F*<sup>T</sup>* and F*<sup>S</sup>* are the horizontal u-momentum, v-momentum, thermal and salt diffusion terms, respectively; q<sup>2</sup> is the turbulent kinetic energy; l is the turbulent macroscale; K*q*<sup>2</sup> is the vertical eddy diffusion

coefficient of the turbulent kinetic energy; *<sup>W</sup>* is a wall proximity function (=1+E2( *<sup>l</sup> <sup>κ</sup><sup>L</sup>* ) 2 , where the parameter L−1=(*ζ*-z)−1+(H+z)−1); F*q*<sup>2</sup> and F*q*2*<sup>l</sup>* represent the horizontal diffusion terms of turbulent kinetic energy and turbulent macroscale; and B1, E1 and E2 are the empirical constants assigned as 16.6, 1.8 and 1.33, respectively.

Mode splitting technique is applied to permit the separation of 2D depth-averaged external mode and 3D internal mode, allowing the use of large time step. 3D internal mode is numerically integrated using a second-order Runge-Kutta time-stepping scheme, while 2D external mode is integrated using a modified fourth-order Runge-Kutta time-stepping scheme. A schematic solution procedure of this 3D model is illustrated in Figure 4. The point wetting/drying treatment technique is included to predict the water covering and uncovering process in the inter-tide zone. In the case of typhoon, the accuracies of the atmospheric pressure and wind fields are crucial to the simulation of storm surge. In this study, an analytical cyclone model developed by Jakobsen & Madsen (2004) is applied to predict pressure gradient and wind stress. The shape parameter and cyclonic regression parameter are determined by the formula suggested by Hubbert et al. (1991) and the available field observations in the Hangzhou Bay (Chang & Pon, 2001), respectively. Please refer to Guo et al. (2009) for more information.

#### **3.2 Boundary conditions**

4 Will-be-set-by-IN-TECH

Fig. 3. Coordinate transformation of the vertical computational domain. Left: *z*-coordinate

*ρo*

*ρo*

*∂Patm*

*∂Patm*

*<sup>∂</sup><sup>x</sup>* <sup>−</sup> *gD ∂ζ*

*∂x*

*∂D <sup>∂</sup><sup>x</sup>* ] + *<sup>∂</sup> ∂σ* ( *Km D ∂u ∂σ* ) + *DFu*

*∂y*

*∂D <sup>∂</sup><sup>y</sup>* ] + *<sup>∂</sup> ∂σ* ( *Km D ∂v ∂σ* ) + *DFv*

*ρ* = *ρ*(*T*, *S*) (6)

*∂q*<sup>2</sup>

*∂q*2*l*

*∂σ* ) + *DFq*<sup>2</sup>

] + *lE*1*<sup>g</sup> ρo Kh ∂ρ ∂σ*

*∂σ* ) + *DFq*<sup>2</sup>*<sup>l</sup>*

(2)

(3)

(7)

(8)

*∂σ* ) + *DFT* (4)

*∂σ* ) + *DFS* (5)

) + *σρ*

*<sup>∂</sup><sup>y</sup>* <sup>−</sup> *gD ∂ζ*

) + *σρ*

*∂σ* <sup>=</sup> *f vD* <sup>−</sup> *<sup>D</sup>*

<sup>−</sup> *gD ρo* [ *∂ ∂x* (*D* 0 *σ ρdσ*�

<sup>−</sup> *gD ρo* [ *∂ ∂y* (*D* 0 *σ ρdσ*�

+

+ *∂SvD ∂y* + *∂Sω ∂σ* <sup>=</sup> *<sup>∂</sup> ∂σ* ( *Kh D ∂S*

+ *∂ωq*<sup>2</sup>

+

*∂ωq*2*l*

*∂vq*2*D ∂y*

*∂vq*2*lD ∂y*

*∂TuD ∂x*

*∂SuD ∂x*

*∂σ* <sup>=</sup> <sup>−</sup> *f uD* <sup>−</sup> *<sup>D</sup>*

*∂TvD ∂y*

+ *∂Tω ∂σ* <sup>=</sup> *<sup>∂</sup> ∂σ* ( *Kh D ∂T*

*∂σ* <sup>=</sup> <sup>2</sup>*Km*

*∂σ* <sup>=</sup> *lE*1*Km*

<sup>−</sup> *Dq*<sup>3</sup> *B*1

<sup>−</sup> <sup>2</sup>*Dq*<sup>3</sup> *<sup>B</sup>*1*<sup>l</sup>* <sup>+</sup>

*<sup>D</sup>* [( *<sup>∂</sup><sup>u</sup> ∂σ* ) 2 + ( *<sup>∂</sup><sup>v</sup> ∂σ* ) 2 ] + <sup>2</sup>*<sup>g</sup> ρo Kh ∂ρ ∂σ*

*<sup>D</sup>* [( *<sup>∂</sup><sup>u</sup> ∂σ* ) 2 + ( *<sup>∂</sup><sup>v</sup> ∂σ* ) 2

*W* + *∂ ∂σ* ( *Kq*<sup>2</sup> *D*

*∂ ∂σ* ( *Kq*<sup>2</sup> *D*

system; Right: *σ*-coordinate system

*∂u*2*D ∂x* + *∂uvD ∂y* + *∂uω*

*∂uvD ∂x* + *∂v*2*D ∂y* + *∂vω*

*∂q*2*D <sup>∂</sup><sup>t</sup>* <sup>+</sup>

*∂q*2*lD <sup>∂</sup><sup>t</sup>* <sup>+</sup> *∂TD <sup>∂</sup><sup>t</sup>* <sup>+</sup>

*∂SD <sup>∂</sup><sup>t</sup>* <sup>+</sup>

*∂uq*2*D ∂x*

*∂uq*2*lD ∂x*

+

+

*∂uD <sup>∂</sup><sup>t</sup>* <sup>+</sup>

*∂vD <sup>∂</sup><sup>t</sup>* <sup>+</sup>

> The moisture flux and net heat flux can be imposed on the sea surface and bottom boundaries, but are not considered in this study. The method of Kou et al. (1996) is used to estimate the bottom shear stress induced by bottom boundary friction, accounting for the impact of flow acceleration and non-constant stress in tidal estuary. A river runoff (Q=1050 m3/s) from the Qiantang River according to long-term field observation is applied on the land side of the model domain. The elevation clamped open boundary condition and atmospheric force (wind stress and pressure gradient) above sea surface are the main driving forces of numerical simulation. In modeling astronomical tide, the time-dependent open-sea elevations are from field observation at stations T7-T8 and zero atmospheric force is given. In modeling typhoon-induced storm surge, the time-dependent open-sea elevations are from FES2004 model (Lyard et al., 2006) and typhoon-generated water surface variations and atmospheric force is estimated by the analytical cyclone model. In this study, the external time step is Δ*tE*=2 sec and the ratio of internal time step to external time step is I*S*=5.

**3.3 Mesh generation**

mid-depth are applied.

**4. Results and discussion**

the presence of typhoon.

lower reach of the estuary.

**4.1 Astronomical tide 4.1.1 Tidal elevation**

direction, 6 *σ*-levels (5 *σ*-layers) is uniformly applied.

As shown in Figures 1 and 2, the Hangzhou Bay has a very irregular shoreline. Therefore, to accurately represent the computational domain of the Hangzhou Bay, unstructured triangular meshes with arbitrarily spatially-dependent size were generated. The area of the whole solution domain defined for astronomical tide modeling is about 5360 km2. The computational meshes were carefully adapted and refined, especially in the inter-tide zone, until no significant changes in the solution were achieved. The final unstructured grid having 90767 nodes and 176973 elements in the horizontal plane (each *σ*-level) was used with minimal distance of 20 m in the cells (see Figure 5). In the vertical direction, 11 *σ*-levels (10 *σ*-layers) compressing the *σ* mesh near the water surface and sea bottom symmetrically about the

Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 185

In modeling typhoon-induced storm surge, a large domain-localized grid resolution strategy is applied in mesh generation, defining very large computational domain covering the main area of typhoon and locally refining the concerned regions with very small triangular meshes. The whole computational domain covers an extensive range of 116-138*o*E in longitude and 21-41*o*N in latitude. The final unstructured grid having 111364 nodes and 217619 elements in the horizontal plane (each *σ*-level) was used with the minimal 100 m grid size near shoreline and the maximal 10000 m grid size in open-sea boundary (see Figure 6). In the vertical

The results from field observation and numerical simulation are compared and further used to investigate the characteristics of tidal hydrodynamics in the Hangzhou Bay with/without

Figures 7 and 8 are the comparison of simulated and observed tidal elevations at 5 stations (T2, T3, T4, T5 and T6) in spring tide and neap tide, respectively. The x-coordinate of these figures is in the unit of day, and, for example, the label '21.25 August 2005' indicates '6:00am of 21/08/2005'. Both the numerical simulation and field observation for spring and neap tides show that the tidal range increases significantly as it travels from the lower estuary (about 6.2 m in spring tide and 3.1 m in neap tide at T6) towards the middle estuary (about 8.1 m in spring tide and 3.7 m in neap tide at T4), mainly due to rapid narrowing of the estuary. The tidal range reaches the maximum at Ganpu station (T4) and decreases as it continues traveling towards the upper estuary (about 4.4 m in spring tide and 2.5 m in neap tide at T2). In general, very good agreement between the simulation and observation is obtained. There exists, however, a slight discrepancy between the computed and observed tidal elevations at T2 (Yanguan). The reason for this may be ascribed to that the numerical model does not consider the tidal bore, which may have significant effect on the tidal elevations at the upper reach. Such impact on tidal elevations, however, decreases and becomes negligible at the

Fig. 4. A schematic solution procedure of 3D estuarine modeling

### **3.3 Mesh generation**

6 Will-be-set-by-IN-TECH

Fig. 4. A schematic solution procedure of 3D estuarine modeling

As shown in Figures 1 and 2, the Hangzhou Bay has a very irregular shoreline. Therefore, to accurately represent the computational domain of the Hangzhou Bay, unstructured triangular meshes with arbitrarily spatially-dependent size were generated. The area of the whole solution domain defined for astronomical tide modeling is about 5360 km2. The computational meshes were carefully adapted and refined, especially in the inter-tide zone, until no significant changes in the solution were achieved. The final unstructured grid having 90767 nodes and 176973 elements in the horizontal plane (each *σ*-level) was used with minimal distance of 20 m in the cells (see Figure 5). In the vertical direction, 11 *σ*-levels (10 *σ*-layers) compressing the *σ* mesh near the water surface and sea bottom symmetrically about the mid-depth are applied.

In modeling typhoon-induced storm surge, a large domain-localized grid resolution strategy is applied in mesh generation, defining very large computational domain covering the main area of typhoon and locally refining the concerned regions with very small triangular meshes. The whole computational domain covers an extensive range of 116-138*o*E in longitude and 21-41*o*N in latitude. The final unstructured grid having 111364 nodes and 217619 elements in the horizontal plane (each *σ*-level) was used with the minimal 100 m grid size near shoreline and the maximal 10000 m grid size in open-sea boundary (see Figure 6). In the vertical direction, 6 *σ*-levels (5 *σ*-layers) is uniformly applied.
