**4.1.2 Current velocity**

8 Will-be-set-by-IN-TECH

Fig. 5. A sketch of triangular grid (upper) and locally zoomed in mesh near Ganpu station

(lower) for modeling astronomical tide

It is clearly seen from Figures 7 and 8 that the maximum tidal ranges occur at the Ganpu station (T4). Thus, it is expected that the maximum tidal current may occur near this region. The tidal currents were measured at four locations H1-H4 across the estuary near Ganpu. These measurements are used to verify the numerical model. Figures 9 and 10 are the comparison between simulated and measured depth-averaged velocity magnitude and direction for the spring and neap tidal currents, respectively. It is seen that the flood tidal velocity is clearly greater than the ebb flow velocity for both the spring and neap tides. The maximum flood velocity occurs at H2 with the value of about 3.8 m/s, while the maximum ebb flow velocity is about 3.1 m/s during the spring tide. During the neap tide, the maximum velocities of both the flood and ebb are much less than those in the spring tide with the value of 1.5 m/s for flood and 1.2 m/s for ebb observed at H2. The maximum relative error for the ebb flow is about 17%, occurring at H2 during the spring tide. For the flood flow the maximal relative error occurs at H3 and H4 for both the spring and neap tides with values being about 20%. In general, the depth-averaged simulated velocity magnitude and current direction agree well with the measurements, and the maximal error percentage in tidal current is similar as that encountered in modeling the Mahakam Estuary (Mandang & Yanagi, 2008).

Fig. 8. Comparison of the computed and measured neap tidal elevations at stations T2-T6. −:

Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 189

computed; ◦: measured

Fig. 7. Comparison of the computed and measured spring tidal elevations at stations T2-T6. −: computed; ◦: measured

10 Will-be-set-by-IN-TECH

Fig. 7. Comparison of the computed and measured spring tidal elevations at stations T2-T6.

−: computed; ◦: measured

Fig. 8. Comparison of the computed and measured neap tidal elevations at stations T2-T6. −: computed; ◦: measured

Fig. 10. Comparison of the computed and measured depth-averaged neap current velocities

Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 191

at stations H1-H4. −: computed; ◦: measured

Fig. 9. Comparison of the computed and measured depth-averaged spring current velocities at stations H1-H4. −: computed; ◦: measured

12 Will-be-set-by-IN-TECH

Fig. 9. Comparison of the computed and measured depth-averaged spring current velocities

at stations H1-H4. −: computed; ◦: measured

Fig. 10. Comparison of the computed and measured depth-averaged neap current velocities at stations H1-H4. −: computed; ◦: measured

Fig. 11. Comparison of the computed and measured spring current velocities at different

Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 193

depths at station H1. −: computed; ◦: measured

The vertical distributions of current velocities during spring tide are also compared at stations H1 and H4. The measured and simulated flow velocities in different depths (sea surface, 0.2D, 0.4D, 0.6D and 0.8D, where D is water depth) at these two stations are shown in Figures 11 and 12. It is noted that the current magnitude obviously decreases with a deeper depth (from sea surface to 0.8D), while the flow direction remains the same. The numerical model generally provides accurate current velocity along vertical direction, except that the simulated current magnitude is not as high as that of measured during the flood tide. The maximum relative error in velocity magnitude during spring tide is about 32% at H4 station. Analysis suggests that the errors in the tidal currents estimation are mainly due to the calculation of bottom shear stress. Although the advanced formulation accounts for the impacts of flow acceleration and non-constant stress distribution on the calculation of bottom shear stress, it can not accurately describe the changeable bed roughness that depends on the bed material and topography.

#### **4.2 Typhoon-induced storm surge**

#### **4.2.1 Wind field**

Figures 13 and 14 show the comparisons of calculated and measured wind fields at Daji station and Tanxu station during Typhoon Agnes, in which the starting times of x-coordinate are both at 18:00 of 29/08/1981 (Beijing Mean Time). In general, the predicted wind directions agree fairly well with the available measurement. However, it can be seen that calculated wind speeds at these two stations are obviously smaller than observations in the early stage of cyclonic development and then slightly higher than observations in later development. The averaged differences between calculated and observed wind speeds are 2.6 m/s at Daji station and 2.1 m/s at Tanxu station during Typhoon Agnes. This discrepancy in wind speed is due to that the symmetrical cyclonic model applied does not reflect the asymmetrical shape of near-shore typhoon.

#### **4.2.2 Storm surge**

Figure 15 displays the comparison of simulated and measured tidal elevations at Daji station and Tanxu station, in which the starting times of x-coordinate are both at 18:00 on 29/08/1981 (Beijing Mean Time). It can be seen from Figure 15 that simulated tidal elevation of high tide is slightly smaller than measurement, which can be directly related to the discrepancy of calculated wind field (shown in Figures 13 and 14). A series of time-dependent surge setup, the difference of tidal elevations in the storm surge modeling and those in purely astronomical tide simulation, are used to represent the impact of typhoon-generated storm. Figure 16 having a same starting time in x-coordinate displays simulated surge setup in Daji station and Tanxu station. There is a similar trend in surge setup development at these two stations. The surge setup steadily increases in the early stage (0-50 hour) of typhoon development, and then it reaches a peak (about 1.0 m higher than astronomical tide) on 52nd hour (at 22:00 on 31/08/1981). The surge setup quickly decreases when the wind direction changes from north-east to north-west after 54 hour. In general, the north-east wind pushing water into the Hangzhou Bay significantly leads to higher tidal elevation, and the north-west wind dragging water out of the Hangzhou Bay clearly results in lower tidal elevation. The results indicate that the typhoon-induced external forcing, especially wind stress, has a significant impact on the local hydrodynamics.

14 Will-be-set-by-IN-TECH

The vertical distributions of current velocities during spring tide are also compared at stations H1 and H4. The measured and simulated flow velocities in different depths (sea surface, 0.2D, 0.4D, 0.6D and 0.8D, where D is water depth) at these two stations are shown in Figures 11 and 12. It is noted that the current magnitude obviously decreases with a deeper depth (from sea surface to 0.8D), while the flow direction remains the same. The numerical model generally provides accurate current velocity along vertical direction, except that the simulated current magnitude is not as high as that of measured during the flood tide. The maximum relative error in velocity magnitude during spring tide is about 32% at H4 station. Analysis suggests that the errors in the tidal currents estimation are mainly due to the calculation of bottom shear stress. Although the advanced formulation accounts for the impacts of flow acceleration and non-constant stress distribution on the calculation of bottom shear stress, it can not accurately describe the changeable bed roughness that depends on the bed material and topography.

Figures 13 and 14 show the comparisons of calculated and measured wind fields at Daji station and Tanxu station during Typhoon Agnes, in which the starting times of x-coordinate are both at 18:00 of 29/08/1981 (Beijing Mean Time). In general, the predicted wind directions agree fairly well with the available measurement. However, it can be seen that calculated wind speeds at these two stations are obviously smaller than observations in the early stage of cyclonic development and then slightly higher than observations in later development. The averaged differences between calculated and observed wind speeds are 2.6 m/s at Daji station and 2.1 m/s at Tanxu station during Typhoon Agnes. This discrepancy in wind speed is due to that the symmetrical cyclonic model applied does not reflect the asymmetrical shape of

Figure 15 displays the comparison of simulated and measured tidal elevations at Daji station and Tanxu station, in which the starting times of x-coordinate are both at 18:00 on 29/08/1981 (Beijing Mean Time). It can be seen from Figure 15 that simulated tidal elevation of high tide is slightly smaller than measurement, which can be directly related to the discrepancy of calculated wind field (shown in Figures 13 and 14). A series of time-dependent surge setup, the difference of tidal elevations in the storm surge modeling and those in purely astronomical tide simulation, are used to represent the impact of typhoon-generated storm. Figure 16 having a same starting time in x-coordinate displays simulated surge setup in Daji station and Tanxu station. There is a similar trend in surge setup development at these two stations. The surge setup steadily increases in the early stage (0-50 hour) of typhoon development, and then it reaches a peak (about 1.0 m higher than astronomical tide) on 52nd hour (at 22:00 on 31/08/1981). The surge setup quickly decreases when the wind direction changes from north-east to north-west after 54 hour. In general, the north-east wind pushing water into the Hangzhou Bay significantly leads to higher tidal elevation, and the north-west wind dragging water out of the Hangzhou Bay clearly results in lower tidal elevation. The results indicate that the typhoon-induced external forcing, especially wind stress, has a significant impact on

**4.2 Typhoon-induced storm surge**

**4.2.1 Wind field**

near-shore typhoon.

**4.2.2 Storm surge**

the local hydrodynamics.

Fig. 11. Comparison of the computed and measured spring current velocities at different depths at station H1. −: computed; ◦: measured

Fig. 13. Comparison of calculated and measured wind fields at Daji station during Typhoon Agnes. (a): wind speed; (b): wind direction. Starting time 0 is at 18:00 of 29/08/1981

Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 195

Fig. 14. Comparison of calculated and measured wind fields at Tanxu station during Typhoon

Agnes. (a): wind speed; (b): wind direction. Starting time 0 is at 18:00 of 29/08/1981

Fig. 12. Comparison of the computed and measured spring current velocities at different depths at station H4. −: computed; ◦: measured

16 Will-be-set-by-IN-TECH

Fig. 12. Comparison of the computed and measured spring current velocities at different

depths at station H4. −: computed; ◦: measured

Fig. 13. Comparison of calculated and measured wind fields at Daji station during Typhoon Agnes. (a): wind speed; (b): wind direction. Starting time 0 is at 18:00 of 29/08/1981

Fig. 14. Comparison of calculated and measured wind fields at Tanxu station during Typhoon Agnes. (a): wind speed; (b): wind direction. Starting time 0 is at 18:00 of 29/08/1981

**5. Conclusions**

estuary.

**6. References**

2001.

530-536, 2009.

In this study, the results from field observation and 3D numerical simulation are used to investigate the characteristics of astronomical tide and typhoon-induced storm surge in the

Astronomical Tide and Typhoon-Induced Storm Surge in Hangzhou Bay, China 197

1. Tidal hydrodynamics in the Hangzhou Bay is significantly affected by the irregular geometrical shape and shallow depth and is mainly controlled by the M2 harmonic constituent. The presence of tropical typhoon makes the tidal hydrodynamics in the

2. The tidal range increases significantly as it travels from the lower estuary towards the middle estuary, 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

3. The flood tidal velocity is clearly greater than the ebb flow velocity for both the spring and neap tides. The maximum flood velocity occurs at H2 with the value of about 3.8 m/s, while the maximum ebb flow velocity is about 3.1 m/s during the spring tide. During the neap tide, the maximum velocities of both the flood and ebb are much less than those in the spring tide with the value of 1.5 m/s for flood and 1.2 m/s for ebb observed at H2. 4. The vertical distributions of current velocity at stations H1 and H4 show that the current magnitude obviously decreases with a deeper depth (from sea surface to 0.8D), while the

5. Tropical cyclone, in terms of wind stress and pressure gradient, has a significant impact on its induced storm surge. In general, the north-east wind pushing water into the Hangzhou Bay significantly leads to higher tidal elevation, and the north-west wind dragging water

Cao, Y. & Zhu, J. "Numerical simulation of effects on storm-induced water level after

Chang, H. & Pon, Y. "Extreme statistics for minimum central pressure and maximal wind

Chen, C., Liu, H. & Beardsley, R. "An unstructured, finite-volume, three-dimensional,

Guo, Y., Zhang, J., Zhang, L. & Shen, Y. "Computational investigation of typhoon-induced

Hu, K., Ding, P., Zhu, S. & Cao, Z. "2-D current field numerical simulation integrating Yangtze Estuary with Hangzhou Bay," *China Ocean Engineering*, vol. 14(1), pp. 89-102, 2000. Hu, K., Ding, P. & Ge, J. "Modeling of storm surge in the coastal water of Yangtze Estuary and Hangzhou Bay, China," *Journal of Coastal Research*, vol. 51, pp. 961-965, 2007.

*of Atmospheric and Oceanic Technology*, vol. 20, pp. 159-186, 2003.

contraction in Qiantang estuary," *Journal of Hangzhou Institute of Applied Engineering*,

velocity of typhoons passing around Taiwan," *Ocean Engineering*, vol. 1, pp. 55-70,

primitive equation ocean model: application to coastal ocean and estuaries," *Journal*

storm surge in Hangzhou Bay, China," *Estuarine, Coastal and Shelf Science*, vol. 85, pp.

out of the Hangzhou Bay clearly results in lower tidal elevation.

Hangzhou Bay. Some conclusions can be drawn as below:

Hangzhou Bay further complicated.

flow direction remains the same.

vol. 12, pp. 24-29, 2000.

Fig. 15. Comparison of calculated and measured water elevations during Typhoon Agnes. (a): Daji station; (b): Tanxu station. Starting time 0 is at 18:00 of 29/08/1981

Fig. 16. The simulated surge setup at two stations during Typhoon Agnes. (a) Daji station; (b) Tanxu station. Starting time 0 is at 18:00 of 29/08/1981
