# Marine wave module

## Introduction to the model

The marine wave module adopts SWAN, a third-generation wave model that computes waves in shallow seas. This model was developed and maintained by the Department of Civil Engineering of Delft University in the Netherlands. From the first publicly released version (SWAN 30.51) to the current version (SWAN 40.81), it has been continuously improved, with gradually improved performance and enhanced functions. The SWAN model uses an equilibrium equation based on the principle of conservation of energy. It has taken into account both the common features of the third-generation marine- wave model and the different requirements for simulation in shallow water. First, the SWAN model selects the fully implicit finite difference scheme, which is unconditionally stable so that the computational space grid and time step are not constrained. Second, in the source terms of the equilibrium equation, in addition to wind loads, four-wave interaction, fracture and friction, deep fracture and three-wave interaction are also considered. Moreover, the grid of the SWAN model has gradually become a triangular finite element grid from the previous rectangular grid. The SWAN model takes into account many physical processes, including the latest results of current marine-wave forecast research [30, 31, 32].

The SWAN model takes many physical processes into account, including the latest results of current marine wave forecast research. The factors considered are:

- 1) Wave propagation process
- a) Refraction caused by current and unsteady water depth changes
- b) The shoaling effect caused by water bottom and current changes
- c) Obstacles and reflections in counter-current propagation
- d) Propagation of waves in geometric space
- e) The obstruction to waves caused by sub-grid obstacles and the propagation of waves through sub-grid obstacles
- f) Wave-induced setup
- 2) Generation and dissipation of waves
- a) Wind input
- b) White-cap dissipation
- c) Breakage caused by shoaling
- d) Bottom friction
- e) Three-wave and four-wave non-linear interaction

The SWAN model can be used in calculation of wind waves and surges of laboratory scale and continental shelf sea scale. The WAM and WAVE- WATCH *III* models and SWAN itself can be easily embedded into the SWAN model. Moreover, the parallel computing module has been added to the 40.20 version and above of the SWAN model. In addition, the grid of the SWAN model has gradually become a triangular finite element grid from the previous rectangular grid [33, 34, 35].

## Model application examples and result verification

1) Model building

The triangular finite element grid will be refined for study areas, where the large area ranges from 117°E to 127°E and 35°N to 41°N and the spatial resolution is 1/30° x 1/30°; small areas include Qinhuangdao (119.1°E to 120°E, 39.3°N to 40.1°N) and Caofeidian (117.9°E to 119.4°E, 38.7°N to 39.6°N), and the spatial resolution is 1/200° x 1/200°. The entire large calculation area is shown in Figure 2.8.

The wind field used in the temperate zone process is the hindcasting wind field; its resolution is 1/30° x 1/30°. The wind field of the small areas is obtained from the interpolation of this wind field. The wind field is input every 15 minutes. The sea-wave spectrum takes 36 frequencies and 12 directions at each grid point. By integrating the source function term and the propagation term, the wave field output once every hour is obtained.

**FIGURE 2.8: **Model calculation area

Coastal boundary conditions: For waves that are about to cross and leave the coastline, the wave energy boundary, the deep water boundary (i.e., the eastern boundary of the Bohai Sea), and the incident wave at deep-water boundary cannot be observed, and SWAN assumes that the wave can freely enter and exit the calculation sea area. Therefore, the boundary should be far enough away from the observation point in order to avoid the error caused by this assumption.

2) Model test

In order to confirm the applicability of this model to the simulation of sea waves in the Bohai Sea and the near-shore area, the SWAN model was first used for the numerical simulation of a few typical large-wave processes affecting the Bohai Sea area. Three typical strong weather processes are selected and compared with data about the measured waves at Qinhuangdao and Phillip observation stations. These are the process of typhoon 7203 in 1972, the process of typhoon 8407 in 1984 and the large-wave process caused by the temperate weather system 1011 in 2003 [36, 37, 38].

a) Simulation of the large-wave process caused by typhoon 7203 in 1972 The track of typhoon 7203 is shown in Figure 2.9. This typhoon entered the Bohai Sea at 14:00 on July 26 and left the Bohai Sea at 02:00 on July 27. In the entire process, the air pressure strength of the center of the typhoon was 975 hPa. Comparison between the wave height *H* хдо calculated and observed at Qinhuangdao station (119.62°E, 39.92°N) is shown in Figure 2.10.

FIGURE 2.9: The track of typhoon 7203

FIGURE 2.10: Comparison between the simulated wave height and observed wave height of typhoon 7203 at Qinhunagdao station

b) Simulation of the large-wave process caused by typhoon 8407 in 1984 The track of typhoon 8407 is shown in Figure 2.11. Comparison between

the wave height *H*i/ю calculated and observed at Qinhuangdao station (119.62°E, 39.92°N) is shown in Figure 2.12.

c) Simulation of the large-wave process caused by system 1011 in 2003 From October 11 and 12, affected by both the southwest inverted trough

and southwards strong cold air, 4- to 6-m high waves appeared in the Bohai

FIGURE 2.11: The track of typhoon 8407

FIGURE 2.12: Comparison between the simulated wave height and observed wave height of typhoon 8407 at Qinhunagdao station

Sea, the large waves with height of 3.5 m appeared in the coastal waters near Qinhuangdao and Tangshan in Hebei, and 4-m high waves appeared in the coastal waters near Cangzhou and Huanghua. These waves caused huge economic losses to near-shore seawalls and marine aquaculture. The chart of surface weather at 20:00 on October 11 is shown in Figure 2.13. The comparison

FIGURE 2.13: Chart of surface weather at 20:00 on October 11, 2003

FIGURE 2.14: Comparison between the measured value and the calculated value of simulated waves at Qinhuangdao station in October 2003

between the numerical simulation results and the wave observation results from October 9 to 14, 2003 in Qinhuangdao is shown in Figure 2.14.

From the comparison between the calculation results of several typical large-wave processes and the corresponding position observation results, it is clear that the SWAN model has a good simulation capability for large-wave processes in the Bohai Sea and coastal waters in Hebei Province.

# Marine current module

## Introduction to the model

The marine current module uses the FVCOM model jointly developed by the University of Massachusetts and the Woods Hole Oceanographic Institution. The model is used mainly for the coastal and estuarine tidal circulation. The greatest feature and advantage of the FVCOM model is that it combines the finite element method, which fits the boundary easily and enables the local refinement, and the finite difference method, which facilitates the discrete computation of the marine primitive equations (Figure 2.15). In the finite element method, a triangular grid is used, a linearly independent basis function is provided, and its specific coefficient is to be obtained. The method is characterized by a triangular grid that fits the boundary easily and enables the local refinement. The finite difference method facilitates the discrete computation of the marine primitive equations. It is characterized by clear dynamics basics, directly perceived difference and efficient calculation. FVCOM integrates the advantages of the above two methods. The integral form of equation and better calculation format used in the numerical calculation make the momentum, energy and mass have better conservation. The dry-wet method is used to deal with the moving boundary of tidal flat. The applied Mellor and Yamada level-2.5 turbulence closure sub-model makes the whole model closed in physics and mathematics, *a* is used vertically to reflect the irregular bottom boundary, and inner and outer films are separated so as to save the calculation time. [39, 40, 41, 42]

FVCOM uses a triangular grid, and the Surface-water Modelling System (SMS) software is used to design the Bohai Sea. Using the triangular grid makes it easy to correctly fit the shoreline and enable local refinement. Detailed refinement can be applied to complex shorelines, harbor basins and

FIGURE 2.15: Triangular grid-fitting diagram oil and gas fields; the maximum resolution can be obtained in an area as far as 5 m.

The model also has the following main characteristics [43, 44]:

- 1) A turbulence closure model is used to provide the vertical mixing coefficient.
- 2) Sigma coordinates are used vertically in order to better fit submarine relief.
- 3) Horizontally, orthogonal curvilinear grid and staggered “C” grid are used to better match coastal shapes.
- 4) The horizontal and temporal difference schemes are explicit, while vertical difference schemes are implicit.
- 5) Internal and external molds are calculated separately. The external mold is two-dimensional and the time step is relatively short, while the internal mold is three-dimensional and the time step is relatively long.
- 6) The model includes complete thermodynamical equations.
- 7) The model includes a set of substance diffusion and transport and Lagrangian particle-tracking sub-modules.

## Model configuration

1) Grid configuration

The main computational domain of the model is the entire Bohai Sea, with a focus on the areas in the vicinity of major ports (such as Tianjin Port) and offshore oil and gas platforms. The Bohai Strait has strong tidal currents. Moreover, the largest tidal currents in the Bohai Sea area also appear in the Laotieshan waterway in the north of the strait. In the event of a marine pollution accident (such as an oil-spill accident) in the port area in winter, a large amount of pollutants may enter the Bohai Sea under the effects of the north wind and the strong tidal currents in the Bohai Strait. As a result, the Bohai Sea will be seriously polluted [45, 46]. Therefore, after all factors are taken into account, the computational domain of the model is expanded on the basis of the Bohai Sea. In other words, the expanded computational domain includes a part of the north Yellow Sea area, as shown in Figure 2.16(a). This figure shows the locations of major oil and gas drilling platforms within the Bohai Sea. The unstructured triangular grid is naturally refined at Bohai Strait and the complex shorelines, bay mouths, key ports, and oil and gas fields within the Bohai Sea area (see Figure 2.16(b)), in order to ensure the accurate simulation of currents and tides. Grid refinement has two levels. The grid accuracy of the first-level refinement area is 100 m, which is mainly concentrated in the vicinity of Tianjin Port, the Bohai Strait, the major oil and gas fields within the Bohai Sea area and the major ports along the Bohai Sea. The grid accuracy of the second-level refinement area is 1', which covers all areas other than the above-mentioned areas. Figure 2.17 shows grid refinement for the waters near Tianjin Port. It can be seen that the resolution of the grid has almost reached the level of simulated terrain in the main near-shore waters.

FIGURE 2.16: Grid settings of research domain

Therefore, the natural refinement of the FVCOM’s triangular finite element grid can be used to effectively simulate and forecast the oil spills that may occur in the main areas of concern.

2) Selection of model parameters

The FVCOM model operation requires initial temperature and salinity fields, open boundary forcing and water-depth data. The initial temperature and salinity field used for the calculation in this study is the annual mean temperature and salinity field obtained from the historical observation data. The open boundary of the model is forced by the harmonic constants of tide. Harmonic constants of five tidal constituent *(М**2**, S^, K,0, P)* are used for calculation. The tidal harmonic constants used are all derived from the tidal

FIGURE 2.17: Grid refinement for the waters near Tianjin Port

FIGURE 2.18: Block division in charts with different resolution

model simulation results of China’s coastal waters t hrough adjoint variational method. ArcGIS and other specialized software are used to splice the nautical charts that have different resolutions, as shown in Figures 2.18 through 2.19 [47, 48].

In addition, the related terrain and shoreline information extracted from the basic geographic information database of National Marine Information

FIGURE 2.19: Distribution of deep-water points with different resolution

FIGURE 2.20: High-precision Bohai Sea and Yellow Sea terrain

Center is supplemented and the method of nearest-point interpolation of set thresholds is used to complete the production of high-precision terrain data products for the forecast area, preparing for the configuration and development of the marine module of the forecast system. Figure 2.20 is an example showing the high-precision Yellow Sea terrain after processing.