This paper uses modeling to analyze the tsunami hazard and determine where future tsunami disasters may occur. Two kinds of disastrous tsunami effects are considered—tsunami inundation on land and tsunami flow impact in coastal waters. The study area includes marine areas 3 km from the coastline, which is the main area for activities such as marine aquaculture and marine tourism.

Figure 1 is the analysis framework for the tsunami prevention zones. There are two main considerations for research on prevention zones: (1) On the land areas, the tsunami inundation areas are classified as tsunami prevention zones. Objects on the ground within inundation areas including commercial facilities and housing, nuclear power plants, and industrial complexes may be affected by a tsunami to a certain extent. (2) In marine areas, the impact of tsunami currents on coastal facilities is the main consideration. Tsunami forces were used to calculate the impact of tsunami flow. Facilities that could be affected by tsunami flows include ports, tourist places, and marine aquaculture operations.

The areas affected by tsunamis differ depending on the source of the tsunami. Therefore, an analysis of prevention zones should be based on a particular source and tsunami magnitude. For the purpose of this paper, an earthquake in the Ryukyu Trench was assumed to be the tsunami source (see Fig. 1). The COMCOT model was used to calculate the physical parameters of the tsunami. This model, developed by Cornell University, uses a leapfrog scheme on a staggered and nested grid system to solve both linear and nonlinear shallow water equations. It has been successfully used for the simulation of several historical tsunami events (Heidarzadeh and Satake, 2014; Hou et al., 2016).

A three-level nested grid was used in the tsunami model to analyze tsunami prevention zones for Putuoshan Island. The first level of the model covers the hypothesized tsunami source in Ryukyu Trench and Putuoshan Island, while the third level covers only Putuoshan Island and its coastal waters. According to the distance between the tsunami source and the Putuoshan Island, the total calculation time in the model was 15 h. In deep water, the tsunami wave is affected mainly by the Coriolis force and the pressure gradient, so the governing equation of the first level uses linear shallow water equations in spherical coordinates. When the tsunami reaches shallower water, nonlinear interaction increases. Therefore, nonlinear shallow water equations in Cartesian coordinates are used in the second and third levels.

The linear equations in spherical coordinates are shown below.

$$\frac{\partial \eta }{\partial t}+\frac{1}{Rcos\phi }\left\{\frac{\partial P}{\partial \psi }+\frac{\partial }{\partial \phi }\left(cos\phi Q\right)\right\}=-\frac{\partial h}{\partial t},$$

1

$$\frac{\partial P}{\partial t}+\frac{gh}{Rcos\phi }\frac{\partial \eta }{\partial \psi }-fQ=0,$$

2

$$\frac{\partial Q}{\partial t}+\frac{gh}{R}\frac{\partial \eta }{\partial \phi }+fP=0.$$

3

The nonlinear equations in Cartesian coordinates are shown below.

$$\frac{\partial \eta }{\partial t}+\left\{\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}\right\}=-\frac{\partial h}{\partial t},$$

4

$$\frac{\partial P}{\partial t}+\frac{\partial }{\partial x}\left\{\frac{{P}^{2}}{H}\right\}+\frac{\partial }{\partial y}\left\{\frac{PQ}{H}\right\}+gH\frac{\partial \eta }{\partial x}+{F}_{x}=0,$$

5

$$\frac{\partial Q}{\partial t}+\frac{\partial }{\partial x}\left\{\frac{PQ}{H}\right\}+\frac{\partial }{\partial y}\left\{\frac{{Q}^{2}}{H}\right\}+gH\frac{\partial \eta }{\partial y}+{F}_{y}=0,$$

6

where *η* is the water fluctuation; (*P*, *Q*) stand for the volume flux in the *X* and *Y* direction; (*φ*, *ψ*) are the latitude and longitude; *F* is the Coriolis force; *H* = *η* + *h* represents the total water depth; (*Fx, Fy*) denote the bottom friction in the *X* and *Y* direction; *g* is gravity acceleration; *R* is the radius of the earth. The grids settings of numerical model are shown in Table 1.

Table 1

Nested grids of the numerical model

Grids | Coverage | Resolution | Grid Dimension |

Level 1 | 18°–40° N, 115°–143° E | 2´ | 840*763 |

Level 2 | 29°–31° N, 121°–123° E | 1/4´ | 472*544 |

Level 3 | 29.96°–30.08° N, 122.35°–122.47° E | 1/32´ | 240*280 |

ETOPO2v2 2-arcminute data (**NGDC, 2020**) was used for simulation at the first level, which covers an area from 18°N to 40°N and from 115°E to 143°E. The second level, which covers the entire archipelago where Putuoshan Island is located, uses SRTM 15 + 15-arcsecond bathymetry data (**Tozer, 2019**). The bathymetry data for the third level were derived from the fusion of measured bathymetric data with a resolution of 1/32 arcminutes.