## 2 Materials and Methods
### Environmental Capacity Assessment System (ECAS)
#### 2.2.2.1 Environmental Capacity Estimation  
In this study, EC refers to the maximum allowable pollutant load in the bay without considering the allocation principle between pollution sources, only focusing on the attributes of the marine environment itself and the stipulated water quality objectives. The water quality of the grid points in the simulated area has a certain response relationship with the emission of each pollution source in a region, that is, the response relationship matrix between the pollutant concentration of monitoring points and the intensity of each emission source. The response relationship matrix is calculated by the following hydrodynamic model and water quality model. At the same time, the properties of the marine environment itself, such as hydrologic conditions and degradation capacity of the environment, are reflected in the response field of the pollution source when calculating the response relationship. Therefore, the calculation of EC can be transformed into a linear programming problem, with the water quality objective as a constraint condition and the pollutant discharge load as a target function ([PERSON] and [PERSON], 2017). The problem is to take the water quality target as the restriction condition, at the selected water quality control point, and calculate the maximum sum of the pollution load emissions of each sewage outlet; additionally, the pollutant concentration is prohibited from exceeding its corresponding environmental standard. Hydrodynamic Model  
1. Basic hydrodynamic model. The model adopts the two-dimensional flow continuity equation and motion equation:1 Continuity equation:  
\[\frac{\partial\zeta}{\partial t}+\frac{\partial p}{\partial x}+\frac{\partial q}{ \partial y}=0 \tag{2}\]
2 Motion equations:  
\[\frac{\partial p}{\partial t}+\frac{\partial}{\partial x}\bigg{(}\frac{p^{2}}{ h}\bigg{)}+\frac{\partial}{\partial y}\Big{(}\frac{pq}{h}\Big{)}+gh\frac{ \partial\xi}{\partial x}+gp\frac{\sqrt{p^{2}+q^{2}}}{C^{2}h^{2}}-\Omega q-fVV_{ x}=0 \tag{3}\]  
\[\frac{\partial q}{\partial t}+\frac{\partial}{\partial x}\bigg{(}\frac{q^{2}}{ h}\bigg{)}+\frac{\partial}{\partial y}\Big{(}\frac{pq}{h}\Big{)}+gh\frac{ \partial\xi}{\partial y}+gq\frac{\sqrt{p^{2}+q^{2}}}{C^{2}h^{2}}-\Omega p-fVV_ {y}=0 \tag{4}\]  
where:  
\(t\): time;  
\(g\): acceleration of gravity \((m/s^{2})\);  
\(\xi(x,y,t)\): free water level (m);  
\(h(x,y,t)\): depth of the water (m), the distance from the bottom of the sea to the stationary sea surface;  
\(p,q(x,y,t)\): flow density in the \(x-,y-\) direction, that is, the width of the flow \((m^{3}/s/m)\);  
\((u,v)\): \(x-,y-\) directional perpendicular mean velocity component;  
\(C(x,y)\): the coefficient of Chezy, its relation to the Manning number M is \(C=M\times h^{1/6}\);  
\(f(V)\): wind friction factor \(=\gamma_{a}^{2}\rho_{a}\); \(\gamma_{a}^{2}\) is the wind stress coefficient, \(\rho_{a}\) is the air density;  
\(V,V_{x},V_{y}(x,y,t)\): wind speed, and \(x-,y-\) component of wind speed in direction \((m/s)\);  
\(\Omega(x,y)\): Coriolis coefficient \(f=2\omega\sin\phi\), \(\omega\) is the rotational speed of the earth, \(\phi\) is geographic latitude. Equations (2)-(4) constitute the basic governing equations for solving the tidal flow field. 2. Boundary conditions. In the numerical model adopted in this study, two kinds of boundary conditions should be given, namely, the open boundary condition and the closed boundary condition. 1 Open boundary condition:  
The open boundary condition is the water boundary condition. In this study, the tidal level is given as the open boundary.