## 3 Methods
### Navigation Risk Assessment Model
#### 3.2.2 Data Processing  
Five evaluation factors with a great impact on ship navigation were selected in Section 3.2.1. However, before conducing the risk assessments, the risk factor value of each criterion should be obtained in each of the four seasons. First, the spatial resolution of the gridded data are unified to 0.125\({}^{\circ}\)\(\times\) 0.125\({}^{\circ}\). Second, the risk values of each factor under severe sea conditions are calculated from the gridded wind, wave, ocean currents, and sea fog data from 2016 to 2020. Then, the risk grid values of each factor are standardized. When setting the thresholds for the different evaluation criteria, we follow the methods employed in previous research [21; 41].  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Fog** & **Wind** & **Wave** & **Currents** & **Water Depth** & **Rainfall** & **Total** \\ \hline Number & 13 & 17 & 18 & 7 & 9 & 4 & 68 \\ Proportion & 19.2\% & 25.0\% & 26.5\% & 10.3\% & 13.2\% & 5.8\% & 100\% \\ Ranking & 3 & 2 & 1 & 5 & 4 & 6 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistics of accident-related factors.  
First, the sea fog criterion calculates the occurrence frequency of sea fog in each grid in the different seasons following Equation (4):  
\[\mathrm{F}_{i}^{j}=\frac{\sum\mathrm{f}_{i,k}}{\mathrm{d}^{j}}, \tag{4}\]  
where \(\mathrm{F}_{i}^{j}\) represents the occurrence frequency of sea fog in grid \(i\) in season \(j\), \(\mathrm{f}_{i,k}\) represents the occurrence of sea fog in grid \(i\) on day \(k\), \(\mathrm{f}_{i,k}\in[0,\ 1]\), 0 represents no sea fog, 1 represents sea fog, and \(\mathrm{d}^{j}\) represents the total number of days in season \(j\).  
The wind criterion, for wind speeds greater than 11.7 m/s in each grid, in different seasons is calculated via Equation (5):  
\[G_{i}^{j}=\frac{\sum g_{i,k}}{\mathrm{d}^{j}}, \tag{5}\]  
where \(G_{i}^{j}\) represents the frequency of wind speeds greater than 11.7 m/s in grid \(i\) in season \(j\), \(g_{i,k}\) represents wind conditions for grid \(i\) on day \(k\), \(g_{i,k}\in[0,\ 1]\), 0 represents wind speeds slower than 11.7 m/s, 1 represents winds speeds greater or equal to 11.7 m/s, and \(\mathrm{d}^{j}\) represents total days in season \(j\).  
Calculation of the wave and currents criteria are same as for the wind criterion, where the thresholds for the wave and currents criteria are 2 m and 1 m/s, respectively.  
The water depth is a static criterion, where each grid risk value of water depth is calculated using Equation (6):  
\[\mathrm{D}_{i}=\left\{\begin{array}{cc}0&d_{i}>30\;\mathrm{m}\\ 1-\frac{d_{i}}{30}&0\;\mathrm{m}<d_{i}<30\;\mathrm{m}\\ 1&d_{i}<0\;\mathrm{m}\end{array}\right., \tag{6}\]  
where \(\mathrm{D}_{i}\) represents the risk value of water depth in grid \(i\), and \(d_{i}\) represents the original water depth value.  
After calculating these criteria, it is necessary to standardize the grid values to 0-1. The standardization formula used in this paper is shown in Equation (7):  
\[\mathrm{x}^{\prime}=\frac{\mathrm{x}-\mathrm{x}_{\mathrm{min}}}{\mathrm{x}_{ \mathrm{max}}-\mathrm{x}_{\mathrm{min}}}, \tag{7}\]  
where \(\mathrm{x}^{\prime}\) represents the standardized value, \(\mathrm{x}\) represents the original risk value, \(\mathrm{x}_{\mathrm{min}}\) represents the minimum value, and \(\mathrm{x}_{\mathrm{max}}\) represents the maximum value.