## 3 Weather Component Analysis during the \"Oriental Star\" Accident
### Predicted CP Following \"Oriental Star\" Last Route  
In the \"Oriental Star\" case, the sliding moving average and a specific Kriging algorithm were adopted to interpolate the weather components at specific ship positions based on AIS data with a 10-min time interval. Kriging Method Optimization [19], known for its good performance and used for optimal, 3D space relation, linear, and unbiased purposes, was finally chosen after comparison to two other traditional interpolation algorithms. For the position of the ship corresponding to each time interval, the forecast data of the ECMWF numerical product with a lead of 24-36 h, 48-60 h, and 72-84 h are obtained by the space-time interpolation method. The formula is defined as follows:  
\[\overset{\sim}{z}_{0}=\sum_{i=1}^{n}\lambda_{i}z_{i} \tag{1}\]  
\[\gamma(h)=\frac{1}{2n}{\sum_{i=1}^{n}\left(z(x_{i})-z(x_{i}+h)\right)^{2}} \tag{2}\]  
\[c(h)=E[z(x)z(x+h)]-m^{2} \tag{3}\]  
where \(\overset{\sim}{z}_{0}\) is the estimated value at the point \((x_{0},y_{0})\), and \(\lambda_{i}\) is the weight coefficient, indicating the contribution of the observation value at each sample space point to the estimated value. The weight coefficient must satisfy the condition that the estimated value must be unbiased and optimal. \(\gamma(h)\) is also called the variogram and is a measure of the degree of spatial correlation between points. \(c(h)\) is the covariance function in the region, and \(m\) is the mean. The solving process is skipped here, and finally, it is simplified by the Lagrangian multiplier method:  
\[\begin{cases}\sum_{j=1}^{n}\lambda_{i}c\big{(}x_{i},x_{j}\big{)}-\mu=c(x_{i}, x)\\ \sum_{i=1}^{n}\lambda_{i}=1\end{cases} \tag{4}\]  
Figure 5: Upper-level air temperature trend at different pressure levels at the location of the “Oriental Star” shipwreck. The vertical lines mark the shipwreck time.  
Among them \(c\left(x_{i},y_{j}\right)\) is the covariance, and \(\mu\) is the coefficient in the Lagrangian multiplier method. The above formula can also be expressed in matrix form:  
\[\begin{bmatrix}c_{11}&c_{12}&\dots&c_{1n}&1\\ c_{21}&c_{22}&\dots&c_{2n}&1\\ \dots&\dots&\dots&\dots&\dots\\ c_{n1}&c_{n2}&\dots&c_{nn}&1\\ 1&1&\dots&1&0\end{bmatrix}\begin{bmatrix}\lambda_{1}\\ \lambda_{2}\\ \dots\\ \lambda_{n}\\ -\mu\end{bmatrix}=\begin{bmatrix}c(x_{1},x)\\ c(x_{2},x)\\ \dots\\ c(x_{n},x)\\ 1\end{bmatrix} \tag{5}\]  
Therefore, \(\lambda_{i}\) can be solved by matrix inversion, and \(c(x_{i},x)\) is obtained by \(\gamma(h)\) fitting the function \(\gamma(h)=c(0)-c(h)\).  
With the above algorithm, different quantities of rainfall that the \"Oriental Star\" would have expected to receive per 15 min were calculated in Figure 6. The ship experienced an ordinary rainfall process shortly after its departure at UTC 1600 Z on 28 May, and both the CP and LSP predicted this weather process. After then, no rain was present until in the mid-day of 1 June. Among all the variables, only the CP at a one-day lead time showed a dramatic increase and decrease trend. These rapid variations closely corresponded with the on-site severe downburst and wind gusts that caused the ship to capsize. Although they correspond to 90 min earlier than the actual accident time, it is still remarkable considering its lead time. In contrast, CP predictions at other lead times and all LSP predictions on the ship's last time are almost negligible; this agreed with the horizontal fields in Figure 4. Therefore, it is suggested that the one-day-lead CP prediction before the \"Oriental Star\" shipw has a great potential as a strong wind gust early warning, which is missing in the LSP variable.