# Prediction of Arrival Time of Vessels Considering Future Weather Conditions
## 4 Verification of the Prediction Accuracy of the Proposed Method  
The accuracy of the prediction method in Section 3 is verified in this section. Among the previous methods described in 2.1, those of [PERSON] et al. [14], [PERSON] et al. [15], and [PERSON] et al. [16] calculate the optimal voyage route but do not predict the arrival time. Moreover, the study of [PERSON] et al. [19] only focused on calculating the future voyage speed. Consequently, in this study, the method of [PERSON] et al. [6] was chosen for comparison. We use historical operation data of vessels traveling between Japan and Taiwan with home appliance-related cargoes and between Japan and the United States with automobile industry-related cargoes. The target vessels and their routes are shown in Table 1.  
In Table 1, TS TOKYO and TS OSAKA are vessels with home appliance cargoes and NEW CENTURY 1 and NEW CENTURY 2 are the vessels with automobile industry cargoes. Four routes are considered for TS TOKYO and TS OSAKA: between Kobe and Nagoya, Nagoya and Yokohama, Tokyo and Keelung (Taiwan), and Keelung and Taichung (Taiwan). One route is considered for NEW CENTURY 1 and NEW CENTURY 2 between Toyohashi and Long Beach (USA). The arrival time to the destination port is predicted for each route. The past vessel data used to predict the arrival time for each respective vessel are given below. All the past data were acquired from Vessel Historical Track and Berth Calls, which are APIs provided by Marine Traffic. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vessel Name** & **Depature Port** & **Arrival Port** & **Depature Time** \\ \hline \multirow{4}{*}{TS TOKYO} & KOBE & NAGOYA & 2020/4/18 16:44 \\ \cline{2-4}  & NAGOYA & YOKOHAMA & 2020/4/19 17:48 \\ \cline{2-4}  & TOKYO & KEELUNG & 2020/4/22 10:24 \\ \cline{2-4}  & KEELUNG & TAICHUNG & 2020/4/25 18:32 \\ \hline \multirow{4}{*}{TS OSAKA} & KOBE & NAGOYA & 2020/4/23 11:18 \\ \cline{2-4}  & NAGOYA & YOKOHAMA & 2020/4/24 12:08 \\ \cline{2-4}  & TOKYO & KEELUNG & 2020/4/26 2:23 \\ \cline{2-4}  & KEELUNG & TAICHUNG & 2020/4/29 11:30 \\ \hline NEW CENTURY 1 & TOYOHASHI & LONG BEACH & 2020/8/8 10:18 \\ \cline{1-1} \cline{2-4}  & NEW CENTURY 2 & & 2020/7/30 10:08 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Target vessels used to verify the prediction method. * TS TOKYO, TS OSAKA  
A total of 405 routes between Japan and Thailand sailed by 13 vessels from January 2019 to March 2020 carrying home appliance industry cargoes
* NEW CENTURY 1, NEW CENTURY 2  
A total of nine routes between Toyohashi (Japan) and Long Beach (USA) sailed by eight vessels  
Moreover, as described in Section 3.1, the past weather data were obtained from the Research Institute for Sustainable Humanosphere, Kyoto University. Table 2 shows a part of the past vessel data. As shown in Table 2, we link voyage data and weather data based on each datum's longitude and latitude. Each column contains the following information. MMSI, SPEED, LON, LAT, COURSE, HEADING, and TIMESTAMP are from voyage data. Moreover, HTSGW, PERPW, DIRPW, UGRD, and VGRD are from weather data. These columns' meanings are shown in Table 3.  
In this verification, the mean absolute percentage error (MAPE) for each voyage is calculated as shown in Equation (5). \[MAPE=\left|\frac{\left(\text{Predicted arrival time}-\text{Departure time}\right)-\left(\text{Actual arrival time}-\text{Departure time}\right)}{\text{Actual arrival time}-\text{Departure time}}\right|\times 100\;(\%) \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Mmsi** & **Speed** & **Lon** & **Lat** & **Course** & **Heading** & **Timestamp** & **Htsgw** & **Perpw** & **Dirpw** & **Ugrd** & **Vgrd** \\ \hline
538007662 & 164 & 136.938 & 34.61643 & 315 & 315 & 2019/1/10:01 & 1.05 & 5.10 & 320 & 4.81 & \(-\)4.45 \\ \hline
538007662 & 173 & 136.7697 & 34.85543 & 0 & 359 & 2019/1/10:00 & 0 & 0 & \(-\)10 & 1.52 & \(-\)1.91 \\ \hline
538007662 & 0 & 136.7413 & 34.97633 & 9 & 339 & 2019/1/1:59 & 0 & 0 & \(-\)10 & 2.01 & \(-\)0.381 \\ \hline \hline \end{tabular}
\end{table}