# Prediction of Arrival Time of Vessels Considering Future Weather Conditions
## 3 Proposed Method
### (A) Route Calculation  
An illustrative overview of the route calculation is illustrated in Figure 4. Steps A1 to A3 are used to find a route appropriate for the future weather conditions from the past routes of vessels similar to the considered vessel. Figure 4: Overview of vessel routing procedure. Figure 3: Comparison between this study and a previous study. In step A1, routes with the same departure and destination ports are extracted from the data for vessels similar to the considered vessel. Although the use of past data for the same vessel would maximize the prediction accuracy, a sufficient amount of data may not be available for that vessel on the routes. Therefore, data for similar vessels are used in addition to data for the same vessel to ensure a sufficient quantity of data can be extracted. Although it is a challenging problem to identify similar vessels, vessel dimensions (such as the total length or width) can be determined from the vessel type (such as tankers or container vessels), weight, and GRT, as illustrated in Figure 4[24]. Hence, a route that takes into account the current weather conditions can be extracted from past data for similar vessel types and GRTs. In the illustration, no vessels are found with exactly the same GRT as the considered vessel, so the order of GRT (e.g., 10,000-ton class, 20,000-ton class, or 30,000-ton class) is considered. Figure 5 shows an example where the considered vessel is a container ship with a GRT of 21,643, and data on similar container ships in the 20,000-ton GRT class are selected. In addition, some routes include outliers due to vessel breakdown, accidents, etc. The AIS information includes voyage status, and it can be used to remove routes including abnormal voyage statuses. Step A2 consists of acquiring past and future weather conditions for each past route found in A1 and quantifying the error involved. The sets, indexes, and constants used in the quantification process are detailed below. Moreover, Figure 6 shows a graphical image of the sets, indexes, and constants. In Figure 6, quantification is conducted for two routes. Among the constants presented above, the past wave height, wave direction, wave period, east-west winds, and north-south winds are acquired at the transit time for each site. The future constants cannot be similarly acquired because the future transit time for each site has not been determined. Therefore, the future constants are acquired by approximating the future transit time at each site as the time required to travel between the transit sites in the past. For example, Figure 4 shows that it takes one hour to travel from the departure port to site A; therefore, the future wave height, wave direction, wave period, east-west winds, and north-south winds at site A are determined for one hour from the current time. In this study, the above constants were obtained from the Research Institute for Sustainable Humanosphere, Kyoto University, which publishes weather data from the Japan Meteorological Agency [25]. In particular, we used grid point values (GPV) as the wave forecast and the global spectral model (GSM) as the wind forecast. Figure 5: Example of similar vessels. After acquiring the aforementioned constants, the error in the weather conditions at each site is calculated from the square of the error between the past and future constants. Equation (1) shows that the errors of all the sites can be summed to yield the error in the weather conditions for the route of interest. This process is applied to all the routes extracted in A1. \[ \begin{split}\sum_{s}\bigl{(}HTSGW_{rs}^{Past}&-HTSGW _{rs}^{Future}\bigr{)}^{2}+\bigl{(}DIRPW_{rs}^{Past}-DIRPW_{rs}^{Future}\bigr{)}^{2 }\\ &+\bigl{(}PERPW_{rs}^{Past}-PERPW_{rs}^{Future}\bigr{)}^{2}\\ &+\bigl{(}UGRD_{rs}^{Past}-UGRD_{rs}^{Future}\bigr{)}^{2}+\bigl{(} VGRD_{rs}^{Past}-VGRD_{rs}^{Future}\bigr{)}^{2}\end{split}  \tag{1}\]  
In step A3, the voyage calculated in A2 with minimal error in the weather conditions is selected to be the one whose weather is closest to the future conditions.