# Prediction of Arrival Time of Vessels Considering Future Weather Conditions
## 3 Proposed Method  
A method for predicting the arrival time of vessels is proposed in this section. The shortcomings of the method proposed by [PERSON] et al. were identified in Section 2.2. That is, (A) the route calculation does not include the future weather conditions that are typically considered to ensure vessel safety, and (B) the voyage speed calculation does not consider regionality or future weather conditions. To increase the prediction accuracy of the arrival time, the weather conditions, vessel safety, and regional voyage speeds should be considered in (A) and (B).  
As [PERSON] et al. [22] noted, the vessel route for (A) can be freely selected, and captains almost always employ the same selection criteria. Hence, given the influence of weather, a limited number of routes can be selected. We can use this consideration to calculate routes with little deviation from the actual ones; that is, we can analyze the past routes of target vessels and choose those routes whose weather conditions are similar to the current conditions.  
As discussed in Section 2.2, [PERSON] et al. used past data on the considered vessel on routes with the same departure and destination ports to calculate the average voyage speed (B). In contrast, we consider the weather conditions and regionality of the voyage speed when calculating the voyage speed for each transit site along a route and thereby the time of arrival at the destination port. The voyage speed at each site is calculated from positional information, namely, the latitude and longitude, the weather information at each point, and past data, similar to the dynamic information of the vessel.  
Here, the parameters adopted by [PERSON] et al. [19] are used to determine the dynamic information about the vessel and weather information. The parameters for the weather information are the wave height, wave period, and wind speed, while the bow direction is used as the parameter for the dynamic vessel information. Figure 3 shows the main parameters used in this study and in the study of [PERSON] et al. Here, our method incorporates the regionality of the voyage speed by replacing the parameters considered by [PERSON] et al., such as the number of engine and propeller rotations, with positional information, namely, the latitude and longitude.  
Figure 2: Voyage speed distribution for various areas.  
However, there is only a limited amount of data in which all parameter sets such as the ship type, total tonnage, longitude, latitude, wave height, wave period, wind speed, and bow direction match, and the prediction accuracy will deteriorate when only a small quantity of data can be used. On the other hand, a sufficient amount of past data can be obtained for the individual parameters. Here, we can use Bayesian learning [23] to make estimations from small quantities of data by combining probability distributions for each parameter. In particular, our method generates a probability distribution of voyage velocities from the past data for every parameter and then combines the distributions. This strategy resolves the problem of limited data availability.  
The route calculation and voyage speed calculation are detailed below.