## 4 Validation
### Simulation Input
#### 4.2.3 Ice Conditions  
Based on ice charts provided by [27], for each considered date and navigation leg, the prevailing ice conditions are determined in terms of the average ice conditions \(H_{eq\_avg}\) and the most difficult ice conditions \(H_{eq\_max}\). Specifically, the average ice conditions along a leg \(H_{eq\_avg}\) is determined as per Equation (2).  
\[H_{eq\_avg}=\frac{H_{min}+H_{max}}{2}*\frac{C_{min}+C_{max}}{2}+H_{ridging\_avg}, \tag{2}\]  
where \(H_{min}\) represents the minimum ice thickness, \(H_{max}\) represents the maximum ice thickness, \(C_{min}\) represents the minimum ice concentration, \(C_{max}\) represents the maximum ice concentration, and \(H_{ridging\_avg}\) is an assumed 6 cm increase in equivalent ice thickness caused by ridges (where ice ridging occurs). The assumed value of \(H_{ridging\_avg}\) is based on [28], according to which ice ridges in the Bothnan Bay increase the level ice thickness by 6-14 cm equivalent ice thickness. The most difficult ice conditions occurring along a leg \(H_{eq\_max}\) is determined as per Equation (3).  
\[H_{eq\_max}=H_{max}*C_{max}+H_{ridging\_max}, \tag{3}\]  
where \(H_{max}\) represents the maximum ice thickness, \(C_{max}\) represents the maximum ice concentration, and \(H_{ridging\_max}\) is an assumed 14 cm increase in level ice thickness caused by ridges (where ice ridging occurs) [28].  
Figure 4: Navigation legs (L) and ports.  
Extracts of calculated and applied \(H_{eq\_avg}\) and \(H_{eq\_max}\) values are presented in Tables 2 and 3. The complete ice data are found in Appendix B (see Tables A3 and A4). It should be noted that the assumed values of \(H_{eq\_avg}\) and \(H_{eq\_max}\) are subject to significant uncertainty originating both from the source, i.e., the ice charts, which presents ice data in terms of approximate thickness and concentration ranges, and from the assumption that the ice conditions are homogenous over the considered navigation legs. To account for this uncertainty, during an individual simulation run, each value of \(H_{eq\_max}\) and \(H_{eq\_max}\) presented in Tables 2 and 3 is multiplied with two coefficients, one representing the uncertainty in ice thickness, and the other representing the uncertainty in ice concentration. Both coefficients are determined by drawing a random number from a normally distributed set with a mean of 1 and a standard deviation of 10%.  
Figure 5: Ship model-specific hv curves for three different operation modes: icebreaker (IB) assistance at distance, operation in a brash ice channel, and independent operation in level ice [26].  
Ships operating in ice may encounter brash ice channels created and maintained by IBs and other ships. The duration for which an ice channel remains open and navigable depends on multiple factors including the amount of maritime traffic, the local geography, as well as the prevailing wind and currents [29]. In addition, strong winds in combination with a physical boundary might result in compressive ice, which may significantly increase a ship's ice resistance [30]. Anyhow, due to a lack of related data and suitable engineering models, such factors are not systematically considered. Instead, it is assumed that along fairways with very significant traffic (L 1 and 2), a brash ice channel is available with a 75% probability, along fairways with significant traffic (L 3, 5, 6, 7, 9, 10, and 12), a brash ice channel is available with a 50% probability. On the open sea, where the traffic is limited (L 15), brash ice channels are assumed not to be present. In protected waters with fast ice (L 4, 8, and 11, 13, and 14), brash ice channels are assumed to be present throughout the simulation.