# Simulation Tool for Winter Navigation Decision Support in the Baltic Sea
## 4 Model Data  
The case study presented in this article includes winter traffic from 15 January 2010 to 15 February 2010. A total of 115 vessels are incorporated. These vessels are categorized into 18 vessel types with similar hv curves. The hv curves are characterized by cubic polynomials, where the coefficients are calculated from regression formulae that have been internally established by a design company and validated against extensive measurement data [16]. A matching algorithm has been designed to assign each vessel the most relevant hv curve profile, based (among other factors) on its dimensions and power. A detailed description of the hv curve derivation and matching is beyond the scope of this article. Knowing the ice thickness, the corresponding vessel speed can be calculated using the hv curves. A vessel's actual speed in ice is not necessarily the same as its achievable speed (as estimated from hv curves). However, as a simplification, it has been assumed to be the same in this model. The hv curves can be used to calculate speeds under six different conditions: channel ice, level ice, floe ice, ridges, pressure, and assistance at a distance. The model is designed to include all six types. For demonstration purposes, the test cases presented in this paper have been built for an open water, level ice, and assisted at a distance condition. The level ice thickness in the model varies by area and by day. If the speed drops below the specified threshold, the vessel waits for icebreaker assistance. Once the icebreaker arrives, the speed is calculated for the \"assisted at a distance\" condition. This applies for all vessels and icebreakers as well, which have their own hv curves. The traffic data used in the model have been obtained through the research project WINMOS II [17]. The data include information about origin and destination ports; arrival, departure, and time spent at port; vessel name and type (for hv curve); and next destination. These data have been preprocessed to obtain Table 2. The vessel itineraries used in the model are a result of AIS data processing work described in this conference article [18]. Based on this work, it possible to know whether a ship is at port or sea. The information in Table 2 is used an input to the simulation model. Every vessel is assigned a unique code or identifier to track its movements and KPI throughout the simulation. Similarly, every port is also assigned an identifier. The simulation also displays vessel names (anonymized) during the visualization. The departure time from the port is converted to minutes from the start of the simulation run. Since the period considered begins on 15 January 2010, midnight (0000) of 15 January is the start of the simulation run. All other departure times are relative to this starting point. Another important component of these data is the hv curve identifier. Each vessel is assigned a vessel type, which determines the hv curves that apply to it. The hv curve code or identifier is an input to the model. Based on the code, the relevant hv curve information is referenced by the vessel during the run. The hv curve expressions for speeds in level ice (\(y_{l}\)) and the assisted at a distance condition (\(y_{d}\)) are as shown below. \[y_{l}=a_{l}*h^{3}+b_{l}*h^{2}-c_{l}h+w\]  
\[y_{d}=a_{d}*h^{3}+b_{d}*h^{2}-c_{d}h+w\]  
In these equations, \(h\) stands for equivalent ice thickness. The terms \(a\), \(b\), and \(c\) are the coefficients for the ice condition (curve parameters) and \(w\) is the open water speed. A typical set of coefficients for an hv curve is shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline
**Shipcode** & **Portcode** & **Shipname** & **Deptime** & **Hvcode** \\ \hline
0 & 5 & Ship\_1 & 5400 & 0 \\ \hline \end{tabular}
\end{table} 
Table 2: Snapshot of processed traffic data. This table corresponds to the coefficients for the vessel type \"Example_ship\" which has been assigned the identifier \"0\". The suffix \"1\" is for level ice, while \"d\" is for the assisted at a distance condition.