# System Dynamics Modeling for Estimating the Locations of Road Icing Using GIS
## 2 Materials and Methods
### Scenario Selection  
The weather and spatial scenarios used the data of Suncheon ASOS on 11 December 2008 as the main samples. Traffic accidents caused by road icing actually occur under various conditions, especially at night, dawn and early morning. It takes a long time to simulate all these cases, and the efficiency of simulation also decreases. Thus, it was necessary to select a representative weather situation in which road icing may occur. 11 December 2018, was the day when the largest number of freezing rain-related traffic accidents occurred during the period from 2018 to 2020 in Jeollanam-do, Korea. On that day, freezing rain phenomenon occurred, in which supercooled rain in the air at room temperature is frozen upon hitting the ground at sub-zero temperature [36]. In this study, the data of the day were set as a scenario, and the formation of road icing caused by freezing rain was modeled and simulated. The model was also verified through a comparison with actual areas vulnerable to traffic accidents.  
The data of 11 December 2018 were used as a scenario because they were the latest among the freezing rain observation data of days when freezing accidents occurred, but there are a number of precipitation scenarios that can be applied to modeling. Table 5 shows a list of such scenarios. The model and simulation are versatile for scenarios related to ordinary rain or freezing rain and can be applied to situations where the moisture in the air near waterfront areas condenses at the dew point in the cold morning even if it is not precipitation. In addition to freezing rain, the model deals with various types of precipitation in cold weather. Even when snow falls, the model can estimate the location of road icing. However, when snow is set as input, it is necessary to translate the melting time into the model when estimating the road surface moisture [40].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Name** & **Data Source** & **Range** & **Content** \\ \hline Air Temp & ASOS (Suncheon) & AM 00:00–PM 13:00 &
\begin{tabular}{c} Scenario input \\ Evolution algorithm train set \\ Scenario input \\ Evolution algorithm train set \\ Scenario input \\ Scenario input \\ Scenario input \\ Scenario input \\ Scenario input \\ Scenario input \\ Scenario input \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 4: Major meteorological data of the model and their contents.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Name** & **Data Source** & **Resolution** & **Content** \\ \hline DEM & Lidar Satellite & \
\begin{tabular}{c} 5 m \\ (Interpolation, 1 m) \\ \end{tabular} &
\begin{tabular}{c} Hillshade formation \\ Scenario input \\ Evolution algorithm train set \\ Scenario input \\ Scenario input \\ Scenario input \\ Scenario input \\ Scenario input \\ Scenario input \\ Scenario input \\ Scenario input \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 3: Major spatial data of the model and their contents.  
Figure 3 shows the trends in air and road temperatures acquired from ASOS (Suncheon, 2018 and 11 December 2018). In Figure 2(b), precipitation occurred approximately from AM 9:00 to PM 12:00. Precipitation generally does not lead to road icing, but the freezing rain phenomenon occurred during the same time in Figure 2(a) because the air temperature was higher than 0 \({}^{\circ}\)C and the road temperature was lower than 0 to 1 \({}^{\circ}\)C.  
The time range was set to 14 h from AM 12:00 to PM 13:00. As can be seen from the case analysis in the introduction, road icing traffic accidents mostly occur in the morning while air temperature reaches its peak at PM 13:00 on average. In other words, it is necessary to simulate the time period from the morning hours with low air temperature and solar radiation intensity as well as heavy traffic to PM 13:00, when frequency of road icing occurrence decreases due to high solar radiation intensity. This tendency was reflected, and the time range was set to 14 h including the morning for efficiency of the simulation.