## 3 Methodology  
Two main analyses were performed in this research. First, the freeze-thaw depths were predicted by applying the MTO, MTQ, and TCCA methods, and the results were compared with the actual recorded frost depths measured from the field. In the next step, the analysis was used to evaluate the implications of these climate change projections in terms of frost penetration, frost heave, and thaw depth for several airports in Canada, as well as the U.S.A. The field data were obtained mainly from the Long-Term Pavement Performance (LTPP) database and includes nine cities located in Canada and the United States. Among the evaluated cases under the first analysis, only one case (St. Celestin, QC) was not obtained from the LTPP database, but rather through published data from Boutonnet and St-Laurent, 2003 [15]. The field data were then compared to the frost penetration depths calculated according to each site's freezing index, in the case of the MTO and TCCA, and soil characteristics, in the case of the MTQ. The locations investigated under Analysis I were mainly chosen according to data availability, with the aim of representing different climate scenarios across Canada and the U.S.A. It can be recognized that each of the selected cities are located in a different province.  
In the second analysis, a total of ten Canadian airports, which play key roles in the Canadian air transportation, were evaluated. The selected locations represent different climate scenarios within the country and compare how differently climate change will impact freeze-thaw penetration depth in those cities. Table 1 shows the locations evaluated in each analysis. It should be noted that all the airports within this analysis are of high importance to their corresponding provinces; therefore, it was deemed necessary to evaluate the implications of climate change for them. These airports are also well spread across the Canadian territories, representing different climate scenarios.  
Table 2 shows the field data, including the section ID according to the LTPP database, the year in which the frost depth data were collected, the closest city to the data collection point, and the maximum frost penetration depth recorded in the referred year. The last two columns of the table include the Annual Mean Temperature (AMT, \({}^{\circ}\)C) and the Air Freezing Index (FI, \({}^{\circ}\)C-days), for which the raw data were obtained through Environment Canada [16] for the cases in Canada and the National Solar Radiation Database (NSRDB) [17] for the cases in the U.S.A. The AMT values were calculated considering the annual mean temperature from the two years, referenced in column two of Table 2.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Analysis I** & **Analysis II** \\ \hline Canada: & & Not underlain by permafrost \\ \(\bullet\) & Winnipeg, MB & \(\bullet\) & Toronto Airport (YYZ) \\ \(\bullet\) & Viscount, SK & \(\bullet\) & Montreal International Airport (YUL) \\ \(\bullet\) & Beatrice, ON & \(\bullet\) & Quebec City International Airport (YQB) \\ \(\bullet\) & St. Celestin, QC & \(\bullet\) & Calagary International Airport (YYC) \\ \(\bullet\) & Virden, MB & \(\bullet\) & Regina International Airport (YQR) \\  & & \(\bullet\) & Winnipeg International Airport (YWG) \\ U.S.A. & & Underlain by Permafrost \\ \(\bullet\) & New Haven, VT & \(\bullet\) & Yellowknife Airport (YZF) \\ \(\bullet\) & Bemidji, MN & \(\bullet\) & Iqaluit International Airport (YFB) \\ \(\bullet\) & Great Falls, MT & \(\bullet\) & Baker Lake Airport (YBK) \\ \(\bullet\) & Hamlin, NY & \(\bullet\) & Cambridge Bay Airport (YCB) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Locations evaluated in Analyses I and II.