## 4 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{(**a**)} \\ \hline \multicolumn{10}{c}{Franz Jose Terminal Point Distance GAM} \\ \hline \multicolumn{10}{c}{Distance - s(Average\_TMIN) + s(CO2) + s(Average\_PRCP) + s(Global\_Mean)} \\ \hline Parametric coefficients: & Estimate & Std Error & T value & Pr (\(>\)\(\mid\)T 1) \\ \hline Intercept & \(-\)5.4894 & 0.3898 & \(-\)14.1 & 2 \(\times\) 10\({}^{-16}\) \\ \hline Smooth Terms & EDF & REF DEF & F & \(p\)-Value \\ \hline s(Average\_TMIN) & 1.274 & 1.49 & 3.456 & 0.073 \\ \hline s(CO2) & 2.868 & 2.987 & 47.024 & 2 \(\times\) 10\({}^{-16}\) \\ \hline s(Average\_PRCP) & 1 & 1 & 0.046 & 0.8303 \\ \hline s(Global\_Mean) & 1 & 1 & 5.429 & 0.0223 \\ \hline Model & AIC & Deviance & Adj R\({}^{2}\) & \\ \hline  & 480.799 & 86.1 & 85 & & & & & & \\ \hline \multicolumn{10}{c}{Franz Josef Area GAM} \\ \hline \multicolumn{10}{c}{Area \(\sim\) s(Average\_TMAX) + s(CO2) + s(Average\_PRCP) + s(Global\_Mean)} \\ \hline Parametric coefficients: & Estimate & Std Error & T value & Pr (\(>\)\(\mid\)T 1) \\ \hline Intercept & 3211.96 & 58.77 & 54.65 & 2 \(\times\) 10\({}^{-16}\) \\ \hline Smooth Terms & EDF & REF DEF & F & \(p\)-Value \\ \hline s(Average\_TMAX) & 1.988 & 2.4 & 1.671 & 0.186 \\ \hline s(CO2) & 2.311 & 2.654 & 4 & 6.33 \(\times\) 10\({}^{-2}\) \\ \hline s(Average\_PRCP) & 1.363 & 1.607 & 1.167 & 0.2345 \\ \hline s(Global\_Mean) & 1 & 1 & 6.232 & 0.0224 \\ \hline Model & AIC & Deviance & Adj R\({}^{2}\) & \\ \hline  & 380.5743 & 71.9 & 61.8 & & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Generalized Additive: Models. (**a**) Terminal Point of Franz Josef as Response. (**b**) Area of Franz Josef as Response. (**c**) Terminal Point of Gorner as Response. (**d**) Area of Gorner as Response. Find the complete set of models in Appendix A. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{(**d**)} \\ \hline \multicolumn{10}{c}{Gorner Area} \\ \hline \multicolumn{10}{c}{Model Index Predictors} \\ \hline
1 & CO2 & & & & & & & & & & \\ \hline
2 & & CO2 Average\_TMAX & & & & & & & & \\ \hline
3 & & & Average\_PRCP CO2 Average\_TMAX & & & & & & & \\ \hline
4 & & Average\_PRCP CO2 Average\_TMAX Global\_Mean & & & & & & & & \\ \hline \multicolumn{10}{c}{Subsets Regression} \\ \hline Model & R- & Adj, R- & Pred. R- & & & & & & & & \\  Square & Square & Square & C(p) & AIC & SBIC & SBIC & MSEP & FPE & HSP & APC \\ \hline
1 & 0.88 & 0.88 & 0.88 & 10.5 & 1798 & 1562 & 1805 & 11,904,380,369 & 146,881,258 & 1,792,815 & 0.12 \\ \hline
2 & 0.89 & 0.89 & 0.88 & 6.0 & 1794 & 1558 & 1803 & 11,200,129,510 & 139,795,855 & 1,707,838 & 0.12 \\ \hline
3 & 0.89 & 0.89 & 0.88 & 6.7 & 1794 & 1559 & 1806 & 11,145,284,672 & 140,706,326 & 1,720,988 & 0.12 \\ \hline
4 & 0.89 & 0.89 & 0.88 & 5.0 & 1706 & 1483 & 1721 & 10,264,439,570 & 138,078,149 & 1,778,893 & 0.12 \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._Figure 8(Top) displays a time series for the changes to the terminal point for Franz Josef (left) and Gorner (right) glaciers from the years 2000 to 2021. According to the left-hand side of Figure 8(Top), the time series for Franz Josef's shows that the terminal point has oscillated between advancing and receding in the beginning years of 2000-2010. However, after the year 2000, it has been continuously receding; by 2021, the terminal point had receded close to 800 m by 2021 in comparison to its starting point in 2000. For Gorner glacier on the right-hand side of Figure 8(Top), the time series displays a continuous pattern of decline over the years from 2000 to 2021. By 2021, the terminal point has reced close to 500 m in comparison to its starting point in 2000. When trying to measure the physical variations to both glaciers through their terminal point location, the data reflects that both glaciers have been receding significantly.