## 3 Results
### Thresholds for Early Warning  
Building on the high predictive performance of the GAM model, we applied ROC analysis to identify critical thresholds in key ecosystem variables--GWT, LAI, NEE, and Rn--that distinguish between high- and low-mortality transition states. ROC analysis evaluates the diagnostic ability of each predictor by quantifying its sensitivity (true positive rate) and specificity (true negative rate) in classifying binary outcomes--in this case, whether a given plot-year experiences high (>25%) or low (\(\leq\)25%) tree mortality. Using Youden's Index, which identifies the threshold that maximizes the difference between sensitivity and 1-specificity, we derived optimal cutoff values for each variable (Table 4). For context, we first converted the continuous tree mortality rates into a binary classification variable, designating plot-years with mortality above the median as high-mortality cases and those below or equal to the median as low-mortality cases. Based on this classification, ROC curves were constructed for each key predictor to evaluate their ability to discriminate between high- and low-mortality states. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Response Variable** & **Predictor Variables** & **Multiple R\({}^{2}\)** & **\(p\)-Value** & **F-Value** & **AIC** \\ \hline Mortality \(\sim\) & GWT & 0.75 & 0.002 & 17.99 & 84.07 \\  & GWT+LAI & 0.89 & 0.002 & 20.52 & 75.33 \\  & GWT+LAI+NEE & 0.93 & 0.0006 & 35.55 & 71.48 \\  & GWT+LAI+NEE+Rn & 0.98 & 0.0001 & 124.01 & 57.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the Generalized Additive Model (GAM) analysis ranking predictor variables: groundwater table depth (GWT), leaf area index (LAI), net ecosystem exchange (NEE), and net radiation (Rn) based on their explanatory power for variation in tree mortality. For each variable, the optimal threshold was identified as the point on the ROC curve that maximizes Youden's Index, calculated as sensitivity plus specificity minus one. This approach identifies the cutoff value at which the predictor achieves the best overall classification accuracy by balancing true positive and true negative rates. These threshold values reflect the critical boundaries beyond which the probability of high tree mortality increases significantly. The overall classification performance of each predictor was evaluated using the area under the curve (AUC), which reflects the model's ability to discriminate across all possible thresholds (Figure 5). An AUC of 1.0 indicates perfect classification, while a value of 0.5 denotes no predictive ability. An AUC value of 1.0 represents perfect classification, whereas a value of 0.5 indicates no predictive power. In this study, GWT achieved an AUC of 1.0, indicating near-perfect separation between mortality states. LAI and Rn also exhibited strong classification performance with AUCs of 0.90 and 0.80, respectively, while NEE showed moderate discriminatory ability with an AUC of 0.67. Using our ROC curve and Youden's Index to quantify each variable's ability to discriminate between high- and low-mortality states yielded threshold values of 2.23 cm (min. = 1.37, max. = 3.68) for GWT, 2.99 (min. = 2.90, max. = 3.30) for LAI, 1.27 g C m\({}^{-2}\) d \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Threshold Value** & \multicolumn{2}{c}{**95\% Confidence Interval**} \\ \cline{3-4}  & & **Lower Limits** & **Upper Limits** \\ \hline GWT & 2.23 & 1.37 & 3.68 \\ LAI & 2.99 & 2.90 & 3.30 \\ NEE & 1.27 & \(-\)1.11 & 5.64 \\ Rn & 167.54 & 163.23 & 213.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal thresholds for key variables identified through ROC analysis. Threshold values are calculated based on Youden’s Index to maximize the distinction between high- and low-mortality transition states. Figure 5: ROC curves with optimal thresholds for key ecosystem predictors distinguishing high- versus low-mortality states. Optimal thresholds (T) for GWT, LAI, NEE, and Rn were determined by maximizing Youden’s Index.