## 3 Results and Discussion
### GAM Model Results  
A plot of the performance of the 102 models in the GAM process, grouped by \(R^{2}\) is presented in Figure 6. The models are noted to post \(R^{2}\) between 0.09 and 0.86 in model training and model validation. The performances of the models in training and validation datasets (blue and orange bars respectively) indicate relative stability in model numbers across the models. The performance of the models by the lag-time of the variables (between 1- and 3-month lags) is provided in Figure 7. As expected, the analysis of the GAM process by lag time indicates that the 1-month lag of the predictors perform better in predicting VCI3M as used to define drought (in green). While a lag time of 2 month (in blue) still has some predictive power (R\({}^{2}\) \(>\) 0.5), even longer lags fail to produce good correlations (in yellow). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**County** & **Extreme** & **Severe** & **Moderate** & **Combined** \\ \hline Mandera & 8 & 31 & 43 & 82 \\ Marsabit & 8 & 26 & 70 & 104 \\ Turkana & 4 & 28 & 64 & 96 \\ Wajir & 9 & 25 & 61 & 95 \\ Total & 29 & 110 & 238 & 377 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of monthly drought phases for the counties in the study region (March 2001 to December 2015). The 3-monthly aggregated VCI is classified according to thresholds proposed in Klisch and Atzberger [22], [PERSON] et al. [40] and [PERSON] et al. [42]. The 3-monthly VCI is provided for each county leading to 712 possible episodes. Figure 6: Model performance by range of \(R^{2}\) in the GAM process. It is deducible that the GAM process models with \(\mathbb{R}^{2}\geq 0.7\) (Table 5) are all 1-month lag variables. In fact, the first 2-month lag variable first appears at a model ranked at position 22 with an \(R^{2}\) of 0.61 while the first 3-month lag variable is in a model ranked at position 52 with an \(R^{2}\) of 0.33. The poor performance of higher lags of these variables is expected, since longer lags are contributing less to current vegetation status and the chances of unexpected climate variations occurring between time of forecasting and the forecasted event increasing. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No** & **Model** & \(\mathbf{R^{2}}\) & \(\mathbf{R^{2}}\) & **Overfit** & **Overfit** & **Lag Time** \\  & & **Training** & **Validation** & **Index** & **Overfit** & **Lag Time** \\ \hline
1 & VCIDekad\_lag1+SP1 IM\_lag1 & 0.86 & 0.85 & 0.01 & No & 1 \\
2 & VCIDekad\_lag1+SP1 BM\_lag1 & 0.86 & 0.85 & 0.01 & No & 1 \\
3 & VCIDekad\_lag1+RFE1 IM\_lag1 & 0.85 & 0.85 & 0.01 & No & 1 \\
4 & VCII\_lag1+SP1 BM\_lag1 & 0.85 & 0.84 & 0.01 & No & 1 \\
5 & VCIIM\_lag1+SP1 IM\_lag1 & 0.85 & 0.84 & 0.01 & No & 1 \\
6 & VCIIM\_lag1+RFE1 IM\_lag1 & 0.85 & 0.84 & 0.01 & No & 1 \\
7 & VCIDekad\_lag1+RCI1 IM\_lag1 & 0.85 & 0.84 & 0.01 & No & 1 \\
8 & VCIIM\_lag1+RCI1 IM\_lag1 & 0.84 & 0.83 & 0.01 & No & 1 \\
9 & VCIDekad\_lag1+RCI3M\_lag1 & 0.84 & 0.83 & 0.01 & No & 1 \\
10 & VCIDekad\_lag1+RFE3M\_lag1 & 0.84 & 0.83 & 0.01 & No & 1 \\
11 & VCIIM\_lag1+RCI3M\_lag1 & 0.84 & 0.83 & 0.01 & No & 1 \\
12 & VCIIM\_lag1+RFE3M\_lag1 & 0.83 & 0.83 & 0.01 & No & 1 \\
13 & VCI3M\_lag1+SP1 BM\_lag1 & 0.82 & 0.82 & 0.01 & No & 1 \\
14 & VCIDekad\_lag1 & 0.81 & 0.80 & 0.01 & No & 1 \\
15 & VCISM\_lag1+RCI3M\_lag1 & 0.81 & 0.80 & 0.01 & No & 1 \\
16 & VCIIM\_lag1 & 0.81 & 0.80 & 0.01 & No & 1 \\
17 & VCISM\_lag1+SP1 IM\_lag1 & 0.81 & 0.79 & 0.01 & No & 1 \\
18 & VCISM\_lag1+RCI1 IM\_lag1 & 0.78 & 0.77 & 0.01 & No & 1 \\
19 & VCISM\_lag1+RFE3M\_lag1 & 0.78 & 0.77 & 0.01 & No & 1 \\
20 & VCISM\_lag1+RFE1M\_lag1 & 0.78 & 0.76 & 0.01 & No & 1 \\
21\({}^{1}\) & VCISM\_lag1 & 0.72 & 0.69 & 0.02 & No & 1 \\ \hline \hline \end{tabular}  
* The VCISM\_lag1 model (No. 21) marginally fails the threshold. However, we included it in the selection for the ANN process since it is the interesting case of the base model with the lag of the predicted variable.  
\end{table} 
Table 5: GAM models with \(\mathbb{R}^{2}\geq 0.7\) in decreasing order.