## 3 Results and Discussion
M06, which input structure consisted of SPI values lagged by 1, 2, 3, and 4 months, as well as by 11, 12, and 13 months, achieved performance values of r: 0.9514, NSE: 0.9049, and RMSE: 0.3116. Within the scope of this study, the models developed using SPI3 as input data demonstrated lower performance values compared to those utilizing SPI12 data. This suggests that the predictive capabilities  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Models** & \multicolumn{2}{c}{**SVM-PSO**} & \multicolumn{4}{c}{**ANFIS-PSO**} & \multicolumn{4}{c}{**ANFIS-GA**} \\ \hline  & **r** & **NSE** & **RMSE** & **r** & **NSE** & **RMSE** & **r** & **NSE** & **RMSE** \\ \hline M01 & 0.9172 & 0.8284 & 0.4185 & 0.9343 & 0.8726 & 0.3606 & 0.9352 & 0.8743 & 0.3582 \\ M02 & 0.9258 & 0.8563 & 0.3830 & 0.9348  
and insights derived from SPI12 values were significantly more robust for generating accurate models than those based on SPI3. Potential factors contributing to this disparity could include the higher temporal resolution of SPI12, which may capture longer-term forecasting and the peak points more effectively in time series. ANFIS-PSO, although demonstrating promising results, delivered a slightly lower performance than that of SVM-PSO. Despite this difference, both methods demonstrated comparable effectiveness. The choice between them may depend on the specific application requirements. Exploring hybrid or ensemble approaches that combine the strengths of both methods could possibly enhance the predictive power. M04, achieving performance values of r: 0.9511, NSE: 0.9038, and RMSE:0.3133, emerged as the top-performing model within ANFIS-PSO. The input structure of this model comprised SPI values that were lagged by 1 and 2 months, as well as by 11, 12, and 13 months. Following the ANFIS-PSO analyses, M05 and M06 produced results very close to those of M04, suggesting similar effectiveness. ANFIS-GWO exhibited the lowest performance among all the models tested. This suggests a potential misalignment between the ANFIS architecture and the GWO optimization approach. In contrast to the models incorporating SPI12 in their input structures, those created with SPI3 data consistently underperformed. The best-performing model in this class was M12, with performance values of r: 0.8135, NSE: 0.5374, and RMSE: 0.7079. To enhance a more comprehensive model performance comparison, Figure 6 presents a 3D scatter plot visualization of selected top-performing models. This graphical representation provides a deeper understanding of the relationships between different performance parameters across these models. As shown in Figure 6, the model with the best performance is located at the far right and bottom. Specifically, the ANFIS-ABC-M04 model outperforms all other models evaluated. Its superior performance is likely attributed to the effective combination of ANFIS-ABC and the M04 input structure, which together excel at capturing complex data patterns. Figure 6: Three-dimensional scatter graph for some models with the best performance values, where ANFIS-ABC-M04 analysis of ANFIS with ABC optimization for M02, SVM-PSO-M06 analysis of SVM with PSO optimization for M06, etc. Ridge charts provide an alternative method to visually compare and contrast the model performance. This visualization technique offers a structured overview, facilitating a deeper understanding of the relative strengths and weaknesses of different models (Figure 7). Interestingly, unlike the statistical performance metrics, SVM-PSO-M02 and ANFIS-ABC-M02 appear to most accurately reflect the observed values in the ridge chart (Figure 7). When the other models were examined, it was evident that there were peaks on the graph, especially the initial region, contrary to the observed values. However, subsequent comparative graphs clearly align more closely with the expected outcomes. The prediction performance across the models can be assessed visually in Figure 8, which displays box plots and normal distributions for both the prediction models and observed values.