## 3 Results and Discussion
While the time series indicate that both models are relatively effective at capturing peak values, their statistical performance is not as good as ANFIS-ABC-M04 and SVM-PSO-M06, except for the initial observed values. This pattern is consistently also observed in the scatter plots. Figure 12 presents the results of the RSR analysis. According to the results, the ANFIS-PSO, ANFIS-GA, and ANFIS-ABC algorithms outperformed the other algorithms in terms of the RSR. ANFIS-PSO achieved the best performance according to the RSR metric, while ANFIS-ABC excelled in the statistical analysis. Although ANFIS-PSO emerged as the top performer based on the RSR method, statistical comparisons suggest that the performance of all three algorithms is quite similar. Therefore, this study concludes that all these three algorithms are successful, consistent with what the statistical results suggest. Overall, while the statistical results were generally comparable among the models, the ANFIS-ABC-M04 model consistently demonstrated superior performance when both the graphical methods and statistical metrics were evaluated. Based on these findings, the ANFIS-ABC-M04 model is identified as the optimal model and algorithm for future drought prediction modeling applications in the region. Our findings are consistent with those of other studies that have utilized similar algorithms, model input structures, and the SPI for drought prediction modeling. For instance, highlighting the importance of river flows, [PERSON] [100] used Fuzzy Systems, along with a series of optimization algorithms, including ABC, Firefly Algorithm (FA), and Hunter search algorithm (HUS), to predict streamflow in Susurluk Basin. The author reported that the ABC optimization algorithm yielded superior results compared to other methods. Similarly, [PERSON] and [PERSON] [42] investigated the performance of various optimization methods, such as ABC, adaptive ABC (aABC), GA, PSO, and harmony search (HS), combined with ANFIS for identifying nonlinear static systems. They used several performance criteria, including the Wilcoxon test and RMSE, and revealed that ABC with ANFIS was the best-performing method after aABC, while ANFIS-GWO and ANFIS-PSO achieved successful results, according to our findings. Numerous studies in the literature further support the success of these algorithms. For instance, [PERSON] et al. [36] conducted a study on drought prediction using the Effective Drought Index (EDI) and various machine learning algorithms and optimization techniques. They determined that ANFIS, when combined with PSO, GA, and the Generalized Regression Neural Network (GRNN), produced promising results for estimating the EDI, particularly with the ANFIS-PSO and ANFIS-GA models. In another study on drought prediction modeling in Barrak Valley, [PERSON] et al. [101] compared SVM-PSO with a series of hybrid methods, including SVM, back-propagation neural network (BPNN), and an integration of SVM. In their study, SVM-PSO was more effective than other methods. In this study, SVM-PSO was found to be the most successful algorithm after ANFIS-ABC, and it is one of the most effective algorithms in this study. Thereby, the information in the two studies overlaps with each other. \begin{table}
\begin{tabular}{l|c|c c c} \hline
**Performance Rating** & **Unsatisfactory** & **Satisfactory** & **Good** & \\ \hline RSR value & RSR \(\geq\) 0.7 & 0.7 \textgreater{} RSR \(\geq\) 0.6 & 0.6 \textgreater{} RSR \(\geq\) 0.5 & 0.5 \(\geq\) RSR \\ \hline \end{tabular}
\end{table} 
Table 5: RSR range and the corresponding performance rate. Figure 11: Time series and scatter graphs 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. The RSR method, as previously described, evaluates the algorithm performance by considering both the RMSE and standard deviation. In Table 5, the evaluation criteria of the model performances based on this method are presented.