## 3 Results and Discussion
### Discussion of Results  
From the previous investigations, it can be noticed that the soft computing models are in the classification of box or semi box models. Thus, this results in complexity in the uncertainty of the study. In soft computing models, input data are applied to minimize the model's errors in the training (calibration) stage. In fact, the model's errors are dependent on the system's input data. Thus, it is important to examine the model's efficiency to determine the soft computing model's uncertainty generated by variations in initial data. In this article, a specified percentage of inputs was used to calibrate the soft computing models. The number of 2000 iterations was considered appropriate to carry out the input sampling cycle. For each random instance, 2000 model parameters were generated from calibrated patterns. In this method, uncertainty of all input data (e.g., precipitation, discharge, and SSL) were considered in the evaluation of model performances. Two important indices quantified the uncertainty values. The p index, percentage of measured data bracketed by 95% (95 PPU) uncertainty, was applied to measure the uncertainty values. First, the cumulative distribution was generated for the final outputs. The 95 PPU was computed at the lower (2.5%) and upper (97.5%) bounds of the obtained distribution. A p value of 1 showed that the model had a good performance. Average thickness of the 95 PPU was used to determine the r index. This index was computed by dividing the average thickness by the standard deviation of the measured data.  
1. \(p\) index:  
The extent of p indices varied from 0.6 to 0.90. As can be seen in Figure 11, the \(p\) values of 0.8 and 0.9 covered a large extent of the ANFIS-BA model. As observed in Figure 15, all models had the lowest \(p\) values for the first and second combination. The MFNN models had more uncertainty because the \(p\) values decreased with MFNN models. The MFNN-WA models had the worst performance because the \(p\) value varied from 0.6 to 0.7 to a large extent in these models.  
Figure 15: _Cont._2. \(r\) indices  
The average thickness of 95 PPU for the ANFIS-BA model was less than that of the other models because the \(r\) value varied from 0.15 to 0.20. A large extent of the MFNN-WA model had \(r\) values of 0.25 and 0.30 and thus had more uncertainty compared to the ANFIS-BA models. Generally, the previous results and uncertainty results showed that the ANFIS-BA and ANFIS-WA models had the best performances among all models.  
Although different studies show that regression and ANN models have successful performances [35], this study showed that the ANFIS models were better than the ANN models. In addition, the results were different when different optimization algorithms were used to improve the ANFIS and ANN models. This study showed that dependence on the performance of the ANFIS and ANN models was high for SLL prediction. The general results indicated that the soft computing models with BA had better results than the prediction models with WA. The BA could accurately find the ANFIS and MFNN parameters. Thus, the selection of simple and accurate algorithms is important for soft computing models. The magnified maps were generated by an inverse distance weight (IDW) interpolation (Figure 16). Seven combinations were used for the soft computing models because the previous results showed that the combinations mentioned had the best performance among all models. The kappa index was used to evaluate the agreement between the simulated and observed maps. The improved ANFIS and MFNN models had better performances than the standalone ANFIS and MFNN models. In addition, the ANFIS-BA model generated more accurate results (kappa: 0.90) compared to the other models used.  
Figure 15: Computation of uncertainty value.