The MVP method shows better statistical performance in terms of NSE, RMSE, PBIAS, MAE, and RSR than all previous methods. The MVP method significantly improves the PBIAS than the previous methods, indicating superior model performance (Table 3). The best fit is observed in the MVP method compared to other methods between observed and simulated values (Figure 4(e)). The MVP method improves the accuracy in estimating average runoff as the deviations from the observed values during the calibration (−0.7 m3/s) and validation (1.67 m3/s) periods were minimal. On the other hand, the estimation of peak runoff exhibited marginally higher deviations as compared to the other methods. The scatter plot shows better agreement of observed and simulated runoff with higher R2 of 0.73 and 0.63 for the calibration and validation periods, respectively (Figures 5(g) and (h)).
Performance evaluation of the mathematical models for runoff estimation
S. No. . | Mathematical model . | NSE . | RMSE (m3/s) . | nRMSE . | PBIAS (%) . | MAE (m3/s) . | SE (m3/s) . | RSR . |
---|---|---|---|---|---|---|---|---|
1 | SCS-CN | 0.54 | 117.99 | 4.36 | 59.80 | 71.50 | 2.76 | 0.68 |
2 | SCS-CN with slope correction | 0.55 | 117.05 | 4.33 | 58.67 | 71.01 | 2.74 | 0.67 |
3 | SCS-CN with λ-optimization calibration | 0.72 | 72.02 | 2.33 | 20.20 | 30.98 | 1.69 | 0.53 |
4 | SCS-CN with λ-optimization validation | 0.61 | 68.17 | 2.94 | 17.11 | 29.50 | 1.60 | 0.63 |
5 | MS calibration | 0.68 | 77.15 | 2.50 | 22.53 | 33.49 | 1.81 | 0.57 |
6 | MS validation | 0.57 | 71.65 | 3.09 | 21.14 | 30.66 | 1.68 | 0.66 |
7 | MVP calibration | 0.73 | 70.34 | 2.28 | 2.28 | 30.26 | 1.65 | 0.52 |
8 | MVP validation | 0.63 | 66.42 | 2.86 | −7.19 | 29.88 | 1.55 | 0.61 |
9 | ASMA-SCS-CN calibration | 0.72 | 71.07 | 2.30 | 4.44 | 30.38 | 1.66 | 0.53 |
10 | ASMA-SCS-CN validation | 0.62 | 67.31 | 2.90 | −4.00 | 30.09 | 1.58 | 0.62 |
S. No. . | Mathematical model . | NSE . | RMSE (m3/s) . | nRMSE . | PBIAS (%) . | MAE (m3/s) . | SE (m3/s) . | RSR . |
---|---|---|---|---|---|---|---|---|
1 | SCS-CN | 0.54 | 117.99 | 4.36 | 59.80 | 71.50 | 2.76 | 0.68 |
2 | SCS-CN with slope correction | 0.55 | 117.05 | 4.33 | 58.67 | 71.01 | 2.74 | 0.67 |
3 | SCS-CN with λ-optimization calibration | 0.72 | 72.02 | 2.33 | 20.20 | 30.98 | 1.69 | 0.53 |
4 | SCS-CN with λ-optimization validation | 0.61 | 68.17 | 2.94 | 17.11 | 29.50 | 1.60 | 0.63 |
5 | MS calibration | 0.68 | 77.15 | 2.50 | 22.53 | 33.49 | 1.81 | 0.57 |
6 | MS validation | 0.57 | 71.65 | 3.09 | 21.14 | 30.66 | 1.68 | 0.66 |
7 | MVP calibration | 0.73 | 70.34 | 2.28 | 2.28 | 30.26 | 1.65 | 0.52 |
8 | MVP validation | 0.63 | 66.42 | 2.86 | −7.19 | 29.88 | 1.55 | 0.61 |
9 | ASMA-SCS-CN calibration | 0.72 | 71.07 | 2.30 | 4.44 | 30.38 | 1.66 | 0.53 |
10 | ASMA-SCS-CN validation | 0.62 | 67.31 | 2.90 | −4.00 | 30.09 | 1.58 | 0.62 |