## Author Contributions

Conceptualization, J.W.L. and S.D.C.; methodology, J.W.L. and S.O.L.; software, J.W.L.; validation, J.W.L., S.D.C. and S.O.L.; formal analysis, J.W.L., S.D.C. and S.O.L.; investigation, J.W.L., S.D.C. and S.O.L.; resources, S.O.L.; data curation, J.W.L.; writing—original draft preparation, J.W.L.; writing—review and editing, J.W.L., S.D.C. and S.O.L.; visualization, J.W.L.; supervision, S.O.L.; project administration, S.O.L.; funding acquisition, S.O.L. All authors have read and agreed to the published version of the manuscript.

**Figure 1.**
Conceptual rainfall-runoff model with four serially connected tanks (A, B, C and D) with soil moisture stores at the top Tank A.

**Figure 1.**
Conceptual rainfall-runoff model with four serially connected tanks (A, B, C and D) with soil moisture stores at the top Tank A.

**Figure 2.**
Map of South Korea at the top panel and zoomed area showing the location of the selected five stations for model calibration and their upstream catchments.

**Figure 2.**
Map of South Korea at the top panel and zoomed area showing the location of the selected five stations for model calibration and their upstream catchments.

**Figure 3.**
GLUE derived posterior distribution of parameters for Station 1,002,640 (**a**) ${O}_{A1}$ (outlet constraint of the lower outlet at Tank A, initially ranged from 0~0.5), (**b**) ${K}_{2}$ (soil moisture exchange rates between the top two tanks, initially ranged from 0~100), (**c**) ${H}_{A2}$ (storage level to the upper outlet at Tank A, initially ranged from 0~150 m) and (**d**) ${H}_{c}$ (storage level to the outlet at Tank C, initially ranged from 0~20 m).

**Figure 3.**
GLUE derived posterior distribution of parameters for Station 1,002,640 (**a**) ${O}_{A1}$ (outlet constraint of the lower outlet at Tank A, initially ranged from 0~0.5), (**b**) ${K}_{2}$ (soil moisture exchange rates between the top two tanks, initially ranged from 0~100), (**c**) ${H}_{A2}$ (storage level to the upper outlet at Tank A, initially ranged from 0~150 m) and (**d**) ${H}_{c}$ (storage level to the outlet at Tank C, initially ranged from 0~20 m).

**Figure 4.**
DREAM derived posterior distribution of parameters for Station 1,002,640 (**a**) ${O}_{A1}$ (outlet constraint of the lower outlet at Tank A, initially ranged from 0~0.5), (**b**) ${K}_{2}$ (soil moisture exchange rates between the top two tanks, initially ranged from 0~100), (**c**) ${H}_{A2}$ (storage level to the upper outlet at Tank A, initially ranged from 0~150 m) and (**d**) ${H}_{c}$ (storage level to the outlet at Tank C, initially ranged from 0~20 m).

**Figure 4.**
DREAM derived posterior distribution of parameters for Station 1,002,640 (**a**) ${O}_{A1}$ (outlet constraint of the lower outlet at Tank A, initially ranged from 0~0.5), (**b**) ${K}_{2}$ (soil moisture exchange rates between the top two tanks, initially ranged from 0~100), (**c**) ${H}_{A2}$ (storage level to the upper outlet at Tank A, initially ranged from 0~150 m) and (**d**) ${H}_{c}$ (storage level to the outlet at Tank C, initially ranged from 0~20 m).

**Figure 5.**
Uncertainty ranges of 95% simulations derived from the GLUE and DREAM approaches using the tank model with observed discharges (∙) and areal averaged precipitation by the Thiessen polygon network at Station 1002640.

**Figure 5.**
Uncertainty ranges of 95% simulations derived from the GLUE and DREAM approaches using the tank model with observed discharges (∙) and areal averaged precipitation by the Thiessen polygon network at Station 1002640.

**Figure 6.**
GLUE derived ranges of the four selected parameters across the five calibration stations ((**a**) ${O}_{A1}$, (**b**) ${K}_{2}$, (**c**) ${H}_{A2}$ and (**d**) ${H}_{C}$).

**Figure 6.**
GLUE derived ranges of the four selected parameters across the five calibration stations ((**a**) ${O}_{A1}$, (**b**) ${K}_{2}$, (**c**) ${H}_{A2}$ and (**d**) ${H}_{C}$).

**Figure 7.**
DREAM derived ranges of the four selected parameters across the five calibration stations ((**a**) ${O}_{A1}$, (**b**) ${K}_{2}$, (**c**) ${H}_{A2}$ and (**d**) ${H}_{C}$).

**Figure 7.**
DREAM derived ranges of the four selected parameters across the five calibration stations ((**a**) ${O}_{A1}$, (**b**) ${K}_{2}$, (**c**) ${H}_{A2}$ and (**d**) ${H}_{C}$).

**Figure 8.**
Comparison of convergence rates measured by Nash–Sutcliffe efficiency (NSE) between the three optimization algorithms at Station 1,002,640 ((**a**) 20,000 iterations and (**b**) 5000 iterations).

**Figure 8.**
Comparison of convergence rates measured by Nash–Sutcliffe efficiency (NSE) between the three optimization algorithms at Station 1,002,640 ((**a**) 20,000 iterations and (**b**) 5000 iterations).

**Figure 9.**
Comparison of calibrated results using the three optimization algorithms with their performance measure of NSE values at Station 1002640.

**Figure 9.**
Comparison of calibrated results using the three optimization algorithms with their performance measure of NSE values at Station 1002640.

**Figure 10.**
Comparison of the NSE measures developed from 100 sets of randomly selected initial parameters for the three optimization algorithms across the five calibration stations ((**a**) Station 1002640, (**b**) Station 1003630, (**c**) Station 1011690, (**d**) Station 1303680 and (**e**) Station 3009650).

**Figure 10.**
Comparison of the NSE measures developed from 100 sets of randomly selected initial parameters for the three optimization algorithms across the five calibration stations ((**a**) Station 1002640, (**b**) Station 1003630, (**c**) Station 1011690, (**d**) Station 1303680 and (**e**) Station 3009650).

**Figure 11.**
Ranges of two most sensitive parameters (**a**,**b**) and one least sensitive parameter (**c**) developed from 100 different initial parameters using the dynamically dimensioned search (DDS) algorithm.

**Figure 11.**
Ranges of two most sensitive parameters (**a**,**b**) and one least sensitive parameter (**c**) developed from 100 different initial parameters using the dynamically dimensioned search (DDS) algorithm.

**Figure 12.**
Ranges of two most sensitive parameters (**a**,**b**) and one least sensitive parameter (**c**) developed from 100 different initial parameters using the robust parameter estimation (ROPE) algorithm.

**Figure 12.**
Ranges of two most sensitive parameters (**a**,**b**) and one least sensitive parameter (**c**) developed from 100 different initial parameters using the robust parameter estimation (ROPE) algorithm.

**Figure 13.**
Ranges of two most sensitive parameters (**a**,**b**) and one least sensitive parameter (**c**) developed from 100 different initial parameters using the shuffled complex evolution (SCE) algorithm

**Figure 13.**
Ranges of two most sensitive parameters (**a**,**b**) and one least sensitive parameter (**c**) developed from 100 different initial parameters using the shuffled complex evolution (SCE) algorithm

**Figure 14.**
Cross-validation of three sites (Station 1: 1002640, Station 2: 1003630 and Station 5: 3009650) where calibrated parameters at one site are applied to the other sites. It is indicated by the shaded background when the calibrated parameters are reapplied to the same site. Model performance is reporting by the median and variation of NSE values from 100 simulations.

**Figure 14.**
Cross-validation of three sites (Station 1: 1002640, Station 2: 1003630 and Station 5: 3009650) where calibrated parameters at one site are applied to the other sites. It is indicated by the shaded background when the calibrated parameters are reapplied to the same site. Model performance is reporting by the median and variation of NSE values from 100 simulations.

**Table 1.**
Five calibration stations used in this study with their key geographical characteristics (catchment size, average slop, and maximum of standard deviation (SD) of altitude), annual total rainfall and years used for calibration and verification.

**Table 1.**
Five calibration stations used in this study with their key geographical characteristics (catchment size, average slop, and maximum of standard deviation (SD) of altitude), annual total rainfall and years used for calibration and verification.

Station No (Station Name) | Longitude/Latitude | Catchment Area (km^{2}) | Average Slop (%) | Altitude Max/ SD (m) | Rainfall (mm/yr) | Calibration Year | Validation Year |
---|

1002640 (Sangbangrim) | 128.42/ 37.43 | 527.9 | 47.9 | 1574.7/183.2 | 1336 | 2011 | 2012 |

1003630 (Osa Ri) | 128.51/ 37.10 | 4786.2 | 49.6 | 1574.6/238.8 | 1246 | 2012 | 2013 |

1011690 (Wolhak Ri) | 128.21/ 38.12 | 301.1 | 63.3 | 1701.5/262.0 | 1587 | 2011 | 2014 |

1303680 (Osipcheon Br.) | 129.23/ 37.70 | 371.7 | 58.1 | 1353.8/252.6 | 1249 | 2018 | 2012 |

3009650 (Youngchon Br.) | 127.32/ 36.25 | 83.4 | 44.2 | 872.0/126.6 | 1313 | 2011 | 2016 |

**Table 2.**
Comparison of various performance measurements for the calibration stations with the number of iterations set to 20,000. The performance measurements include Nash–Sutcliffe efficiency (NSE), bias, coefficient of determination (${R}^{2}$) and mean absolute error (MAE).

**Table 2.**
Comparison of various performance measurements for the calibration stations with the number of iterations set to 20,000. The performance measurements include Nash–Sutcliffe efficiency (NSE), bias, coefficient of determination (${R}^{2}$) and mean absolute error (MAE).

Station | NSE | $\mathbf{BIAS}\text{}\left({\mathbf{m}}^{3}/\mathbf{sec}\right)$ | R^{2} | $\mathbf{MAE}\text{}\left({\mathbf{m}}^{3}/\mathbf{sec}\right)$ |
---|

DDS | ROPE | SCE | DDS | ROPE | SCE | DDS | ROPE | SCE | DDS | ROPE | SCE |
---|

1002640 | 0.90 | 0.90 | 0.90 | 0.5 | 2.1 | 0.8 | 0.92 | 0.90 | 0.92 | 9.1 | 9.4 | 9.1 |

1003630 | 0.91 | 0.89 | 0.90 | −0.2 | −15.4 | −0.3 | 0.91 | 0.89 | 0.90 | 35.1 | 44.0 | 36.7 |

1011690 | 0.78 | 0.82 | 0.82 | 0.7 | 0.8 | 0.8 | 0.79 | 0.87 | 0.86 | 7.6 | 8.3 | 8.0 |

1303680 | 0.82 | 0.77 | 0.81 | 5.7 | 6.2 | 5.7 | 0.85 | 0.83 | 0.85 | 8.8 | 9.6 | 9.1 |

3009650 | 0.85 | 0.80 | 0.82 | 1.3 | 1.9 | 1.2 | 0.87 | 0.83 | 0.86 | 2.5 | 3.1 | 2.7 |

**Table 3.**
Validation of calibrated parameters to different events and its performance measured by NSE values (median and variation from 100 simulations with different initial parameter sets).

**Table 3.**
Validation of calibrated parameters to different events and its performance measured by NSE values (median and variation from 100 simulations with different initial parameter sets).

Algorithm | NSE | Station |
---|

1002640 | 1003630 | 1011690 | 1303680 | 3009650 |
---|

DDS | Median | 0.78 | 0.82 | 0.62 | 0.46 | 0.68 |

95%ile–5%ile | 0.08 | 0.07 | 0.10 | 0.51 | 0.25 |

ROPE | Median | 0.80 | 0.82 | 0.51 | 0.50 | 0.70 |

95%ile–5%ile | 0.09 | 0.07 | 0.10 | 0.42 | 0.29 |

SCE | Median | 0.79 | 0.81 | 0.53 | 0.66 | 0.77 |

95%ile–5%ile | 0.01 | 0.01 | 0.02 | 0.01 | 0.19 |