# Sensitivity Analysis to Investigate the Reliability of the Grid-Based Rainfall-Runoff Model

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Catchment and Data

^{2}and 977 km

^{2}, respectively. Approximately 73% of the Danseong catchment comprises steep mountains (mean slope 16.2%, maximum elevation 1834 m, minimum elevation 47 m), and 21% of the area near the river is farmland. The Seonsan catchment is gentler than Danseong catchment (mean slope 12.8 %, maximum elevation 1292 m, minimum elevation 38 m). Approximately 65% of the Seonsan catchment area is low mountains, 28% is farmland, and 4% is urban.

## 3. Material and Sensitivity Analysis Method

#### 3.1. Grid-Based Rainfall-Runoff Model

_{r}is return flow into the overland flow, ∆y is the width of control volume, A is channel cross-sectional area, Q is discharge in the channel, q

_{L}is lateral flow from overland flow, q

_{ss}is subsurface flow, q

_{b}is baseflow, S

_{0}is surface slope, and S

_{f}is friction slope. Input data for the GRM include hydrological topographic factors (slope of each grid and flow direction) extracted by a digital elevation model (DEM), and soil and land cover data. These data are inputted in raster file format. In this study, we converted the 30 m × 30 m DEM provided by the National Geographic Information Institute (http://www.ngii.go.kr) into 500 m × 500 m data to generate input topographic data of the target catchments. For land cover data, the upper-category land cover map of the Ministry of Environment (http://www.me.go.kr) was used. Soil texture and soil depth maps were produced using the high-precision soil map provided by the National Academy of Agricultural Science (http://www.naas.go.kr), in order to apply the Green-Ampt infiltration model. Table 2 shows the parameters used in the GRM. Note that all grids had different attribute/parameter values extracted from GIS data. The parameters related to land cover and soil of the GRM collectively adjusted the attribute/parameter values of these grids using ratios.

#### 3.2. The Sobol’ Method

_{i}is the ith parameter

**X**represents the vector of all parameters not including X

_{~i}_{i}, and Y is the scalar objective function value. The inner variance of the numerator means that the variance of Y is considered over all possible values of X

_{i}while maintaining X

**fixed. The outer expectation of the numerator is considered over all possible values of X**

_{~i}_{~i}. Thus, the numerator of TSI represents the expected variance that would be left if all parameters were fixed, not including X

_{i}[49]. The variance of Y in the denominator indicates total unconditioned variance.

_{obs,i}is the observed flow with time interval i (10 min in this study), $\overline{{Q}_{obs}}$ is the mean value of observed flow, Q

_{sim,i}is the simulated flow, and n is the number of time steps. NSE ranges from −∞ to 1, where 1 indicates a perfect match between observed flow and simulated flow. NSE squares the difference between observed flow and simulation flow values; thus, a relatively greater weight is given to high flow fitting on the hydrograph [54,55,56]. However, the TSI value can turn into a bias due to a large negative NSE value, because NSE values range from −∞ to 1. For this reason, we employed NSE* [57], modified from NSE. The NSE* objective function is expressed as:

## 4. Results and Discussion

#### 4.1. Parameter Sensitivity Analysis Reflecting the Scale of Rainfall Events

#### 4.2. Parameter Sensitivity Analysis Reflecting Different Objective Functions

#### 4.3. Parameter Sensitivity Analysis Reflecting Different Catchment Characteristics

#### 4.4. Effect of Parameter Range on Sensitivity

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Rainfall time series and observed hydrographs for the eight rainfall events in Danseong and Seonsan catchments. (

**a**) Danseong 1; (

**b**) Danseong 2; (

**c**) Danseong 3; (

**d**) Danseong 4; (

**e**) Seonsan 1; (

**f**) Seonsan 2; (

**g**) Seonsan 3; (

**h**) Seonsan 4.

**Figure 3.**Schematic of grid-based rainfall-runoff method (GRM) [40].

**Figure 4.**Parameter sensitivity of rainfall events in Danseong catchment, calculated for three objective functions: (

**a**) NSE*; (

**b**) 0.5(NSE* + NSElog*); (

**c**) NSElog*.

**Figure 5.**Parameter sensitivity of rainfall events in Seonsan catchment, calculated for three objective functions: (

**a**) NSE*; (

**b**) 0.5(NSE* + NSElog*); (

**c**) NSElog*.

**Figure 6.**Parameter sensitivity of the four rainfall events in Danseong catchment, calculated for the three objective functions: (

**a**) Danseong 1; (

**b**) Danseong 2; (

**c**) Danseong 3; (

**d**) Danseong 4.

**Figure 7.**Parameter sensitivity of the four rainfall events in Seonsan catchment, calculated for the three objective functions: (

**a**) Seonsan 1; (

**b**) Seonsan 2; (

**c**) Seonsan 3; (

**d**) Seonsan 4.

**Figure 8.**Differences in parameter sensitivity of Danseong and Seonsan catchments, calculated for the three objective functions. Numbers in symbols indicate parameter numbers in Table 2. (

**a**) NSE*; (

**b**) 0.5(NSE* + NSElog*); (

**c**) NSElog*.

**Figure 9.**Sensitivity changes of parameters for different parameter ranges for the Danseong catchment (using NSE* objective function): (

**a**) Danseong 1; (

**b**) Danseong 2; (

**c**) Danseong 3; (

**d**) Danseong 4.

**Figure 10.**Sensitivity changes of parameters for different parameter ranges for the Seonsan catchment (using NSE* objective function): (

**a**) Seonsan 1; (

**b**) Seonsan 2; (

**c**) Seonsan 3; (

**d**) Seonsan 4.

Catchment | Event Number | Periods | Rainfall (mm) | Peak Flow (m^{3}/s) |
---|---|---|---|---|

Danseong | 1 | 2011.07.03, 20:00– 2011.07.05, 12:00 | 43 | 687 |

2 | 2012.07.14, 15:00– 2012.07.16, 15:00 | 63 | 1232 | |

3 | 2012.09.16, 17:00– 2012.09.18, 07:00 | 225 | 11,970 | |

4 | 2015.07.12, 01:00– 2015.07.14, 01:00 | 123 | 2173 | |

Seonsan | 1 | 2010.08.11, 00:00– 2010.08.12, 20:00 | 66 | 1361 |

2 | 2010.09.01, 20:00– 2010.09.03, 12:00 | 43 | 491 | |

3 | 2011.07.09, 11:00– 2011.07.12, 20:00 | 154 | 1814 | |

4 | 2012.09.16, 15:00– 2012.09.19, 00:00 | 198 | 3542 |

Number | Parameter | Lower | Upper | Unit | Description |
---|---|---|---|---|---|

1 | ISSR | 0 | 1 | - | Initial soil saturation ratio |

2 | MSLS | 0.0001 | 0.01 | - | Minimum slope of land surface |

3 | MSCB | 0.0001 | 0.01 | - | Minimum slope of channel bed |

4 | CRC | 0.008 | 0.2 | - | Channel roughness coefficient |

5 | CLCRC | 0.6 | 1.3 | - | Correction factor for land cover roughness coefficient |

6 | CSD | 0.8 | 1.2 | - | Correction factor for soil depth |

7 | CSP | 0.9 | 1.1 | - | Correction factor for soil porosity |

8 | CSWS | 0.25 | 4 | - | Correction factor for soil wetting front suction head |

9 | CSHC | 0.05 | 20 | - | Correction factor for soil hydraulic conductivity |

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**MDPI and ACS Style**

Shin, M.-J.; Choi, Y.S.
Sensitivity Analysis to Investigate the Reliability of the Grid-Based Rainfall-Runoff Model. *Water* **2018**, *10*, 1839.
https://doi.org/10.3390/w10121839

**AMA Style**

Shin M-J, Choi YS.
Sensitivity Analysis to Investigate the Reliability of the Grid-Based Rainfall-Runoff Model. *Water*. 2018; 10(12):1839.
https://doi.org/10.3390/w10121839

**Chicago/Turabian Style**

Shin, Mun-Ju, and Yun Seok Choi.
2018. "Sensitivity Analysis to Investigate the Reliability of the Grid-Based Rainfall-Runoff Model" *Water* 10, no. 12: 1839.
https://doi.org/10.3390/w10121839