# Simulink Implementation of a Hydrologic Model: A Tank Model Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Simulink Modeling Framework

#### 2.2. The Tank Model

#### 2.3. Watershed Evapotranspiration

#### 2.3.1. Potential Evapotranspiration

#### 2.3.2. Crop Coefficient

#### 2.3.3. Soil Water Stress Coefficient

## 3. Simulink-Tank Model Structure

#### 3.1. Watershed Evapotranspiration Module

#### 3.2. 3-Tank Module

## 4. Case Study

^{2}, of which 68%, 8%, 10%, and 14% is comprised of forest, paddy, upland, and other land uses, respectively.

## 5. Application and Discussion of the Simulink-Tank Model

#### 5.1. Dynamic Description of a Hydrologic System

#### 5.2. Parameter Calibration for the Simulink-Tank Model Using Optimization Techniques within MATLAB

#### 5.2.1. Objective Function

#### 5.2.2. Optimization Results

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Schematic of the modified Tank model [35].

**Figure 8.**Comparison of observed and simulated runoff using (

**a**) a time-series; (

**b**) a scatter plot for the calibration period; (

**c**) a scatter plot for the validation period (Case 1, objective function: $NSE$).

**Figure 9.**Comparison of observed and simulated runoff using (

**a**) a time-series; (

**b**) a scatter plot for the calibration period; (

**c**) a scatter plot for the validation period (Case 2, objective function: $NS{E}_{sqrt}$).

Parameter | Alpha | ${\mathit{a}}_{11}$ | ${\mathit{a}}_{12}$ | ${\mathit{h}}_{11}$ | ${\mathit{h}}_{12}$ | ${\mathit{b}}_{1}$ | ${\mathit{a}}_{2}$ | ${\mathit{h}}_{2}$ | ${\mathit{b}}_{2}$ | ${\mathit{a}}_{3}$ | ${\mathit{h}}_{3}$ | ${\mathit{b}}_{3}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Min. | 0 | 0.08 | 0.08 | 5 | 20 | 0.1 | 0.03 | 0 | 0.01 | 0.003 | 0 | 0 |

Max. | 0.5 | 0.5 | 0.5 | 60 | 110 | 0.5 | 0.5 | 100 | 0.35 | 0.03 | 0 | 0.11 |

**Table 2.**Monthly crop coefficients for the four land-use types used with the FAO Penman–Monteith approach.

Crop Coeff. | January | February | March | April | May | June | July | August | September | October | November | December |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Forest | 0.47 | 0.46 | 0.55 | 0.59 | 0.74 | 0.72 | 0.87 | 1.01 | 0.98 | 0.87 | 0.64 | 0.45 |

Paddy | 0.20 | 0.20 | 0.20 | 0.65 | 0.70 | 0.99 | 1.30 | 1.17 | 0.83 | 0.20 | 0.20 | 0.20 |

Upland | 0.36 | 0.36 | 0.37 | 0.37 | 0.58 | 0.78 | 0.82 | 0.82 | 0.76 | 0.57 | 0.37 | 0.36 |

Others | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 |

Year | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |
---|---|---|---|---|---|---|---|---|

Rainfall (mm) | 1260 | 1458 | 1541 | 1977 | 2211 | 1481 | 1448 | 767 |

**Table 4.**Model calibration and validation statistics. PBIAS: percent bias; NSE: Nash–Sutcliffe Efficiency.

Case | Period | ${\mathit{R}}^{2}$ | $\mathit{N}\mathit{S}\mathit{E}$ | $\mathit{N}\mathit{S}{\mathit{E}}_{\mathit{i}\mathit{n}\mathit{v}}$ | $\mathit{P}\mathit{B}\mathit{I}\mathit{A}\mathit{S}$ (%) |
---|---|---|---|---|---|

1 | Calibration | 0.95 | 0.95 | −0.15 | −4.4 |

Validation | 0.80 | 0.79 | 0.34 | −7.5 | |

2 | Calibration | 0.94 | 0.94 | 0.07 | −3.6 |

Validation | 0.81 | 0.80 | 0.57 | −7.3 |

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**MDPI and ACS Style**

Song, J.-H.; Her, Y.; Park, J.; Lee, K.-D.; Kang, M.-S.
Simulink Implementation of a Hydrologic Model: A Tank Model Case Study. *Water* **2017**, *9*, 639.
https://doi.org/10.3390/w9090639

**AMA Style**

Song J-H, Her Y, Park J, Lee K-D, Kang M-S.
Simulink Implementation of a Hydrologic Model: A Tank Model Case Study. *Water*. 2017; 9(9):639.
https://doi.org/10.3390/w9090639

**Chicago/Turabian Style**

Song, Jung-Hun, Younggu Her, Jihoon Park, Kyung-Do Lee, and Moon-Seong Kang.
2017. "Simulink Implementation of a Hydrologic Model: A Tank Model Case Study" *Water* 9, no. 9: 639.
https://doi.org/10.3390/w9090639