# Using the General Regression Neural Network Method to Calibrate the Parameters of a Sub-Catchment

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. General Regression Neural Network

_{i}is the learning sample corresponding to the i-th neuron, and $\mathsf{\sigma}$ is the standard deviation of the input parameter, which is also known as the smoothing factor.

#### 2.2. Case Study

^{2}, and comprises porous asphalt, a vegetation retention tank, permeable high-pressure concrete bricks, and impervious bricks with areas of 181.04 m

^{2}, 100.6 m

^{2}, 245.7 m

^{2}, and 160.2 m

^{2}, respectively. It should be noted that, as shown in Figure 3b, the vegetation retention tank is designed to be an independent sub-catchment. Therefore, the catchment in the study area was divided into two sub-catchments. Sub-catchment 1 includes the permeable pavement and impervious bricks, and sub-catchment 2 contains only the vegetation retention tank. The porous asphalt and permeable high-pressure concrete bricks contained in sub-catchment 1 are considered to be permeable pavement; thus, the permeable pavement area is 426.74 m

^{2}.

#### 2.3. Method

#### 2.4. Performance Criteria

- 1.
- Root-Mean-Square ErrorRoot-mean-square error (RMSE) is used to measure the deviation between the observed value and the true value and is defined as$$RMSE=\sqrt{\frac{{\sum}_{i=1}^{n}{\left(Actual(i)-Predicted(i)\right)}^{2}}{n}},$$
- 2.
- Mean Absolute Percentage ErrorThe mean absolute percentage error (MAPE) is used to measure the relative error between the average test value and the real value of the test set and is defined as$$MAPE=\frac{1}{n}{\sum}_{i=1}^{n}\left|\frac{Predicted(i)-Actual(i)}{Actual(i)}\right|\times 100\%,$$
- 3.
- Nash–Sutcliffe Efficiency CoefficientThe Nash–Sutcliffe efficiency coefficient (NSE) is defined as$$NSE=1-\frac{{\sum}_{i=1}^{n}{\left(Actual(i)-Predicted(i)\right)}^{2}}{{\sum}_{i=1}^{n}{\left(Actual(i)-Average(i)\right)}^{2}},$$

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Location of the study site in Taipei city. The left-hand image shows the location of the city, and that on the right shows the study area.

**Figure 3.**Schematic diagram of the study area: (

**a**) onsite monitoring locations; (

**b**) photograph of the vegetation retention tank onsite.

**Figure 4.**Schematic diagram of the three proposed research steps. Note: SWMM—storm water management model; GRNN—general regression neural network; Q

_{p}—peak flow; V—total flow volume; W—width; S—slope.

**Figure 5.**Effect of smoothing factor on GRNN performance under different cross-validations (CV(1)–CV(7)).

**Figure 6.**Relationship between actual values used in storm water management model (SWMM) and predicted values obtained by GRNN.

**Figure 9.**Comparison of observed and simulated runoff values using model-calibrated parameters: (

**a**) calibration; (

**b**) validation.

Parameters | Sub-Catchment 1 | Sub-Catchment 2 |
---|---|---|

Area (ha) | 0.058694 | 0.01006 |

Width (m) | 1–10, Basic value: 5 | 8 |

Slope (%) | 0.1–0.3, Basic value: 0.2 | 0.1 |

Imprev (%) | 27.23 | 0 |

N-Imprev | 0.012 | — |

N-perv | 0.012 | 0.04 |

Destore Imprev (mm) | 5 | — |

Destore–Perv (mm) | 5 | 0.2 |

Infil. Model | Horton | Horton |

Zero Imperv (%) | — | — |

Hyperparameter | Value |
---|---|

The number of neurons in input layer | 2 |

The number of neurons in pattern layer | 18 |

The number of neurons in summation layer | 2 |

The number of neurons in output layer | 2 |

Smoothing factor | 0.13 |

Parameter | RMSE | MAPE | NSE |
---|---|---|---|

W | 0.3946 | 5.04% | 0.9950 |

S | 0.0219 | 8.78% | 0.9878 |

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**MDPI and ACS Style**

Cai, Q.-C.; Hsu, T.-H.; Lin, J.-Y.
Using the General Regression Neural Network Method to Calibrate the Parameters of a Sub-Catchment. *Water* **2021**, *13*, 1089.
https://doi.org/10.3390/w13081089

**AMA Style**

Cai Q-C, Hsu T-H, Lin J-Y.
Using the General Regression Neural Network Method to Calibrate the Parameters of a Sub-Catchment. *Water*. 2021; 13(8):1089.
https://doi.org/10.3390/w13081089

**Chicago/Turabian Style**

Cai, Qing-Chi, Tsung-Hung Hsu, and Jen-Yang Lin.
2021. "Using the General Regression Neural Network Method to Calibrate the Parameters of a Sub-Catchment" *Water* 13, no. 8: 1089.
https://doi.org/10.3390/w13081089