# Application of Particle Swarm Optimization for Auto-Tuning of the Urban Flood Model

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Outline of the Urban Flood Model

#### 2.2. Description of the Case Study

^{3}bounded on the river side by an overflow-type levee. The area surrounded by a thin white line indicates each sub-catchment in which 2DG is computed. The points with X and Y indicate the locations of the Shin-Yokohama and Tarumachi manholes, respectively, at which the water levels are recorded. The capital characters A and B along the Tsurumi River indicate the locations of the upstream and downstream boundaries of 1DR, respectively. At the upstream boundary, time-varying discharge is determined by the measured water level and the H-Q curve at A. The downstream boundary condition is determined by the tide water level at the Tsurumi River mouth. In this case study site, the trunk sewer network pipelines have a total length of 336.7 km, and 8820 manholes connect these pipelines. Grid sizes of this case study were set to 200 m for 1DR and 40 m for 2DR and 1DS, respectively.

#### 2.3. Sensitivity Analysis

#### 2.4. Setup of PSO for Auto-Tuning of the Urban Flood Model

#### 2.5. Application of PSO to the Case Study Site

^{1⁄3}) < n < 0.03 (s/m

^{1⁄3}) and 4 (m) < α < 6 (m), respectively. In this study, the validity of the present PSO is tested for different combinations of ${N}_{x}$ and ${N}_{y}$. Overall predictive skills of the auto-tuned urban flood model were then evaluated by NSE, Kling–Gupta efficiency (KGE), Root Mean Square Error (RMSE), and normalized RMSE (NRMSE).

## 3. Results and Discussions

#### 3.1. Model Sensitivity to Manning’s Roughness

#### 3.2. Model Sensitivity to the Coefficient, α

#### 3.3. Application of the Present PSO-Based Auto-Tuning System

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic chart of the urban flood model (Wu et al., 2022) [34].

**Figure 2.**Locations and computational domain of the case study site, the Tsurumi River basin, Japan.

**Figure 5.**Comparisons of the time-varying water level at the Shin-Yokohama manhole in cases 0, A1, A2, A3, A4 and A5. In the figure, n

_{1DR}and n

_{1DS}are the roughness of the river bed and the pipeline for case 0, respectively.

**Figure 6.**Comparisons of the time-varying water level at the Shin-Yokohama manhole in cases 0, B1, B2, B3, and B4.

**Figure 8.**Spatial distribution of the tuned Manning’s roughness (

**top**) and the coefficient, α (

**bottom**).

Case | ${\mathit{n}}_{1\mathit{D}\mathit{R}}\left({\mathbf{sm}}^{-1/3}\right)$ | ${\mathit{n}}_{1\mathit{D}\mathit{S}}\left({\mathbf{sm}}^{-1/3}\right)$ | α (m) |
---|---|---|---|

0 | 0.025 | 0.013 | 5 |

A1 | 0.25 | 0.013 | 5 |

A2 | 0.0025 | 0.013 | 5 |

A3 | 0.025 | 0.13 | 5 |

A4 | 0.25 | 0.0013 | 5 |

A5 | 0.25 | 0.13 | 5 |

B1 | 0.025 | 0.013 | 0.05 |

B2 | 0.025 | 0.013 | 0.5 |

B3 | 0.025 | 0.013 | 50 |

B4 | 0.025 | 0.013 | 500 |

**Table 2.**Comparisons of performance metrics, NSE, KGE, RMSE and NRMSE, of the computed results before and after the auto-tuning.

Case | NSE | KGE | RMSE (m) | NRMSE |
---|---|---|---|---|

case 0 | 0.55 | −0.70 | 0.36 | 0.23 |

after tuning | 0.69 | 0.65 | 0.29 | 0.19 |

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**MDPI and ACS Style**

Jiang, L.; Tajima, Y.; Wu, L.
Application of Particle Swarm Optimization for Auto-Tuning of the Urban Flood Model. *Water* **2022**, *14*, 2819.
https://doi.org/10.3390/w14182819

**AMA Style**

Jiang L, Tajima Y, Wu L.
Application of Particle Swarm Optimization for Auto-Tuning of the Urban Flood Model. *Water*. 2022; 14(18):2819.
https://doi.org/10.3390/w14182819

**Chicago/Turabian Style**

Jiang, Lechuan, Yoshimitsu Tajima, and Lianhui Wu.
2022. "Application of Particle Swarm Optimization for Auto-Tuning of the Urban Flood Model" *Water* 14, no. 18: 2819.
https://doi.org/10.3390/w14182819