# Efficient Urban Inundation Model for Live Flood Forecasting with Cellular Automata and Motion Cost Fields

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Cellular Automata

#### 2.2. Motion Costs

#### 2.3. System Architecture

## 3. Case Study

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**The 3D web-interface WupperWWEM for the visualization of “live” flood warning in an urban area of Wuppertal [40].

**Figure 7.**Spatial distribution of model performance for water depth. Green indicates very good or perfect agreement. (

**a**) NSE; (

**b**) RMSE; (

**c**) IoA.

**Figure 8.**Spatial distribution of model performance for velocity. Green indicates very good or perfect agreement. (

**a**) NSE; (

**b**) RMSE; (

**c**) IoA.

**Figure 9.**Residual plots (ANUGA-CAMC) for water depth (

**left**) and velocity (

**right**): (

**a**,

**c**,

**e**) Water depth at gauges 1–3; (

**b**,

**d**,

**f**) Velocity at gauges 1–3.

**Figure 10.**Residual plots (ANUGA-CAMC) for water depth (

**left**) and velocity (

**right**): (

**a**,

**c**,

**e**) Water depth at gauges 4–6; (

**b**,

**d**,

**f**) Velocity at gauges 4–6.

Name | Formula | Range | Ideal Value |
---|---|---|---|

Nash-Sutcliffe Model Efficiency (NSE) | $1-\frac{{\sum}_{t=1}^{n}{({y}_{s,t}-{y}_{r,t})}^{2}}{{\sum}_{t=1}^{n}{({y}_{r,t}-{\overline{y}}_{r})}^{2}}$ | (−∞, 1) | 1 |

Root Mean Square Error (RMSE) | $\sqrt{\frac{1}{n}{\sum}_{t=1}^{n}{({y}_{s,t}-{y}_{r,t})}^{2}}$ | (0, ∞) | 0 |

Index of Agreement (IoA) | $1-\frac{{\sum}_{t=1}^{n}{({y}_{s,t}-{y}_{r,t})}^{2}}{{\sum}_{t=1}^{n}\left(\right|{y}_{s,t}-{\overline{y}}_{r}|+|{y}_{r,t}-{\overline{y}}_{r}{\left|\right)}^{2}}$ | (0, 1) | 1 |

n is the number of time steps; ${y}_{s,t}$ is the simulated output at time step t; | |||

${y}_{r,t}$ is the reference output at time step t; ${\overline{y}}_{r}$ is the mean of the reference output |

**Table 2.**Summary of model performance for cells containing water at the end of the simulation (Figure 6).

NSE | RMSE | IoA | ||
---|---|---|---|---|

Water depth | Mean | 0.61 | 0.39 m | 0.65 |

Median | 0.67 | 0.25 m | 0.67 | |

Velocity | Mean | 0.34 | 0.13 ms${}^{-1}$ | 0.39 |

Median | 0.38 | 0.11 ms${}^{-1}$ | 0.42 |

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**MDPI and ACS Style**

Issermann, M.; Chang, F.-J.; Jia, H. Efficient Urban Inundation Model for Live Flood Forecasting with Cellular Automata and Motion Cost Fields. *Water* **2020**, *12*, 1997.
https://doi.org/10.3390/w12071997

**AMA Style**

Issermann M, Chang F-J, Jia H. Efficient Urban Inundation Model for Live Flood Forecasting with Cellular Automata and Motion Cost Fields. *Water*. 2020; 12(7):1997.
https://doi.org/10.3390/w12071997

**Chicago/Turabian Style**

Issermann, Maikel, Fi-John Chang, and Haifeng Jia. 2020. "Efficient Urban Inundation Model for Live Flood Forecasting with Cellular Automata and Motion Cost Fields" *Water* 12, no. 7: 1997.
https://doi.org/10.3390/w12071997