# The Significance of the Spatial Variability of Rainfall on the Numerical Simulation of Urban Floods

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## Abstract

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## 1. Introduction

## 2. Material and Methods

#### 2.1. Computer Model

#### 2.2. Input Data

#### 2.2.1. Study Area

#### 2.2.2. Elevation

#### 2.2.3. Observed Flood Extents

#### 2.2.4. Friction

#### 2.2.5. Drainage

- West Hull pumping station (capacity 32 ${\mathrm{m}}^{3}$ ${\mathrm{s}}^{-1}$), draining the whole study area plus a smaller part of the city north of it.
- Saltend Waste Water Treatment Work (outflow 22 ${\mathrm{m}}^{3}$ ${\mathrm{s}}^{-1}$), treating most of Hull, including the study area.

#### 2.2.6. Infiltration

#### 2.2.7. Precipitation

## 3. Results

#### 3.1. Model Calibration

- Union of observed flooded extents as the “real-world” reference.
- No infiltration.
- Water depth threshold of 20 cm.

#### 3.2. Qualitative Analysis

#### 3.3. Quantitative Analysis

## 4. Discussion and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CSI | Critical Success Index |

DEM | Digital Elevation Model |

EA | Environment Agency of the United Kingdom |

GIS | Geographical Information System |

GLC30 | Global Land Cover |

GRASS | Geographic Resources Analysis Support System |

HCC | Hull City Council |

KED | Kriging with External Drift |

LiDAR | Light Detection And Ranging |

LOOCV | Leave-One-Out Cross-Validation |

MAE | Mean Absolute Error |

RMSE | Root Mean Square Error |

SVE | Saint–Venant Equations |

USDA | United States Department of Agriculture |

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**Figure 1.**Location of the Hull study area within Great Britain (satellite imagery Copernicus Sentinel 2016) [2].

**Figure 3.**Identified flooded areas. Light blue: EA only. Dark blue: HCC only. Green: intersection of both administrations.

**Figure 5.**Accumulated rainfall obtained from Kriging with External Drift on 25 June 2007. The circles represent the rain gauges used. The triangles are the weather radars. The study site is represented by a black polygon. Please note that during this event, only the Hameldon Hill radar (located in the west of the image) was operating.

**Figure 6.**Evolution of rainfall intensity above the study area obtained with Kriging with External Drift. Event of 25 June 2007. (

**a**) 00:00–01:00; (

**b**) 03:00–04:00; (

**c**) 06:00–07:00; (

**d**) 09:00–10:00; (

**e**) 12:00–13:00; (

**f**) 15:00–16:00; (

**g**) 18:00–19:00; (

**h**) 21:00–22:00.

**Figure 9.**Values of Critical Success Index obtained during the calibration process. They are calculated using the maximal water depth maps obtained with uniform rainfall and a combination of infiltration values, water depth thresholds and observed extents.

**Figure 10.**Comparison between observed extents and maximal computed water depths. (

**a**) Uniform rainfall; (

**b**) Kriging with External Drift.

**Figure 11.**Differences in maximal water depths between the results using uniform rainfall and those using Kriging with External Drift.

**Figure 12.**Evolution in time of the flood volume, flooded surface and Critical Success Index. The flooded surface and CSI are calculated for water depths above 20 cm.

Feature | LISFLOOD-FP | FloodMap | Itzï |
---|---|---|---|

Flow equation | Damped partial inertia [23,24] | Partial inertia [22] | Damped partial inertia [23,24] |

Adaptive time step | Global | Local | Global |

1D river model | Yes | Yes | No |

Infiltration model | No | Green–Ampt | Green–Ampt |

GIS integration | Loose | Loose | Tight |

Map time series | |||

as input | No | No | Yes |

Free software | No ${}^{1}$ | No | Yes (GNU GPL) |

Parallel processing | OpenMP | MPI | OpenMP |

Parameter | Value |
---|---|

$\alpha $ | 0.7 |

$\Delta {t}_{max}$ ($\mathrm{s}$) | 2.0 |

$\theta $ | 0.7 |

Collecting Entity | Area (${\mathbf{k}\mathbf{m}}^{2}$) |
---|---|

Environment Agency | 5.16 |

Hull City Council | 6.18 |

Intersection of both | 2.33 |

GLC30 Class | Category from Chow [28] | Manning’s n ($\mathbf{s}{\mathbf{m}}^{-1/3}$) |
---|---|---|

Cultivated land | Mature field crops | 0.040 |

Forest | Cleared land with tree stumps, heavy growth of sprouts | 0.060 |

Grassland | Pasture with short grass | 0.030 |

Water bodies | Natural stream: clean, straight, full stage, no rifts or deep pool | 0.030 |

Artificial surfaces | Gunite, good section | 0.019 |

Hydraulic Conductivity ($\mathbf{m}\mathbf{m}/\mathbf{h}$) | Surface ($\mathbf{ha}$) | Surface (%) |
---|---|---|

1.00 | 18.88 | 0.30 |

1.50 | 654.5 | 12.0 |

3.50 | 4507.5 | 82.3 |

10.9 | 295.6 | 5.40 |

Observed | |||
---|---|---|---|

Flooded | Not Flooded | ||

Computed | Flooded | hits | false alarms |

Not flooded | misses | correct negatives |

Rainfall | CSI | Flooded Area (ha) | Surface Flooded (%) |
---|---|---|---|

Uniform | 0.36 | 934.62 | 17.07 |

KED | 0.35 | 861.06 | 15.73 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Courty, L.G.; Rico-Ramirez, M.Á.; Pedrozo-Acuña, A.
The Significance of the Spatial Variability of Rainfall on the Numerical Simulation of Urban Floods. *Water* **2018**, *10*, 207.
https://doi.org/10.3390/w10020207

**AMA Style**

Courty LG, Rico-Ramirez MÁ, Pedrozo-Acuña A.
The Significance of the Spatial Variability of Rainfall on the Numerical Simulation of Urban Floods. *Water*. 2018; 10(2):207.
https://doi.org/10.3390/w10020207

**Chicago/Turabian Style**

Courty, Laurent Guillaume, Miguel Ángel Rico-Ramirez, and Adrián Pedrozo-Acuña.
2018. "The Significance of the Spatial Variability of Rainfall on the Numerical Simulation of Urban Floods" *Water* 10, no. 2: 207.
https://doi.org/10.3390/w10020207