# Urban Flood Modelling under Extreme Rainfall Conditions for Building-Level Flood Exposure Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Available Datasets

#### 2.2. Extreme Rainfall Assessment

#### 2.2.1. POT Threshold Selection

_{1}< … < u

_{l}, each having n

_{i}exceedances, i = 1, …, l. Let H

_{0}

^{(i)}denote the null hypothesis that the distribution of n

_{i}exceedances above the threshold u

_{i}follows the GPD. Following the forward stop rule of G’Sell et al. [32], a rejection rule was constructed by returning a cutoff level $\widehat{k}$, such that H

_{1}to ${H}_{\widehat{k}}$ are rejected:

_{i}I = 1, …, l are the corresponding p-values of the l hypotheses. If there is no $\widehat{k}$∊ [1, …, l], there is no rejection of the null hypothesis.

_{(1)}≤ … ≤ y

_{(n)}, based on the maximum likelihood estimator of θ, ${\widehat{\theta}}_{n}$, under the null hypothesis H

_{0}. F denotes the cumulative distribution function of the GPD for each candidate threshold.

_{r}

_{+1}with r = 0, 1, … are expressed as linear functions of the specific probability weighted moments (PWM):

_{3}= λ

_{3}/λ

_{2}, and L-kurtosis, τ

_{4}= λ

_{4}/λ

_{2}, calculated as functions of the L-scale, λ

_{2}, and the third, λ

_{3}, and fourth, λ

_{4}, L-moments, respectively. Let a

_{r}be the unbiased estimator of a

_{r}for an ordered sample x

_{1:n}≤ … ≤ x

_{n:n}:

_{3}= l

_{3}/l

_{2}, and L-kurtosis, t

_{4}= l

_{4}/l

_{2}, calculated as functions of the sample L-scale, l

_{2}, and the third, l

_{3}, and fourth, l

_{4}, sample L-moments, respectively.

#### 2.2.2. Scaling Rainfall Extremes

_{d}and I

_{λd}, corresponding to durations d and λd, respectively, can be related by the following equation [46,47,48]:

_{y}is the number of observations per year and ζ

_{u}is the total exceedance rate of the threshold u. Confidence intervals for return levels estimated using both the GEV and GPD are assessed using the delta method [49].

#### 2.3. Flood Exposure

#### 2.4. Modelling System and Model Set Up

^{2}), so the total number of computational cells in the flow domain was 125,192, covering an area of 0.78 km

^{2}. The representation of the buildings in the model was performed following the ‘Building Hole’ approach where a non-flow boundary is generated around buildings to redistribute the rainfall to the nearest grid square (for a full description and performance relative to other methods, see Iliadis et al. [1]). Following the previously described approach, this study explored the likelihood of flood exposure for 1165 buildings. The roughness coefficient (Manning’s n) was defined as 0.02 for impermeable areas and 0.035 for permeable areas. Due to the limitations in the Hellenic National regulations in urban flood modelling, and the intended design of the combined sewer system for storms with a return period of 10 years in the city centre of Thessaloniki (based on design cross-sections of existing combined sewers), a simple assumption was made in this work, that 20% of the rainfall enters the drainage system. In other countries, i.e., the UK, there is an instruction to flood modellers, when they do not combine the drainage system with the surface, to exclude specific rainfall from the model (e.g., 6 mm–15 mm).

## 3. Results

#### 3.1. Extreme Rainfall Assessment

^{2}, for all return periods. Figure 7 presents the linear relationships between the log-transformed quantiles (log-transformed return levels) of rainfall intensity and log-transformed scale factors of different durations, for return periods of 5 years (left panel) and 50 years (right panel). The plots include the linear function equations for rainfall durations in the intervals of 5 min to 30 min and 30 min to 24 h, and the respective coefficients of determination. Table 2 presents estimates of the self-similarity index (estimates of −β) assessed for all return periods and for the two groups of rainfall duration.

#### 3.2. Modelled Flow Depth

#### 3.3. Exposure Likelihood to Buildings

## 4. Conclusions

- Typical storm events have durations spanning 1 h to 2 h, so both durations have been used here to see how sensitive the damages are to storm duration. For storms of the same return period, a modest increase is found for the 2 h storm relative to the 1 h storm.
- The CityCAT model provides valuable insights into flood depths and water flowpaths, identifying a major water flowpath along Agias Sofias street, which is highly susceptible to flooding during intense rainfall events. The presence of small ponds in various parts of the studied catchment further highlights the potential for localised flooding.
- The estimated likelihood of flood exposure to buildings reveals the vulnerability of urban features to flood risk. Due to the previous flood events in the area, the number of buildings at high risk for both storm events underscores the importance of addressing flood impacts on the built environment.
- The modelling system is suitable for assessing the performance of flood-resilience strategies such as retention ponds, surface drainage improvements, and permeable pavements.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**An overview of the study area in Thessaloniki, Greece: (1) the city centre and the computational domain (with red colour); (2) the urban features, where grey denotes the buildings, green denotes the permeable areas and yellow to brown shading indicates the surface elevation of the area.

**Figure 2.**Schematic workflow of the flood exposure analysis tool for the classification of buildings according to the water depth in the buffer zone [50].

**Figure 3.**Example of the buffer zone to calculate inundation depth from grid squares [50].

**Figure 5.**GPD parameter stability plots for daily rainfall in Thessaloniki for the interval 1958–2021.

**Figure 6.**Rainfall ML return levels and 95% confidence interval (mm) assessed by fitting the GPD to daily rainfall in Thessaloniki for the period 1958–2021.

**Figure 7.**Scaling of rainfall return level estimates at the station of Mikra, in Thessaloniki, for return periods of 5 (

**left panel**) and 50 (

**right panel**) years.

**Figure 8.**IDF (

**top panel**) and DDF (

**bottom panel**) curves for Thessaloniki for return periods of 2, 5, 10, 20, 50, 100, 200, and 500 years.

**Figure 9.**Storm profiles corresponding to the constructed DDF curves for Thessaloniki, Greece: (

**a**) 39 mm rainfall with a 1 h duration; and (

**b**) 46 mm rainfall with a 2 h duration.

**Figure 10.**Example of maximum flood depths from a CityCAT simulation for a 50-year storm event with durations of (

**a**) 1 h and (

**b**) 2 h, for the centre of Thessaloniki.

**Figure 11.**Flood depths and flow direction (black arrows) for a 50-year storm event with durations of (

**a**) 1 h and (

**b**) 2 h at Palaion Patron Germanou and Pavlou Mela streets (marked as (b) in Figure 1).

**Figure 12.**Flood depths and flow direction (black arrows) for a 50-year storm event with durations of (

**a**) 1 h and (

**b**) 2 h at Proxenou Koromila (marked as (c) in Figure 1).

**Figure 13.**Flood depths and flow direction (black arrows) for a 50-year storm event with durations of (

**a**) 1 h and (

**b**) 2 h at a part of Mitropoleos street (marked as (d) in Figure 1).

**Figure 14.**Maximum flood depths and flood exposure of buildings for a 50-year storm event with durations of (

**a**) 1 h and (

**b**) 2 h for the centre of Thessaloniki.

Exposure Class | Mean Depth (m) | 90th Percentile (m) |
---|---|---|

Low | <0.10 | <0.30 |

Medium | <0.10 | ≥0.30 |

≥0.10–<0.30 | <0.30 | |

High | ≥0.10 | ≥0.30 |

**Table 2.**Self-similarity indices, −β, for all return periods and rainfall durations of 5 min–30 min and 30 min–24 h.

Return Period (Years) | 5 min–30 min | 30 min–24 h |
---|---|---|

2 | 0.5415 | 0.7286 |

5 | 0.5674 | 0.7379 |

10 | 0.5908 | 0.7400 |

20 | 0.6136 | 0.7407 |

50 | 0.6418 | 0.7407 |

100 | 0.6614 | 0.7403 |

200 | 0.6794 | 0.7398 |

500 | 0.7008 | 0.7390 |

Storm Scenarios | Medium | High |
---|---|---|

50-year event with a duration of 1 h | 90 | 165 |

50-year event with a duration of 2 h | 99 | 186 |

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## Share and Cite

**MDPI and ACS Style**

Iliadis, C.; Galiatsatou, P.; Glenis, V.; Prinos, P.; Kilsby, C.
Urban Flood Modelling under Extreme Rainfall Conditions for Building-Level Flood Exposure Analysis. *Hydrology* **2023**, *10*, 172.
https://doi.org/10.3390/hydrology10080172

**AMA Style**

Iliadis C, Galiatsatou P, Glenis V, Prinos P, Kilsby C.
Urban Flood Modelling under Extreme Rainfall Conditions for Building-Level Flood Exposure Analysis. *Hydrology*. 2023; 10(8):172.
https://doi.org/10.3390/hydrology10080172

**Chicago/Turabian Style**

Iliadis, Christos, Panagiota Galiatsatou, Vassilis Glenis, Panagiotis Prinos, and Chris Kilsby.
2023. "Urban Flood Modelling under Extreme Rainfall Conditions for Building-Level Flood Exposure Analysis" *Hydrology* 10, no. 8: 172.
https://doi.org/10.3390/hydrology10080172