# Efficient Hazard Assessment for Pluvial Floods in Urban Environments: A Benchmarking Case Study for the City of Berlin, Germany

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## Abstract

**:**

## 1. Introduction

## 2. Data

## 3. Models

#### 3.1. Two-Dimensional Hydrodynamic Simulations

^{−1/3}· s for buildings and 0.013 for other surface types [36,37,38].

#### 3.2. The Fill–Spill–Merge (FSM) Method

- 1
**DEM prepossessing and derivation of effective rainfall**: The first step in delineating a watershed is to fill sinks, in which existing depressions (called also sinks and pits) in the DEM are filled to guarantee stream connectivity. However, excess runoff is accumulated in these depressions in urban watersheds. Therefore, it is vital to identify them in urban areas as they are more prone to urban flooding. Depressions were identified by computing the elevation difference between the filled DEM and the original DEM in ArcGIS (v. 10.5.1). After that, only depressions with a depth of more than 0.20 m (the vertical accuracy of the original DEM) and surface areas bigger than 1000 m^{2}were considered. We calculated the flow direction and the flow accumulation using the D8 algorithm from the filled DEM and used them to estimate the flow paths, spilling points, and the vertical hierarchy of the depressions. Finally, we obtained the partially filled DEM by filling the depressions in the original DEM except for the selected depressions. The partially filled DEM was used to estimate the contributing watershed for each depression. The curve number method was used to estimate the effective rainfall for each pixel. Therefore, the curve number map for Berlin was created based on the soil type, hydrologic condition from [29] and land use from an open street map [30], Figure 3 shows the implemented workflow.- 2
**Flood routing**: In general, rainfall is transformed to either evapotranspiration, infiltration, or surface and sewer system runoff. Runoff at the surface and in the urban storm drainage system could contribute to pluvial flooding in terms of inundation of areas in depressions. This study neglected the latter because of the difficulties of obtaining the detailed urban storm drainage system data if they exist. In addition, the urban storm drainage system tends to be ineffective in the case of intensive rainstorms [41,42]. Using the Hydrologic Engineering Center—Hydrologic Modeling System (HEC-HMS) model [43], we estimated the excess runoff based on the SCS method [44] for precipitation depths ranging from 30 to 150 mm (10 mm increments), performed the runoff routing, and estimated the stored depth and volume at each depression.- 3
**Hazard mapping**: We estimated the water depth and inundation extent inside the depressions by subtracting the obtained water level minus the elevation for each pixel from the original DEM in ArcGIS (v. 10.5.1).

#### 3.3. TWI Method

#### Maximum Likelihood Estimation

- 1
**Mesoscale estimations**: The terrain in Berlin is relatively flat. Therefore, we calculated the $P\left(FP\right|\tau ,W)$ using the spatial extent of the case study area as follows:$$P(FP|\tau ,W)=\frac{{A}_{urban}\left(FP\right)}{{A}_{urban}}$$- 2
**Microscale estimations**: $P\left(IN\right|FP,\tau ,W)$ and $P(\overline{IN}|\overline{FP},\tau ,W)$ were calculated using the spatial extent of the selected window within the study area, as shown in Figure 5 as follows:$$P(IN|FP,\tau ,W)=\frac{{A}_{\mathrm{W}}(IN,FP)}{{A}_{\mathrm{w}}\left(FP\right)}$$$$P(\overline{IN}|\overline{FP},\tau ,W)=\frac{{A}_{\mathrm{W}}(\overline{IN},\overline{FP})}{{A}_{\mathrm{w}}\left(\overline{FP}\right)}$$

#### 3.4. Benchmarking Experiments

^{2}, respectively. Depressions represent 14% and 8% of case study 1 and 2 areas, respectively. Depressions with a surface area more than 1000 m

^{2}represent approximately 89% of the area of the total depression in the two case studies. The estimated historical precipitation depth that caused flooding in the period between 2005 and 2019 for the two case studies ranges from 30 to 150 mm based on the rainfall radar data analysis [31,32].

- 1
- True positive (TP): correctly classified as flooded;
- 2
- True Negative (TN): correctly classified as non-flooded;
- 3
- False positive (FP): incorrectly classified as flooded;
- 4
- False negative (FN): incorrectly classified as non-flooded.

## 4. Results and Discussion

#### 4.1. Maximum Likelihood Estimation

#### 4.2. Water Depth (h) Threshold

#### 4.3. Evaluating FSM and TWI Methods Performance

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Digital elevation model (DEM) of Berlin, the two case studies and the city districts. (

**b**) The spatial distribution of TWI for Berlin and the city districts.

**Figure 2.**Process of the FSM method. (

**a**) Runoff flowing process between depressions. (

**b**) Schematic of the nested depressions. (

**c**) Vertical hierarchical tree.

**Figure 10.**Flood-prone area (FP) for different water depth thresholds for a 100 mm precipitation depth.

**Figure 11.**(

**a**) TWI threshold ($\tau $) for different water depth thresholds (h). (

**b**) Percentage of inundated areas for different water depth thresholds (h).

**Figure 14.**Comparison of the inundation extent for a 100 mm precipitation event: (

**a**) Comparison of TELEMAC-2D model and the TWI method inundation extents. (

**b**) Comparison of TELEMAC-2D model and the FSM method inundation extents.

Index | Equation | Range |
---|---|---|

Sensitivity (TPR) | $\frac{TP}{TP+FN}$ | 0 < TPR < 1 |

Matthews correlation coefficient (MCC) | $\frac{TP\times TN-FP\times FN}{\sqrt{(TP+FP)\times (TP+FN)\times (TN+FP)\times (TN+FN)}}$ | −1 < MCC < 1 |

Flood Area Index (FAI) | $\frac{TP}{TP+FP+FN}$ | 0 < FAI < 1 |

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**MDPI and ACS Style**

Seleem, O.; Heistermann, M.; Bronstert, A. Efficient Hazard Assessment for Pluvial Floods in Urban Environments: A Benchmarking Case Study for the City of Berlin, Germany. *Water* **2021**, *13*, 2476.
https://doi.org/10.3390/w13182476

**AMA Style**

Seleem O, Heistermann M, Bronstert A. Efficient Hazard Assessment for Pluvial Floods in Urban Environments: A Benchmarking Case Study for the City of Berlin, Germany. *Water*. 2021; 13(18):2476.
https://doi.org/10.3390/w13182476

**Chicago/Turabian Style**

Seleem, Omar, Maik Heistermann, and Axel Bronstert. 2021. "Efficient Hazard Assessment for Pluvial Floods in Urban Environments: A Benchmarking Case Study for the City of Berlin, Germany" *Water* 13, no. 18: 2476.
https://doi.org/10.3390/w13182476