# Pluvial Flooding in European Cities—A Continental Approach to Urban Flood Modelling

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## Abstract

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## 1. Introduction

^{2}. Therefore, the authors estimated intensity–duration–frequency (IDF) curves based on approximately 200 gauges around the world (pooled together and then partitioned by the different climatic areas based on the Köppen–Geiger classification). Subsequently, the IDF curves for each climatic region were regressed using annual average rainfall in order to estimate extreme rainfall worldwide. Nevertheless, the authors consider this method fit-for-purpose, since despite the fact that local features will undeniably result in very significant errors on a local scale, the errors of the DEM used (Shuttle Radar Topography Mission, SRTM, DEM with a 3 arc second resolution ~90 m) are expected to be the dominant source of uncertainty of the hydrological model.

^{3}/s) than E-Hype (1124 m

^{3}/s) or VIC (1279 m

^{3}/s) but these differences in performance might be partly explained by different calibration methodologies and datasets.

- the quality of the available DEMs, especially in forested regions and urban areas where the satellite information might correspond to the top of the canopy/building instead of the elevation of the ground;
- the quality of the precipitation data, which is very variable in time and place, and the fact that different types of rainfall inputs (gauge, radar, satellite or reanalysis) results in different orders of magnitude in terms of monetary loss from flooding results;
- the lack of data to calibrate hydrological models, especially in ungauged catchments.

## 2. Data

- EU-DEM [8]—a Digital Elevation Model over Europe “produced using Copernicus data and information funded by the European Union”. The EU-DEM is a hybrid product based on SRTM and ASTER GDEM data with 25-m resolution (projection 3035: EU-DEM-3035).
- Urban Morphological zones 2000 [10] defined as “set of urban areas laying less than 200 m apart”. This European Environment Agency (EEA) dataset was built based on the urban land cover classes of the CORINE Land Cover dataset. This data was necessary to define the “urban area” inside each city since the definition of “city” in the urban audit dataset can include non-urban areas, and sometimes even estuaries (see Figure S2 in Supplementary Materials for some examples).
- E-obs [11], an European daily gridded data set for precipitation and maximum and mean surface temperature at a 0.25 degree resolution for the period 1950–2013. E-obs is based on observations from 2316 stations, although the number changes over time showing a sharp rise in the number of gauges from 1950 to 1960 and a dip in 1976 (for stations with less than 20% missing monthly data). However, the spatial coverage throughout Europe is every uneven, with the UK, Ireland, the Netherlands and Switzerland having a much higher gauge density.
- Several observed sub-daily rainfall datasets were combined:
- -
- A total of 38 European gauges with time-series of annual maximum hourly rainfall, provided by Dr Panos Panagos, from the Joint Research Centre, that were collected under the auspices of the REDES project [12].
- -
- Some 192 UK gauges with time-series of annual maximum hourly rainfall (provided by Dr. Stephen Blenkinsop from Newcastle University) that were collected under the auspices of the CONVEX project [13]. These data were collected from three sources: the UK Met Office Integrated Data Archive System (MIDAS), the Scottish Environmental Protection Agency (SEPA) and the UK Environment Agency (EA). Not all these gauges were used, since that would mean the density of gauges used in the UK would be well above the density of gauges in the rest of Europe, therefore affecting the results of the analyses.
- -
- One gauge (Catraia) with hourly time-series for the South of Portugal downloaded from the Portuguese National Water Resources Information System (http://snirh.pt/).
- -
- IDF curves were collated for:

## 3. Methods

#### 3.1. Historical Intense Hourly Rainfall

^{2}, correlation between variables, predictive power of the used variables, and statistics of the residuals) were used. However, the robustness of the regression across possible ranges of values of predictors had to be carefully considered, since the model must be applied to all Europe. Therefore, lower R

^{2}values and higher errors at each gauge were preferred to overfitting the regression to the available gauge data, which could result in unrealistic RP10 when the regression is applied throughout Europe.

^{2}value is not very high (0.57) and the Bastia gauge has a large residual of 24.6 mm. Figure 4 shows maps of the residuals for all gauges. Figure 5 compares the observed and estimated RP10 for all gauges with the confidence intervals for the observed values. Here it can be seen that the confidence intervals for Bastia (green square on the top-right corner of the plot) are very large (the 10-year return period can be between 16 mm/h and 128 mm/h) which is due to the high interannual variability of the Mediterranean climate and the short record length (10 years of data). Removal of the Bastia record was considered due to the large confidence interval and residual but it was decided to be preferable to retain the data in this analysis as an example of the unusually intense rainfall regimes to be expected in some parts of Europe, and the inadequacy of this, and future, observing networks in characterizing them.

#### 3.2. Urban Hydrodynamic Model

## 4. Results and Discussion

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Map of Europe with the hourly rainfall for a 10-year return period for all available gauges. Return periods were calculated assuming a GEV (Generalized Extreme Value) distribution for all gauges. The number of years available for each gauge varied between 6 and 63 (median = 17 years).

**Figure 4.**Maps of Europe showing the residuals of the linear regressions used to estimate the hourly rainfall for a 10-year return period. (

**a**) Shows absolute residuals (in millimetres) while (

**b**) shows relative residuals (calculated as a percentage of the observed rainfall level for a 10-year return period).

**Figure 5.**Observed Vs estimated hourly rainfall for a 10-year return period for all gauges. When possible, the observed values are shown with their respective 0.05 confidence interval (horizontal lines). For four gauges (Athens, Barcelona, Firenze and Málaga) confidence intervals are not available because the time-series for these gauges were not available and their 10-year return period rainfall was retrieved from the literature (published intensity–duration–frequency (IDF) curves). Predictive intervals (0.95 level) are also shown (vertical lines). The diagonal dotted line shows the 1:1 line.

**Figure 6.**CityCat (City Catchment Analysis Tool) flood maps for Vienna using a 70-mm/h storm (base map: Map data—Google, DigitalGlobe).

**Figure 7.**Map of Europe showing the estimates from the regression model for hourly rainfall for a 10-year return period. The locations of the gauges used are shown as black dots.

**Figure 8.**Example of events curves for four cities: BG007C—Vidin (Bulgaria), ES003C—Valencia (Spain), GR006C—Volos (Greece), and UK017C—Cambridge (UK) calculated from the CityCat results. The red vertical dashed line shows the RP10 (hourly rainfall for a 10-year return period) and the dotted blue line shows the corresponding percentage of city flooded.

**Figure 9.**Percentage of city flooded for historical hourly rainfall for a 10-year return period. These percentages are based on the rainfall event and the elevation map used for each city and do not have in consideration adaptation measures already implemented in these cities (like sewer systems) which will be different in different cities.

**Figure 10.**Map of northern Italy with location of cities (

**a**); flood maps of IT510C—Monza (

**b**) and IT511C—Bergamo (

**c**) and the cities’ pluvial flood impact functions—percentage of city flooded (meaning a height of water above 5 cm) per rainfall event (

**d**). These two cities were chosen to exemplify how very similar RP10s can result in considerably different percentages of flooding.

© 2017 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/).

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**MDPI and ACS Style**

Guerreiro, S.B.; Glenis, V.; Dawson, R.J.; Kilsby, C.
Pluvial Flooding in European Cities—A Continental Approach to Urban Flood Modelling. *Water* **2017**, *9*, 296.
https://doi.org/10.3390/w9040296

**AMA Style**

Guerreiro SB, Glenis V, Dawson RJ, Kilsby C.
Pluvial Flooding in European Cities—A Continental Approach to Urban Flood Modelling. *Water*. 2017; 9(4):296.
https://doi.org/10.3390/w9040296

**Chicago/Turabian Style**

Guerreiro, Selma B., Vassilis Glenis, Richard J. Dawson, and Chris Kilsby.
2017. "Pluvial Flooding in European Cities—A Continental Approach to Urban Flood Modelling" *Water* 9, no. 4: 296.
https://doi.org/10.3390/w9040296