A combined remote-sensing and flood-modelling approach is adopted to simulate the occurrence and extent of flooding following a range of design precipitation events under current and expected future climate conditions. To include the influence of spatial variations in urban land cover (changes in ISs), simulations are performed for two different urban configurations corresponding to historical (1984) and present-day (2013–2015) observations of the urban surface.

The data processing and evaluation procedures being carried out are divided into the following three separate types of analyses: (a) urban development analysis, (b) flood modelling and (c) quantification of the influence of urban development and climate change on exposure to flooding (Fig. 1). Initially, we analysed Landsat TM (Landsat 5) (1984) and Landsat OLI (Landsat 8) (2013–2015) imagery to quantify IS fractions at a pixel level of 30 × 30 m for historical and current urban land-cover conditions. Secondly, the outputs of the remote-sensing analyses are combined with soil infiltration data and regionally downscaled estimates of current and expected future precipitation extremes to enable 2-D overland flow simulations and flood-hazard assessments within a flood-modelling framework. The importance of two different assumptions about the temporal development of the drainage system was tested, that is, a “stationary” and an “evolutionary” scenario. In the latter we assume that the design of the drainage system is updated to match the degree of urban development in the period 1984–2014 (2013–2015), as well as the projected intensity of extreme precipitation towards the end of this century (2081–2100) for representative concentration pathways (RCP) RCP 4.5 and RCP 8.5 (Meinshausen et al., 2011), respectively. This is based on the notion that urban drainage systems are often developed in parallel to (planned) urban development and in some cases, are based on the future projections of precipitation from climate models (Chocat et al., 2007; Arnbjerg-Nielsen, 2011; Gregersen et al., 2014). This allows us to examine quantitatively the efficiency of expanding the urban drainage system, which is currently the most common large-scale adaptation measure in protecting urban areas from pluvial flooding. Flood-hazard maps representing the extent and depth of flooding are generated for various combinations of urban land cover, intensities of extreme precipitation (i.e. different return periods) and climate scenarios. High-intensity precipitation events with intensities corresponding to RPs of 10, 20, 50 and 100 years are included in the analysis. Finally, the relative influence of urban development and climate change on exposure to flooding is evaluated through a comparison of multiple flood-hazard maps. The impact of recent urban development is isolated by simulating the occurrence of identical design precipitation events for both historical and current levels of urban IS fractions. Conversely, design precipitation intensities are varied to reflect both current and expected future precipitation intensities, and imperviousness is kept constant while evaluating the expected impacts of different climate change scenarios. A total of 84 combinations of input parameters with regard to degree of imperviousness, climate scenario, climate model projection, precipitation return period, soil water infiltration and drainage system development were simulated for each city. Twelve of these were performed for historical (1984) levels of imperviousness, while an additional 72 were conducted for the present-day (2013–2015) cities. A pairwise cross comparison of multiple flood-hazard maps is carried out to quantify the relative importance of changes in land cover as compared to climate change for the overall exposure to pluvial flooding. All climate-change impact scenarios are simulated with IS corresponding to the present-day situation – for example, reflecting the increased hazards without implementing suitable adaptive measures as part of future urban development.

Since urban land use is generally characterized by a large degree of heterogeneity (roads, buildings, vegetation, water and bare soil within small distances), it is often highly problematic to categorize and map urban structure and development on the desired scale accurately (Dams et al., 2013). For the purpose of this analysis, we define an “inner urban zone” for each city based on the land cover/land use classification in the CORINE 2012 Land Cover (CLC) inventory (CORINE, 2012). The categories that are considered urban in this context are the following: urban fabric, industrial and commercial units, port areas, airports, dump sites, green urban areas, and sport and leisure facilities. In the following, urban development and changes in flood exposure are considered only within this zone.

A number of techniques have been developed to estimate the quantity and location of ISs as a proxy for urban land cover, including traditional field surveys with GPS, manual digitizing from hard copy maps and, more recently, pixel- or feature-based methods using remotely sensed imagery (Weng, 2012). As most urban development occurs at decadal time scales, temporal coverage is a key parameter when monitoring changes to urban land cover. While state-of-the-art high-resolution satellite imagery (less than 5 m) only dates back to the late 1990s and early 2000s, medium-resolution data (e.g. Landsat imagery) offer complete spatial and temporal coverage of global changes to urban land cover during the past 30 to 40 years, from 1984 onwards, at a spatial resolution of 30 m.

In this study, the quantification of spatio-temporal changes in imperviousness is based on a linear relationship between vegetation cover and IS fractions (Fig. 2a, b), which exists in many urban environments (Bauer et al., 2002; Lu et al., 2014; Kaspersen et al., 2015). Linear regression models (Table S1 in the Supplement) developed by Kaspersen et al. (2015) relating the soil-adjusted vegetation index (SAVI) to levels of imperviousness were applied to estimate IS fractions for the four cities both historically and for the present day.

Multiple Landsat images are compiled into maximum value composites (MVCs) to reduce the influence of inter-annual and intra-annual variations in the timing of maximum vegetation cover (Table S2 in Supplement). Based on these composites, the impervious surface (IS) fractions for individual grid cells are calculated as IS=a×mvcSAVI+b, where a and b are regression parameters to be estimated individually for each city.

Initial IS fractions were corrected for pixel values of less than 0 and greater than 100 % to restrict the output from the linear regression models that exceed the range of 0–100 %. Impervious surface fractions are estimated at a spatial resolution of 30 m, which is the same resolution as the short-wave (visual and near-infrared) bands in the Landsat TM and OLI sensors. These are later resampled to a spatial resolution of 25 m, using a nearest neighbour assignment approach to match the resolution of the digital elevation model (DEM) used for overland flow calculations. In order for the reflectance data, and thus the subsequent SAVI images and IS fractions, to be comparable between the Landsat TM (historical images) and OLI (present-day) sensors, the difference in the spectral response function between the two sensors is corrected for by applying conversion factors to each of the individual bands of the TM or the OLI sensor (depending on the regression models) (Flood, 2014). Further information on the different analytical steps involved in the processing of Landsat data may be found in Kaspersen et al. (2015).

Several empirical and theoretical methods have been developed to describe infiltration characteristics during precipitation of varying intensities, these being the key engines controlling overland run-off generation in hydrological models (Tomicic, 2015). Some of the most widely applied methods include Horton's equation, the Green–Ampt method and the Soil Conservation Service method (Horton, 1933; Green and Ampt, 1911; USDA, 1986). All three methods assume that the infiltration rate decreases with time, but they use different equations (and input data) to determine the initial and final losses and the slope of the curve describing the infiltration rate. Even simpler techniques, where infiltration is defined as a constant or proportional loss, may be sufficient to describe the run-off for some applications.

By definition, run-off is the proportion of precipitation that does not infiltrate. Soil infiltration properties, which are primarily controlled by soil texture, topography (slope) and soil structure (granular vs. compact soils), are therefore important (together with the degree of soil sealing) in determining the total amount of surface run-off during precipitation. Similarly, the soil water/moisture content at the onset of precipitation will significantly influence the amount of run-off.

In this study, run-off is calculated for each pixel and each time step in the design storm precipitation time series. We will consider Rt as the net run-off from each pixel at time t. It consists of two components, one arising from impervious areas Rt,IS and the other from non-impervious areas Rt,non-IS. This dual approach is necessitated by the relatively coarse spatial resolution (30 m) of the Landsat imagery and the large heterogeneity of urban areas, which in many cases causes both pervious and ISs to be present within individual grid cells: Rt=Rt,non-IS+Rt,IS. Run-off from the pervious areas is here based on a simplified version of Horton's infiltration model (Horton, 1933). Equation 3 presents Horton's original infiltration model where ft is the infiltration rate at time t, f0 is the initial infiltration capacity, fc is the constant or equilibrium infiltration rate and k is the soil-specific decay constant: ft=fc+f0-fce-kt. Assuming that soils are fully saturated at the onset of the precipitation, which means that the initial loss (f0) is negligible, we can apply the simplified Horton's infiltration equation (Eq. 4), where the infiltration capacity is constant during individual high-intensity precipitation events. For extreme precipitation events, some authors further report the initial loss to be negligible for the total infiltration/run-off (Stone et al., 2008). Adopting this simplifying assumption, we can apply the same soil texture data set across the different cities. In addition, a constant infiltration rate can be used during the entire duration of the modelled precipitation and for all design events. The fact that infiltration capacities are conservative under this assumption may lead run-off from pervious surfaces to be exaggerated in situations where the soils are not saturated at the beginning of the rainfall event. This may also result in slightly conservative estimates of soil sealing (e.g. due to urban development). Due to a large variation in reported initial infiltration capacities, and because such values are difficult to extrapolate to other geographical areas, a constant infiltration rate is preferred in the current study. As all grid cells are quantified by their degree of imperviousness, IS values are included to represent the impervious surface fraction for each pixel, causing a decrease in infiltration as the degree of imperviousness increases. Note that ft=0 for IS = 100 %. This leads to the simplified infiltration model for pervious areas (IS values are specified as percentages): ft=fc(100-IS). From this simplified infiltration model, the run-off contribution from pervious areas, Rt,non-IS, is calculated for each pixel and time step using Eq. 5, where Pt is the precipitation rate and ft the infiltration rate. IS values are the share in percent of each grid cell covered by ISs. Rt,non-IS=(Pt-ft)(1-IS)ifPt>ftand,Rt,non-IS=0ifPt<ft. Run-off from impervious areas is calculated by assuming that there is no infiltration (Jensen, 1990; Butler and Davies, 2011). However, the presence of a drainage system is simulated by removing run-off corresponding to precipitation from a 5-year return period, Pt,RP 5. Hence the contribution to the net run-off from the impervious areas Rt,IS is given by the following: Rt,IS=(Pt-Pt,RP 5)IS. Run-off from grid cells that includes both pervious and impervious areas, Rt,%IS, can be calculated by combining Eqs. 5 and 6 with information on the shares of the two types of surfaces within the individual grid cells: Rt,%IS=(Pt-ft)(1-IS)+(Pt-Pt,RP 5)IS. The runoff from each grid cell is allowed to infiltrate later during the events, i.e. runoff flowing from fully saturated surfaces to areas with excess capacity will infiltrate accordingly. To accommodate this, a net infiltration rate is defined in MIKE 21 allowing for infiltration of both precipitation and runoff at any stage during the events. The average run-off ratio over the entire precipitation event, Rr, can therefore be calculated using Eq. 8, i.e. the share of precipitation which does not infiltrate or is transported via the sewer system. The ratio is calculated prior to the horizontal movements of water and driven by the characteristics of the DEM in the MIKE 21 overland flow model (see Sect. 2.5 for information on the flood modelling). Rr=∑Rt∑Pt In the current study, potential soil infiltration rates are estimated for each city using information on the dominant soil texture and the average slope of the urban area (Fig. 3). Soil-texture data at a spatial resolution of 10 × 10 km from the European Soil Portal are used to provide information on the general soil properties at the city level (JRC, 2016). An average of the four grid cells closest to the cities was converted to a single average soil-texture class. The average slopes were calculated using the EU-DEM, which was also used for the overland flow model. Data from the United States Department of Agriculture (USDA) on soil-type specific infiltration are used as the basis for estimating the potential infiltration rates, as well as to highlight the variations in soil textures and topography between the different cities (USDA, 2016) (Fig. 3). High and low values of potential infiltration are included to examine the sensitivity of the modelling approach to variations in this parameter and to provide a quantitative measure of uncertainty to be used in the ensuing analyses of exposure to pluvial flooding.

Climate change is expected to increase the intensity and frequency of precipitation extremes in both the short and long terms for most regions globally, including Europe (Fowler and Hennessy, 1995; Larsen et al., 2009; Field et al., 2012; Sunyer et al., 2015a). Climate projections generally suggest that the most severe extremes with the shortest (sub-daily) durations are likely to be enhanced more than less severe (daily) extremes (Larsen et al., 2009; Arnbjerg-Nielsen, 2012). In this analysis, we consider two different climate scenarios: RCP 4.5 and RCP 8.5. The RCP 4.5 scenario describes a mitigated future with increases in near-surface air temperatures of 1.8 ∘C (1.1–2.6 ∘C) towards the year 2100 compared to the present-day reference period, while the RCP 8.5 scenario represents a world where the increased radiative forcing corresponds to an increase of 3.7 ∘C (2.6–4.8 ∘C) in 2100 (Intergovernmental Panel on Climate Change, 2014).

The impact of climate change on extreme precipitation intensities is represented using a change factor (CF) methodology, i.e. by estimating the relative difference between climate model outputs (extreme precipitation intensities) for future and present-day conditions respectively (Willems et al., 2012; Sunyer et al., 2015b). Extreme value analyses are carried out for both present-day (1986–2005) and future (2081–2100) time slices for maximum hourly precipitation (within one day) to estimate the intensities for return periods of 5 to 100 years (RP 5, RP 10, RP 20, RP 50 and RP 100). The extreme value series are derived from the two time slices using a partial duration series (PDS) based on an average of three extreme events per year, following Sunyer et al. (2015b). A generalized Pareto distribution (GPD) is then fitted to the derived extreme value series to estimate the intensities for different return periods. In contrast to Sunyer et al. (2015a), the shape parameter in the GPD is not estimated using a regionalization approach but calculated individually for each grid cell. This potentially causes a large diversity in resulting CFs between neighbouring grid cells. The CFs are calculated for each return period (RP 5–RP 100) and applied to the statistic of present-day design precipitation events to obtain the characteristics of future precipitation. The same CF is used for all durations in the intensity duration frequency (IDF) curves.

An ensemble of 10 regional climate projections extracted from the CORDEX archive are used to estimate different CFs (Giorgi et al., 2009). All the simulations were carried out by the Swedish Meteorological and Hydrological Institute (SMHI) and use SMHI's regional climate model RCA4 to downscale climate projections from 10 different general circulation models (GCMs) to a horizontal resolution of 50 km. Three different CFs are estimated for each city and climate scenario: a CF corresponding to the ensemble mean, as well as CFs corresponding to the 10th and 90th percentiles (based on the 10 simulations; 80 % of the models are within the 10th and 90th percentile) to represent some of the model uncertainty. In all cases, the CFs are calculated based on the nine grid cells located closest to the four cities. This is done to avoid selecting individual pixels with abnormally low or high values, which could be present because of the spatially heterogeneous shape parameter in the GPD.

Overland flooding can occur as a consequence of extreme precipitation when the urban drainage system is surcharging or when soil infiltration and storage capacities are exceeded. Water can pond on the surface or flow in preferential flow paths along streets or between buildings depending on the local topography. When modelling overland flooding, several modelling concepts are available. Some methods integrate 1-D modelling of flow in the sewage system with a 1-D description of overland flow (Maksimović et al., 2009). Others use modified software originally intended for estuarine and coastal modelling to interact with the drainage system, e.g. MIKE FLOOD by DHI or TUFLOW (MIKE Powered by DHI, 2016; BMT Group Ltd., 2016). The pros and cons of these methods have been widely discussed (Mark et al., 2004; Leandro et al., 2009; Obermayer et al., 2010), and the choice of method is highly dependent on the aim of the study: e.g. 1-D solutions are fast but offer a poor approximation of complex (non-unidirectional) flows.

In this study we use the overland flow model in MIKE 21 (MIKE powered by DHI, 2016), which computes 2-D overland flows in response to given extreme precipitation input based on, for example, terrain data, including a DEM. The main data input to MIKE 21 for the analyses conducted in this study are time series of precipitation and infiltration rates for the geographical locations being examined, along with a DEM for routing the excess surface water after the onset of precipitation. This modelling approach does not include an explicit representation of subsurface flows nor of the urban drainage system. Instead, the drainage capacity of the pipes is included by modifying the precipitation input over the entire urban area by assuming a general maximum pipe capacity based on precipitation intensities (Chow et al., 1988; Henonin et al., 2013). Here the maximum drainage capacities are assumed to correspond to precipitation with a return period of five years (RP 5). The intensities of precipitation events with return periods exceeding this level are reduced accordingly for the ISs to reflect this assumption (see Eq. 6 in Sect. 2.3). The result gives the run-off generated at a pixel level. This is then routed between pixels to allow for further losses if downstream pixels have surplus infiltration capacity. Effectively this means that the run-off ratio prior to horizontal flows is calculated for each grid cell for every time step (minutes) using Eq. 7.

Evidently, by neglecting the exact location and characteristics of the urban drainage system, errors are introduced which particularly influence the results with respect to the extent and location of flooding derived from the model. However, it is assumed that these effects will be localized and that their significance will decrease for more extreme precipitation events (Paludan et al., 2011).

IDF curves are used to construct time series of Chicago design storms for 5-, 10-, 20-, 50- and 100-year RPs (Gregersen et al., 2014; BMLFUW, 2016; Coste and Loudet, 1987). The IDF curves are derived from historical measurements of precipitation from weather stations located in (or in the surrounding areas of) each of the cities and are considered to be representative of precipitation characteristics in both 1984 and 2014. The duration of a precipitation event is set to 4 h in all our simulations to ensure that the results are comparable in both time and space. Figure 4 shows maximum 1 h intensity and total precipitation for the different precipitation events and cities under present-day and future climatic conditions. The EU-DEM, which offers elevation estimates over the European continent at a 25 m spatial resolution, is used as the basis for calculating surface water flows after the onset of precipitation (EEA, 2013). Soil water infiltration rates are calculated for each grid cell by combining IS fractions with information on soil textures and the average slope at the city level (see Sect. 2.3 for more details).

The results of the urban development analyses show that the four cities have experienced increasing imperviousness throughout the past 30 years, which is consistent with the predominant trend towards urbanization worldwide, with absolute changes ranging from 6.6 % points in Nice to 11.6  % points in Strasbourg (Table 1). From visual inspection we find that the increases in ISs are primarily driven by cities expanding into non-urban areas. However, there is also a tendency towards the intensification of existing urban land cover in all four cities. Detailed quantitative analyses of the locations of change are highly relevant for other applications, including risk assessment, but they lie outside the scope of this paper.

The results of the extreme value analysis indicate a general increase in the intensity of extreme precipitation towards the end of the 21st century for both the RCP 4.5 and RCP 8.5 scenarios, with CFs of approximately 1–1.6 (Table 2). Average CFs are found to vary less (approximately 1.1–1.3 for RCP 4.5 and 1.2–1.3 for RCP 8.5), leading to expected intensity increases of 10–30 %. As expected, the average CFs are found to increase the most for the most extreme events (RP 100), and in the majority of cases (except for Nice) those for RCP 8.5 are found to be higher than for RCP 4.5. In addition, we observe a large variation in CFs when using the different GCMs, as the 90th percentile and 10th percentile values differ considerably from the ensemble mean. For Vienna and Odense, few models project a decrease in the intensity of extreme precipitation (CFs < 1) for the RCP 4.5 scenario. The variation in CFs between different models confirms the findings of previous research efforts (e.g. Hawkins and Sutton, 2011) that model uncertainty remains a primary source of uncertainty in precipitation projections.

Figure 5 shows the run-off ratios for the different cities in 1984 and 2014 (2013–2015) divided into the proportions for impervious (Rt,IS) and pervious areas (Rt,non-IS). As expected, the total run-off ratio is highest for the most extreme events (i.e. RP 100) and decreases with the intensity of the precipitation. Regional differences in precipitation characteristics, degree of imperviousness and soil infiltration properties cause total run-off ratios to vary considerably between the different cities, with present-day run-off ratios ranging from 26–44 % for Odense to 52–79 % for Nice. In general we find that Rt,non-IS accounts for the largest part of the total run-off, although with differences between different locations and events. Some important observations should be noted. First, we see that run-off from pervious areas (Rt,non-IS) is most important for the smallest events, and vice versa for impervious areas (Rt,IS). Secondly, regional differences in imperviousness and especially soil infiltration causes Rt,non-IS to dominate run-off for Nice, while the shares are comparable for Odense, Vienna and Strasbourg. Finally, an increase in run-off ratios during 1984–2014 can be identified for all four cities consistent with the increase in the IS fractions also found in this period (Table 1). Not surprisingly, we find that Rt,IS increased and Rt,non-IS decreased during 1984–2014 (2013–2015). Overall we find the amount of run-off from pervious urban areas to be considerable, suggesting that in many cases future precipitation intensities lead to higher amounts of surface run-off than can be infiltrated into the soils.

The primary outputs from the flood-model simulations are in the form of flood-hazard maps showing the maximum flood depth and extent for each individual simulation (Fig. 6). We will quantify the impacts of urban development and climate change through a cross comparison of multiple flood-hazard maps. The results of the combined remote-sensing and flood-modelling analyses (Fig. 7) depict a clear pattern of increased flooding for events with longer return periods and for events simulated with elevated levels of imperviousness, the latter due to urban development during 1984–2014. Flooding is defined here as occurring when maximum surface water depths exceed 10 cm. Similarly, the effects of climate change are found to increase pluvial flooding substantially for all return periods and for both climate scenarios, with RCP 8.5 having a larger impact in most cases. Only in the case of Nice are the results for RCP 4.5 and RCP 8.5 comparable. In all of the following figures, we show explicitly the results of changing the ISs and the simulated effect of climate change, and hence error bars representing uncertainties in the estimated impacts of urban development and climate change, respectively, are calculated based on variations in the potential soil infiltration rates and climate factors for each of the four cities. The range of uncertainties related to the projection of future precipitation intensities are found to be largely comparable to those of soil infiltration estimates (Fig. 7). However, there is a tendency towards a greater influence of uncertainties on soil infiltration for the smallest events and vice versa for precipitation with the highest intensities. In addition, in all cases except for Nice we observe that the uncertainty increases with the intensity of precipitation, and the error bars widen when we move towards the most extreme events (Fig. 7). There are notable differences in how severely the urban areas are impacted by flooding depending on their geographical location, climate conditions, soil properties and topographies. For Odense, the observed share of total area prone to pluvial flooding approximates to 5 % for the most severe events while approaching 10 % for Vienna and Strasbourg and 20 % for Nice. The results of the flood-model simulations where the drainage system is updated to follow urban development (2014d in Fig. 7) and climate change (RCP 45d and RCP 85d in Fig. 7) suggest several important implications. First, developing the urban drainage system in relation to increases in imperviousness (i.e. due to urban development) appears to compensate fully for the increase in flooding caused by the additional run-off from sealed surfaces. In contrast, updating the drainage system according to increases in precipitation intensities (i.e. caused by climate change) only marginally reduce flooding for the largest events, primarily because the increased capacity is small when compared to both the current and future changes in the intensity of these very severe events.

In comparing the absolute changes in exposure to flooding caused by urban development and projected climate change respectively, we find that the relative influence of these two drivers varies considerably between the different cities (Fig. 8). To compare the influence of 30 years of urban development in 1984–2014 with climate change in a 100-year perspective (1986–2005 to 2081–2100) the results are normalized and shown in terms of “change per year”. For Odense, Vienna and Strasbourg, the influence of recent urbanization is comparable to that of increased precipitation extremes under the RCP 8.5 (Odense) and RCP 4.5 scenarios (Vienna and Strasbourg), whereas climate change is the most important driver for Nice. This is consistent with the variations in the properties of soil infiltration between the four cities (Fig. 3). The relative importance of climate change increases in all cases when moving towards the most extreme events (i.e. RP 50 and RP 100). We observe a large uncertainty related to the climate change projections, especially for the most extreme events, with a few models even projecting a decrease in precipitation intensities and in overall flood exposure for Vienna and Odense (error bars below 0 for RP 20–RP 100). For Odense, Vienna and Strasbourg, we find that the absolute changes in pluvial flooding increase with the intensity of the events for both urban development and climate change, whereas the same trend is not observed for Nice. This difference could be explained by the presence of extensive topography (average slope of 8 %) within Nice, causing surface waters to flow over greater distances. As a result, changes to ISs that occur outside the urban zone may to some degree influence the simulated flooding within this area. Also, the findings imply that continued urban development over a 100-year period could potentially facilitate an increase in flooded areas corresponding to approximately 1–2 % of the total urban area (0.01 % year-1 – horizontal lines), increasing to 5 % for some cities (0.05 % year-1 – horizontal lines) as a consequence of high-end climate change (RCP 8.5). The results presented in Fig. 8 confirm that updating the drainage system in relation to increases in imperviousness is an efficient strategy to mitigate the adverse effect of soil sealing (no increase in flooding for UDd in Fig. 8). Conversely, developing the drainage system according to the impact of climate change on precipitation intensities only marginally reduces flooding (RCP 45d and RCP 85d in Fig. 8).

Lastly, we have assessed the sensitivity of our results to the selected threshold (10 cm), which is often defined as the surface water depth where damage begins to occur. The results are normalized to indicate the average change in flooded area every time absolute imperviousness increases by 1 % on the city scale. We explore the influence of urban development on flood exposure for four different thresholds, ranging from 1 to 20 cm (Fig. 9). First, we observe that the estimated effect of urban development increases more for higher thresholds (20 cm) as compared to lower flood depths. This relationship is generally present for all cities and precipitation events. A small variation in flood response is observed in most cases, confirming that the findings are only marginally sensitive to the choice of flood threshold. The large increase in flooded area for the 20 cm threshold (> 10 %) in the case of RP 10 for Odense is due to a very small area being affected by flooding at high flood depths for this event, and thus a high predisposition for experiencing a significant relative change in the case of increasing imperviousness. Secondly, we find that the influence of urban development decreases rapidly for all flood thresholds as we move towards the most extreme precipitation events. In addition, we find that the relative importance of urban development and climate change is unaffected by variations in flood thresholds, indicating that our findings are robust to the selection of this parameter.