Flood hazard is represented with a set of inundation maps taken from Alfieri et al. (2015), with a recent update by Dottori et al. (2021a), which cover most of the European domain at a grid resolution of 100 m. We provide here a brief description of the inundation maps, noting that no new work was done in the present study to modify these data. The dataset consists of six raster maps of inundation depth corresponding to flood return periods of 10, 20, 50, 100, 200, and 500 years, assuming no flood protection in place (flood protection is considered in the risk assessment step, Fig. S1). These maps represent the inundation depth and extent in all river sections with an upstream area larger than 500 km2. They do not include the effect of pluvial and coastal flooding. They also do not include river and flash flooding in the most upstream catchments, with an upstream area smaller than 500 km2. Inundation maps were produced by merging the results of thousands of 2D hydraulic simulations along the European river network, based on the hydrodynamic model LISFLOOD-FP (Bates et al., 2010). The input hydrographs of flood simulations were defined consistently with the peak discharges and flow duration curves of a 25-year-long simulation taken from the European Flood Awareness System (Thielen et al., 2009) and based on the hydrological model LISFLOOD (Van der Knijff et al., 2010). Additional details on the methods and models used to produce the maps are described in Alfieri et al. (2014, 2015) and in Dottori et al. (2021a), together with some skill assessment of the simulated maps versus official flood maps for different European countries and river basins.

In the grid-based approach, two different land cover maps are used: CORINE 2012 (version 18.5) and LUISA (version 2). They indicate the dominant land use type in each 100×100 m2 grid cell. The CORINE land cover map (Büttner et al., 2014) and its predecessors have been used in many European flood risk studies (e.g. Alfieri et al., 2018; Lugeri et al., 2010; Serinaldi and Kilsby, 2017). CORINE, however, overlooks most of the road network (Rosina et al., 2018) because even large motorways typically cover less than 50 % of a 100×100 m2 grid cell (see Fig. S2). Therefore, roads have been manually added to the land cover map in some studies (e.g. Jongman et al., 2012; cf. Meneses et al., 2019). The LUISA land cover map is a spatial and thematic refinement of CORINE 2012 using various additional data sources, such as rasterized-object datasets (Rosina et al., 2018). Therefore, motorways and trunk roads that were absent in CORINE are now present in LUISA as coarse grid representations of the original lines. However, due to the 100×100 m2 resolution of the grid, the actual road width is overestimated in most areas (Fig. S2).

To correct for the underrepresentation of infrastructural land use (and other land use types) in CORINE and LUISA, they assume for each land use class some percentage of infrastructure (Tables S1 and S2). This assumption follows from Huizinga's suggestion (2007, p. 22 of chap. 2) to map the damage functions to CORINE using a cross-tabulation by the EEA (2006), which then became the default implementation method. To enable a comparison with the object-based approach, we only consider the percentage of infrastructure per land use class, whereas the contributions of the other damage curves are ignored (Tables S1 and S2). An implication of these percentages is that, although motorways and trunk roads are mostly missing in CORINE, damage for (local) roads in urban and industrial areas (amongst others) is still calculated, albeit without any explicit spatial reference to the actual road position but rather based on their average presence in these land use types. Also, note that in the land cover category “road and rail networks and associated land”, only a 27 % infrastructural land use is assumed (Tables S1 and S2), which to some extent corrects the overestimation of the actual road widths in LUISA. In summary, the grid-based land cover category “road and rail networks and associated land” roughly corresponds to the object-based road types “motorway” and “trunk road”, and the infrastructure percentages in the other grid-based land cover categories roughly correspond to the object-based road types “primary”, “secondary”, “tertiary”, and “other road”.

This section details the set-up of the object-based model (Sect. 2.3.1) and the application of the Huizinga reference curve (Sect. 2.3.2) in the object-based approach.

For hydrological reasons, the analysis includes the 27 member states of the European Union (EU) (excluding Cyprus and Malta); the United Kingdom and the European Free Trade Association countries of Liechtenstein, Norway, and Switzerland (not Iceland); and the (potential) candidate countries of Albania, Montenegro, North Macedonia, and Serbia (not Turkey). We excluded the EU's remote overseas areas such as the Azores, the Canary Islands, and Guadeloupe as well as small islands.

The new damage curves cover several aspects of the direct tangible costs. It includes clean-up costs, resurfacing of top and deeper asphalt layers, repairs of road embankments, and where applicable also the repair of electronic signalling and lighting. It includes neither structural damage to bridges and tunnels nor emergency response costs such as the placement of sand bags or signposting of traffic diversions.

To construct the new damage curves, multiple steps are taken. First, we compile an overview of road construction costs, from which we derive a cost bandwidth per OSM road type (Tables S5–S7). Expert judgement is used to construct a coherent system of absolute cost values, ratios between the different road types, and a scale factor for roads with more or less than the default number of lanes, while accounting for differences in national real GDP per capita. Second, an inventory is created consisting of road clean-up, repair, and reconstruction costs expressed as percentages of the road construction costs of the first step (Table S8). Third, repair activities are linked to the road repairs needed following a river flood, derived from the literature and photo imagery of river floods in Europe. Fourth, the repair activities and corresponding damage percentages (percentage of construction costs) are fitted to the depth–damage curves. These depth–damage curves with corresponding narratives are verified in expert workshops with flood risk and transport modelling experts and experts from the Dutch road operator (see Acknowledgements). An overview of the damage curves and supporting narratives (reasoning from the road construction and maintenance costs presented below) is given in Figs. S3 and S4 and Tables S9 and S10.

The damage estimates come with considerable uncertainty, which primarily originates from the bandwidth of the construction costs and the space between the upper and lower estimate of the flow velocity. This uncertainty space is sampled to obtain (1) a deterministic estimate of the expected annual damage, as well as (2) a probability distribution around this estimate. Motorways and trunk roads with street lighting tags in OSM are assumed to have sophisticated road accessories; damage curves C1 and C2 are applied (Fig. 3) in combination with a construction cost sample from 50 % to 100 % of the range (Table 1, note c). In the probabilistic sample, per road segment, a random choice is made between the 50th, 75th, and 100th percentiles of the range, and in the deterministic sample, the 75th percentile is used for each segment. For motorway and trunk roads without street lighting tags, simple road designs are assumed; damage curves C3 and C4 are applied in combination with a random choice from the 0th, 25th, and 50th percentiles of the range in the probabilistic and the 25th percentile in the deterministic sample. For all other road types, for each road segment a random choice is made from the entire construction cost range in the probabilistic approach and 50 % in the deterministic sample. To account for the uncertainty in flow velocity in the probabilistic approach, we quasi-randomly sample 1000 z scores assuming a normal distribution with the low-flow curve at -2 standard deviations and the max flow curve at +2 standard deviations from the mean flow damage. This assumption was made because of the lack of reference data. This results in 1000 estimates of the damage per segment (1 for each z score). Per z score, the damage of all road segments is aggregated to construct Fig. 5d. In the deterministic sample, the average of the minimum and maximum flow curves is taken.

As a reference, we compare our model to road repair data reported by the Bavarian government (Table S17). On 4 and 5 June 2013, an approximately 1:100-year flood caused a dike breach near the confluence of the Danube River and its tributary, the Isar River, close to the town of Deggendorf. The inundated area spanned the cloverleaf junction of the motorways A92 and A3, as well as 6.6 km of the A3 and 2.8 km of the A92 (Fig. 8). Both roads have 2×2 lanes + 2 safety lanes and are 30 and 26 m wide, respectively. They are accurately represented as 2×2 motorways in OSM. The roads are located on embankments and have a fairly simple road design, i.e. no lighting or electronic signalling. We estimate water depths and damage to these roads and surrounding area from reports (Rogowsky, 2016), videos, photos, and satellite imagery (Table S17). We then mask the 1:10-year flood hazard map (which better resembled the reported inundation than the 1:100-year flood map) over the extent of the observed inundation and calculate the damage using the object-based model. This offers a partial validation of the damage curves for motorways with a simple design; more data are needed to validate the entire methodology.

The grid-based approach estimates the total expected annual damage (EAD) for the CORINE and LUISA land cover map at EUR 536 million and 301 million per year, respectively (Fig. 5a), whereas only EUR 228 million per year is estimated by the object-based approach (Fig. 5b). Both approaches use the same hazard data, and both use the Huizinga vulnerability curve so that the differences are mainly attributable to the exposure data. A surprising observation concerning the exposure data is the large amount of infrastructural damage (65 %) attributed to the CORINE land cover type “water”. This peculiarity originates from Huizinga's suggestion (Huizinga, 2007, p. 2-22) to map the damage functions to CORINE using a land cover cross-tabulation from the European Environment Agency (EEA, 2006, cf. Table S1). The EEA shows that some cells that contain “waterbodies” in CORINE contain infrastructure in a reference map. Consequently, some percentage of infrastructure is assumed for all CORINE waterbodies, for which large damage is calculated, because sometimes large inundation depths are modelled for waterbodies. This peculiarity was manually removed in the model implementation of LUISA (Table S2), such as it was in the recent PESETA IV (Projection of Economic impacts of climate change in Sectors of the European Union based on bottom-up Analysis) study (Dottori et al., 2020). Another difference is the strong increase in damage to “road and rail networks and associated land”, from EUR 15 million per year in CORINE to EUR 144 million per year in LUISA, resulting from integrating the motorway network into the LUISA land cover grid (Rosina et al., 2018).

It should be noted that the object-based approach only reports damage to road infrastructure, whereas the grid-based approach also reports damage to rail infrastructure. However, the area occupied by the railway network is usually limited compared to the road network. Moreover, since the very narrow railway line elements have not been explicitly integrated in the LUISA grid (Rosina et al., 2018), they are mostly overseen, and hence their contribution to the LUISA damage is small. Therefore, we assume that the LUISA class “road and rail networks and associated land” corresponds to the motorway network and that the other LUISA land use classes correspond to the underlying road network. Accordingly, in the grid-based approach, motorways contribute 48 % and the underlying road network contributes 52 % to the total road infrastructure damage (Fig. 5a). In the object-based approach, motorways contribute 9 %; trunk roads contribute 7 %; and the underlying road network contributes 85 % (Fig. 5b, percentages rounded). This relatively minor contribution of motorways in the object-based approach results from the way in which the Huizinga curve is implemented: damage per square metre is multiplied by the road width. Motorways, however, are relatively more expensive than is to be expected from merely their width. Therefore, the damage to motorways is underestimated in Fig. 5b. The other way around, the other road types are less expensive than is to be expected from their width. Therefore, damage to the underlying road network is overestimated in Fig. 5b. This emphasizes the need for damage curves that correct for road characteristics beyond only the road width, as used in the next section.

With the new depth–damage curves the EAD is estimated at EUR 231 million per year (Fig. 5c), which is again below the grid-based LUISA estimate (EUR 301 million per year, Fig. 5a). The total damage with the new curves (EUR 231 million per year, Fig. 5c) is somewhat higher than the object-based implementation of the Huizinga damage curve (EUR 216 million per year, Fig. 5b), and the contribution per road type is substantially different. Notably, the contribution of motorways (26 %) has become much larger. The other contributions are 7 % for trunk, 22 % for primary, 15 % for secondary, 7 % for tertiary, and 23 % for other roads (Fig. 5c).

The object-based approach also gives insight into the uncertainty surrounding the deterministic estimate of EUR 231 million per year. The mean of the stochastically generated samples is EUR 229 million per year, and the median is EUR 230 million per year (Fig. 5d), which approximates the deterministic estimate well. The interquartile range (containing 50 % of the samples) is EUR 172 million to 284 million per year. The lower tail (Fig. 5d) is truncated because outliers in low-flow velocity cannot cause damage below zero, whereas at the high tail high-flow velocities cause large damage.

Figure 6a shows how the object-based risk (deterministic estimate) is geographically spread over Europe. Germany, France, and Italy are exposed to the highest flood risk (EUR 45 million, 43 million, and 23 million per year, respectively; see Figs. S5 and S6). In these countries, the risk is concentrated around the rivers that rise in the Alps and then flow through regions with dense road networks, such as the Danube and Rhine flowing through southern Germany, the Rhone flowing through south-eastern France, and the Po flowing through northern Italy. These three countries have additional flood hotspots in the Elbe River, Garonne River, and Tiber River basins, respectively. Of the top 10 NUTS 2 regions with the largest damage, 5 are in France, and 2 are in Italy (Table S16).

Another concentration of high flood risk is found on the Scandinavian Peninsula. This can be partly explained by the high GDP per capita and the relatively large NUTS regions. However, also when correcting for these factors, we find that the sparse road networks in these countries indeed have the potential to be inundated with large water depths, causing large damage. The regions Pohjois-ja Itä-Suomi (Finland) and Hedmark og Oppland (Norway) are in the top 10 of the NUTS 2 regions with the largest risk (Table S16).

Because the value of the exposed assets is scaled to the national GDP per capita, the risk is relatively high in high-income countries. If the risk is expressed as share of the GDP per NUTS 3 region, other high-risk regions emerge: the central European countries of the Czech Republic, Slovakia, and Hungary and also Croatia and Latvia (Fig. 6b). Although these countries contribute little to the total damage in Europe, the relative impact of road disruptions in these countries is large. Note that these regional (NUTS 3) risk aggregations are influenced by the size of the regions in the NUTS classification; smaller regions show relatively smaller risk in Fig. 6. Therefore, aggregation at different levels reveals slightly different spatial patterns (Fig. S6, Tables S14–S16).

The flood risk of all motorways and trunks in the EU road network is now presented on a high-resolution map (see Fig. S8). To illustrate how this map can be used to identify flood hotspots in the EU road network, we highlight three notable regions (Fig. 7).

The Netherlands stands out in Fig. 7a because many of its motorways have the potential to be inundated, although at the same time, the aggregated flood risk is among the lowest of the countries in Europe (Fig. S5). This can be explained by the very high river flood protection standards in the country (return period of 1:1000 years or higher in most places), which make the likelihood of flood events very small. However, if dikes did breach, many roads would be inundated with large water depths, causing large damage. Also, this could severely hinder the possibilities for evacuation, especially in the centre of the country.

The Alps are identified as a high-risk region. For example, in France, the model predicts large EAD for the A41 from Grenoble to Chambéry and the A43 from Chambéry to Saint-Jean-de-Maurienne (Fig. 7b). Both motorways are located in narrow flood plain valleys along rivers. This exposes them to large flood hazards, which is also recognized in local flood risk studies (e.g. Strappazzon and Pierlot, 2017). Similar exposure of motorways can be found in other Alpine regions, such as the A9 from Sion to Montreux (Switzerland), the A22 from Lake Garda to Bolzano (Italy), and the A12 from Landeck via Innsbruck to Kufstein (Austria).

In the Balkans, the E70 motorway from Zagreb (Croatia) to Belgrade (Serbia) is subject to large flood risk (Fig. 7c). This road follows the course of the Sava River for about 400 km. The flood plains of the Sava River were struck by a large flood in 2014 (International Sava River Basin Commission, 2014). According to our model, the flood waters could hit the motorway at several locations. For some road segments the EAD is notably high. This is primarily the result of a large flood hazard rather than a large value of exposed assets because the GDP of Croatia and Serbia is below the average of the (former) EU-28.

As described in Sect. 2.4, the Deggendorf flood event is used as a reference for the damage estimates of the model (Fig. 8). During the flood event, the pavement of the A3 motorway was submerged over 6.6 km because the road embankment was lower than the water level in the surrounding area, resulting in water depth of 0.5 m above the road pavement, on average. After the flood, the A3 was covered with debris (a gas tank, hay bags covered in plastic, wooden logs, plastic bags, and pallets), sand, and mud, requiring a major clean-up. At the cloverleaf, there were rifts in the asphalt, requiring small asphalt works. Small strips of asphalt (but not the entire road) were milled and resurfaced. The embankment of the A92 was higher than the embankment of the A3 so that its pavement remained dry over the entire 2.8 km, except for a small depression at an underpass with a local road (see Table S17).

The Bavarian State Ministry for Housing, Construction and Transport was granted EUR 3.8 million for rehabilitating the Deggendorf cloverleaf junction (Table S17). The model calculates damage of EUR 3.4 million for the low-flow curve (C3) and EUR 28.6 million for the high-flow curve (C4). The video imagery and the limited asphalt damage (Table S17) suggest that flow velocities were relatively low so that one expects the damage more towards our low-flow than the high-flow damage curve, which is indeed the case.

When interpreting these results, one should consider that German motorways are relatively cheap compared to those in other EU countries (after scaling for GDP, see Table S6), which could imply that rehabilitation works are also relatively cheap (cf. ECA, 2013). Additionally, most damage seems to have occurred to the cloverleaf itself, rather than the straight sections of the two highways. Finally, it is likely that the road owner made additional repair costs beyond what was funded using the EUR 3.8 million grant.