The German National Meteorological Service (DWD) provides with KOSTRA 2020 a German-wide grid (5 km × 5 km) of statistical heavy rain events with different durations (5 min to 7 d) and return periods (1–100 years), based on the period 1951–2020. Recently, the German Federal Agency for Cartography and Geodesy has released maps of simulated inundation (depth, extent, flow velocity) as a response to two heavy rainfall scenarios (one with a return period of 100 years and one extreme scenario of 100 mmh-1), applying a simplified hydraulic methodology . However, it is important to be aware that those simulations ignore any storm runoff reduction or retention, e.g. due to inflow into the urban drainage system (gully inflow) or due to infiltration into unsealed surfaces, such as parks, green areas, green infrastructure or pervious sealing. That means, these maps show effects of urban surface hydraulics only, but not for hydrological processes, such as infiltration or urban water retention.

In order to cover a wide range of heavy rain intensities (Table ), this study includes synthetic rain events with a duration of one hour, based on the KOSTRA 2020 return periods of 1, 5, 10, 20, 50 and 100 years. As the study area is located in KOSTRA tile number 105190, this corresponds to rain totals of 14.8–48.9 mm for the investigated return periods . Additionally, as suggested by , an extreme event with a rain total of 100 mm was included.

The temporal resolution of the synthetic rain events is 5 min, following Euler-II distribution, as it is established in Germany for the design of drainage systems . For example, the 100 year event has a rain total of 48.9 mm, with the following 12 consecutive 5 min rain totals: 3.3, 4.5, 7.4, 20.7, 2.3, 2.3, 1.6, 1.6, 1.6, 1.2, 1.2 and 1.2 mm. The maximum 5 min intensity of the selected rain events ranges from 75.6 to 248.4 mmh-1 for the KOSTRA events, for the extreme event it is 508.0 mmh-1.

The conventional stormwater management scenario (hereafter “gully” scenario) is designed following the recommendations for drainage systems of DIN EN 752-2. Here, the capacity of drainage systems in urban or residential areas is designed to fully meet a precipitation event with a return period of 5 years and a duration of 15 min. As our study area is located in the highly urbanised city centre of Berlin, we define gullies with a corresponding inflow capacity of 16 mm at the beginning of the rain event on all roads in the study area.

This simplification does not allow to represent processes such as sewer overflow to the surface. We opted for this approach nevertheless, as the detailed sewer network of our study area is not publicly available and the sewer system is not the focus of this study.

The assessed GI scenarios consist of single and combined GI measures, including three types of infiltration-based GI (see for more details on the GI measures):

Bioretention system (BR): A shallow depression that collects surface runoff from surrounding impervious areas. The soil layer is covered with plants over a storage layer made of sand or gravel to obtain an elevated hydraulic conductivity. Optionally, at the bottom, there is an underdrain to the sewer system. BRs help to reduce runoff and remove pollutants.

For the maximum GI scenarios, potential GI extents were defined as follows: BR on 10 % of the study area, including roads and residential subcatchments after subtracting the area covered by buildings (BRmax), GR on all buildings (GRmax) and PP on 50 % of the roads (PPmax). Based on these definitions, the medium GI scenarios were defined as half of the maximum extents (BRmed, GRmed and PPmed). Additionally, two combined scenarios were defined, GRmax + PPmed and BRmax + GRmax. For both of them, GRmax was combined with one of the other GI types because there is no spatial overlap between them.

Table  provides an overview of the retention scenario definitions and the respective percentage of the study area that is impervious, pervious or covered by GI. The base and gully scenarios include no GI, with an impervious area of 55.3 % and a pervious area of 44.7 %. For the GI scenarios, the GI area is subtracted from the impervious and/or pervious areas, resulting in impervious areas ranging from 20.0 %–54.1 %, pervious areas of 40.4 %–44.7 % and GI areas of 3.4 %–36.0 %.

The GI types BR, GR and PP are implemented in SWMM as “LID Controls”, i.e., “Bio-Retention Cell”, “Green Roof” and “Permeable Pavement”. For the required input parameters, we extracted typical design parameters and soil hydraulic parameters from . As loamy sand is common in Berlin, we used the soil hydraulic parameters from this soil type. Table  shows the resulting set of parameters.

The unit area of a certain GI type is replicated within each subcatchment until reaching the defined spatial extent. In the case of GR and PP, the surface width per unit is used to define how the overland flow leaves the GI unit. For BR, instead, the surface width is zero as the runoff just spills over the berm. BR and PP receive all runoff from impervious and pervious areas of the same subcatchment, while GR can receive only the direct rainfall.

The rainfall-runoff modelling was conducted using the dynamic hydrologic-hydraulic model SWMM. For runoff simulation, the study area was divided into subcatchments, each with its own pervious and impervious fraction . Evapotranspiration was not included, as it is negligible when considering single events.

Based on the land use dataset, the study area was divided into 230 subcatchments, with two subcatchment types: roads, covering 25 % of the study area, and residential, covering the remaining 75 %. The residential subcatchments summarise building blocks, including backyards and parks, instead of considering each building separately. The subcatchments' average slope was calculated from the DEM.

For infiltration, the SCS-Curve Number (CN) method was used. CNs for each subcatchment were assigned by combining the land use dataset with the soil map, resulting in CNs ranging from 61–98, with an area-weighted mean CN of 91 (Fig. ). A higher CN indicates higher impermeability and less infiltration.

Different from the remaining study area, the GI modules use the Green-Ampt method. For each subcatchment, the runoff generated by the impervious area is routed to the pervious area, and what remains is routed to the GI, when there is BR or PP. As the sewer system is not publicly available, the gully water absorption was represented by increasing the depression storage of the roads.

From the simulation results, the runoff hydrographs for each subcatchment were forwarded as input to the hydrodynamic model for subsequent modelling of the surface flood dynamics.

For the hydrodynamic simulations, the open source TELEMAC system is used. TELEMAC incorporates a 2D module that applies a finite element scheme with a semi-implicit solver on a triangulated mesh to solve the Shallow Water Equations .

The hydrodynamic model has an unstructured mesh with a resolution of 2 m which results in a total of approximately 768 000 nodes and 1 458 000 elements. Buildings are represented as holes in the model. The roughness coefficients are derived from the land use data using the guidelines from . The topography is interpolated from the DEM.

The output hydrographs from the hydrologic model are represented in the hydrodynamic model by single nodal inflows and serve as the only input into the hydrodynamic model. The river Spree and the Landwehrkanal are used as outlet boundary conditions in the northeast and south and east, respectively. The northwest boundary in the hydrodynamic model is moved outward compared to the hydrologic model to generate a less undulating model boundary line, which facilitates defining the boundary conditions here. The northwest boundary is defined as a closed wall, which prohibits water from leaving through this boundary, but does not create extensive backwater effects into the study area, as the model is spatially extended at this boundary. A more detailed description of the hydrodynamic model and the validation of the boundary conditions is provided in .

The maximum water depths and velocities are extracted from the simulation results and rastered with a 1 m × 1 m resolution. These rasters are then forwarded to the building damage model.

In order to further assess the potential benefits of the GI measures, a building damage model was used. Despite the existence of numerous models to estimate flood damage to buildings, most were developed for typical riverine floods, whilst research has shown that different flood pathways show different damage patterns . Therefore, the “Flood Damage Estimation Tool” FlooDEsT; was adopted as it was specifically developed for urban pluvial floods.

The model is based on survey data from past urban pluvial flood events between 2010 and 2016 in Germany see. However, the survey data provides no data points from our study area. The survey data were split for training and testing. Using a recursive partitioning algorithm, the XGBoost , the model generates an additive ensemble of decision trees, where sequential trees are trained to correct the residual errors made by previous ones. The recursive partitioning algorithm is powerful at capturing non-linear relationships between the predictors (hazard characteristics, building characteristics) and the outcome variable (relative building damage). The input variables are a mix of physical and conceptual variables: water depth [m], flood intensity (in form of classes of people stability in flood waters), the presence of contaminants in the water, building area, building age, presence of a basement, and implemented adaptation measures in form of a score. For a detailed description of the input variables, especially how scores are calculated, consult .

After the random sampling process, despite some variation in the estimated damage degree, in 97 % of the runs the estimations fell under the same damage class, which indicates great stability of results. The model calibration performed well with a RMSE of relative building damage of 0.03 with the training data and 0.06 with the test data after 7 boosting rounds (i.e. additive trees). Relative building damage is the ratio between repair or replacement costs and the building value. Hence, 0.06 means a 6 % relative damage.

In the application, the model needs the maximum water depth and flow velocity from the hydraulic model (from which flood intensity is derived) and building information from cadastral data (either authoritative or OpenStreetMap data). Maximum water depth and flow velocity do not necessarily occur at the same time, and this is a potential bias in our approach, in which we potentially overestimate the hazard. We do so for a compatibility of approaches with other data sources, namely (official) flood hazard maps, which often provide solely the maximum water depth and flow velocity of a scenario. The same occurs in the survey data used for training, where only maximum water depth and maximum “intensity” are reported.

Additionally, the tool uses smart random sampling to impute missing variables, such as building-level features, from the existing survey data distribution, which secures representativeness of buildings affected by this flood pathway, reducing exposure bias. Regardless of property size or market value, damage classes based on relative damage are provided, facilitating comparison. The damage classes are defined as follows: Low = 0 %–5 %, Medium = 5 %–10 %, High = 10 %–15 %, Very high = 15 %–100 % relative damage.

In order to compare the GI impact on runoff volume with other studies, we selected examples from those studies reviewed in based on similarity of study area, event and retention scenario characteristics. More specifically, we considered only events with a duration of 0.5–2 h and rain totals of 10–60 mm and 90–110 mm, as the rain totals modelled in our study range from 15–49 mm and 100 mm was added as an extreme event. Regarding the area covered by GI, we selected those studies with 1 %–10 % of the study area for BR, with 10 %–45 % for GR and with 4 %–20 % for PP. Finally, the impervious area for selecting a study was restricted to 20 %–50 % for GR and 15 %–70 % for PP. Due to the smaller amount of available studies, this last criterion was not applied when selecting BR studies. The selection resulted in 25 events from 6 studies, relative runoff reduction from these studies is shown in Table :

used the model smart-green (MOBIDIC-U and a QGIS plugin) to investigate GR in a 1.9 km2 study area in Milan, Italy (MAP 800 mm). The GR is composed of a 200 mm soil layer and a 150 mm drainage mat.

Regarding BR, relative runoff reduction in the reviewed studies is 44 %–73 % lower than in our study. A possible explanation for this difference is that the impervious area is 46 %–75 % higher in these studies. This increases runoff formation in the remaining study area and reduces the relative runoff reduction of BR. The BR extent of the event from is 38 % lower than in our study, which also decreases the runoff retention. However, for the two compared events from , the BR extent shows no significant difference. Rain totals are with at most 15 % not significantly higher in the compared studies.

For GR, most of the examples from result in much higher runoff reduction. This can be a result of the 36 %–49 % lower imperviousness of the study area. In terms of the GR extent, has two settings, with GR covering 10.3 % or 15.4 % of the study area. In the first case, this is 29 % less GR then in the GRmed scenario and results in 43 % less to 64 % more runoff reduction. In the second case, this is 5 % more GR then in the GRmed scenario, resulting in 6 %–120 % more runoff reduction. Furthermore, the GR layers investigated by are more thick, which allows to retain more water.

With respect to the GR extent, the scenarios from are between GRmed and GRmax, i.e. the GR extent is 48 % larger than GRmed and 26 % smaller than GRmax. The imperviousness of the study area is closer to GRmed, as it is 22 % higher than GRmed and 91 % higher than GRmax. The runoff reduction from turns out to be centred between the runoff reduction of the corresponding scenarios, with 30 %–45 % more runoff reduction than GRmed and 21 %–24 % less runoff reduction than GRmax.

PP shows less runoff reduction in both reviewed studies. When comparing to , the 63 %–72 % lower runoff reduction can be caused by the 42 % higher imperviousness of the study area compared to PPmed and 28 % smaller PP extent. However, with regard to , the impervious area is 7 %–25 % smaller and the PP extent 9 %–63 % larger than in the corresponding scenarios of this study. Still, runoff retention is 75 %–92 % lower. This is even more surprising, as the saturated hydraulic conductivity of the different layers of the upper 35 cm is with 133–606 mmh-1 much higher than in our study (43–150 mmh-1, see Table ). Only the plain fill below has with 10.2 mmh-1 a lower conductivity.

and investigated flood volume reduction by GI in Berlin. studied the impact of extensive GR, intensive GR and GR with enhanced retention (retention roof), among other GI measures. They investigated the same study area as our study, using the software InfoWorksICM . coupled the models hms⁺⁺ with SWMM and assessed the impact of retention roofs and gullies in a 13 km2 study area in the centre of Berlin, with 35 % roof and 16 % road surfaces.

Despite the similarity of the study areas, GI extents and rain event characteristics, comparability is limited by the use of different measures of flood volume. While defined flood volume as the sum of maximum water level in each mesh element with at least 10 cm water depth, used the sum of maximum water level of all mesh elements. In our study, the percentage of the study area with a maximum water level > 10 cm is used. Besides, the reviewed GR scenarios and the reference base scenarios are combined with the sewer system in most cases, whereas our study uses GI and base scenarios without gullies.

Comparing relative flood reduction despite these limitations in comparability, we see that reports the most similar results for the 100 year event, with a flood volume reduction of 32 % for extensive GR and 34 % for intensive GR and retention roofs. This is very close to GRmax with a 30 % reduced area with maximum water level > 10 cm.

For the 100 mm event, flood volume reduction according to is 14 % for extensive GR and 34 % for intensive GR and retention roofs, while GRmax results in a reduction of the area with maximum water level > 10 cm of 20 %. It is noticeable that in the study of there is hardly any difference in relative flood volume reduction between intensive GR and retention roofs regarding the 100 year and the 100 mm event, showing that the 100 year event does not make full use of the retention potential of those GR types.

Comparing the gully water retention to a base scenario without drainage system, report a much larger impact of the drainage system than our study. For the 100 year event, result in 31 % reduction of flood volume while our gully scenario results in 13 % less area with maximum water level > 10 cm. For the 100 mm rain event the relative difference still increases, with 26 % compared to 3 % from our gully scenario.

Possible explanations for the difference are the different study areas, different models and model parametrisations or the different implementation of the drainage system itself. While used the drainage system model from BWB, which is a restricted dataset, in our study a simplified approach was used by defining gully water absorption due to the official drainage system requirements. Alternatively, a virtual drainage system based on open data could be created using the method presented by . It depends on the use case, if the additional effort for the drainage model setup is worth for including a more complex drainage system in the model chain.

Furthermore, the discrepancy in the flood mitigation impact between the compared studies can be explained by the use of different measures of flood volume itself. Strong reductions at localized hotspots with very high maximum water depth could result in a disproportionate decrease of total flood volume compared to the area-based indicator used in this study.

tested the effect of GI (GR and green open spaces) on building damage reduction in Milan (Italy), considering progressive higher intensities of green conversion and different rainfall scenarios. Overall, it was found that GI can reduce flood impact, but proportionally, the higher gains occur for lower rain intensities. The 100 year event corresponds to 54.7 mm in 1 h. A 100 % implementation of GR potentially reduces building damage by ca. 21 % for the 100 year event (or ca. 39 % of the expected annual damage (EAD), integrating all rainfall scenarios), whilst a conversion of 50 % to GR reduces damage by ca. 17 % for the 100 year event (32 % reduction of EAD). In turn, a conversion of 25 % of potential green areas reduces building damage by ca. 13 % for the 100 year event (or 25 % reduction of EAD).

Our analyses do not convey absolute monetary values, but relative ones. Yet, our 100 year scenario with 100 % GR (GRmax) would reduce the number of damaged buildings in any damage class by 14 % and the number of buildings suffering medium damage or higher by 67 %. GRmed in turn could reduce the number of damaged buildings by, respectively 6 % (any damage level) or 42 % (medium or higher damage).

show that a combination of GI in Barcelona (Spain), reducing the impervious area by 14 % could almost halve the EAD (46 % reduction); whilst an impervious area reduction of 2 % in Badalona (a town next to Barcelona) would reduce EAD by less than 4 %.

Although we have not tested an equivalent combination of GI, scenarios GRmed and PPmax have similar percentages of GI area to the Barecelona case study, with 14.6 % and 12.2 %, respectively. The PPmax scenario for the 100 year event would reduce the number of damaged buildings by 24 % or reduce buildings with medium or higher damage by 12 %. The BRmed scenario has with a GI area of 3.4 % a similar extent to the Badalona case study and results in a reduction of damaged buildings by 7 % or a reduction of buildings with medium and higher damage by 26 %.