Floods are one of the most destructive natural hazards and lead to severe social and economic impacts (European Union, 2007; Alfieri et al., 2016). The number of people exposed to recent flooding which occurred in many central European countries highlights the importance of assessing flood hazards. During the extensive June 2013 floods in Germany, for example, more than 80 000 people in eight federal states had to be evacuated (Thieken et al., 2016). The vulnerability of settlements calls for improved flood forecasting, which includes underlying uncertainties and impacts.

In this study, we present a novel methodology that uses a multi-model combination of two-dimensional (2D) hydrodynamic (HD) models to assess the impact of flooding based on water depths, which are termed in this study flood hazards. These hazards can be evaluated for key urban features, such as buildings, roads, bridges and green spaces (Leandro et al., 2016). This study focusses in particular on buildings. Furthermore, the hazard maps serve a variety of purposes, e.g. flood impact assessment, spatial planning, early warning and emergency planning (Hammond et al., 2013), for target users. For this paper, the users consist of a group of decision makers, such as the Bavarian Environment Agency and disaster relief organizations in Germany, the Federal Agency for Technical Relief or the German Red Cross.

In deterministic flood forecasting, the predictions of forecasting models, precipitation forecasts, hydrological models and HD models are used to generate flood hazard maps. These maps form the basis of flood risk management and are utilized to assess the impact of floods (Schanze, 2006; Hagemeier-Klose and Wagner, 2009). Although advances are continually being made in real-time forecasting, they are still inherently uncertain (Meyer et al., 2009; Bates et al., 2014; Beven et al., 2018). The decision-making process based on uncertain predictions can have a huge economic impact and possibly lead to life and death situations (Leedal et al., 2010). Thus, a thorough assessment is required of the extent to which uncertainties affect the flood hazards. In addition, forecasts that inform policy or risk management decisions should include major sources of uncertainty and communicate them coherently (Todini, 2017).

Researchers have addressed various sources of uncertainties in flood modelling, such as precipitation measurements, spatial interpolation of the precipitation, model parameters, model structure (Nester et al., 2012; Leandro et al., 2013), discharge data, measured discharge and uncertainty estimation techniques (Dotto et al., 2012). Although uncertainties arising from precipitation and HD models are significant, the generation of discharges using a hydrological model is considered as one of the most uncertain steps in flood forecasting (Di Baldassarre and Montanari, 2009). Substantial research has been dedicated to the field of discharge forecasting and reducing uncertainties by using methods such as generalized likelihood uncertainty estimation (Beven and Binley, 2014), global sensitivity analyses (Pappenberger et al., 2008) and the Shuffled Complex Evolution Metropolis algorithm (Dotto et al., 2012). To find the appropriate method, Pappenberger et al. (2006) have provided a decision tree that helps users select a suitable method for a given solution. Furthermore, in a recent study Boelee et al. (2018) reviewed uncertainty quantification methods to provide practitioners with an overview of ensemble-modelling techniques. An overview of existing ensemble forecasts in operational use can be found in Cloke and Pappenberger (2009) and Todini (2017). Most notably, in the federal states of Rhineland-Palatinate (Bartels et al., 2017) and Bavaria (Laurent et al., 2010) discharge ensembles are generated using the COSMO-DE-EPS precipitation ensemble as input to a distributed hydrological model LARSIM (Large Area Runoff Simulation Model). These and similar developments offer a potential framework for quantifying uncertainties. A challenging issue in natural hazards, however, remains the effective communication of the quantified uncertainties to decision makers (Doyle et al., 2019). Researchers have questioned how uncertainties should be communicated to reduce the risk of wrong or inappropriate decisions (Bruen et al., 2010; Todini, 2017).

In operational flood forecasting, hazard maps are provided in the form of exceedance probability scenarios, and generally, only one scenario is considered for emergency planning. Normally, a 50 % exceedance probability scenario (or median) is expected to be close to the deterministic best-model approach (Di Baldassarre et al., 2010). In other examples (Beven et al., 2014, 2015; Disse et al., 2018), model results of various exceedance probabilities are provided on separate or combined maps. Kolen et al. (2010) stated that there is a need for new methodologies that employ a multi-model combination approach by including several scenarios for improving decision-making. A multi-model combination is based on the results of several models and creates a more robust forecasting system with a better representation of uncertainties (Kauffeldt et al., 2016). Although the multi-model combination approach has been used widely in the field of discharge forecasting (Shamseldin et al., 1997; See and Openshaw, 2000; Oudin et al., 2006; Weigel et al., 2008), the approach is not commonly used in the field of real-time flood hazard forecasting. The long computational time required by the HD models restricts the use of such an approach in real-time forecasting. However, the use of a simple model structure and/or high-performance computing makes it possible to simulate HD models in real time, thus making it feasible to use multi-model combination approaches. Zarzar et al. (2018) have used a multi-model combination framework consisting of hydrometeorological and HD models to visualize flood inundation uncertainties in which they have used an average of HD model raster outputs to obtain the percentage of ensemble agreement.

We develop a methodology for obtaining a multi-model combination as an effective alternative to the traditional best-model approach for producing detailed hazard maps, which are termed building hazard maps. This term can be defined as a map that highlights buildings that are affected by or are vulnerable to flooding with differentiated exceedance probabilities of flood inundation extents projected on building use. In this paper, we have designed three scenarios with differentiated exceedance probabilities, each referring to the subjective classification of buildings with varying flood impact. To the best of our knowledge, this combination approach has not yet been used to assess the impact of flooding. The maps help prevent serious damage to buildings and aid in evacuation planning in the case of flooding. The methodology is applied for the flood event of January 2011 in the city of Kulmbach, Germany.

The framework to generate building hazard maps (as shown in Fig. 1) consists of three components: (1) hydrological modelling – discharge ensemble forecasts were produced using forecasted precipitation; (2) HD modelling – the water depths were simulated using a pre-calibrated 2D HD model; and (3) post-processing of the model results – a multi-model combination was used to produce flood hazard maps based on a classification of buildings. The framework was tested for the flood event of January 2011 in the city of Kulmbach, Germany. The first two components of the framework were developed in previous studies (Beg et al., 2018; Bhola et al., 2018a, b). The particular focus of this study is on the development of the framework of a multi-model combination in the post-processing component. For the sake of clarity, each component is described in detail in chronological order.

In this section, we present the results of five percentiles and the performance of the multi-model combination. To assess the methodology, the flood event of January 2011 was used to quantify uncertainties in discharge hydrographs. The forecasts corresponding to 10 %, 25 %, 50 %, 75 % and 90 % percentiles were further used as input boundary conditions to the 2D HD model, and water depths were stored. Furthermore, the flood inundation maps and building hazards were then classified.

Prior work in hydrology has demonstrated the effectiveness of multi-model combinations in improving flood forecasts as compared to the best-model approach (Weigel et al., 2008). However, these methodologies were previously limited to discharge ensemble forecasts and were not researched for hazard maps. In this study, we extend the use of multi-model combinations to produce flood hazard maps for buildings depending on their use and related damage potential.

First, the five simulation results are presented in Fig. 7 as inundation and building hazard maps. It should be noted that few buildings show very high hazards due to their proximity to the Mühl canal (Fig. 7a). Even though there was no overtopping of water from the canal, because of buildings' geolocation being near to the canal, these were assigned automatically with the highest hazard, starting with a discharge of M10%. Ideally, this should be prevented by removing the river channel elements from the dataset before assigning the water depths to the buildings as in Bermúdez and Zischg (2018). However, and without retracting our conclusions, it was decided not to include it in this work in order to keep the automation process simple. Up to a discharge of M50%, no inundation in the city centre was observed as the dykes were not breached. It can be observed in Fig. 6 that the increment in the number of affected buildings is gradual, especially with respect to the buildings belonging to the very high hazard class. As the peak discharge increases in M75%, the dykes at the B289 road were breached and water entered the city centre and more buildings were affected. Most damage was observed in M90% with 307 affected buildings, out of which 125 buildings show very high hazard, an increment of 46 from M75%. The affected buildings were located in the city centre (Fig. 7e), mainly in industrial and commercial areas. Similarly, the streets Theodor-Heuss-Allee and E.-C.-Baumann-Straße were inundated starting from a discharge of M50%.

In operational use, the mean of the discharge ensemble or M50% would normally have been used as the best model, which, according to Fig. 7c, is in agreement with the post-event information. However, this match might not always be representative, especially in the case of an event of a different or higher magnitude, as discussed in Di Baldassarre et al. (2010). They argued that visualizing flood hazards as a probability is a more accurate representation as compared to a single best model, which might misrepresent the uncertainty in the modelling process.

With the objective of visualizing uncertainties, three scenarios based on exceedance probability were used to combine HD model results and are presented in Fig. 8. In scenarios I and II, 84 and 107 buildings were affected, which shows that the impact of high- and average-exceedance-probability scenarios was less than that of M50% in which a total of 126 buildings were affected, out of which 67 buildings were classified in the very high hazard class.

Furthermore, as a majority of the buildings were classified in class II and III, the resulting map of a low-exceedance-probability scenario corresponds closely with M50% and M75%, with 142 affected buildings. In scenario II, 63 buildings were classified in the very high hazard class, which increased to 71 in scenario III. Similarly, 22 buildings belonged to both moderate and high hazard classes, and shifting to scenario III, the number increased to 33 and 38 in the moderate and high classes respectively.

In Fig. 9, a comparison is presented between the best model (M50%) and the multi-model combinations, and the areas with prominent changes are highlighted in red circles. The figure presents building hazards resulting from the combination of exceedance probability scenarios and locates 16 more buildings than are affected when compared to M50%. The buildings that belong to class III (Fig. 9b) were assigned the results of M75% and show a very high hazard. Figure 9a shows that an adjacent building belonging to class II (ID 1393) was not flooded. This demonstrates that the methodology was implemented accurately and prioritized measures such as flood impact assessment, spatial planning, early warning and emergency planning, according to the damage potential of a building. The prioritization is important in order to focus on a combination of various evacuation strategies to prevent damage and save lives (Kolen et al., 2010). Hence, decision makers must be made aware of the impact associated with a low exceedance probability to improve their planning strategies (Pappenberger and Beven, 2006; Uusitalo et al., 2015).

A potential drawback of the combination is that the hazard classification may shift from low to very high in two adjacent buildings belonging to different classes. This might confuse evacuation planners by presenting inconsistent information. To tackle this issue, more information and specific guidelines should be provided to them on how to use the maps. In addition, continuous flood inundation maps are hard to obtain, especially at the boundaries of two combinations. There might be a step rise in the water depths while shifting from the results of one model to another. To address this issue, future research should be conducted to provide consistency in interpolation and in combining models (see Zazar et al., 2018). In addition, in order to avoid the confusion, these maps could be forecasted for a regular interval of 3–4 h.

Overall, the methodology is independent of the choice of models, i.e. hydrological and HD, and is transferable to other study areas. In order to use the methodology in real time, the runtime of the flood forecasting modelling should be below the flow travel time. In this study, a 50-member ensemble forecast was used from Beg et al. (2018), where the entire process took 25 min with a three-core desktop in parallel mode to generate a forecast of 12 h. Various percentile discharges were then run simultaneously in the HD model, which required 30 min to simulate a 12-hour event on an eight-core, 2.4 GHz (Intel E5-2665), including the initial start (Bhola et al. 2018a). Post-processing of the model results would consume an additional 15 min. Therefore, real-time hazard maps are delivered to decision makers in 70 min. A faster runtime can be ensured by using a simple model structure (Leandro et al., 2014) and/or high-performance computing (Kuchar et al., 2015). In the absence of such infrastructures or with a very large catchment size, HD models can be replaced with alternatives, such as terrain-based models (Zheng et al., 2018) and satellite images (Voigt et al., 2007). In addition, a database of prerecorded inundation scenarios as shown in Bhola et al. (2018a) can expand the application of this methodology.

Molinari et al. (2014) have stated that a comprehensive uncertainty assessment improves emergency responses by assessing the potential consequences of flood events. Therefore, our methodology would allow the target users to benefit from hazard maps enabling them to better prioritize and coordinate evacuation planning based on the stakeholder perception to risk. The maps could further serve as a tool for flood risk assessment. The methodology can be used for flood mitigation and flood forecast planning in the form of emergency management training, where forecasted hazard scenarios can be presented to the training groups. By visualizing inundation scenarios, potential damage at the building level which has been prioritized based on the desired classification can be estimated with this methodology and made available together with each forecasted scenario.

In summary, we have presented a new methodology for flood impact assessment using a multi-model combination in the form of building hazard maps with differentiated exceedance probability. These maps offer an alternative way to communicate the underlying uncertainties in forecasting models and are ready to use for decision makers in the field of flood risk management. The entire forecasting framework consists of three stages: (i) generation of discharge ensemble forecasts, (ii) 2D HD simulations using the generated forecasts and (iii) hazard maps using multi-model combinations. The framework was applied to the city of Kulmbach, and three multi-model combinations were designed based on exceedance probability. The model results of M50% show a good match with binary information collected after the flood event. The low-exceedance-probability scenario corresponds closely with M50% and M75%. We expect this multi-model combination to improve the current visualization techniques in operational flood risk management and evacuation planning. In this study, we have considered only buildings as a feature; additional urban features, such as bridges (Gebbeken et al., 2016) and roads (Goerigk et al., 2018), should be included in the future to extend the methodology. Furthermore, other sources of uncertainty, such as HD model parameters, model structures and measured data, should also be incorporated for a comprehensive assessment. In addition, the economic, social and hazardous effects of carrying out an evacuation in the case of a false alarm must be considered. Hence, a validation of the combination is crucial to building trust in its prediction in real time. Further research investigating multi-model combinations and validation in other study areas may be beneficial. In order to design a multi-model combination, a group consisting of researchers, operational bodies and experts in the field of flood risk management should be consulted. A more extensive study on the validation of the multi-model combination may be required, possibly by using measuring gauges, post-event surveys (as conducted in Thieken et al., 2005), satellite images (as in Triglav-Čekada and Radovan, 2013), and/or crowdsourced data (Bhola et al., 2018b).

In the future, damage potential classification can be further improved by including additional criteria, such as population density or water quality, and with this the applicability of this method can be extended. For example, the assessment of the damage potential of commercial enterprises, substances or machinery containing elements that could be a source of water pollution could be included (Krieger et al., 2017). In addition, other classification methods for buildings and hazard types should be evaluated, especially to further dissect the impact of class III in commercial and industrial sectors. Finally, the output of the framework can be extended to hazard maps uploaded to a web-based GIS to improve visualization and to provide layers of additional information, such as inundation pathways and weak spots in the river and floodplains, to provide sufficient details to intervene (aid in planning). This additional information would enhance the usefulness to different target users, such as planners, decision makers and flood forecasting agencies.