Flood risk assessment is an important prerequisite for risk management decisions. To estimate the risk, i.e. the probability of damage, flood damage needs to be either systematically recorded over a long period or modelled for a series of synthetically generated flood events. Since damage records are typically rare, time series of plausible, spatially coherent event precipitation or peak discharges need to be generated to drive the chain of process models. In the present study, synthetic flood events are generated by two different approaches to modelling flood risk in a meso-scale alpine study area (Vorarlberg, Austria). The first approach is based on the semi-conditional multi-variate dependence model applied to discharge series. The second approach relies on the continuous hydrological modelling of synthetic meteorological fields generated by a multi-site weather generator and using an hourly disaggregation scheme. The results of the two approaches are compared in terms of simulated spatial patterns of peak discharges and overall flood risk estimates. It could be demonstrated that both methods are valid approaches for risk assessment with specific advantages and disadvantages. Both methods are superior to the traditional assumption of a uniform return period, where risk is computed by assuming a homogeneous return period (e.g. 100-year flood) across the entire study area.

In recent decades several large flood events occurred across Europe resulting in direct damage exceeding EUR 1 billion

Following the European flood directive, flood risk is defined as “the combination of the probability of a flood event and of the potential adverse consequences […]”

In a traditional approach, the hydrological load is estimated by means of extreme-value statistics using river gauge data and transformed into corresponding inundated areas by hydrodynamic models

Generation of spatially heterogeneous flood events in terms of precipitation fields or discharges is of current scientific interest

The two presented approaches estimate the hydrological load in the river network at multiple locations but are different in their nature. This leads to the key question of the present study: does it matter which approach is chosen in the context of flood risk modelling, and what are the advantages and disadvantages of the two? We answer this question by comparing the set of heterogeneous flood events from the HT-model with the one resulting from a weather generator and subsequent rainfall–runoff modelling. Both methods are embedded in a probabilistic flood risk model used to estimate the effect of chosen methods on flood losses. To the best of the authors' knowledge, there is no study to date in which the two approaches are directly compared. Additionally, the flood risk corresponding to homogeneous flood scenarios of certain return periods (“traditional” approach) is derived and compared to the other two approaches.

This paper is organised as follows: first, the study area is shortly described. In Sect. 2 the flood risk model is introduced and the two different approaches for heterogeneous event generation are presented in details. Section 3 presents the results of the comparison, which are discussed in the following section. Finally, conclusions summarise the major findings.

The flood risk model is applied in the westernmost province of Austria, Vorarlberg. The region is characterised by a strong altitudinal gradient between the Rhine River valley (

Study area and the location of meteorological and river gauging stations.

The probabilistic flood risk model (PRAMo) used in the presented work consists of three different modules: the hazard module comprising the generation of long time series of flood events; the vulnerability module used to evaluate possible adverse consequences of flood events with a certain exceedance probability; and the risk assessment module, which combines the results of the hazard and vulnerability modules to estimate the loss per event and resulting risk

Flowchart of the PRAMo flood risk model including two different approaches for flood event generation.

In this study, data of 17 gauging stations (1971–2013) are applied for the HT approach. The continuous simulation of the WeGen approach is based on daily time series from 1971 to 2013 for 45 meteorological stations (cf. Fig.

The hazard module generates time series of spatially distributed synthetic flood events. In the first approach, we apply the conditional extreme-value model (HT-model) proposed by

For the set of synthetic flood peaks at each of the 17 gauge locations we estimate the return period based on the generalised extreme value (GEV). A flood event is characterised by exceedance of a certain streamflow at a single location or multiple locations with a defined time period. As a threshold for defining a widespread flood event, a return period of 30 years was selected in the present study. The output of the HT-model in terms of synthetic flood peaks is available at the locations of gauging stations. Hence, for the river segments without observations, the flows and their respective return periods need to be estimated. We apply the top-kriging approach

The second approach is based on a stochastic weather generator used to drive a hydrological model. Long-term daily precipitation and temperature series are generated, with a multi-site, multi-variate weather generator based on the auto-regressive model

Following the generation of meteorological data at the locations of the weather stations, a spatial interpolation to continuous meteorological fields is necessary for the application of the rainfall–runoff model. Complex methods for spatial interpolation can be applied

Finally, the semi-distributed conceptual rainfall–runoff model HQsim is applied to simulate streamflow across all catchments of the study area

While the hazard module computes the hydrological load, the vulnerability module assesses the possible negative consequences in terms of exposed objects and monetary damage. The module is based on the widely used approach of combining the exposure and susceptibility of elements at risk in the inundated areas

At the scale of a community (on average 28 km

The estimation of monetary damage for the elements at risk is based on the relative damage functions combined with the total asset values. A damage function describes the relative loss of value as a function of water depth

The damage estimation is conducted on a single-object basis for residential buildings only. To derive the flood losses, the available inundation maps are combined with the asset datasets and damage function. Subsequently, the object-based loss data are aggregated for each community. The absolute building values indexed to 2013 according to the construction price index

The risk assessment module brings together the results of the hazard and vulnerability modules to generate a time series of losses and calculates the resulting risk curve for the area of interest

Validation results of the weather generator and the revised disaggregation procedure for all stations (

A core element of the probabilistic flood risk model is the generation of plausible, spatially heterogeneous flood events. To investigate the spatial coherence of synthetic events generated by two different approaches, two spatial dependence measures proposed by

To assess the performance of the continuous modelling approach, extreme precipitation of simulated data is compared to observed station data (daily: 1971–2013; hourly: 2001–2013) for the weather generator and disaggregation procedure. The median and the uncertainty range represented by the 5 and 95 % quantiles of 100 model realisations are compared to the observed data. Figure

The rainfall–runoff model is calibrated (2001–2007) and validated (2008–2013) in a classical split-sample approach

Comparison of observed (42 years) and simulated conditioned exceedance probability

Spatial dependence measure

For the analysis of spatial coherence, 100 simulations using each of the two event generation approaches (HT-model and WeGen) were carried out. Each simulation comprised 42 years of data corresponding to the length of the observed discharge series. Figure

In general, the spatial dependence declines with the level of extremeness. For more extreme runoff situations, the dependence structure is less stable and prone to a large variability. The HT-model results in the lower triangle reproduce the observed spatial patterns between the stations well. The observed measure is in

To analyse the dependence structure of high flows across the study area, the measure

To compare the effect of the two approaches of synthetic event generation on the overall estimated loss, flood risk curves are calculated. Confidence intervals are derived based on 30 realisations of 1000-year simulations. Furthermore, the risk curve based on the assumption of homogeneous return period floods across all catchments is derived based on five inundation maps corresponding to the return periods between 30 and 300 years. The two synthetic event generators result in a comparable range of overall estimated flood risk (see Fig.

Risk curves for WeGen and HT-model approach in comparison to the results of a homogeneous scenario. The median and quantile confidence intervals are based on 30 realisations of 1000 years of simulation. Monetary values are normalised to the year 2013.

The sets of generated heterogeneous flood events reflect a large variability of plausible spatial patterns. Hence the estimated flood risk is the result of a combination of these patterns. Figure

Examples of flood events with an estimated flood damage of EUR

Both approaches, the HT-model and the WeGen approach, simulate complex, spatially heterogeneous patterns of synthetic flood events. In the present study, the HT-model outperforms the WeGen approach in terms of reproducing the observed dependence patterns of peak flows at the gauging stations. The HT-model makes use of the observed river gauging data and models their dependence structure directly. In contrast, the WeGen approach models the dependence structure only indirectly based on the meteorological input data.

The overall river network and especially small ungauged tributaries do however rely on the top-kriging interpolation in the case of the HT-model approach and are not able to react independently to the larger river system. This explains the higher dependence structure on the community node points, while at the river gauges the results do correspond well to the observed values. Nevertheless, in both cases the capability to capture spatial effects of a certain spatial scale in the end depends on the density of the measuring network and its data quality.

The WeGen approach seems to overestimate the overall spatial dependence in the study area in comparison to the observed values. This was also found in a previous study, comparing a different set of gauging stations

Only one possible combination of weather generator, disaggregation procedure and rainfall–runoff model was applied for the WeGen approach. Thus, by the application of an alternative weather generator with different assumptions about the spatial dependence or tail distribution, the resulting risk estimates may change. This counts as well for the application of a different rainfall–runoff model or alternative disaggregation procedure

The two approaches to synthetic event generation differ substantially in terms of estimated damage from the one assuming a uniform return period across the whole study area (Fig.

Relative number of flood events exceeding a 30-year flood threshold and corresponding relative number of affected communities. The results are based on 30 000 years of simulation.

A fundamental difference between the two approaches resides in the way of considering the hydrological processes. The HT-model takes a purely statistical approach by analysing the dependence of peak discharges above a certain threshold. It does not explicitly consider hydrological processes which generate extremes. For instance, the non-linearity of catchment response is not explicitly taken into account, but only so far it is imprinted in the previously observed peaks used for model parameterisation. The combination of the weather generator and rainfall–runoff modelling describes the hydrological processes in a spatially consistent and time-continuous way. Hence, the effect of soil moisture accumulation and pre-event catchment conditions are explicitly modelled. By the application of a fully distributed, physically based model, the hydrological process description could even be improved, for example, by solving full energy balance equations for snow melt or evapotranspiration

Summary of advantages and disadvantages of the WeGen and HT-model approach to generating heterogeneous flood events.

In general, continuous hydrological modelling generates full hydrographs at all locations, which allows for direct coupling with hydraulic models as, for example, applied in

In addition, the continuous modelling approach is capable of explicitly modelling scenarios of changing hydrological boundary conditions. For instance, changes in the climate system can be taken into account in the generation of meteorological fields by conditioning the rainfall and temperature probability distributions

The presented approaches are subject to different uncertainties. The confidence intervals presented in Fig.

A further important point, currently not considered in both approaches, is dike failure scenarios. In the study area, for example, no inundation is considered for the Rhine River due to its high protection level. Nonetheless, the probability of a dike failure is non-zero and could have a devastating effect. In this sense, the consideration of flood volumes beside peak estimates could be another important extension to describe the severity of flood events

A traditional validation of the overall risk model in terms of a comparison of observed to simulated data is hardly possible as comprehensive databases of loss events are often not available

The question of whether the choice of method for generating heterogeneous flood events for flood risk modelling matters can be answered in different ways. Both approaches, the HT-model and continuous WeGen approach, were generally capable of modelling spatially plausible flood events across the study area. By direct comparison to observed spatial patterns, the HT-model approach performed better than the WeGen approach in our study area in terms of correctly representing the observed dependence structure. A stronger modelled dependence of extreme precipitation resulted in high areal rainfall in the WeGen approach and higher overall risk compared to the HT-model. The median damage from 30 000 years of simulation is about 17.5 % larger in the WeGen approach than in the HT-model. The representation of the dependence structure for simulation of extremes needs to be further improved for the weather generator. Nevertheless, the choice of method for generating heterogeneous flood events might have a smaller impact than, for example, the choice of the applied damage functions

To conclude, both methods are valid approaches to overcoming the simplified assumption of uniform return period across a study area. Accordingly, when designing a flood risk study, the choice of the approach should consider the specific advantages and disadvantages of the two methods and data availability. If computational efficiency and quick transferability are in focus, the HT-model approach might be a better choice. In contrast, if unsteady hydraulic modelling is required for the targeted application, the continuous modelling of generated meteorological fields is more appropriate.

For Austria, daily meteorological and river gauging data are available at

Based on the initial ideas of KS and SV, the study was designed in collaboration with all authors. BW prepared the initial data, implemented and applied the continuous modelling approach and analysed the results. KF programmed the spatial interpolation scheme for the meteorological data and supported the rainfall–runoff modelling. The risk model and the HT application were mainly developed by KS. The manuscript was drafted by BW with support of SV. All authors contributed to the review and final version of the manuscript.

The authors declare that they have no conflict of interest.

We thank all the institutions that provided data, the Zentralanstalt für Meteorologie and Geodynamik (ZAMG), the Deutscher Wetterdienst (DWD), and particularly the Hydrographischer Dienst Vorarlberg. The simulations were conducted using the Vienna Scientific Cluster (VSC). Finally, we want to thank the editor, Margreth Keiler, and the two reviewers (Martina Kauzlaric and anonymous) for taking their time to critically evaluate this article and to provide valuable and constructive feedback.

This work results from the research project HiFlow-CMA (KR15AC8K12522) funded by the Austrian Climate and Energy Fund (ACRP 8th call). Furthermore, we would like to thank the vice-rectorate for research and the faculty of Geo- and Atmospheric Sciences at the University of Innsbruck for providing open-access funding.

This paper was edited by Margreth Keiler and reviewed by Martina Kauzlaric and one anonymous referee.