Floods are worldwide the most common natural disaster (Douben, 2006). Drivers for coastal floods are usually a combination of tides, waves, precipitation, storm surges, and strong river discharge (Zscheischler et al., 2020). They pose a big threat to some of the most important economic centers in Europe and the 50 million people living in the low-elevation coastal zone (Neumann et al., 2015). The damage caused by floods is potentially even higher when two driver of floods, like strong river discharge and high coastal water levels, occur at the same time or in close succession (Seneviratne et al., 2012). Leonard et al. (2014) defined compound flood events as an “extreme impact that depends on multiple statistically dependent variables or events”. There has been a number of studies conducted for compound flood events in the past, like Zscheischler and Seneviratne (2017) or Hendry et al. (2019), which found that neglecting the dependence of drivers results in a large underestimation of coastal flood risks. Due to their severe nature, compound flood events are becoming more and more relevant for risk assessment and scientific research.

Due to the large damage that can be caused, it is essential to understand how compound floods will change in the future because of anthropogenic climate change (Zscheischler et al., 2018). To better analyze different climate futures, the fifth Assessment Report (Pachauri et al., 2014) of the Intergovernmental Panel on Climate Change (IPCC) introduced four Representative Concentration Pathways (RCP) scenarios. These pathways represent different possible climate futures based on different developments of factors such as greenhouse gas and aerosol concentrations, or land use (Moss et al., 2010). Recently, the RCP scenarios have been extended by the Shared Socioeconomic Pathways scenarios, which have been used for the climate simulations in the AR6 report (IPCC, 2021). However, due to the availability of required data at high spatial resolution, the present study utilizes data from RCP2.6 and RCP8.5 scenarios for assessing future climate change. RCP2.6 assumes a reduction in carbon dioxide emission starting from 2020 and negative emission at the end of the century and is therefore often referred to as the “peak” scenario (Van Dingenen et al., 2018). This scenario is in line with the goal of the Paris Agreement, which aims to limit the global mean temperature rise to below 2K (United Nations, 2015). It requires a massive reduction in the emission of other greenhouse gases like methane (Van Vuuren et al., 2011b). RCP8.5 on the other hand projects a rise in greenhouse emissions throughout the century and is generally seen as a worst-case scenario (Hausfather and Peters, 2020). Both scenarios are accompanied by a rise in mean sea level which will pose a major threat along the coastlines (Vousdoukas et al., 2018).

The potential changes in coastal flood damage due to sea level rise were investigated by various studies. Vousdoukas et al. (2020) estimate up to e 239 billion annual costs from damage caused by coastal flooding toward the end of the century in Europe for RCP8.5 if no countermeasures are taken. The damages caused by coastal floods will therefore represent a noticeable share of some countries' national gross domestic product (GDP) at the end of the century in case of a high-emissions scenario like RCP8.5 (Feyen et al., 2020). Despite those findings, a study recent by McEvoy et al. (2021) revealed that still not all European countries plan for sea level rise and therefore do not improve their flood protection accordingly.

There are several studies investigated future changes to compound flood events in Europe. Most of them were local while a few addressed the problem from a global perspective. These comprise, for example, the studies by Bermúdez et al. (2021) for the rivers Mandeo and Mendo in Spain, Harrison et al. (2022) for the estuaries Humber and Dyfi in the United Kingdom, Kew et al. (2013) for the Rhine delta, Klerk et al. (2015) for the Rhine–Meuse delta, Pasquier et al. (2019) for the Broadland River in England, and Poschlod et al. (2020) for Norway. While a European perspective is to some extent inherent in global studies, like in Bevacqua et al. (2020), Couasnon et al. (2020), and Ridder et al. (2022), they lack regional details due to coarse resolution. To the authors' knowledge, the studies of Bevacqua et al. (2019) and Ganguli et al. (2020) are the only ones that analyze future changes to compound flood events in Europe on a continental scale. Bevacqua et al. (2019) carried out their analysis for the period of 2070–2099 and considered precipitation and sea level under emission scenario RCP8.5. They projected a strong increase of compound flood events, due to the warmer atmosphere allowing storms to carry more moisture, in addition to sea level rise. Ganguli et al. (2020) studied changes under RCP8.5 using high-resolution dynamically downscaled RCM simulations available at a EURO–CORDEX domain for the time period 2040–2069. Their analysis focused on discharge and sea level extremes in northwestern Europe. For the majority of locations, they reported a lower risk of compound flood events in the projected scenario due to a lower dependence between storm surges and river discharge extremes, which they attributed to a potential poleward shift of the North Atlantic jet. Furthermore, they noted that considering the projected SLR suggests an increase in compound flood potential across low elevated lands, i.e., ~30% of sites. Both studies were conducted for different decades of the current century and focused on different drivers. Their results can therefore hardly be directly compared. However, those studies did not provide a detailed analysis on changes in different scenarios. Our work aims to contribute further to this scientific discussion by adding detailed analysis of the scenarios RCP2.6 and RCP8.5 to it.

For the analysis of the dependence of the factors driving compound flood events tail correlation coefficient methods or copulas are often utilized (Xu et al., 2022). They are used to evaluate the complex dependence structures and describe the bivariate joint distribution (Couasnon et al., 2020). For robust estimates, large data sets are needed (Serinaldi, 2013; Serinaldi et al., 2015) which are often unavailable. For this reason we use a Monte Carlo–based approach that is less dependent on sample size (Heinrich et al., 2023) to study the dependence between drivers of compound flood events.

In the present study, we focus on a detailed analysis of changes in compound flood events in Europe toward the end of the current century (2070–2099). Using high-resolution coastal water levels, discharge data, and regional sea level projections from the Sixth Assessment Report (AR6) of the IPCC, we provide an assessment of future changes in compound flooding across northern and central Europe. The assessment is made for the high-emission scenario RCP8.5 and the low-emission scenario RCP2.6 to account for different climate futures. Especially for RCP2.6 very little scientific analysis in terms of compound flood analysis has been done, with most studies focusing on the more extreme high-emission scenario RCP8.5. First, we compare the historical runs of the dynamically downscaled global climate models to reconstruction data in order to evaluate their skill in representing compound flood events. We used their output to simulate discharge and coastal water levels. Afterwards, we examine how different aspects of extreme events change for the two emission scenarios which includes sea level rise caused by global warming. This is combined with an analysis on how much future developments in coastal water levels and discharge contribute to those changes. Furthermore, we analyze changes in the extreme event seasonality, i.e., the number of months in which extreme events can occur. Additionally, we investigate if future scenarios show differences in the intensity of extreme events. Finally, we look into potential changes in correlations between discharge and coastal water levels extremes. This enables us to examine if the underlying mechanisms that might cause compound flood events may change in the future.

Spatial and temporal consistent long time series of daily river runoff (discharge) and coastal water levels are required to study compound flood events. These were derived from existing climate change scenario simulations at a sufficiently high spatial resolution. We selected two data sets from the COordinated Regional climate Downscaling Experiment [CORDEX; Giorgi et al. (2009)], i.e., from its EURO–CORDEX initiative¹ that provides regional climate projections for Europe at 12.5km (0.11°) resolution (Jacob et al., 2014). These two data sets comprise regional climate model (RCM) simulations (Section 2.1) that were dynamically downscaled from simulations of two different global climate models (GCMs). The simulations cover a historical period (1950–2005) and two different future climate scenarios each that range until the end of the 21st century (2006–2099) without any gaps. The RCM simulations were then used to generate the necessary data for the analysis of compound flood events. For one thing, time series of daily river runoff were simulated with the Hydrological Discharge model (Section 2.2). For another, tide-surge levels were generated with the Tidal Residual and Intertidal Mudflat model (Section 2.3). A flowchart of the modeling framework can be seen in Supplementary Figure S1. Note that the choice of the EURO–CORDEX simulations was largely constrained by the data requirements of the coastal water levels simulations. In addition, we utilized long-term reconstructions of river runoff and coastal water levels (Section 2.4) to evaluate the simulated compound flood events during the historical period.

In our study we consider and analyze data from central and northern Europe. Our analysis region is shown in Figure 1 in which the names of all seas, regions and river catchments that are used in the the study are introduced. Figures used in the remainder of this study show only the largest rivers to avoid visual clutter. All together there are 181 river mouths shown by circles, regardless of the rivers being displayed in the following figures.

In the following sections we first evaluate the historical runs of our data sets, then investigate the changes of the separate drivers before proceeding to look into future changes to compound flood events.

Comparing the historical runs of the REMO data sets with the reconstruction data (Section 4.1) showed a very similar behavior. Both REMO data sets show a number of compound flood events that is similar to those of the reconstruction data sets, even if the compound flood events for northern Norway are overestimated. Furthermore, there is a certain amount of variability due to the events being infrequent and the analysis time period being comparably small. For both REMO data sets the majority of compound flood events happen in the winter months. Also, the 2σ maps (Figure 3), which show if a river has more compound flood events than expected by chance, show a similar pattern, with the western-facing coasts tending to be above the 2σ range. The deviations we observe are potentially caused by slightly different storm trajectories in the REMO data sets and natural climate variability which does not allow a one to one comparison since they are not based on reanalysis.

If sea level rise is neglected, we do not see changes in the coastal water levels. There are studies that project an increase in cyclone number and mean wind speed (e.g., Zappa et al., 2013) as well as a poleward shift of the storm tracks (e.g., Kjellström et al., 2018). However, those results are sensitive to the chosen forcing and the choice of the global climate model (Feser et al., 2015; Ozturk et al., 2022). Gonzalez et al. (2019) concluded that those projections should be viewed with some caution. Discharge on the other hand shows a change in the number of extreme event days and intensity. These changes in discharge are caused by an increase in global temperature. Higher temperature results in the atmosphere carrying more moisture, which eventually leads to more extreme precipitation events in most parts of northern Europe in winter (Pfahl et al., 2017). Furthermore, due to warmer winters, the snow melt will start sooner (Blöschl et al., 2017), leading to a seasonality shift in many regions like Scandinavia. Hattermann et al. (2015) found that a combination of those factors would lead to an increase in winter discharge for almost all large German rivers. This makes it important to have proper discharge data available that take snow melt into account like in the current study, instead of only precipitation. The period of strong discharge events will begin earlier in winter and therefore lasts for an extended period in comparison to the historical time frame. This, combined with more precipitation events leads to changes in the number of extreme event days. The increased annual precipitation (Rajczak and Schär, 2017) will result in a generally higher discharge level in Europe (Thober et al., 2018). An exception to this is northern Spain where we see a reduction in intensity and extreme discharge days due to less precipitation. While the signals are very clear in the REMO data sets for RCP8.5, this is not the case for RCP2.6. Like in Di Sante et al. (2021), clear changes to discharge can be seen for Scandinavia and the Baltic States, but not for most of central and western Europe. The decrease in extreme discharge event days under RCP2.6 might be caused by the warmer temperature leading to less snow melt-generated discharge. Overall, our results match the generally expected future discharge changes.

Due to sea level rise and increased discharge, we expect a strong increase in compound flood events toward the end of the century in both scenarios. The changes are significant for both RCP scenarios, but much stronger in RCP8.5. Our analysis reveals that sea level rise will be the main contributor to those changes for most of Europe (see Figures 9, 10). However, even if sea level rise is ignored, the changes in discharge under RCP8.5 are large enough to cause major shifts in compound flood event frequency. Despite that, it is essential to take into account, that changes in discharge event frequency and intensity will have impacts on a local scale. The developments of sea level rise and discharge will furthermore cause an increase in the compound flood event season duration which is projected to extend up to 5 months under RCP8.5 at the end of the current century. Furthermore, we see that by adapting the thresholds to future scenarios, the pattern in Figure 8 remains similar, indicating that the generating mechanism for most compound flood events stays the same. If those thresholds are not adapted and stay on the historical level, nearly all rivers show more events than in the past. Our results, therefore, align with the work of Bevacqua et al. (2019) who projected a rise in compound flood events toward the end of the century. Our results do not find any indication of a widespread lower risk of compound flood events over central Europe as described by Ganguli et al. (2020). One reason for the difference in results might be that their study investigated the middle of the century (2040—2069), while the climate change signals increases in magnitude throughout the century. It also must be noted that ourapproach to classify compound flood events is different to the one used by Ganguli et al. (2020). The present study utilizes a Peaks over Threshold approach, while the former uses annual maxima high coastal water levels and high river discharge within ±7-days of occurrence of the high coastal water level.

As discussed, sea level rise is the dominant factor responsible for future changes in compound flood events. To assess how sea level rise may affect the number of compound events for different global warming levels, we added the corresponding sea level rise to the historical tide-surge data sets and left the discharge unchanged. As shown in Figure 2, the Bothnian Bay and Bothnian Sea do not experience sea level rise and will therefore not be explicitly named every time in the following as an exception to the general trends. A sea level rise associated with a 1.5K global warming already rises the number of compound flood event days strongly. Here, SSP1-2.6 (Figure 11) and SSP5-8.5 (Figure 12a) will double the amount of compound flood event days for southern England, eastern coast of Great Britain, Ireland, and the Western Baltic. Nearly all European rivers will experience an increase of 50% or more, with the exception of northern Norway. With global temperature rise crossing a warming of 2K all of Europe would experience twice the number of compound flood events compared to the historical reference period (Figure 12b), except for northern Norway and the northwestern German coast. In a similar fashion, a 3K temperature increase would triple the numbers of compound flood event days (Figure 12c) and 4K would raise it by a factor of 5 (Figure 12d). This demonstrates, that even if the global warming will be limited to 2K or less, the resulting sea level rise will impose a massively increased risk on the European countries.

It should also be taken into account that the number of annual compound flood events underlies natural variability. This can be seen in the variations of the 5 year average (Figure 13). A clear separation between RCP2.6 and RCP8.5 starts to emerge around the 2060s for both REMO data sets. The climate signal strength and amount of changes depend on the forcing and the time period, with most changes happening in the second half of the century. Nevertheless, a generally rising trend can be seen for the entire time period.

A large-scale study like this comes with inevitable caveats. Only data sets from two downscaled different global models were available due to the required high temporal resolution for the TRIM simulation. Due to not having an ensemble of available data sets we yielded uncertain changes in the discharge under RCP2.6 for parts of Europe. This goes hand in hand with compound flood events being a phenomenon that underlies large variability as seen in Figure 13. Therefore, even 30-year time frames have a certain amount of variability, especially with the ongoing influence of climate change. Furthermore, the evaluation of the model performance showed that the general patterns can be represented, but differences exist nonetheless due to limitations in the modeling frameworks. Additionally, the uncertain absolute amount of sea level rise, as well as the linear superposition of tides with sea level rise, adds a noticeable uncertainty to the question of how strong the changes in future extreme events will be since it is the predominant factor. Note that due to the large scale of the domain of our study, it was not possible to take local factors like flood protection and topography into account.

In the present study, we conducted an analysis of future changes in compound flood events over northern and central Europe and the contributing factors to it without the use of copulas. We have demonstrated that the number of compound flood events will strongly increase in the future, regardless of the scenario. Furthermore, we analyzed future changes in discharge and coastal water levels. To the authors' knowledge, this is the first study that investigates these changes without the use of copulas in Europe. It is important to point out that this study should be seen as a general trend analysis for future scenarios and not as an actual prediction that can be used for precise flood risk assessment. Scenario RCP2.6 shows a less extreme increase in compound flood events compared to RCP8.5. The main contributor to those changes is sea level rise, while changes in river discharge are less severe but are not negligible. The sea level rise will lead to a strong increase in compound flood events, even when the global warming is limited in line with the Paris Agreement. The magnitude of those changes increases toward the end of the current century. In general, REMO–Had and REMO–MPI show strong agreement for RCP8.5, but less for RCP2.6. Additionally, we see in a future with adjusted thresholds that west-facing coasts experiencing a higher number of flood events than expected by pure chance, just like in the historical reference period. This implies that the strongest compound flood events in future scenarios will still be caused by a common driver like a specific weather constellation. Future work can further examine climate change under RCP2.6 and RCP8.5 by utilizing an ensemble of global climate models. This, paired with a better understanding of sea level rise on a local level, will be important to lower the uncertainty in changes to future compound flood events, which is essential for accurate risk assessment.

The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

PH developed the analysis methods, performed the data analysis, and wrote the manuscript. SH initiated the study and contributed the HD discharge data while LG generated the TRIM data. RW and SH supervised the research activities, revised the manuscript, and contributed to the interpretation of the results. RW acquired the funding. All authors contributed to the article and approved the submitted version.