The atmospheric part of the regional climate model (Wang et al., 2015; Gröger et al., 2015; Dieterich et al., 2019a) is based on Rossby Center regional atmosphere (RCA) model (Samuelsson et al., 2011; Strandberg et al., 2014) version 4. RCA was set up for the European Coordinated Regional Climate Downscaling Experiment (EURO-CORDEX) domain (Fig. 1). The horizontal resolution is 0.22∘ on a rotated grid, which results in a metric resolution of ∼24 km (Table 1). The vertical resolution is given by 40 hybrid levels. At the lateral boundaries, the model is driven either by reanalysis data (ERAI, Dee et al., 2011) or global climate model output. Hence, there is no feedback from the RCA to outside the model domain. This means that ARs enter the model domain from the parent global model but then develop freely and independently of the model. The forcing data are prescribed at 6-hourly time intervals.

The land–surface boundary is defined according to ECOCLIMAP (Champeaux et al., 2005) and used to calculate mass and energy fluxes between the Earth's surface and the atmosphere. Over the North Sea and Baltic Sea, RCA is interactively coupled to the 3-D ocean model NEMO (Nucleus for European Modelling of the Ocean; Madec, 2012, Fig. 1, Table 1). Sea ice temperature, sea ice fraction, sea ice albedo, and water temperature over this region are explicitly modeled by NEMO. Air–sea mass and energy fluxes are then calculated in the atmosphere model and used to drive NEMO, which is set up at a resolution of 2 nautical miles (∼3.7 km) and 56 vertical varying z* layers. Coupling is managed by the OASIS coupler (Valcke et al., 2003). However, with its high resolution and short time stepping, NEMO is very expensive to run. Therefore, outside the coupled domain, i.e., the Mediterranean and North Atlantic, RCA is driven by reanalysis data or global climate model output.

The climate model RCA has been intensively validated and comprehensively described (e.g., Wang et al., 2015; Gröger et al., 2015, 2019, 2021a; Dieterich et al., 2019a, b). It has been employed in previous studies to investigate the present climate and simulate the mean response to global climate change by downscaling global climate scenarios (Dieterich et al., 2019a; Gröger et al., 2019, 2021a). Gröger et al. (2021a) showed that the RCA-NEMO coupled ensemble is well within the range of the high-resolution EURO-CORDEX ensemble (Jacob et al., 2014). However, significant differences arise for interactively coupled areas over the sea (Gröger et al., 2021a, b). This applies to both climatic mean changes and climatic extremes (e.g., dry periods, cold spells, heat waves).

The above-described model was used to downscale a set of global model climate scenarios taken from the CMIP5 suite. Table 2 lists the downscaled RCA simulations as well as the applied scenarios (first row) and individual model configurations (first column).

The chosen climate scenarios follow the protocol of the Representative Concentration Pathways (RCPs) used in CMIP5 and derive from three different GHG emission assumptions. The low-emission scenario RCP2.6 assumes both vigorous mitigation actions (van Vuuren et al., 2007, 2011) to limit the global mean temperature increase to +2 ∘C compared to the pre-industrial period and negative emissions during the last decade of the 21st century. RCP4.5 is a moderate-emission scenario in which emissions peak at mid-century (2040) and remain constant after ∼2080, at a value about half of that at the end of the historical period (Clarke et al., 2007; Thomson et al., 2011). In the totally unmitigated scenario (RCP8.5) (Riahi et al., 2007, 2011), rising emissions until the end of the century are assumed. The three scenarios impose a maximum radiative forcing of 2.6, 4.5, and 8.5 W m-2 compared to pre-industrial conditions.

In addition to the climate simulation, we produced a hindcast run with RCA forced by ERAI reanalysis data at the lateral boundaries (RCA-ERAI, Dee et al., 2011, Table 2). In this study, the hindcast was compared with the original ERAI data, which have a resolution of only 0.75∘ but the same temporal resolution of 6 h (Table 1). The original ERAI data were interpolated onto the grid of the RCA climate model using the bilinear remapping technique provided by the Climate Data Operators software package (Schulzweida, 2021). This comparison demonstrated the added value of downscaling. For a full description of the ERAI reanalysis data set, the reader is referred to Dee et al. (2011).

A number of studies have addressed methods to detect ARs, based on model simulations in a Eulerian framework (Lavers et al., 2011, 2012; Nayak et al., 2014; Nayak and Villarini, 2017; Gao et al., 2015; O'Brien et al., 2020). An overview of some of those methods can be found in Shields et al. (2018). In our study, we employed the detection algorithm developed by Lavers et al. (2012) and Lavers and Villarini (2013), as it has been successfully applied in hindcast simulations and in future projections (Lavers and Villarini, 2013; Lavers et al., 2013). In this algorithm, vertically integrated atmospheric water vapor transport ([kg m-1 s-1], hereafter IVT) is calculated at every 6-hourly model output time step. The vertical integration is done over pressure levels ranging from 1000 to 300 hPa (Lavers et al., 2012): 1IVT=1g∫1000300qudp2+1g∫1000300qvdp2, where g is gravitational acceleration [m s-2], q is specific humidity [kg kg-1], u and v are horizontal wind components [m s-1], and dp [Pa] is the pressure level difference of adjacent pressure levels.

Next, the detection algorithm is launched (Lavers and Villarini, 2013). It is composed of the following steps:

From the 6-hourly IVT time series between 1970–1999, all time steps at 12:00 UTC are extracted.

Note that for the ERAI data set and the RCA-ERAI (Table 2) hindcast simulation, the analysis period is 1979–2008, as ERAI data from before 1979 are not available.

Figure 3 provides an example of an AR that caused intense rain over France and Germany and was detected in the ERAI reanalysis (left) and in the ERAI hindcast simulation (right). The detection procedure is performed separately for the historical and future periods and for each model (Table 2).

Unlike previous studies (e.g., Lavers et al., 2013; Gao et al., 2016; Ramos et al., 2016), in this study we did not use the historical thresholds to detect ARs in a future climate. Instead, the IVT thresholds were calculated based on the respective climatologies between 2070 and 2099. This was done to keep the empirical relationship between the 85th percentile IVT and the moisture content in ARs derived for the present climate. Hence, according to weather data for the years 1998–2005, the 85th percentile at noon (12:00 UTC) corresponded roughly to the median moisture content of the observed ARs (see Lavers and Villarini, 2013, for details).

Figure 2 shows that the 85th percentile can strongly increase in the future climate depending on the scenario, the latitude, and the respective model. An example is RCA-CAN for which the IVT threshold increases by nearly 40 % in RCP8.5 north of 55∘ N (Fig. 2b). In this simulation, the 85th percentile IVT from the historical run at 55∘ N corresponds to the 68th percentile in the future period.

Hence, in this study, a stable empirical relationship between the 85th percentile and the median was assumed. Consequently, our approach limits the influence of the larger mean atmospheric moisture content in the future climate and instead emphasizes dynamic changes.

The impact of ARs under present and future climate was investigated by calculating the following indices:

ARF is the AR frequency expressed as a percent of AR days per total days within a 30-year period. A calendar day is classified as an AR day if within the 24 h at least one AR event is recognized. Even if only one of the four 6-hourly time steps during the day is impacted by an AR, the day is counted as an AR day. Consequently, an AR lasting 18 h and extending over 2 d is counted as 2 AR days. No distinction was made regarding whether an AR day was associated by precipitation or not.

A comparison of the latitude-dependent IVT thresholds of the RCA simulations with those derived from ERAI is shown in Fig. 2a. As expected, the RCA-ERAI (triangles in Fig. 2a) hindcast simulation was closest to the ERAI reanalysis (filled squares). Notable discrepancies between the two data sets occurred at latitudes 40 and 35∘ N. Due to the rotated grid of the RCA, the positions of 35 and 40∘ N at 10∘ W were closest to the western lateral boundary of the RCA (Fig. 1). The discrepancies most likely stem from known issues with lateral boundary coupling, as occurs in limited area models with one-way coupling to the global models (e.g., Davies, 2014; Chikhar and Gauthier, 2017). Moreover, the southern model boundary at 35∘ N lies in the transition zone between dry air masses from the subtropics and the wet air masses of the westerlies. In this transition zone, large gradients in moisture content over short distances can be expected. Consequently, small differences in the mean position of the transition zone can cause large differences in the local moisture content.

The pronounced differences that characterize the different RCA historical simulations (Fig. 2a) reflect the different climates derived from the parent global models at the lateral boundary. First, the parent global models differ in their thermodynamic equilibrium states, such that both the air temperatures and the moisture loads at the lateral boundary of the RCA differ as well. As a result, the large-scale atmospheric circulation also differs among the global models (e.g., Brands, 2022), as the Equator-to-pole temperature gradients are likewise different (Harvey et al., 2014). This further influences the meridional position of the westerlies in the respective models. For example, the maximum moisture transports are located around 50∘ N in RCA-HAD, RCA-CAN, and RCA-MIROC but at 45∘ N in the other historical runs.

There was no evidence of a linear relationship between climate warming and the increase in IVT thresholds (Fig. 2b). For example, in RCA-HAD the IVT at 35∘ N in the low and moderate warming scenarios (RCP2.6 and RCP4.5) increased by ∼10 % and ∼15 %, respectively (Fig. 2b). In the strongest warming scenario (RCP8.5), however, the IVT decreased by ∼5 %. This suggests that, over the long term, dynamic changes influence the IVT. Also decadal variations in wind components and specific humidity have to be considered in this context (Thandlam et al., 2022).

Table 3 summarizes the number of ARs for each run of the climate ensemble and the ERAI reanalysis data set and for the RCA-ERAI hindcast run. The results were almost identical for the RCA-ERAI hindcast (322) and ERAI reanalysis itself (321), which was used to drive the RCA. This indicates that the number of ARs in the RCA is primarily controlled by the parent global model at the lateral boundaries. This is not surprising since ARs develop in open-ocean regions far outside the model's domain. However, within that domain, the RCA develops freely, leaving its own fingerprint on ARs, by controlling their intensity, geometry, and lifetime (Fig. 3). The RCA fingerprint is likely to become stronger with growing distance from the lateral boundaries. Analogously, ARs in the respective RCA climate simulations (Table 3) will reflect the ARs generated from the driving global climate model. Consequently, the RCA historical climate ensemble had a fairly large spread during the historical period, ranging from 262 (RCA-MIROC) to 421 (RCA-NorESM). The difference between the ensemble mean (RCA-MEAN) of the historical simulations (RCA-MEAN = 359) and the RCA-ERAI hindcast run (n=322) was small compared to the standard deviation over the RCA historical ensemble (58).

Compared to the historical period, RCA-MIROC increased by 15 % in RCP4.5 but only by 5 % in the strongest warming scenario (RCP8.5, Table 3) which is lowest increase in the ensemble. Hence, there was no linear scaling with global mean warming compared to the other models. This can be explained by the changes in the large-scale circulation in the parent global model, such as induced by shifts in the eddy-driven jet (Gao et al., 2016).

A comparison of the moisture transported by ARs over land is shown in Fig. 4a, which depicts the potential of ARs to force local heavy-precipitation events. Note that the moisture content over land is lower in the RCA-ERAI run than in the ERAI (∼5 %, Fig. 4a). This is in line with the model's cold bias in air temperature (Gröger et al., 2021a), thus favoring a lower moisture content. The lower moisture content in RCA-MEAN than in the RCA-ERAI hindcast simulation should also be pointed out. Overall, this suggests a systematic negative bias in the moisture content over land in the RCA model. The distribution of diagnosed AR durations (Fig. 4b) does not indicate systematic differences between the ERAI reanalysis, the hindcast run, and the mean historical climate simulations. For all model realizations, about half of the detected ARs lasted 1 d or less (Fig. 4b).

Maps of ARFs over land are presented in Fig. 5a. As expected, during the historical period, ARs were most abundant over the UK and the coastal regions of western Europe. Further inland, AR frequencies declined as the ARs lost moisture due to rainfall and thus no longer met the IVT threshold. Strong moisture losses also occurred along the Norwegian coast, where AR landfalls caused heavy rain events due to orographic uplift.

We then evaluated the potential of ARs to cause annual maxima of daily precipitation (Fig. 5b, % AMP). Locally, ARs explained up to ∼60 % of the yearly maxima over southwestern Norway. A strong imprint was likewise seen over the western UK and along European coasts, where ARs were responsible for up to 50 % of the annual maxima in RCA-MEAN and RCA-ERAI.

Besides their potential to cause yearly precipitation maxima, ARs give rise to heavy-precipitation events. The fractional contributions of ARs to heavy precipitation (% 95P) and to the total precipitation (% TP) are shown in Fig. 5c and d. The spatial pattern mainly mirrored the AR frequency pattern, but it also reflected the varying long-term mean hydrological conditions in Europe: in semi-arid regions such as the Iberian Peninsula and along the western coast of Italy, % 95P increased to almost 60 % and 30 %, respectively. Under the humid climate of central and western Europe, the % 95P was smaller, but it reached 40 % in western France and the southern UK (Fig. 5c). In the mountainous regions of Norway and in the Alps, i.e., regions with very high mean precipitation and frequent convective rain events, the influence of sporadic ARs was accordingly low. A similar pattern characterized the fractional contribution to the total annual precipitation (% TP, Fig. 5d). Maxima occurred over western France and the western Iberian Peninsula, where ARs accounted for up to 10 % of the total precipitation.

The effect of downscaling was assessed by comparing the 0.75∘ ERAI reanalysis (Fig. 5, right column) with the 0.22∘ RCA-ERAI hindcast simulation (Fig. 5, middle column). The lower resolution of ERAI eliminated much of the spatial variability, thus highlighting the effect of the downscaling by RCA. This was most visible in the noisy precipitation-related indices % AMP, % 95P, and % TP (Fig. 5b–d). This was expected because spatial precipitation patterns are modulated by stochastic processes associated with, e.g., small convection cells and further affected by topography. The representation of convection cells and topography has been shown to benefit from a higher resolution (e.g., Feser et al., 2011; Hohenegger et al., 2020; Stevens et al., 2020). The pronounced effect of a higher topographic resolution was seen over the Iberian Peninsula. Here, RCA-ERAI clearly resolved the distinct effect of the prominent west–east topographic features seen in the fractional contributions to the precipitation budget. Those features appeared as small distinct WSW–ENE bands of alternating high and low % 95P and a % TP that followed the topographic elements built up by the Sistema Central plateau, the Sierra Morena mountains, and the Penibaetic orogenic system (Fig. 5c and d, and middle columns). By contrast, in ERAI (Fig. 5c and d, right column), there was a simple decline of the % 95P, while the % TP occurred at a longer distance from the coast and did not reflect any topographic imprint. For the Iberian Peninsula, the added value of regional downscaling was previously reported for the simulation of mean precipitation and mean temperature patterns (Gómez-Navarro et al., 2011).

Another noteworthy difference was the considerably larger number of AR-related annual maxima (% AMP, Fig. 5b) over Norway, western Scotland, and Italy in RCA-ERAI than in ERAI. In the latter, the AR influence on % 95P and % TP was much more extensive in eastern Europe. However, there are no major topographical elevations in eastern Europe, which suggests that resolution is not the only factor accounting for this difference. Rather, differences in the model's physics (e.g., cloud formation) and the surface boundary conditions (e.g., surface temperature, surface roughness parametrization) between RCA-ERAI and ERAI could influence the extent of AR penetration into eastern Europe.

Finally, we note that the comparison between different spatial resolutions might also reflect different noise levels. This noise occurs when isolated grid points located outside the ARs at a given time step exceed the IVT threshold but do not satisfy the geometric and temporal requirements. The different noise levels would then contribute to the total effect of downscaling.

Global climate models can have considerable biases on a regional scale. Consequently, when driven by global climate models at the boundaries, RCA will not perform as well as hindcast models when the driving lateral boundaries are constrained to reanalysis data. Therefore, in the following, before assessing climate change scenarios, we briefly compare the results of the RCA historical ensemble mean (RCA-MEAN, Fig. 5, left column) with the RCA-ERAI hindcast (Fig. 5, middle column) and ERAI reanalysis data (Fig. 5, right column).

For ARF, % AMP, % 95P, and % TP, RCA-MEAN reasonably well reproduced the spatial pattern obtained with the RCA-ERAI simulation. The spatial correlation coefficients between RCA-ERAI and RCA-MEAN were 0.98 for ARF (Fig. 5a), 0.86 for % AMP (Fig. 5b), 0.82 for % TP (Fig. 5c), and 0.92 for % 95P (Fig. 5d). Similar to RCA-ERAI, the imprint over eastern Europe was distinctly weaker according to RCA-MEAN than according to the ERAI data set.

Pronounced differences between RCA-MEAN and RCA-ERAI also occur over the Iberian Peninsula, where the values of % AMP, % 95P, and % TP are systematically higher in RCA-MEAN. Overall, the best match between RCA-MEAN and RCA-ERAI is for the parameter ARF (Fig. 5a). As ARF is calculated only from the IVT, it is less effected by biases in precipitation. Thus, the main contributor to the biases of RCA-MEAN seen in % AMP, % 95P, and % TP are attributable to the simulated precipitation, not to the IVT. We note that the exact reproduction of precipitation pattern is difficult in coarse-resolution models due to insufficient description in cloud physics and/or the treatment of convective energy (e.g., Prein et al., 2013; Hohenegger et al., 2020).

The detected ARs were also characterized by a strong seasonal cycle that was well reproduced by RCA-MEAN. Figure 6 shows that ARs were most abundant during fall and early winter. The only notable difference was in August, when the relative share was about twice as large in the RCA historical ensemble than in the ERAI hindcast. In addition, RCA-MEAN and RCA-ERAI highly overestimate the number of ARs in September compared to ERAI but underestimate it in October. However, overall, ARs were better represented in the model's climate mode (RCA-MEAN) than in the RCA-ERAI hindcast simulation.

The relative change in average moisture transported by ARs for each of the GHG emission scenarios and each of the downscaled global models is summarized in Fig. 7. ARs became consistently more intense; i.e., they had a higher moisture load, in a warmer climate. The average intensity at the end of the century indicated by RCA-MEAN increased by 6 % (RCP2.6), 13 % (RCP4.5), and 24 % (RCP8.5). These values are generally in line with the corresponding increases in the IVT thresholds (Fig. 2b).

The number of detected ARs also increased (Table 3). For RCA-MEAN, this number increased by 9 %, 19 %, and 24 % in RCP2.6, RCP4.5, and RCP8.5, respectively. These values were roughly proportional to the increase in intensity. However, not only the frequency of ARs but also the spread of the individual realizations at the end of the century increased. The relative change in the ensemble spread (Table 3, second row) increased even more than the ensemble average (RCP2.6 = 17 %, RCP4.5 = 24 %, RCP8.5 = 56 %). This highlighted the large uncertainty with respect to the chosen global model used for downscaling. Advanced approaches for weighted model averaging have been developed to reduce this type of uncertainty and have been tested for ARs occurring over the US (Massoud et al., 2019, 2020; Wootten et al., 2020).

The change in the spatial patterns is shown in Fig. 8. An overall increase in AR day frequency was determined for scenarios RCP4.5 and RCP8.5 (Fig. 8a). The strongest increase occurred near the Bay of Biscay and adjacent land areas (western France and southern UK). This response over land was more or less consistent across the RCP scenarios but differed in strength, ranging from ∼+0.2 % to >+1.8 % in RCP4.5 and RCP8.5 (Fig. 8a). This corresponds to a relative increase of 20 %–120 % (RCP4.5) or 40 %–250 % (RCP8.5) over the Iberian Peninsula, the UK, France, Germany, and along the Norwegian coast.

Figure 8b shows the changes in the yearly maximum precipitation attributed to ARs (% AMP). The most robust change was the strong increase over the western central part of Europe, extending from western France along the coast of Belgium, the Netherlands, northern Germany, and Denmark up to the southern coast of Norway. Further sites of stronger AR impact were also visible along the northwestern area of the Iberian Peninsula and the southern UK, whereas over southern Scandinavia there were no robust changes. However, in this area, % AMP was already very high during the historical period (Fig. 5b), which limited the potential for further increases. This increase over the UK, France, western Germany, and the Iberian Peninsula was by far the strongest in the unmitigated RCP8.5 scenario. In the moderate scenario (RCP4.5), the changes were less pronounced in eastern central Europe (Germany, Denmark). In the mitigation scenario (RCP2.6), robust changes were restricted to a small area in NW France (Brittany, Normandy).

The higher AR frequencies and moisture loads also had consequences for local precipitation budgets. The fractional contributions of ARs to the heavy-precipitation fraction (% 95P, Fig. 8c) and to the total annual precipitation (% TP, Fig. 8d) increased nearly everywhere for RCP4.5 and RCP8.5. The most pronounced changes were in regions where the % 95P and % TP were already large under historical conditions (Fig. 5c and d). In RCP8.5, the strongest increases primarily occurred in the western Iberian Peninsula and along the French coast (Bay of Biscay), where heavy rain precipitation increased by up to +30 % and up to 20 %, respectively, compared to the historical period.

The elevated AR fractional contributions % 95P and % TP in RCP4.5 and RCP8.5 (Fig. 8c and d) suggested that in these scenarios the increase in the AR-induced precipitation rates was higher than the increase in the average precipitation rates.

The relative changes in mean precipitation and AR-induced precipitation for RCP8.5 are compared in Fig. 9. The mean precipitation change (Fig. 9a) was consistent with the typically dryer conditions over southern Europe and the typically wetter conditions over northern Europe (e.g., Jacob et al., 2014; Kjellström et al., 2018; Teichmann et al., 2018; Gröger et al., 2021a; Christensen et al., 2022). Hence, mean precipitation rates increased only slightly, by at most 12 %, over central Europe or even decreased over southern Europe. By contrast, AR-induced precipitation increased ∼25 %–40 % over central Europe (Fig. 9b). Decreasing AR precipitation also occurred in southern Europe but the reductions were weaker than the reductions in the mean rates. The exception was Norway, where AR-induced precipitation decreased while the mean rates increased. The lower AR precipitation rates well agree with the low response in western Norway of the % AMP, which locally even decreased (Fig. 8b).

The dynamic changes were investigated by exploring the route followed by ARs east of the 10∘ W meridian. In this analysis, AR masks were used (see Fig. 3), and for the model's land grid cells the corresponding latitudinal position where the AR crosses the 10∘ W meridian was determined. All land grid cells overlain by the respective AR were then flagged with the latitudinal bin at 10∘ W (for example, 45∘ N for the bin 45–50∘ N). The flagged masks were then used to calculate, for every land cell, the percent share for every latitudinal bin (with the sum of all bins at every land point defined as 100 %). This was done for the periods 1970–1999 and 2070–2099. Then, the future change (difference between 2070–2099 and 1970–1999) was calculated for RCP8.5. Finally, the latitudinal bins were consolidated into three main meridional bands: south of 45∘ N, 45–60∘ N and north of 60∘ N.

Our analysis showed not only the more frequent occurrence of ARs in the future at all latitudes but also a change in their composition (with respect to the meridional band where they originate). AR contributions from >60∘ N declined everywhere (Fig. 10a), with a ∼20 % reduction over Norway, but also over many European mountainous regions, such as the Pyrenees, Massif Central, the Alps, and mountains in the Balkans (Fig. 10a). The smaller fraction was paralleled by a relative increase in ARs originating from south of 45∘ N (Fig. 10c), while the fraction from 45–60∘ N was more or less unchanged (Fig. 10b).

The larger fraction of more southern ARs over Norway (and the smaller fraction from >60∘ N) has two implications: (1) the more southern ARs will carry warmer air masses to Scandinavia, such that precipitation will tend to fall more often as rain than as snow. (2) Moisture transport via southern ARs implies that the moisture is routed over longer distances across the central continent before it arrives in Norway. ARs traversing the continent can no longer take up significant amounts of moisture but instead lose moisture via precipitation. By contrast, ARs originating from >60∘ N and crossing the open North Atlantic can take up moisture until they make landfall at the Norwegian coast. This is in particular the case during the warm season when SSTs are high enough to allow convection or during winter when moisture convergence advects moisture from adjacent areas. These changes likely account for the lower AR precipitation rates determined along the western coast of Norway (Fig. 9b).

Climate models are designed and validated to simulate the mean state and mean variability of the long-term climate. Hence, the validation of climatic extremes during model development is relatively small. As a result, the models results will differ more for extreme regimes. Figure 11 shows the inter-model standard deviations for the different percentiles of precipitation. The percentiles were calculated for all nine models (Table 2) covering the historical period. For the higher percentiles, the spread over the models clearly increases, such that uncertainties are highest in the extreme precipitation range, i.e., the range where AR precipitation is expected to occur. Therefore, to assess the uncertainties associated with model choice, in the following we consider the spread in the ensemble members with respect to ARF, % AMP, and % 95P.

Figure 12a depicts the frequency of AR days. All realizations exhibited a coherent spatial pattern that was similar to the RCA ensemble mean (Fig. 8a), indicating the latter as a representative indicator of the bulk response. The uncertainties in the model spread as indicated by the ensemble's standard deviation (Fig. 12a) were highest in the southern UK, France, Belgium, the Netherlands, Luxembourg, and the western Iberian Peninsula. In conclusion, the uncertainty in the response is highest in those regions where ARs are frequent already during the historical period (Fig. 5a). RCA-HAD, RCA-CAN, RCA-IPSL, and RCA-GFDL showed the strongest response, whereas the response in RCA-MIROC and RCA-ECE was exceptionally weak. The weak climate impact in RCA-MIROC is a direct consequence of low increase in detected ARs (∼5 %, Table 3). Only a single model shows a clear signal along the Norwegian coast (RCA-HAD) and whole Scandinavia.

The response of AR-forced annual maximum precipitation events (% AMP) is shown in Fig. 12b. No clear consistent response was detected over western Norway, i.e., the region where in the historical climate the % AMP was highest (Fig. 5b). Some models (RCA-CAN, RCA-MPI, RCA-GFDL, RCA-IPSL) showed distinct locations over Norway where the impact of ARs was smaller in the future, probably linked to the aforementioned decrease in ARs arising from >60∘ N. The most coherent change across the realizations was the relatively strong increase over western France, which in some realizations extended further east. However, also in this region the local ensemble variability was pronounced and in RCA-ECE the % AMP in fact decreased.

Uncertainties with respect to the contribution to heavy precipitation (% 95P) were highest in France and the Iberian Peninsula (Fig. 12c). High inter-model variation was determined also for the southern tip of the Iberian Peninsula, where the standard deviation was highest. In this region, the contribution of ARs was either reduced, as in RCA-HAD, or increased by as much as 50 %, as in RCA-CNRM. Larger uncertainties were likewise identified for central Europe (France, Belgium, Netherlands, Germany), with the direction of change being consistently positive. In RCA-HAD, RCA-CNRM, RCA-ECE, and RCA-MIROC, the changes over eastern France and Germany were extremely low. A notable decrease, occurring in the UK, was modeled only by RCA-HAD.

In summary, our analysis showed a robust inter-model agreement for the general spatial pattern. However, local uncertainty is high especially in % AMP (i.e., the most severe precipitation events, Fig. 12b), where even the direction of change is not consistent.

Our results generally agree with those of the global CMIP5 models (e.g., Lavers et al., 2013; Gao et al., 2016; Ramos et al., 2016), with both indicating more frequent and more intense ARs over Europe. With respect to previous studies, the effect of climate change on AR frequency has been shown to strongly depend on the chosen reference period. Studies that applied the 85th percentile threshold derived from the historical period also to the future period often reported a doubling of the AR frequency (e.g., Lavers et al., 2013; Ramos et al., 2016; Gao et al., 2016). However, as noted above, we calculated separate 85th percentile thresholds for these two periods, and the AR frequency increase was therefore lower (because the IVT thresholds for the future period were higher; Fig. 2) than that in the aforementioned studies but nonetheless 20 %–30 % across the models.

The main differences with respect to global projections occurred over Norway and the Iberian Peninsula, two hotspots of AR impact in Europe. Over the Iberian Peninsula, the distribution of AR-related heavy precipitation was clearly modulated by topographic structures, including the Sistema Central Plateau, the Sierra Morena mountains, and the Penibaetic orogenic system. These valleys and ridges will lead to zonal bands of high and low increases in AR precipitation over the Iberian Peninsula in the future. Over Norway, our regional ensemble did not predict a robust climate change signal for the frequency of ARF, % AMP, % 95P, or % TP (Fig. 8). Global CMIP5 models indicated an increase in the regional % TP and % 95P of at least 10 %–20 % according to RCP8.5 (Gao et al., 2016, Fig. 9 therein). In our regional model, % AMP was either negative or positive, depending on the global model, and thus did not yield a clear signal (Fig. 12b).

Our finding that in a future high-emission scenario ARs from south of 45∘ N will be more common over Europe than ARs from >60∘ N points to larger-scale atmospheric circulation in the parent global models. While such changes cannot be analyzed in our limited area model, it can be proposed that they are related to changes in the storm track (Zappa et al., 2013) and/or systematic changes in regional weather systems (Pasquier et al., 2019).