2.1 Model ensemble

The AGCM used here, HadGEM3-GA3.0, is the Global Atmosphere 3.0 configuration of the HadGEM3 family of the Met Office Unified Model (Walters et al., 2011). We use an ensemble of simulations at three different horizontal resolutions: N96 with a grid spacing of 135 km at 50^∘ N, N216 (60 km), and N512 (25 km). There are 85 vertical levels, the same at all three resolutions. These simulations were conducted within the UPSCALE project and their generation and analysis required exceptionally large computing resources and big data infrastructure (Mizielinski et al., 2014). These resources allowed five simulations to be produced at N512 resolution, each lasting 26 years from 1986 to 2011 and using OSTIA sea surface temperature forcing (Donlon et al., 2012). Lower resolution simulations with the same forcing were conducted at N216 resolution (3×26 years) and at N96 resolution (5×26 years). These experiments were designed to test the sensitivity of the simulated climate to horizontal resolution only and therefore parameter changes between the different resolutions have been kept to the minimum necessary to ensure numerical stability (Demory et al., 2014; Johnson et al., 2016). Convection is parameterised at all three resolutions.

We have also conducted a sensitivity experiment to test the role played by the orography boundary conditions as the resolution is increased. This experiment was conducted with the HadGEM3-GA6.0 configuration of the Met Office Unified Model (Walters et al., 2017) and is described in Sect. 5.2. HadGEM3-GA6.0 was the closest available model configuration to HadGEM3-GA3.0 at the time the sensitivity experiment was conducted. Differences between GA6.0 and GA3.0 include small adaptations to the semi-implicit semi-Lagrangian dynamical core from “New Dynamics” (Davies et al., 2005) to ENDGame (Wood et al., 2014) and the new “5A” subgrid orographic drag parameterisation (Vosper, 2015; Wells, 2015) replacing the previous “4A” scheme (Webster et al., 2003).

2.2 Observed precipitation

We evaluate the simulated precipitation against gridded observed precipitation from the E-OBS dataset (Haylock et al., 2008), version 9. As part of the ENSEMBLES project (van der Linden and Mitchell, 2009), this dataset was designed for the evaluation of daily precipitation across Europe in RCMs at similar resolutions to the AGCM simulations used here. This makes E-OBS the dataset of choice for our purposes and we refer to differences of model precipitation from E-OBS as model biases. Nonetheless, gridded precipitation data are subject to uncertainties from both the measurement error of point observations and the limited spatial representativity of gauges (Frei and Schär, 1998). A general dry bias, which can be exacerbated in mountainous terrain and for localised extremes, has been reported for E-OBS (Flaounas et al., 2012; Hofstra et al., 2009; Isotta et al., 2015).

2.3 Extreme value analysis

We evaluate daily extreme precipitation by fitting a generalised extreme value (GEV) distribution to daily precipitation averaged over a number of European river basins (Table S1 in the Supplement). We choose basins with surface areas larger than 50 000 km² so that even at N96 resolution the basins will be represented by several model grid boxes. The GEV distribution is defined as in Coles (2001) and is characterised by three parameters referred to as location μ, scale σ, and shape ξ. Illustrations of how these three parameters influence the GEV distribution will be provided in Sect. 4.1 and Fig. S1 in the Supplement. We estimate the GEV parameters using the block maxima approach, in which each block consists of daily mean precipitation in a river basin throughout one season. The estimation is carried out in a two-step process. First, we estimate μ, σ, and ξ for each basin and each season using maximum likelihood estimation Coles (2001). We find that this yields plausible spatial variations of μ and σ with typically similar values in neighbouring basins, while there is considerable scatter in ξ with no systematic dependence on the basin location or area. This indicates that the shape parameter cannot be robustly fitted for each basin separately with the available data. We therefore conduct a second estimation step, in which we fix the value of ξ to the average value of all basins for each season, and then, also using maximum likelihood estimation, determine the values of μ and σ for each basin. Uncertainty in the fitted GEV parameters is estimated by parametric resampling.

4.1 Examples

In this section, we present results of extreme value analysis and evaluate the amount, frequency, and annual cycle of extreme precipitation in terms of GEV distributions. GEV distributions are conveniently shown in terms of return value plots, also called Gumbel diagrams. The effect of the GEV parameters on the distribution is illustrated for fictitious data in Fig. S1. The larger the values of these parameters, the larger the precipitation extremes. An increase in the location parameter μ corresponds to a constant increase in return value for all return times (Fig. S1a). The scale parameter σ is associated with the interannual variability of extreme precipitation. The larger the σ, the larger the increase in return value for a given increase in return time (Fig. S1b). The shape parameter ξ determines the behaviour of the tail of the GEV distribution and determines if the distribution is bounded (ξ<0) or unbounded (ξ>0) for large return times (Fig. S1c). The shape parameter is held constant for all basins as explained in Sect. 2.3 ($\mathit{\xi }=-\mathrm{0.13}$, −0.05, −0.02, and −0.05 for DJF, MAM, JJA, and SON, respectively).

Examples of fitted GEV distributions for three river basins are shown in Fig. 4. Each panel shows GEV distributions for the four seasons alongside the observed precipitation maxima. The top row (Fig. 4a–c) shows results for the Loire river basin. The annual cycle of extreme precipitation is not very pronounced for this basin, and estimated 50-year return values are between about 22 (spring) and 26 mm day⁻¹ (autumn), although the differences between the seasons are not statistically significant (Fig. 4a). The precipitation extremes simulated by the N96 model are very different from those in the observations. The estimates are larger than for E-OBS (50-year return values between about 30 for summer and 40 mm day⁻¹ for winter) and there is a clear annual cycle with larger extremes during the cold season (Fig. 4b). At N512 resolution, the model-simulated extremes are in closer agreement with E-OBS than at N96 resolution (Fig. 4c): the annual cycle is very small and 50-year return values are between 23 and 29 mm day⁻¹. Quantitatively, the reduction of the extreme precipitation biases can be corroborated by comparing the estimated values of the GEV location parameter μ and scale parameter σ between E-OBS, N96, and N512. For all seasons, E-OBS and N512 agree more closely with one another than with N96 (Fig. 4a–c). For the Loire basin, the biases in modelled extreme precipitation and their reduction at N512 resolution are consistent with the results seen for mean precipitation, i.e. a winter wet bias at N96 resolution that is alleviated at N512 resolution (Fig. 1).

Figure 4Fitted GEV distributions for (a–c) Loire, (d–f) Elbe, and (g–i) Po river basins, and for (a, d, g) E-OBS observed precipitation, (b, e, h) the N96 model, and (c, f, i) the N512 model. 95 % resampling confidence intervals are shown as shaded areas for winter (DJF) and summer (JJA). Block maxima (circles) are shown at return periods $\frac{m+\mathrm{1}}{m+\mathrm{1}-i}$, where m is the number of these maxima, i.e. here the number of years × ensemble members, and $i=\mathrm{1},\mathrm{\dots },m$ is their rank. Results for N216 are generally between those for N96 and N512 (not shown). The three basins are indicated in Fig. 5a and d.

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Fitted GEV distributions for the Elbe basin are shown in Fig. 4d–f. For this basin, there is a pronounced annual cycle of extremes. The largest extremes occur during summer with a 50-year return value of about 30 mm day⁻¹, while the same return value for winter is only about 17 mm day⁻¹ (Fig. 4d). The amplitude of the annual cycle is underestimated in the N96 model. The quantitative agreement with E-OBS is close in summer (50-year return values of about 30 mm day⁻¹ in both datasets), but the simulated winter extremes are larger than the observed ones and the N96 50-year return value is about 25 mm day⁻¹ (Fig. 4e). At N512 resolution, the model better captures the annual cycle of extreme precipitation but also somewhat overestimates the 50-year return values, which are about 34 mm day⁻¹ in summer and 19 mm day⁻¹ in winter. For a shorter return period of 2 years, however, all three datasets are in close agreement on a return value of about 15 mm day⁻¹ during summer. This example illustrates how the quantification of a single return value or return period only insufficiently characterises extreme precipitation, which is why two GEV parameters are used for quantitative model evaluation in this study.

The third basin we discuss is that of the Po river (Fig. 4g–i). In this basin, daily precipitation extremes are considerably larger in autumn than in the other seasons. This behaviour is also captured by HadGEM3-GA3.0 at both resolutions, yet the magnitude of the simulated extremes is much larger than in E-OBS, especially at N512 resolution. The 50-year return value for autumn is about 53 (55, 73) mm day⁻¹ in E-OBS (N96, N512). Moreover, and especially during winter, both the N96 and N512 models overestimate the interannual variability of precipitation extremes as shown by the overestimation of the scale parameter σ: for return periods of less than 2 years, a number of winter seasons never exceed a precipitation amount of 10 mm day⁻¹, which is not seen in E-OBS. On the other hand, winter precipitation extremes are overestimated by our model for return periods greater than 2 years. These results clearly show that the resolution increase from 135 to 25 km is not a panacea for improving the representation of extreme precipitation, and we will summarise results for all of the European basins in the remainder of Sect. 4 to assess the overall effect of increased resolution on model performance.

Before proceeding with this assessment, we briefly discuss the goodness of the GEV distribution fits, which can be assessed by comparing the observed maxima (open circles) with the parametric GEV fits (solid lines) for the different examples shown in Fig. 4. For most cases, the statistical model fits the observed maxima well, but there are a few discrepancies for larger return periods of more than about 20 years. For example, for the Po and in particular the Elbe basin, a small number of very heavy precipitation events, which exceed the GEV fit by more than the sampling uncertainty, can be seen during summer for the observations and the N512 model (Fig. 4d, f, g, i). Such discrepancies are partly due to the fact that we choose a constant shape parameter ξ for all basins (see Sect. 2.3). These results illustrate that our parametric approach is valid in general and serves our purpose of characterising the variation of daily extreme precipitation across European river basins, and of evaluating GCM simulated extreme precipitation. Especially for return periods of more than 20 years, however, our estimates of return values in individual basins/seasons should not be used as the only source to inform impact studies or adaptation and mitigation measures. While our results can provide initial guidance for such applications, they will need to be considered in the context of local expertise, process-based case studies of individual heavy precipitation events, and additional local observations if available.

4.2 Winter

The estimates of the location and scale GEV parameters for winter based on E-OBS are shown in Fig. 5a and d. There is a large-scale gradient from high values of μ and σ in the west and south-west of Europe to smaller values in the east and north-east. This geographical variation is similar to that in mean precipitation (Fig. 1a), but there are some interesting differences. For example, comparatively high values of both GEV parameters are seen for some southern European basins (e.g. Po, Guadalquivir) even though the mean precipitation for these basins is not larger than for basins further north. This may indicate fewer but stronger precipitation events in these basins.

Figure 5Estimated GEV parameters for December–February daily basin-average precipitation: (a–c) location parameter μ and (d–f) scale parameter σ, both in mm day⁻¹, and for (a, d) observations (E-OBS), (b, e) N96 bias, and (c, f) N512 bias with respect to E-OBS. Stippling (hatching) shows statistically significant differences between the models and E-OBS (between N512 and N96). Letters L, E, and P show the Loire, Elbe, and Po basins.

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The N96 bias in the GEV parameters is shown in Fig. 5b and e. As can been seen from the predominance of green colours, both the location and scale parameters tend to be overestimated, so the wet bias seen for mean precipitation (Sect.  3) is also found in the extremes. The magnitude of the bias varies strongly between basins and can be as high as about +60 % for μ (Elbe) and about +80 % for σ (Loire), and the median of the absolute relative bias, i.e. of $max\left(\frac{{\mathit{\theta }}_{\mathrm{N}\mathrm{96}}}{{\mathit{\theta }}_{\text{E-OBS}}},\frac{{\mathit{\theta }}_{\text{E-OBS}}}{{\mathit{\theta }}_{\mathrm{N}\mathrm{96}}}\right)-\mathrm{1}$, across all basins is 22 % for θ=μ and 17 % for θ=σ (Table 2). The wet bias is particularly pronounced for the basins in the North European Plain, from the Loire in the west to the Vistula in the east, where both μ and σ are overestimated. For some southern European basins (Guadalquivir, Ebro, Po), there are significant negative biases in μ and significant positive biases in σ, indicating a difference in the character of the simulated and observed extreme value distribution.

4.3 Summer

During summer, the GEV location parameter μ takes larger values in the centre, north-west, and north-east of Europe than in the south-west (Iberia), south-east, and east (Fig. 6a), in rough agreement with the geographical variation of mean precipitation (Fig. 1d). Particularly high values of μ are seen for basins draining the Alps (e.g. Rhône, Po, Upper Danube) and for the Kuban draining the Caucasus Mountains. The scale parameter σ generally follows the geographical distribution of μ, but we find comparatively larger values of σ for drier climates, as can be seen, for example, when comparing the Iberian to the French river basins.

Figure 6As Fig. 5 but for summer (June–August).

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More so than in winter, there is a dependence of both μ and σ not only on geographical location and local climate, but also on the size of the river basin considered. Larger extremes, i.e. greater values of μ and σ, are seen for smaller basins. A case in point are the Dniester and Southern Bug basins compared to the neighbouring larger basins of the Danube and Dnieper. This appears to be due to the nature of summer (convective) precipitation, which is smaller in scale and shorter in duration than frontal winter precipitation. Convective summer rain, though locally intense, may therefore not take large values when averaged over a large river basin over a day.

The biases of μ and σ for the N96 model are shown in Fig. 6b and e. These biases are generally smaller than in winter, and for many basins they are not statistically significant. There is a general tendency for dry biases in the south and wet biases in the north of Europe, especially in μ. The median relative bias across all basin is 9 % for μ and 10 % for σ (Table 2).

The sensitivity to the resolution increase (Fig. 6c, f) is smaller than in winter, consistent with the results for mean precipitation, and has mixed effects for the biases with respect to E-OBS. At N512, stronger heavy precipitation is seen over the Alps, rather than to the north-west of the Alps over France at N96, leading to weaker extremes and smaller biases for some basins (especially Loire, Seine) and to stronger extremes and a larger bias in particular for the Po basin.

4.4 Summary statistics

Two metrics are used to summarise model performance. The first metric is the median absolute relative bias as already introduced and discussed in Sects. 4.2 and 4.3. The values of this metric are shown in Table 2. The second metric is obtained by counting for each resolution for how many basins the minimum bias is attained at this resolution, so that a higher count corresponds to a better model performance. The values of this metric are shown in Table 3.

Table 2Median across all basins of absolute relative bias (%; see Sect. 4.2) in μ and σ. Numbers in bold indicate the resolution with the smallest bias.

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Table 3Number of basins with smallest bias in μ and σ. For example, the number 4 for μ in DJF at N96 resolution means that for 4 out of all 33 basins the bias in μ of the N96 model is smaller than that of both the N216 and N512 models. Numbers in bold indicate the resolution with the largest count.

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Both metrics agree on the following qualitative results: extreme precipitation is overall better represented as resolution is increased from N96 to N512. The clearest and strongest improvement is seen in autumn for both the location parameter μ and the scale parameter σ (see also Fig. S3). There is also an improvement in μ in winter and spring, but, for Europe as a whole, biases in σ do not decrease with higher resolution in these seasons. The resolution sensitivity in both GEV parameters is small in summer, with possibly a slightly better performance for the N96 model. Arguably, this result is due to the fact that extreme orographic precipitation in the higher resolution models is larger than that in E-OBS, as also seen for mean precipitation (Fig. 1). The performance of the N216 model is generally in between that of the N96 and N512 models, consistent with the result obtained for mean precipitation (Fig. 2), and also seen in maps of GEV parameter biases analogous to the ones shown in Figs. 5 and 6 (not shown).

5.1 North Atlantic storm track

European precipitation is strongly determined by the character of the North Atlantic and Mediterranean storm tracks. According to Hawcroft et al. (2012), roughly 70 % of European winter precipitation is associated with extratropical cyclones. It is therefore logical to ask to what extent the resolution sensitivity seen in the precipitation is due to resolution sensitivity in the simulation of the storm track. By analysing the historical simulations of the models participating in phase five of the Coupled Model Intercomparison Project (CMIP5), Zappa et al. (2013) identified four models with a comparatively good representation of the North Atlantic storm track. These four models have horizontal grid spacings of about 100 km, which is at the high end of CMIP5 model resolutions. The resolution dependence of European precipitation in the EC-EARTH AGCM version 2.3 was analysed by van Haren et al. (2015) by comparing simulations at ≈112 and ≈25 km grid spacing, and the authors find that at 25 km EC-EARTH has a better representation of the winter North Atlantic storm track and therefore precipitation over Europe.

Similar to Blackmon (1976) and van Haren et al. (2015), we evaluate the representation of the North Atlantic storm track in HadGEM3-GA3.0 by calculating the standard deviation of the 2–8-day band-pass-filtered 500 hPa geopotential height. The results are shown in Fig. 7 for winter. At all resolutions, the HadGEM3-GA3.0 storm-track location and strength is similar to that in ERA-Interim (Fig. 7a, b, d, g). The model biases with respect to ERA-Interim (Fig. 7c, f, j) show an overestimation of the Mediterranean storm-track strength by about 10 %, and an underestimation of about 10 % over north-east Europe, though these differences are not significant given the interannual variability. The resolution sensitivity in the storm-track strength over Europe attains values of about 5 % of the mean (Fig. 7e, h, i). Interestingly, the resolution sensitivity is of opposite sign for the two resolution increases: there is a reduction in storm-track strength when going from N96 to N216 over central and western Europe and the Mediterranean (Fig. 7e), but then an increase of similar magnitude over much of Europe when going from N216 to N512 (Fig. 7h).

Figure 7Standard deviation of 2–8-day band-pass-filtered 500 hPa geopotential height (m). (a) ERA-Interim reanalysis, (b, d, g) model (HadGEM3-GA3) at resolutions N96, N216, and N512, (c, f, j) model biases with respect to ERA-Interim, and (e, h, i) differences between model resolutions. Stippling shows statistically significant differences.

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We proceed by revisiting the resolution sensitivity in mean precipitation, shown in Fig. 1 and in greater detail in Fig. 8, and by comparing it to the sensitivity seen in the storm track. In winter, precipitation decreases with resolution over the North European Plain and increases over north-western and western European coasts, Iberia, and to the south of the Alps and Italy (Fig. 8i). In contrast to the sensitivity in the storm track, this pattern can be seen for both steps of resolution increase (Fig. 8e, h), showing that the storm-track sensitivity is not the main factor explaining the sensitivity seen in mean precipitation. At the same time, the precipitation sensitivity is generally smaller for the N216 to N512 resolution increase than for the N96 to N216 increase, especially so over the North European Plain, where the drying with higher resolution is comparatively small (Fig. 8h). This is consistent with increased storm-track activity in this region when going to N512 resolution (Fig. 7h), suggesting that storm-track changes with resolution may somewhat modulate the total precipitation sensitivity in HadGEM3-GA3.0.

Figure 8Winter (December–February) mean precipitation. (a) Observations (E-OBS), (b, d, g) model (HadGEM3-GA3.0) at resolutions N96, N216, and N512, (c, f, j) model biases with respect to E-OBS, and (e, h, i) differences between model resolutions. Stippling shows statistically significant differences.

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Similar conclusions can be drawn for summer: the storm-track strength decreases as resolution is increased from N96 to N216 and it increases as resolution is increased from N216 to N512 (Fig. S6e, h). Over the north-west of Europe and the North Sea there is a slight increase of precipitation when going to N512 resolution (Fig. S7h), consistent with the corresponding increase in storm-track strength (Fig. S6h). In other parts of Europe, however, the precipitation response to resolution is qualitatively similar for the two steps of resolution increase (compare Fig. S7e with Fig. S7h).

In the transition seasons, too, there is an decrease of storm-track strength for the N96–N216 resolution increase (Figs. S4e and S8e), but an increase of storm-track strength for the N216-N512 resolution increase (Figs. S4e and S8e). With the exception of Iberia in spring, no such fundamental difference is seen for the resolution sensitivity of mean precipitation (Figs. S5e, h and S9e, h).

We have shown here, using a simple metric based on synoptic-scale geopotential-height variance, that mean storm-track changes with resolution do not primarily explain mean precipitation changes with resolution in our model. More detailed analyses based on individually tracked extratropical cyclones (Hoskins and Hodges, 2002) and the precipitation associated with them (Hawcroft et al., 2012) are required for a comprehensive assessment of the role of storms in the resolution sensitivity of extreme precipitation in particular. We are currently conducting such analyses in a separate study.

5.2 Orography

It has been shown in previous sections that in and around mountainous areas there is particularly high sensitivity to resolution in both mean (Figs. 1 and 8) and extreme (Figs. 4–6) precipitation. We therefore investigate the role of orography explicitly in this section. To this end, we conduct a sensitivity experiment in which we use HadGEM3-GA6.0 (see Sect. 2.1) at high resolution (N480, i.e. very similar to N512) but apply orographic boundary conditions at coarse (N96) resolution. This sensitivity experiment is similar to the orography experiment in Schiemann et al. (2014), except that in this study we bilinearly interpolate the N96 orography onto the N480 grid to avoid “blocks” of grid boxes of constant orographic height on the N480 grid. The interpolation is applied both to the (resolved) grid-box mean orographic height and to the boundary conditions used by the parameterisations that represent different effects of subgrid orography. The sensitivity of European mean precipitation to resolution seen in HadGEM3-GA6.0, i.e. for N96–N216–N480 resolution increases, is very similar to that seen in HadGEM3-GA3.0 (not shown).

The results of the orography sensitivity experiment are shown in Fig. 9 for winter. The panels on the diagonal show mean precipitation for the observations (E-OBS), the N480 experiment with N96 orography (N480_N96), and the N480 control experiment (N480_N480), and the off-diagonal panels show the differences between these three fields. These results can be compared to the corresponding results of the full resolution sensitivity experiment, especially the ones corresponding to the N96–N512 resolution increase (Fig. 8). First, comparing N96 with N480_N96 (Figs. 8a–c and 9a–c), it can be seen that the precipitation distribution and its bias with respect to E-OBS are broadly similar in these two experiments. Likewise, the total resolution sensitivity (Fig. 8i) and the effect of introducing high-resolution orographic boundary conditions (Fig. 9e) are similar, both in terms of the geographical distribution and the magnitude of the response. This similarity is particularly clear near complex orography such as the Alps and along the Scottish and Norwegian coastlines, but there is also agreement in a large-scale drying with higher resolution (and with more highly resolved orography) over a wide area of the North European Plain and some precipitation increase over the very north-east of Europe. An exception to this overall similarity is the Iberian Peninsula, where the full response to the resolution increase is a precipitation increase, but N480_N480 is drier than N480_N96 over much of the peninsula. In summer, the total precipitation sensitivity is also very similar to the response to increasing the resolution of orography only (compare Figs. S5i and S11e). In summary, these results show that better resolved orography at the higher resolution is a major factor determining the total model sensitivity to resolution in mean precipitation over Europe.

Figure 9Winter (December–February) precipitation in mm day⁻¹ in (a) observations (E-OBS), (b) the N480 model with N96 orography, and (d) the N480 control simulation. (c, f) Model bias with respect to E-OBS and (e) difference between the two model simulations. Stippling shows statistically significant differences.

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We proceed by comparing the effect of orography with the total sensitivity to resolution for extreme precipitation. The ratios of GEV parameters of the N512 and N96 model for winter are shown in the upper panels of Fig. 10 and should be compared with the same ratios for the N480_N480 and N480_N96 models in the lower panels of Fig. 10. Analogous figures for the other seasons are shown in the Supplement (Figs. S12–S14). As seen earlier, the resolution increase leads to an overall reduction of both the location and scale parameters at the N512 resolution (Fig. 10a, c). This reduction is particularly pronounced over the North European Plain in north-west and central Europe. At the same time, the GEV parameters increase with resolution for some of the Alpine basins (Rhône, Po, Upper Danube). In this north-west/central part of Europe, a fairly similar pattern can be seen when considering the resolution increase in the orographic boundary conditions in isolation (Fig. 10b, d). In other parts of Europe (the Iberian Peninsula, eastern Europe), there is no clear correspondence between the sensitivity to more highly resolved orography and the total resolution sensitivity. In summer, too, the total and orography-only responses are broadly similar and agree on smaller extremes at higher resolution for most basins (Fig. S14). In summary, orographic effects dominate the sensitivity to resolution in simulated extreme precipitation around the Alps and over the North European Plain, but not necessarily in other parts of Europe.

Figure 10Winter (December–February) ratios of fitted GEV parameters for (a, b) the location parameter μ and for (c, d) the scale parameter σ, between (a, c) the N512 and N96 simulations and between (b, d) the N480 control simulation and the N480 simulation with N96 orography. Hatching shows statistically significant differences.

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