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Open Access

Peer-reviewed

Research Article

How climate models reproduce the observed increase in extreme precipitation over Europe

Abstract

The last years extreme precipitation and flooding events demonstrate the necessity to investigate how climate models represent the response of extreme precipitation to a warming climate to better prepare for flooding hazards. In this study we investigate heavy to extreme precipitation that has been observed over Europe since the 1950s, and how this increase is represented in climate models, with a particular focus on the frequency vs. intensity increase of heavy precipitation events. We compare observations and reanalysis against global and regional downscaled climate models which include one or multiple ensemble members. We find that some of the climate models manage to reproduce the observed increase in extreme precipitation with around a 20% increase for the 99th percentile from 1955-1984 to 1985–2014, with a large diversity between the models. The inter-model diversity for increase in extreme precipitation is found to show a larger spread compared to the intra-model spread represented by the variability between the different ensemble members. Model results show, similarly to observations, that frequency increases more than intensity, with around 20% vs. 5% increase, respectively, for the 99th percentile. This pattern strengthens with rareness of extreme events, however, the diversity between the models also increases with extremeness of the events. Results presented here show the need to account for the change in the very extreme events (> 99.9th percentile), as excluding these rare events may conceal how extreme future events will be. Over the land grid points, the frequency increase of extreme precipitation per intensity increase shows little variability for the global models, while the regional downscaled models, show a large variability in this frequency- intensity ratio, also larger than found for observations and reanalysis. The reasons why the models respond differently to climate change and how they respond to future global warming need to be investigated further.

Citation: Steensen BM, Myhre G, Hodnebrog Ø, Alterskjær K (2025) How climate models reproduce the observed increase in extreme precipitation over Europe. PLOS Clim 4(4): e0000442. https://doi.org/10.1371/journal.pclm.0000442

Editor: Juan A. Añel, Universidade de Vigo, SPAIN

Received: January 25, 2024; Accepted: March 22, 2025; Published: April 29, 2025

Copyright: © 2025 Steensen et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Daily precipitation observations and the gridded E-OBS datasets are openly available for download trough the European Climate Assessment&Dataset web site https://www.ecad.eu/dailydata/. ERA-5 data is openly available through the Copernicus Climate Data Store (CDS) (https://cds.climate.copernicus.eu/cdsapp#!/search?type=dataset). CMIP6 and CORDEX data are openly available through the Earth System Grid Federation (esgf).

Funding: This study was supported by The Research Council of Norway in the form of grants awarded to GM (250573,325270) and the insurance company If in the form of a salary for BMS, GM, ØH, KA. The specific roles of this author are articulated in the ‘author contributions’ section. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

There is observational evidence of an increase in extreme precipitation since the 1950s over Europe [1]. 70% of stations over Europe experience positive trends in Rx1day (the day of the year with maximum precipitation) between 1950 and 2018 [2], and there has been an increase in days exceeding the 90th and 95th percentile during the last century for stations over Europe [3]. Both studies found that stations over Northern Europe more often showed statistically significant positive trends compared to the Mediterranean region. Even with a decreasing north-south gradient for the lower percentile heavy precipitation, recent extreme precipitation events and flooding with large economic losses occurred both over northern and southern Europe [4–7]. These events show the importance of studying how the change in extreme precipitation events since the 1950s is represented in models to be sufficiently prepared for future risk.

The Clausius-Clapeyron (CC) relationship states that the water vapor holding capability of the atmosphere increases by 7% per degree (K). This thermodynamic law, and the change in the atmospheric energy budget because of increased greenhouse gas concentrations and global warming causes an intensification of the global hydrological cycle [8,9]. Both observations and models show that climate responds to this by reducing the number of days with light precipitation and increasing days with heavy precipitation [10–12], and the frequency increase for hourly heavy precipitation is found to be greater than the daily frequency increase [13]. Global climate models (GCMs) that are part of CMIP6 [14] (Coupled Model Intercomparison Project Phase 6) manage to simulate changes in extreme rainfall [15]. CMIP6 models show increase in heavy to extreme precipitation compared to CMIP5 [16,17]. However there is a large model spread in precipitation for both the historical period and the different climate projections over Europe [14,18,19] with CMIP6 projections showing large uncertainties in the magnitude and, in some regions, even the sign of future changes in heavy precipitation [15,16,20].

Here we examine the representation of precipitation events above percentile thresholds in climate models compared to observations, an analysis that offers valuable insight into the factors contributing to model diversity in the future projections. Results show that the higher percentiles, which represent events occurring less frequently than once a year, show larger increases compared to percentiles representing annual events [20,21]. In addition, frequency has a higher relative increase compared to the intensity when analyzing the shift towards heavier precipitation. To investigate the full response in extreme precipitation to global warming, both the change in frequency and intensity need to be investigated for future mitigation [22]. An extreme event occurring twice as often in a warmer climate could be more damaging than simply knowing it might increase in intensity by 50%.

This study includes analysis of observed daily precipitation at stations, as well as a gridded interpolated observational dataset (E-OBS [23]) with two resolutions. As this gridded product is based on interpolated fields, regions with low station density are more uncertain [24]. The study also includes ERA-5 reanalysis data [25] to better account for these regional uncertainties. Since higher resolution models compare better to observations [26,27] we also include some higher resolution regional climate models (RCMs) downscaled from global models from CORDEX (COordinated Regional Climate Downscaling Experiment) [28]. However, CORDEX models have been shown to have higher than observed precipitation values for the most extreme cases [29,30], making it important to examine the differences between RCMs and GCMs for the highest percentiles.

The goal of this study is to evaluate model simulations against observations of changes in extreme precipitation over Europe since the 1950s for both changes in intensity and in frequency. The following section gives a further description of data and methods used in the study, results are presented in section three, and the last section includes discussion and conclusions.

Data and methods

Observations

S1 Table lists all the datasets and models used in this study. Daily station data are collected from the ECA&D-Daily dataset [31], and only stations with at least 80% time coverage for each time period are included in the analysis. Spatial coverage for the ECA&D-daily data varies from country to country; while the Netherlands and Germany have a dense coverage, the number of available stations over for example France and Italy is limited. The E-OBS dataset with European gridded observations has also been analyzed [23] as a supplement to station data. E-OBS has been analyzed at two different resolutions, both the original resolution of 0.25°x0.25° and the more recent higher resolution of 0.1°x0.1°. Since v.16, the E-OBS gridded product is calculated by using a new interpolation method that has shown changes to the precipitation field. The newer version of E-OBS includes an uncertainty estimate found by calculating ensembles based on Gaussian Random Field simulations. However, the uncertainty is very dependent on station density and does not represent uncertainty in areas with low station density [23,24] and the ensemble uncertainty is therefore not included in the analysis here. An older version of E-OBS (v.15) [32], used in [21], is also included for comparison. Results are presented for Europe, confined within the geographical region of 24°W-40°E, and 37°N-71°N. A smaller region in the south-east of Europe is excluded (30°E-40°E and 37°N-45°N) due to low station density. All stations and model data are evaluated over the same region with only land grid cells. Fig 1a) shows the station location as well as the regions used in the analysis.

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Fig 1. Maps of total change in precipitation above the 99.9 percentile.

For station data (left) and for the gridded E-OBS with 0.1 degrees resolution (right) from 1955-1984 to 1985-2014. The left Figure also shows the extent of the area in the analysis for models in grey and hatched for the ClimEx data.

https://doi.org/10.1371/journal.pclm.0000442.g001

Models

While ERA-5 is included as a reanalysis dataset, rain-gauge data is not included in the assimilation in ERA-5, and the precipitation in ERA-5 is therefore independent of the station observations [25]. A total of 15 CMIP6 General Circulation Models (GCM) with one or more ensemble members are included in the analysis (S1 Table). Results are presented for each model, although some models share the same physics or parameterizations, and are therefore not fully independent [33]. It has previously been found that weighting models based on independence and performance does not considerably alter the results [20]. The simulations used here are the CMIP6 “historical” experiment with natural and anthropogenic emissions up to 2014. Due to the increase in computer resources, several models provide large ensemble (LE) simulations to investigate natural variability [34]. The analysis here includes three models with 40 or 50 ensemble members as well as nine members of the high resolution GCM EC-Earth3-Veg, while the other LE models have lower resolution.

We also include four regional models downscaled from different GCMs as part of the Euro-CORDEX [28]. Since the CORDEX models are downscaled from GCMs that were part of CMIP5 [35] and historical simulations ends in 2005, the years 2006–2014 follow the RCP4.5 emission scenario, chosen due to a larger number of models available for this scenario. In addition, all 50 members of the ClimEX dataset are included in the analysis [36]. This dataset consists of a regionally downscaled version of the CanESM2 50-member ensemble (part of CMIP5), by using the Canadian Regional Climate Model, version 5 (CRCM5) from 1950 until 2099 with emissions from the representative concentration pathway RCP8.5 from 2006 onwards. ClimEX and CORDEX is run with different future scenarios, however there are only small differences in the first years of these different scenarios[37]. The resolution of the ClimEX dataset is equal to CORDEX (12 km), but the domain over Europe does not extend as far north and east (only ~64.5°N and ~ 37°E respectively, hatched region in Fig 1a).

Methods

Results in this study are presented as the percent change between two different 30-year periods. Even though the simulations from ClimEX start from 1950, there is a recommended five year spin up time for the members to become independent. Therefore, the reference period starts from 1955 and ends after 1984. The second period is the consecutive, 1985–2014, as this is when the historical simulations for CMIP6 end and station observations available from ECA&D-Daily are reduced for later periods.

Percentiles are used to determine the thresholds for precipitation extremes from the reference period for all days (both with and without precipitation). For the most extreme percentile, 99.97, (there are four events above the set threshold meaning that) the threshold is set at the fourth most extreme event during the 30-year reference period. The change in frequency is calculated as the change in the number of events above this threshold. Change in intensity is calculated as the change in precipitation summed up over the same number of extreme events in both periods, while increase in total precipitation is calculated as the change in precipitation summed up over all events above the threshold. This study analyses multiple percentile thresholds to explore how heavy (from 95 up to 99.9th percentile) to extreme (from 99.9 to 99.97th percentile) precipitation changes with global warming. Thresholds range from the lower 95th percentile (approximately 183 events per decade) to the highest 99.97th percentile, similar to those used in [21].

For the frequency change presented in Fig 2, the bins represent the percentile thresholds from the reference period, i.e., 5% of the events fall within the first bin from 90% to 95% in the reference period. The change in frequency is given as the percentage change in the number of events that fall within each respective bin. For the rest of the results presented in this study, the increases are presented as all the events above a threshold, and not binned.

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Fig 2. The percent change in frequency of heavy-to extreme precipitation.

Change from 1955-1984 to 1985-2014 for station data, the different E-OBS datasets, ERA-5, CMIP6 models, CORDEX and ClimEX datasets. Thresholds for the bins are defined from the reference period, with the percentile as the lower bound of the bin. a) shows the increase for the percentiles 90,95,97.5 99.0, 99.5, 99.75 and 99.9, while b) shows the results if the higher extreme 99.97 bin is included. For models with multiple ensemble members, the mean increase over all ensemble members is shown. Light green shaded area shows the spread of the CMIP6 models, and light blue for the CORDEX models.

https://doi.org/10.1371/journal.pclm.0000442.g002

Each model is evaluated over the original grid, however only for land grid cells to compare with observations. Percentiles and the changes between the two periods for intensity, frequency and total precipitation are calculated separately for each station or land grid cell, and then averaged over the European region. Similarly, if a model has two or more ensemble members, statistics are calculated for each ensemble member as if it was one model, and the result is taken as a mean over the ensemble outcomes.

Results

Figure 1 illustrates the difficulty of visualizing changes in extreme rainfall over regions as often there is no clear signal found for stations and gridded data. There is a large variability between the stations, even among stations located in the vicinity of each other. Fig 1 also illustrates the difficulty caused by varying station coverage over Europe, causing challenges for the resulting E-OBS interpolation in areas with low station coverage; the strongest positive increases in E-OBS data are found in regions where the station density is low, such as over France and regions in Eastern Europe. Given this strong inhomogeneity, changes in extreme precipitation are better represented when aggregated in space. A method to complement the idealized schematics for how precipitation responds to global warming have been proposed [11], and updated results are shown in Fig 2 for the CMIP6 and CORDEX data.

Fig 2 a) shows the increase in the frequency of heavy (<=99.9th percentile) to extreme (>99.9th percentile) precipitation within individual percentile bins, illustrated in the same way as in [11]. Almost all models and observational datasets show an increase between the reference and the recent 30-year period, and a general higher increase the higher the percentile. Station data show a lower increase in frequency of occurrences above the 99.9 percentile threshold compared to the 99.75 percentile threshold, but this is dependent on period and station selections, ref. [11] did not find this decrease between the two highest percentiles. As shown in the earlier study, most models fall below the observed values (especially for the bins below the 99.75 percentile threshold), and CORDEX models have a lower increase compared to CMIP6 models. Results from the new versions of the gridded observational datasets E-OBS 0.1 and E-OBS 0.25 are almost identical and show that there is a larger increase between the periods compared to station data and ERA-5 data. E-OBS analyzed only at the grid cells where there are stations available, and the older version E-OBS 0.25 v15, shows similar results as the station data. These results underline the uncertainty of the newer interpolation method for E-OBS over regions where the station density is poor [24].

Studies have shown the importance of including higher percentiles than 99.9 representing extreme precipitation since they have a higher increase compare to lower percentiles [21]. Fig 2 b) shows the results when one additional higher percentile is included, 99.97, which corresponds to around one event every ten years. By definition, the probability for the reference period of falling within the > 99.9 to the > 99.97 bin is 0.07%, while it is 0.03% for the highest >99.97 bin. Results in Fig 2 b) show that most of the cases that fall within the > 99.9 percentile bin, the highest bin in a), would also fall within the higher >99.97 bin in b), even though from the reference period there is a lower probability of falling within this highest bin. The higher increase is also due to the point that when the change is calculated between few events, a smaller growth in the number of events is needed for the percent increase to be large. The results also show that when not including the higher percentiles (such as 99.97) the results may conceal how extreme the events are within the less extreme bins. This supports the need to include these extreme and high percentiles [21].

Results in Fig 2 only show changes in frequency given for different bins, but to understand the total shift in extreme precipitation, changes in intensity and total precipitation above a threshold is also interesting. Fig 3 shows bar graphs of increase in total precipitation summed over the percentile threshold, intensity, and frequency for each of the datasets: station observations, gridded observations, reanalysis, global and regional climate models. All models and observational datasets show an increase in total extreme precipitation, and a stronger increase with increasing percentiles. Most of this increase is caused by the increase in frequency, as found by [21]. There are however some differences in the results compared to [21] due to stations, area and time periods studied. Similar to the results presented in Fig 2, the increase in E-OBS observational datasets for the whole region is higher compared to observations at stations and the reanalysis data.

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Fig 3. Percent increase in heavy to extreme precipitation.

Bar graphs showing percent increase from the reference to the recent period, in heavy to extreme precipitation above the six percentile thresholds from left to right: 95, 99, 99.72, 99.9, 99.95, 99.97, for total precipitation above the thresholds (top), increase in intensity (center) and increase in frequency (bottom) (not binned). See methods for description. Identity of the datasets are given on the x-axis on the lower panel. Where multiple ensemble members are available for a model, the results represent the ensemble mean and the number of members is given after the model’s name. The lines represent + /- one standard deviation between the ensemble members.

https://doi.org/10.1371/journal.pclm.0000442.g003

Fig 3 also shows that there is a large spread between the different CMIP6 models for the higher percentiles. For CMIP6 models where ensemble simulations are available, the uncertainty given as the standard deviation between the ensemble members reveals that the spread between the ensemble members is smaller than the difference between the individual models. For example for the increase in total precipitation above the 99.9 percentile threshold, CNRM-CM6–1-HR have an increase of 10.2% as the lowest increase of the models and the mean over the nine ensemble members of EC-Earth3-Veg has the highest increase with 38.6% increase. Especially MIROC6 and ClimEX show small variability between the members with standard deviations (std.s) of 6.4 and 5.8% respectively even with large ensembles of 50. Conversely EC-Earth3-Veg with the highest increase for the mean over the ensemble members also have the largest spread between the members (std 15.5%). Even with the largest ensemble member spread, the variability does not cover the spread between the models. This indicates that the increase in heavy to extreme precipitation is linked to the physics and dynamics of the models in addition to the internal climate variability provided by the ensembles.

To explore the previously identified north-south drying gradient [3,26], S1 Fig show the same as Fig 3 but only for grid points and stations south of 45°N. Similar to what has been shown before, there is a decrease for the lower percentile thresholds over the southern Europe. For station data there is a decrease for all thresholds except the 99.7th for intensity increase, however there is also a limited number of stations in this region that qualify for our 80% time coverage condition. ERA5 data also show a decrease over most of the lower percentiles, with only a small increase for the highest percentiles. The other datasets (CMIP6 and CORDEX models) show either a small decrease or a reduced increase over the lower percentiles compared to when averaging over all of the European domain. For the higher percentiles, the increases are similar. The results also show that the frequency is more reduced than intensity.

Fig 4 shows maps of total precipitation change (% increase) for a low and high percentile to examine the regional differences. Similarly to Fig 1, E-OBS shows strong spatial variability, especially in regions with low station density. Over France the change in ERA-5 is of opposite sign to E-OBS. Results are also shown for EC-Earth3-Veg, with a mean over the nine ensembles chosen as the GCMs that show the highest increase in extreme precipitation, in addition to a CORDEX model. All datasets show the north-south drying gradient for the lower 99 percentile, although it is not as strong in the EC-Earth3-Veg ensemble mean compared to the other datasets. The north-south gradient is not as clear for the highest percentile of 99.97 where results show a high spatial inhomogeneity caused by the chaotic nature of extreme precipitation events. Results for the highest percentile is also only based on the four most heavy extreme events, and strong reductions and increases are found both north and south over Europe. For EC-Earth3-Veg, the ensemble mean is averaged over the members and includes more datapoints and is therefore smoother compared to the other results that represent only one dataset, even though Fig 3 shows that there is a large variability between the members.

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Fig 4. Maps of total change in precipitation.

% increase in total precipitation between the two periods 1955-1984 vs. 1985-2014 for the lower 99 percentile (upper row) and the highest 99.97 percentile (lower row) for E-OBS with 0.1-degree resolution, ERA-5 reanalysis data, mean over the 9 members of EC-Earth3-Veg and the IPSL-CM5A-MR downscaled with WRF as part of CORDEX. Notice different color labels for the two percentiles.

https://doi.org/10.1371/journal.pclm.0000442.g004

To understand more of the results, S2 Fig shows the daily precipitation for the events exceeding the two thresholds (99 and 99.97) in the first 30-year period (1955–1984) and S3 Fig shows the relative change in precipitation amount above the two thresholds between the two time periods. The figure shows that the EC-Earth3-Veg ensemble members have generally less precipitation over mountainous areas, and contrasting the other datasets, lack localized areas of higher precipitation for the highest percentile. This can indicate that orographic precipitation is underrepresented in the lower resolution GCM. Additionally, the weaker convective events are averaged over the ensemble members. This smoothing is also evident in the difference plots (S3 Fig), where the ensemble mean shows a smoother result with weaker increase, while the other datasets and especially the CORDEX model exhibit a noisier pattern with small, adjacent areas of reductions and increases.

To further study the frequency change compared to intensity for the different models and datasets, Fig 5 shows scatterplots of the increase in frequency compared to intensity for each station or land grid cell for precipitation above the 99.9 percentile in the reference period. The upper left scatterplot shows the results for observations at stations, where one station is one point. Most of the stations have a larger increase for frequency than intensity, resulting in a more tilted alignment of the points as well as the interpolated line with a slope of 3.06. Although some stations exhibit a pattern where the frequency increase is notably strong relative to the increase in intensity, there is a much larger number of grid points in the E-OBS data that exhibit this pattern, indicating that the interpolation method used in E-OBS leads to exaggerated increases in extreme precipitation frequency in low station density areas (see Fig 1). Comparing stations to ERA-5 reanalysis data shows that the spread in frequency vs. intensity increase is comparable. Even with a similar spread between stations and ERA-5, the linear interpolation (blue line) between all the points shows a smaller frequency increase per intensity increase in the reanalysis for this percentile threshold, with a 3.06 slope vs 2.73 for ERA-5.

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Fig 5. Scatterplots of percent increase in intensity and frequency.

The colors show the increase in total precipitation above the 99.9 percentile threshold. Each point represents one station for observations, and a land grid cell for all other datasets. The line represents the linear interpolation between the intensity and frequency increase and the upper left numbers represent the slope of the linear interpolation, for models where more than one ensemble is available, all the land grid cells from each ensemble are included in the interpolation, as well as included in the scatterplot. Grey dashed lines show the 1-1 ratio between frequency and intensity percent increase.

https://doi.org/10.1371/journal.pclm.0000442.g005

Generally, the GCMs show a small spread in the increase in frequency per intensity over the grid cells, the points lie around the linear interpolation line, even for models that include multiple ensemble members and therefore more grid points included in the plot. Only a few models show a larger spread and have some grid cells with high increase in frequency per intensity (for example EC-Earth-Veg). HadGEM3-GC31-MM and UKESM1–0-LL which share the same aerosol and atmosphere model, show a larger spread between the grid cells, and these two models also show a lower slope for the interpolated line (1.86 and 2.13 respectively) compared to the other GCMs.

Scatterplots for CORDEX and ClimEX show that some grid cells have a similar increase in frequency per intensity as the other datasets, but there are also grid cells that have a lower frequency increase, creating a large spread compared to the other datasets in the analyses. This spread could be due to the high extreme precipitation values found in CORDEX models over both periods which result in a generally lower slope of the interpolated line for the regional downscaled models compared to most of the GCMs, the observations and ERA-5 reanalysis (except for one CORDEX model).

To further compare how frequency increase compares to intensity for the different models compared to observations, Fig 6 shows only the interpolated slopes for three percentiles, a lower 99 percentile, the 99.9 percentile and the highest 99.97 percentile. Because frequency increases more than intensity the higher the percentile, the slopes are steeper the higher the percentile. However, the spread in change in frequency increase per intensity between the datasets also gets larger with higher percentile. This illustrates the uncertainty in extreme precipitation increases for the models, as well as the uncertainty with the higher percentiles due to the smaller number of events included in the results.

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Fig 6. Linear interpolated slope of frequency vs intensity increase ratio.

The slope of observations and models with the percent increase in intensity and percent increase in frequency ratio (same as Fig 5) for the 99th, 99.9th and 9.97th percentile, CMIP6 models are shown in green with green shading between the minimum and maximum slope, and CORDEX models are shown in blue with blue shading between the minimum and maximum slope.

https://doi.org/10.1371/journal.pclm.0000442.g006

For the percentiles shown here, the regionally downscaled models have a lower increase in frequency per intensity increase compared to global models, reanalysis, and observations. For some CORDEX models, there is almost no change in the slope the higher the percentile. Compared to station data, ERA-5 and some of the CMIP6 models show a similar increase in steepness, although with some models showing higher and lower increases. E-OBS only evaluated at stations show similar results as station data, while both of the E-OBS datasets with all data show higher steepness compared to all the models.

Even though the CORDEX and ClimEX models show similar increases in total precipitation above the percentiles over Europe (Fig 3), the increase in frequency per increase in intensity is lower than the observations, ERA-5 and most GCMs. This can be attributed to several grid points exhibiting a lower increase in frequency compared to intensity. The large spread found between CMIP6 models illustrates the uncertainty in how the hydrological cycle is represented in the models. Even in models with large ensembles, the increase in frequency per intensity is consistent over the different members, and therefore not dominated by natural variability.

Discussion and conclusions

Results presented here show that some GCMs part of the CMIP6 historical simulations manage to reproduce the % increase in heavy-to extreme precipitation observed since 1955 over Europe with around a 20% increase for the 99.9th percentile, consistent with previous studies [15,17,38]. The models also indicate that frequency increases more than intensity for this percentile, with increases of ~ 20% and ~ 5%, respectively, similar to observations. Some models, however, show a smaller increase compared to observations, while others show a larger increase revealing the model spread [18]. Although some models agree with observations for % increase over Europe, the results show that GCMs do not include the highest values due to low resolution in mountainous regions and convective parameterization. CORDEX models however show higher than observed values for extreme precipitation [29].

In this study we also show the importance of including percentiles higher than 99.9 to better assess the extremity of future events. Fig 2 demonstrates that excluding the higher percentiles may lead to underestimating the potential hazards of future events. It has also been shown that the extreme precipitation over the higher percentiles increase more, both in intensity and frequency [20,21]. Here we investigate how extreme precipitation is represented in historical CMIP6 simulations and selected EURO-CORDEX models over Europe, comparing them with observations and ERA5 reanalysis data.

There is a large variability between the models for the change in historical total extreme precipitation above the percentiles, and a spread between the models for the intensity and frequency changes. For models with multiple ensemble members, the variability between the members, represented as a standard deviation, is smaller than the spread in results between individual models. This suggests that the variability in extreme precipitation changes is influenced by model dynamics as well as natural variability.

We also find that the regional differences (north-south drying gradient) are smaller to non-existing the higher the percentile, especially the CMIP6 and CORDEX models show small differences over the Mediterranean compared to all of Europe. Observations and reanalysis data show only a small increase for the highest percentiles. This inconsistency between observations and models can be caused by lack of stations in this region that overcomes the 80%-time coverage qualification, as the results from the gridded observations show similar results as the CMIP6 and CORDEX models. Reanalysis data is also more unreliable before satellite data were included in assimilation [25], and how this affect extreme precipitation should be investigated further. Another effect on regional levels is that heavy and extreme precipitation enhanced by orographic effects and parameterized convective precipitation events are also less pronounced in the CMIP6 models due to lower resolution. In contrast, the CORDEX models are found to have higher than observed extreme precipitation in mountainous regions as well as in localized areas across Europe [29,30,39].

The difference between GCMs and RCMs is also evident when comparing the increase in the frequency-to-intensity ratio of precipitation changes. Individual CMIP6 models show relatively small variability in this ratio across the land grid cells included in the study. Even for models that include several ensemble members, the spread in the alignment of grid points for each ensemble member is smaller than what the different models display indicating that the frequency increase per intensity is model dependent, with similarities for models that share the same physics.

Since the CORDEX models have localized areas with heavy precipitation in both periods and a higher resolution, the spread is larger since grid cells with extreme high values in the first period may not experience proportional increases compared to other grid cells. However, total precipitation increase is comparable to observed increase, although with higher intensity increase than observations and the other datasets. RCMs are found to have a better representation of the hydrological cycle [27,29], though for simulations to capture changes in intensity and duration of heavy and extreme precipitation they need to be on convection permitting scales (~4km) [40–42]. Global warming has shown to increase strong convection in RCMs, while weak to moderate convection will decrease [43]. Historical European CORDEX simulations have also shown to have summer discrepancies with observed temperature caused by aerosol reductions that are not represented in the simulations [44].

The span of results presented in this study shows that to mitigate flooding and hazards in the future for specific areas further studies benefit from comparing multiple lines of evidence, for example CMIP6 models, CORDEX data, as well as high-resolution convective-permitting models over the specific area of interest. The investigation would highly benefit from a dense station network, particularly in mountainous areas. Biases in RCMs are a combination of model biases from both the GCM driving the RCM and the RCM itself [39]. RCMs may have parameterizations for convective precipitation tuned to a region, while GCMs need to keep a global energy balance [45]. Including both types of models are therefore valuable.

With the recent extreme precipitation events over Europe that caused flooding and large damages, to further understand how the models project the response of global warming in the hydrological cycle with less uncertainty is crucial. The results presented here demonstrate that changes in precipitation above the extreme percentiles represented in climate models depend on multiple factors beyond natural variability. These include the model’s physics, dynamics, parameterizations, and the ability to include high-precipitation events driven by orographic effects or convective processes. Understanding the uncertainty in future projections caused by model diversity is important. Even with the large uncertainty, a hydrologist working to adapt a region for future extreme precipitation needs to account for the fact that extreme events in the current climate will become more frequent and intense in the future.

Supporting information

S1 Table. List of data and models used in the study.

Name of datasets, description, resolution, and number of ensemble members (ens) included. For GCMs included in CMIP6 the number of grid cells for lon/lat is listed due to how the grid is set up in some models, making them difficult to compare.

https://doi.org/10.1371/journal.pclm.0000442.s001

(XLSX)

S1 Fig. Percent increase in heavy to extreme precipitation.

Same as Fig 3, however only over grid points and stations south of 45ºN.

https://doi.org/10.1371/journal.pclm.0000442.s002

(TIF)

S2 Fig. Maps of precipitation over thresholds.

The mean daily precipitation for the events during the first 30-year period 1955–1984, over lower the 99th percentile threshold (upper row) and the highest 99.97th percentile threshold (lower row) for E-OBS with 0.1-degree resolution, ERA5 reanalysis data, mean over the 9 members of EC-Earth3-Veg and the IPSL-CM5A-MR downscaled with WRF CORDEX model.

https://doi.org/10.1371/journal.pclm.0000442.s003

(TIF)

S3 Fig. Maps of precipitation change over thresholds.

Similar to Fig S2, however the daily mean relative changes in precipitation for the events above the thresholds in the two 30-year periods 1985–2014 vs. 1955–1984.

https://doi.org/10.1371/journal.pclm.0000442.s004

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