We use the precipitation severity index (PSI; ) to detect extreme precipitation events according to three different but complementary characteristics of heavy precipitation: intensity, spatial extent and persistence. The PSI in its current form is an adaptation of the storm severity index (SSI; ) and is a unitless index that indicates the degree of daily precipitation severity with respect to a predetermined climatological threshold (in our case the 80th percentile). Large PSI values represent high intensity, geographically extensive and temporally persistent precipitation events.

We perform Lagrangian convective cell tracking for the years 2001 to 2020 for a region of 200×200 km centered over Berlin. Pixels of YW RADKLIM radar data exceeding a threshold of 8.12 mm h-1 were identified as convective cells . The displacement of the cell is projected applying the 700 hPa wind of ERA5. If in the consecutive timestep a convective cell has been found in the area defined by a search radius around the projected position, both cells are assigned to the same cell track. If multiple cells are found within the search radius, the cell with the minimum distance is assigned to the cell track.

We calculate Lagrangian backward trajectories following , based on ERA5 reanalysis data , in a mid-European region around the center of maximum precipitation (red box in Fig. ). We start the trajectories from 1000 to 200 hPa in steps of 50 hPa for every hour of 29 June 2017, with a horizontal grid spacing 80 km and going back 240 h in time. From all trajectories, we selected those that have a relative humidity of at least 80 % in the target box and for which the specific humidity decreases during the last timestep (precipitation) . Along each selected trajectory, moisture uptake has been computed based on hourly specific humidity increases in the planetary boundary layer associated with evapotranspiration from the surface. The boundary layer height is available as a diagnostic model variable in the ERA5 data set and, again following , is multiplied by a factor of 1.5 to account for potential uncertainties in this diagnostic estimate. These uptakes have been weighted according to their contribution to the precipitation (moisture loss) at the target location, taking into account that earlier moisture uptake may contribute less due to precipitation loss on their way to the target region.

To assess the overall losses caused by the 29 June 2017 HPE, we review reports from the German Insurance Association (GDV), which published loss estimates for severe extreme precipitation events in Germany in the period 2002–2019 , and other technical reports . At the household level, we use losses, flood-duration and flood-depth data derived from household surveys in Berlin and Brandenburg . We furthermore use survey data from private households in Hersbruck (affected in 2005), Lohmar (affected in 2005), Osnabrueck (affected in 2010) and Muenster (affected in 2014) . In the surveys, affected households were asked, inter alia, when they were last affected by heavy rain and what impact they suffered. The results of the surveys are based on the responses of those households and are thus subjective.

The standard GEV distribution applied to heavy precipitation in this work is given by 1G(R)=exp⁡-1+ξR-μσ-1/ξ, where μ denotes the location parameter, σ the scale (σ>0) and ξ the shape parameter. A special case of the standard distribution (Eq. ) is the Type I or Gumbel distribution obtained in the limit ξ→0 used as well in previous works e.g.: 2F(R)=exp⁡-exp⁡μ-Rσ. This simplification allows estimation of the two free GEV parameters μ and σ by means of the method of moments, which is less computationally intensive and has been proven useful in the past e.g.. Characteristic of the Gumbel distribution is an exponential decay of the probability density function, meaning that only two free parameters of the GEV fit have to be estimated. However, the Gumbel is not a heavy-tailed distribution and is characterised by constant skewness and kurtosis.

We fit block maxima series to Eqs. () and () obtained by splitting the sample into non-overlapping intervals of the same size and then taking the maximum value of each interval. Previous studies have demonstrated that the annual block maxima approach is suitable for mid-latitude precipitation series . We specify the uncertainty of the models by using 95 % confidence intervals obtained from 1000-fold boot/strapping (re-sampling with replacement) from the maxima series of the original data set , following the ordinary non-parametric bootstrap percentile method of . From these 1000 samples the 2.5 % and 97.5 % quantiles of the wanted property (either return periods or return values) indicate their confidence boundaries.

We further implement a duration-dependent (d-GEV) model with seven parameters, which covers different durations to achieve a more efficient usage of observations. This way, information about short timescales (minutes to hours), can be derived, to a certain extent, from information of longer time scales (hours to days). Duration-dependency is incorporated into the GEV in order to reduce assumptions about the underlying distribution and have a free shape parameter ξ in the GEV . Another reason for using the GEV instead of one of their special cases is that Gumbel, and the other two GEV special cases Fréchet and Weibull, require large data sets to fulfil the limiting theorem for large block sizes . The d-GEV includes all three types and is a good choice if block size does not reach the asymptotic regime required for Gumbel. A duration-dependent GEV (d-GEV) as suggested by and refined by is introduced by varying the characteristic parameters of the GEV as follows: 3Gd(R;d)=exp⁡-1+ξR-μ(d)σ(d)-1/ξ,σ(d)=σ0(d+θ)-η+η2+τ,μ(d)=μ̃σ0(d+θ)-η+τ,ξ=const., where μ̃ is the re-scaled location parameter, σ0 is the scale offset, θ is the duration offset, η1 and η2 are duration exponents and τ is the intensity offset. Parameters were estimated with maximum likelihood estimation (MLE), a flexible and efficient parameter estimation method which is known to provide asymptotically unbiased and smallest-possible variant estimates . However, MLE is more computationally expensive than the method of moments. justified the use of the MLE for duration-dependent extreme precipitation studies as the explicit consideration of the dependence between durations in a model leads to only marginal differences in estimation. The d-GEV has been recently applied successfully by .

For the conditional climate-change attribution experiment (Sect. ), high-resolution ensembles (17 members) of the event under present and pre-industrial conditions are simulated with the COSMO-CLM . For the present climate, ERA5 reanalysis is dynamically downscaled to 0.11∘ for 17 members (Fig. S3) using the domain-shift ensemble technique e.g.. All members are then further dynamically downscaled to a convection-permitting 0.025∘ resolution over a geographically fixed subdomain (see Sect. ). To create the pre-industrial ensemble, the warming signal since the pre-industrial period, here taken as 1850–1859 versus 2007–2016 (over the 0.11∘ domain), is first computed from a subset of 17 Coupled Model Intercomparison Project Phase 6 (CMIP6) models . The warming signal (Fig. a) is then subtracted from the ERA5 initial and boundary conditions of the 0.11∘ simulations (surface temperatures are modified based on the warming signal at the lowest model level). A similar procedure is repeated for soil temperature. The atmospheric moisture content is adjusted based on the assumption that relative humidity remains constant. Pressure at the COSMO-CLM height levels is adjusted by numerically integrating the hydrostatic balance equation downwards from the model top . The 0.11 and 0.025∘ simulations are initialised on 28 June at 12:00 and 23:00 UTC, respectively, giving sufficient spin-up and adjustment time prior to the analysis period of 07:00 to 22:00 UTC the following day (chosen based on the analysis in Fig. S4). The attribution analysis consists of comparing the precipitation between the 0.025∘ ensembles with the pre-industrial ensemble as the reference state. COSMO-CLM model settings are as described in . Further details of the simulations and the CMIP6 models can be found in the supplementary material.

Simulations with the ICOsahedral Non-hydrostatic (ICON) atmospheric model were conducted to examine the possible role of anthropogenic aerosols in the analysed event. The model domain covered central Europe (Fig. ), for which one-way nested simulations at resolutions of 625 m and 1.25 km, respectively, are produced with 90 vertical levels. Two hectometer ICON simulations are carried out with two different imposed concentrations of cloud condensation nuclei, i.e. one with low concentrations, corresponding to current conditions (CLN), and one with elevated aerosol concentrations (POL), corresponding approximately to the peak aerosol concentrations over central Europe observed in the mid-1980s.

The 29 June 2017 HPE occurred under the influence of an upper-level trough extending between the Iberian Peninsula and Poland (TrW pattern) between 28 June and 1 July. During this period, several shortwave surface lows developed on the northern side of the trough (Fig. a) inducing favourable conditions for convective development. Two small-wave surface lows caused most of the precipitation collected over Berlin during 29 June. The first system, named Rasmund, remained quasi-stationary east of the British Isles between 28 June and 1 July, reaching values of the pressure at the mean sea level (PMSL) of 994 hPa (Fig. a). The second surface low, Rasmund II, originated in the night from 28 to 29 June over central Europe (Czech Republic), displaced towards northern Poland over the course of 6 h, and showed PMSL of 990 hPa along the German–Polish border at 12:00 UTC.

The mesoscale circulation associated with the mid-tropospheric low Rasmund II over northern Poland (550 dam; Fig. a) brought a warm and moist cyclonic inflow, crucial for the development of heavy precipitation over Berlin. The equivalent potential temperature (θe) at 850 hPa (Fig. b) showed values up to 305 K from the Mediterranean up to Poland and Berlin, indicative of a high moisture availability and optimal conditions for associated stationary deep–moist convection. Mixed-layer convective available potential energy (ML-CAPE) at the site was moderate, of approx. 250 J kg-1, while convective inhibition (CIN) was close to zero, as shown for the Lindenberg station (black dot in Fig. ) at 06:00 UTC 29 June 2017.

The triggering mechanism was a low-level convergence line fostered by the counter circulations of Rasmund and Rasmund II over eastern Germany (Fig. ), . The encountering circulations also imposed a weak southerly flow atop with ∼10 m s-1 at 500 hPa (not shown) and less than 5 m s-1 at 850 hPa (black arrows in Fig. b). The weak mid-tropospheric flow was responsible for the slow displacement of the convective systems.

Values of precipitable water vapour (PWV) up to 40 mm were measured at the Lindenberg station, near Berlin (Fig. S1 in the Supplement) at 11:30 UTC, and it is probable that water vapour mixing ratios of more than 6.5 g kg-1 were present at 2500 m a.g.l. (above ground level) over Berlin 3 h prior to precipitation initiation. This was shown by WRF 1.5 km simulations (Sect. ) covering the greater Berlin area (Fig. ). For a selected grid point located northwest of Berlin (black dot in Fig. a) WRF simulates water vapour mixing ratios of more than 13 g kg-1 in the lowest 100 m above ground between 10:00 and 19:00 UTC together with a strong low- to mid-level jet evolving after 13:00 UTC (Fig. a). This low-level jet is probably induced by the temperature gradient between the colder and drier air masses in southwest Germany and the warm and moist air masses over northeastern Germany (Fig. b). The simulated rain water mixing ratios exceeded 3.5 g kg-1 (Fig. b), potentially indicating a warm-rain type precipitation event e.g. which is associated with a strong downdraft of ∼5 m s-1 (Fig. S2).

Thunderstorm activity in the border region between northeastern Germany and Poland was already active in the morning starting at 05:00 UTC, shaping up a convective line moving westward from Poland towards the city of Berlin, producing the first cloud-to-ground lightning (Fig. a). The system strengthened and hit Berlin mainly between 09:00 and 10:00 UTC. Afterwards, the system weakened and moved only slightly further west due to weak upper-level flow. The convective line remained relatively stationary over the greater Berlin area and west of it until noon (Fig. a). Upstream of the system, a second thunderstorm line followed, crossing the border between Poland and Germany between 14:00 and 15:00 UTC. In the late afternoon, the direction of the convective cells changed and they were transported northward affecting Mecklenburg–Western Pommerania and the Baltic Sea after 18:00 UTC.

Due to the weak upper-level flow (Fig. a), the thunderstorms were associated with low propagation speeds leading to high local rain rates. Figure b shows daily precipitation totals with values up to 200 mm. The convectively enhanced precipitation fell mainly in the course of 12 h in the German states of Brandenburg (BB), Berlin (BE), and southern Mecklenburg–Western Pommerania (MV). Very high values above 100 mm were recorded in and northwest of the city of Berlin and in an area between Ludwigslust (MV) and Perleberg (BB). For example, Berlin–Tegel (BE) recorded 24 h precipitation of 196.9 mm, while Zeesen (BB) registered 149.9 mm (Fig. b and Table S1 in the Supplement). In many places, more precipitation was measured within 24 h than the climatological mean for the whole month of June .

The unusual precipitation totals made the 29 June 2017 HPE one of the most extreme events in the climatology of the greater Berlin area. Based on the PSI method (Sect. ; ), the 29 June 2017 event around Berlin was the 29th most severe event in the 1951–2021 period (Fig. ). This event showed a PSI value (1.71), well above the 99th percentile of the climatology indicating an extreme event. The PSI quantifies the severity of an event considering grid-point precipitation intensity, surface of affected area and persistence. The 29 June 2017 HPE showed a PSI value 2.3 and 1.8 times larger than the 29 June 2005 event in Hersbruch and Lohmar (Table ; number 2 in Fig. ) and the 29 July 2014 event in Muenster and Greven (Table ; number 6 in Fig. ), respectively. The 26 August 2010 event in Osnabrueck (Table ; number 5 in Fig. ) is the only event of those assessed in the household surveys with a similar meteorological severity and a similar extent of the damages (EUR 90 million) caused. Compared to other events, the 2002 event in Saxony (number 1 in Fig. ) showed the most similar meteorological severity. The Ahr flooding in July 2021 (number 9 in Fig. ) had a PSI value 2.1 lower than the 29 June 2017 HPE due to the weaker grid point intensity (131 mm compared to 196.9 mm) and, especially, to the lack of observations over affected areas in Belgium and the Netherlands in REGNIE.

The convective activity and number of cells triggered were also top ranked compared to other historical cases. Implementing a lagrangian cell tracking algorithm (Sect. ) using 5 min, 1 km radar data (YW RADKLIM), for the period 2001 to 2020, we found that the only event with more cells triggered than the 29 June 2017 HPE was the Saxony 12 August 2002 event . Also outstanding with regard to the number of convective cells triggered were the events on 21 June 2007, 22 July 2007 and 12 July 2018, where flooding was reported for northern Bavaria, west and southwest Germany, and Berlin, respectively e.g.. The former two events showed a strong meteorological severity, with a PSI in the 99th percentile of the climatology and the latter showed a moderate severity with a PSI close to 0.6. Figure  also shows the inverse relationship between the length of the tracks and their number, i.e. the larger the number of cells triggered, the shorter their mean length.

Insured losses in the Berlin–Brandenburg area amounted to EUR 60 million making the 29 June 2017 HPE the most damaging extreme event in Berlin and Brandenburg since 2002. Insurance data of the GDV showed that 1.8 % of the buildings in Berlin incurred damages during the event, with an average loss of EUR 6830. The Oberhavel district was more heavily affected, with 5.3 % of the buildings damaged and an average loss of EUR 10 550 . In Berlin, the long-lasting rainfall overloaded the sewer system, resulting in widespread inundation that caused disruption of traffic (i.e. blocked roads), flooded basements and underground stations, and intangible consequences including restrictions in daily routine and mental discomfort . The high number of rainfall-related missions on these 2 d forced the Berlin fire brigade to declare an “exceptional weather situation status” . The small municipality of Leegebruch (∼6800 inhabitants, located 40 km north of Berlin in the Oberhavel district) was even more severely affected due to its location in a topographical depression and a typically high groundwater table. The resulting inundation cut off the settlement from its surroundings, affected 40 % of the municipality and persisted for several weeks .

Table  compares the meteorological severity, the impacts and the number of surveyed households between the 29 June 2017 HPE in Berlin and Leegebruch event and the events in Muenster and Greven (2014), Osnabrueck (2010) and Hersbruck and Lohmar (2005). The meteorological indicators show that the Berlin–Leegebruch-2017 event was characterised by its large spatial extent and long rainfall duration. As shown in Sect. , the long rainfall duration was caused by the slow propagation of the convective system given the weak mid-tropospheric winds. The maximum accumulated precipitation in Berlin (Table ) somewhat differs from the REGNIE observations (Fig. b) since the values of CatRaRe are based on the RADKLIM RW 1 h product that uses a different gridding method and data source.

Figure  allows for a more detailed view of the impacts and related mechanisms by looking at the distributions of surveyed flood indicators and monetary losses at a household level. The results reveal that basements were inundated less severely in Leegebruch-2017 and Berlin-2017 than in the other events. Further, the inundation durations in Berlin-2017 and Leegebruch-2017 exceed the inundation durations of the other events. Monetary losses to buildings were particularly large in Leegebruch-2017, Muenster-2014 and Osnabrueck-2010, where approximately 75 % of the surveyed households reported a loss of EUR 1000 and more. In Leegebruch-2017, almost half of the surveyed households suffered building loss in the largest two categories (≥ EUR 10 000).

Altogether, a clear relationship between precipitation indices (intensity, duration, extent) and resulting losses across the group of study cases could not be found. Instead, flood characteristics at the affected buildings (inundation depth and duration) can explain much (although not all) of the incurred losses. Ultimately, flooding in urban areas is a complex process that depends not only on the meteorological nature of an event but also on the local characteristics of the terrain defined by topography, land use, sewer system capacity and operability, and hydro-geology, as well as on socioeconomic conditions such as settlement structure, building codes and private risk mitigation.

A sufficiently moist environment is needed for deep moist convection to develop . Section  showed how a very moist atmosphere with up to 40 mm of precipitable water vapour preconditioned the initiation of convection in the greater Berlin area. Now the question is where did the precipitating moisture originate? To this end, we use Lagrangian backward trajectories based on hourly ERA-5 data (Sect. ).

We found that land masses were the main sources of moisture uptake. Out of the selected 15 074 trajectories fulfilling the selection criteria, 82.9 % originated over land areas, whereas only 17.1 % of the precipitating moisture evaporated over the ocean. With this method, about 49.8 % of the precipitating moisture for the day of 29 June could be traced back to its moisture source. The eastern European region (around 10 to 32∘ E and 37 to 60∘ N) was by far the main source of moisture uptake (63.0 %). Additionally, the moisture uptake in this region was relatively evenly distributed, ranging from Poland (east of the precipitation event) towards Croatia and Italy, with a maximum moisture uptake of about 4.6 mm per single grid point (Fig. ). Other but less important land moisture sources were the western European region (around 12∘ W to 10∘ E and 37 to 60∘ N), with a contribution of 13.9 %, and the northern African region (around 20∘ W to 32∘  and 20 to 37∘ N), with a contribution of 5.9 %. The oceanic moisture sources were primarily the Mediterranean Sea (11.9 %) and Atlantic Ocean (4.6 %), but these played a minor role compared to the moisture uptake over land. A similarly important role of moisture recycling from land sources has been found previously for an extreme precipitation event in eastern Europe in May 2010 and for the central European floods in June 2013 . In the case of the 29 June 2017 HPE studied here, moisture recycling likely happened on relatively short timescales of 1–2 d, as June 2017 was generally dry, but northeastern Italy, Slovenia, Austria and southeastern Poland were affected by convective precipitation on 28 June. The moistening of the soil due to prior precipitation is thus hypothesised to be an important precondition for the Berlin event.

We provide an estimation on how rare the 29 June 2017 HPE was calculating probabilities of exceedance p and return periods tRP fitting observations of extreme precipitation to GEV models (Sect. ). Return values RVRP (quantiles) and the associated return periods tRP, or directly the probability of exceedances p, are related to the GEV distribution as tRP=1/(1-G(RVRP)) . For example, a probability of exceedance p=0.01 for annual data can be interpreted as on average 1 event in 100 years rare an event has been. This information is also used by reinsurance companies and hydrological studies.

We start by estimating return periods using the Gumbel distribution (Eq. ) per grid point (1×1 km2) for 24 h precipitation totals in Germany based on a 70 year time series (REGNIE; Fig. ). The results show return periods of more than 200 years between Ludwigslust (MV), Perleberg (BB) and Berlin, covering a total area of 8729 km2. Past work has shown how estimated return periods that are much longer than the observational record exhibit large uncertainty . This is why we truncate all return periods above 200 years (Fig. ), acknowledging that the 70 year observational record might be too short to provide accurate values for such long return periods.

The second approach, consisting of fitting a GEV distribution to spatial averages of different size, also showed very large return periods; however, decreasing with increasing size of the considered areas. The rationale behind this analysis is that return periods at individual grid points may not best characterise the event and its associated impacts since an event with a very long return period at a given site can have a small spatial extent. Such spatial averaging of observations is also required for validation of simulated return periods in climate models and assessment of the model biases see e.g..

For this approach we fit a standard GEV distribution (Eq. ) and estimate return periods of the yearly block maxima of REGNIE precipitation data from 1951 to 2020, spatially averaged over three boxes of different size (brown, grey and pink boxes in Fig.  and Table S2). The results show that the return period of the event decreases with increasing box size. At the finest analysed scale (340 km2; pink polygon in Fig. ), the extreme event has a return period of over 420 years, which decreases to 75 years for the largest area (11 100 km2; brown polygon in Fig. ). Compared to other historical events, the 29 June 2017 HPE was the most extreme in the time series when considering the smallest analysed region; however, an event with a larger spatially-averaged precipitation sum and thus a larger return period was detected on 8 August 1978 in the two larger areas (grey and brown boxes). In the supplementary material, the return period of the 29 June 2017 HPE is compared to the July 2021 heavy rainfall event impacting Western Europe.

One useful approach to reduce uncertainty in the estimation of return periods from temporally short observational records is using different accumulation durations between 1 h and 3 d (Eq. ); however, at the expense of more demanding computing power. The d-GEV model (Eq. ) is applied to grid point intensity from RADKLIM RW (2001–2020; Fig. a). For this data set, the estimated d-GEV shape parameter ξ has a median value of 0.24. Accumulations (duration d) of 1 d showed very high return periods (>800 years) for seven grid points in northwestern Berlin. Over this area, most grid points showed return periods between 50 and 200 years. The small grid box size of 1 km × 1 km could explain the very high return periods in cases of statistical outliers. On shorter timescales of 8 and 1 h, northwestern Berlin shows lower return periods, between 10 and 100 years for the two former temporal aggregations and between 2 and 10 for the latter (Fig. a). The short time range of historical RADKLIM data (20 years), however, limits the reliability of these spatially resolved return period estimates.

To overcome the short timespan of the RADKLIM data set, we implement a duration-dependent GEV model (Eq. ) on DWD ground station data at Berlin–Tempelhof (Fig. ). The return levels (quantiles) for any exceedance probability and timescale (duration d) are presented in intensity–duration–frequency (IDF) curves (Fig. ). This station was chosen because data records are longer than the RADKLIM data. Aggregations of 10 min span 1995 to 2020 and daily aggregations cover the period 1948 to 2020. The longer time series lead to shorter and – due to the reduced uncertainty – potentially more plausible return periods. The analysis shows return periods of 100 years for durations above than 10 h, 114 years for daily aggregations. However, confidence intervals in the IDF curves also remain large (Fig. b).

All used approaches highlight that the analysed event was rare, with return periods longer than 100 years in the Berlin area. The efficient use of information from the observation data (accumulation periods from 10 min to 3 d) lead to more plausible return period estimation from the d-GEV model compared to Gumbel using daily accumulations. However, long data records with high measurement frequency and enough computing resources are not always available, in which case a non-duration-dependent model using daily data could be a better choice. Finally, including a climate change signal into the d-GEV estimation could improve the results, since the assumption of a non-changing climate leads to overestimated return periods for events that become more likely with climate change.

A full understanding of an observed extreme event requires addressing the question of how the event relates to anthropogenic influences. This is particularly important with respect to climate-change communication with stakeholders and the general public.

For conditional attribution, the modelling approach involves simulating an event under present climate conditions and then repeating the simulation with modified boundary conditions. This modification consists of subtracting the vertical thermodynamical climate change signal , and is thus particularly amenable to high-resolution (convection-permitting) regional model experiments, which have many advantages for modelling extreme precipitation . The modelling approach is, in essence, an adaptation of the surrogate global-warming method . The results presented here are based on the model simulations described in Sect. , where the analysis is performed over an area of 81 520 km2 centred on the event location (Fig. S3). Model evaluation and technical details are found in the Supplement.

The thermodynamical climate change signal is vertically heterogeneous, with stronger warming in the mid and upper troposphere (Fig. a). Based on a mean tropospheric (1000–300 hPa) temperature of ∼269 K and warming of 1.36 K, this implies an increase in saturation vapour pressure of ∼10.5 % , which exceeds the 7.5 % increase in precipitable water (time average; not shown) which we find over our eastern Germany analysis region (Fig. S3).

In our present climate simulations, we find a low, though statistically significant (p<0.02), increase in total precipitation volume of 4 %. This can be better understood by analysing both changes in the precipitation distribution and physical characteristics of the convective system (Fig. b). Changes in total precipitation volume associated with a given quantile of precipitation intensity increase as the quantiles become higher. Indeed, at the lowest intensity quantiles, the associated precipitation volumes are found to decrease, which partly offsets the volume increases associated with the higher intensity quantiles (Fig. b). By breaking the total precipitation volume into its area and depth components, it can be seen that the change in precipitation intensity shows a signal very similar to that of the total precipitation volume. The spatial extent of the precipitation, meanwhile, decreases (-2 %) in the warmer climate, in line with the results of and . It is thus clear that it is not changes in the spatial extent of the system but rather higher local intensities which drive the increase in total precipitation volume. The intensities increase for approximately the upper half of the precipitation distribution, peaking at a 10.4 % increase for the highest quantiles. This increase exceeds the increase in precipitable water (see above), implying that local moisture convergence was an important factor for the most extreme intensities.

It is worth noting that, based on the average tropospheric warming signal (see above), the intensification of the highest quantiles corresponds (almost exactly) to what would be expected from the Clausius–Clapeyron relation. Had the precipitation–temperature scaling been computed using the lower troposphere or the 2 m temperature instead, a super Clausius–Clapeyron increase would have been found. Currently, it is still a matter of debate as to which temperature is most appropriate to use when computing the scaling rate . It is plausible that the total precipitation would not have shown an attributable change but that the most intense quantiles would have. This insight is also of relevance for impact studies: the effect of climate change was found to be dependent on the spatial scale of interest. We conclude by stating that climate change since the pre-industrial era served to increase the magnitude and, in particular, the highest precipitation intensities of the event.

Another influence of anthropogenic activities, transport, industry, etc. on heavy precipitation is via cloud-active aerosols. Aerosols may affect deep convection in various ways and thus exert an anthropogenic effect beyond the impact of global warming. For instance, an increased aerosol number reduces droplet size by increasing the condensation nucleal and the droplet concentration leading to enhanced precipitation .

We study the role of cloud-active aerosols within the 29 June 2017 HPE through sensitivity experiments with the ICON model at 625 m resolution, comparing two scenarios (Sect. ). The first one has factual concentrations representative of the 29 June 2017 HPE, which is a comparatively clean situation (CLN). The second one, has aerosol concentrations representative of the peak aerosol conditions in the mid-1980s, or polluted scenario (POL). The simulated distribution of precipitation is compared with RADKLIM for the period from 06:00 UTC 29 June 2017 to 06:00 UTC 30 June 2017 (Fig. ), in order to assess the importance of aerosols for this extreme event.

The results show that POL simulates an increased cloud number and cloud mass due to the larger aerosol loading (not shown) with the corresponding heavy precipitation increase. This is especially so for intensities exceeding 150 mm d-1 (Fig. c). We quantified this increase in probability to be of 70 % in the high aerosol conditions in the 1980s compared to the factual case (CLN) during the 29 June 2017 HPE. In POL, 4.3 % of grid points exceeded 150 mm 24 d-1 in the high aerosol case compared to 2.3 % in the low aerosol simulation (CLN).