The sensitivity of intense rainfall to aerosol particle loading-a comparison of bin-resolved microphysics modelling with observations of heavy precipitation from HyMeX IOP 7 a

Note to the editor We thank all of the reviewers, whose comments have led to significant improvements in the analysis and our manuscript. Each question and remark of the reviewer is answered below point by point. Changes in the manuscript and the reply to the individual remarks of the reviewers are marked in red for easier notice. We would like to point out, however, that our choice of NHESS as publication journal has motivated our focus on the study of the surface precipitation over a region, which is often affected by flash floods. Following the request of the reviewer we have added some more discussion on in-cloud processes, however the in-depth analysis of the cloud microphysics and their comparison with the available airborne probes will be published in another more appropriate journal.


Introduction
Heavy precipitation often occurs in autumn in the Cévennes-Vivarais (CV) region in southern France resulting frequently in 20 casualties in part due to difficulties of operational weather forecast models to predict their location, timing and amplitude for timely alerts (e.g. Sénési et al., 1996;Romero et al., 2000;Delrieu et al., 2005;Silvestro et al., 2012;Rebora et al., 2013).
In order to evaluate the performance of precipitation forecast model typically radar observations and/or rain gauge measurements are used. Among other instruments, both types of observations were available during the HyMeX campaign (Ducrocq et al., 2014) from September to early November 2012 over the Western part of Mediterranean Sea.
with airborne data in order to analyse the in-cloud features will be presented in a future work.
The comparison between simulated rain accumulations and results of the Quantitative Precipitation Estimate (QPE) for IOP7a (Boudevillain et al., 2016) is given in Sect. 4. Section 4 also presents the temporal evolution of 5 minutes rain rates recorded from numerous rain gauge stations, which are analysed, and their evolution is compared to the modelled ones. 25 Finally, in Sect. 5, simulated raindrop spectra are confronted with observed ones from disdrometer measurements. Section 6 summarizes the findings and conclusions of this study.

Model configuration and model setup
We use for this study the detailed microphysics model DESCAM (Detailed Scavenging Model, Flossmann and Wobrock, 2010) which is driven by the 3D dynamics of the anelastic and non-hydrostatic model of Clark et al. (1996) and Clark 30 (2003).
water vapour mixing ratio). Finally, the collection processes between water and ice (riming) and ice crystals only (aggregation) are also taken into account. For a complete presentation of the microphysical scheme see Flossmann and Wobrock (2010).
In order to provide the model with realistic cloud condensation nuclei we used primarily (HymRef) the aerosol number 25 concentrations observed by aircraft measurements on 26 September 2012 (Rose et al., 2015) which took place between 100 and 150 km south of the precipitation event and represents the most polluted conditions encountered during the HyMeX experiment in autumn 2012. The data collected from the different instruments (for details see Sect. 3) were fitted to three log-normal distributions. The parameters for the description of the size distribution (number N, mean diameter D m and standard deviation ) are given in Table 1. In order to study the role of the prevailing aerosol particle concentration on 30 precipitation two additional realistic case studies are performed with different aerosol concentrations. The first sensitivity study, called hereafter HymLow, uses the aerosol number concentration encountered during a flight on 27 October 2012 (during IOP16 of HyMeX), which also took place over the Northern Mediterranean. IOP16 encountered the lowest particle concentration observed during the entire HyMeX experiment. The minimum and maximum pollution levels observed during autumn over the French Mediterranean coastline thus ranged from 1700 to 2900 particles cm -3 . As these total numbers are both quite important a third number concentration with lower concentration is used. This third size distribution called Remote, represents the lowest number concentrations documented by long-term aerosol observations during autumn for the southern part of France from the nearby monitoring station puy de Dôme ( Fig. 1; Venzac et al., 2009). The size distribution 5 of 26 September is taken as reference for the following cloud simulations (called hereafter HymRef), the other two distributions (HymLow and Remote) will be used for sensitivity tests. Figure 2a gives the distribution of the number concentration for the three scenarios.
We know from the aircraft observations that the particle number strongly decreases in the first 3 km of the atmosphere (Kagkara, 2019). This exponential decrease in number concentrations was also represented in the initial conditions for each 10 of model simulations. For altitudes above 3 km the aerosol number concentration was kept constant with the values observed at 3 km, i.e. approx. 990 cm -3 for the HymRef scenario (Fig. 2b). The analysis of the aerosol particle composition by mass spectroscopy indicated a slight predominance of insoluble matter. For the following simulations we assume therefore, that aerosol particles are a mixture of soluble (ammonium sulphate, 40%) and insoluble (silicate-like, 60%) matter of an assumed same molecular weight of 132 g/mole which can act as CCNs or INPs. 15 providing hourly rainfall data with a spatial resolution of 1 km 2 (see e.g. Fig. 4a). The KED precipitation analysis uses 250 hourly rain gauges and four operational weather radars of the French weather service Météo-France. This operational set-up of the Cévennes-Vivarais Mediterranean Hydrometeorological Observatory (OHMCV, Boudevillain et al., 2011) covers an area of 32 000 km 2 . The region of Fig. 3 only shows the S-band radar positions at Nîmes and Bollène and a limited number of rain gauges restricted to the area of interest for precipitation occurring during the IOP7a event. All 31 individual tipping-25 bucket rain gauges from the 'service de prévision des Crues du Grand -Delta' (SPC-GD, one of the 22 flood forecasting services in France), indicated in Fig. 3 recorded the rain rate with a 5 minutes resolution and will later be used to better understand the temporal evolution of the intensive rain event.

Observations used for the comparison study
As DESCAM explicitly simulates the spectra of cloud and rain droplets a comparison of the modelled surface rain spectra with disdrometer measurements is also attempted. Two disdrometers, located at La Souche and Saint-Etienne-de-Fontbellon intense convective period took place from 7:30 to 9:30 UTC in the area of rain gauges 9, 10,[13][14][15]19 and 23 (i.e. close to the X-band radar observational area), where rainfall varied locally for these places between 25 to 70 mm and lasted more than 2 hours (Details about the time evolution of local precipitation will be illustrated in Sect. 4.4).
Convective rain fall occurred until 11:00 UTC and terminated due to the arrival of a cold front which brought stratiform and 25 less intense precipitation in the afternoon over the Cévennes-Vivarais region. For a more detailed description of the meteorological conditions see Ducrocq et al. (2014).
Figures 5a-c show simulated and observed X-band radar reflectivity fields obtained for a beam elevation of 1.5°. Radar reflectivity in Fig. 5a is calculated from the results of simulation HymRef for the innermost domain, using the sixth moment of the modelled hydrometeor size distribution to determine the radar reflectivity factor Z dBZ (Planche et al., 2010). Here Z dBZ at 7:50 UTC was selected, as it reflects well the predominant orientation and the spatial distribution of the precipitating cells over the northern Cévennes and the Vivarais.
The X-band radar observations only cover the south-western part of the innermost model domain and allow the comparison for a quite limited area of precipitation (marked by the circular surface of 60 km in diameter) encountered during IOP7a.
Reflectivity observed at 7:50 UTC (Fig. 5b) shows that precipitating cells have the same orientation as in the model. 5 Compared to the measurements the modelled rain band inside the radar range is slightly shifted to the east and the convective cells south from the radar position are less important than the observed one. For the simulation HymRef the formation of the convective cells starts (at 7:20 UTC) in this southern range of the radar but rainfall is still weak. Rain gauge observations however indicate that strong convective showers already occurred 20 to 30 km south of the radar location. Figure 5c shows the convective cells that develop around 9:00 UTC during the second convective period. Strong convection 10 formed at this time further to the north, next to the radar location, and cells propagate in northward direction. This deviation from the dominantly south-western track of rain cells could not be reproduced in the model. Important RWC of 2-2.5 g m -3 mainly forms close to the melting level. The 0°C levels varied due to the strong vertical motion over the complex terrain between altitudes from 3.3 and 3.7 km. We can also detect in Fig. 6b that raindrops appear in elevated layers up to -20°C. The IWC, however, reached much higher altitudes but the presences of ice values larger than 20 1 g m -3 rarely exceeded a height of 8 km, which is in agreement with aircraft in-situ and cloud radar observations performed during the same time period. The illustration of the field of IWC indicates that the cloud system mainly developed to midtropospheric layers and convection did not exceed 7-8 km. Thus, the tropopause level could not be attained and consequently no anvil formation took place. Figure 6a also includes two contour lines for relative humidity of 90% and 98%. The high humidity in the lower layers is caused by the southern flow from the nearby Mediterranean Sea. Relative humidity of 90% 25 appears around 1000 m asl, 98% 200 to 300 m above. Cloud base height, i.e. the formation of cloud droplets is located at altitudes around 1200-1300 m.
The formation of the convective system was triggered by orographic lifting over the Cevennes Vivarais Mountains. The rapid cloud formation and intensification was in addition favoured by the high vapour loading in the lower atmospheric layers, arriving from the warm Mediterranean Sea and persisting for several hours. 30 In the following sections we will compare the model results with the surface observations of rain accumulation, rain rates and droplet spectra and address also the differences in the model results for the three aerosol scenarios.

Rain accumulation
Figures 4a-d show rain accumulation for the period from 6:00 to 11:00 UTC as determined by the KED analysis and simulated by the cloud model for three different scenarios of aerosol particle concentrations. Figure 4, in contrast to Figs. 1 and 3, uses the kilometric coordinates of the third model domain (i.e. the innermost domain). Precipitation after 11:00 UTC was still ongoing but appeared only very locally and with low intensity (< 2 mm h -1 ). The KED results indicate that largest 5 rain accumulations with 115 mm occurred over the Vivarais Mountains. A small second maximum with 76 mm developed 20 km to the north. The location of the main maximum is reasonably reproduced by all simulations . Spatial deviations between observed and modelled rain maxima are within a radius of 5 to 7 km. The orientation of the modelled rain band is quite similar to the observed one. The location of the secondary maximum in the northern precipitation field is also reproduced especially for the simulations with the intermediate aerosol loading case (HymLow, Fig. 4d). 10 Strongest difference between observations and model results occur in the surface extension of rain. We note that the width of the observed rain band is much larger than the simulated one as it extends more to the west. This area of precipitation with a local maximum of 74 mm of rain at (x,y) = (540,640 km) was caused by the second convective phase from 9:00 to 10:30 UTC which was less pronounced in all simulations.
The differences in surface rain extension between observation and model becomes most obvious when the total water mass 15 of the 5 h rain accumulation (i.e. from 6:00 to 11:00 UTC) is calculated by integration over the entire domain displayed in  Table 2 gives the surface integrated total mass of rain water resulting from the KED analysis and from the simulations HymRef, HymLow and Remote accumulated until 11:00 UTC. In the Table 2, different thresholds of rain accumulation are used to calculate the precipitation amounts. When considering precipitation events with a threshold exceeding 2, 10 or 20 mm for each model grid point, we note that the simulated rain accumulation remains 40 to 50 % 20 smaller than the observed ones. Restricting however to the areas with only strong precipitation where rain accumulation exceeds 50 mm, differences with the simulations are reduced to 10 to 20% only. This result can also be expressed in terms of the area coverage of precipitation: while the observed surface accumulating of at least 10 mm covers 6300 km 2 accordingly to Fig. 4a, the model results only in 2100 km 2 for HymRef and in 2700 km 2 for Remote. Surface accumulating of more than 50 mm, however, were observed for an area of 1060 km 2 , while the simulated areas are close with 700 to 820 km 2 depending 25 on the scenario (HymRef and Remote, respectively).

Spatial and time evolution of the rain field
The QPE, determined by means of the KED technique, provides the rain accumulation on an hourly basis. Figure 7a illustrates the hourly rain accumulation between 7:00 and 11:00 UTC. Four surfaces coloured in red, green, orange and blue display the temporal shift of the rain field from the east to the west in increments of 1 hour. The coloured surfaces delimit 30 regions with rain accumulation larger than 20 mm per hour.
Figures 7b and c show the same results for the simulation with the strongest (HymRef) and the weakest aerosol loading (Remote). We can see that the shift of the rain field from 7:00 to 11:00 UTC is less pronounced than in the KED analysis of Fig. 7a. This is again a consequence of the underestimated second convection zone to the west and to the south as already indicated in Sect. 4.1. Furthermore, it becomes evident that regions with maximum rain accumulation are those where rain lasted for more than 2 or 3 hours. Figure 7c shows that the rain pattern is mostly steady-state in the Remote case which 5 finally results in the strongest rain accumulation as already noted in Table 2. At the end of the three different scenarios, as described in the Sect. 4.1, the spatial rain accumulation field shows some differences, especially in the location of their maximum. The Taylor diagram (Fig. 8) visualizes the skills of the different scenarios in simulating the rain accumulation field. The HymRef scenario simulates the spatial pattern of precipitation quite well and better than the simulations using the two other aerosol particles loadings. 10

The effect of the initial aerosol particle number concentration
Comparing the results for the different simulations in Table 2, it becomes obvious that the total rain mass is highest for the Remote aerosol particles distribution, then decreases for the case HymLow where aerosol particle number increased by a factor of two and is the lowest for the highest aerosol number concentration of HymRef. The last line in Table 2 gives the observed and simulated maxima of rain accumulation. The maximum of rain accumulation for Remote, i.e. cleanest 15 atmospheric conditions, exceeds the results for HymRef and HymLow considerably.
The increase in rain accumulation with decreasing initial aerosol concentration is associated with an increase in strength and intensity of the main rain field to the south due to an earlier onset of rain and an intensification of the rain amount in zones with weak precipitation (see e.g. isolated rain area in the south-eastern corner of the model domain in Fig. 4).
The differences in rain accumulation for the three aerosol scenarios result from the activation and condensation processes in 20 the initial phase of cloud development, which is driven by the number concentration of cloud condensation nuclei. Under atmospheric conditions with low particle concentrations droplets can form precipitation more rapidly as the field of water vapour supersaturation becomes stronger (Planche et al., 2010). Consequently, also the development of the ice microphysical processes, as well as the latent heat release, are modified causing changes in the dynamical development of the simulated cloud. 25 Detailed studies of the effect of aerosol particle number and solubility on precipitation formation have already be done with the same dynamical-microphysical model DESCAM for individual short living convective systems over Central Europe (Planche et al., 2010) as well as over Florida (Leroy et al., 2009). In these previous studies the rain duration was much shorter (< 30 min) and accumulation did not exceed 30 mm. The results of the present study for orographically generated and long-lasting steady state convection confirm our previous findings: more rain occurs when low particle numbers prevail. Figure 9 displays the spatial frequency distribution (PDF) of observed and simulated 5 h integrated rain accumulation in the range from 10 and 150 mm. The comparison of this distribution function displays a reasonable similarity between simulations and KED analysis, i.e., a strong decreasing trend of the frequency with increasing rain intensity. A closer look to Fig. 9 confirms the previous results that the underestimation of simulated rain mainly occurs in the range of weak to medium accumulation, i.e. from 15 to 40 mm (note the logarithmic axis of Fig. 9). In addition, we can detect that the frequency of 5 rain events > 70 mm is for all model results higher than in the KED analysis.
The differences in the frequency distribution between the three aerosol cases Remote, HymLow and HymRef confirm the role of the particles number concentration on the amount of the rain accumulation. Using the number concentration for Remote conditions, a rain accumulation of up to 154 mm is simulated by the model. The number of grid points with more than 120 mm remains however quite low (0.1% of the simulated rain surface). For the two simulations with the higher particle 10 concentrations observed during HyMeX (HymLow and HymRef) the maximum rain accumulation does not exceed 120 mm.
However, the rainfall from the lower aerosol concentration HymLow exceeds the total rain mass from the HymRef case (see Table 2). Figure 9, thus, confirms that the increase in total precipitation is caused by an increasing number of locations with high rain accumulation (larger than 60 mm).

Time evolution of local precipitation 15
In a further step we evaluate the capacity of the model to reproduce the temporal variability of the rain. Herefore, we use the rain gauge measurements whose positions are indicated in Fig. 3 by the numbers 1 to 31. They recorded temporally highly resolved rain rates during 5 minutes interval. Measurements for four stations with long lasting and intense rain periods are displayed in Fig. 10. These stations are all located in the Vivarais region where strongest rainfall occurred during this day (compare Fig. 4a). 20 Rainfall started shortly after 6:00 UTC over the most northern stations St. Félicien (29) and Lamastre (26) (Figs. 10a and b).  The temporal evolution of other grid points can of course deviate from these, but the ones selected for Fig. 11 document quite well the overall characteristics of the modelling results.
We note that when comparing the modelled time series (Fig. 11) with the observed ones ( Fig. 10) two features are most striking: (1) the amplitude of the observed rain rates are more fluctuating than the simulated ones, that means, the simulated local rain 5 evolution shows a more continuous increase and decrease and, (2) the maxima of the observed 5 min rain rate attain higher values than in the simulations.
We detect the absence of rain rates exceeding 8 mm (but visible in the measurements in Figs. 10a and d) as the modelled rain rates (Fig. 11) generally stay below 4-5 mm per 5 min. For this comparison, we need to consider that the model results represent rainfall over a grid box of 500 x 500 m 2 while rain gauges have a collection surface only of about 0.04 m 2 . 10 In the observations, as well as the model, however, the appearance of very strong rain events (with more than 7 mm/5 min) is always preceded by 15 to 20 minutes of rain of moderate intensity. The time evolutions as presented in Fig. 11 confirm that the simulated areas with strong precipitation are caused by long lasting and continuous rain episodes, while the observations indicate stronger intensities over shorter time intervals, a feature which is sub-grid in the model and, thus, cannot be confirmed. 15 Comparing the results of the HymRef with the Remote scenario it becomes evident that not only the rain accumulation but also the strength of the 5 min rain rates increased in the presence of less cloud condensation nuclei. Maximum rain rates with more than 8 mm per 5 minutes were recorded several times by the rain gauges. Model simulations for high aerosol numbers of HymRef do not exceed rain rates larger than 6 mm, while the simulations with the low aerosol numbers (Remote) can reach up to 9 mm for a few places (but not for the two grid points illustrated in Fig.11). A frequency analysis of the 5 20 min rain rates (Fig. 12) summarizes the differences between the model scenarios and the observations. This figure confirms the presence of rain rates stronger than 6 mm/5min in the observations as well as its absence in the simulation HymRef with high aerosol number concentrations. The model scenario Remote can produce the rain rates larger than 6 mm but their occurrence remains significantly below the observed ones.
In addition, the frequency analysis in Fig. 12 also demonstrates that the model produced more often rain in the range of 1.5 25 to 4.5 mm/5min, which is finally responsible for the strong rain accumulation obtained in the simulations. The different scenarios lead to modified developments of the precipitation fields. In addition to a rain rate increase, we note a modification in the surface area covered by rain during the intense convective period (see Figs. 4 and 7).
As DESCAM is a bin resolved cloud model, we attempt in a final step of our model evaluation a comparison between simulated and observed raindrop size distributions (RSD). During IOP7a two disdrometers counted raindrops, one at La Souche in 950 m and the other at StEF at 350 m asl (see Fig. 3). The disdrometer at StEF recorded rain spectra from 6:30 to 7:30 UTC, the one at La Souche from 7:30 to 9:10 UTC, both with a 1-minute time resolution. 5 The shape of the number concentration varied essentially with total rainwater content (RWC) whose values reached up to 7 g m -3 when integrating over the observed RSD. We restrict however our analysis to the spectra below 3.5 g m -3 as such spectra already provide high rain rates from 6 to 11 mm/5 min depending on the size of the mean mass diameter (i.e. 9 of the 70 spectra with RWC higher than 4.9 g m -3 were excluded). Figure 13a shows the RSD of the La Souche disdrometer measurements distinguished into four categories of RWC: 0.5, 1, 2 10 and 2.9 g m -3 . The spectra displayed are averages over all RSD for which RWC deviates ±20% from the selected mean value of 0.5, 1 and 2 g m -3 . However, the RSD of RWC of 2.9 g m -3 represents a mean for spectra holding 2.7 to 3.5 g m -3 . Figure   13a illustrates that the increase in RWC is accompanied by the presence of larger drops. In addition, we can see for the spectra with 2 and 2.9 g m -3 the number of droplets < 1 mm is significantly higher than for the spectra with low RWC. Figure   13c displays the corresponding mass distributions of the RSD given in Fig. 13a. In order to better illustrate the mass 15 contribution of the different drop sizes to the RWC, we plotted both axis of the mass spectra in a linear scale. At first glance we can discover that drops smaller than 1 mm only contribute very little to the averaged RWC and the mean mass diameter shifts from 1.3 mm for the observed RSD with 0.5 g m -3 to almost 3 mm in the case with strong RWC of 2.9 g m -3 . Figure 13b and d show corresponding illustrations from the model simulation. The model data used for this comparison occurred between 7:50 to 10:00 UTC. We considered simulated RSD only from surface grid points where the topographical 20 elevation was between 900 and 1000 m and modelled RWC ranged around 0.5, 1 and 2 g m -3 (also within an interval of ±20%). The results restrict to the RSD simulated by the scenario HymRef. The maximum RWC modelled in this case at this elevation never exceeded 2.4 g m -3 which explains the absence of the 2.9-curve (in the scenario Remote, which is not presented here, stronger rain events with 2.7 g m -3 between 900 and 1000 m were encountered).
The simulations of number and mass distribution clearly demonstrate that the sizes of the simulated raindrops increase with 25 increasing RWC. In contrast to the observations the number concentration for the smaller drop sizes, however, decreases with increasing RWC. This behaviour in the model is associated to the fact that large raindrops can only form through collision-coalescence with smaller precipitating drop sizes. In the simulation, cloud base is located between 1300 to 1400 m asl, i.e. about 400 m above the ground, and thus no cloud droplets are present at the surface. Figure 13b illustrates quite well this process as the larger sizes increase at the cost of smaller raindrops in the range from 0.3 to 1.5 mm. Concerning the 30 observations, we need to keep in mind that the location of La Souche is in a mountainous region of 950 m. We cannot exclude that the observational site was closer to cloud base or even immersed in the cloud, explaining the presence of an increased number of small raindrops. A comparison with the raindrop spectra observed at StEF in 350 m asl confirms partially this hypothesis as the number concentration for drops < 1 mm is generally a factor of 2-3 smaller (Zwiebel et al., 2016), a decrease of this number with increasing RWC, however, could also not be detected.
The comparison between observed and modelled RSD was restricted so far to the scenario HymRef presenting a relatively high concentration in aerosol particles. In Fig. 14 we compare the mass distributions resulting from all three different 5 scenarios already discussed above. In order to get a statistically reliable result we only compare data at surface level ranging between 500 and 600 m as rain occurred most frequently in this elevation in the time span from 7:30 to 10:00 UTC. As a consequence, each mass spectrum is an average over 2800 to 3200 individual RSD. Their mean RWC is 0.88 g m -3 for HymRef as well as for HymLow, but 0.96 g m -3 for the Remote scenario. We note from Fig. 14 that the initial aerosol number concentration also influences the final RSD. The mean mass diameter shifts from 2.2 mm for HymRef to 2.9 mm for the 10 lowest initial aerosol distribution (Remote). The simulation with about 1700 particles cm -3 is located between the two other cases.

Summary and Conclusion
A major objective of this study was to test if a bin resolved microphysics module in a 3D mesoscale model is successful in reproducing a real case of intense precipitation usually observed over the western Mediterranean basin. The heavy 15 precipitation event in the Cévennes-Vivarais region observed during the HyMeX field experiment IOP7a in autumn 2012 was selected and analysed. Results for the QPE indicate a maximum rain accumulation of 115 mm during 5 h over the Vivarais Mountains. Heavy precipitation with more than 50 mm covered a surface of about 1060 km 2 . The high quantity of rain was caused by the permanent formation of new convective cells over the same mountainous barrier.
The simulation with the bin-resolved cloud model produces quite well the location of the rain maximum and also the surface 20 area covered by heavy precipitation (> 50 mm). In the surrounding regions with lower rain amounts, however, model results underestimate the surface covered rain area by more than a factor of 2. A comparison of the temporal development of the observed rain field shows that the triggering of convection occurred for a wider spatial spread than in the simulation.
We suspect that the initial and boundary conditions imposed by the IFS/ECMWF data at 0:00 and 12:00 UTC with a grid resolution of 0.25° provided a too homogenous structure for the fields of wind, temperature and humidity. During the 25 integration time from 0:00 to 6:00 UTC prior to convection formation the model could not produce the small mesoscale atmospheric heterogeneities which exist under real conditions. These differences, e.g. in atmospheric humidity, become obvious in the temporal and spatial delayed onset of rain, as its formation starts almost one hour before and 25 km more to the south than in the simulations (Fig. 4).
Model simulations were initialised with three different scenarios of aerosol number concentrations. For the reference case the convection formation were used. The second scenario prescribed the lowest number concentration of HyMeX in autumn 2012 with 1700 cm -3 (HymLow) sampled by aircraft measurements, and the third one (Remote) the lowest concentration of 1000 cm -3 available from long-term observations collected in the North of the French Massif Central. It was found that the decrease in the aerosol concentration from 2900 to 1000 cm -3 enhances rain accumulation by 20 % and also the area covered by heavy precipitation (see Figs. 4 and 7). In addition, a frequency analysis of the spatial distribution of the rain 5 accumulation shows that the gain in precipitation for low aerosol loadings is mainly caused by the increase of the number of locations with rain accumulations > 60 mm.
In a further step of our analyses we compared the local behaviour of the modelled precipitation with measurements of 5 minutes rain rates sampled from 31 individual gauges. The temporal evolution of observations indicates that the highest rain rates of 5 to 9.5 mm/5min do not appear immediately but only after a period of weak to medium rainfall lasting at least 15 to 10 20 minutes. Model results presented in Sect. 4.4 confirm this observational result.
After achieving their maximum the observed rain intensities drop significantly between 5-9 mm in the following 5 minutes and thereafter rain ceases or remains low until new convective precipitating cells occur. This abrupt drop in rain rate could not be reproduced in the model. Decreasing intensities of 6 mm/5min can also occur in the simulations but rainfall continues generally without intermittency. Consequently, the simulated rain rates are less fluctuating and more continuous than the 15 observed ones, also because they represent a mean value over a 500 m grid, in contrast to the more localised (i.e. punctual rain gauge) observations.
Comparisons with spatially high resolved X-band radar observations indicate that the modelled grid resolution is not sufficient to resolve the fine scale structure of the convective cells encountered. Consequently, the modelled convective clouds are less fluctuating, and the resulting rain is of more continuous character and maximum rain rates are probably less 20 strong than the observed ones.
The analysis of the rain rate for the different aerosol scenarios also highlights differences occurring when low or high number concentrations were used. Rain intensities reach up to 9 mm/5min for simulations of the Remote case while only 6 mm/5min were simulated when high particle concentrations were used for the HymRef scenario.
One of the main weaknesses in cloud microphysics modelling is generally the simulation of the raindrop size distribution 25 (RSD) as most cloud models with parameterized microphysics have significant problems to realistically reproduce shape, number and mass of the RSD (Varble et al., 2014;Taufour et al., 2018;Tridon et al., 2019;Planche et al., 2019). The shape of the number and mass size distributions presented in Sect. 5 compare quite well with disdrometer measurements sampled for this precipitation event. The observations illustrate as expected that the RSD becomes wider with increasing rainwater content (RWC). This is also well simulated by the bin resolved modelling. The analysis of the disdrometer measurements 30 shows in addition that the number concentration of all droplet sizes (starting at diameters of 0.3 mm) increases with increasing RWC. This behaviour could not be detected in the simulated spectra as the number concentration for drop diameters smaller 1.5 mm decreases with increasing RWC. In order to explain this model results we note that the simulated cloud base was located about 400 m above the ground. Due to the cut off from smaller raindrops prevailing inside the cloud the evolution of the RSD was mainly determined by collision-coalescence, which increases the size of the large drops and reduces the number of the small ones.
RSD measurements presented in Sect. 5 are located at 950 m asl. We cannot rule out that cloud base was sometimes below 5 this elevation and the instrument was immersed into the cloud at least part of the time where numerous smaller drops are present. The analysis of a second disdrometer, located at 350 m asl, supports this hypothesis. For RWC of 2 g m -3 number concentration for drop sizes from 0.3 to 1 mm ranged typically between 700 to 1000 m -3 and thus remains significantly below those counted for the mountain station La Souche in 950 m. But even for this second disdrometer an important reduction in small raindrops as simulated by the model cannot be reproduced. Also, other observational studies on strong 10 precipitations events (Raupach et al., 2019 or Thurai andBringi, 2018) confirm the behaviour that drop size concentration typically does not decrease with decreasing drop diameter.
A possible explanation of this difference in the modelled rain spectra could be attributed to the treatment of breakup process of large raindrop sizes in the model. At the moment only spontaneous breakup is treated accordingly to Hall (1980) and becomes active for droplet sizes larger than 5 mm. We cannot exclude that in particular under the conditions of strong RWC 15 also collisional breakup is occurring (Low and List, 1982) and the redistribution of the 'broken-up' drops will privilege the formation of smaller drop sizes. Another possible explanation for the underestimation of the small raindrop sizes can be caused by the lack of corresponding cloud particles in elevated cloud layers. A comparison of the modelled ice particle distribution in altitudes around -12°C (or 5 km) with aircraft observations indicates an underestimation of the number of ice crystals smaller than 1 mm. A detailed comparison with airborne data in order to analyse the in-cloud features, in particular 20 related to the ice phase, will be presented in a future work.
Finally, also for the raindrop size distribution the influence of the aerosol loading can be detected. As presented in Sect. 5 we can see that the mean mass diameter increases from 2.2 mm for the strong aerosol concentration of HymRef up to 2.9 mm for the lowest aerosol charge in the Remote scenario. Thus, the variation of 2900 to 1000 aerosol particles per cm 3 results in a significant modification of the mean mass diameter of the RSD. Information regarding the cloud condensation nuclei number 25 should, thus, also be taken into account in parameterized models.
However, the differences encountered for the modelling of rain accumulation, rain rate as well as raindrop spectra remain quite small when restricting our comparison to the aerosol concentration (i.e. HymRef and HymLow) that really were encountered during HyMeX. Only a further important reduction in the particle concentration to remote continental conditions highlights the potential role of the aerosol particle number. 30 Regarding the other objective of the current investigation, our study showed the potential of a bin-resolved modelling to reproduce the heavy precipitation periods usually observed over the Cevennes area. Even though the weaker precipitation was underestimated in the model, the peak values that would warrant an alert to the population were well represented. This bin-resolved modelling also provides a better understanding of the rain microphysics processes compared to bulk models as the microphysics is explicitly represented.
In order to improve the bulk models for routine forecast, the microphysical parameterizations should probably include a dependency on the cloud condensation nuclei distribution, as well as a possible evolution of the form of the hydrometeor spectra. Bin resolved models like DESCAM could provide some guidance for their development.       Fig. 6a) also indicate the regions with relative humidity larger 90 and 98 %, isothermes in °C are depicted in Fig 6b). The cross section is oriented in NNW direction and its projection on the y-axis presents the abscissa. and Remote (in green). The radial coordinate shows the standard deviation of the rain field, normalized by the observed standard deviation. The azimuthal variable shows the correlation of the modelled rain accumulation field with the observed 5 one. The distance between the reference KED data (i.e. OBS) and individual points corresponds to the root mean square error (RMSE).  Numbers behind the names give their location, as indicated in Fig. 3, as well as the elevation asl and the accumulated rain 5 amount.  HymRef. The equivalent mass distributions for the observed spectra are given in c), for the modelled spectra in d). The spectra were selected in four rainwater categories; each can deviate ± 20% from the given RWC value.