Hectometric scale simulations of a Mediterranean heavy precipitation event during HyMeX SOP1

Abstract. Offshore convection occurred over the Mediterranean sea on 26 October 2012 and was well documented during the first Special Observation Period (SOP1) of the Hydrological cycle in the Mediterranean Experiment (HyMeX). This paper analyses the triggering and organizing factors involved in this convection case study, and examines how they are simulated and represented at hectometric resolutions. For that purpose, a Large Eddy Simulation (LES) of this real case study is carried out with a 150 m horizontal resolution over a large domain encompassing the convective systems, as well as the low level flow 5 feeding convection over the sea. This LES is then compared to a reference simulation performed with a 450 m grid spacing in the heart of the so-called "grey zone" of turbulence modelling. Increase of horizontal resolution from 450 m down to 150 m is unable to reduce significantly, for this case study, deficiencies of the simulation, more related to an issue of initial and lateral boundary conditions. Indeed, some of the triggering factors, such as a converging low level flow driven by a surface low pressure system, are simulated quite similarly for both simulations. 10 However, differences for other mechanisms still exist since larger surface precipitation amounts are simulated at 450 m. It is found that the lack of a good representation of entrainment with a 450 m grid spacing along the edge of clouds causes a too quick triggering of deep convection at this resolution, associated with fast-track microphysical processes and enhanced dynamics. Furthermore, this first LES of a real Mediterranean precipitating case study highlights a convective organisation with very fine scale features within the converging low level flow, features that are definitively out of range of models with 15 kilometric horizontal resolutions.

depending on the model's effective resolution (Wyngaard, 2004). Indeed, there are still uncertainties about how turbulence should be modeled at these resolutions. Past studies have investigated the impact of a one-dimensional (1D) versus a threedimensional (3D) representation of the turbulence at sub-kilometric horizontal resolution. Verrelle et al. (2015) showed that a 3D turbulence leads to stronger mixing and greater cloud cover. Machado and Chaboureau (2015) carried out simulations using 1D turbulence which produced too many small cloud systems and rainy cells with a shorter lifespan. Additionally, Verrelle et al. 5 (2017) compared kilometric deep convection simulations, up to 500 m resolution, to LES and showed that subgrid turbulent kinetic energy at these resolutions was underestimated with the eddy-diffusivity turbulence scheme, due to an underestimation of thermal turbulence production while resolved vertical velocities tend to be overestimated. Based on simulations carried out with 500 m grid spacings, Martinet et al. (2017) found that, for a specific case study of HyMeX SOP1 (IOP16a), not only cloud organisation but also the simulated environment and processes governing convection are strongly sensitive to the formulation 10 of the mixing length. Indeed, when turbulent mixing is weak (i.e. weak subgrid turbulent kinetic energy), the resolved winds are increased, leading to greater low level moisture advection, higher hydrometeor contents, marked low level cold pools, and therefore more intense simulated convective systems. This strong sensitivity obtained by Martinet et al. (2017) motivates the adoption of a Large Eddy Simulation (LES)-like approach, enabling a more suitable representation of turbulence within and at the edge of convective clouds and also within the 15 atmospheric boundary layer. In a LES framework, eddies that contain most of the kinetic energy are resolved whereas smaller eddies, that carry less than 20% of the total kinetic energy, are represented by subgrid processes. Although several studies have demonstrated the need to use grid spacing of about 100 m to represent the convective flow correctly (Bryan et al., 2003;Petch, 2006;Stein et al., 2015;Zängl et al., 2015;Dauhut et al., 2015Dauhut et al., , 2016, most of these works were carried out using an idealized framework and/or using a small domain. To the authors's knowledge no LES numerical simulation 20 of a real case study of Mediterranean HPE over a large domain has previously been performed. The purpose of this paper is to evaluate and analyse the impact of increasing horizontal resolution to LES in a numerical simulation of Mediterranean HPE, using a true topography in addition to realistic initial and forcing conditions. The present study goes further analysing how the physical mechanisms and convective organization are represented from sub-kilometric horizontal resolutions down to LES. For that purpose, a large domain encompassing the convective systems as well as the low level flow feeding convection 25 over the sea is considered. The paper focuses on the same offshore convection case study described in Duffourg et al. (2016) and Martinet et al. (2017) (IOP16a), which took place on 26 October 2012 during the SOP1 of the HyMeX field programme (Ducrocq et al., 2014).
This article is organized as follows. A quick review of the case study and the involved mechanisms are provided in section 2. The numerical model and the simulation setup are presented in section 3. Both simulations with hectometric horizontal 30 resolutions and LES, respectively, are compared in terms of rainfall field analysis and convection organization in section 4.
The physical processes at cloud scale leading to very deep convection and convection organization are assessed in section 5.
Finally, the study is summarized and conclusions are given in section 6, where perspectives for future work are also suggested. This section presents the HPE observed on 26 October 2012 and well documented during the HyMeX SOP1. During this event, a large part of the Northwestern Mediterranean was concerned by intense precipitation which locally led to flash flooding. Figure 1 shows the synoptic scale situation, valid at 0600 UTC on 26 October 2012. The synoptic situation was characterized 5 by a large deep upper-level low centred over Spain. A short-wave trough along with an associated potential vorticity anomaly (not shown) circulated ahead of the main system (i.e. offshore intense convective systems), passing over southeastern Spain, France and then Italy. Moreover, a large low is also anchored over Spain as seen with the mean sea level pressure (Figure 1).
At low levels, Figure 2 shows that deep convection was embedded within a very moist flow all along the system life-cycle.
A surface low pressure formed and strengthened downstream of the Iberian mountainous regions, between Spain and Balearic 10 Islands. It was strongly associated with the eastward propagation of the upper level trough.
Such favourable meteorological conditions described above led to the generation of several convective systems over the Mediterranean Sea. The first convective cells appeared just East of the Spanish coast around 0600 UTC on 26 October. Convection started to organize while moving northeastwards and forming an intense south-north oriented line (marked CS1) ( Figure   2b). It appeared that, in addition to offshore convection, the meteorological situation was also favourable for orographic forcing 15 over the southern slopes of the Massif Central throughout the day on 26 October 2012. The southermost cells behind CS1 also developed and organized into a second mesoscale convective system (marked CS2), which headed eastnortheastwards towards

Triggering mechanisms
An exhaustive evaluation of Meso-NH simulations for the convective systems involved in IOP16a can be found either in Duffourg et al. (2016) or Martinet et al. (2017) at 2.5 km and 500 m horizontal resolution, respectively. Height (m) M e d it e r r a n e a n S e a

Massif Central
Var Gulf of Lion The numerous dedicated airborne and ground-based observations during the HyMeX SOP1 (suites of water vapour lidars, wind profilers, radiosoundings and boundary-layer drifting balloons, among others) over the sea and along the coast of the northwestern Mediterranean offered a unique framework for validating the convective systems simulated over the sea by kilometric scale numerical models initialized and driven by kilometric resolution analyses. Indeed, Duffourg et al. (2016) showed that these convective systems during IOP16a were fed during their evolution over the sea by moist and conditionnally unsta-5 ble air masses. A southwest to southeasterly converging low level flow over the sea is the main triggering mechanism acting to continually initiate and maintain the renewal of convective cells, contributing to the back-building systems CS1 and CS2.
Lifting is also partly due to evaporative low level cooling. In addition it appears that this low level cooling also controls the organization into a mesoscale convective system. Martinet et al. (2017) found that the mechanisms mentioned above, as well as the dynamics of the convective systems, are 10 sensitive to the mixing length formulation used in turbulence parameterization, at horizontal resolution of 500 m. These elements motivate an increase of the horizontal resolution up to LES scale in this present study to assess how the involved physical mechanisms are represented 3 Description on the numerical experiments

The Meso-NH model
The French non-hydrostatic mesoscale numerical model Meso-NH (Lac et al., 2018) was used for the simulation of the IOP16a case study. The Gal-Chen and Somerville (1975) vertical coordinate is used with 140 vertical levels. The vertical grid spacing is stretched with altitude, from 10 m close to the surface to 250 m aloft. The top of the domain is at 20 km altitude, and a Rayleigh 5 damping is progressively applied above 15 km altitude to the perturbations of the wind components and the thermodynamical variables with respect to their large-scale values, in order to prevent spurious reflections from the upper boundary.
The prognostic variables are the three Cartesian components of velocity, the dry potential temperature, the different water mixing ratios and the turbulent kinetic energy. Pressure perturbations are determined by solving the elliptic equation obtained by combining air mass continuity and momentum conservation equations. The transport scheme for momentum vari-10 ables is the Weighted Essentially NonOscillatory (WENO) scheme (Shu and Osher, 1988) of the 5 th order combined with the fourth order Runge-Kutta time-splitting method (Lunet et al., 2017), while the other 20 variables are transported with the Piecewise Parabolic Method (PPM) scheme (Colella and Woodward, 1984). A bulk one-moment mixed microphysical scheme (Caniaux et al., 1994;Pinty and Jabouille, 1998) governs the equations of the six water species: water vapour, cloud water, rain water, primary ice, snow aggregates, and graupel. The turbulence parametrization is based on a 1.5-order closure (Cuxart et al., 15 2000) and the calculation of the turbulent flow is performed through a three dimensional (3D) scheme for horizontal resolution below kilometric grid spacings. For horizontal resolution of about a few hundred meters and coarser grids, the mixing length follows the method of Bougeault and Lacarrère (1989) whereas for LES resolution, the mixing length formulation follows the one proposed by Deardorff (1972), which is directly proportional to the grid volume. The numerical set-up used in this study also used other parametrization schemes including the Rapid Radiation Transfer Model parametrization (Mlawer et al., 1997),

Simulation design
In this present study a LES of the IOP16a case study is carried out with the Meso-NH model. As in Duffourg et al. (2016) 25 or Martinet et al. (2017), the initial and lateral boundary conditions of the simulations are provided by the AROME-WMED analyses (Fourrié et al., 2015). Since it is not suitable to initialize and drive the LES simulation using directly the AROME-  and LR150 simulate fairly well the areas of strong precipitation over Southeastern France. The surface rainfall over land is well reproduced in terms of magnitude and location over the Var region and over the southeastern part of the Massif Central, compared to observations ( Figure 4).
As for precipitation over the sea, it is worth mentioning that radar quantitative precipitation estimation is impacted by large uncertainties, and in any case should be viewed cautiously. Nevertheless, two areas of strong accumulated surface rainfall are observed over the sea in Figure 4c; a first one located near 4 • E and a second one a few tens of kilometers southwest near 5 • E.

5
These regions of large precipitation are caused by the convective systems CS1 and CS2 mentioned earlier. Although only one convective system is simulated (i.e. CS2), its evolution over the sea is well simulated by both LR450 and LR150, except for a location too far west and stronger offshore rainfall just east of Spanish coast (see area circled in Figure 4). This precipitation pattern is explained by a former convective system triggered earlier in the simulation and not dissipating in time. But, the spatial distribution and magnitude of precipitation appear stronger for LR450 compared to LR150. The results presented here 10 for LR450 are fairly comparable to those obtained by Martinet et al. (2017) with a 500 m horizontal resolution. Differences are probably due to both different initial conditions and numerical schemes in both simulations.

a)
v Surface precipitation (mm)  In order to assess the consistency of these results along all the simulation period, time series of surface precipitation, averaged over the subdomain represented in Figure 4, are calculated. This domain encompasses the evolution of the convective system over the sea and not taking account here precipitation on land. Figure 5 shows the surface precipitation averaged over the whole One can remark that the surface precipitation simulated by LR450 is greater than LR150 from 0600 until near 1100 UTC on 26 October 2012 ( Figure 5a). However, it must be emphasized that the largest surface rainfall in LR450 from 0600 UTC until 0900 UTC are mainly due to more spatially widespread precipitation, whereas between 0900 UTC and 1100 UTC stronger rainfall rates contribute more to the largest precipitation for LR450. The sensitivity of these results to precipitation threshold has also been examined (not shown). Indeed, higher precipitation thresholds (> 20 mm h −1 ) confirm that LR450 simulates 5 stronger rainfall over a greater spatial area after 0900 UTC.
These results with more simulated precipitation with a horizontal resolution of 450 m, compared to the LES, are somewhat different than those obtained by Fiori et al. (2017) or Hanley et al. (2015) for instance, who found that the largest surface rainfall amounts are simulated at the finest scale. Nevertheless around 1200 UTC, the surface rainfall simulated by LR150 becomes greater ( Figure 5a). Both LR450 and LR150 are now compared by analysing the time evolution of the convection over the sea. It is worth mentioning that a convective system is triggered earlier shortly after the beginning of the simulation and was maintained in the simulation for too long. This former convective system is responsible for the large surface precipitation accumulation just east of the Spanish coasts ( Figure 4). The first convective cells of interest are actually triggered a bit late in both simulations near 0700 UCT on 26 October 2012 (not shown), leading to a different behaviour and evolution during the triggering stage 5 compared to observations. Figure 6 represents the simulated radar reflectivities at 0900 UTC and 1200 UTC at 850 hPa compared to observations, respectively, as well as horizontal winds at 950 hPa. As mentioned previously, the circulation, in which the convective system evolves, was characterized by strong low level convergence, controlled by a surface low pressure located between Spain and Balearic Islands. This pattern enhances locally convergence in the southwesterly to southeasterly low level flow. This surface 10 low pressure is simulated quite similarly in both LR450 and LR150 (Figure 6b and d). The mature stage is characterized by continual renewal of convective cells along the low level convergence around 0900 UTC as shown in Figure 6a and b. This particular organization is also visible in the observed radar reflectivities (Figure 6c). It appears that the convective system develops faster in LR450 with convection extending more northeastwards. As a matter of fact, when comparing both simulations at upper levels, i.e. analysing the infrared brightness temperature, one can see a more spatially extended convective system with 15 a more pronounced cloudy anvil in LR450 (Figure 7a and b). In the other hand, one can also remark that, for both simulations LR450 and LR150, the coldest area in terms of brightness temperature is less spatially extended compared to the observations (Figure 7c and f). This is probably related to a lack of iced hydrometeors at upper levels in the simulations. As the surface low pressure moves east-northeastwards, the low level flow strengthens and convergence increases, organizing into a very pronounced line. Near 1200 UTC on 26 October 2012, differences between both LR450 and LR150 become barely discernable 20 and precipitating structures are more comparable (Figure 6c and d). Both simulations show at this time a convective system tilting along a slight southwest-northeast axis that is fairly comparable with the observed radar reflectivities (Figure 6f).
In summary, increase of horizontal resolution from 450 m until 150 m for this case does not significantly improve some deficiencies of the simulation. Indeed, the low level convergence could be closely controlled by the surface low pressure, and both LR450 and LR150 handle its strengthening very similarly. Moreover, only a single convective system is simulated in both 25 LR450 and LR150 instead of two compared to observations, and too strong surface rainfall is simulated just east of Spanish coast. Nevertheless, significant differences appear between both simulations during the mature stage of the convective systems, especially in terms of accumulation of surface precipitation, spatial extent of the simulated systems, intensity (between 0900 UTC and 1100 UTC) and development of convection over the Mediterranean Sea.

Triggering mechanisms 30
In this section, the differences highlighted in terms of simulated surface precipitation patterns, convective organization and intensity are explained by analysing the environment and the mechanisms associated with the convective systems. It has been shown in the previous section that the mature stage is simulated differently by both LR450 and LR150. The system of interest is triggered around 0700 UTC just east of another decaying one, offshore of the Balearic Islands, slowly moving Thereafter and as also discussed previously, the systems simulated in both simulations adopt different behaviours during 5 their mature stage. Figure  Another mechanism responsible for lifting is also present and competes with the low level convergence. Indeed, both simulations reproduce a low level cold pool (LLCP) underneath the convective system. However, the cooling is more spatially widespread with stronger horizontal gradients greater than 2 • C for LR450, favouring more lifting. The LLCP interacts with the low level flow and also enhances locally the area of convergence, as shown in Duffourg et al. (2016) with their simulations at 2.5 km horizontal resolution. The less intense LLCP for LR150 probably leads to a less deflected flow, stronger moisture 5 advection and triggering of convection downstream compared to the system simulated by LR450.
In order to assess how these differences on mechanisms impact the dynamics of the simulated convective systems, Figure   9 presents time series of the mixing ratios for the precipitating hydrometeors as well as the strongest updraughts, averaged over the whole subdomain shown in In previous section 4, both simulations were compared by upscaling the LES at the same resolution as LR450. It has been shown that the increase in horizontal resolution does not modify significantly the environment of the precipitating system.
The triggering mechanisms, such as the low level convergence, are not modified significantly, except for the LLCP which is strengthened by possible enhancement of rainfall evaporation at low-levels in the convective system.
In the LES, the precipitating structures are simulated and represented at a finer scale. It offers the possibility of analysing 5 the dynamics more precisely and the convective organization down to the cell scale. Therefore, in the rest of the paper, the LES simulation will be presented at the native horizontal resolution (HR150). Figure (Figure 10d).
Within the southermost part of the precipitating system, one can see intense convective cell trains, oriented southwest to northeast, triggered and organised along the low level convergence. Figure 11 shows a vertical cross section along a convective cell between 0745 UTC and 0815 UTC (A-B axis in Figure 10), in both LR450 and HR150, of the simulated precipitating 15 hydrometeor contents (rain, graupel and snow aggregate contents) and the non precipitating (cloud and ice) water contents.
Vertical motions (updraughts and downdraughts) are also represented. At the beginning of the developing stage at 0745 UTC, the non precipitating hydrometeors depict for LR450 a rather shallow cloud with a base below 500 m ASL (Above Sea Level).
There are some mixed hydrometeor contents appearing at 0800 UTC but they are limited to 5-6 km height (Figure 11c). Very However, the cloud appearance is quite different and especially more realistic for HR150. Indeed, the structure is still organized with pronounced hydrometeor amounts advected upwards within convective updraughts but, in this case, there are stronger gradients of vertical velocity located all along the edge of the convective cell, i.e. downward motions in the 25 environment neighbouring and abutting strong updraughts at the edge cloud. Moreover in HR150, the cloud takes a clearly discernible cumuliform appearance throughout all the period of the developing stage, that might be an indication of a better representation of cloud-edge entrainment and therefore a better representation, at this scale, of horizontal turbulent mixing between the cloud and its environment (Figure 11b,d and f).
In order to illustrate that point, Figure 12, 13 and 14 show horizontal cross sections of vertical velocities, subgrid turbulent 30 kinetic energy (TKE) at 6 km and 8 km height, and both dynamical (DP) and thermal (TP) contributions in the TKE production at 6 km height, throughout the convective cells displayed in Figure 11, respectively. As one can see in Figure 12a and 12c and  At 150 m horizontal resolution, these eddies, as well as the updraft cores, are becoming better resolved as ascents exceed 12 m s −1 over large areas. Furthermore, the strongest updraughts are neighboured by strong downdraughts (exceeding 10 m s −1 ) just outside the cloud-edge that might be associated with a subsiding shell (Figure 12b and 12d). At 150 m the unresolved flow is mainly located at cloud edges and a significant part of the TKE contribution comes from the 3D dynamical production linked to the entrainment process. As a matter of fact, a clearly signature is simulated along the cloud-edge in HR150 ( Figure 14d). As at 450 m horizontal resolution, that might lead to less entrainment of dryer environmental air in the clouds and thus LR450 simulates a too rapid development of the convective system and greater surface rainfall compared to HR150.
This issue of representation of entrainment between clouds and their environment at LES scale has been also assessed by other previous studies (Bryan et al., 2003;Heus et al., 2009;Khairoutdinov et al., 2009;Glenn and Krueger, 2014, among others  by the mesoscale meteorological forcing through the lateral boundary conditions. As a result, even a LES with a horizontal resolution of 50 m does not significantly improve the quantitative precipitation forecast (Talbot et al., 2012). These previous studies confirm that increase horizontal resolution to LES grid spacing is necessary to better represent the small-scale processes governing deep convection organization, even if there is still further progress to be made in current parameterizations at this scale.

5
Furthermore, the LES simulation also better represent the spatial and temporal convective organization at cell scale within the precipitating system. Figure 15 illustrates a 3D rendering of the convective cell simulated by HR150 between 0900 UTC and 0940 UTC. One can see at 0900 UTC a well developed cumulus cloud, and forming a well simulated arcus cloud just in front of very intense rainfall underneath the storms (Figure 15a). It is possible to track the cell across the following ten minutes. It continues to expand spatially and vertically in the following ten minutes while developing a stratiform part and stronger subsidence downstream (Figure 15b). Finally around 0940 UTC, the convective cell reaches its mature stage ( Figure   15c), before loosing its identity and it is no longer discernible as it merges gradually with the rest of the precipitating system (not shown) .

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An animation of this 3D rendering performed with very high temporal resolution (every one minute) is very useful to better understand the 3D circulation within the precipitating system. The animation is available at https://doi.org/10.6096/mistrals-hymex.1540 (Nuissier, 2019). The southwest to southeasterly low level flow initiates convective cells just at the inner edge of the resulting strong convergence that, hereafter, propagate northwards while developing in the southwesterly upper level flow.

Conclusions
This study examines the impact of increasing horizontal resolution to Large Eddy Simulation (LES) in a numerical simulation of a real case study of Mediterranean HPE. For that purpose and for the first time, a large domain encompassing the convective 5 systems, as well as the low level flow feeding convection over the Mediterranean sea, is considered. The goal here was to assess precisely how the physical mechanisms and convective organization are represented from sub-kilometric scale down to LES horizontal resolution. The paper focuses on an offshore convection case study, which took place on 26 October 2012 during the HyMeX SOP1. Figure 16 summarises the precipitation structures of the convective systems as well as the triggering mechanisms analysed during this HyMeX case study.

10
The convective systems observed during IOP16a were fed all along their evolution over the sea by moist and conditionally unstable air masses. A southwest to southeasterly converging low level flow is the main triggering mechanism acting to continually initiate and maintain the renewal of convective cells, contributing to a back-building-shaped system (Figure 16b). The low level convergence was enhanced strongly by a surface low pressure located between Spain and Balearic Islands ( Figure   16a). 15 First, a LES carried out at 150 m horizontal resolution is compared, at the same scale, to another simulation performed with a 450 m grid spacing. On one hand, the increase of horizontal resolution from 450 m until 150 m is not able to improve significantly, for this case study, deficiencies of the simulation. Indeed, the simulated converging low level flow is quite similar in both simulations and only a single convective system is represented by both simulations instead of two compared to observations.
Although the present study does not present any sensitivity experiments to assess their precise role, initial and lateral bound-20 ary conditions might impact the simulations. The predictability of this heavy precipitation event, associated with offshore deep convection over the sea, is relatively low compared with more classical events anchored over the mountain range foothills. The direct orographic forcing appears less crucial while the convective systems were moving over the sea, but the neighbouring mountains are able to deflect the environmental mesoscale flow. Moreover, the model physics could also have a strong impact on the simulations. As a matter of fact, Martinet et al. (2017) showed for this case study that the formulation of the mixing 25 length impacts the simulated surface precipitation through, in some cases, greater low levels moisture advection and hydrometeor contents within the convective system. Moreover, Thévenot et al. (2016) and Rainaud et al. (2017) even showed that taking into account the wave effect or sea surface conditions in different parameterizations of the sea state is able to modify locally the spatial distribution of the precipitation, although the overall rainfall pattern is globally well reproduced.
All these aspects are important but it must be emphasized that, during IOP16a case, the location and the evolution of deep 30 convection over the sea (in particular the split into two distinct systems CS1 and CS2) are closely controlled by the upstream conditions (i.e. low levels moisture convergence generated by a surface low pressure located between Spain and Balearic Islands) and how they propagate inside of the LES domains. This split of deep convection over the sea is a real challenge for this case study. Another numerical experiment could consider a larger LES domain encompassing these upstream conditions. Although this LES over a very large domain would suffer from expansive computing time, it would be able to address whether a higher resolution simulation of these features is crucial. Furthermore, there were numerous dedicated observations, in particular over the Mediterranean sea, during HyMeX SOP1 that captured fairly well the wind and moisture spatial and vertical features of the upstream flow heading towards the French Mediterranean coastal regions . A 5 posteriori assimilation of these field research observations could improve the quality of kilometric scale analyses arising from AROME-WMED for example. As a matter of fact, a reanalysis, including HyMeX observations, was carried out recently with AROME-WMED (Fourrié et al., 2019). New initial and lateral boundary conditions providing by this reanalysis may help improve the representation of the mesoscale flow over the sea for this case study.
On the other hand, the increase of horizontal resolution modifies the representation of some of triggering and organizing 10 mechanisms controlling the precipitating system. More intense low level cold pools are simulated with a horizontal resolution of 450 m, probably related to evaporation of greater falling precipitation at least at the beginning of the simulation. As a matter of fact, at 150 m the unresolved flow is mainly located at cloud edges and a significant part of the turbulent kinetic energy contribution comes from the 3D dynamical production linked to the entrainment process. As a consequence, it is possible to argue that the entrainment process, especially along the cloud-edge, is strongly underestimated at 450 m horizontal resolution, 15 that might lead to less entrainment of dryer environmental air in the clouds that could explain why LR450 simulates a too rapid development of the convective system, greater surface rainfall and stronger low level cold pools compared to HR150.
Obviously, the results presented here need to be confirmed considering more convective case studies and using more statistical approaches. However, this first LES of a real Mediterranean precipitating case study highlighted an organization in fast-propagating and developing cell trains within the converging low level flow (Figure 16), features that are definitively out 20 of range of the kilometric resolution. In a general way, the goal of ongoing and future works is to better represent in the models at hectometric scales the key processes, such as turbulence and microphysics, that are crucial to progress in heavy precipitation forecasts.