Regularly during fall, heavy-precipitation events (HPEs) occur over the northwestern Mediterranean basin and more particularly over the mountainous coastal regions of France, Spain, and Italy. In most cases, large amounts of precipitation are recorded in less than 1 d (typically more than 200 mm in less than 24 h and sometimes in only a few hours) when a mesoscale convective system (MCS) develops and stays over the same area for several hours among others.

Several past case studies, especially within the framework of the Hydrological cycle in the Mediterranean Experiment (HyMeX) Special Observation Period (SOP1), have extensively investigated the mechanisms and physical processes associated with such high-impact events, based on numerical experiments with kilometric horizontal resolutions and dedicated observations . Over the Western Mediterranean region, HPEs evolve often within a favourable synoptic pattern, including an upper-level trough centred over the Iberian Peninsula and/or high values of geopotential anchored over central Europe, driving a persistent low-level moist and conditionally unstable marine flow directed towards the coastal mountainous regions. Due to regional and local effects, the low-level flow is then deflected by neighbouring mountain ranges (Pyrénées, Massif Central, and the Alps) or islands such Corsica and Sardinia. In order to trigger deep convection, a lifting mechanism is needed to focus and finally release the conditional convective instability at the same location. Orographic lifting of the conditionally unstable low-level marine flow impinging the foothills neighbouring the Western Mediterranean is a well-studied mechanism for renewing convection triggering at the same location . Lifting can also be due to local convergence in the low-level circulation induced by the orography of the region or lee cyclogenesis . A low-level cold pool, possibly forming under the MCS, can also lift the low-level flow at its leading edge and/or modify the low-level circulation locally and enhance convergence areas .

While these previous studies have shown that a horizontal resolution of about 1 km is able to simulate many of the observed features of Mediterranean HPEs, as well as their associated key physical mechanisms, they have difficulties representing the time at which convection is triggered and how it is organized. The increase in horizontal resolution to sub-kilometric grid spacings could be a way for improvement. Indeed, have shown, for an idealized convective case, that an increase in horizontal resolution of 500 m simulates stronger updraughts within convective cells associated with a greater cloudy coverage. and carried out numerical modelling HPE case studies over Italy with grid spacings ranging from 5 km to 200 m. Similar to idealized studies, they found that smaller convective cells with a stronger intensity are simulated with a horizontal resolution finer than 500 m. found that, when the horizontal grid spacing is reduced to 500 m, precipitation is more widespread, maximum values are lower, and individual convective cells are smaller. These previous studies concluded that surface precipitation amounts are enhanced and convective structures are better represented at a sub-kilometric scale.

Nevertheless, the increase in horizontal resolution may pose problems especially for the turbulence parameterization within the so-called “grey zone” (GZ), typically in the range of horizontal resolutions of about a few hundreds of metres and also depending on the model's effective resolution . Indeed, there are still uncertainties about how turbulence should be modelled at these resolutions. Past studies have investigated the impact of a one-dimensional (1D) versus a three-dimensional (3D) representation of the turbulence at sub-kilometric horizontal resolution. showed that a 3D turbulence leads to stronger mixing and greater cloud cover. carried out simulations using 1D turbulence, which produced too many small cloud systems and rainy cells with a shorter lifespan. Additionally, compared kilometric deep-convection simulations, with up to 500 m resolution, to a large-eddy simulation (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, found that, for a specific case study of HyMeX SOP1 (IOP16a), it is not only cloud organization but also the simulated environment and processes governing convection that are strongly sensitive to the formulation 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 motivates the adoption of an LES-like approach, enabling a more suitable representation of turbulence within and at the edge of convective clouds and also within the atmospheric boundary layer. In an LES framework, eddies that contain most of the kinetic energy are resolved, whereas smaller eddies, which 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 among others, 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 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 for 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 over the sea is considered. The paper focuses on the same offshore convection case study described in and (IOP16a), which took place on 26 October 2012 during the SOP1 of the HyMeX field programme .

This article is organized as follows. A quick review of the case study and the mechanisms involved are provided in Sect. . The numerical model and the simulation setup are presented in Sect. . Both simulations with hectometric horizontal resolutions and LES, respectively, are compared in terms of rainfall field analysis and convection organization in Sect. . The physical processes at cloud scale leading to very deep convection and convection organization are assessed in Sect. . Finally, the study is summarized and conclusions are given in Sect. , where perspectives for future work are also suggested.

This section aims at assessing the impact of increasing horizontal resolution by comparing both simulations over the same spatial scale. For that purpose the reference LES fields are upscaled at a coarser horizontal resolution of 450 m (hereafter LR150). The fields are thus coarse grained by averaging the LES fields as in or . We focus on the life cycle of heavy precipitation occurring over the sea mainly on the morning of 26 October 2012, with a mature phase happening between 06:00 and 12:00 UTC. During this period, the triggering mechanisms within the convective systems are examined.

In Sect. , 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 the environment of the precipitating system significantly. The triggering mechanisms, such as the low-level convergence, are not modified significantly, except for the LLCP, which is strengthened by the 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 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  highlights the spatial distribution of the rain and cloud mixing ratios at 1500 m height for both LR450 and HR150, which are compared to the simulation at 2.5 km horizontal resolution. If the kilometric simulation develops a convective structure within the low-level convergence, it is unable to organize small convective cells, as depicted at hectometric resolution (Fig. a compared to b and c). This simulated organization with trains of very small convective cells are also depicted and confirmed by radar observations (Fig. d).

Within the southernmost part of the precipitating system, one can see intense convective cell trains, oriented southwest to northeast and triggered and organized along the low-level convergence. Figure  shows a vertical cross section along a convective cell between 07:45 and 08:15 UTC (A–B axis in Fig. ), in both LR450 and HR150, of the simulated precipitating 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 07:45 UTC, for LR450 the non-precipitating hydrometeors depict a rather shallow cloud with a base below 500 m a.s.l. (above sea level). There are some mixed hydrometeor contents appearing at 08:00 UTC, but they are limited to 5–6 km height (Fig. c). Very quickly – 15 min later – at 08:15 UTC, strong upward motions are simulated within the cell, associated with large graupel contents of up to 9 km height (Fig. e). When reaching the top of the troposphere, a cloudy anvil forms and fans out downstream of the upper-level southwesterly flow.

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 environment neighbouring and abutting strong updraughts at the cloud edge. Moreover in HR150, the cloud takes a clearly discernible cumuliform appearance throughout the entire period of the developing stage, which 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 (Fig. b, d, and f).

In order to illustrate that point, Figs. , , and show horizontal cross sections of vertical velocities, subgrid turbulent kinetic energy (TKE) at 6 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 Fig. . As one can see in Figs. a and c and a and c, at 450 m horizontal resolution, the updraught cores are partly resolved, as vertical velocities do not exceed 12 m s-1, and are also partly unresolved, with TKE sometimes higher than 30 m2 s-2. This TKE is produced by both dynamical and thermal processes and is mainly localized within the updraught cores. The eddies near the cloud edges, which are subgrid at 450 m horizontal resolution, are not represented by the turbulence scheme. These results are in a good agreement with those obtained by and , who have shown that a commonly used eddy-diffusivity turbulence scheme underestimates the TKE at kilometric and hectometric (500 m) horizontal resolution, especially at the cloud edges but also in the updraught cores where the thermal production is misrepresented as the scheme does not enable the countergradient structures present in the updraught to be reproduced.

At 150 m horizontal resolution, these eddies, as well as the updraught 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 (Fig. b and d). 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 clear signature is simulated along the cloud edge in HR150 (Fig. d). 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, which might lead to less entrainment of drier environmental air in the clouds, and thus LR450 simulates too rapid a development of the convective system and greater surface rainfall compared to HR150.

This issue of the representation of entrainment between clouds and their environment at LES scale has been also assessed by other previous studies among others. For example, also compared LES with horizontal resolutions of 150 and 450 m for a continental deep-convection case. They found that, even if moving from a kilometric grid spacing to LES does improve the representation of their case study, their LES-150 m does not adequately represent the associated small-scale forcing mechanisms. Moreover, in that case, higher resolutions worsen results due to relatively more environmental entrainment, and moisture updraughts thus appear too diluted. On the other hand some previous studies also confirm the point that LESs are primarily impacted by the mesoscale meteorological forcing through the lateral boundary conditions. As a result, even an LES with a horizontal resolution of 50 m does not significantly improve the quantitative precipitation forecast . These previous studies confirm that increased horizontal resolution for 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.

Furthermore, the LES simulation also better represents the spatial and temporal convective organization at the cell scale within the precipitating system. Figure  illustrates a 3D rendering of the convective cell simulated by HR150 between 09:00 and 09:40 UTC. At 09:00 UTC one can see a well-developed cumulus cloud, forming a well-simulated arcus cloud just in front of very intense rainfall underneath the storms (Fig. a). It is possible to track the cell across the following 10 min. It continues to expand spatially and vertically in the following 10 min while developing a stratiform part and stronger subsidence downstream (Fig. b). Finally around 09:40 UTC, the convective cell reaches its mature stage (Fig. c) before loosing its identity, and it is no longer discernible as it merges gradually with the rest of the precipitating system (not shown).

An animation of this 3D rendering performed with very high temporal resolution (every 1 min) is very useful to better understand the 3D circulation within the precipitating system. The animation is available at 10.6096/mistrals-hymex.1540 . 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.

This study examines the impact of increasing horizontal resolution for 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 systems and 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 a 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  summarizes the precipitation structures of the convective systems as well as the triggering mechanisms analysed during this HyMeX case study.

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 (Fig. b). The low-level convergence was enhanced strongly by a surface low pressure located between Spain and the Balearic Islands (Fig. a).

First, an 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 in horizontal resolution from 450 until 150 m is not able, for this case study, to improve significantly 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 boundary 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 appeared less crucial while the convective systems were moving over the sea, but the neighbouring mountains were 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, for this case study showed that the formulation of the mixing length impacts the simulated surface precipitation through, in some cases, greater low-level moisture advection and hydrometeor contents within the convective system. Moreover, and even showed that taking into account the wave effect or sea surface conditions in different parameterizations of the sea state is able to locally modify 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 the IOP16a case, the location and the evolution of deep 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-level moisture convergence generated by a surface low pressure located between Spain and the 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 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 . New initial and lateral boundary conditions provided 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 in horizontal resolution modifies the representation of some of triggering and organizing mechanisms controlling the precipitating system. More intense low-level cold pools are simulated with a horizontal resolution of 450 m, probably related to the 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, which might lead to less entrainment of dryer environmental air in the clouds that could explain why LR450 simulates too rapid a 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 (Fig. ), features that are definitively out of range of the kilometric resolution. In a general way, the goal of ongoing and future work is to better represent the key processes in the models at hectometric scales, such as turbulence and microphysics, that are crucial to progress in heavy-precipitation forecasts.