The weather radar data used in this study consist of 24 hydrological years (September–August), between 1990–1991 and 2013–2014, observed by the Electrical Mechanical Services (EMS/Shacham) non-Doppler C-band weather radar (5.35 cm wavelength), located at Ben Gurion Airport (Fig. ; 31.998∘ N, 34.908∘ E). Its effective range is 185 km. Raw radar reflectivity data were translated to quantitative precipitation estimates (QPEs) using a fixed Z–R relationship (Z=316⋅R1.5) and applying physically based corrections and gauge-based adjustment procedures see details in. This produced QPEs at 1 km2 and roughly 5 min resolutions. Examining the radar QPE and comparing it with rain gauges at an hourly and yearly resolution yielded a root-mean-square error of 1.4–3.2 mmh-1 and 13–220 mmyr-1, respectively, and a bias of 0.8–1.1 (hourly) and 0.9–1.1 (yearly) . This archive has previously been used for a series of studies focusing on high-intensity precipitation, including precipitation frequency analysis , floods , and characterisation of convective rain cells . A few of the following issues potentially affecting the QPE should be mentioned. The radar was turned off during the dry season and, for technical reasons, sometimes during the wet season; thus, a few severe storms were missed and are not included in the archive. A long-term decline in the availability and quality of radar data might have decreased the number of high-quality archived HPEs over the years, mainly since 2010. As we did not aim to provide a complete climatology, these aspects were not expected to influence the results of the study. For technical reasons, the radar products were not always available at their intended temporal resolution (approximately 5 min) and longer gaps may exist between consecutive radar scans. Gaps of less than 20 min between consecutive radar scans were linearly interpolated to recreate the 5 min resolution; gaps of more than 20 min were treated as missing data. Due to the uneven spatial distribution of the rain gauges, adjustment procedures may inadequately represent the south-easternmost areas covered by the radar, where the gauge network is most sparse. Finally, due to overshooting of the radar beam, precipitation occurring east of the Dead Sea (Fig. ) is generally underestimated.

The WRF model was configured using three two-way nested domains, with a 1 : 5 resolution ratio between them (Fig. ) and 68 vertical levels (model top is at 25 hPa). The inner domain (551 pixels×551 pixels) was set at a 1 km2 horizontal resolution, in order to be comparable with the radar data. To comply with the Courant–Friedrichs–Lewy numerical stability criterion, model time steps in the innermost domain were between 4 and 8 s . However, to spare computer storage, outputs were saved at 10 min intervals. When analysed, the WRF grid was interpolated using nearest-neighbour interpolation from a Lambert projection grid to a similar-sized grid on a transverse Mercator projection, as in the radar archive. It is important to note that a 1 km2 spatial resolution enables the explicit resolution of convection, without the use of parameterisation e.g.. The two outer domains used the WRF Tiedtke scheme for the parameterisation of convection . The model input data were 6-hourly ERA-Interim reanalyses, at approximately an 80 km horizontal resolution, and with 60 vertical levels, including sea surface temperature, along with basic meteorological parameters . The model was used to simulate the HPEs identified in the radar archive (Sect. ; Table S1 in the Supplement). Each simulation started 24 h prior to the beginning of the event, rounded down to the previous 6 h, and finished at the end of the HPE, rounded up to the next 6 h. Therefore, the spin-up period of each simulation was at least 24 h. Additional model settings, presented in Table , were selected because they are considered suitable for convection-permitting simulations e.g..

HPEs have various definitions in different research fields and geographical regions. For example, climatologically, HPEs are commonly associated with a specific time interval (i.e. sub-daily to a number of consecutive days) during which precipitation depth surpasses a threshold representing a predefined quantile (e.g. 95th or 99th) or a high but constant intensity (e.g. 10, 20, or 50 mmd-1; see). In contrast, hydrological definitions usually focus on the resulting flood. In general, a good definition of a HPE should also include the areal dimension to enable hydrological and social impacts to be taken into account .

Here we define HPEs by the exceedance of local, quantile-based thresholds over a sufficiently large area. The decision to set local thresholds was due to the sharp climatic gradient characterising the study area. To decrease the computational effort and guarantee adequate temporal sampling, the HPE identification was based on a radar database comprising hourly intervals for which at least 60 % of the expected radar scans were available . For a set of durations between 1 and 72 h, we defined the threshold as the 99.5th quantile of the non-zero (i.e. more than 0.1 mm) hourly amounts observed in each radar pixel. The range of examined durations was chosen to represent both short- and long-lived HPEs. It should be noted that the same storm can be identified as a HPE for multiple durations. Depending on the duration and location, the amounts obtained are equivalent to annual return periods of roughly 2–10 years (Fig. ). To account for the spatial scale, we classified all time intervals during which at least 1000 pixels (i.e. 1000 km2) exceed their local threshold as HPEs. Jointly, these thresholds (99.5 % for each pixel, and an aggregation of 1000 pixels for an event) settle the trade-off between having too many (or too few) events and accounting for HPEs that are too local (or only including the most widespread rainstorms). These selected thresholds enable the analysis of a reasonable number of diverse HPEs, with some being quite local and others more widespread.

The selection procedure yielded 76–98 individual events for each of the examined durations, summing to 120 when overlaps between durations were included. Similar to , storms were separated by at least 24 h with less than 100 pixels displaying rainfall of more than 0.1 mm. As the ERA-Interim data are available at a 6 h resolution, rainstorms that were too short (less than 12 h) were excluded from the analysis. Storms longer than 144 h were excluded to avoid major changes in sea surface temperature during events. In addition, events were discarded manually when the radar data were abundantly contaminated by ground clutter due to anomalous propagation or when other data-quality issues were observed. The final list of HPEs consisted of 41 independent events spanning 3.4±1.6 d on average (Table S1).

For each of these events, a filter was used to remove pixels with residual ground clutter. Pixels in which the probability of rain detection (POD, i.e. the fraction of time in which the pixel exceeds 0.1 mmh-1) exceeds 10 % and is larger than 1.9 times the average POD of the surrounding area (25km×25 km) were removed. The extent of the explored area and of the ratio were chosen subjectively after examining ranges between 1 and 3 (for the ratio) and 5 and 50 km (for the areal extent). Additional areas known to be persistently contaminated by ground echoes (from our experience and earlier studies) were masked out manually (e.g. the circular area near the radar). Together, these procedures excluded approximately 0.5 % of the radar pixels.

We classified the HPEs into two classes representing the most common rainy synoptic circulation patterns prevailing in the region: MC and ARST. To do so, we relied on the semi-objective synoptic classification by , based on daily (at 12:00 UTC) meteorological fields at the 1000 hPa pressure level from the NCEP/NCAR reanalysis (2.5∘ spatial resolution). We classified a HPE as a MC if one of the following conditions occurred: (i) most of the days comprising the HPE were considered, according to , as days with either a MC or a high-pressure system following a MC; (ii) one of the days during the HPE was a MC and none of them were an ARST. Similarly, we classified a HPE as an ARST if (i) most of its days were classified as ARST according to or (ii) one of its days was an ARST and none of them were a MC. The above-mentioned tropical plume synoptic pattern is not part of our classification because of its low frequency and because it does not appear in near-sea-level pressure meteorological fields. Specifically, one HPE (HPE 41; Table S1) was characterised, during its 5 d span, first by the prevalence of a tropical plume and then by a MC; it was classified here as a MC. Despite the simplification, these two classes have recently been shown to exhibit distinct characteristics of rainfall intensity distribution . Indeed, 85 % and 15 % of HPEs were classified as MCs and ARSTs, respectively (Table S1), reasonably following the expected proportions of the two synoptic circulation patterns .

Inaccurate initial conditions in the presence of non-linear precipitation-generation processes, along with the presence of atmospheric instabilities, may limit the atmospheric predictability and, consequently, modelling skill . Moreover, increasing the model resolution may pose difficulties in a pixel-by-pixel evaluation of the forecasts e.g.. Approaches that are more suitable for high-resolution rainfall fields range from simple visual comparisons to more sophisticated, object-oriented or filtering methods capable of representing spatiotemporal properties of the fields e.g.. In this study, we applied visual comparisons and several numerical measures to compare the observed radar QPE with the WRF-derived rain field.

Of the 41 identified HPEs, 35 occurred during MC synoptic prevalence and the rest during ARST prevalence. Despite the dependence of the identification on the quality and availability of the radar data, our analysis can be considered “quasi-climatological”, as the selected HPEs do not exhibit obvious biases with respect to the rain climatology in the region: (i) their seasonality follows the seasonal pattern of EM rainy days (Fig. ), although HPEs occur more frequently at the beginning of the winter, presumably due to the high sea surface temperatures; (ii) HPEs are identified throughout the radar archive (with zero to seven HPEs per year); (iii) the frequency of the prevailing synoptic circulation patterns during HPEs (Table S1) resembles the frequency observed on rainy days ; and (iv) HPEs characterised by ARST prevalence are common only during the transition seasons (Fig.  in this paper; e.g.).

For most examined durations, rain amounts defining the HPEs are larger near the Mediterranean coast, extending a few kilometres off- and onshore (Fig. ). This resembles the observed pattern of high rain intensities near the coast, rather than inland , which has also been reported for extreme precipitation quantiles observed from both weather radar and satellite sensors . In contrast, short durations (less than 12 h) exhibit the highest rain intensities in the arid areas of the region. The frequency of rain in the arid areas is lower than in the rest of the region ; thus, the 99.5 % quantiles are based on fewer data. Nevertheless, the reported higher extreme rain amounts for shorter durations are in agreement with previous studies, which showed that highly localised convective rainfall is more common during HPEs in the desert than in other climatic environments in the EM . In the mountains, the opposite case is seen: rainfall is produced more significantly through stratiform (or shallow convection) processes, and rain amounts for short durations are therefore relatively lower . For the longer durations, rain intensities in the mountains are comparable to the intensities near the coast, probably resulting from the tendency of rain to persist in orography-affected regions e.g..

Affected by higher rain intensities, the centre of mass of the precipitation field for each of the HPEs is located near the EM coastline (Fig. ). Nevertheless, a seasonal pattern appears, with a general landward shift of the centre of mass during the rainy season (Fig. ). This is caused by land–sea differential heating and heat capacities and resembles the seasonal pattern of rain intensities in the EM . In fact, this points out the observed preference of convective clouds to form above high-temperature surfaces, i.e. the sea surface or nearby coastal plains in autumn or early winter as well as farther inland in the spring. In terms of seasonality, the WRF-simulated centres of mass exhibit a similar, even if slightly less obvious, landward pattern. It must be noted that ARST-type events in the WRF results are biased eastwards compared with the radar results, which could be related to the WRF's worse performance with respect to such events (e.g. Sect. ). Moreover, the exact location of the radar-observed centre of mass can suffer from range degradation, which may cause these centres to be biased towards the radar location.

According to the definition applied in this study, a given event can be considered a HPE for more than one duration. This can happen when the thresholds associated with the examined durations (Sect. ) are exceeded either at the same location or in different regions. The durations associated with each HPE are listed in Table S1. The co-occurrence of each HPE duration with the rest of the examined durations is shown in Fig. ; these co-occurrence values are similar to values determined in the Alps by . For example, 79 % of the HPEs at a 24 h duration are also HPEs at a 72 h duration. Figure 5 indicates a high dependence (i.e. co-occurrence) of the short-duration HPEs (3–12 h). Similarly, there is a high dependence within the long-duration HPEs (24–72 h). Nevertheless, even the shortest (duration) HPEs examined here show a rather high co-occurrence with the longest (duration) HPEs (probabilities in all cases greater than or equal to 0.5).

Figure  shows the rainfall accumulated during all HPEs as estimated by the weather radar, modelled by the WRF, and measured by rain gauges (Fig. a, b, and d, respectively). Bias, defined herein as the normalised difference between WRF rainfall and radar QPE WRF-radarradar, in percent, is shown in Fig. c. In 69 % of the studied region, the bias lies between +200 % and -67 %, although some areas show a strong positive bias (Fig. c). The three stations highlighted in the figure (the values shown for radar and WRF represent the average of the nine pixels surrounding the gauge locations) show how this large bias is mostly caused by radar underestimation. In fact, these areas are generally located far from the radar or in the eastern portion of the radar coverage, where radar QPE suffers from range degradation and beam overshoot due to the presence of mountains. In some other areas, the bias seems related to residual beam blockages. Underestimation (a bias less than zero) is also apparent in regions with ground clutter, and some spatial inconsistencies related to the interpolation of a few fully blocked beams can also be noticed. To avoid interference of these radar estimation inaccuracies with our results, we focus only on the areas in which the bias lies between +200 % and -67 % (Fig. c). Still, a portion of the area close to the radar is characterised by negative bias, which could be attributed to simulated rain intensities that are too low. A similar pattern was also shown in where it was attributed to intensities that were too low during deep MCs.

Visual comparison of observed (radar) and simulated (WRF) rainfall fields yielded mostly (subjectively) good results in terms of the spatial rainfall patterns, such as widespread versus localised rainfall. As an example, Fig.  presents a well-simulated HPE case (HPE 1, Table S1). In addition, the distributions of rainfall among pixels were generally well represented (Fig. d). At the same time, pixel-based comparisons were deemed inappropriate for such an analysis, as shown in the scatter plot (Fig. e). Most of the examined HPEs led to similar observations, with the exception of two HPEs in which the WRF model clearly failed to represent the rainfall patterns. An example of such a poor simulation is given in Fig.  (HPE 5, Table S1). Both of these poorly simulated HPEs were characterised by relatively short total storm spans (1.7 and 2 d), just exceeding the durations that defined them as HPEs (6 and 3–24 h, respectively). Synoptically, they were classified as ARSTs, a system generally characterised by local, short-lived convection associated with a localised rainfall-triggering mechanism . The skill of mesoscale models (e.g. WRF) is poorer in simulating these types of events, mainly due to their short predictability and stochastic nature see e.g.. Although a deeper understanding of these aspects can be beneficial for improving future simulations, it falls outside the scope of this study and requires future dedicated research efforts.

The FSS of the first HPE (Fig. f) further manifests the accuracy of the simulated rainfall fields. The forecast has a larger FSS than the uniform FSS for all of the examined cumulative rainfall amounts less than or equal to 50 mm, even at the model resolution (1 km). For larger cumulative rainfall, the FSS is unstable due to the limited number of observations of such cases; thus, no conclusions about the suitability of the results can be made for the occurrence of such high cumulative rainfall. It is only for the higher rainfall amounts, e.g. 125 mm, corresponding to less than 1 % of the pixels in this HPE, that the model forecast is unskilled at all spatial scales, i.e. the uniform FSS outperforms the WRF forecast FSS (yet, these results are also based on a limited number of data).

During EM rainstorms, cumulative rainfall values are distributed unevenly in space, and extremely high rainfall depths are embedded within the larger aerial coverage of lower rainfall depths e.g.. Thus, forecasting the spatial distribution (location and spatial frequency) of low cumulative rainfall is easier than forecasting the distribution of the high end of cumulative rainfall, even when averaging is conducted over large scales. The minimal scale at which the FSS of the model's forecast is higher than the uniform FSS was calculated for the occurrence of a range (1–200 mm) of cumulative rainfall depths for all of the identified HPEs (Fig. ). This allows for the estimation of the minimal scales for skilful rainfall detection for rain depths that are equal to or greater than an arbitrary cumulative rain depth threshold. For example, the original model resolution yielded a skilful forecast for the occurrence of cumulative rainfall depths of less than 25 mm in 50 % of the HPEs (Fig. ). The figure also shows that the occurrence of cumulative rainfall exceeding 45 mm, in most cases, is only skilfully forecasted on a relatively large spatial scale (tens of kilometres). During ARSTs, the minimal scale was much higher than during MCs (not shown); however, it is important to remember that two of these HPEs were poorly simulated.

The SAL analysis (Fig. ) showed good performance of the model, except for a substantial positive amplitude bias (inter-event amplitude component median of 0.80, i.e. a bias of 130 %, as defined in Sect. , and interquartile range of 0.37–1.02). Two events stood out with a bias smaller than zero; these were the above-mentioned poorly simulated HPEs. In general, MC-type HPEs exhibited much greater bias than ARSTs (inter-event amplitude component median of 0.85 versus -0.07). However, it must be noted that the median of ARST-type HPEs includes the two poor simulations and is therefore predicted to be more negative. Surprisingly, where visual comparisons seemed better, and the structure component was closer to zero, the amplitude component actually suffered from more positive biases; for example, the structure component of HPE 1 (Fig. , Table S1) is 0.04, while its amplitude component is 1.03. Furthermore, the median amplitude of events characterised by a structure component larger than the median structure is 27 % higher than the amplitude of events with a structure smaller than the median value.

The structure component was well modelled in most cases, showing the ability of the WRF to accurately generate precipitation objects (0.06 and -0.06 to +0.26 for the median and interquartile range, respectively; 0.05 and 0.09 are the medians for MC- and ARST-type events, respectively). This is particularly important in regions and for events where rainfall is generated via both convective and stratiform processes, or when intense rainfall is embedded within larger-scale low-intensity precipitation . The slight positive tendency of the structure component could either indicate that the model creates rain fields that are too smooth (lower intensity rain and objects that are too large), that radar data are too noisy, or, most probably, a combination of both error sources.

Relatively low values of the location component (0.25 and 0.18 to 0.31 for the median and interquartile range, respectively; 0.26 and 0.22 are the medians for MC- and ARST-type events, respectively) demonstrate the model's high capability to spatially distribute precipitation objects. Medially, 34 % of this component is composed of the error in the centre of mass location (namely L1; i.e. a median error of 30 km in the location of the centre of mass), and the rest is from the average location of each precipitation object (L2). Namely, the model prediction of the centre of mass of the rain field is quite satisfying, but the prediction of individual precipitation objects is a bit poorer. The contribution from the L2 component to the location component (Sect. S2 in the Supplement) indicates that modelled precipitation objects are not distributed the same as the observed ones. This is probably due to a mismatch in the positioning of the simulated cells. Given the good ability of the radar to represent the location of rain cells, attenuation and range-degradation of the radar data should only have minor effects on L2. In either case, location values are rather small, exhibiting good spatial distribution of precipitation objects. Nonetheless, the same two challenging ARST-type HPEs for which the model was unable to simulate the rainfall in a satisfying manner stand out with high location values (0.46 and 0.85), yielding large spatial inconsistency with respect to observations (see above, e.g. Fig. ).

The overall positive bias seen in the amplitude component (Fig. ) could result from an underestimation of the radar QPE or an overestimation of the WRF simulation. Possible reasons leading to radar underestimation have been discussed above and may contribute to this bias even after the most severely biased regions have been masked. However, this positive bias still needs to be considered when addressing the actual cumulative rainfall amounts predicted by the model. In contrast with the overall bias (Sect. 4.2) almost no event showed a negative bias. mainly attributed positive biases to deep lows over complex-terrain regions.

The overall good representation of precipitation objects implies that precipitation processes generated by the model represent actual processes and rainfall characteristics .

This work characterises rainfall patterns during 41 HPEs in the EM and evaluates the ability of a high-resolution WRF model to properly simulate their cumulative rain field and spatiotemporal behaviour, with a specific emphasis on their convective component and the prevailing synoptic system. A successful outcome will pave the way for downscaling global climate projections to induced changes in rainfall patterns on a regional scale during HPEs, with an understanding of the strengths and weaknesses of the regional results. However, it is important to note that the identification of HPEs in global climate models constitutes yet another challenge see discussions e.g. in.

To overcome the diverse climatology of the EM, we identified HPEs using pixel-based weather radar climatology. We used a uniquely long, quality-controlled and gauge-adjusted high-resolution weather radar archive to characterise the rainfall patterns. A convection-permitting high-resolution WRF model configuration was used to simulate the same HPEs, and the results of this modelling effort were compared to the radar QPEs. For most of the 41 HPEs, model simulations gave valuable results: using the FSS we determined that (i) WRF simulations are highly accurate for cumulative rainfall less than 25 mm (Fig. ; Sect. ), and (ii) accumulation of more than 45 mm produces variable results among different cases (Figs. , , and ; Sect. ). In other words, skilful results are gained if the model output is averaged over at least a few tens of kilometres. SAL analysis of cumulative rainfall showed that the rainfall location and structure were correctly reproduced by the model and were similar to the weather radar data observations in 39 out of the 41 HPEs. Conversely, rainfall amplitude was highly (positively) biased, with some of the bias likely due to radar underestimation; however, a model positive bias cannot be excluded. Furthermore, we found that ARST-type HPEs are not as well simulated as MC-type events, at least in terms of the FSS and the spatial structure of rainfall.

In general, rain amounts forming HPEs are higher near the EM coastline with the exception of (i) short (examined) durations, for which the highest rain amounts are observed in the desert regions, and (ii) the longer-duration HPEs, for which rain amounts in mountainous regions are comparable to those on the coast. Identified HPEs occurred during the wet season (October–April), primarily in November–February. Their centre of mass was close to the Mediterranean coastline and shifted landward during the season. We analysed the areal distribution of rainfall for various durations, the autocorrelation structure of the convective rainfall fields, and DAD curves to obtain quantitative information on the characteristics of the rainfall fields, the ability of the WRF model to simulate them, and the processes generating them, such as the aggregation of small and short-lived rain cells to produce a HPE.

High-intensity threshold-forming HPEs near the Mediterranean Sea (Fig. ) are expected, due to its warm surface waters and high moisture fluxes; they are also apparent in other regions of the Mediterranean e.g.. High rain intensities in the desert are somewhat more intriguing. For example, mentioned that there is contrasting evidence with respect to whether rain intensities in the desert are higher than in non-desert regions. An opposing trend between mean annual rainfall and short-duration rain intensities was also described by , using rain gauges, and by , using both rain gauges and weather radar. This trend is related to the higher surface temperatures in desert regions, which may enhance convective activity e.g., as well as to a deeper boundary layer e.g. and the prevalence of rainfall from ARST circulation patterns, which generally cause higher rain intensities . Such a sharp spatial change in the climatology of the rain intensities defining HPEs can only be captured using high-resolution, high-spatiotemporal-coverage data (such as the radar QPE presented here) and reproduced by high-resolution, convection-permitting models.

Mediterranean-climate, and even more so desert-climate HPEs, can produce rain amounts of the same order of magnitude as the mean annual rainfall e.g.. Thus, the frequent co-occurrence of short- and long-duration HPEs is to be expected, and dividing events into short versus long duration is not straightforward. However, our dataset comprises events with different characteristics: local and intense as well as widespread; the rainfall-triggering mechanisms and potential hydrological impact can be quite different.

Comparison of the DAD curves in Fig.  with reported floods in Mediterranean and desert environments in the EM shows that a portion of the HPEs analysed here are prone to produce floods in smaller catchments and in desert regions, characterised by rather short (approximately 7 h) and low total precipitation rain spells. Other HPEs analysed here could generate floods in larger catchments and in Mediterranean climate regions, characterised by longer rain spells and higher rain depths (1 d and 52 mm, respectively) . Specifically, the convective part of the rainstorm is known to generate the highest-magnitude floods, even in Mediterranean climate areas e.g.. The short spatiotemporal autocorrelation distances observed for the convective rain fields once again highlight the spottiness of HPE rainfall in the EM region , and they were well simulated by the WRF model (Fig. ).

ARST synoptic circulation is often associated with flash floods in the desert part of the region , and its rainfall is commonly caused by the mesoscale triggering of convection ; therefore, it is less predictable e.g., as is also evident from this study (e.g., Figs. , ). ARSTs are also characterised by smaller rain field autocorrelation distance (Fig. ). Thus, it is crucial for future studies to understand the reasons for the poor modelling results observed for 2 of these 41 HPEs. This is evident in the coarser model domains as well (Fig. S2). Possible aspects to be inspected include the parameterisation schemes adopted (Table ); however, as we used convection-permitting resolution, problems could arise from other issues. In particular, as errors in the moisture field tend to propagate rapidly, the correct amount of moisture must be entered into the model in the correct location to properly reproduce rainfall on the mesoscale e.g.. In this study, we used ERA-Interim reanalysis data (approximately an 80 km horizontal resolution), which may not be accurate enough to resolve some conditions, but they are on the same scale as outputs of global climate models. Future studies should consider using higher-resolution input data, such as the newly released ERA5 data .

Nonetheless, the autocorrelation structure of the rain fields was in generally well simulated for most HPEs (Sect. ). This suggests that even if an event is less predictable, some of the rainfall characteristics can still be simulated. This result is encouraging in terms of the use of convection-permitting models, e.g. in nowcasting, because it means that wind patterns (determining orientation and ellipticity) are well forecasted.

The use of a long record of radar QPEs enabled us to provide a high-resolution quasi-climatological characterisation of the rainfall patterns during HPEs with a resolution and spatial coverage that cannot be achieved using rain gauges. However, rainfall characteristics could not be adequately retrieved in regions suffering from radar data-acquisition problems. Nevertheless, the resultant skill of the WRF rainfall fields supports its use for representing HPEs in regions that are not well covered by radars. As the analyses were performed in a region exhibiting a strong climatic gradient, we suggest that similar results be obtained in other parts of the world, at least in areas characterised by similar climates.

The main added value of convection-permitting models is seen in area averages, rather than over small-scale regions . Therefore, over large catchments (e.g. larger than a few hundred square kilometres, as suggested by the minimal scale presented in Fig. ), their forecasts are expected to be relatively useful and accurate. Nonetheless, the use of a deterministic convection-permitting model is still unsatisfactory for pinpointing the highest observed rain accumulations. Although such models are becoming more common in weather and climate forecasting and research , they are still not adequate for short-term hydrological applications, such as flash flood predictions. The structure of the high cumulative rainfall is predicted quite well; however, it still suffers from a positive bias, and is not exactly well located (e.g. Figs. , ). In order to provide better flood predictions, especially for small catchments and for flash flood generation controlled by infiltration-excess, there is a need for more structured approaches, such as ensemble forecasts and data assimilation of meteorological observations e.g.. These would provide probabilistic (rather than deterministic) information, and could therefore account for the uncertainty characterising the location in high-resolution models e.g..

Characterisation of rainfall patterns during HPEs has special significance in the EM: on the one hand, the region suffers from a severe water shortage; on the other hand, it is prone to devastating floods. Both are predicted to worsen in response to climate change e.g.. Modelling could help understand the effects of climate change on these two aspects but, before assessing the projections for a change in rainfall patterns induced by climate change, we need to consider what aspects of these patterns are still not well captured by weather models, posing a challenge for future predictions. For example, we showed here that rainfall during ARSTs is less adequately forecasted. These ARST HPEs are known to cause flash floods and, as ARSTs might occur more frequently due to global warming , this low predictability should be addressed.

The work presented herein is a step towards better understanding rainfall patterns during HPEs in the EM; we are currently extending the research to relate specific rainfall patterns to atmospheric conditions at high-resolution and to analyse how the predicted climate change will affect the rainfall characteristics outlined in this paper. Another research direction worth following would involve combining our procedures with satellite-based climatology. However, to date, satellite products present temporal (≥0.5 h, mostly ≥3 h) and spatial (≥0.04∘, mostly ≥0.25∘) resolutions e.g. that are insufficient to adequately sample the fine-scale properties of convective rainfall fields, particularly in arid areas.