Convection-Parameterized and Convection-Permitting Modelling of heavy precipitation in decadal simulations of the greater Alpine region with COSMO-CLM

. Heavy pPrecipitation (HP) is a challenging phenomenon with high impact on human lives and infrastructures and thus a better modelling of its characteristics can improve its understanding and simulation at climatedecadal time scales. The achievement of Convection Permitting Modelling (CPM) resolutions ( Δ x < 4 km) ∆𝑥 < 4𝑘𝑚 ) has brought relevant advancements in itsthe representation of HP. . . However, further research is needed on how specifically the very high 15 resolution and switching-off of the convection parametrization affects the representation of processes related to HPheavy precipitation.However, further research is needed not all implications of reaching CPM are known especially for model variables beyond affecting precipitation. In this study, we evaluate reanalysis drivendecadal simulations forof the greater Alpine area overin the period 2000-2015 and assess the differences in representing heavy precipitation and other model variables in a CPM setup with a grid-size of 3 km and a Regional Climate Model (RCM) setup at 25 km resolution with the 20 using the COSMO-CLM model. We validate our simulations against high-resolution observations (EOBS, HYRAS, MSWEP, and UWYO). The results indicate that CPM represents higher precipitation intensities, better rank correlation, better hit rates for extremes detection, and an improved representation of heavy precipitation amount and structure for selected events compared to RCM. However, CPM overestimates grid point precipitation rates, which is in agreement with findings in past literature. The study and presents a revisited version of the Precipitation Severity Index (PSI) for severe event detection, which.

zonal flow regimes.Whereas in summer, 5 WTs are needed to classify the majorityinduce bring of heavy precipitation events.
They are, associated with upper-level elongated troughs over western Europe, sometimes evolving into cut-off lows, or by winter-like situations of strong zonal circulation.Relevant Pprecipitation differences up to 200 mm d -1 exist during specific events between CPM and RCM, up to 200 mm d -1 as shown by composite plots derived from the principal components of heavy precipitation.The results indicate that CPM represents higher precipitation intensities, better rank correlation, better hit rates for extremes detection, and an improved representation of heavy precipitation amount and structure for selected events compared to RCM.However, CPM overestimates grid point precipitation rates, which is in agreementagrees with findings in past literature.Both Either RCM orand CPM can simulate more precipitation than their counterpartshow these large differences however, CPM systematically simulates represents more precipitation at the mountain tops.However, in other regions the RCMs may show higherlarge intensities in other regions, as well.Integrated Water Vapour and Equivalent Potential Temperature at 850 hPa are systematically larger in RCM compared to CPM in heavy precipitation situations (up to 2 mm and 3 K respectively), due to a wetter mid-level conditions and an intensified emission of latent heat flux over the Sea.At the ground level, CPM emits larger more latent heat flux than RCM over land (15 W m -2 ), bringing however during summer this only occurs north of the Alps.The consequence is that CPM simulates more larger specific humidity north of the Alps (1 g kg - 1) and hence largerhighermore CAPE values (100 J Kkg -1 )., whereas RCM, on the contrary simulates a wetter surface level over Italy and the Mediterranean Sea.Surface temperatures in RCM are up to 2 °C higher in RCM than in CPM, . .Regarding surface temperature RCM simulates up to 2 °C more than CPMespecially north of the Alps.This causes , also emitting larger outbound long wave radiation to be larger in RCM compared to CPM over those areas (10 W m -2 ).Our analysis emphasizes the improvements of CPM for heavy precipitation modelling and highlights the differences against RCM that should be considered when using or simulating decadal data withCOSMO-CLM climate simulations with COSMO-CLM.showsthe added value of CPM and highlights the large differences against RCM that should be considered when using decadal simulations.

Introduction
Heavy Pprecipitation Eevents (HPEs) cause tremendous damages and casualties in central Europe (Alfieri et al., 2016;Khodayar et al., 2021;Ranasinghe et al., 2021).In a warming climate, the occurrence and intensity of such events is projected to increase as assessed in Chapter 8 of the Intergovernmental Panel on Climate Change (IPCC) and previous publications (Douville et al., 2021;Pichelli et al., 2021), due to the intensification of the hydrological cycle (Rajcack and Schär, 2013;Ban et al., 2018).Such events may occur both during winter and summer fostered by Deep Moist Convection (DMC), a large vertical transport of precipitating air masses (Emanuel;1994).In Wwinter, heavy precipitation typically occurs under strong synoptic forcing (Keil et al., 2020), caused by the large-scale advection of positive vorticity in cold upper-level layers (Holton, 2013).The associated synoptic patterns have been studied in past literature (e.g., Knippertz et al., 2003;Werner and Gerstengarbe, 2010;Stucki et al., 2012) referring a strong influence of northerly cut-off geopotential lows and elongated troughs as well as of the Atlantic zonal flow.In summer, DMC is often triggered by favourable local and mesoscale conditions close to the surface, including a warm and moist low-level and a triggering mechanism (Doswell, 1996).When these conditions coincide with the arrival of a mesoscale low-pressure system, highly damaging precipitation is likely to occur.
Understanding heavy precipitation processes, their variability and trends at the decadal time scales is needed to provide better prevention and adaptation strategies.Considering modelling approaches, dynamical downscaling with Rregional Cclimate Mmodels (RCM) has proven to be an important toola valuable tool towards this end (e.g., Jacob et al.,2013).Recently, the development of Convection-Permitting Models (CPMs) led to a step forward (Coppola et al., 2018;Prein et al., 2020;Lucas-Picher et al., 2021), since) since a parametrized description of deep convection is no longer needed.An explicit representation of convection is often applied for horizontal grid spacings lower than ca. 5 km.Also improved is the representation of the model's land type, use and elevation (Prein et al., 2015;Heim et al., 2020).These advancements led to improvements in representing the daily precipitation's diurnal cycle (Kendon et al., 2012;Berthou et al., 2018;Ban et al., 2021); its structure, intensity, frequency, and duration (Berthou et al., 2019;Berg et al., 2019); its sub-hourly rates (Meredith et al., 2020); and orographic triggering (Ban et al., 2018).These improvements are consistent over the main modelling regions worldwide.
However, not all problems are solved, since CPMs have also shown relevant wet biases, inducing an overestimation of extreme intensities (Kendon et al., 2012).CPM uncertainties arise from shortcomings in the physical parameterizations, the coupling of the numerics and the physics-dynamics, deficiencies in the representation of the initial conditions and the lack of sufficient high-resolution observations for validation (Lucas-Picher et al., 2021).
Particularly relevant for the improvement of heavy precipitation in CPM is the better representation of DMC processes, especially when convection is triggered close to the surface (Bui et al., 2018).In fact, several studies have shown that CPMs induce stronger updraughts that leads to stronger convection (Meredith et al., 2015a;Meredith et al., 2015b).This is also observed in Numerical Weather Prediction (NWP) simulations (Barthlott and Hoose, 2015;Panosetti et al., 2018).When convection occurs over an area of complex orography, the finer representation of the mountains in CPM increases the triggering of convection (Langhans et al., 2012;Vanden Broucke et al., 2018;Heim et al., 2018;Vergara-Temprado et al., 2020), leading to a better agreement with radar observations (Purr et al., 2019).Regarding other model variables, previous papers argued that CPM improve the simulation of surface temperature (Ban et al., 2014;Prein et al., 2015;Hackenbruch et al., 2016), due to a better representation of the orography, as well as the cloud coverage (Lucas-Picher et al., 2021).Regarding the soil-moistureprecipitation feedback, past work has shown that RCM tends to show a positive sign (Hohenegger et al., 2009;Leutwyler et al., 2021) whereas CPM can show both negative and positive signs at the sub-continental and continental spatial scales, respectively.The reason is that wetter soils induce more frequent precipitation at RCMs but more intense events in CPM with, however, a weak impact no frequency (Leutwyler et al., 2021).CPM seem to better agree with observations as previous observations showed a negative sign of the feedback due to an increased sensible heat flux over drier soils, and mesoscale variability in soil moisture which intensifies afternoon convection (Taylor et al., 2012).Moisture biases also affect the development of heavy precipitation where a wet bias was found for established RCM models (Lin et al., 2018;Li et al., 2020), as well as in CPM simulations (Risanto et al., 2019;Bastin et al., 2019;Caldas-Alvarez and Khodayar, 2020;Li et al., 2020).
However, how both RCM and CPM deal with the moisture wet bias still is an open question.Regarding atmospheric instability Li et al., (2020), found larger Convective Available Potential Energy (CAPE) during the afternoon in CPM, which was correctly converted to larger precipitation at the Tibetan Plateau.Finally, the scale dependency of other variables of interest for convective development such as Equivalent Potential Temperature at 850 hPa (  850 ), has been seldom investigated.
The model evaluated in this paper is the COnsortium for Small scale Modelling in Climate Mode (COSMO-CLM; Schättler et al., 2016, Rockel et al. 2008) which is especially suitable for studying differences between RCM and CPM due its flexibility for configuration in convection parametrized and convection permitting resolutions.COSMO-CLM is a well-established regional climate model used by several research and applied-science institutions in Europe (Sørland et al., 2021) and hence there is interest in knowing quantifying its skill in simulating how it simulates heavy precipitation andits associated processes in a CPM set-up.
One established technique to work with large data sets, such as decadal climate simulations is Principal Component Analysis (PCA).PCA is a powerful method to reduce the dimensionality of a set (Joliffe, 2022) and to extract the principal underlying features.One of its applications is the derivation of the leading spatial patterns of atmospheric fields during specific situations, e.g., heavy precipitation (Knippertz 2003, Seregina et al., 2020).Provided PCA, also calculates the correlation between the days of the set and the derived spatial pattens, it can be used to construct composite maps of relevant model variables associated with the respective spatial patterns of a specific model variable, e.g., precipitation.Although PCA has been used for these applications in the past, to our knowledge, it has not yet been applied to study model differences between RCM and CPM.In this work we will derive composites of relevant model variables and study differences between both modelling set-ups.
The aim of this work is to evaluate reanalysis-driven RCM (25 km) and CPM (3 km) decadal long simulations of the greater Alpine area in the period 2000-2015 and assess their differences in representing heavy precipitation and associated environments.This paper is organized as follows: in Sect. 2 we introduce the dataset and methods employed; in Sect. 3 we present the main synoptic weather types bringing heavy precipitation; in Sect. 4 we evaluate heavy precipitation intensity and occurrence in the climate decadal simulations; in Sect. 5 we validate precipitation, humidity, and temperature fields of selected heavy precipitation events; in Sect.6 we introduce the spatial patterns of precipitation derived from PCA, In Sect.7 we present the differences of model variable composites and in Sect.8 we show provide our conclusions.

Observational datasets
We use observations from different sourcesvarious sources for validation and comparison of the climate simulations (Tab.1).
We employ the Ensembles OBSservations (EOBS) gridded precipitation and relative humidity at the surface (ℎ) products at 25 km resolution (EOBS-25km), which are provided by the European Climate Assessment & Dataset (ECAD) centre at 0.25° (ca. 25 km) of spatial resolution for the period 1950-2020.We use v.22.0e(Dec 2020) employing a 100-member ensemble created through stochastic simulations based on interpolated station data from national institutions including 9000nine thousand rain gauges (Cornes et al., 2018).EOBS-25km has been widely used in previous literature for validation purposes (e.g., Tramblay et al., 2019;Bandhauer et al., 2021) and has been shown to have low median absolute biases with respect to other regional European precipitation products such as CARPATCLIM or Spain02 (Cornes et al., 2018).
The HYdrologische RASterdatensaetze (HYRAS) gridded precipitation dataset, provided by the German Weather Service (DWD) is available at 1 km (ca.0.01°), 5 km (ca.0.05°) and daily resolution.HYRAS covers Germany and neighbouring catchments in parts of Switzerland, Austria, the Netherlands, France, Belgium, and Poland (Fig. 1).The version v2 covers the period 1951-2015 and was derived using multiple linear regression and inverse distance weighting interpolation of 6200 rain gauges considering the orography (Rauthe et al., 2013, Razafimaharo et al., 2020).HYRAS-5km has a remarkable very high quality and its high-resolution enables a good representation of local scale features, outperforming the coarse resolution of EOBS-25km (Hu et al., 2020).However, it is only available over Germany and nearby catchments.(Beck et a., 2019).MSWEP has a higher median correlation (up to 0.67) against stations, compared to CMORPH (0.44) and TMPA-3B42 (0.59) (Beck et al., 2017).We use the MSWEP product to profit from its high accuracy, shown in previous studies, globally (Beck et al., 2017(Beck et al., , 2019;;Xiang et al., 2021) as well as in specific geographies (Du et al., 2022;Peña-Guerrero et al., 2022).MSWEP has the advantage of covering sea surfaces and is adequate for precipitation event evaluation because it includes gauge data from CPC and GPCC.
The radiosonde data archived by the University of Wyoming (UWYO) are used to validate the RCM and CPM humidity and temperature profiles.The stations are located close to large European cities, with an average distance of 250 km between stations.The temporal resolution ranges between 6 h, 12 h and 24 h and the provided information includes height, atmospheric pressure, temperature, and dew point temperature on ca.30 levels.The UWYO soundings have often been used as reference for validation studies (e.g., Ciesileski et al., 2014;Yang et al., 2020).

Setup of the COSMO-CLM, RCM and CPM simulations
We use COSMO-CLM, a non-hydrostatic model using the fully compressible atmospheric equations (Schättler et al., 2016), incorporating sub-grid turbulence, convection and grid scale clouds and precipitation parameterizations.COSMO-CLM uses a soil model called TERRA-ML (Doms et al., 2011) to parametrize the mass and heat exchanges between the surface and the atmosphere (Rockel et al., 2008).
In this work, we systematically compare reanalysis driven regional climate simulations with a typical RCM resolution (25 km; hereafter named RCM) and at convection permitting resolution (~ 3 km, named CPM).All simulations were performed with the version COSMO-CLM5 and use a setup specifically optimized for these resolutions.
The CPM simulation uses a COSMO-CLM5 subversion with a few bug-fixes and additional output variables but no changes in the numerics or formulation of the physics.The setup has been optimized for convection permitting scales and is used in the CORDEX Flagship Pilot Study on Convection (Coppola et al., 2018) and the simulation has been evaluated in Ban et al. (2021).This means that there are differences in the specific tuning parameters, where the main difference is the switching of the deep-convection parametrization (Tiedtke;1989;Baldauf et al.;2011;cf. Tab. 2).The simulation is performed by downscaling the RCM simulation described above over the grater Alpine area (ALP-3 domain, with a 3km (0.0275°) resolution for the period 2000 -2015.
Another convection-permitting simulationhere called KLIWA-2.8km (cf.Tab.2)is used auxiliary just in Sect. 4 (Fig. 6) to extend the period for the comparison of the historical events.The grid spacing of this simulation is 2.8km (0.025°) and covers a smaller modelling domain over southern Germany and the Alps (cf.Fig. 1) for the period 1971-2000.It is forced by ERA40 re-analysis (Uppala et al., 2005) in a three-step nesting approach (Hundhausen et al., 2022).This simulation uses a slightly older subversion missing a few bug fixes.The main differences to CPM can be found in Tab. 2.
Two areas are investigated in our study.The first, denominated southern Germany (SGer, Fig. 1) encompasses the northern Alps, and southern Germany up to North-Rhein-Westphalia and Saxony.This area is selected to fulfil the requirements of the modelling and observational data sets (availability, coverage, time span).The second area, CPM (Fig. 1), covers the greater Alpine domain including the northern Mediterranean basin and is used for comparison of the model performance RCM vs. CPM.

The Precipitation Severity Index (PSI)
We re-adapted the PSI, an index previously used to detect heavy precipitation events (Piper et al., 2016) and severe windstorms (Leckebusch et al., 2008;Pinto et al., 2012) to include precipitation persistence.By doing so we can consider three different, but intertwined aspects of heavy precipitation: grid-point intensity, spatial extent of affected area and temporal persistence.It is re-defined as follows: The PSI values at a certain time step T (  ) are obtained from the ratio between grid point daily precipitation (  ) and a user-defined threshold.In this paper we set this threshold to be the 80-percentile (   ) all-day to neglect grid points whose precipitation is lower than the set threshold one for day T (  ≤    ).This is done by means of the function  (  ,    ).We consider the spatial extent by summing the ratios over the spatial extent () of the study region along the directions  and j.The ratios are multiplied by the area of one grid cell (∆) 2 .The precipitation persistence is considered in the calculation through the sum over time ().The ratios at each grid point for day T and the previous  days ( = 2 in our case) are added for the PSI calculation, provided precipitation was continuous and larger than    at that same grid point , . . .The daily PSI value is normalized to the area of the simulation domain  =  •  • (∆) 2 multiplied by (1 + ) to consider the addition of grid points with persistent precipitation.Prior to the PSI calculation, we include a correction for latitude stretching of the grid as (()) following (North et al., 1982).
To assess the performance of the PSI, we calculate Spearman's rank correlations between the PSI and a simpler field sum index (  ).We use daily precipitation data from HYRAS-5km between 01-Jan-1971 and 31-Dec-2015 over the investigation area SGer (Fig. 1).We testevaluate different combinations of the PSI parameters    and  (Eq.1).Fig. 2 shows the rank correlations against  and the three top-ranked events of each implementation and the daily precipitation of the 22-Oct-1986 event. . .We find a high rank correlation between the PSI and  for low values of    and .For instance, when we set    as the percentile-80 of the 1971-2015 period and  = 0 (equivalent to considering no persistent precipitation) the rank correlation is 0.97, indicative of a very similar functionality between the PSI and  (Fig. 2a).For instance, in this configuration the third event in the ranking differs between the PSI (20-Dec-1993) and𝑓𝑙𝑑𝑠𝑢𝑚 (20-Nov-2015).The reason behind is that the 20-Dec-1993 event occurred over a flat area, unfrequently affected by heavy precipitation (Fig. S1 in the Supplementary Material; SM).The PSI prefers ranks this event to 20-Nov-2015 (affecting mainly complexcomplex terrain) because the threshold set to the 80-percentile is lower over flat terrain and thus easier to surpass over flat terrain (Fig. S1).
As we increase    and , the rank correlation decreases, implying a different ranking of the events (Fig. 2a).For example, a percentile-95 for    and  = 2 brings a rank correlation of 0.86 which favours the detection of events with larger grid-point intensity and temporal persistence.For illustration, the 22-Oct-1986 event (Fig. 2b, c, d) is ranked as the most severe event in the period in this configuration due to precipitation totals between 50 mm d -1 and 150 mm d -1 impacting for three consecutive days the same areas, e.g., the Colmar region or the Marburg-Siegen area (see Fig. 2, b, c, and d).The remainder events can be seen in the SM.
To conclude, the advantage of the PSI with respect to a simpler field sum index is its capability to detect rarer and more persistent events.Rarer events can be found because the threshold    guarantees the selection of events where either heavy precipitation falls over climatologically drier areas or where extreme intensities take place over typically wet areas (e.g., complex terrain).For its part  = 2 favours the detection of events where heavy precipitation occurred continuously on the same grid point up to a maximum of wo days.That said, a low percentile threshold (    ) or  = 0 will bring a functionality no different to .This makes the PSI a flexible solution that can be tailored to the user´s needs.Finally, the PSI is also flexible to set the threshold    to a fixed amount, e.g., 120 mm d -1 , to ensure that only grid points above that threshold will be included in the calculation.This is a possible configurationconfiguration that could be used in future studies.

Principal Component Analysis
Principal Component Analysis (PCA) is a method to reduce the dimensionality of a data set, by transforming it to a new coordinate system of variables called Principal Components (PCs;Joliffe, 2002).The functions that allow the transformation from the original set to the PCs space are called Empirical Orthogonal Functions (EOFs).The transformation is performed in such a way that the explained variance is concentrated in a small number of components the new variables.By construction, the leading EOF1 has the largest explained variance, followed by EOF2, and so on.In this paper, we investigate the PCs and EOFs of 500 hPa geopotential height fields (Sect.3) and daily precipitation (Sect.6).Similarly to Ulbrich et al., (1999), we obtain EOFs representing the spatial patterns of the target variable, that account for the main modes of variance.On the other hand, the PCs are time series which provide the information of the correlation of each EOF to a specific day in the series.
Given that the explained variance is now concentrated in a small number of variables, it is important to discern how many EOFs should be retained.With this aim, we use a method of parallel analysis based on the randomization of eigenvalues named the random-λ rule (Peres-Neto, 2005).The procedure is as follows, 1) a random data array is created with the same dimensions as the data array under study, 2) PCA is applied on the random array, 3) steps 1 and 2 are repeated up to 1000 times, retaining the eigenvalues showing a significance over 95 % (alpha= 0.05).4).If the original eigenvalues exceed the critical values from the random data, then we reject the null-hypothesis (Peres-Neto, 2005).The random-λ rule is more suitable than other methods of parallel analysis such as the N-rule (Preisendorfer and Mobley, 1988) since it does not assume a normal distribution for the array of random values and thus works better for variables such as precipitation.

Validation metric Fractions Skill Score
The Fractions Skill Score (FSS) provides an estimation of the model's skill in representing the fraction of surface affected (or not) by heavy precipitation (Skok and Roberts, 2016).A perfect forecast has thus an FSS of 1.A simulation with no skill has an FSS of 0. In this work, we set a threshold of 40 mm d -1 to define structures affected by heavy precipitation.The threshold is in the range of values implemented by Roberts and Lean (2008) for simulations of spring convective rain over southern England.We select this threshold to be able to identify clear precipitation structures otherwise masked by the choice of a too large or too low threshold analogously to Caldas-Alvarez et al., (2021).Equation 2defines the FSS following Roberts and Lean (2008).
) [2] The fractions of surface affected by heavy precipitation are represented by   and   , for the observations and the model, respectively.Both are calculated as the number of grid points affected by precipitation over the defined threshold (40 mm d -1 ) divided by the total number of grid points of a domain.FSS is computed as the ratio of the sums of fraction differences for M sub-boxes within the investigation domain.These M sub boxes are defined as sub-domains around M grid points with N near neighbours.N in our case is 12twelve since most of the events we validate have shown a skill larger than the target skill defined as   = 0.5 +   2 ⁄ for  = 12.For detailed explanation, refer to Roberts and Lean (2008), Skok et al., (2016), andCaldas-Alvarez et al., (2021).

Synoptic weather types
We obtain the predominant large-scale situations associated with heavy precipitation applying PCA.We analyse the EOFs of geopotential height at 500 hPa, based on the RCM simulation, for the period 1971-2015.We select dates of heavy precipitation in the 98-percentile of severity (PSI) in the HYRAS-5km "all-day" data set over the investigation region SGer (Fig. 1).Figures 3 and 4 provide, respectively, the dominating weather types of heavy precipitation for summer (MAMJJA) and winter (SONDJF).The comparison against the CPM is not shown here since only negligible differences exist with respect to RCM, sinceM.This is because the boundary conditions from the forcing reanalyses (ERA) strongly determine the large-scale features under play (Prein et al., 2015).
In winter, four synoptic patterns of 500 hPa geopotential height suffice to explain the majority of HP eventsnatural variability, following the random-λ rule with a 95% significance in the t-test (Peres-Neto et al., 2005).They account for 74% of thee heavy precipitation episodes.The first mode, representing 29 % of the events, is characterized by wave trains of low pressure associated with northerly incursions of polar air (Fig. 3).The synoptical situation is analogue to the Stationary Fronts (STF) category proposed by Stucki et al., (2012).In this situation, heavy precipitation over the Alps is associated with strong upper levelupper-levelupper-level lifting over northern Italy and large southwesterlysouth-westerly advection of moisture from the Mediterranean.Historical cases belonging to this category, as identified by the PCA, are the second phase of the 23-31 October storms in 1998 (Fuchs et al., 1998) or the late November events in 2015 (Tab.3, https://www.wetter.de/cms/so-war-das-wetterim-november-2015-2566771.html), for instance.The second mode, accounting for 22 % of the events, shows strong northsouth gradients of the 500 hPa height and fast zonal circulations (Fig. 3).This synoptic pattern has been identified as a Zonal Flow (ZOW; Stucki et al., 2012) or as a narrow and elongated streamer (Massacand et al., 1998).The zonal circulation favours moisture advection from the Atlantic and can produce large precipitation in non-convective environments (Stucki et al., 2012).
The 29 December 2001 event belongs to this precipitation mode, for instance.The third and four modes account for 12 % and 11 % of precipitation episodes, respectively and show similarities with the 500 hPa geopotential heights of the second mode (Fig. 3).However, the third synoptic pattern shows a weaker Azores high, favouring the advection of Atlantic moisture with a southwesterlysouth-westerly component.The fourth mode, for its part, shows a weaker polar low, which favours the development of anti-cyclonic circulation (Fig. 3). .
In summer, five synoptic patterns of 500 hPa geopotential height are discernible from random noise (Peres-Neto et al., 2005), accounting for 77 % of the events.The first mode, corresponding to 27% of the considered dates, shows an extended upperlevel trough from the British Isles down to southern France (Fig. 4).This configuration shows elements of an Elongated Cut-Off (ECO) and of CAnarian Troughs (CAT; Stucki et al., (2012).In such situations upper-level lifting occurs east of the trough together with southerly moisture advection either from the southwest or the southeast, respectively.Such situation occurred for instance during the first stages of the large central European flooding of early June 2013 (Kelemen et al., 2016).If a blocking situation occurs, for instance Omega blocking, the persistence of precipitation is enhanced and can lead to recurrent events (Kautz et al., 2021) at the eastern flank of the ECO or CAT .The second summer precipitation mode (Fig. 4), accounting for 19% of the events, presents a similar pattern to the third and four modes of winter precipitation (Fig. 3) with the characteristic strong zonal flow from the Atlantic.Examples of this synoptic configuration are the March 1988 events flooding the Rhein river (southern western Germany; Prellberg and Fell, 1989) or the 15 June 2007 events affecting southern Germany (https://www.wetteronline.de/extremwetter/schwere-gewitter-und-starkregen-schaeden-durch-tief-quintus-2007-06-15-tq).
The third precipitation mode, explaining 12 % of the analysed days (Fig. 4), shows similarly to the first mode, an ECO, however, with an eastward shifting of the Azores ridge and the possibility of evolving to a Pivoting Cut-Off Low (PCO; Stucki et al., 2012).If the PCO finally realizes and reaches the Mediterranean it is accompanied by a cyclonic flow, which advects brining moisture towards Central Europe, which originatesing inat the Balkan region.This has been demonstrated to be the case for the second phase of the June 2013 flooding (Kelemen et al., 2016).The fourth summer precipitation mode (Fig. 4), accounts for 11% of the considered episodes and represents situations of northeasterlynorth-easterly development of the upperlevel trough.The low pressure evolves into a CAT situation inducing a southwesterlysouth-westerly moist inflow to the Alpine region (Stucki et al., 2012).The 08 July 2004 floods in Baden-Wuerttemberg (southwestern Germany; http://contourmap.internet-box.ch/app/okerbernhard/presse2.htm) are a good example of such situation.The fifth precipitation mode, 8 % of the events, shows an STF pattern, similarly to the first winter precipitation mode (Fig. 3).Such a configuration was present during the Rhein-Necker flooding (western Germany) in June 2005 (https://www.rnz.de/nachrichten/metropolregion_artikel,-unwetter-folgen-in-mannheim-besonders-viele-gebaeudeschaedendurch-regen-_arid,482078.html).

Evaluation of heavy precipitation
After identifying the synoptic situations responsible for heavy precipitation, we evaluate the RCM and CPM simulations between 2000 and 2015 (Tab.2) in terms of probability, intensity, and detection capability against observations.The ability of CPM to represent larger precipitation rates agrees with previous literature (Ban et al., 2014;Prein et al., 2015;Fosser et al., 2014), which has been related to the enhanced intensities over orographic terrain (Langhans et al., 2012;Vanden Broucke et al., 2018;Ban et al., 2021).The comparison against HYRAS-5km (black), shows a good agreement by RCM and CPM for values between 1 mm d -1 and 50 mm d -1 .However, CPM (red) overestimates heavy precipitation for grid point maxima.This is a well-known deficit of CPM (Kendon et al., 2012;Berthou et al., 2018).despite its many advantages e.g., improvements in the representation of the diurnal cycle (Kendon et al., 2012;Lin et al., 2018), or better event representation (Chan et al., 2012;Ban et al., 2018).It should also be noted that even for grid resolutions down to 1 km the updrafts might not me simulated with the right intensity, which can help explain the overestimation of precipitation at these high resolutions (Vergara-Temprado et al., 2020).It is also worth noting that Also, the comparison against observations canmust be done carefully as heavy rain measurements might suffer from under catchment problemsviewpoint, which can be responsible of as the misplacement of the heavy large precipitation can lead to strong losseslocal reductions, reaching even 58 % in the worst scenarios (Vergara-Temprado et al., 2020).Furthermore, problems associated with the gridding of precipitation observations and the fact that rain-gauges in the Alpine region tend to be located at the valleys, add uncertainty to the estimation of precipitation.and any validation of model data.
To further assess the performance of COSMO-CLM in representing precipitation extremes we analyse the detection capability of RCM (blue circles) and CPM (red dots) by means of a dot diagram, showing the 500 most severe events detected with the PSI in the period 1971-2015 over SGer in (Fig. 6).The CPM dataset is extended to 1971 with the aid of the KLIWA-2.8km simulation that has a similar horizontal resolution (2.8 km) and is obtained using the same model (CCLM).However, several inconsistencies exist between CPM and KLIWA-2.8 (refer to Sect.2.2 for further details).We use HYRAS-5km (black circles and EOBS-25km (grey squares) as reference.
CPM (red dots) showed a higher spearman's rank correlation (0.48) than RCM (blue circles; 0.41) as shown in the legend of Finally, the detection of cases in winter and summer in all dataset's points at the PSI as a suitable method for extremes detection in all seasons.

Event scale evaluation
In the previous section, we assessed an overestimation of grid-point heavy precipitation for the convection-permitting simulation CPM, but a good performancea reliable performance in detecting severe precipitation events in a 44-year climatology.Here we evaluate the performance of CPM at the event scale validating eight chosen events.We focus on the period 2000-2015 and the investigation area CPM (Fig. 1).
Table 3 shows eight selected events selected using the PSI, which were also included in the derivation of the synoptic weather types in Sect.3. Table 3 includes provides information about the duration of the events, the observed total precipitation, maximum grid point intensities, percentage of affected area (, i.e., percentage of grid points with precipitation over the 80th percentile),, severity (PSI), and associated Weather Types (WT).We subjectively shortlisted the events to consider not only those events with of large severity (PSI) and but also to have a sufficient winter and summer cases, which led including to the consideration of two events with daily totals below 120 mm d -1 , i.e.,namely 03-Nov-2002 and 08-Jul-2014.The events showed a large severity (PSI) and were afterwards short listed subjectively to include both winter and summer events.Therefore, some of them, e.g., 03-Nov-2002 or 08-Jul-2014, did not show heavy daily precipitation values but are however interesting for evaluating the model performance.

Precipitation
We focus evaluate the model performance focusing on two aspects of heavy precipitation, (1) amount, calculated as aggregated precipitation in time and space, and ( 2) structure, validated by means of the FSS metric (Sect.2.3.3).For both metrics, we use MSWEP-11km (Tab. 1) as the observational reference, after coarse-graining all compared datasets to a common grid of 25 km.MSWEP-11km is used provided its large accuracy due to the inclusion of rRain gGauges (Beck et al., 2017) and since precipitation occurs to a large extent over the Mediterranean Sea, where HYRAS-5km and EOBS-25km have no coverage.
Table 4 shows the relative differences in precipitation amount aggregated in space and time between the model and observations as  .= ( − )/ in percent.CPM performed better than RCM in six out of the eight selected cases for precipitation amount.The largest improvement occurred for the 31-May-2013 event, which corresponds to the synoptic pattern S1 associated with the occurrence of ECOs and the advection of southwesterlysouth-westerly moisture (Fig. 4).Using CPM brought generally largerlarger precipitation rates, in agreement with the findings of Sect.4, allowing for better scores of aggregated precipitationprecipitationss.
Regarding FSSstructure, CPM performed well in, in general terms, for 7 out of 8 events with FSS reaching values over 0.7.
RCM, for its part, performed well for 5 out of 8 events (Tab.4).The 31-May-2013 event is again an example of good performance by CPM, where the FSS scores reached 0.87 in CPM (0.26 in RCM).The main reason for this improvement was the ability of CPM to represent larger precipitation structures over the Alps in a better agreement with MSWEP-11km.The spatial distributions of precipitation by RCM, CPM and HYRAS-5kmMSWEP-11km are shown in Fig. S2 of the SM.
Only the event 08-Aug-2007 showed a bad performancea deficient performance by CPM, both for precipitation amount and structure.This event occurred under a S1 synoptic situation associated with an elongated troughs or cut-off lows (Fig. 4).The reason behind the bad performance in this case in CPM is the large underestimation of precipitation in CPM, which also hampers the structure representation.
Overall, these results showed that CPM outperforms RCM brings added value in the representation of precipitation amount and structure compared to RCM.The advantage of CPM relies on the better location of orographic precipitation and the increased larger precipitation intensities.brought by the more intense updrafts and larger number of cells triggered.

Humidity and temperature
In addition to precipitation errors, temperature and humidity biases could affect our interpretation of the model differences between RCM and CPM.To reduce uncertainty, Here we validate specific humidity (ℎ) and temperature () profiles from RCM and CPM against radiosondes from the University of Wyoming (UWYO) and surface relative humidity (ℎ) against EOBS-25km for the eight selected events (cf.Tab. 3).
Figure 7 shows the temporal Mean Bias (MB; thick line), the standard deviation of the differences (shaded area), and the Root Mean Square Errors (RMSE; dashed line) of specific humidity (Fig. 7a) and temperature (Fig. 7b).The model output is interpolated to the location of eleven sounding stations, which were selected to have sufficient availability and fulfil the condition of a surface height difference not larger than 50 m.where only a height difference lower than 50 m between the station height and the model´s orography is allowed.This requirement is introduced to avoid including large humidity and temperature biases from differences in surface topography between the model and the observations.We include all available soundings during the duration of the eight events (Tab.3) in the calculation, with a temporal resolution between 6 h and 12 h.
Humidity is slightly overestimated by RCM throughout the whole profile and by CPM above 800 hPa (Fig. 7a).The overestimation by both models reaches 0.2 g kg -1 at 700 hPa.Below 800 hPa, CPM, reduces the mean bias reaching -0.1 g kg - 1-1 , indicating a generally drier planetary boundary layer.RMSE values are very similarsimilar for both simulations being close to 1.5 g kg -1 below 700 hPa.These results are promising for COSMO-CLM since neither RCM orand CPM show small biases even if they do not have an active data assimilation scheme and whence the model is exclusively constrained by the boundary conditions of the forcing data (ERA-interim).
Regarding temperature (Fig. 7b), COSMO-CLM shows a warm bias, reaching 0.5°C at the 925 hPa layer for both resolutions.
RMSE (Fig. 7b, dashed line) is very similarremarkably similar between both simulations, above 2 °C, with a slight improvement by CPM (red).
The humidity (Fig. 7.c) and temperature (Fig. 7.d) profiles show a wetter mid-troposphere (between 700 hPa and 925 hPa) in RCM than in CPM and a very similara similar temperature profile between both simulations with a good agreement against observations.CPM simulates slightly better the vertical humidity profile than RCM with a steeper humidity-height gradient.
This was also observed in earlier studies with COSMO and COSMO-CLM (Caldas-Alvarez and Khodayar, 2020;Caldas-Alvarez et al., 2021).COSMO-CLM compensates the modelling errors simulating a wetter lower troposphere in RCM to help activate the deep convection parameterization scheme (Tiedtke, 1989).Being of the low-level control type, the Tiedtke deep convection scheme requires a sufficient moisture amount below the cloud base to initiate convection (Doms et al., 2011).
By doing so RCM simulates precipitation totals of the same order as CPM that relies more upon the intensification of vertical wind speeds than humidification to simulate convective precipitation.Furthermore, the higherlarger humidity in the midtroposphere helps reduce the simulated dry-air entrainment increasing the total simulated precipitation.Both simulations show a reliable performance considering the decadal timescales Provided the observations available below 925 hPa in the UWYO soundings were scarce, we employ the gridded EOBS-25km dataset (Tab. 1) to investigate the COSMO-CLM biases at the surface (Fig. 8).We represent the spatial distribution of temporal mean bias (colour shading) and the temporally-spatially averaged mean bias and RMSE of daily surface relative humidity.We calculate relative humidity biases for this validation, given no surface specific humidity gridded observations with sufficient accuracy were available for our region and period of investigation.
COSMO-CLM underestimates surface relative humidity for both RCM (Fig. 8a) and CPM (Fig. 8b), w.Which is consistent with the well-known dry and hot bias of CPMs, provided our selected events occur mostly in summer.This is especially so at the Po Valley (Italy) and the southern Italian Peninsula.However, CPM (Fig. 8b), slightly improves the surface relative humidity deficit at locations north of the Alps, e.g., northwesternnorth-western France, the Czech Republic and western Austria.These corrections in the northwesternnorth-western part of the simulation domain, reduce the temporal and spatial MB by 3%.However, provided the larger spatial variability of this variable in CPM, due to the better orography representation, the RMSE is worsened by 5 %.
The profile and surface humidity and temperature validation has shown that: a) COSMO-CLM performs well in simulating the humidity and temperature lapse-rates, albeit small biases up to 0.2 g kg -1 in humidity and 0.5 °C (warm bias) in temperature exist; b) CPM simulates slightly better the vertical humidity profile with a steeper gradient than RCM; c) CPM reduces the positive surface relative humidity bias over locations north of the Alps, e.g., western France, the Czech Republic and eastern Austria.

Main modes of heavy precipitation variability in RCM and CPM
To understand how differentlywhere RCM and CPM represent the main spatial patterns of heavy precipitation differently, we use PCA (Sect.2.3.2) on events detected in HYRAS-5km in the period 2000-2015.We do this to observe differences in the spatial distributions of heavy precipitation during the most frequent precipitation modes and reduce the dimensionality of the data set.We combine the severe events into one set and apply PCA to obtain the EOFs and their corresponding spatial distributions.We do this separately for winter (SONDJF) and summer (MAMJJA) events for both RCM and CPM, using days above the percentile-90 of daily PSI values.In total, 290 events per season are considered to derive the EOF maps shown in Fig. 9 and in Fig. S3 in the SM.We do this to reduce the dimensionality of the set to the principal components.For this analysis, we focus exclusively on precipitation EOFs with a similar structure between RCM and CPM, dismissing the remainder EOFs.
This is done to ensure we compare model differences in similarly simulated meteorological situations.
Figure 9 shows the four leading EOF maps for Wwinter events (panels a, c, e, and g) and the three leading modes in Ssummer (panels b, d, and f) as simulated by CPM.The corresponding figures for RCM can be found in the SM (Fig. S3).Only CPM is shown here due to the large similarity in the spatial distributions of these EOFs with RCM.The PCA determines that the precipitaitonprecipitation EOFs start to remainder EOFs differ substantially between substantially between RCM and CPM after t.The leading four winter EOFs in winter and the third in summer.The four leading EOFs in winter explain 48% of the variability for RCM and 47% for CPM, being the first mode the most frequent one (22% of cases).For summer events the three leading modes of precipitation stand for 37 % of the situations in RCM and 33 % in CPM).
The visual inspection of the first EOF for Wwinter events (Fig. 9a) shows that this the mode associated with orographic precipitation over the Alps and the northern Apennines in the Genoa region.EOF-2 (Fig. 9c) for its part shows precipitation either affecting continental Europe, north of the Alps (negative mode; brown) or affecting the Mediterranean, including the Italian and Balkan peninsulas with a marked orographic signal (positive mode; green).EOF-3 (Fig. 9e) combines precipitation over northern Europe with Mediterranean precipitation in its positive mode (green).The negative mode (brown) affects the southern Mediterranean basin between Italy and France as well as the southern and Maritime Alps.Finally, EOF-4 (Fig. 9g) finally shows a positive mode associated with precipitation over the Gulf of Lyons, the Balearic SeaSea, and the Pyrenes (green), and a negative mode affecting northeastern Italy (brown).Both The latter situations of heavy precipitation in the Mediterranean have been studied in detail in the HyMeX project (Khodayar et al., 2021).
The first EOF for summer events (Fig. 9b) is associated with orographic precipitation over the Alpine region, similarly to winter EOF-1, albeit affecting parts of northern Europe, where convection can trigger more easily during the summer months.
To summarize, Our analysis shows that RCM and CPM simulate similarly the main precipitation modes up to the fourth principal component in Wwinter and the third in Ssummer.These precipitation modes account for 47 % of the precipitation variability in Wwinter and 37 % in Ssummer, implying that the remainder precipitaitonprecipitation variance shows remarkable differences between RCM and CPM. a large part of the precipitation differences belongs to the secondary modes of precipitation

Model differences between RCM and CPM using composites
To further analyse model differences between RCM and CPM, we derive composites of model variables from each EOF in Fig. 9.We focus on model variables influencing the simulation of heavy precipitation e.g., Integrated Water Vapour (IWV), Convective Available Potential Energy (CAPE), soil-atmosphere heat fluxes, etc.To derive the composites, we select the days where daily precipitation showed the largest resemblance to the positive and negative modes of the precipitation EOFs.In other words, we select the days showing the largest positive (negative) correlations to the positive and negative modes of each precipitation EOF.This is done separately for RCM and CPM selecting the days with positive and negative correlations larger than one standard deviation of the whole setfull set.This leads to composites of ca. 30 days per positive and negative mode.
We then average in time the spatial distribution of the selected days and obtain maps of the differences between RCM and CPM as in Fig. 10.For heavy precipitation differences, we work with composites of the days assigned to each EOF, whereas for the other model variables we use the day prior to heavy precipitation.This done to study the model differences in the preconditioning of the event.

Heavy precipitation
The composites show relevant differences in precipitation amount (up to 8.5 mm h -1 i.e., 204 mm d -1 ) between RCM and CPM throughout the complete greater Alpine domain, irrespective of the simulation and meteorological situation.Spatially averaged, both RCM and CPM can represent larger precipitation than their counterpart, however, in summer, CPM represents larger precipitation at the mountain tops e.g., the Alps, the Apennines.This holds for all analysed EOFs and both positive and negative correlations of the principal components.For illustration, Fig. 10a shows the composite differences of the negative principal components of EOF-2 in Wwinter.Differences up to 6 mm h -1 are located east of the Spanish coast (RCM, blue) over the Apennines (Italy) and over the eastern and the Dinaric Alps (CPM, red).Spatially averaged, RCM simulates larger precipitation (0.21 mm h -1 ) for this EOF.Fig. 10b shows the positive principal components of EOF-3 in summer, where again, CPM simulates larger precipitation than RCM over the Apennines (Italy), the Dinaric Alps (Balkans), and to a lower extent over the western Alps (Switzerland) and the Central Massive (France).All remainder composites are included in the SM.
These results highlight that RCM and CPM can simulate comparable precipitation amounts in the timely averages of daily precipitation (for the investigated EOFs).Regarding the larger precipitation amounts simulated by CPM over the mountain ranges, a plausible explanation is the intensification of vertical winds observed in previous studies comparing horizontal resolutions (e.g., Langhans et al., 2012;Barthlott and Hoose, 2015;Vergara-Temprado et al., 2020).Another explanation is provided by Vergara-Temprado et al., (2020) addressing that the "increase in precipitation with resolution could be happening as smaller grid boxes are easier to reach saturation".However, the presented analysis does not allow splitting the contributions from resolution increase from other factors, e.g., changes in the physics or physical parameterizations (see Sect. 2.2).

Integrated Water Vapour (IWV) and Equivalent Potential Temperature at 850hPa (𝜽 𝒆 𝟖𝟓𝟎 )
Two variables typically regarded as precursors of heavy precipitation are IWV and   850 (Doswell et al., 1996;Stucki et al., 2016).The differences of the composites show larger IWV in RCM compared to CPM throughout the whole greater Alpine region in .This applies to all analysed EOFs and their respective positive and negative components.The IWV differences can be as large as 2 mm and take place especially over the Mediterranean Sea and the Po Valley.Regarding   850 , shows differences up to 4 K more we observe larger values in RCM compared to CPM that can be as large as 4 K. Atmospheric water vapour is the main precursor of the   850 differences as RCM tends isto be wetter than CPM in the 850 hPa level (Fig. 7).For illustration Fig. 11 shows the composite differences of IWV (colour shading) and   850 (contours) for the same principal components as Fig. 10.The composites show IWV differences up to 1 mm over the Mediterranean Sea and up to 2 K for   850 (Fig. 11a).Likewise, the negative principal components of EOF-3 show IWV differences up to 3 mm over France and 3 K differences in   850 by RCM (blue; Fig. 11b).The remainder composites can be found in the SM.

Soil-Atmosphere interactions
Regarding variables The composite analysis allows us to study differences between RCM and CPM for variables such as surface heat fluxes, surface humidity and temperature, Convective Available Potential Energy (CAPE) and Outgoing Longwave Radiation (OLWR), w.We find that CPM simulates larger outbound latent heat emissions than RCM over landland, but that RCM represents larger latent heat fluxes than CPM over the Sea (up to 15 W m -2 ).These differences cause CPM to simulate larger near-surface specific humidity than RCM over land from northern Europe down to the Alpine barrier.South of the Alps and over the Mediterranean Sea, the opposite occursoccurs, and RCM simulates generally a wetter near-surface conditions with differences up to 1 g kg -1 .An example of these model responses is illustrated in Fig. 12 (panels a and c) for the positive principal components of Ssummer EOF-2 (Fig. 9.d).Provided the larger surface specific humidity simulated in CPM, north of the Alps, CAPE is also larger with respectcompared to RCM due to itsthe relationship between close-to-ground moisture and this variable (Fig. 12.e).
Likewise Analog to the latent heat fluxes, sensible heat fluxes shows relevant differences, with RCM emitting up to 20 W m - 2 more than CPM over land, especially in Ssummer (Fig. 12.b).This causes surface temperature to be generally largerlarger in RCM than in CPM (up to 1.3 ºC), although exceptions exist as is the case of the composites of sSummer EOF-2 shown in Fig. 9d.Finally, the temperature differences close to the surface influence OLWR, whereby RCM emits larger OLWR than CPM for most of the analysed modes and their corresponding composites Fig. 12.f is however an exception with CPM emitting larger OWLR.All composite plots can be found in the SM.
In general, Tthe previous results applyhold for both for Ssummer and Wwinter events.AalthoughHowever during Wwinter, CPM emits morelarger latent heat flux than RCM over all land areas during winter.Also, it is worth noting that the surface temperature differences are weaker in the southern part of the domain, e.g., over Italy and the Po Valley where CPM can some shoeven show higherlarger surface temperature in CPM.This agrees with previous findings assessed in Sangelantoni et al., (2022) where an ensemble of CPMs showed amplified drier-warmer conditions during heat waves with respect to an RCM ensemble.We should also mention that tThese signals cannot be attributed to severe precipitation regimes exclusively as they were present in the seasonal means for IWV, surface temperature and humidity, and outbound latent and sensible heat flux (see Figs. S16 and S17 in the SM).FinallyFinally, we would like to emphasize that our analytical approach does not allow us to relate the soil-atmosphere differences between RCM and CPM with the observed precipitation differences of Sect.7.1.
The surface conditions play a relevant role for convection initiation, specially under weakly forced environments (Keil et al., 2020) and are thus worth investigating.
In the pre-conditioning of winter events, CPM simulates larger outbound latent heat fluxes than RCM over land (by about 15 W m -2 ), but the opposite occurs over the Mediterranean.Over large water bodies, RCM simulates about 30 W m -2 more than CPM.This holds for all composites derived from the EOFs presented in Sect.6 (Fig. 9).For illustration, Fig. 12a shows the composite differences of the negative principal components of EOF-3 (Fig. 9e).CPM exceeds RCM in 15 W m-2 over land, but RCM shows ca. 15 Wm-2 more latent heat emissions than RCM.The remainder composites can be found in the SM.
Sensible heat fluxes have shown no clear differences between RCM and CPM over the Mediterranean Sea.Over land, during Winter, we cannot assert the magnitude of these differences since the soil temperatures are too low to show any net outbound heat emissions.Figure 12b illustrates these results where differences over the sea are close to zero and green colours denote no positive outbound heat emissions over land.Inbound directed fluxes are dismissed to avoid confusion with the interpretation of the signs in the difference plots.
Specific humidity and temperature at the surface are influenced by differences in the simulation of latent heat fluxes in RCM (Figs. 12c and 12d).Provided the larger outbound latent heat flux over land in CPM, the regions north of the Italian Peninsula show generally larger surface specific humidity in CPM than in RCM (by about 1 g kg -1 ).On the contrary, close to the Sea surface RCM is wetter than CPM in all analysed EOFs (by about 1 g kg -1 ).Over Italy, the surface specific humidity differences are also larger in RCM influenced by the sea southerly winds, which inflow maritime air masses.Regarding temperature, RCM simulates a warmer surface level (land and sea) of variable magnitude between 1 and 2 °C.This applies for all composites except one.This signal is also present in the seasonal means already and cannot be considered exclusive of heavy precipitation situations (Fig. S16 of the SM).
Differences in surface humidity representation influence the representation of CAPE, however, for winter events the RCM vs CPM show no systematic differences due to the low CAPE values.This can be seen in Fig. 12e and the remaining composite plots in the SM.
Finally, the higher temperatures over land and sea in RCM induce larger outbound long wave surface radiation than CPM, by ca. 10 W m -2 (Fig. 12f).This, like surface temperate, applies to all analysed composites except one.
Regarding Summer events, CPM again shows larger emissions of latent heat flux over land than RCM (ca.15 W m -2 ) but now these differences are limited to the Alps and northern Europe (Fig. 13a).For its part, RCM again shows larger latent heat emission over the Sea but also throughout the Italian peninsula up to the Po Valley.This is the case for all summer composites except one (see SM).
Sensible heat fluxes during summer events are larger in RCM than in CPM over land and Sea up to 20 W m -2 , although these differences tend to be smaller on coastal areas and the Po valley (Fig. 13b).
The previous results must be interpreted with caution.First, the north-south signal of latent heat flux differences is already present in the seasonal means (see Fig. S16 in the SM), and hence cannot be understood as characteristic of heavy precipitation situations exclusively.Second, the partition between latent and sensible heat fluxes is governed, although not exclusively, by the water content in the upper soil layers.Unfortunately, the RCM and CPM simulations used in this study bear a different integration of volumetric water soil and cannot be compared.Finally, because we obtain composites from the days prior to heavy precipitation, our results could be affected by earlier precipitation.In other words, if the events were preceded by some precipitation in either RCM or CPM, the upper soil levels will inevitably show a soil wetter than its counterpart.
For surface specific humidity RCM represents larger values than CPM over the Mediterranean as well as the Po Valley and the Italian peninsula (ca.1.2 g kg -1 ).Over northern Europe CPM tends to simulate larger specific humidity.Figure 13c shows the CPM (red) and RCM (blue) specific humidity differences over northern Europe and the Mediterranean region respectively.
Regarding temperature, RCM represents ca.1.3 °C more than CPM especially north of the Alps throughout the whole domain.
Over the Mediterranean Sea and the Po Valley these differences are weaker or even favourable for CPM (EOF-2).This is shown in Fig. 13d.
The lower temperature in RCM over the Po Valley agrees with previous findings assessed in Sangelantoni et al., (2022).The authors of this study, comparing an ensemble of CPM and RCM simulations, observed that CPM amplifies the drier-warmer conditions during heat waves with respect to the RCM ensemble.Furthermore, they assessed that "latent heat flux modulation tends to characterize not only HW events but also the whole summer season.Although our composites do not show such a clear excess by CPM over the Po Valley, they show a tendency that warmer conditions can be simulated by CPM over this area.
Regarding CAPE, CPM shows larger values over land than RCM, whereas RCM simulates larger CAPE over the Sea (Fig. 13e).A plausible explanation are the surface specific humidity differences assessed before that can influence the instability of the lowest air masses, used in the same calculation.Finally, the outbound long wave radiation, similarly to Winter events, shows larger values by RCM, compared to CPM (Fig. 13f).

Conclusions
The recent advancements in Convection Permitting Modelling (CPM; horizontal resolution below ca. 4 km) have been of pivotal relevance for the understanding and simulatingon of heavy precipitation, at decadal time scales.These events with high impact, are projected to be more intense and frequent in a warming climate.Therefore, despite the improvements already assessed, for the simulation of heavy precipitation.further research is needed to understand the implications of reaching CPM in the simulation of for model variables that affect the precipitation formation processes.In this study we evaluated reanalysisdrivendecadal COSMO-CLM simulations forof the greater Alpine region overin the 2000-2015 period and assessed the differences between a Regional Climate Model (RCM), set-up (grid-sizeof 25 km), and a CPM set-up (grid-size of 3 km).The main results are presented below: • CPM represents larger precipitation intensities, a better rank correlation, better hit rates for extremes detection, and a better representation of precipitation amount and structure for selected heavy epsiodesepisodes than RCM.However, (30 W m -2 ).The consequence is a wetter surface level (1 g kg -1 specific humidity) and larger CAPE (140 J Kg -1 ) in CPM north of the Alps (1 g kg -1 ), and but a wetter surface level in RCM over the Mediterranean Sea and Italy, possibly transportedassociated with by the the southerly Mediterranean winds.In turn, RCM simulates larger sensible heat fluxes over land which leads to a generally hotter surface level than in CPM (by about 1.5 °C).Although theseThese differences are weaker to the south of the Po Valley.Finally, the higher temperatures over land in RCM bring larger emissions of outbound long wave radiation compared to CPM (9 W m -2 ).
• For Winter events, latent heat fluxes in CPM were larger over land than in RCM (up to 15 W m -2 ) on the day prior to severe precipitation.Over the Sea, the opposite occurs, and RCM simulates larger heat fluxes compared to CPM (30 W m -2 more).The consequence is a wetter surface level in CPM over land areas north of the Alps compared to RCM (1 g kg -1 ).However, RCM simulates more specific humidity over the Sea and Italy, possibly due to the effect of the southerly winds.Regarding differences in surface temperature, RCM showed for most of the analysed EOFs a warmer surface level (by about 1.5 °C).This, in turn, brought larger emissions of outbound long wave radiation in RCM compared to CPM, up to 9 W m -2 .
• For Summer events, CPM simulates larger latent heat fluxes over land than RCM, although restricted to locations north of the Alps in this season.Surface sensible heat fluxes, on the contrary, are larger over land in RCM than in CPM (up to 20 W m -2 more), although these differences are weaker over the Po Valley.The consequence is that CPM simulates larger surface specific humidity north of the Alps whereas RCM simulates larger specific humidity over the Mediterranean and Italy.The different partition of heat fluxes leads to a higher surface temperature in RCM than in CPM over the Alps and northern Europe.Over the Po valley and Italy these differences are weaker or even favourable to CPM.Finally, the larger specific humidity north of the Alps in CPM leads to larger CAPE over land, whereas outbound long wave radiation is larger in RCM, linked to the warmer surface level in this set-up.
It is worth mentioning that for variables such as surface specific humidity and temperature, or surface heat fluxes, the signal of the differences between RCM and CPM was already present in the seasonal means (Fig. S16 and S17).This implies that they are not exclusive of heavy precipitation situations but that could be present in other weather regimes.For instance, the fact that CPM represents larger temperature at the Po Valley in the summer means adds on the findings by Sangelantoni et al., (2022) where an amplification of heat waves over the same area was found in a CPM ensemble. .
Our study has some limitations that need to be briefly addressed.First, we only assess one regional climate model and hence our results cannot be generalized to other RCMs.Second, as is common in heavy precipitation studies the under-catchment problem might be present in the observations used for validation (Groisman and Legates 1994;Golubev, 1986;Goodison et al., 1997;Vergarara-Temprado et al., 2020).Finally, we would like to point out that our study compares two different simulations where the differences observed are due to the use of a different horizontal resolution (25km vs 3km) but also to the different fine-tuning of the settings and the different boundary data.
Notwithstanding these limitations, our study provides evidence of the added value of CPM and of the remarkable differences 685 existing between RCM and CPM.These systematic differences must be considered when using one set-up or the other in decadal simulations.This is relevant for future research in the field but also for third-partiesthird parties interested in using climate information at decadal time scales.Examples of endeavours where high-resolution climate data are bringing added value are, for instance, the downscaling of climate change projections (Pichelli et al., 2021)

Figure 5
Figure5shows empirical Probability Distribution Functions (PDFs) of daily precipitation between 1971 and 2015 over SGer (Fig.1).All datasets represent similar probabilities for precipitation intensities between 0 mm d -1 and 50 mm d -1 .The upper box in Fig.5shows a zoom-in for the lower intensities.Beyond 50 mm d -1 CPM (red) starts to diverge from RCM (blue) and the observations (HYRAS-5km in black and EOBS-25km in grey).CPM (red) can represent daily grid point intensity up to 280 mm d -1 , whereas RCM (blue) can only attain 150 mm d -1 .HYRAS-5km, for its part, reaches a maximum grid point intensity of 215 mm d -1 and E-OBS-25km reaches 180 mm d -1 .This shows that the Figure5hence demonstrates that the coarser resolution data sets represent lower precipitation intensities and that .Finally, the differences in probability for intensities above 50 mm-d 1 are to be noted.In this regard CPM shows the largest probabilities of representing heavy precipitation intensities (>120 mm d -1 ).

Fig. 6 .
Fig. 6.Likewise, CPM outperforms RCM with regards to The same applies to hit rate (number of hits divided by number of occurrences) with values of 47.2 % for CPM and 45.88 % for RCM (not shown).The improvement shown by CPM with respect to RCM shows the added value of high-resolution in detecting heavy precipitation events in a climatology.The rank correlations of both resolutions remain below 0.5 given the difficulty of exactly represent the same 500 events in a 44-year climatology representing 3% of all considered days.Figure 6 also allows observing shows relevant periods of heavy precipitation clustering, e.g., spring-summer of 1971, winter 1989, the years 2000 to 2002 and autumn 2013.Regarding Finally, EOBS-25km (grey squares), it has a rank correlation of 0.94 against HYRAS-5m indicating a good accuracy for this product.

Figure 9 .
Figure 9. Empirical Orthogonal Functions of precipitation for SONDJF (a, c, e, g) and MAMJJA (b, d, f) events in CPM.The EOFs are obtained using the 290 most severe heavy precipitation events in each season (90-percentile).

Figure 12 .
Figure 12.Composite precipitation differences between RCM (blue, positive) and CPM (red, negative).All composites correspond to the positive principal components of EOF-2 in summer (MAMJJA) events.(a) Surface outbound latent heat flux, (b) Surface outbound sSensible hHeat flux, (c) Surface specific humidity, (d) Surface Temperature, (e) CAPE, (f) Surface outbound long wave radiation.Green colours in Latent and Sensible heat fluxes denote inbound directed fluxes and are thus not shown.

Figure 13 .
Figure 13.As Fig. 12 but for the negative principal components of EOF-3 for winter (SONDFJ) events.

between the model and observations for the duration of each event (see Tab. 3), calculated as
(  −   )   ⁄ .