1 Introduction

Regional climate models (RCMs) have been used in climate science for more than three decades and have added considerable value to global climate simulations at the regional to local scale (Giorgi 2019; Tapiador et al. 2020). To date, the horizontal spatial resolution of RCMs used for regional climate simulations/projections has been mostly in the range of 10–50 km, a resolution at which the hydrostatic assumption is still valid and convective precipitation needs to be parameterized. This last aspect of the model physics contributes significantly to model errors, for example in the simulation of the diurnal precipitation cycle (Wong et al. 2020; Zhou et al. 2023). In addition, this resolution is still too coarse to capture adequately the intensity of the most extreme events, especially at the sub-daily scale (Van de Vyver et al. 2021).

For these reasons, and due to considerable increase in computing capabilities during the last decade or so, the resolution of RCMs has increased to the so called “convection-permitting (CP)” scale, i.e., order of 1–3 km (Prein et al. 2015; Lucas-Picher et al. 2023; Coppola et al. 2020; Ban et al. 2021; Pichelli et al. 2021). At this resolution, deep convective processes can be explicitly simulated with the use of non-hydrostatic dynamical cores, and the first simulations with CP-RCMs have shown significant improvements compared to standard resolution hydrostatic RCMs (Stocchi et al. 2022; Lucas-Picher et al. 2023). In particular, a number of CP-RCM experiments have been carried out over different European domains in the last few years (Schär et al. 2020; Berthou et al. 2020; Ban et al. 2021; Coppola et al. 2021; Pichelli et al. 2021; Stocchi et al. 2022; Lucas-Pischer et al. 2023). Using high-resolution models (CP-RCMs) for climate simulations isn’t just about increasing the horizontal resolution in with existing models (hydrostatic). CP modelling represents a new level of complexity that requires significant improvements and testing. This process goes beyond the use of more advanced computations (non-hydrostatic cores)—several processes need to be improved, such as how the model simulates precipitation, clouds, and physical processes in general. Over the last decade, several RCMs have undergone this transition (Ban et al. 2014; Coppola et al. 2020; Fosser et al. 2014; Kendon et al. 2014; Prein et al. 2015; Liu et al. 2017). It is safe to say that CP resolutions are becoming the standard for most RCM applications, and thus most RCM systems have been upgraded both in their dynamical and physics packages to face this transition.

One such RCM system is the RegCM developed in subsequent versions first at the National Center for Atmospheric Research (NCAR) (RegCM1, Dickinson et al. 1989, Giorgi and Bates 1989; RegCM2, Giorgi et al. 1993a,b; RegCM2.5, Giorgi et al. 1999) and then at the Abdus Salam International Centre for Theoretical Physics (ICTP) (RegCM3, Pal et al. 2007; RegCM4 Giorgi et al. 2012a, b). In particular, RegCM4 included both hydrostatic (Giorgi et al. 2012a, b; Umakanth et al. 2016) and non-hydrostatic (RegCM4-NH, Coppola et al. 2021) dynamical cores, and RegCM4-NH has been used for a variety of applications (e.g., Stocchi et al. 2022; Raju et al. 2022; Valcheva et al. 2023). The main problem with RegCM4-NH, however, is that, due to the use of a simple split-explicit scheme, it requires the use of a relatively short time step to retain stability, which increases considerably the computational cost of running the model.

For this reason, recently, as a result of a collaboration between the ICTP and the Istituto per la Scienze dell’Atmosfera e del Clima (ISAC) of the Italian National Research Council, a new non-hydrostatic version of the model has been developed, RegCM5, as described in Giorgi et al. (2023). In this model development effort, the dynamical core of the weather prediction model MOLOCH (Davolio et al. 2020) was included in the RegCM system. In this dynamical core different processes and waves are solved using different time steps, making the model overall about 5 times faster than RegCM4-NH, and thus making it more applicable to very high- resolution regional climate simulations (Giorgi et al. 2023).

One of the regions where the RegCM system has been substantially applied in the past is the Carpathian Region, which is characterized by complex topographical and land use features. For example, Torma et al. (2008, 2011) customized a high-resolution version of RegCM3 over the region, while Bartholy et al. (2008) and Krüzselyi et al. (2011) analyzed climate change simulations over the Carpathian Basin with different RCMs, including the RegCM3.

The first attempt to compare the hydrostatic and non-hydrostatic dynamical cores of RegCM4 over the Carpathian Region is reported in the work of Kalmár et al. (2021), who completed and evaluated seven experiments using different model physics and dynamical schemes (4 hydrostatic and 3 non-hydrostatic runs) at 10 km horizontal resolution for a 10-year long simulation period (1981–1990). They found clear indications that the use of the non-hydrostatic core leads to an improvement in the simulation of precipitation, especially over the Carpathian Mountain chains. Moreover, intense convective precipitation events (> 80 mm/day) were only simulated when the model was integrated in the non-hydrostatic mode. Therefore, there were encouraging indications that the use of non-hydrostatic models might be especially useful over the region.

Following these previous works, we here test a high-resolution version of the RegCM5 modeling system over the Carpathian Basin. The model is run at a horizontal grid spacing of 2 km for four 1-year long simulations characterized by different precipitation regimes. The aim of the present study is to assess the performance of this new model version for a range of surface climate statistics, with focus on temperature and precipitation. This assessment is carried out against the CARPATCLIM station observation dataset, which was specifically developed for the region (Szalai et al. 2013).

In the next section we first briefly describe model and experiment design, in Sect. 3 we discuss our results, while in Sect. 4 we present our conclusions and plans for future work.

2 Data and Methods

2.1 Model Description and Experimental Design

Here we use the latest version of the ICTP RegCM system, RegCM5, described by Giorgi et al. (2023), whose physics parameterizations are reported in Giorgi et al. (2012a, b) and Coppola et al. (2022). The simulations presented in this study use the following physical schemes: Holtslag planetary boundary layer scheme (Holtslag et al. 1990), CCSM radiation scheme (Kiehl et al. 1996), CLM4.5 land surface scheme (Oleson et al. 2013), and Zeng ocean flux scheme (Zeng et al. 1998). For convective precipitation, deep cumulus convection is disabled, but a simplified Tiedtke cumulus scheme (Tiedtke 1989; 1993; 1996) is used to trigger non-precipitating shallow convection. Precipitation is calculated using a microphysics scheme which solves five prognostic equations for water vapour, cloud liquid water, rain, cloud ice and snow (Nogherotto et al. 2016). As mentioned, RegCM5 uses the MOLOCH non-hydrostatic dynamical core, which is fully compressible, convection resolving model developed at ISAC (Istituto di Scienze dell’Atmosfera e del Clima). It integrates the set of atmospheric equations with prognostic variables (e.g. virtual potential temperature theta, water vapor mixing ratio q, horizontal (u, v) and vertical (w) components of wind velocity, optional turbulent kinetic energy and up to five water species), represented on a projected Arakawa C-grid (Arakawa and Lamb 1977). A hybrid terrain height following coordinate zeta, relaxing smoothly to horizontal surfaces away from the earth surface, is employed. Model dynamics are integrated in time with an implicit scheme for the vertical propagation of sound waves, while explicit, time-split schemes are implemented for the time integration of the remaining terms of the equations of motion. Three-dimensional advection is computed using the Eulerian Weighted Average Flux scheme (Billet and Toro 1997). A small divergence damping is included to prevent energy accumulation on the shorter space scales. Detailed description is given in the work of Giorgi et al (2023).

The integration domain covers the Carpathian Basin and surrounding regions with a grid spacing of 2 km and 41 vertical sigma levels. The model domain and topography are shown in Fig. 1. The domain consists of 483 × 388 grid points in the horizontal and meridional directions, respectively, with a lateral buffer zone of 30 grid points and an exponentially decreasing Newtonian relaxation scheme (Giorgi et al. 1993b). We simulated 4 complete years: 1980, 2006, 2008 and 2010, which were selected from the period 1961–2010, which in turn is the period covered by the CARPATCLIM observation dataset used for model validation. The four years were selected for the following reasons: 1980 is a relatively cold year over the region; in 2006 a devastating storm hit Budapest during the Constitution Day celebrations (Horváth et al. 2007); 2008 was one of the warmest years on record; 2010 was the wettest year since 1901 (www.met.hu). Atmospheric and radiation variables are saved at six-hourly time steps, while surface variables are stored at hourly time steps in RegCM output files. The ERA5 global atmospheric reanalysis from the European Centre for Medium-Range Weather Forecasts (Hersbach et al. 2020) provides the meteorological lateral boundary conditions for RegCM5, without use of intermediate resolution domains. This means that the so-called nesting technique was not applied following previous works carried out over different regions of the world (Coppola et al. 2020; Ban et al. 2021; Dominguez et al. 2024). The simulations are initialized on 1 November and integrated until 31 December of the following year, with the first two months serving as a spin-up period and therefore not considered in the analysis.

Fig. 1
figure 1

Location and topography of the Carpathian Basin. Location of the analysis region within the Carpathian Basin is highlighted with red box; topography is based on the high resolution RCM simulation (0.01°, ~ 2 km). Thin contour lines represent topography with intervals of 500 m. Units are m

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2.2 The Study Area—Carpathian Basin

Our area of interest is the Carpathian Basin. The main topographic features of the region are shown in Fig. 1: the Carpathian Mountain chains to the north and east, a small fraction of the westernmost flanks of the Alps in the west, the northern part of the Dinaric Mountains in the south and the Hungarian Great Plain. The Carpathian Basin covers most of central and eastern Europe between latitudes 44–50 N and 17–27 E and is characterized by the confluence of warm and arid Balkan flows and temperate Central Europe and cold continental Eastern Europe air (UNEP 2007). The climate of the whole Carpathian region is therefore considered as a synergy of oceanic, continental and Mediterranean influences modulated by the local complex topography (Torma and Giorgi 2020). The mountain elevations in the model within the Carpathian domain exceed 2500 m, with steep gradients between the lowlands and the mountain peaks (Fig. 1). The Carpathian region is also characterized by a rich biodiversity covering a significant part of the catchment areas of the two main rivers in the region: Danube and Tisza (UNEP 2007). Several studies have discussed the climate of the Carpathian region using the CARPATCLIM dataset as a reference (Spinoni et al. 2015; Kis et al. 2017; Torma and Kis 2022; Simon et al. 2023).

2.3 Observational Datasets

The evaluation of convection-related processes and phenomena in RCM-CP simulations is highly dependent on the availability of reliable high-resolution observations, either gridded or from station data (Ban et al. 2021; Tabary et al. 2012; Winterrath et al. 2018). In our analysis, which primarily focuses on precipitation, we first compare the model results with data from the driving ERA5 reanalysis. This dataset is based on the ECMWF Integrated Forecasting System model and on a 4D-Var assimilation scheme (Bonavita et al. 2016) including observations from a wide range of platforms (e.g., radiosondes, satellites). The ERA5 reanalysis has a horizontal resolution of about 31 km.

As mentioned, our observational dataset used for model validation is CARPATCLIM, which provides a total of 16 meteorological variables on a daily basis and also includes derived indicators. It covers the Carpathian region over a grid with a nominal resolution of 0.1° × 0.1° for the period 1961–2010 (Szalai et al. 2013). The CARPATCLIM dataset is based on station observations, its data are quality controlled, it covers the whole region of the Carpathians (about 500,000 km2) and is freely available for scientific purposes via the following link: http://www.carpatclim-eu.org/pages/download/. Compared to other observational databases covering the Carpathians (e.g., E-OBS, Cornes et al. 2018), CARPATCLIM has the highest density station coverage. For example, the number of precipitation stations used by E-OBS over the Carpathian Region is 79, whereas the CARPATCLIM database contains data from up to 560 stations (Kalmár et al. 2023). This is one of the reasons why the CARPATCLIM database is considered to be one of the most reliable for this region. However, the quality of such gridded datasets over several sub-regions is questionable due to the uneven density of stations or the relatively low temporal frequency of observations (Lucas-Picher et al. 2013; Prein and Gobiet 2017).

To assess the performance of the model at the local scale, we also used station data provided by the Hungarian Meteorological Service (HungaroMet). HungaroMet provides its monitoring and measurement data free of charge and makes them available via the open data server (Meteorological Database) odp.met.hu. Specifically, here we use the daily precipitation data observed at the Budapest-Szentlőrinc station (19.1822 E, 47.4292 N).

In order to facilitate the comparison of model and observed data, all datasets are interpolated onto a common grid with spacing of 10 km (Torma et al. 2015), i.e., close to the resolution of CARPATCLIM. The interpolation procedure was performed using the distance-weighted average remapping of the Climate Data Operators software (CDO, Schulzweida 2021), which was found to provide the most consistent spatial pattern between different resolutions (e.g. bilinear interpolation might smooth local peaks in precipitation; Torma et al. 2015). For some variables, however, we also analyse RegCM5 data on the original 2 km grid to illustrate the effects of resolution.

3 Results

3.1 Mean Statistics

Our analysis focuses on temperature and precipitation over the inner Carpathian domain shown in Fig. 1. Starting with the mean fields, Figs. 2 and 3 show the spatial distribution of the annual mean temperature and precipitation along with their biases compared to the ERA5 and CARPATCLIM datasets. The means are calculated averaging over the four simulated years (1980, 2006, 2008 and 2010).

Fig. 2
figure 2

Annual mean near-surface air temperatures and biases compared to CARPATCLIM. Unit is given in ℃

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Fig. 3
figure 3

As in Fig. 2, but for precipitation (mm/day). The bias fields (bottom line) are represented in %

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The temperature patterns clearly illustrate the higher resolution of the RegCM5 compared to ERA5, resulting in greater topographic detail. Both model products present only noise-resembling biases over the Carpathian chains, likely due to differences between the model topographies and the effective resolution of the observation data (with sparser stations at high elevations). Over the flatter areas, the ERA5 temperatures are quite close to the observations, while the RegCM5 exhibits a warm bias between 1 and 2 ℃ over the Hungarian Plain, where more observing stations are available (Kalmár et al. 2023). Supplementary Figures S3 and S4 show that this warm bias is mostly due to summer and, to a lesser extent fall temperatures, while a good agreement with observations is found in the winter and spring (Figures S1 and S2).

The annual mean precipitation fields and their biases are shown in Fig. 3. ERA5 tends to slightly overestimate precipitation throughout the analysis region, both in the mountainous and flat areas. Conversely, RegCM5 tends to overestimate precipitation over the mountainous areas and underestimate it, mostly by up to 25%, over the Hungarian Plains. Supplementary Figures S5-S8 indicate that this bias pattern occurs quite consistently in all seasons, although with slightly varying magnitudes. Therefore, it appears that the RegCM5 in its CP configuration tends to produce a strong, and seemingly excessive, topographic forcing on precipitation, although the relatively low density of high elevation stations and the lack of a gauge undercatch correction (Legates and Willmott 1990; Adam and Lettenmaier 2003) likely tend to amplify the positive model biases at high elevations. In addition, RegCM5 might not perfectly capture the complexity of real orographical features even at 2 km horizontal resolution, which might lead to an exaggeration of upslope lifting and precipitation. The warm bias and precipitation overestimation might be interrelated. A warm bias can lead to increased atmospheric instability, particularly over upslope regions. This can trigger more vigorous convection and precipitation in the CP configuration, further amplifying the precipitation bias. The negative bias at low elevations is probably attributable explicitly to the model microphysics scheme, and more tests are needed to assess the model sensitivity to the microphysics representation.

Figures 4 and 5 present the annual cycle of average temperature and precipitation, respectively, using “spider-web” plots. In this case the values are averaged over the entire Carpathian analysis region, and therefore, especially for precipitation in the RegCM5 there is a spatial compensation of errors. Nevertheless, the figures indicate that both the ERA5 and RegCM5 reproduce well the seasonal cycles of temperature and precipitation over the region, with small region-average biases.

Fig. 4
figure 4

Simulated monthly area-averaged mean temperature (black solid line) and observed monthly area-averaged precipitation totals (red, blue and green solid lines) for the period of years (1980, 2006, 2008 and 2010). The average is taken over the interior domain within the region encompassed by red box in Fig. 1. Unit is given in ℃

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Fig. 5
figure 5

Same as Fig. 4 but for precipitation totals. Unit is given in mm/day

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A quantitative measure to assess how well models reproduce observed spatial patterns is the Taylor diagram (Taylor 2001), which combines information on spatial correlation and standard deviation to produce the centered Root Mean Square Distance (C-RMSD, i.e., the root mean square error with the bias removed). Figure 6 shows the Taylor diagrams for mean seasonal precipitation in RegCM5 and ERA5 vs. CARPATCLIM, where all data have been interpolated onto the grid of CARPATCLIM at 0.1° horizontal resolution. We see that in all seasons the spatial standard deviation in ERA5 is in line with that of CARPATCLIM, which suggests that the effective resolution of the CARPATCLIM data is close to that of ERA5, i.e. ~ 30 km. In fact, the RegCM5 shows consistently higher values of standard deviation because of its higher resolution. In terms of correlations, we see that ERA5 tends to have higher values that RegCM5, perhaps also as a result of the different resolutions of these products, but that in general the correlation coefficients are high, 0.6 to 0.8 also in RegCM5. Figure 6 thus shows that, with the caveats on resolution indicated above, both ERA5 and RegCM5 can reproduce the basic spatial patterns of precipitation.

Fig. 6
figure 6

Taylor diagram of mean (1980, 2006, 2008 and 2010) seasonal precipitation for the RegCM (blue color) and for the ERA5 dataset (green color) versus CARPATCLIM dataset. The four panels refer to the four seasons (December-January–February, or DJF; March–April-May or MAM; June-July–August, or JJA; and September–October-November, or SON)

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Figure 7 reports the Taylor diagrams for mean temperature in RegCM5 and ERA5 vs. CARPATCLIM. Similarly to precipitation, RegCM5 shows higher standard deviations than ERA5 in all seasons. However, ERA5 and RegCM5 are in better agreement with CARPATCLIM compared to precipitation and show better agreement in all seasons (0.8–1.2), except for DJF, when there is a slight underestimation of the standard deviation (0.3–0.4). The spatial correlation coefficients are high in all seasons (~ 0.9), except for DJF (~ 0.6). RegCM5 shows a better agreement with CARPATCLIM for C-RMSD compared to ERA5, especially for MAM.

Fig. 7
figure 7

Same as Fig. 6, but for temperature

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Figure 8 illustrates the interannual variability of precipitation over the analysis region by reporting the area average seasonal precipitation for the 4 simulated years. Overall, the ERA5 and RegCM5 reproduce the observed variability, with maximum precipitation in 2010 in all seasons except SON, minimum precipitation in the dry year 2008 (except for SON) and the dry fall conditions in 2006. Some noticeable differences between RegCM5 and ERA5 occur only in summer, evidently because of the more important effects of local convection processes, otherwise it is clear that the boundary forcing from ERA5 strongly affects the model interannual variations.

Fig. 8
figure 8

Areal average of seasonal mean daily precipitation over the region of interest for the 4 years: 1980 (blue), 2006 (yellow), 2008 (red) and 2010 (green). Unit is in mm/day

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An important aspect of the precipitation characteristics is the distribution of precipitation intensity, which can be measured by the intensity probability density function (PDF). Figure 9 shows the PDFs of daily precipitation across the analysis domain in CARPATCLIM, ERA5 and RegCM5. For the latter both the distributions at the original 2 km resolution and interpolated on a 10 km grid consistent with CARPATCLIM are shown.

Fig. 9
figure 9

Daily precipitation intensity empirical probability distribution functions. The frequency versus intensity of daily precipitation events over the Carpathian Basin is presented for the years: 1980, 2006, 2008 and 2010. All data were interpolated onto 0.01° grid (CARPATCLIM: red, ERA5: green and RegCM: blue), noting that RegCM on original 2 km resolution grid is also present (light blue)

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CARPATCLIM shows the occurrence of events with intensities of up to 120–160 mm/day, with one case exceeding 180 mm/day. ERA5 underestimates the observed intensities above 20 mm/day, with maxima reaching only ~ 100 mm/day, and overestimates the frequency of light precipitation events. This is evidently due to the relatively coarse resolution of the ERA5 product. The strongest extremes, exceeding 200 mm/day, are produced by RegCM5 on its original resolution of 2 km, with generally higher frequencies than CARPATCLIM after intensities of ~ 20 mm/day. On the other hand, even when interpolated at the CARPATCLIM nominal resolution of 10 km, we see that RegCM5 still tends to produce stronger events than observed, even though the two distributions are quite close to each other. This confirms that the effective resolution of the CARPATCLIM data is coarser than 10 km (Fantini et al. 2018). Our results highlight that the CARPATLIM dataset has a nominal resolution of an approximate grid spacing of 11 km, but this value does not reflect the true density of meteorological stations used for the dataset. Fantini et al. (2018) reports an average station density of only 2 stations per 1000 km2. This sparsity of stations results in a lower effective spatial resolution, which is closer to 50 km. This resolution limitation is evident in the results presented in Fig. 9. In summary, Fig. 9 clearly shows that resolution has a strong effect on the intensity PDFs, and that the increased resolution of RegCM5 in the CP configuration leads to significant added value in simulating extreme events.

To complement the analysis of daily precipitation, we examined two standard precipitation indices, the Single Daily Intensity Index (SDII), which measures the mean intensity during rainy days, and the wet day frequency (WDF), i.e., the frequency of days with precipitation higher than 1 mm. Note that we calculated these indices in the model after regridding the data to the 10 km CARPATCLIM grid, for consistency with the observations.

Figure 10 shows the patterns of observed, ERA5 and RegCM5 mean SDII, along with the corresponding biases. The topographic effect on the SDII is evident in all datasets, most (least) pronounced in RegCM5 (ERA5). The regional model shows a good agreement with observations, with the exception of an overestimate over the mountain peaks of the southern flanks of the Carpathians. Conversely, ERA5 underestimates the SDII throughout most of the domain, except for some central regions of our analysis area. In terms of WDF (Fig. 11, we see a substantial underestimate by RegCM5 throughout the flat areas of the regions, and an overestimate over the mountain peaks. It is thus clear that the bias in mean precipitation found in Fig. 3 is mostly due to the frequency of precipitation events rather than the intensity. ERA5 tends to overestimate the number of rainy days throughout the domain, a characteristic typical of coarse resolution models (Gutowski et al. 2003; Pichelli et al. 2021).

Fig. 10
figure 10

SDII mean regional patterns over the Carpathian Basin (years: 1980, 2006, 2008 and 2010) at 2 km (a) and on 0.1° (b and c panels). The differences RegCM and ERA5 against CARPATCLIM represented on 0.1° grid (d, and e, panels, respectively). Units are mm/day

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Fig. 11
figure 11

Same as Fig. 9, but for the index WDF (mean frequency of wet days). Units are %

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Summarizing the results of this section, the models show a good performance in reproducing the observed temperature climatology, except for a warm bias over the Hungarian Plains in RegCM5 especially during the warm months. ERA5 tends to overestimate precipitation over most of the analysis region, mostly because of the occurrence of too many rain events counterbalancing an underestimate in precipitation intensity. RegCM5 reproduces well the daily intensity PDFs and the SDII, showing significant added value compared to ERA5, but underestimates precipitation over the flat regions of the domain, mostly as a result of an underestimation of the number of rainy events.

3.2 Examples of Individual Storm Simulations

One of the advantages of utilizing models in CP configuration is the possibility of simulating specific events, for example extremes, at fine spatial scales, and to potentially provide local scale interactions. In this section we provide illustrative examples of both applications.

Figures 12, 13 show two examples of storms occurring in the winter and spring seasons of 2010, which was a record wet year for Hungary, recording a total annual precipitation of 959 mm over the country (130 mm more than the previous record). During this record-breaking year, the monthly totals were below average only in March and October. In particular, an intense snowstorm hit the region at the end of January 2010, producing in some regions more than 42 mm of equivalent water during the night of 30 January. The daily precipitation amounts associated with this event in CARPATCLIM, ERA5 and RegCM5 are shown in Fig. 12 for the period 27 January to 2 February 2010.

Fig. 12
figure 12

Daily precipitation totals over the Carpathian Basin between 27 January and 2 February 2010. Daily precipitation totals are given in mm/day, while near surface wind fields are given in m/s

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Fig. 13
figure 13

Centre of Mediterranean cyclone Zsófia located over the Carpathian Basin between 15 and 18 May 2010. Daily precipitation totals are given in mm/day, while near surface wind fields are given in m/s

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The storm enters the Hungarian Plain from the west on January 30, with relatively dry conditions beforehand. A precipitation squall line is oriented in a northeasterly direction, and is well captured by both ERA5 and RegCM5, although the peak precipitation amounts over northern Hungary and eastern Slovakia are somewhat underestimated. On January 31 the storm moves eastward across eastern Hungary and western Romania, with the precipitation line elongated in a north–south direction crossing eastern Slovakia, eastern Hungary, and western Romania. Again, both ERA5 and RegCM5 capture this storm evolution, although the area of maximum precipitation amounts is more extended than in CARPATCLIM. Finally, the storm leaves the area of interest on February 1, as seen in all three products. Overall, the RegCM5 reproduces well the evolution of this storm, and in addition provides finer spatial detail than the other two products, although it is difficult to assess the added value related to this detail.

The second case study we present is a severe precipitation event which occurred on 15–18 May 2010 (Fig. 13). The most intense precipitation events in the Carpathian Basin can be directly linked to Mediterranean cyclones, which bring warm and humid air from the west and south-west into the Carpathian Basin (Czigány et al. 2008). The Mediterranean cyclone Zsófia reached the Carpathian Basin on 15 May 2010 and crossed the entire basin during the next three days, causing heavy precipitation until 18 May 2010. During this 72-h period, the total precipitation exceeded 200 mm in some regions of the Carpathian Basin, which is about three times higher than the monthly average. Also, for this case, the RegCM5 and ERA5 data are in generally good agreement with the observations, both in timing and areal extent of the precipitation area, with RegCM5 producing again greater spatial detail than the other two datasets.

We examined a number of additional case studies, not presented here for brevity, in which again ERA5 and RegCM5 were able to generally capture the evolution of storm systems crossing the Carpathian Basin. In addition, RegCM5 tends to modulate the forcing field of ERA5, resulting in relatively stronger wind fields. This leads to more intense moisture transport, which in turn leads to higher precipitation totals especially over the upslope mountainous regions. Obviously, a key factor in the model performance is the capability of the driving fields to describe the dynamical evolution of the storms, which is evidently there for ERA5. However, given good quality of the driving boundary conditions, our examples illustrate how the model retains a good performance even when run in “climate mode”, i.e., without reinitialization prior to the storm passage. On the other hand, it is difficult to assess whether the additional spatial detail provided by the model is indeed in the direction of better performance, which would require very dense and detailed observations.

As a final step in our model evaluation, we now analyse the performance at the local scale by comparing simulated individual station observations. For this purpose, we use station data for Budapest obtained from the Hungarian Meteorological Service (HungaroMet; odp.met.hu). Figure 14 shows the daily precipitation sequence for the three simulated years as observed at the Budapest station and as simulated by ERA5 and RegCM5 at the respective grid points closest to the station location (19.1822 E, 47.4292 N). Note that data for the station are available from 2002, so 1980 is not included in these analyses.

Fig. 14
figure 14

Daily precipitation totals for the individual years. RegCM results are depicted with color blue, ERA5 data are represented in color green, whilst CARPATCLIM is represented with red solid lines. Correlation values are also represented for RegCM and ERA5 with respect to CARPATCLIM. Units are in mm/day

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It can be seen that both the ERA5 and RegCM5 reproduce the main precipitation events at the station location, although the magnitude of the event might deviate from the observed. As a quantitative measure of model performance, we calculated the temporal correlation coefficient between daily precipitation series in RegCM5 and ERA5 with respect to the station data. The correlation is always relatively high, in the range of 0.46–0.7, statistically significant at the 95% confidence level and of similar magnitude in the two model products. We also note that the highest correlations are found for 2010, the year with the largest precipitation amounts. This preliminary analysis thus indicates how the model retains a good performance also at the local level when driven by good quality boundary conditions.

4 Conclusions

In this paper we have presented a preliminary analysis of the performance of the newly developed latest version of the RegCM regional modelling system, RegCM5 (Giorgi et al. 2023). The model was run at convection permitting resolution (2 km grid spacing) over a domain covering the Carpathian Basin for four years (1980, 2006, 2008, 2010) with boundary conditions provided by the ERA5 reanalysis. Our analysis focused on different statistics of surface air temperature and precipitation over the region, and the model was validated against the CARPATCLIM high-resolution observation dataset together with observational station data.

In general, the ERA5 reproduced well the temperature and precipitation climatology for the simulated years, and therefore also the RegCM5 showed a good performance, although it exhibited a warm bias over the Hungarian Plains during the warm season and a wet (dry) bias on the mountain chains (flat regions) within the basin. The model thus appears to produce a strong orographic forcing of precipitation, which needs to be better evaluated with high elevation station data. In summary, RegCM tends to produce excessive precipitation at high elevations, probably due to factors such as: relatively low density of high elevation stations, lack of correction for undercatch by rain gauges, relatively stronger wind fields. ERA5 slightly overestimated precipitation over the basin mostly as a result of an excessive number of rain events. It also underestimated the intensity of events above 20 mm/day, likely because of its relatively coarse resolution. The RegCM5 reproduced well the observed daily precipitation intensity distribution as well as the mean intensity of events, although it underestimated (overestimated) the number of rainy events over the flat (mountainous) regions of the analysis regions. Therefore, the added value of the high-resolution model was mostly seen for the simulation of mid to high intensity precipitation events. Both ERA5 and RegCM5 also exhibited a good performance in simulating individual storm events and precipitation time series at individual locations (e.g., Budapest). Note that RegCM5 was driven by ERA5, which is a global reanalysis product that excels at capturing large-scale atmospheric circulation patterns due to its global domain. However, its ability to represent smaller-scale phenomena such as convection and boundary layer processes may be limited. RegCM5, on the other hand, uses a non-hydrostatic core at a higher resolution, potentially allowing a more accurate simulation of these smaller scales. However, uncertainties associated with the representation of complex physical processes and inherent model biases may lead to deviations from ERA5 data (Giorgi 2005). While ERA5 provides valuable driving conditions for RegCM5, discrepancies arise, for example, from the model's representation of physical processes. The physical downscaling process within RegCM generates a climatology that is influenced by the internal dynamical and physical state of the model (Giorgi 2019).

The goal of the present paper was limited to showing that the newly released version of the RegCM5 model produces reasonable climate simulations over the Carpathian region under different climate conditions. Future work should be devoted to assessing in a rigorous way the added value of the CP RegCM5 configuration compared to coarser resolution model versions. This task, however, is hindered by a few considerations. First, the effective resolution of the CARPATCLIM observation data is actually coarser than the model resolution in its CP configuration due to the paucity of observing stations over the region, especially in high elevation areas. Better observation data should be thus assembled over the Carpathians. Second, the model performance at its standard non-CP configuration depends heavily on the choice of convection scheme, and thus for a fair comparison a model optimization exercise should be carried out at coarse resolution before comparing with CP simulations. All these tasks will be carried out in future work as the model is used more extensively by its community of users.

The RegCM5 is a newly developed modelling system, particularly in its dynamical component, and therefore more testing is required to fully assess its performance in different simulation contexts. However, the present preliminary experiments and analysis certainly provide very encouraging indications towards the applicability of the model to the Carpathian Region, particularly in its CP configuration, which has become much more computationally efficient (a factor of 4–5) with respect to the previous model version. We plan to continue testing the model over the region with different physics configurations and longer integration periods. We also plan to extend the analysis to more variables, such as wind circulation, clouds and convection. Eventually our aim is to apply the model to climate change studies over the Carpathian Region.