1 Introduction

Evidently, Earth’s climate is changing, however, recent human-induced global warming affects spatial and temporal variability of precipitation. Significant changes in the mean precipitation as well as in the frequency and intensity of extreme precipitation, have already been identified in many regions of the world (e.g., for Germany: Berg et al. 2013; globally: Asadieh and Krakauer 2015; Dankers et al. 2014; for the Northern hemisphere and Australia: Papalexiou and Montanari 2019). These changes in precipitation are strongly linked to social, economic, and environmental prosperity due to the role precipitation plays in global food production and maintaining biodiversity (Lippert et al. 2009; Gu et al. 2020).

Precipitation is one of the variables with the largest uncertainty in climate models, due to the large number of parameterized processes (such as cloud microphysics, cumulus convection, land surface-, planetary boundary layer (PBL) processes among many others) involved in its simulation (Kotlarski et al. 2005; Giorgi 2019). Stensrud (2007) stated that the most important components of any numerical weather prediction model are the parameterization schemes representing the subgrid-scale physical processes, and precipitation is highly determined by such processes. The accurate representation of precipitation changes is an essential precondition to use climate model simulations for climate-change impact studies. Indeed, many studies deal with the sensitivity analysis of the physical parameterizations employed within RCMs (Regional Climate Models; e.g., Grubišić et al. 2005; Rakesh et al. 2007; Han et al. 2008; Gan et al. 2017). For instance, several studies showed that the convective parameterization schemes are the key sources of errors and uncertainties in the RCM simulations (Bechtold et al. 2004; Déqué et al. 2007; Hohenegger et al. 2008; Gao et al. 2016; Mishra and Dubey 2021). These studies evaluated one or two schemes at a time, whereas we aim to combine several schemes within the parameterized processes as a novelty in this paper.

The RegCM (Giorgi et al. 2012) is historically the first limited area model developed for long-term regional climate simulations. There are multiple possible choices of physical schemes within RegCM4, therefore, a great number of sensitivity analyses can be completed with the RegCM regarding the selection of specific physical schemes (e.g., Güttler et al. 2014; Raju et al. 2015; Sinha et al. 2015; Pieczka et al. 2017; Chung et al. 2018; Velikou et al. 2019; Kumar and Dimri 2020; Nguyen-Xuan et al. 2020; Kalmár et al. 2021; Gosh et al. 2022; Mishra et al. 2023). Güttler et al. (2014) carried out a detailed analysis on the PBL schemes, while Sinha et al. (2015), Raju et al. (2015), Pieczka et al. (2017) and Nguyen-Xuan et al. (2020) demonstrated the performance of convective parameterization schemes, while Chung et al. (2018) and Mishra et al. (2023) investigated the land surface schemes. They focused on specific types of parameterizations only. Although Velikou et al. (2019), Kumar and Dimri (2020) and Kalmár et al. (2021) performed a validation of different physical schemes together, such as PBL, convection and microphysics schemes, but not all possible combinations are included in a systematic way in their analyses. Different schemes represent different approaches to physical processes, while no scheme performs best over every region (Duan et al. 2017; Song et al. 2020). Therefore, the determination of an appropriate scheme combination for a selected study area is crucial for improving the simulation accuracy in any further use. In the present study, we focus on the Carpathian region (located in East-Central Europe), where such complex sensitivity analysis has not been completed before.

Using and testing RCMs not only for standard three-decade-long periods, but for specific shorter periods (e.g. for years when heatwaves or flash floods occur more frequently than usual) and for specific areas — i.e. for regions with complex topography — are beneficial because the modelling of the climate conditions of these regions is quite difficult as it was pointed out by Ceglar et al. (2018) in case of the Carpathian region. For instance, extremely heavy and persistent rain caused severe flooding in East-Central Europe (Poland, Czechia, Slovakia, Hungary, Serbia) in 2010 (Bissolli et al. 2011). Due to the large amount of precipitation over the whole year, 2010 was the wettest year in this region since the beginning of regular meteorological measurements (WMO, 2011). Such unusual conditions arise the necessity to evaluate RCM simulations (Soares et al. 2012). For this purpose, the present study focuses on the quantification of the use of different parameterization schemes and their combinations on RCM outputs, where hindcast experiments were completed applying RegCM4.7 to the Carpathian region. Altogether 24 simulations were carried out to simulate extreme wet conditions occurred in 2010 by using various combinations of the physical schemes (2 schemes for the land surface processes, 2 schemes for cloud microphysics, 3 schemes for cumulus convection and 2 schemes for representing the PBL processes). Most of the schemes used in this study have not been previously tested for this region. Each parameterization combination leads to a different simulated climate, so the spread of the ensemble is an estimate of the model uncertainty arising from the representation of the unresolved phenomena. Specifically, the main aims of this study are (i) to evaluate these elements of RegCM for the Carpathian region and to simulate the regional precipitation characteristics in extreme precipitation conditions, i.e., in 2010, the wettest year, as reliably as possible, and thus (ii) to find the best configuration in terms of excessive precipitation that can be later used in future climate projections and impact studies where precipitation is the main driving factor.

The paper is organized as follows: first, we provide a brief description of the model used in the study and the relevant parameterization schemes. Then, we summarize the main features of model experiments and validation data. Results are shown and evaluated in Sect. 3, followed by the summary and conclusions in Sect. 3.11.

2 Data and methods

2.1 Study area

The simulation domain is shown in Fig. 1. This domain encompasses the region between 1.8°–33.3°E and 41.3°–52.8°N, covering the area of the Carpathian region (which consists of the Carpathian Basin and the Carpathians) and the Alps. However, the analysis focuses on the Carpathian region only, which is characterised by unique orographical and climatological conditions since it is a transition area between the Mediterranean, oceanic, and continental climates. The Carpathian Basin is surrounded by the Alps in the west, by the Dinaric Alps in the southwest, and by the Carpathians in the north and east. The dominant wind direction is western, northwestern, resulting in a west to east spatial gradient of precipitation modulated by local topography (Bartholy et al. 2003). Furthermore, the air mass from the Atlantic region crosses the Alps, it loses humidity resulting in a precipitation decrease towards the east. The annual mean precipitation is 700–800 mm in the western part of the Basin, while the lowest annual precipitation totals occur in eastern Hungary with 550 mm (UNEP 2007; Spinoni et al. 2015).

The Carpathians have a temperate climate, with a continental regime increasingly intensive eastward (Cheval et al. 2014). The altitude, the compact arrangement and the shape of the Carpathians cause disturbances in the climatic zonality and in the general atmospheric circulation (UNEP 2007). The interaction between the mountains and the atmospheric flow is particularly complex, mountains playing a significant perturbation role in the large-scale processes with the overall dimension and orientation of the ranges and finally resulting in the prevailing airflows. Precipitation totals rise with altitude and generally decrease from west to east. The average annual precipitation amounts vary from 600 to 1600 mm and is mostly between 900 and 1200 mm, depending on altitude and local conditions (UNEP 2007; Repel et al. 2021).

Fig. 1
figure 1

The topography (m) of the integration domain for the RegCM4.7 simulations. Validation is shown for the eastern half of the RegCM integration domain covering the CarpatClim domain (indicated by a solid rectangle). In addition, two special geographical subregions with different orographic and climatic conditions are selected: the dashed rectangles indicate the Tatra Mountains (TM) and the Great Hungarian Plain (GHP).

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2.2 Model and experimental design

The model used in this study is RegCM4.7 developed by the Abdus Salam International Centre for Theoretical Physics. The features of RegCM4.7 and detailed descriptions of the model’s physical processes can be found in Giorgi et al. (2012) and in Elguindi et al. (2017). A great number of sensitivity analyses were completed with the RegCM regarding the selection of a suitable integration domain, an adequate horizontal resolution, potential driving models, applied physical schemes and adaptation tools for Central and Eastern Europe (Torma et al. 2011; Güttler et al. 2014; Pieczka et al. 2017; Kalmár et al. 2021). These previous studies and the recommendations from the developers were all taken into account when choosing the physical schemes listed in Table 1. The used model physical schemes for PBL, radiative transfer, land surface processes, cloud and precipitation processes are summarized in Table 1. On the basis of 2 land surface schemes, 2 cloud microphysics schemes, 3 cumulus convection schemes and 2 PBL schemes, the total number of combinations is 24 as they are listed in Table 2.

Table 1 The applied physical parameterization schemes in the 24 different RegCM simulations
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Torma et al. (2011) calibrated some parameters in SUBEX microphysics scheme for the Carpathian region, which have been built into the RegCM4.3, but were changed back to the original values in the RegCM4.7, We used the SUBEX scheme with modification by Torma et al. (2011) in this study, so we use the name SUB4.3.

The initial and lateral boundary conditions (LBC) and the sea surface temperature (SST) values for these 24 simulations were obtained from the ERA-Interim reanalysis with 0.75° horizontal resolution and 6-hour temporal resolution (Dee et al. 2011) for the target year 2010 and the spin-up year 2009. Originally, the spin-up period can vary with the region since the length of the spin-up depends on the soil characteristic and the climate conditions. Jerez et al. (2020) stated that there is not a simple straightforward answer to how long the optimum spin-up period should be. For instance, the spin-up period required for wet and humid region is less as compared to the dry or arid regions and deep soil layer (Cosgrove et al. 2003; Rodell et al. 2005). The dry land areas require a spin-up period of 2–3 years, whereas the monsoon region requires a stabilization period of around 3 months before monsoon period (Lim et al. 2012). In general, the spin-up period is typically at least one year (Christensen 1999; Giorgi and Mearns 1999). Katragkou et al. (2015) also used a spin-up period of 1 year to initialize six hindcast WRF (Weather Research and Forecasting model) simulations with different configurations affecting the radiation schemes, microphysics, and convection over Europe. According to Katragkou et al. (2015), the 1-year spin-up time allowed for adjustment of the soil moisture and temperature. The final selection of spin-up period in this study was based on all these previous studies and conclusions. The horizontal resolution of our simulations is 10 km to represent the fine topography of the target area (Gao et al. 2006), while the number of the vertical levels is 23 using sigma coordinates.

Table 2 The name of the 24 RegCM simulations
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2.3 Validation methodology

A comprehensive assessment of these simulations is important to identify their different overall performances, such as the accuracy of simulated variables against observed fields. To evaluate model performance in case of precipitation, we compared the results to the CarpatClim observational dataset (Spinoni et al. 2015). The CarpatClim is a high-resolution, homogeneous, gridded dataset for the Carpathian region with a 0.1° horizontal resolution, covering the 1961–2010 period, containing all the major surface meteorological variables. A detailed comparison of the CarpatClim dataset to the E-OBS data for 2010 can be found in Kalmár et al. (2023), concluding that CarpatClim clearly reproduces climatic conditions more precisely than E-OBS. In this study, daily and monthly precipitation means were compared to the simulated values for the validation domain (44°–50°N, 17°–27°E, Fig. 1). The RegCM simulations required regridding on the CarpatClim grid and we used the nearest-neighbour method to avoid the oversmoothing of the fields.

In the first step of the analysis, BIASrel metric was calculated between the simulations and CarpatClim (Eq. 1).

$$\:{BIAS}_{rel}=\sum\:_{t=1}^{N}\left(\frac{{OBS}_{t}-{SIM}_{t}}{{OBS}_{t}}\right)\times\:100$$
(1)

where OBS indicates observation (here CarpatClim), while SIM is a particular RegCM simulation. N is the length of the time series (N = 365), t is the timestep. Furthermore, we performed hierarchical clustering of the values of the Box-Whiskers diagrams (minimum, lower quartile (Q1), median, upper quartile (Q3), maximum) derived from the resulting BIASrel metric fields, which helps to obtain information on which of the type of schemes determined the bias values to the greatest extent.

Utilizing a single model with different parameterization combinations in an ensemble approach enables a nuanced exploration of how different settings influence climate simulations. This method enhances our understanding of the sensitivity of the model to various parameterization scheme choices, leading to improved accuracy in projecting climate (Fernández et al. 2007; Argüeso et al. 2011; Mooney et al. 2013). Although the tested land surface schemes (BATS and CLM4.5) differ notably (Chung et al. 2018), in the case of the ensemble mean, we used all the simulations (except for the simulations showing problematic interactions, which we discuss in the Sect. 3), since this way we get information about the uncertainty of the model. The reduction of the size of the ensemble also reduces the information about the uncertainty in the climate model but does not reduce the uncertainty (Wilcke and Bärring 2016). In order to characterise the mean model skill, we calculated the ensemble mean of the RegCM simulations and compared to CarpatClim using different metrics, such as BIASrel, RMSE (Eq. 2) and temporal correlation coefficient (Eq. 3, rt).

$$\:RMSE=\sqrt{\frac{\sum\:_{t=1}^{N}{\left({OBS}_{t}-{SIM}_{t}\right)}^{2}}{N}}$$
(2)
$$\:{r}_{t}=\frac{\sum_{t=1}^{N}\left(OBS_{t}-\overline{OBS}\right)\left(SIM_{t}-\overline{SIM}\right)}{\sqrt{\sum_{t=1}^{N}\left(OBS_{t}-\overline{OBS} \right)^{2}\sum_{t=1}^{N}\left(SIM_{t}-\overline{SIM}\right)^{2}}}$$
(3)

Also, on the basis of Zhou and Yu (2006), the spread of the climate model simulations is used to estimate the uncertainty (Eq. 4, S), which is defined as

$$\:S=\:\sqrt{\frac{1}{M}{\sum\:}_{i=1}^{M}{\left({y}_{i}-\overline{y}\right)}^{2}}$$
(4)

where \(\:{y}_{i}\) are the individual simulations, \(\:\overline{y}\) is the ensemble mean, and M is the number of simulations (except the simulations with problematic interactions) taken into account in the analysis.

In addition, we selected two subregions with different orographic and climatic conditions for detailed validation: the Tatra Mountains (TM), and the Great Hungarian Plain (GHP, Fig. 1). The main reason of the choice of the selected subregions is that the density of stations used in CarpatClim is high in these two areas providing higher confidence in the validation dataset (Kalmár et al. 2023). In order to compare the different simulations in two subregions and to understand how well simulations fit to the reference data in terms of correlation, normalized standard deviation (hereafter standard deviation), and RMS difference, the Taylor diagrams (Taylor 2001) were produced. We used area-averaged daily precipitation fields for the two subregions.

Precipitation is one of the variables with the largest uncertainty in climate models. This is the case for summer precipitation in mid-latitudes, which is controlled by convective processes at small spatial scales, and cloud belts associated with cyclones and atmospheric fronts at larger scales. Uncertainty and errors associated with reproducing the convective processes in climate models are particularly large (e.g., Anthes et al. 1989; Dai 2006; Déqué et al. 2007; Brockhaus et al. 2008; Hohenegger et al. 2008; Kendon et al. 2012; 2021) and contribute significantly to uncertainty in climate simulations, especially in the warm half-year (Kyselý et al. 2016). This is why we analysed convective precipitation of the summer half-year (April-September) beside total precipitation. We calculated the sum of convective precipitation and the proportion of convective precipitation to total amounts. Since CarpatClim does not provide information about convective precipitation, ERA5 reanalysis (Hersbach et al. 2020) of the European Centre for Medium-Range Weather Forecasts (ECMWF) is used to provide convective precipitation on the basis of the Tiedtke scheme. The ERA5 output is available hourly and at a 31 km horizontal resolution, while the number of the vertical levels is 137 from the surface to the top of the atmosphere (Hersbach et al. 2020). It should be noted that both ERA-Interim and ERA5 are reanalyses, the horizontal resolution of which is much coarser (0.75° and 0.25°) than the horizontal resolution of the RegCM simulations. Furthermore, the reanalyses also use a convective parameterization (Tiedtke) to simulate precipitation (both convective and non-convective). However, due to the lack of appropriate observation-based data, only reanalysis can be used for the evaluation of convective precipitation.

For most variables presented in the paper, average values were also calculated from the driving ERA-Interim reanalysis dataset, to examine how precipitation simulated by RegCM is related to the corresponding data from the driving LBCs. This allows us to identify the potential strengths and weaknesses of the regional downscaling.

3 Results and discussion

First of all, Fig. 2 shows the spatial pattern of the precipitation from the CarpatClim observational dataset in 2010, which was the wettest year in the region since 1901 (WMO, 2011). Compared to the 30-year (1981–2010) average of the annual precipitation amounts, the annual precipitation amount was 40% higher in 2010. Higher values occur over the mountains (up to 2200 mm in the highest peaks of Carpathians), and the precipitation decreases from west to east. The effects of the altitude (orographic enhancement) and the distance from the Atlantic Ocean and the Mediterranean Sea influence the precipitation amount (Bihari et al. 2018). Among these, the altitude shows the dominant effect on precipitation with a spatial correlation coefficient of 0.6. The lowest precipitation values occur in the eastern part of the domain with ~ 550 mm in CarpatClim.

Fig. 2
figure 2

The spatial distribution of the annual total precipitation (mm) in 2010 from CarpatClim observational dataset. (Isolines represent topography)

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Figure 3 compares the relative bias (BIASrel) between the RegCM simulations and CarpatClim observational dataset. Five simulations (namely, 04_CLM_WSM5_Grell_UW, 06_BATS_WSM5_Tiedtke_UW, 08_CLM_WSM5_Tiedtke_UW, 10_BATS_WSM5_KF_UW, 12_CLM_WSM5_KF_UW) overestimate the precipitation with more than 200%. All of these simulations use the WSM5 microphysics scheme and UW PBL scheme, which indicates that there is a problematic interaction between these physical schemes. UW PBL scheme parametrises the entrainment process and accounts for enhancement of entrainment by evaporation of cloudy air into entrained air, which is an important process in the breakup of stratocumulus cloud (e.g., Lilly 1968; Nicholls and Turton 1986). While in the Holtslag PBL scheme, the diffusivity is only a function of surface conditions, this diffusion parameterization implicitly assumes that the turbulence within the boundary layer is generated entirely from the surface (Troen and Mahrt 1986; O’Brien et al. 2012). Due to the huge overestimation these five simulations with the combination of WSM5 and UW PBL schemes are omitted from further analysis.

For the easier overview, the simulations are analysed according to the different types of physical schemes.

3.1 Comparing land surface schemes: BATS and CLM4.5

In the most cases CLM4.5 land surface schemes is drier than BATS. This result is in agreement with Kang et al. (2014), Li et al. (2016), Llopart et al. (2017), Maurya et al. (2017) and Chung et al. (2018) in terms of the fact that the CLM land surface scheme reduces the amount of precipitation simulated by RegCM4. Although, other past studies (e.g., Steiner et al. 2005; Diro et al. 2012; Kang et al. 2014; Reboita et al. 2014; Raj Tiwari et al. 2015; Wang et al. 2015; Gao et al. 2017) concluded that the amount of precipitation simulated by the CLM simulations are closer to the observation datasets compared with the simulations using BATS, our results show that in some cases (e.g. 22_BATS_WSM5_KF_HO and 24_CLM_WSM5_KF_HO), BATS is more suitable than CLM4.5. More specifically, CLM4.5 greatly underestimates precipitation over lowlands (by around 50%), while simulation values using BATS are closer to observations (with an underestimation of around 30% only). These differences in response can be attributed to the differences in soil moisture simulated in the model by BATS and CLM4.5 (Chung et al. 2018). Figure 4 shows that the simulations using BATS land surface scheme contain much higher soil moisture content compared to the simulations using CLM4.5. The inter-relationship and feedback between the soil moisture and precipitation were widely discussed in several studies (e.g., Findell and Eltahir 1997; Eltahir 1998; Schär et al. 1999). The soil moisture content in the simulation, released through latent heat, affects the simulated precipitation and vice versa. Differences in how physical processes such as vegetation dynamics, soil hydraulic properties, and surface water routing are represented in the schemes can lead to disparities in simulated soil moisture. The lack of soil moisture in CLM can be attributed to its more detailed soil texture boundary condition in conjunction with its hydrological treatment of the soil column (Steiner et al. 2009), while the overestimation of soil moisture in BATS is largely due to the uncertainty of the prescribed soil properties (Steiner et al. 2009; Kang et al. 2014; Chung et al. 2018; Anwar and Mostafa 2023). For example, the spatial distribution of soil moisture values (Fig. 4) in simulations using the BATS land surface scheme is highly dependent on soil texture type, where BATS uses soil texture categories based on the FAO Soil Map of the World (Wilson 1984). Thus, CLM4.5 generates less precipitation indirectly compared to BATS (Fig. 3). This implies a smaller overestimation in some cases (i.e., 01_BATS_SUB43_Grell_UW, 03_CLM_SUB43_Grell_UW) than BATS, while in other cases (i.e., 21_BATS_SUB43_KF_HO and 23_CLM_SUB43_KF_HO), CLM4.5 generates a larger underestimation of precipitation compared to BATS.

3.2 Comparing the microphysics schemes: SUB4.3 and WSM5

WSM5 is a new scheme in RegCM, so there are only a few studies about the behaviour of this scheme (Coppola et al. 2021; Giorgi et al. 2023; Qin et al. 2023). In this study, all of the erroneous simulations used the WSM5 scheme, which makes the evaluation of this scheme more difficult. Thus, it is difficult to determine which microphysics scheme is more suitable, partially because the results depend on the choice of other schemes (i.e., PBL, land surface, convection scheme). In some cases, WSM5 can reduce dry (21_BATS_SUB43_KF_HO and 22_BATS_WSM5_KF_HO) and wet (13_BATS_SUB43_Grell_HO and 14_BATS_WSM5_Grell_HO) bias compared to the SUB4.3 scheme. (This can be explained by WSM5 being a more complex scheme, which contains five prognostic equations, and they can describe the cloud processes more realistically (Hong et al. 2004). Although WSM5 is a much more complex scheme describing more microphysical processes (Hong et al., 2004), it does not cause a clear improvement compared to the SUB4.3 microphysics scheme.

3.3 Comparing the convection schemes: Grell, Tiedtke and KF

Figure 3 depicts that the choice of the convection scheme causes substantial differences for the BIASrel. In general, simulations using Grell scheme overestimate the precipitation to the greatest extent, it can reach 100–120% in the mountainous area. In contrast, simulations using KF convection scheme underestimate the precipitation, mainly over the lowlands, where the underestimation is around 50–70%, however, using the WSM5-KF combination reduces the underestimation. This underestimation is observed by Gu et al. (2020) as well. Although, there are many studies about the sensitivity of convective precipitation schemes, the results depend on the studied region (e.g., Adeniyi 2019; Mishra et al. 2021; Li et al. 2023). For instance, Adeniyi (2019) found that Tiedtke and KF schemes are closer to the observations, while Grell scheme has dry bias over West Africa. According to Mishra et al. (2021) Grell showed better performance in simulating precipitation over India, while Li et al. (2023) concluded that KF scheme is the best in the upper reaches of the Yangtze River Basin.

Overall, Tiedtke scheme reproduced precipitation the best in our simulations compared to the other convection schemes. Furthermore, in the simulations where the Tiedtke scheme was used, the precipitation patterns are very similar to each other. This suggests that the Tiedtke convection scheme has a large impact on the precipitation compared to other schemes (land surface, PBL, microphysics).

3.4 Comparing the PBL schemes: Holtslag and UW

The effect of the PBL scheme depends on the other schemes as well, but UW scheme tends to reduce the rather wet (01_BATS_SUB43_Grell_UW and 13_BATS_SUB43_Grell_HO) or dry biases (11_CLM_SUB43_KF_UW and 23_CLM_SUB43_KF_HO) of the Holtslag scheme (similar results were shown by Güttler et al. 2014 and Kalmár et al. 2021). The reduction of precipitation errors is mainly observed in lowland areas, while in mountainous areas the effect of the choice of the PBL scheme is less. The reduction could be related to the fact that the UW PBL scheme increases the cloud cover, and thus, reduces net surface shortwave flux resulting in a decrease of the near-surface temperature, which affects precipitation indirectly (Güttler et al. 2014).

Fig. 3
figure 3

The relative mean precipitation bias (BIASrel, %) of the RegCM simulations for 2010. The different parameterization schemes occur as follows: land surface schemes (BATS: columns 1 and 2; CLM4.5: columns 3 and 4), microphysics schemes (SUB4.3: columns 1 and 3; WSM5: columns 2 and 4), convective schemes (Grell: rows 1 and 4; Tiedtke: rows 2 and 5; KF: rows 3 and 6), and finally PBL schemes (UW: rows 1–3; Holtslag: rows 3–6). Reference: CarpatClim (2010)

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So, to sum up the above detailed comparisons, the RegCM is sensitive to the choice of parameterization schemes. In addition, the WSM5–UW combination causes especially problematic interaction, which results in difficulties in the analysis. However, the effect of topography is evident in the precipitation BIASrel of all simulations; in general, higher precipitation values occur in mountainous areas, whereas less precipitation occurs in lowlands. It is well-known that increasing (decreasing) altitude is associated with increasing (decreasing) rainfall (Saavedra et al. 2020). Previous studies showed that the precipitation simulation by RegCM exhibits a significant systematic bias (Oh and Suh 2018), especially in mountainous areas (Gao et al. 2017; Huang et al. 2020; Li et al. 2023).

Fig. 4
figure 4

The soil moisture content (mm) in 2010. The different parameterization schemes occur as follows: land surface schemes (BATS: columns 1 and 2; CLM4.5: columns 3 and 4), microphysics schemes (SUB4.3: columns 1 and 3; WSM5: columns 2 and 4), convective schemes (Grell: rows 1 and 4; Tiedtke: rows 2 and 5; KF: rows 3 and 6), and finally PBL schemes (UW: rows 1–3; Holtslag: rows 3–6)

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3.5 Clustering results

To determine which type of scheme has the most substantial effect on the BIASrel fields, we performed hierarchical clustering of the values of the Box-Whiskers diagrams derived from the error fields. As it was mentioned earlier, only 19 RegCM simulations were analysed in this part of the study.

Figure 5 shows that the choice of the convection scheme played an important role in the formation of clusters (except 22_BATS_WSM5_KF_HO). All of the simulations using the Grell convection scheme overestimate the precipitation (with 50%) with large spatial variation. Simulations with the Tiedtke convection scheme overestimate the precipitation as well, but with a smaller spatial variation than the Grell simulations. Simulations that include the KF convection scheme also form a cluster, with the exception of 22_BATS_WSM5_KF_HO. These simulations tend to underestimate the precipitation with 30–40%. The other scheme types do not affect the clusters substantially. Since the convection is one of the major sources of cloud, and thus, precipitation formation, this result can be expected. However, it is interesting that besides the convection scheme, the microphysics scheme does not contribute a similar part in determining the precipitation bias. Overall, this implies a greater uncertainty in the convection schemes compared to the microphysics schemes.

Fig. 5
figure 5

Box-Whisker’s diagrams for the BIASrel values from Fig. 3. The three different colours indicate the individual clusters

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3.6 Ensemble mean of the RegCM simulations

BIASrel (Fig. 6a), RMSE (Fig. 6b) and temporal correlation coefficient (rt, Fig. 6c) values were also calculated for the ensemble mean of the 19 RegCM simulations to get a robust estimate of the fine scale precipitation pattern. These indicator values depend on the topography mainly: precipitation is underestimated in the lowland areas, while in the mountain areas there is an overestimation. The biggest differences between the ensemble mean and the CarpatClim occur in the mountainous areas where the ensemble mean overestimates precipitation by an average of 70%. Furthermore, in some areas (e.g., Făgăraș Mountains) the overestimation can reach 150%. The topography smoothing in RegCM, due to which high mountain peaks are not represented correctly, may account for this large difference (Kyselý et al. 2016). The RMSE values (Fig. 6b) in mountainous areas can reach 8 mm/day (even 12 mm/day in the Făgăraș snowfields), while RMSE values in lowland areas are around 4 mm/day. However, temporal correlation coefficients do not show such a strong dependence on elevation (Fig. 6c). The highest values (around 0.8) appear in the Tatra Mountains and the western part of the domain, whereas the lowest (around 0.3) correlation coefficients are in the Southern Carpathians. It is possible that the higher values occur in these areas because the station density in CarpatClim is high over the Tatra Mountains, so it is more reliable over these areas, while there are fewer stations used to create in the CarpatClim in the southern Carpathians (Kalmár et al. 2023). On the other hand, in the western areas and mountainous regions, the large-scale flows and the orographic lift have a greater influence on precipitation values. In contrast, surface-atmosphere processes are more pronounced in lowland and so the eastern part of the study area.

Fig. 6
figure 6

The BIASrel, RMSE and temporal correlation coefficient (rt) of the ensemble mean of the 19 RegCM simulations. Reference: CarpatClim (2010)

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In addition, we calculated the uncertainty (S) where we used only 19 RegCM simulations. Figure 7 shows that higher values can be found in the mountainous areas with an average of 2.4 mm/day, and the highest values occur in the Făgăraș Mountains, reaching up to 3.6 mm/day. The lowest S values appear in the lowland area where they are below 0.8 mm/day. Thus, the pattern of S depends on the elevation, the spatial correlation coefficient between S and the elevation of RegCM is 0.72, which is considered a high value. One of the possible explanations is the diversity of the applied parameterization schemes that all affect precipitation on fine scale. Another likely factor is related to the higher precipitation in the mountains compared to the drier lowlands (e.g., Saavedra et al. 2020; Napoli et al. 2019, 2022; Liang-Liang et al. 2022).

Fig. 7
figure 7

The spatial distribution of uncertainty (S, mm/day) of the 19 RegCM simulations (2010)

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3.7 Annual cycle of the precipitation and daily precipitation

As the previous Sect. (3.1–3.6) show, topography plays a substantial role in the performance of simulations. For this reason, the annual cycle of precipitation for the two selected subregions (Tatra Mountains and Great Hungarian Plain, Fig. 1) is also investigated (Fig. 8). For both subregions, most simulations capture the annual cycle well. The largest variability between simulations occurs in summer, with up to 200–250 mm/month between the driest and wettest simulations for both regions. This large summer variability also indicates that the convective precipitation scheme is the most dominant factor of the forming of the precipitation.

In general, the simulations using the KF convection scheme underestimate precipitation, while simulations using the Grell scheme overestimate the annual precipitation cycle in both subregions. Simulations using the Tiedtke scheme reproduce the best the values of CarpatClim observational dataset. More specifically, the ensemble mean underestimates the reference CarpatClim in the lowland area (Fig. 8a), while it overestimates precipitation in the Tatra Mountains (Fig. 8b). The LBCs data, i.e., ERA-Interim is close to the observation, but still underestimates the CarpatClim values in both regions. The ensemble mean for the lowland area underestimates the CarpatClim values by 20–30 mm/month for almost the whole year. In the Tatra Mountains, however, there is a clear overestimation (20–30 mm/month), especially in late spring and early summer.

Although the maximum rainfall occurred in May in almost all simulations (except 13_BATS_SUB43_Grell_HO and 14_BATS_WSM5_Grell_HO) and according to CarpatClim as well, some of the simulations using the Grell convection scheme result in a substantial secondary maximum in July in the Tatra Mountains (simulation 13_BATS_SUB43_Grell_HO), which is less present in CarpatClim.

Fig. 8
figure 8

The annual cycle of the precipitation over the Great Hungarian Plain (a) and Tatra Mountains (b). The numbers indicate the individual RegCM simulations, which are summarised in Table 2. The colour shades of the lines indicate the different convective schemes: shades of blue (Grell), pink (Tiedtke), and green (KF) are related to convection parameterizations. ERAI represents ERA-Interim reanalysis, ENS is the ensemble mean of the 19 RegCM simulations, while CC indicates CarpatClim observational dataset. Reference: CarpatClim (2010)

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Based on the Taylor diagram (Fig. 9), the simulations using the Grell scheme are the furthest from CarpatClim with mostly higher standard deviation, higher RMS difference, and in the case of the Great Hungarian Plain with generally lower correlation coefficients. However, most simulations using the Tiedtke convection scheme result in very similar values of correlation (around 0.8) and standard deviation, which is only slightly greater than for the CarpatClim, especially in the Tatra Mountains. Most simulations using the KF convection scheme result in very low standard deviation ratio relative to CarpatClim, generally below 0.8, and it can be as low as 0.3 (in the case of 23_CLM_SUB43_KF_HO), the correlation values are quite diverse, from 0.4 (23_CLM_SUB43_KF_HO) to 0.8 (22_BATS_WSM5_KF_HO). Simulations using the Tiedtke convective scheme perform better than the other convective schemes where the simulations have similar characteristics otherwise (correlation coefficients are around 0.8 or above, standard deviation values are between 0.95 and 1.2). The correlation and the standard deviation of the ensemble mean are slightly worse than the ERA-Interim values, which implies that the dynamical downscaling does not result in any improvement compared to the driving ERA-Interim reanalysis.

Overall, the simulations better reproduce the CarpatClim in the Tatra Mountains, even though the overestimations are larger there than the underestimations in the lowlands. This is due to the fact that in mountainous areas the orographic effects are present and act as a constant forcing to form clouds and precipitation. In contrast, land use and PBL processes have a greater influence and add more variability on the precipitation in lowland areas than in the mountains.

Fig. 9
figure 9

The Taylor diagram of RegCM simulations for daily precipitation over the Great Hungarian Plain (GHP) and Tatra Mountains (TM). The numbers indicate the individual RegCM simulations, which are summarised in Table 2. ERAI represents ERA-Interim reanalysis, ENS is the ensemble mean of the 19 RegCM simulations. Reference: CarpatClim (2010)

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3.8 Convective precipitation

The sum of the convective precipitation for the summer period (April-September) is shown for the individual RegCM simulations in Fig. 10, and for the ERA5, the ERA-Interim and the ensemble mean in Fig. 11 In general, similarly to total precipitation, the topography has a clear effect on the convective precipitation patterns in all simulations. More specifically, the effects of the different parameterization schemes are discussed below.

3.8.1 Comparing land surface schemes: BATS and CLM4.5

As seen for the total precipitation (Fig. 3), simulations using BATS land surface scheme results in higher convective precipitation values than simulations using CLM4.5 scheme, but the actual difference depends on the other types of physical schemes. For example, for simulations where the KF convection scheme was used, a difference of up to 150 mm in convective precipitation occurred between the BATS and CLM4.5 simulations (e.g., 22_BATS_WSM5_KF_HO and 24_CLM_WSM5_KF_HO), while for the simulations using the Tiedtke convection scheme, there are smaller differences (typically 50 mm, overall less than 100 mm) between BATS and CLM4.5.

Similar results were received by Chung et al. (2018) who showed that the values of Convective Available Potential Energy (CAPE) in the BATS was larger than in the CLM4.5, and thus, implied that the soil moisture has an important effect on the precipitation, which actually depends on the availability of the convective activities. Soil moisture influences the formation of convective precipitation via the release of latent heat flux; so higher surface soil moisture will release higher latent heat, humidifying the lower atmosphere and reducing the height of the mixing layer. This feedback causes the CAPE to increase and the convective inhibition to decrease, allowing a higher amount of convective precipitation to form. This high amount of precipitation formed later contributes to the higher amount of surface soil moisture content, forming a strong positive feedback loop. As Fig. 12 shows the evaporation values strongly depend on which land surface scheme is used. While the values for the simulations using BATS land surface scheme are around 4.5 mm/day, the evaporation values for the simulations using the CLM4.5 land surface scheme are around 2 mm/day. Bonan et al. (2012) showed that CLM has added to addressing an overestimation of forest and other inconsistencies in model physics causing a systematic decrease of the evapotranspiration, which causes a decrease of precipitation in CLM over BATS. Llopart el al. (2021) showed that evapotranspiration greatly influences summer precipitation in the target region.

3.8.2 Comparing microphysics schemes: SUB4.3 and WSM5

The comparison of the microphysics schemes shows that the WSM5 scheme produces higher convective precipitation values compared to SUB4.3 in most cases. Exception occurs when the Tiedtke convection scheme is used: the SUB4.3-Tiedtke combination generates higher values than the WSM5-Tiedtke combination (i.e., 17_BATS_SUB43_Tiedtke_HO and 18_BATS_WSM5_Tiedtke_HO). Note that the convective precipitation total in simulation 16_CLM_WSM5_Grell_HO can reach 1500 mm, which is much higher than in the other simulations. This may presumably be caused by a problematic interaction between the physical schemes, which is not visible when evaluating the total precipitation (Sect. 3.1–3.7).

3.8.3 Comparing convection schemes: Grell, Tiedtke and KF

Overall, the convective precipitation totals are well separated by convective precipitation schemes, which can obviously be expected. However, while the Grell convection scheme produces higher total precipitation values (Sect. 3.1), for convective precipitation, it is the Tiedtke convection scheme that generates higher values (by around 900–1000 mm). The difference between the simulations using the Grell convection scheme can be substantial: in some simulations (e.g., 15_CLM_SUB43_Grell_HO) the sum of the convective precipitation is around 500 mm, while in other simulations (e.g., 13_BATS_SUB43_Grell_HO) the convective precipitation is around 900 mm. This means that in the simulations using the Grell scheme, the other types of schemes (e.g., land surface, microphysics, PBL) also affect the values, and a stronger interaction should be present between the schemes compared to the other convection schemes. The simulations using the KF convection scheme are the driest regarding the convective precipitation, similarly to the total precipitation. The average convective precipitation in these simulations is 300–400 mm. Furthermore, in the case of the KF convective scheme, the choice of the surface scheme also plays an important role: in the case of the BATS-KF combination, the convective precipitation values are higher than in the CLM4.5-KF combination. The KF scheme is a mass flux convection scheme, which is determined by the amount of CAPE (Kain 2004). CAPE is influenced by the evolution of surface processes, such as soil moisture (Hohenegger et al. 2009). Soil moisture depends on the land surface scheme, so when using the KF convective scheme, the choice of the land surface scheme has a great impact on the amount of convective precipitation.

3.8.4 Comparing PBL schemes: Holtslag vs. UW

The choice of PBL scheme has less impact on the amount of convective precipitation and is highly dependent on the choice of other scheme types, especially on the convection scheme. More specifically, the comparison of simulations differing from PBL schemes leads to the following results: (i) Higher convective precipitation values occur with the Grell-UW combination than with the Grell-Holtslag combination. (ii) There is no difference between the Tiedtke-UW combination and the Tiedtke-Holtslag combination. (iii) Convective precipitation values are about 5–10% higher with the KF-UW combination than with the KF-Holtslag combination. The two PBL schemes treat the moisture differently (Güttler et al. 2014), and the KF convection scheme takes into account the processes in the PBL to a greater extent to trigger convection (Kain et al. 2003) than the other convection schemes (Adeniyi 2019).

In addition, all the problematic simulations used the UW PBL scheme, which makes the whole comparisons difficult.

Fig. 10
figure 10

The sum of the convective precipitation (mm) in the summer half-year (April-September, 2010) from the individual RegCM simulations. The different parameterization schemes occur as follows: land surface schemes (BATS: columns 1 and 2; CLM4.5: columns 3 and 4), microphysics schemes (SUB4.3: columns 1 and 3; WSM5: columns 2 and 4), convective schemes (Grell: rows 1 and 4; Tiedtke: rows 2 and 5; KF: rows 3 and 6), and finally PBL schemes (UW: rows 1–3; Holtslag: rows 3–6)

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For the ERA-Interim, the dependence on topography is less noticeable due to the coarse horizontal resolution (0.75°), but the convective precipitation values are around 400 mm in the western part of the domain, and around 600 mm in the eastern part (Fig. 11). Similar values occur in ERA5, but the finer resolution (0.25°) makes the effect of topography more pronounced. The ensemble results in slightly (by 100 mm on average) higher values compared to the reanalyses. The simulations with the BATS-KF scheme combination are the closest to the reanalyses. This is interesting because the two reanalyses calculate the convective precipitation using convective parameterization with a modified version of the Tiedtke scheme (Hersbach et al. 2020).

Fig. 11
figure 11

The sum of the convective precipitation in the summer half-year season (April-September, 2010) for the ERA-Interim reanalysis (ERAI), the ERA5 reanalysis (ERA5) and the ensemble mean of the 19 RegCM simulations (ENS).

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Fig. 12
figure 12

The evaporation (mm/day) in the summer half-year (April-September, 2010) from the individual RegCM simulations. The different parameterization schemes occur as follows: land surface schemes (BATS: columns 1 and 2; CLM4.5: columns 3 and 4), microphysics schemes (SUB4.3: columns 1 and 3; WSM5: columns 2 and 4), convective schemes (Grell: rows 1 and 4; Tiedtke: rows 2 and 5; KF: rows 3 and 6), and finally PBL schemes (UW: rows 1–3; Holtslag: rows 3–6)

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3.9 Annual cycle of convective precipitation and daily convective precipitation

Figure 13 shows the annual cycle of convective precipitation for the Great Hungarian Plain and the Tatra Mountains specifically. For both subregions, the simulations using the Grell or the Tiedtke convection scheme overestimate ERA5 reanalysis in general, while simulations using the KF scheme underestimate ERA5. While the simulations using the Grell scheme overestimated the total precipitation by the largest amount, the simulations using the Tiedtke scheme overestimated the convective precipitation by the largest amount in the whole time period. This implies that the Grell scheme produces more large-scale precipitation whereas the convective processes are more emphasised with the Tiedtke scheme generating overall more convective precipitation in the whole domain.

Overall, the simulations using the Tiedtke scheme reproduce the annual cycle of ERA5 the best in both subregions despite the general overestimation. This can be explained by the fact that ERA5 also uses the Tiedtke convection scheme (although a slightly modified version) to calculate the convective precipitation (Hersbach et al. 2020).

In addition to the maximum convective precipitation in May, the Grell convection scheme produces a secondary maximum in July (up to 230 mm/month) in the Tatra Mountains. Presumably, this high convective precipitation caused by the Grell scheme resulted in the large overestimation of the total precipitation in July (Fig. 8) as well.

The ensemble mean is relatively close to the ERA5 values, but while lower values occur in the Great Hungarian Plain subregion, the ensemble mean in the Tatra Mountains overestimates the ERA5. The ERA-Interim shows a similar annual cycle to ERA5 with around 20 mm/month underestimations in both subregions.

Fig. 13
figure 13

Annual cycle of convective precipitation over the Great Hungarian Plain (a) and Tatra Mountains (b). The numbers indicate the individual RegCM simulations, which are summarised in Table 2. The colour shades of the lines indicate the different convective schemes: shades of blue (Grell), pink (Tiedtke), and green (KF) are related to convection parameterizations. ERAI represents ERA-Interim reanalysis, ENS is the ensemble mean of the 19 RegCM simulations, while ERA5 indicates ERA5 reanalysis. Reference: ERA5 (2010)

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Based on the Taylor-diagram for daily convective precipitation (Fig. 14), the correlation values are high (mostly between 0.6 and 0.8) for most simulations. In general, the characteristics of the convective precipitation are similar to the total precipitation for both subregions. More specifically, the simulations using the Grell scheme are the most diverse in terms of standard deviation. Furthermore, the simulations using the Tiedtke scheme are close to each other (for both subregions separately) and have high correlations (even as high as 0.8), but the standard deviation of the simulations is higher than in the ERA5. Finally, most of the simulations using the KF scheme result in lower standard deviation (except 09_BATS_SUB43_KF_UW over Tatra Mountains) than the ERA5.

Fig. 14
figure 14

Taylor-diagram of RegCM simulations for the daily convective precipitation over the Great Hungarian Plain (GHP) and Tatra Mountains (TM). The numbers indicate the individual RegCM simulations, which are summarised in Table 2. ERAI represents ERA-Interim reanalysis, ENS is the ensemble mean of the 19 RegCM simulations. Reference: ERA5 (2010)

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ERA-Interim is very close to ERA5, where the correlation is around0.9 and a standard deviation is 0.8 for both subregions. The ensemble mean is better in the Tatra Mountains than in the Great Hungarian Plain for both correlation (0.85 vs. 0.79) and standard deviation (1.0 vs. 0.78).

3.10 The Convective-To-Total precipitation (CP/PR) ratio

Figure 15 shows the CP/PR ratio for the 19 RegCM simulations for the summer half-year (April-September). Previous studies (i.e., Kyselý et al. 2016) show that this ratio ranges 30–40% in spring (MAM) and 50–60% in summer (JJA) in Central Europe. The results show that the convective precipitation scheme influences the CP/PR ratio to the greatest extent, similarly to the results of Nguyen-Xuan et al. (2020). In the simulations using the Grell convection scheme, the CP/PR ratio is around 50% on average, while in the simulations using the Tiedtke scheme the ratio can reach up to 90%. This latter one is an extremely high ratio implying that most of the precipitation falls due to convective processes in the simulations using the Tiedtke scheme. Despite the overall dominance of convective precipitation, 90% seems unrealistically high in the target domain. In the case of the Grell convective scheme, the lower CP/PR ratio (~ 30%) may be caused by the fact that the activation of the Grell convective scheme is difficult, so the moisture in the atmosphere is used by the microphysics scheme. Previous studies (Gochis et al. 2002; Zanis et al. 2009; Mishra and Dubey 2021) also found that the Grell convective scheme causes an underestimation of the convective precipitation compared to other convective precipitation schemes (such as Tiedtke, Kain-Fritsch) in the RegCM.

In the simulations using the KF convection scheme, the CP/PR ratio also depends on the choice of the microphysics scheme, more specifically, the ratio reaches 90% in the KF-SUB4.3 combination, while an average ratio of 40% appears in the WSM5-KF combination. The activation of KF convective scheme and the development of the convective clouds depend on the vertical velocity (Kain 2004). Microphysics schemes have an important role in estimating latent heat release from cloud formation and dissipation (Dudhia 1989), which affects vertical velocity and convection as well. Latent heat transfers related to condensation, evaporation, deposition, sublimation, freezing and melting processes are taken into account by microphysics schemes in different ways depending on their structure (Halder et al. 2015; Reshmi Mohan et al. 2018). The two applied microphysics schemes (SUB4.3 and WSM5) are different, so it affects the vertical velocities and the activation of KF convective scheme as well.

The land surface scheme has a small effect on the CP/PR ratio. In general, higher (5–10% on average) values were obtained using CLM4.5, but the ratio mainly depends on the other physical schemes. The PBL scheme also affects the CP/PR ratio, namely, the Holtslag scheme slightly (10%) increases the CP/PR ratio compared to the UW scheme. Finally, the effect of the microphysics scheme is not entirely clear, although in most cases the SUB4.3 scheme increases the CP/PR ratio compared to the WSM5 scheme, especially in the case of the SUB4.3-KF combination. This last comparison cannot be fully carried out due the fact that all of the highly erroneous simulations (Sect. 3.1–3.4) use the WSM5 microphysics scheme.

Fig. 15
figure 15

The convective-to-total precipitation ratio (%) in the summer half-year (April-September, 2010) from the individual RegCM simulations. The different parameterization schemes occur as follows: land surface schemes (BATS: columns 1 and 2; CLM4.5: columns 3 and 4), microphysics schemes (SUB4.3: columns 1 and 3; WSM5: columns 2 and 4), convective schemes (Grell: rows 1 and 4; Tiedtke: rows 2 and 5; KF: rows 3 and 6), and finally PBL schemes (UW: rows 1–3; Holtslag: rows 3–6)

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For both the reanalyses and the ensemble mean, the CP/PR ratio is around 50–60%, with higher values occurring in mountainous areas (Fig. 16). Among the simulations, overall, the simulations using the Grell convection scheme and the simulations using the WSM5-KF combination are the closest to the reanalyses. In another region, Li et al. (2023) found that the KF scheme had the best comprehensive simulation performance for precipitation over Yangtze River Basin.

Fig. 16
figure 16

The convective-to-total precipitation ratio (%) in the summer half-year (April-September, 2010) from the ERA-Interim reanalysis (ERAI), the ERA5 reanalysis (ERA5) and the ensemble mean of the 19 RegCM simulations (ENS).

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4 Summary and conclusions

In this study, we tested different parameterization schemes of the RegCM regional climate model version 4.7 for the Carpathian region. We analysed the precipitation for the year 2010, which was the wettest year in East-Central Europe since the beginning of the regular measurements. In the study, we tested schemes that had not been tested for this region before. The combinations of two land surface schemes, two microphysics schemes, three cumulus convection schemes and two planetary boundary layer schemes were tested, and simulated precipitation was evaluated against the CarpatClim observational data or the ERA5 reanalysis data.

In general, RegCM4.7 is sensitive to the choice of parameterization schemes. The simulations captured the main spatial distribution characteristics of precipitation and the annual cycle in selected subregions. Overall, almost all the scheme combinations resulted in common deficiencies in their precipitation simulations, namely a considerable wet bias in mountainous areas. The overestimation of precipitation in mountainous areas is a known problem of the RegCM in general, and was reported in different regions (e.g., Himalayas: Gao et al. 2017; Huang et al. 2020; Li et al. 2023; Alps: Smiatek et al. 2009; Carpathian region: Kalmár et al. 2021).

On the basis of the results, the following main conclusions can be drawn.

(1) Our results clearly show that the convection scheme is the most important factor of precipitation patterns among the different types of parameterization schemes. Simulations using the Grell convection scheme overestimate the precipitation (by more than 80%), while most simulations using the KF convection scheme underestimate (by around 30%) the precipitation. Although the simulations using the Tiedtke scheme also overestimate the precipitation values (by around 40%), however, they are smaller than the simulations using the Grell scheme.

(2) The effect of the land surface scheme on the precipitation is secondary: the BATS scheme produces a higher soil moisture content than CLM4.5, which indirectly affects the precipitation values and the whole hydrological cycle (e.g., Chung et al. 2018).

(3) The effect of microphysics scheme is less noticeable, and it depends on the other type of parameterization schemes.

(4) Convective precipitation totals are affected by the land surface scheme in addition to the convection scheme. More specifically, higher convective precipitation values occur when using the BATS land surface scheme compared to the CLM4.5 land surface scheme, which is due to higher soil moisture. Soil moisture influences evaporation by providing a source of water vapor to the atmosphere; drier soil leads to less evaporation due to limited water availability. Additionally, soil moisture affects convective precipitation by influencing the amount of moisture available for cloud formation and precipitation; wetter soil can enhance convective activity and increase precipitation rates, while drier soil can suppress convective processes and lead to decreased rainfall. The effects of the PBL scheme and the microphysics scheme are less important, and it is not clear whether the precipitation is overestimated or underestimated when using them in the scheme combinations.

(5) When examining convective-to-total precipitation ratio in simulations using the Tiedtke convection scheme, the ratio reaches 80% of the total precipitation sum in the convective period (April-September). This can be explained by the fact that the Tiedtke scheme is very easily activated compared to the other two convection schemes. The microphysics scheme also plays an important role when using the KF scheme: the ratio is around 90% with SUB4.3 and around 50% with WSM5. Since the Grell convective scheme is rarely activated, the moisture is used by the microphysics scheme. Previous studies (Gochis et al. 2002; Zanis et al. 2009; Mishra and Dubey 2021) have found similar results.

(6) The ensemble mean of the 19 RegCM simulations performs well for most indicators, which may be due to the fact that it smooths out the over- and underestimations of individual simulations.

(7) Overall, taking all results into account, the best simulations seem to be those that use the BATS-WSM5-KF combination over the Carpathian region.

To sum up, this study highlights the importance of analysing the influence of physical schemes (especially the convection schemes) in the RegCM regional climate model. Choosing a less appropriate scheme combination for a particular climatological study of a region or zone for a certain period may cause misleading results. It should be noted that we analyzed one specific year in this study, further extensions are planned for dry and normal years, however, they are out of the scope of this study. Although our investigations are limited to one year, differences still appear between the scheme combinations. The overall combination of parameterization schemes strictly depends on the RegCM version used, the study area, the period, and the variable under investigation.

Based on the simulation results, it is clear that convective precipitation is the main source of the largest uncertainty. Thus, to avoid this in the future, it is recommended to use simulations with an even finer resolution (1–3 km) than what we used here (even though it is computationally expensive), where the convective precipitation is determined by the model dynamics (i.e. convective permitting model simulation), and not by the parameterization schemes (which is considered to be overall less precise).