Introduction

River floods serve as major natural hazards in Europe, both in a social sense and an economic sense (Kundzewicz 2012; Kundzewicz et al. 2016; Paprotny et al. 2018). Given the increasing number of highly populated areas in the world, river floods are considered costly natural disasters (Madsen et al. 2014; Paprotny et al. 2018).

The central part of the continent experiences floods caused mainly by atmospheric precipitation and extended periods of rainfall in the summer. Atmospheric circulation serves as the main determinant of intense rainfall in this temperate part of the world. This subject is discussed relatively extensively in the literature. Most publications concern circulation patterns with dangerous effects of high rainfall totals highlighting that mountain areas are particularly prone to flooding, environmental damage, economic losses, and the loss of human life. Orographic barriers complicate the convective systems; together with an extra supply of inflowing moist air the situation contributes to the occurrence of flood-producing precipitation (Schneidereit and Schär 2000; Ustrnul and Czekierda 2001; Niedźwiedź 2003; Brázdil et al. 2005; Niedźwiedź et al. 2009, 2015; Wypych et al. 2018a; Ustrnul et al. 2023). The unique characteristics of mountain catchments affect the local hydrology. Floods in mountain basins used to be accompanied by several processes coupling between hillslopes and channels (Stoffel et al. 2016). Mountain basins often respond rapidly to intense rainfall having high slopes and a quasi-circular morphology resulting in strong connectivity (Ruiz-Villanueva et al. 2010; Hlavčová et al. 2016; Bryndal et al. 2017; Bryła et al. 2021; Bezák et al. 2023).

Moreover mountain catchments are most susceptible to potential climate change due to characteristics that favor rapid discharge as well as due to the immense sensitivity of mountain ecosystems to changes in temperature (Birsan et al. 2005; Lukasová et al. 2023). Together with changing climate conditions, the water holding capacity (and the water content) of the atmosphere has been modified. Precipitation characteristics, as intensity, duration, or timing which are essential in shaping flood hazard, undergo the changes (Wyżga et al. 2016; Górnik et al. 2017), affecting local hydrological processes (Mudelsee et al. 2003; Mostowik et al. 2019; Holko et al. 2020; Muelchi et al. 2021a, 2021b; Siwek et al. 2023).

Although climate projections show general warming and increase in water vapor, precipitation scenarios show strong regional differences, especially for precipitation extremes, of relevance for flood hazard (Kundzewicz et al. 2006; Pińskwar et al. 2017). If heavy precipitation or the proportion of total rainfall from intense events increases, an increase of the magnitude and frequency of floods will be recorded. The projections, however, are largely uncertain (Arnell and Gosling 2016; Prein et al. 2016; Gadian et al. 2018).

Due to physical processes in the atmosphere, large-scale models project the increase in summer precipitation as well as the amount and frequency of extremes (Christensen and Christensen 2004). However, the review of trend analysis and projections of extreme precipitation and floods in Europe performed by Madsen et al. (2014) confirms their seasonal and regional differentiation. Regional studies prove complex and nonuniform spatial patterns of extreme precipitation changes. Decreasing summer trends were detected for Central Europe: e.g., by Hänsel et al. (2008) and Łupikasza et al. (2011) for Germany, by Brázdil et al. (2021) for Czech Republic, or by Łupikasza (2010), Łupikasza et al. (2016), Pińskwar et al. (2019), and Łupikasza and Małarzewski (2021) for different parts of Poland. Positive trends have been observed in the UK but only since the beginning of the twenty-first century (Maraun et al. 2008) as in the twentieth century drier summer was recorded on the British Isles (e.g., Osborn and Hulme (2002), as well as NE Spain (Ramos and Martinez-Casanovas 2006). Incoherent results have been obtained also while studying mountainous areas (Micu et al. 2021). Drier summers but with increasing number of convective precipitation events are projected for the Southern Carpathians, while in winter all examined characteristics of precipitation show similar patterns of projected increases for the late twenty-first century compared to the recent climate (Gaál et al. 2014; Skarbit et al. 2022).

The findings presented in numerous studies affirm the heightened sensitivity of precipitation trends to the specific time frame under consideration.

As already provided with references, spatial pattern of summer precipitation trend in Europe is very complicated and does not give any significant sign of changes in a continental scale (Frei et al. 2006; Niedźwiedź et al. 2009; O’Gorman 2015; Pfahl et al. 2017). This uncertainty results in a complex and difficult process of modelling the environmental response to precipitation-based indices. Although the increase in spatial resolution of precipitation data enables to access the regional weather patterns, for the mountain areas the models are still biased mostly due to the lack of long and dense enough measurement series necessary for complex topography.

The purpose of the paper is to assess the long-term variability of extreme precipitation events across the Carpathian region in Poland in the context of ongoing climate change and its possible impact on extreme hydrological phenomena.

Study area

Southern Poland largely consists of the Carpathian Mountains and their piedmont areas. It is an important geographic area for the formation of floods and high water levels. Frequent high precipitation and variable relief in the region affect hydrological events throughout most of Poland. The main problem consists of floods in the warm part of the year (May–October) caused by intense atmospheric precipitation (Kundzewicz et al. 2012; Kundzewicz et al. 2014; Kundzewicz et al. 2017; Twardosz et al. 2016; Wypych et al. 2018a; Ustrnul et al. 2023).

The Polish Carpathians are a major part of the Western Carpathians and a small part of the Eastern Carpathians. The mountain range is located in southern Poland in the upper Vistula river basin (Fig. 1A). This area stretches about 330 km east to west and has a surface area of about 20,000 km2, which includes its piedmont region. The highest peaks exceed 2000 m above sea level.

Fig. 1
figure 1

Study area: (A) the Polish Carpathians in Europe, (B) location of meteorological gauging sites and water level gauges in the study area (catchment numbers as in ESM – Table 1)

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Extreme precipitation constitutes a hydrological hazard in the Carpathians themselves due to variable relief and poor parent material permeability. Mountain catchments in the region are quite short and form a dense network of rivers and streams, smaller in the southern part due to the higher permeability of soils and geological formations (Pociask-Karteczka 2016).

Very steep and relatively narrow river valleys also help contribute to the occurrence of extreme hydrological events in the Polish Carpathian region. In addition, flood wave concentration times are short and flood waves are relatively high (Dynowska 1995).

The core of the mountain range consists of a crystalline massif that includes limestone. This type of parent material is characterized by relatively high infiltration due to highly porous debris cones on crystalline slopes and karst water circulation in limestone, which helps retard discharge. However, the largest part of the Carpathians (except for the internal part) consists of flysch characterized by low water storage capacity. Variable relief in the region along with intensive land use yields powerful flash floods in the Outer Carpathians. Maximum unit runoff from the flysch part of the mountain area may be similar to that in the Tatra Mountains—a high crystalline massif—despite lower precipitation (Kundzewicz et al. 2014, 2017).

In a climatological sense, the Polish Carpathians are characterized by typical “mountain” rainfall and temperature conditions as well as spatial variances due to latitudinal changes in relief and elevation. The 0 °C isotherm of mean annual air temperature runs at an elevation of about 1850 m in the Tatra Mountains (highest range). Without appropriate precipitation conditions, this makes permanent snow cover and ice cover impossible. Temperatures in the cool half of the year do guarantee the presence of snow, especially at higher elevations in the Tatras and elsewhere. The snow cover leads to a pluvio-nival hydrological regime among Carpathian rivers.

Annual atmospheric precipitation totals as well as daily extreme values also vary spatially in the region (Cebulak et al. 2000). The western part of the study area experiences oceanic effects via higher precipitation totals Most rainfall is recorded in the warm half of the year across the entire study area (Fig. 2A). This characteristic distribution of rainfall together with higher elevations yields the fact that Western Carpathian tributaries of the Vistula River contribute much more discharge than their eastern Carpathian counterparts. A few days-long rainfall with the precipitation totals amounting to a few hundred millimeters results in floods encompassing the whole or a considerable part of the Polish Carpathians and even the whole Upper Vistula Basin. The eastern part, with lower elevations and more continental climate, is characterized by rare occurrence of large floods caused by summer rainfall.

Fig. 2
figure 2

Warm period (May–October) precipitation totals in the Polish Carpathians: (A) long-term mean (1951–2022); anomalies of future projections 2026–2060 (multimodel ensemble with respect to the 1991–2020 period): (B) RCP 4.5, (C) RCP 8.5

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It is important to note that the Polish Carpathians form a significant orographic barrier in Europe, particularly relevant during the warmer half of the year. In cyclonic conditions, the advection of humid air from the north produces a windward effect (Mudelsee et al. 2004). This phenomenon is especially pronounced under Vb trajectory conditions, which bring moist and warm air from the Mediterranean into the cooler continental interior. As the air mass ascends over the Carpathian mountain ranges, it leads to intense precipitation. Sustained heavy rainfall, with rates of 100–300 mm per day, results in elevated water levels in Carpathian rivers, often causing severe flooding events (Niedźwiedź et al. 2009, 2015; Ustrnul and Czekierda 2009; Wyżga et al. 2016; Wypych et al. 2018a; Ustrnul et al. 2023).

The previously described characteristics of the Carpathian part of the upper Vistula river basin yield the highest risk of flooding in Poland despite the presence of more than a dozen reservoirs designed to reduce flood risk.

Eight catchments were selected for the purpose of this paper—each from a different part of the Carpathians (ESM – Table 1, Fig. 1B). The list of catchments includes—from west to east—Soła, Skawa, Raba, Dunajec, Biała, Wisłoka, Wisłok, and San.

The catchments selected for this study are located in various physical geographic regions of the Polish part of the Carpathian Mountains. Some catchment characteristics can be described using numerical parameters. In addition to climate issues, key parameters that affect discharge are morphometry, catchment geometry, land use, and parent material permeability. Catchment surface area directly affects runoff volume (ESM – Table 1). Catchment elevation and slope exposure do not directly affect runoff, but do affect climate conditions (precipitation, temperature, evaporation) that affect runoff.

Although the highest amount of summer precipitation as well as extreme daily areal precipitation and other parameters is recorded in Dunajec catchment (Table 1), the most elevated (ESM – Table 1), the absolute discharge for the period under consideration occurred at Żywiec water gauging site (Soła catchment), characterized also by other hydrological extremes (Table 1) due to the highest catchment gradient (ESM – Table 1). Presented catchment hydroclimate conditions confirm the previously described predominance of western part of the Polish Carpathians in flood formation. The Carpathians are characterized by the strongest hydrological dynamics in Poland. This is the outcome of interactions between the local climate, elevation, and relief.

Table 1 Main characteristics* of precipitation totals and water resources in summer half-year (May–October) in the selected Carpathian basins
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Carpathian rivers are characterized by fast circulation of water and are recharged by atmospheric precipitation in the summer and the melting of snow in the spring. Precipitation-based floods are typical of the region, especially its western part. Snowmelt-based floods are also typical, especially in the eastern part of the Carpathians in Poland.

Materials and methods

The paper is based on both meteorological (including rainfall) and hydrological (discharge) data for an over 70-year period: 1951–2022 obtained from the Institute of Meteorology and Water Management–National Research Institute. This is the longest time period for which both rainfall and discharge data are available for the entire study area. In addition, although the primary recharge regime in the Polish Carpathians is a pluvio-nival regime, only the warm part of the year (May–October) was analyzed as mostly prone to extreme precipitation events also followed by flooding.

The primary source of meteorological data consisted of daily precipitation totals obtained by weather stations and climatological research sites as well as rainfall gauging sites located in selected catchments (Fig. 1B). A total of 23 stations and sites contributed data to this paper. The data with monthly resolution were checked for homogeneity using the standard normal homogeneity test (SNHT) developed by Alexandersson (1986). In light of the focus of the study on extreme events, any detected examples of heterogeneity were subjected to weather-dependent analysis in order to avoid smoothing effects of daily data (WMO 2016). In addition to in situ data, the precipitation totals from E-OBS database were also used in the study with spatial resolution of 0.1° latitude and longitude (Cornes et al. 2018, v28.0e, https://cds.climate.copernicus.eu)—it constitutes a valuable supplementary source of precipitation data for areas not adequately covered by meteorological stations.

Meteorological information was verified using atmospheric precipitation data as well as snow cover data for selected events. The snow cover data included snow amounts and snow water content—where possible. Air temperature data were also used for verification purposes. The supplementary data were used to analyze cases where high recorded discharge was coupled with a substantial lack of precipitation in a predetermined, preceding period of time. In some cases, no precipitation had been recorded. This type of analysis was only needed for discharge in May when high river discharge can be explained by abrupt melting of the snow cover at higher elevations. This is especially true of the Dunajec catchment, which collects water from the highest elevations in the Carpathian Mountains—i.e., the Tatra Range (Fig. 1A).

The hydrological data, used to define the role of precipitation extremes in flood events, include daily discharge values for 1951–2022 for eight water gauging stations in the analyzed catchments: Soła, Skawa, Raba, Dunajec, Biała, Wisłoka, Wisłok, San. Eight water gauging sites were selected based on data availability. Each site covers a major river in the study area. The selected catchments feature an undisturbed runoff regime (Fig. 1B). This was not an easy task due to the large number of reservoirs in the Carpathian region. Most of the reservoirs are designed to reduce flood risk and produce a direct and significant impact on the natural relationship between atmospheric precipitation and river discharge. Given the strong human footprint in the region and the number of manmade structures along rivers, the quantity and quality of hydrological data will not improve in the years to come.

The future precipitation conditions for the period 2026–2060 were investigated based on the output from EUR-11 CORDEX experiments (Jacob et al. 2014, http://www.euro-cordex.net/). Driving General Circulation Models (GCMs) and the driven Regional Climate Models (RCMs) available in the repository were taken into account with daily temporal resolution including also driving ensemble members and validated regarding their representativeness for Central European climate characteristics (Meitner et al. 2023). Finally, 5 GCM-RCM model pairs were chosen as the best reflecting precipitation conditions in the region (no strong biases detected) (ESM – Table 2). Selected combinations were calculated for two greenhouse gas concentration trajectories: RCP 4.5 and RCP 8.5. The spatial resolution of the future projections is 0.11°.

The precipitation versus runoff relationship was estimated based on daily discharge data (Q) which were further used to calculate specific runoff (q) and runoff volume (V) for each catchment as well as on mean areal precipitation totals (RR) calculated for each studied catchment via the Thiessen polygon method using gridded data. Hypsometric methods could not be used due to the uneven distribution of grid points. The relationship was analyzed using daily precipitation totals (24 h – 1 day) and multi-day precipitation totals (cumulative totals from 48 h – 2-day, 72 h – 3-day, 96 h – 4-day, and 120 h – 5-day) via a moving time window.

The main part of the research study evaluates precipitation patterns with the special focus on the extremes in the Polish Carpathians in the context of present-day climate change. To distinguish the extreme events except for the grids, also daily totals from the stations were analyzed and the occurrence of extremes was noted based on existing work in hydrology (Robson and Reed 1999; Kundzewicz et al. 2005; Svensson et al. 2005) and meteorology (Groisman et al. 1999; Frei and Schär 2001; Klein Tank and Können 2003) using probability method with 90th and 95th percentiles of the thresholds of extreme events (respectively: RR90p, RR95p for precipitation and Q90p, Q95p for the discharge). This made it possible to analyze the frequency of extreme events and associated patterns over a period of over 70 years. Extreme precipitation thresholds (RR90p, RR95p) were calculated for the warm season within the whole period, i.e., 1951–2022 including the days with precipitation above 0.1 mm. The role of extreme precipitation events in seasonal precipitation totals as well as their long-term tendencies was also examined. Although the study focused on long-lasting rainfall (with respect to areal mean, cumulative totals), in addition, cases where extremely high daily totals (downpours) were noted and analyzed for several stations. Future projections were calculated for the whole study area with the special focus on selected catchments. Since high within-ensemble variability of projected precipitation has already been confirmed (Wypych et al. 2018b), uncertainty of the results needs to be stressed. To assess the range of the possible changes in precipitation amount, all five GCM-RCMs were taken into account, with particular respect to maximum and minimum of the results as well as multimodel ensembles for both examined RCPs 4.5 and 8.5.

It needs to be stated that only meteorological catchment attributes were considered in this study. These attributes are known to cause high water levels, especially in mountain areas due to local geology, relief, soil types, and vegetation. Atmospheric circulation was not considered in the study, although it is a direct cause of extreme precipitation, as shown by numerous other research studies. In effect, atmospheric circulation is responsible for extreme hydrological events. Since, according to the high variability of precipitation, spatial resolution of the research includes mostly mesoscale processes and the only parameter projected were monthly totals. Therefore, no further modelling was executed to project possible flooding frequency.

Results

A direct relationship between daily precipitation totals and discharge was discovered in the course of the study. In light of the delay in the precipitation-discharge reaction, precipitation series up to 7 days long were studied (period prior to discharge event). Hence, daily totals were studied individually for this period of time, as were cumulative totals for selected groups of days. These totals were then compared with daily discharge. Research has shown that most catchments exhibit a strong relationship between precipitation totals and discharge for the 2 days preceding a precipitation event. The correlation coefficient reached close to 0.7 in the studied catchments (0.55 to 0.76, Table 2). The coefficient appears to be high given that the discharge data were collected only once per day (06 UTC) for such a long period of time, and that no cumulative or mean discharge values are available for the predetermined intervals. An exception in this case is the Wisłok catchment, which exhibits the strongest relationship for at least 5-day precipitation totals. Catchment size is an issue in this case. The Wisłok catchment is more than twice the size of the other studied catchments. The precipitation versus discharge relationship is also affected by catchment morphometry (EMS – Table 1). Similar research results were obtained by Kostka and Holko (2002), Holko et al. (2006), Młyński et al. (2018a), and Holko et al. (2020) as well as Niedźwiedź et al. (2015) for the Tatra region alone.

Table 2 Relationships (Pearson’s correlation coefficient) between precipitation totals (RR) calculated for selected periods and the discharge in the selected Carpathian basins
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Runoff response time with respect to extreme precipitation events in small catchments in the Tatra Mountains in Slovakia is quite short at about one hour. Maximum discharge is observed about six hours following the event. Extreme discharge in larger catchments in the Polish Tatras was noted after three to five days following a precipitation event. Researchers consistently agree that the precipitation versus runoff relationship depends on the hydrological properties of the catchment including its saturation state and evapotranspiration rate, while elevation is perceived as less important (Sokol and Bližňá 2009).

Extreme cases

According to the precipitation-discharge relationship estimated in this research study, the 2-day precipitation amount (preceding discharge) is the most important variable to be subjected to further analysis (RR). Hence, 2-day precipitation events (totals) were identified above selected percentiles: 90th, 95th. These series became the basis for further analysis in the long term. A similar method was used to identify cases of extremely high discharge. The strength of the inferred relationships—given their resemblance of the normal distribution—was defined using the Pearson coefficient of correlation. Extremely high atmospheric precipitation was analyzed in relation with corresponding discharge. Calculations were performed for each catchment separately. Three of the studied catchments deserve particular attention due to their location in Poland as well as catchment characteristics (Fig. 1B, ESM – Table 1, Table 1)—Soła, Dunajec, and Wisłoka. These three catchments represent three different parts of the study area—western part, central part, eastern part. Research has shown that the precipitation-discharge relationship—in terms of noted hydrological extremes—in the western part of the study area is stronger (correlation coefficient > 0.70) than in its eastern part (correlation coefficient < 0.60). In addition, research suggests that discharge is affected not only by atmospheric precipitation, but also by selected catchment characteristics and the local network of rivers. Catchments characterized by lower atmospheric precipitation totals, but with large gradients and a dense network of rivers, are more likely to experience extremely high discharge: more than 800 m3s−1: Soła and more than 600 m3s−1: Biała (Fig. 3), which, having only shallow, slope aquifers, is characterized by the runoff-irregularity coefficient (the ratio of the highest and the lowest discharge on record) at one of the upper part of the catchment water gauge stations reaching 7500 (Stoffel et al. 2016). Figure 3 lists indirectly all extreme hydrological events in the Polish Carpathians in the last several decades: 1958, 1962, 1970, 1972, 1997, 2001, 2003, 2010. In addition, the relationship between precipitation and discharge becomes less substantial with increasing severity of the criteria used to define extreme events.

Fig. 3
figure 3

Relationship between precipitation extremes (RR > 95p) and discharge (Q) in the examined catchments (May–October)

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The aforementioned study noted an increased number of days with atmospheric precipitation in the 40 to 60 mm range, defined as low-risk precipitation, over the last 50 years. This increase is used to explain the increase in so-called small floods—exceeding the 75th percentile—in the High Tatras. The next step was to analyze relationships between predefined extreme events identified for each studied catchment. The differences between each studied catchment are small. In most cases, R values exceed 0.7 (ESM – Table 3).

The long-term pattern of extremes is also quite regular (Fig. 4). One key difference that can be observed is between catchments in the western part of the study area (Soła) and those in the eastern part (Wisłoka). This difference has already been noted in terms of the precipitation-discharge relationship. In the western catchments, there is substantial agreement between precipitation extremes and hydrological extremes. This is especially true of the following years: 1974, 1980, 1985, 1996. In these cases, approximately 40 events were noted with discharge exceeding the 90th percentile (Fig. 4). The largest number of such cases (60) was noted in 2010, with multiple days with very high water levels and flooding between May and July. The same four years (1974, 1980, 1985, 1996) included a number of extreme cases exceeding the 95th percentile. Extremes in the eastern part of the Polish Carpathians did follow a different pattern. Both analyzed variables follow a more synchronized pattern. In this region, the years with an exceptional pattern of extremes were 1974, 1980, 1997, and 2010. A similar pattern can also be noted in catchments in the western part of the Polish Carpathians.

Fig. 4
figure 4

Variability of the number of precipitation (RR) and hydrological (Q) extremes distinguished by the 90th and 95th percentile in selected catchments (May–October)

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The Dunajec catchment—found in the central part of the study area—is somewhat unique in terms of hydrological extremes producing the largest floods in the long history of the region. It includes the highest elevations in the Carpathian mountain chain—the Tatra Mountains. The catchment includes the northern slopes of the Tatras—an area that receives much more precipitation than the southern slopes of the Tatras located in Slovakia, due to circulation patterns in southern Poland (Niedźwiedź et al. 2015). The agreement between the number of days with extreme precipitation and that with extreme discharge is less consistent than it is in other catchments in the study area. The correlation coefficients calculated for the number of precipitation events and the number of hydrological events for the 90th and 95th percentiles range from 0.69 to 0.74. In most years, the number of extreme precipitation events is slightly higher than the number of extreme discharge events. Several years were identified when the number of hydrological extremes was much higher than the number of precipitation extremes (e.g., 1960, 1962, 1965, 1980, 1989, 2010). The one year that stands out even in this group of substantial discrepancies between extremes is 1965.

The explanation for this fact is somewhat complex. First, many cases of high discharge were noted in May when the snow cover in the Tatras is still thick, and air temperatures are high, which leads to rapid melting of snow. In some cases, high discharge events were caused by a combination of rainfall and the melting of snow. Another factor that also contributes to high river discharge at higher elevations is groundwater flow patterns. The geology of the Western Tatras and Bielskie Tatras includes a very large share of limestone and dolomite characterized by karst features and substantial groundwater flow (Dynowska 1995). The Dunajec catchment then receives part of this groundwater supply in periods without rainfall. Other smaller sources of water in this catchment include water trapped in rather thick alluvial and fluvioglacial layers of the local soil as well as water trapped in the catchment’s weathering cover.

In summary, a variety of factors weaken the precipitation-discharge reaction in the Dunajec catchment. The most important factors include groundwater recharge and the melting of snow in the spring season. These same factors also affect hydrological extremes in other catchments in the study area, but to a much smaller extent (Stoffel et al. 2016).

Relationships of this type between catchment characteristics, meteorological conditions, and discharge were previously analyzed, e.g., for the Swiss Alps (Weingartner et al. 2003; Birsan et al. 2005). In the study area in Poland, the areas most prone to flooding are middle elevations in mountain areas. Examples include the upper parts of the Soła and Skawa catchments as well as the Dunajec catchment as a whole. High-intensity rainfall and steep gradients play a key role in these areas. On the other hand, precipitation intensity plays a key role in flooding at lower elevations. This includes short periods of heavy rainfall or downpours. Flood risk is reduced above the precipitation inversion line along with decreasing precipitation amounts. Furthermore, some of the precipitation above this line is stored in the form of snow.

A closer look at all the data involved shows that years with substantial flooding in Poland (1970, 1972, 1997, 2001, 2003, 2010) were not unique in terms of the number of extremes, as identified using the percentile method in the context of precipitation and discharge. Research has shown that these years did not include a significant number of extreme events. On the contrary, there were fewer extreme events than usual, but the events that did occur were quite extreme in terms of precipitation and discharge. These extreme events recorded by most water level gauges and precipitation gauges may be easily observed only thanks to the use of the most severe of criteria in the extreme event identification process—precipitation totals over 100 mm and/or totals above the 99th percentile. However, the use of such severe criteria in the analysis of long-term data is not a good solution given a fundamental statistical problem—a very small sample of data.

Annual maxima

Given the already mentioned problem with statistical representativeness in long-term analysis (Groisman et al. 1999), only annual maxima were taken into consideration—maximum discharge and maximum 2-day precipitation totals for each studied catchment (areal analysis). Previously, research has shown the hydrological and meteorological diversity of the Polish Carpathians. In Western Carpathian catchments (represented by Soła and Dunajec, Fig. 5), annual maximum discharge was produced by maximum atmospheric precipitation (2-day totals) in most cases (over 60%).

Fig. 5
figure 5

Left panel: maximum 2-day extreme precipitation totals (RR, areal mean) and discharge (Q) in selected catchments (May–October). Right panel: seasonal (May–October) runoff totals (mm) and precipitation totals (mm) in selected catchments

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This percentage decreases from west to east in the Polish Carpathian mountain chain. The case of the Wisłoka River in southeastern Poland is unique in that it does experience a flood delay relative to precipitation due to the large size of its catchment area.

Long-term variability and future projections

The last stage of the study focused on long-term changes in seasonal precipitation totals and seasonal discharge totals in response to previous research results. The data show a clear lack of a relationship between precipitation extremes and hydrological extremes (Fig. 5); however, a relatively close relationship between precipitation and discharge in the Polish Carpathians at the seasonal level can be observed (Fig. 5). The corresponding correlation coefficient exceeds 90%, which helps explain the role of precipitation in the water balance of Carpathian catchments. It is important to note that maximum discharge varies much more substantially over the long term than does maximum atmospheric precipitation (Fig. 5). The coefficient of variance can exceed 100% in extreme cases (Biała, San), while in most cases, it exceeds 75%. Variances in precipitation maxima are much less pronounced at 30 to 50% (highest at 68%—Biała). In all catchments, there is no discernible trend over the 70-year study period.

Future projections for the period 2026–2060 calculated for two greenhouse gas concentration trajectories using 5 different GCM-RCM combinations show no spatial consistency. Five models ensembles demonstrate higher future precipitation totals than recorded at the end of twentieth century (Fig. 2B and C) for most of the Polish Carpathians region. The highest positive anomalies (up to 12%) are projected for the northern parts of Carpathian foothills whereas the central parts of the area under consideration, along Polish-Slovak border, e.g., the upper Biała river basin (Fig. 1B), may expect dryer warm half-year conditions (with respect to 1991–2020 period). The eastern part of the examined region will possibly get only 2–3% more rain in period 2026–2060. Higher precipitation totals are projected for RCP 8.5 scenario but the differences are almost neglectable. The highest discrepancy was calculated for Dunajec river basin (3.4%), farther on for Wisłoka (2.1%), Soła, San, and Skawa (2%) catchments.

The smallest contrast (0.3%) characterizes the driest Biała river basin. At the same time, RCP 4.5 scenario gives more inter-annual variability (Fig. 6). The range of warm half-year sums reaches 67 mm on average while for RCP 8.5, the mean max-min difference is about 50 mm. In spite of the mentioned differences, all the projected changes are statistically insignificant. Similarly is the trend in the number of days with extreme precipitation (Fig. 6).

Fig. 6
figure 6

Future projections of the warm season (May–October) precipitation totals (RR totals) and number of precipitation extremes (RR extremes) in selected catchments (areal mean, 5 models ensemble, and min-max whiskers)

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Despite the research resolution, the present study and the previous ones (Piniewski et al. 2016; Pińskwar et al. 2016; Romanowicz et al. 2016) confirm large inter-model and inter-scenarios differences. They refer not only to the magnitude of the tendency but even its sign. In general, as already described, the RCP 8.5 scenario is more rainy than RCP 4.5. However, for particular models and selected regions, the situation differs (Table 3). More precipitation has been projected by high pathway for the whole area of the Polish Carpathians while modelled by CLMcom using MPI-M-MPI-ESM-LR and CNRM-CERFACS-CNRM-CM5 GSM model (Table 3) whereas KNMI projects the less rain for RCP 8.5. Moreover, the other models give different results for distinctive catchments with no spatial pattern. It confirms that precipitation projections are associated with high uncertainty and if used to hydrological models they must be thoroughly validated and parametrized with local factors of very fine resolution.

Table 3 Summer half-year (May–October) precipitation totals (areal means of selected catchments) according to different GCM-RCM* model pairs and different RCP scenarios (2026–2060)
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Discussion and conclusions

Changes in precipitation totals in the Carpathians were discussed, e.g., by Cheval et al. (2014) and indirectly by Spinoni et al. (2013). The authors confirmed no spatial pattern in precipitation variability as well as the lack of statistically significant tendency in a region. Similar results were achieved by some local studies conducted for the Polish Carpathians or their foreland (e.g., Cebulak (1997); Niedźwiedź et al. (2015); Skowera et al. (2016); Łupikasza et al. (2016); Pińskwar et al. (2017); Młyński et al. (2018b); Wypych et al. (2018b)). No significant trends were detected in annual and seasonal precipitation totals as well as in frequency of precipitation extremes (RR ≥ 30 mm, RR ≥ 50 mm) which can be used as the index of flood favorable conditions. However, at some stations, slight decreasing tendency in precipitation totals has been signalized. Simultaneously, annual and seasonal changes in runoff were a subject of detailed analyses. A decrease of a different magnitude was reported for the area of Western Carpathians (Piniewski and Marcinkowski 2018; Mostowik et al. 2019; Górnik 2020; Siwek et al. 2023). The same trends were detected in the Swiss Alps (Muelchi et al. 2021a, 2021b) while contrarily Ruiz-Villanueva et al. (2010) detected weak upward trend in the discharge as well as flood magnitude in Central Spain or Didovets et al. (2019) in Eastern Carpathians.

No clear trend is observable in the Carpathian catchments examined over the period of 70 years. This is not surprising, as some research has already shown that variances in precipitation do not adequately explain long-term variances in discharge in mountain area catchments (Birsan et al. 2005; Borga et al. 2007; Hlavčová et al. 2016). In addition, the relationship between precipitation and discharge becomes less substantial with increasing severity of the criteria used to define extreme events. Similar results were obtained by Bičárová and Holko (2013) who analyzed the relationship between precipitation and discharge in the High Tatras along the Polish-Slovak border. Ruiz-Villanueva et al. (2010) and Hlavčová et al. (2016) indicate the need of deep analysis of terrestrial factors, especially human impacts, in a region to explain the variability of floods and emphasize that there is no possibility to extrapolate the trends into the future. Similar results were achieved by Piniewski et al. (2016) for the whole upper Vistula river basin while modelling hydroclimatic conditions, as well as Pińskwar et al. (2016) who projected future precipitation only for the northern foothills of the Tatra mountains (confirming also the increase in mean extreme precipitation) and Romanowicz et al. (2016) who projected flood hazard in particular headwater catchments of the Vistula river.

The research conducted primarily in the Western Carpathian region of southern Poland—a key region in the hydrology of the country—has shown very strong linkages between extreme precipitation events and extreme discharge events. This conclusion applies to the entire study area and all analyzed catchments. The precipitation-discharge relationship determined for the Polish Carpathians suggests that flood risk in this part of Poland will increase with changing precipitation conditions. As emphasized by Blöschl et al. (2017, 2019), changes in the annual distribution of precipitation totals followed also by the changes in their form (solid vs. liquid) as well as the variability of snow cover characteristics would be followed by trends not only in floods intensity but also in flood timing.

The analysis for the period 1951–2022 did not highlight any statistically significant trends related to precipitation extremes; however, due to the exceptional character of very rare events, these results need to be interpreted with particular carefulness (Frei and Schär 2001). Future projections do not give any univocal information about warm season precipitation conditions in the Polish Carpathians within the nearest decades, either. Moreover, there is a significant difference between climate models, even in a sign of changes, what confirms the difficulty in modelling hydrological conditions and emphasizes the uncertainty of their results (also Didovets et al. (2019)).

In the context of the key relationships determined in the course of the study, additional runoff factors need to be considered for the Polish Carpathians. However, it is becoming increasingly difficult to find “near natural” catchments where these types of studies could be conducted. The construction of reservoirs and the introduction of other flood management systems are needed to protect communities from flooding. However, this severely limits the areas where research can be conducted without all types of interference. In addition, both meteorological and hydrological data series are not yet fully homogeneous despite the use of increasingly advanced measurement devices. One potential solution to this problem is the use of grid databases. The analysis of areal averages for catchments with evenly distributed rain gauges has shown that in situ data are consistent with information obtained at grid points. Hence, it appears reasonable to use modelling data in situations where measured precipitation data are somehow inadequate.

Existing research on atmospheric precipitation and its effects on flood frequency does not yet provide an unambiguous answer to questions about change patterns. Numerous studies from various European countries generally confirm an increase in atmospheric precipitation totals in some parts of the continent. The knowledge about changes in precipitation extremes is very important for adaptation for future flood risk; however, the current precipitation-discharge relationships are not sufficiently able to predict with high accuracy the frequency of hydrological extremes.