The study area covers the mountain basin of the Hornad River in eastern Slovakia (Figure 1). There are 3 hydrological stations on the river: Spisska Nova Ves, Margecany and Kysak. Daily flow observations are made at these stations.

The catchment area of the Hornad river to the Kysak hydrological station is 2337.01 km2 and constitutes 55% of the total catchment area of the Hornad river. The river catch-ment is located at an altitude of 1549.9.7 m above sea level. Up to 235.1 m above sea level (Table 1).

In the structure of land use in the Hornad catchment, closed by the Kysak hydrological post, forest areas had the highest share (57.8% of the area), while arable land constituted only 18% of the basin area. Built-up areas occupied 3.4% (own calculations based on Corine 2018 (CLC, 2018). Over the years 1990–2018, the land use within the Hornad River catchment area has not changed significantly, with the exception of the catchment area enclosed by the Spisska Nova Ves hydrological post. The Spisska Nova Ves outpost closes the highest part of the Upper Hornad catchment area, the area of which is only 337.98 km². In 1990, forests covered 60.5% of the catchment area, while the area of arable land was 21.0%. In 2018, a change in land use is visible, as the share of forest areas decreased and accounted for 46.8% of the catchment area. The area of arable land, urban and industrial lands has increased. Details of use are shown in Table 2 and Figure 2.

The system of two water reservoirs, Ružín I and Ružín II, has a significant impact on the hydrological regime of the Hornád River. These reservoirs are located on the Hornad River between the Kysak and Margecany hydrological stations. The Ružín I and II reservoir system was built in 1963–1970, while its energy part was not fully operational until 1973. The system consists of two facilities: the Ružín I facility at km 78.35 of the river, which forms an accumulation reservoir, and the Ružín II facility at km 68.24 of the river, which forms an expansion tank that also enables the repumping of the processed streams. Ružín I consists of an accumulative reservoir, a stone dam with a height of 64.0 m and a hydroelectric power plant. The total capacity through the Ružín I barrage is 700 m³/s. There are two reversible Francis turbines installed in the power plant, operating in the gradient range from 30 to 52.7 m. The installed capacity of the hydropower plant is 60 MW, and the annual energy production is 136.0 GWh.

The power plant works in a pumped storage system. Ružín II has a 27 m high concrete dam that forms an expansion tank with a total volume of 3.7 million m³. The total capacity through the Ružín II barrage is 752 m³/s. The hydroelectric power plant operates continuously with one horizontal turbine, which operates in the range of slopes from 7.5 to 13.6 m. The installed power of this turbine is 1.9 MW. The task of the water reservoir is to equalise the flows caused by the operation of the pumped storage power plant at the Ružín I reservoir.

The variability of the flows of the upper section of the Hornad River was presented using data obtained from the Slovak Hydrometeorological Institute. The data included the daily values of flows obtained for three hydrological stations: Spisska Nova Ves, Margecany and Kysak from the hydrological years 1973–2020. Data on precipitation and air temperature were obtained from the website Intersucho (2022). Based on the daily values, monthly and annual values were calculated. The degree of volatility of flows in months and annual terms was carried out on the basis of the volatility of the Cv flows and the flashiness index, i.e., the Richard-Bakers Index (RBI), which characterises the short duration of the phenomenon. The flow variation index Cv was calculated as the standard deviation of all daily flow values divided by the average annual flow. The flashiness index proposed by Baker et al. (2004) was used to determine the rate of changes in short-term flows, which is called the RB Index (RBI) after the authors. R B   i n d e x = ∑ i = n n q i − q i − 1 ∑ i = 1 n q i

Where: q–average daily flow, i–day, n = 365 (366)

The RBI is a dimensionless index that ranges from 0 to 2 (Královec et al., 2016; Fiala et al., 2020). The index expresses how the flow changes between two units of time (days). Zero represents a constant flow, while a higher index value indicates increased flow frequency. Streams that rise and fall quickly are considered faster than those that maintain a smoother flow (Fongers, 2008).

In addition to the RBI index, the paper also calculated the trend of annual flows over a multi-year period, which is commonly used for the hydrological characteristics of rivers (Kliment and Matoušková, 2009; Zelenakova et al., 2014; Déry et al., 2016; Gudmundsson et al., 2021; Kubiak-Wójcicka et al., 2021; Nagy, 2021). The correlation coefficient r was used to determine the relationship between the RBI, Cv and flow rates. Statistical calculations were performed using the programme ‘R'.

The analysis of MK trends for precipitation, air temperature and flows is presented in Table 3.

The mean annual sum of precipitation in the Hornad River basin was 761.9 mm, while the average annual air temperature was 6.9°C during the multi-year period 1973–2020. The highest precipitations was recorded in 2010—1219.2 mm, while the lowest in 1993—541.9 mm. The distribution of precipitation during the year is highly diversified. The highest average monthly sums in the analyzed period were recorded in June (103.4 mm) and July (107 mm), while the lowest in January (32.3 mm) and February (34.5 mm). The greatest variability of monthly precipitation occurred in October. The hottest year was 2007 (8.6°C), while the coldest was 1996 (5.1°C). During the analysed multi-year period 1973–2020, a statistically significant upward trend in air temperature is visible (Figure 3; Tab. 3). The warmest months of the year are July and August (16.6°C), while the coldest is January (−4.0°C).

The course of the average annual flows of the Hornad River is shown in Figure 4. The average annual flow in the analyzed multi-year period at the Spisska Nova Ves hydrological station was 2.96 m³/s), at the Margecany station it was 7.85 m³/s, and at the Kysak station (17.38 m³/s). The increase in flows at the Margecany and Kyska stations is due to a more than doubling of the catchment area. The highest annual flows were recorded at all three hydrological stations in 2010, which was caused by high rainfall. The lowest annual flows were recorded at the Spisska Nova Ves hydrological station in 1982 (1.35 m³/s), at the Margecany hydrological station in 1993 (3.36 m³/s) and at the Kysak station in 2012 (7.62 m³/s). In the analysed multi-year period, an upward trend in flows is visible, the highest being at the Margecany station (above the Ružín Reservoir) and Kysak (below the Ružín reservoir), while the lowest trend was recorded at the Spisska Nova Ves hydrological station, but this is not a statistically significant increasing trend. On an annual level, the highest average monthly flows were recorded in April, while the lowest in January. Low flows in January are associated with the amount of precipitation during the month (the lowest precipitation totals), the type of precipitation (most often snowfall) and negative air temperature. High flows in April are associated with an increase in air temperature (above 0°C), which contributes to the melting of the snowpack.

The annual RBI index at the Spisska Nova Ves hydrological station ranged from 0.08 (1999, 2003) to 0.20 (2010), while at the Margecany hydrological station these values ranged from 0.09 (1986, 1999) to 0.17 (2010) (Figures 5, 6). The higher amplitude of the RBI values was recorded at the Kysak station, i.e., from 0.06 (2012) to 0.24 (1973) (Figure 7). The high value of the RBI index at the Kysak station in 1973 resulted from the start-up of the hydroelectric power plant, as well as from the high sums of precipitation recorded in June and July 1973. Compared to other lowland watercourses, the obtained RBI values are higher, which proves the variable flows in the analysed multiannual period. A higher amplitude of the RBI values was recorded at the Kysak station than at the Margecany and Spisska Nova Ves stations, which is related to the large area of the basin closed by the Kysak station and the work of the water reservoir.

In the period of 1973–2020, there no upward or downward trend appears in the RBI and Cv index at the hydrological stations Spisska Nova Ves and Margecany, despite visible slight fluctuations over time.

The analysis of the annual values of the Cv index showed that for the Spisska Nova Ves stations the Cv value ranged from 0.25 to 0.66 (amplitude 0.41), for Margecany stations from 0.21 to 0.57 (amplitude 0.36), and Kysak from 0.16 to 0.54 (amplitude 0.38). The highest Cv value was recorded at all three hydrological stations in 2010. The lowest Cv value at the Kysak station was recorded in 2012 (0.16), while at the Spisska Nova Ves station in 1986 (0.25) and at the Margecany station in 1986 (0.21). The Kysak station showed a clear downward trend in the Cv and RBI variability index in the analysed period 1973–2020, which may be related to the operation of the Ružín I and Ružín II reservoirs.

Analysis of the monthly mean RBI values showed that in the period 1973–2020 the RBI values ranged from 0 to 0.49 at the hydrological stations Spisska Nova Ves and Margecany, while at the Kysak station the RBI indicator ranged from 0 to 0.57, which indicated high changes in short-term flows. The maximum value of the RBI index was recorded in June 1973 (0.57) at the Kysak station and in July 2008 at the Margecany station (0.49) and the Spisska Nova Ves station (0.48). The high RBI values were associated with high precipitation, which was one of the highest sums of monthly precipitation in the analysed multiannual period (with a monthly sum of precipitation above 170 mm). The sum of monthly precipitation in June 1973 for the catchment area closed by the Kysak post was 181.9 mm. In July 2008, the rainfall in the catchment closed by the Margecany post was 211.6 mm, while in the Spisska Nova Ves catchment it was 197.6 mm. In addition, rainfall in July was preceded by precipitation of 50–70 mm in the period from March to June. In the analysed multi-year period 1973–2020, the highest RBI values were recorded in the summer half-year (May–October), mainly in July and August, which accounted for about 70%–75% of the analysed multi-year period. In the winter half of the year (November-April), the share of maximum RBI values accounted for 25%–30% of the analysed multi-year period.

Figures 8–10 show the distribution of the Cv and RBI index in a monthly approach. A wide interquartile range with the range of interquartile deviations of the Cv index was recorded at the Spisska Nova Ves and Margecany stations, while a slightly smaller one is seen at the Kysak station. The most outlier maximum values of Cv were recorded in March at the Spisska Nova Ves and Margecany stations, while at the Kysak station the maximum values were recorded in July. The large range of deviations in the Cv index may be due to the small catchment area, which responds quickly to changing meteorological conditions. In the case of the RBI distribution, the most outlier maximum values (RBI> 0.4) were recorded in November, December, February, June and July at the Spisska Nova Ves station, while in November, February and July at the Margecany station. The most outlier maximum RBI values (>0.4) at the Kysak station were recorded in June, July and August, while in the remaining months there was a narrow interquartile range, which indicates a smaller flood range resulting from the regulation of flows through the water reservoir. In the event of very extreme floods, it is not possible to control the flows through the reservoir due to its limited capacity, which results in an exceptionally large change in daily flows during the month.

Determining the size of the mutual relations between rainfall and hydrological conditions at all stations consisted in calculating the values of the correlation coefficients r between the RBI and Cv and between the RBI and monthly precipitation totals. The results show good relations between the RBI and Cv throughout the year at the Spisska Nova Ves and Magrecany stations, for which the r correlation value was higher than 0.77, and in October, November and December it was over 0.9 (Figure 11). Weaker correlations were obtained at the Kysak station, which is particularly visible in the period from April to July (r ranges from 0.58 to 0.73).

Diversified results were obtained in the study of the relationship between the RBI index and monthly rainfall totals. The conducted analysis showed that a greater differentiation of the RBI index is seen between the posts located above the Ružín reservoir (Spisska Nova Ves and Magrecany) and the post located below the reservoir (Kysak). The correlation coefficient r between the RBI and monthly rainfall totals shows a high correlation for the Spisska Nova Ves and Magrecany stations. The correlation coefficient r is at a level of 0.8 in November, December and October for the Spisska Nova Ves and Magrecany stations (Figure 12). Low correlation values were recorded in February and March, which is the effect of feeding the river as a result of the thaw. Weak correlation between the RBI and rainfall at the Kysak station is visible in September (r = 0.34) and May (r = 0.41), which may be due to the regulation of flows in the river by the operation of the water reservoirs.

In the analysed period of 1973–2020, a statistically significant upward trend in precipitation and air temperature in the individual catchments was recorded. An upward trend in flows was also recorded at all hydrological stations, but it was not statistically significant. The annual RBI flood rates showed slight RBI differences between the catchments, which are affected by the catchment’s physical properties and the operation of the Ružín Reservoir. At the hydrological stations of Spisska Nova Ves and Margecany, RBI values ranged from 0.08 to 0.20, while greater fluctuations in the RBI index were recorded at the Kysak station (from 0.06 to 0.24). Greater variation of the RBI index was recorded on a monthly basis. The RBI values ranged from 0 to 0.49 at the Spisska Nova Ves and Margecany hydrological stations, while at the Kysak station, the RBI ranged from 0 to 0.57, which indicated large changes in short-term flows. The obtained RBI values are characteristic of a mountain region. The RBI for the mountainous rivers of Slovakia and Austria ranges between 0.06 and 0.43 (Holko et al., 2011). For example, the RBI spread for rivers in the central part of the United States averaged 0.006 to 0.3 per year (Fongers, 2008). On the other hand, the RBI values for the rivers of Ethiopia were much higher and ranged from 0.011–1.113 (Berhanu et al., 2015). Studies conducted for four drainage basins in Indonesia showed that the average annual flood rate ranged between 0.29 and 0.39, and high RBI values occurred during the dry and transitional seasons (Pratama et al., 2018). For comparison, the RBI values for a lowland river in Poland (the Vistula in the estuary section) were definitely lower and ranged from 0.02 to 0.156 (Kubiak-Wójcicka, 2018). The diversified values of the RBI index are visible in the monthly approach at the individual hydrological stations. The analysis of data for the mountain section of the Hornad River in Slovakia showed that high RBI values in monthly terms were recorded at the Kysak hydrological station, which was under the influence of the Ružín I and Ružín II reservoirs. In the case of average flow values, the RBI index is higher at the Ružín post located below the water reservoir (Kysak) compared to the posts located above the reservoir (Spisska Nova Ves and Margecany). At higher flow rates due to heavy rainfall (over 80 mm per month), there was an increase in the RBI value, which was related to the limited possibilities of water collection by the reservoir. On the other hand, in months with rainfall amounts below 30 mm, the flows recorded at the post located below the water reservoir are evenly distributed over time, which is regulated by the reservoir’s operation. In this situation, there were slight changes in the RBI. According to Johnson et al. (2022), the RBI indicator should not be used in small mountain streams due to the inability to capture the fluctuations that occur over short periods of time, e.g., from hour to hour. Rainfall in first-order drainage is closely related to the response stream due to high connectivity in the landscape. The new RBI index, unlike many other hydrological parameters, has a low annual variation tolerance. Consequently, fewer flux years are required to quantify flux flash. Based on our findings, the RBI indicator is useful for detecting gradual changes in the flow regime, which may be related to the operation of water bodies, changes in the water management in the basin (Kubiak-Wójcicka, 2018) or land use. A specific case study for the Hornad River in Slovakia captured the details that are important for water management strategies within a mountain catchment area. For more detailed analyses of the impact of a water reservoir on the hydrological regime of a river, additional hydrological indicators should be used, which will allow regime changes to be determined in a long-term perspective. One has to agree with other authors (Kubiak-Wójcicka and Kornaś, 2015; Bonato et al., 2019) that interdisciplinary research involving various stakeholders is important. Extensive research and community engagement should be reflected in local actions and development strategies.