Trend Analysis of Selected Low-Flow Indicators in Catchments of the Vistula River Basin

Abstract

Climate change is altering the frequency, duration, and seasonality of low flows, which are critical for water availability, ecosystem functioning, and river management. Low-flow characteristics, defining the minimum, often seasonal, flow levels in rivers or streams primarily fed by groundwater, snow or glacier melt, or lake drainage, are essential for assessing hydrological droughts and water resource vulnerability. In the Upper Vistula River Basin, variable precipitation and rising air temperatures increase the risk of droughts, impacting both natural systems and human water use. This study analyzed long-term trends in annual low flows and associated parameters, including drought frequency, duration, and deficit volume, across 41 small- and medium-sized catchments. Two datasets were considered: 25 stations with 58-year daily discharge records (1961–2019) and 41 stations with 38-year records (1981–2019). Low flows were identified using the threshold level method (TLM) at 70% and 90% exceedance (FDC70 and FDC90). Trends were assessed with the Mann–Kendall test, and spatial drought patterns were mapped to evaluate regional variability. Deep and shallow low flows occurred at all analyzed cross-sections. For the period 1961–2019, deep low flows (FDC90) occurred almost annually in 18 of the 25 cross-sections since 2012. Statistically significant increasing trends in deep low-flow parameters were detected in five cross-sections for 1961–2019 and in seven cross-sections for 1981–2019. Shallow low flows (FDC70) occurred in all sections; four rivers exhibited annual shallow droughts during 1961–2019, whereas 12 rivers showed annual events in 1981–2019. Summer droughts predominated over winter events, reflecting enhanced evapotranspiration and higher seasonal water demand. These findings highlight the relevance of analyzing low-flow parameters for understanding hydrological droughts. Such information can support water resource management, planning, and ecosystem protection under variable climatic conditions.

1. Introduction

Water resources are among the most critical issues, not only for meeting the water demands of populations but also for maintaining and protecting the good ecological status of rivers. Therefore, from the perspective of water resource planning and management, it is essential to identify and assess changes that may occur in river flow time series [1]. River flows depend on numerous climatic factors, and climate change is expected to significantly alter the hydrological cycle [2]. Changes in precipitation and temperature directly affect river discharge and groundwater levels. It is projected that the global mean surface temperature will increase throughout the 21st century, which may lead to substantial changes in the hydrological cycle [3,4]. Climate refers to the average weather conditions over a long period, whereas climate change denotes long-term shifts in these conditions [5].

Climate change and related hydrological variables exhibit variability in both space and time. River flows vary depending on the geographical location of the watercourse as well as the temporal scale. For instance, they may occur as short-term events lasting only minutes, as in the case of flash floods, or as long-term changes spanning decades, which are relevant for water resource assessments [1,6]. Consequently, identifying trends in hydroclimatic variables—such as precipitation, air temperature, and river discharge—and analyzing their spatial and temporal patterns is of considerable scientific and practical importance [7,8]. Catchment size also plays a crucial role. In smaller catchments, the impact of anthropogenic activities is generally expected to be less pronounced than in larger ones [9]. However, to detect trends with sufficient reliability, long-term measurement series are required in order to account for the natural variability of the underlying processes.

In the context of water resource management and planning at the catchment scale, knowledge of low-flow characteristics is a key factor, as many human activities depend on surface water resources. This is particularly relevant for water abstraction, wastewater discharge, and the protection of water quality and aquatic ecosystems [2,10]. It is estimated that the economic cost of the drought that occurred in 2003 amounted to approximately 12 billion euros across Europe. The associated heat waves resulted in more than 30,000 deaths [11]. Therefore, in water resource forecasting and management, knowledge of trends in hydrological variables constitutes valuable and essential information [12].

Drought is a complex, gradually developing process whose effects cumulate and are visible after a long period of time. It is a natural phenomenon that cannot be controlled [13]. There are many definitions of drought in the literature [14,15,16,17] emphasizing its various aspects; therefore, they can be considered complementary [18]. Drought is often defined according to disciplinary perspectives. Four related types of drought are frequently identified: meteorological, agricultural, hydrological, and socio-economic, all of which are characterized by temporal and spatial variability [11,18,19,20,21,22].

According to the WMO [23], the commonly used definition of a drought is a prolonged lack or severe deficiency of precipitation, which can be characterized as a period of abnormally dry weather with a sufficiently prolonged lack of precipitation, causing a serious hydrological imbalance. It is a climatic phenomenon that can occur almost anywhere in the world [18].

In turn, refs. [21,24] define hydrological drought in terms of the impact of drought periods on surface or subsurface hydrology, without providing a meteorological explanation of this phenomenon. Van Loon [21] defines hydrological drought as a deficiency of water within the hydrological system. It manifests itself through extremely low river discharge, reduced lake levels, and declining groundwater levels. Often referred to as a “creeping disaster,” drought develops gradually, which makes its onset difficult to detect [21]. However, ref. [24] defines hydrological drought as “a period during which streamflows are insufficient to fulfill established requirements within a given water management system.”

To understand hydrological drought, its processes, and its impacts, it is necessary to identify its key characteristics, including the timing of occurrence, duration, severity (or intensity), and spatial extent [21]. These characteristics can be determined using drought indices. Drought indices can generally be divided into two groups: those based on standardized indices and those based on threshold levels. In this study, the threshold level method (TLM) is applied. According to this method, a drought event is defined as a period during which river discharge falls below a defined threshold value, allowing both its onset and termination to be clearly identified [25]. Using the TLM, it is possible to determine the characteristics of low-flow periods, such as their duration (expressed in days) and deficit volume [11,21,26]. Thresholds are commonly derived from percentiles of the flow duration curve, which represents the discharge exceeded for a given percentage of time [21,26]. Percentiles ranging from the 70th to the 95th are frequently applied. In this study, the 70th and 90th percentiles are used, corresponding to flows that equal or exceed 70% and 90% of the time, respectively. This approach ensures that the same number of days in the record is drought-affected, although the temporal distribution of drought events may vary [11]. The analysis of river flow trends has been the subject of numerous studies worldwide. In the Czech Republic, ref. [4] investigated the temporal evolution of annual and seasonal low-flow regimes. They analyzed 7-day annual, summer, and winter low flows; the number of days with discharge below two low-flow thresholds; and deficit volumes. Their results indicated a similar number of positive and negative trends in both mountain and lowland catchments, with most catchments exhibiting statistically insignificant trends. Birsan et al. [8,27] examined flow trends in Swiss and Romanian catchments. In Switzerland, they observed an increase in annual flows, with particularly great changes in winter [8]. In contrast, for catchments in Romania, an increasing trend was detected for winter flows and minimum spring streamflows, while a decreasing trend was observed for summer flows. These patterns were linked primarily to changes in air temperature. Meanwhile, the increasing trend in autumn flows was associated with increasing precipitation amounts [27].

Trends in river flows in eastern Slovakia were analyzed by Zelenakova et al. [28]. Hannaford and Marsh [29] investigated trends in runoff and low flows in the United Kingdom and reported no significant increasing trends in low-flow conditions. In Spain, Coch and Mediero [1] analyzed trends using two low-flow indicators: the 7-day annual minimum streamflow and the 10th percentile of the annual flow duration curve. Their results revealed a decreasing trend for both indicators in the northern part of the country.

The identification of possible trends for low-flow and hydrological droughts across Europe was the subject of analyses by [11,30,31], among others. However, this did not include basins located in Poland. In Poland, trends in various hydrological indicators, including annual minimum flow, annual minima of 7-day averaged daily flows, and the standardized precipitation–evapotranspiration index (SPEI), have been widely studied [9,32,33,34,35,36]. The dynamics of drought occurrence were analyzed by [26,37,38]. However, many of these studies focus on individual catchments or small regions, which limits the generalization of their findings. The Upper Vistula River Basin analyzed in this study accounts for 25% of the entire Vistula River Basin. It is important in terms of water resources, as it influences the water availability in the middle reaches of the Vistula River. Hydrological droughts observed in recent decades in Central and Eastern Europe, occurring as a result of climate change, have become more frequent and prolonged, thereby significantly affecting water resources. Although there have been studies on the upper Vistula River area, such as [37], studies on various types of base flows for long time series are limited. With this in mind, and recognizing the problem of increasing instability of water resources, a decision was made to fill this gap. This study hypothesizes that hydrological drought characteristics (number of drought events, their duration, and deficit volume) exhibit temporal variability across the analyzed periods. The aim of the study was to identify long-term trends in annual low flows and selected parameters of low-flow events, such as their number, duration, and volume, in 41 small- and medium-sized catchments located in the Upper Vistula River Basin. The study not only provides a statistical analysis of changes but also determines the spatial variability of droughts, thereby forming a basis for the development of local-scale climate change adaptation strategies.

2. Materials and Methods

The data used for the analysis consisted of daily streamflow records obtained from the Institute of Meteorology and Water Management—National Research Institute (IMGW-PIB). The primary selection criterion for study sites was that the streams are not subject to water abstractions for purposes such as hydropower generation. The second criterion was the availability of continuous discharge observations spanning at least 30 years.

The analysis was conducted for 41 gauging stations representing small- and medium-sized catchments located within the Upper Vistula River Basin (Figure 1,

Table 1. Characteristics of the analyzed cross-sections.

No	River	Cross-Section	Latitude	Longitude	Period of Record	Catchment Area [km2]	Physico-Geographical Region
1	Rudawa	Balice	50.0930	19.8066	1971–2019	283.09	Silesia–Krakow Upland
2	Uszwica	Borzęcin	50.0650	20.7055	1956–2020	260.65	Northern Subcarpathian
3	Brennica	Górki Wielkie	49.7536	18.8708	1956–2020	81.47	Northern Subcarpathian
4	Szkło	Charytany	50.0033	22.9386	1971–2020	754.63	Northern Subcarpathian
5	Iłownica	Czechowice	49.9136	18.9863	1951–2020	201.34	Northern Subcarpathian
6	Nidzica	Dobiesławice	50.3041	20.4741	1957–2020	643.2	Lesser Poland Upland
7	Sękówka	Gorlice	49.6547	21.1702	1961–2020	122.21	Outer Western Carpath.
8	Mleczka	Gorliczyna	50.0855	22.4872	1951–2020	525.09	Northern Subcarpathian
9	Tanew	Harasiuki	50.4775	22.4741	1951–2020	2029.55	Northern Subcarpathian
10	Hoczewka	Hoczew	49.4238	22.3283	1971–2020	169.06	Eastern Beskids
11	Morwawa	Iskrzynia	49.6772	21.8644	1973–2020	108.01	Outer Western Carpath.
12	Łososina	Jakubkowice	49.7394	20.6300	1961–2020	346.48	Outer Western Carpath.
13	Skawa	Jordanów	49.6363	19.8300	1961–2020	96.6	Outer Western Carpath.
14	Kalnica	Wetlina	49.1888	22.4291	1972–2020	118.91	Eastern Beskids
15	Koprzywianka	Koprzywnica	50.5958	21.5730	1951–2019	500.15	Lesser Poland Upland
16	Kirowa Woda	Kościelisko	49.2758	19.8680	1966–2019	34.72	Central Western Carpath.
17	Biała	Koszyce	49.9972	20.9494	1951–2019	954.41	Northern Subcarpathian
18	Wiar	Krówniki	49.7669	22.8230	1951–2019	785.92	Outer Western Carpath.
19	Białka	Łysa Polana	49.263	20.1150	1961–2020	63.54	Central Western Carpath.
20	Żylica	Łodygowice	49.7272	19.1361	1972–2020	51.83	Outer Western Carpath.
21	Biała	Mikuszowice	49.7794	19.0741	1956–2020	32.83	Outer Western Carpath.
22	Poprad	Muszyna	49.3500	20.8852	1971–2020	1698.94	Outer Western Carpath.
23	Niedziczanka	Niedzica	49.4113	20.3022	1971–2020	135.88	Outer Western Carpath.
24	Wisznia	Nienowice	49.9377	22.9169	1951–2020	1188.17	Northern Subcarpathian
25	Łubinka	Nowy Sącz	49.6352	20.7047	1971–2020	66.37	Outer Western Carpath.
26	Prądnik	Ojców	50.1947	19.8325	1971–2020	68.69	Silesia–Krakow Upland
27	Żabniczanka	Żabnica	49.5647	19.1802	1971–2020	23.88	Outer Western Carpath.
28	Wisłoka	Żółków	49.7300	21.4591	1952–2020	582.93	Outer Western Carpath.
29	Wieprzówka	Rudze	49.9616	19.4425	1961–2019	152.38	Northern Subcarpathian
30	Bukowa	Ruda Jastk.	50.5975	22.1397	1961–2020	648.99	Northern Subcarpathian
31	Czarna	Polana	49.3025	22.5741	1972–2020	94.27	Eastern Beskids
32	Skawinka	Radziszów	49.9400	19.8088	1971–2020	317.68	Northern Subcarpathian
33	Wisłok	Rzeszów	50.0397	22.0155	1951–2020	2079.93	Outer Western Carpath.
34	Trzebośnica	Sarzyna	50.3272	22.3475	1961–2020	249.72	Northern Subcarpathian
35	Raba	Stróża	49.7969	19.9247	1956–2020	643.79	Outer Western Carpath.
36	Biały Dunajec	Szaflary	49.4241	20.0247	1961–2020	209.75	Outer Western Carpath.
37	Solinka	Terka	49.2997	22.4291	1961–2020	308.93	Eastern Beskids
38	Czarna Nida	Tokarnia	50.7741	20.4530	1951–2020	1212.01	Lesser Poland Upland
39	Osława	Zagórz	49.5133	22.2688	1951–2020	502.8	Eastern Beskids
40	Jasiołka	Zboiska	49.5744	21.6983	1973–2020	263.98	Outer Western Carpath.
41	Lubaczówka	Zapałów	50.10055	22.8900	1961–2019	857.52	Northern Subcarpathian

). Catchments with an area exceeding 10,000 km² were excluded from the analysis due to the potential influence of factors that may disturb the natural flow regime [9,39]. In addition, gauging stations with data gaps of one year or longer were not considered. Although it is difficult to completely exclude the influence of human activity on flow variability, the relative contribution of such disturbances must be considered [9].

According to [40], the analyzed cross-sections are located within the following physico-geographical regions: the Silesia–Krakow Upland, the Lesser Poland Upland, the Northern Subcarpathians, the Outer Western Carpathians, the Central Western Carpathians, and the Eastern Beskids (Figure 1, Table 1). The Silesia–Kraków Upland, the Lesser Poland Upland, the Outer Western Carpathians, the Central Western Carpathians, and the Eastern Beskids constitute the source areas of most tributaries of the Upper Vistula, whereas the Northern Subcarpathians form a transit zone for the Vistula and the estuary area for rivers and streams originating in the Subcarpathians and the Subcarpathian Upland. The basin area is also geologically diverse, which results in considerable soil variability. Four main types of relief can be distinguished in the study area: mountain, upland, foothill, and lowland [41].

The length of the dataset used in the analysis varies from one site to another. The minimum length of the daily flow series used in the analysis is 47 years, while the maximum length is 69 years (Table 1). The analysis of time series with different lengths and covering different periods may lead to biased or misleading interpretations [42]. Therefore, in addition to conducting the statistical analysis for the selected stations for the entire period of record, the stations were grouped into two groups. The decision to divide the data into two subsets represents a trade-off between longer time series available for fewer stations and shorter time series available for a larger number of stations. Group 1 was selected to obtain the longest possible measurement period. It included 25 river gauging stations with 58-year records (1961–2019). Group 2, in contrast, was selected to increase the number of gauging cross-sections. It comprised 41 river gauging stations with 38-year records (1981–2019) [9]. The choice of the 1981 cutoff for the shorter period was based solely on data availability, to include as many stations as possible while maintaining a sufficiently long record for trend analysis.

Next, annual minimum flows were extracted (Qmin). These values were computed over a hydrological year, i.e., from November 1 to October 31. Also, trend analysis was conducted for the number, duration, and deficit volumes of shallow and deep droughts identified using the threshold level method (TLM). For this purpose, the 90th (FDC90) and 70th (FDC70) percentiles of the annual flow duration curve were adopted as threshold levels. The use of both thresholds allows distinguishing between changes in the number of droughts and their severity, providing a more comprehensive assessment of drought dynamics under regional hydroclimatic variability. FDC70 captures moderate but more frequent low flows, reflecting early stages of drought development, while FDC90 is associated with the depletion of groundwater and overall water resources in the catchment. To exclude short-term events that could artificially influence low-flow characteristics—particularly their frequency—a minimum event duration of 7 days was assumed. Additionally, it was assumed that successive low-flow events separated by flows exceeding the threshold discharge and lasting no more than three days were combined into a single event. If a low-flow period begins in one hydrological year and ends in the next, it is not divided but attributed in its entirety to the year in which it is centered [37]. For both shallow and deep droughts, additional characteristics were determined, including: (i) drought frequency, defined as the ratio of the number of drought events to the number of years; (ii) drought-day frequency [days], defined as the ratio of the total number of drought days to the number of years; (iii) mean drought volume [m³], calculated as the ratio of the cumulative deficit volume to the number of drought events; and (iv) mean duration of a drought [days], defined as the ratio of the total number of drought days to the number of drought events.

The study also included a spatial analysis of drought variability characteristics, such as the number of events, mean drought duration (T_mean), and mean drought deficit (V_mean). The calculations were performed for the FDC90 and FDC70 thresholds for the period 1981–2019, during which a larger number of cross-sections were available. A separate map was developed for each analyzed parameter, allowing for the assessment of the spatial variability of hydrological drought characteristics and the identification of differences in drought risk levels within the study area. To assess the spatial variation in hydrological drought risk, a procedure similar to that proposed in [43] was applied, using characteristics describing low-flow events, i.e., the number of events (N), mean duration (T_mean), and mean deficit (V_mean). To ensure the comparability of the analyzed parameters, their value ranges were divided into four classes based on the quartiles of each parameter’s distribution (

Table 2. Low-flow category [43].

Category	Color Assigned to Category	Low-Flow Hazard	Low-Flow Frequency	Mean Low-Flow Duration Tmean	Mean Low-Flow Volume Vmean
[Xmin, X25%]		Low	Low	Low	Low
[X25%, X50%]		Moderate	Moderate	Moderate	Moderate
[X50%, X75%]		High	High	High	High
[X75%, X100%]		Very	Very	Very	Very

). It was assumed that the level of risk increases with increasing values of the analyzed indicators.

The World Meteorological Organization (WMO) recommends using the Mann–Kendall test to assess trends in low-flow characteristics. The Mann–Kendall test is a non-parametric, rank-based method widely used for detecting monotonic trends in time series [42]. Since hydrological data are often not normally distributed and may contain outliers or exhibit non-linear behavior, this test is considered particularly suitable for hydrological applications [1,4,9,44,45]. The Mann–Kendall test identifies monotonic increasing or decreasing trends by comparing successive observations in a time series [1]. The Mann–Kendall test was performed, accounting for autocorrelation in the time series, using the modified variance approach proposed by [46]. The analysis was conducted for low-flow deficits, which are the result of other low-flow characteristics, as well as for the FDC70 threshold, due to the lower occurrence of zero values. The correction was applied only to those time series in which statistically significant autocorrelation was detected. A positive value of the standardized test statistic Z indicates an upward trend, whereas a negative value indicates a downward trend [47]. In this study, a significance level of 0.05 was adopted. Accordingly, trends with p ≤ 0.05 were considered statistically significant.

3. Results

Low-flow events determined for the threshold level FDC90

In the analyzed area, deep low flows occurred at all gauging stations during the period 1961–2019. For 18 of the 25 rivers in Group 1, deep drought events have been recorded almost annually since 2012. For deep low flows, the lowest number of years without an event was observed for the Solinka River, amounting to 14 years in the 1961–2019 period and 6 years in 1981–2019 (Figure 2). In contrast, the Niedzica River recorded the highest number of years without drought events (40 years in 1961–2019). In the shorter period (1981–2019), the Niedzica and Brennica Rivers each recorded more than 23 years without deep drought events.

The detailed characteristics of deep low flows (FDC90) are summarized in

Table 3. Parameters of low flows for FDC90 for the two analyzed periods.

Parameter	Number of Low Flows	Low-Flow Day Frequency [Days]	Mean Low-Flow Volume [m3]	Mean Low-Flow Duration [Days]
FDC90_1961–2019
Min	0.9	22.1	57,397.6	15.4
Mean	1.4	27.2	502,931.1	20.3
Max	1.7	33.3	1,564,031.1	33.8
FDC90_1981–2019
Min	0.8	12.0	43,550.1	14.2
Mean	1.6	29.4	433,677.3	19.5
Max	2.1	41.3	1,238,781.2	33.7

. For the period 1961–2019, the mean low-flow day frequency was approximately 27 days, while the mean low-flow duration was about 20 days. The Łysa Polana cross-section exhibited the highest values among the analyzed sections, with a mean low-flow duration of 38 days and a low-flow day frequency of 33 days. In contrast, the shortest mean low-flow duration was recorded for the Terka cross-section (approximately 17 days). For 20 out of 25 stations, the number of low-flow events exceeded one event on average.

In the 1981–2019 period, the mean low-flow day frequency increased slightly to approximately 29 days, while the mean low-flow duration was about 19 days. At 68% of the stations, the number of low-flow events exceeded 1.5 events.

Temporal and spatial variability of low-flow events for the threshold level FDC90

Spatial distributions of low flows for the FDC90 threshold level and for individual indicators—number of low flows, mean duration (T_mean), and mean volume (V_mean)—showed variability among the analyzed stations depending on the indicator. Some similarities between the maps were apparent, but there were also clear differences in the characteristics of low flows across different regions (Figure 3).

Stations located in the Silesia–Kraków Upland and Lesser Poland Upland exhibited moderate to high low-flow hazard, although the dominant parameter varied between locations. In the eastern and northeastern parts of the Northern Subcarpathians, the hazard was classified as very high due to event duration. In the Outer Western Carpathians, differences were also observed between individual stations. Based on the number of low-flow periods, the hazard ranged from low to very high. For stations in the southern part of the region, as well as in the Central Western Carpathians, low flows occurred rarely, but in terms of duration, the hazard was very high. Conversely, the central part of the Outer Western Carpathians was characterized by moderate to very high hazard in terms of the number of low flows, while duration and volume indicated low to moderate hazard. The Eastern Beskids showed a high number of low-flow events, with hazards ranging from moderate to high in terms of duration.

Trend analysis using the Mann–Kendall test revealed pronounced spatial differentiation in the evolution of hydrological low-flow characteristics across the studied regions. With regard to deep low flows (FDC90) and both multi-year periods, consistent spatial trends and tendencies in their occurrence were evident for all analyzed low-flow parameters (

Table 4. Mann–Kendall test results for FDC90 low flows and the 1961–2019 period (bold indicates statistically significant trend for p ≤ 0.05).

River	Cross-Section	Number of Low Flows	Low-Flow Duration	Low-Flow Volume
Uszwica	Borzęcin	increasing	increasing	increasing
Brennica	Górki Wielkie	no trend	no trend	no trend
Iłownica	Czechowice	increasing	increasing	increasing
Nidzica	Dobiesławice	decreasing	decreasing	decreasing
Sękówka	Gorlice	increasing	increasing	no trend
Mleczka	Gorliczyna	increasing	increasing	increasing
Tanew	Harasiuki	increasing	increasing	increasing
Łososina	Jakubkowice	increasing	increasing	increasing
Skawa	Jordanów	increasing	increasing	increasing
Koprzywianka	Koprzywnica	increasing	increasing	increasing
Biała	Koszyce	decreasing	no trend	no trend
Wiar	Krówniki	increasing	increasing	increasing
Białka	Łysa Polana	no trend	no trend	no trend
Biała	Mikuszowice	increasing	increasing	increasing
Wisznia	Nienowice	increasing	increasing	increasing
Wisłoka	Żółków	increasing	increasing	increasing
Bukowa	Ruda Jastk.	increasing	increasing	increasing
Wisłok	Rzeszów	no trend	no trend	no trend
Trzebośnica	Sarzyna	increasing	increasing	increasing
Raba	Stróża	no trend	no trend	no trend
Biały Dunajec	Szaflary	decreasing	decreasing	decreasing
Solinka	Terka	increasing	increasing	increasing
Czarna Nida	Tokarnia	increasing	increasing	increasing
Osława	Zagórz	no trend	no trend	no trend
Lubaczówka	Zapałów	no trend	increasing	increasing

, Figure 4). During the period 1961–2019, most stations exhibited statistically significant increasing trends and non-significant tendencies. Statistically significant increasing trends were identified at five gauging stations, whereas at one station (Szaflary), a statistically significant decreasing trend was observed for all analyzed parameters (Table 4).

For the period 1981–2019, spatial analysis showed that, for stations located in the Northern Subcarpathians, Lesser Poland Upland, Eastern Beskids, and Outer Western Carpathians, upward trends and tendencies in the analyzed low-flow parameters prevailed. Statistically significant upward trends and tendencies were identified at seven stations (Czechowice, Hoczew, Jordanów, Koprzywnica, Krówniki, Rudze, and Sarzyna) for all analyzed parameters. In contrast, in Silesia–Krakow Upland and the Central Western Carpathians, only statistically significant decreasing trends and non-significant tendencies were visible. At two stations (Łysa Polana and Muszyna), statistically significant decreasing trends were observed for all low-flow parameters (Figure 4).

Low-flow events determined for the threshold level FDC70

Shallow low-flow events occurred at all studied stations. During 1961–2019, four rivers (Łososina, Skawa, Białka, and Biały Dunajec) experienced shallow low flows annually. For the period 1981–2019, for which twice as many cross-sections were available, three times as many rivers (12) exhibited annual low-flow events (Figure 5). The largest number of years without shallow low flows during 1961–2019 was 19 years (Niedzica), and for 1981–2019 it was 12 years (Prądnik and Niedzica).

During 1961–2019, the mean low-flow day frequency was 89 days, while the mean low-flow duration was approximately 25 days. At the Jordanów cross-section, both the number of low-flow events and the low-flow day frequency were the highest among the analyzed rivers, amounting to about 6 events and 198 days, respectively. For the 1981–2019 period, low-flow day frequency and mean low-flow duration were approximately 98 days and 25 days, respectively (

Table 5. Parameters of low flows for FDC70 for the two analyzed periods.

Parameter	Number of Low Flows	Low-Flow Day Frequency [Days]	Mean Low-Flow Volume [m3]	Mean Low-Flow Duration [Days]
FDC70_1961–2019
Min	1.4	22.5	149,003.6	16.4
Mean	3.7	89.2	1,561,801.3	24.8
Max	8.0	197.7	5,931,737.4	51.6
FDC70_1981–2019
Min	1.6	28.3	119,606.1	16.5
Mean	4.1	97.6	1,307,975.1	24.5
Max	8.1	203.2	6,510,805.4	48.5

). At 38 of the 41 analyzed stations, the number of low-flow events exceeded 3 days. The highest low-flow day frequency, 203 days, was recorded for the Skawa River.

Temporal and spatial variability of low-flow events for the threshold level FDC70

Similar to FDC90, the spatial distribution of shallow low-flow characteristics (FDC70) for the period 1981–2019 reveals clear differentiation among stations depending on the analyzed parameter (number of low flows, mean duration (T_mean), and mean deficit (V_mean)) (Figure 6). At stations located in the Silesia–Kraków Upland, hazard was classified as low to moderate based on the number and volume of low-flow events, while duration was classified as very high. Stations in the Lesser Poland Upland show variability across parameters; for example, at Tokarnia, hazard was very high for the number and volume of low-flow events but high for duration. In the eastern and northeastern parts of the Northern Subcarpathians, high and very high hazards were primarily associated with volume, while the number of low-flow events remained low to moderate. The Outer Western Carpathians displayed substantial internal variability, with low flows ranging from low to very high across the region. Southern stations, similar to those in the Central Western Carpathians, were characterized by low hazard but long-lasting low flows (duration classified as very high). In contrast, the central part of the Outer Western Carpathians exhibited a moderate to very high number of low-flow events, whereas duration and volume were generally classified as low to moderate. The Eastern Beskids were distinguished by a high number of shallow low-flow events; however, duration was predominantly classified as low across most stations.

With regard to shallow low flows (FDC70) and both multi-year periods, similar trends and tendencies in occurrence were evident for all analyzed low-flow parameters (

Table 6. Mann–Kendall test results for FDC70 low flows and the 1961–2019 period (bold indicates statistically significant trend for p ≤ 0.05).

River	Cross-Section	Number of Low Flows	Low-Flow Duration	Low-Flow Volume
Uszwica	Borzęcin	increasing	increasing	increasing
Brennica	Górki Wielkie	increasing	no trend	no trend
Iłownica	Czechowice	increasing	increasing	increasing
Nidzica	Dobiesławice	no trend	no trend	no trend
Sękówka	Gorlice	increasing	increasing	increasing
Mleczka	Gorliczyna	decreasing	no trend	no trend
Tanew	Harasiuki	decreasing	no trend	no trend
Łososina	Jakubkowice	increasing	increasing	increasing
Skawa	Jordanów	increasing	increasing	increasing
Koprzywianka	Koprzywnica	no trend	increasing	increasing
Biała	Koszyce	no trend	decreasing	decreasing
Wiar	Krówniki	increasing	increasing	increasing
Białka	Łysa Polana	increasing	no trend	no trend
Biała	Mikuszowice	no trend	decreasing	no trend
Wisznia	Nienowice	no trend	no trend	increasing
Wisłoka	Żółków	no trend	no trend	no trend
Bukowa	Ruda Jastk.	decreasing	increasing	increasing
Wisłok	Rzeszów	no trend	no trend	no trend
Trzebośnica	Sarzyna	increasing	increasing	increasing
Raba	Stróża	no trend	no trend	no trend
Biały Dunajec	Szaflary	decreasing	decreasing	decreasing
Solinka	Terka	no trend	no trend	increasing
Czarna Nida	Tokarnia	no trend	increasing	increasing
Osława	Zagórz	no trend	no trend	no trend
Lubaczówka	Zapałów	no trend	decreasing	decreasing

, Figure 7). During the period 1961–2019, most stations exhibited statistically significant increasing trends and tendencies. Statistically significant increasing trends and non-significant tendencies were observed at two cross-sections (Gorlice and Trzebośnica), whereas at Szaflary, a statistically significant decreasing trend and non-significant tendency were recorded for all analyzed parameters (Table 6).

For the years 1981–2019, at cross-sections located in the Eastern Beskids and Outer Western Carpathians, statistically significant increasing trends and non-significant tendencies in the analyzed low-flow parameters prevailed. Statistically significant increasing trends and tendencies were observed at four stations (Górki Wielkie, Czechowice, Gorlice, and Iskrzynia) for all analyzed parameters. In contrast, for the Lesser Poland Upland and Central Western Carpathians, statistically significant decreasing trends and non-significant tendencies were visible. At Szaflary and Zapałów, statistically significant decreasing trends and non-significant tendencies were recorded for low-flow events (Figure 7).

For the low-flow volume of the FDC70 and both analyzed multi-year periods, the autocorrelation coefficient was calculated, and the results are summarized in

Table 7. Results of the autocorrelation coefficient analysis for FDC70 for the analyzed multi-year periods.

River	Cross-Section	1961–2019	1981–2019
Uszwica Brennica Iłownica Nidzica Sękówka Mleczka Tanew Łososina Skawa Koprzywianka Biała Wiar Białka Biała Wisznia Wisłoka Bukowa Wisłok Trzebośnica Raba Biały Dunajec Solinka Czarna Nida Osława Jasiołka Lubaczówka Rudawa Szkło Hoczew Morwawa Kalnica Kirowa Woda Żylica Poprad Niedziczanka Łubinka Prądnik Żabniczanka Wieprzówka Czarna Skawinka	Borzęcin Górki Wielkie Czechowice Dobiesławice Gorlice Gorliczyna Harasiuki Jakubkowice Jordanów Koprzywnica Koszyce Krówniki Łysa Polana Mikuszowice Nienowice Żółków Ruda Jastk. Rzeszów Sarzyna Stróża Szaflary Terka Tokarnia Zagórz Zboiska Zapałów Balice Charytany Hoczew Iskrzynia Wetlina Kościelisko Łodygowice Muszyna Niedzica Nowy Sącz Ojców Żabnica Rudze Polana Radziszów	0.231 0.099 0.462 0.564 0.139 0.291 0.383 0.188 0.081 0.425 0.247 0.481 −0.008 0.394 0.478 0.225 0.427 0.127 0.434 0.166 0.048 0.057 0.365 0.070 0.070 0.560	0.094 0.036 0.501 0.537 0.138 0.267 0.340 0.123 −0.106 0.466 0.145 0.361 0.063 0.409 0.298 0.044 0.347 0.215 0.395 0.019 0.044 −0.078 0.362 −0.211 −0.001 0.538 0.062 0.452 0.126 0.131 0.136 −0.042 −0.175 0.231 0.184 0.055 0.380 0.061 0.185 0.037 0.312

. The autocorrelation coefficient values for the analyzed series (1961–2019) ranged from −0.08 to 0.564. At 12 cross-sections, a significant positive first-order autocorrelation (r₁ > 0.255) was observed. For the second analyzed multi-decade period (1981–2019), the autocorrelation coefficient ranged from −0.211 to 0.538. In most cross-sections (29), no statistically significant autocorrelation was detected (r₁ > 0.315). However, the application of autocorrelation correction did not substantially affect the significance of the detected trends.

For low-flow parameters such as duration and volume, and for the periods 1961–2019 and 1981–2019, the mean magnitude of change was calculated. The calculations were performed for the 70% threshold level (FDC70), using Sen’s slope estimator for physiogeographical regions (

Table 8. Magnitude of change in low-flow event parameters.

Region	1961–2019	1981–2019
Low-flow duration
Silesia–Krakow Upland	n/a	0.0
Lesser Poland Upland	6.1	−10.2
Northern Subcarpathians	1.3	0.9
Outer Western Subcarpathians	2.7	3.0
Central Western Carpathians	−5.5	−7.6
Eastern Beskids	1.3	4.9
Low-flow volume
Silesia–Krakow Upland	n/a	−1502.6
Lesser Poland Upland	361,832.7	−23,029.6
Northern Subcarpathians	75,977.5	265,438.7
Outer Western Subcarpathians	193,818.7	−50,571.2
Central Western Carpathians	−532,240.0	−699,782.4
Eastern Beskids	260,889.9	423,960.8

n/a indicates that no data are available for the respective multi-year period due to the absence of the catchment.

). For the Central Western Carpathians, mean values of both duration and volume of low-flow events showed a decrease. The mean decadal change for 1961–2019 was about −6 days for duration and −530 000 m³ for volume (based on 25 catchments), while for 1981–2019 it was about −8 days and −700 000 m³ (41 catchments). In contrast, the Northern Subcarpathians and Eastern Beskids exhibited increases in both duration and volume. For 1961–2019, the mean decadal change ranged from +1.5 days for duration to +76 000 m³ (Northern Subcarpathians) and +260 000 m³ (Eastern Beskids) for volume. For 1981–2019, duration increased by about +1 day (Northern Subcarpathians) and +5 days (Eastern Beskids), with volume changes of +265 000 m³ and +424 000 m³, respectively.

Annual minimum flow trend

Trends in annual minimum flows (Qmin) were analyzed for two multi-year periods (1961–2019 and 1981–2019) using the Mann–Kendall test (

Table 9. Summary of Mann–Kendall test results for annual minimum flows (Qmin) for the analyzed periods.

1961–2019 (25 Stations)		1981–2019 (41 Stations)
Increase (%)	Decrease (%)	Increase (%)	Decrease (%)
36	64	56	44

). For 1961–2019, statistically significant trends were observed at six cross-sections. A statistically significant increasing trend was recorded at Górki Wielkie, whereas statistically significant decreasing trends were identified at Sarzyna, Szaflary, Nienowice, Jordanów, and Koprzywnica. During 1981–2019, statistically significant increasing trends were found at Łysa Polana, Szaflary, and Muszyna, while statistically significant decreasing trends were observed at Rzeszów, Nienowice, Czechowice, and Rudze.

Different trend directions were observed between the two periods for the Jakubkowice, Ruda Jastkowska, Gorliczyna, and Harasiuki cross-sections. For 1961–2019, the Jakubkowice, Ruda Jastkowska, and Gorliczyna cross-sections exhibited statistically significant increasing trends and non-significant tendencies in Qmin, whereas during 1981–2019, Qmin exhibited statistically significant decreasing trends and non-significant tendencies compared to the longer period. Conversely, the Harasiuki cross-section showed the opposite pattern, with Qmin increasing in the shorter period relative to 1961–2019.

4. Discussion

This section is organized to follow the key findings presented in the Section 3, addressing temporal and spatial variability, trends at different low-flow thresholds, multi-year period comparisons, and seasonal patterns.

Temporal and spatial variability of low flows

Building on the results for FDC90 low-flow events, this section examines their temporal and spatial variability across the study area. The results of this study indicate a clear intensification of hydrological low-flow characteristics in the Upper Vistula River Basin, particularly in terms of duration and volume. The Upper Vistula area analyzed in this study is considered moderately to highly vulnerable to hydrological drought [37]. Spatial differentiation of low-flow parameters suggests that susceptibility varies between physiographic regions and depends on the applied threshold level (FDC70 vs. FDC90). This is confirmed by the analyses conducted by [37] for the Upper Vistula River Basin. Shallow low-flow events (FDC70) occur almost annually in many catchments, whereas deep events (FDC90) are less frequent but more severe, with significant implications for water management. The average number of years with drought for FDC70 was 51 for the 1961–2019 period and 35 for the 1981–2019 period. Using the FDC90 threshold reduces the number of gauging stations with zero years without droughts. Similar relationships between the number, duration, and volume of low-flow events and the applied threshold level were reported in [38], which is consistent with our findings. However, some differences may arise due to variations in the study period (1999–2022 in [38]) and the smaller number of catchments analyzed. Similar average values for catchments in the Upper Vistula Basin were reported in [37], where they reached 29 years for FDC70 and 24 years for FDC90. The analysis indicates that the characteristics of low-flow events vary depending on the physical and geographical features of the catchment area, which is consistent with previous studies [26]. In the Central Western Carpathians, low flows occur relatively rarely but tend to persist longer, reflecting a regime characterized by a low frequency of prolonged drought episodes. Conversely, the Eastern Beskids exhibit relatively short, low flows despite a locally high number of low-flow events and relatively large volumes, indicating a more dynamic hydrological response with rapid depletion and recovery. Similar relationships between rare but long-lasting low flows in the Central Western Carpathians were reported in [43], which analyzed a comparable multi-year period (1975–2019) and 49 selected gauging stations located in the Upper Vistula Basin. However, in contrast to our study, ref. [43] included multiple stations along the same river, whereas this study considers only one gauging station per river. For the Eastern Beskids, similarly to our findings, low flows were also characterized by a large number but short durations in the study [43]. This is related to a more dynamic hydrological response with fast depletion and restoration of resources, which is largely due to local soil permeability, catchment retention capacity, and precipitation distribution. Low-permeability soils combined with intensive summer rainfall in the Eastern Beskids cause fast surface runoff, limiting permanent retention, while in the Central Western Carpathians, varied soil permeability and frequent orographic rainfall slow down the processes associated with prolonged low-flow conditions due to higher storage and delayed system response.

In the Northern Subcarpathian region, soils with average permeability and moderate precipitation cause rare but prolonged low-flow events of moderate volume, while in the Silesian-Krakow Upland, low flows in terms of volume are classified as low to moderate risk. These relationships are consistent with local hydrological, soil, and climatic conditions, and similar results were obtained by [37,43], showing that droughts in the Eastern Beskids and Outer Western Carpathians are short [43]. Overall, these comparisons confirm that the observed spatial variability of low-flow characteristics is consistent with previous studies, while the identified differences can be largely explained by variations in catchment selection and local hydrological conditions.

Comparison of shallow and deep low-flow trends

Following the analysis of temporal and spatial variability, trends between shallow (FDC90) and deep (FDC70) low-flow events were compared to identify differences across thresholds. The comparison reveals both similarities and regional contrasts between the two thresholds. In the Central Western Carpathians and the Eastern Beskids, consistent statistically significant trends are observed for both thresholds, indicating a strong control of the regional hydrological regime on low-flow dynamics. In the Central Western Carpathians, statistically significant decreasing trends and non-significant tendencies dominate, likely reflecting higher groundwater storage capacity and more persistent precipitation, which buffer the development of prolonged low-flow conditions. In contrast, the Eastern Beskids are characterized by predominantly statistically significant increasing trends for both thresholds, which may be associated with limited retention capacity, low-permeability soils, and intense but short-lived summer rainfall leading to rapid runoff and reduced effective recharge.

In the Northern Subcarpathians and the Outer Western Carpathians, trends differ between thresholds. For deep low flows (FDC90), statistically significant increasing trends prevail, whereas shallow low flows (FDC70) show a more heterogeneous pattern. This discrepancy suggests that deep low flows are more sensitive to long-term groundwater depletion and increasing evapotranspiration, while shallow low flows respond more dynamically to short-term precipitation variability.

Comparative analysis of multi-year periods

Next, trends over two multi-year periods (1961–2019 and 1981–2019) were compared to assess changes in low-flow characteristics. The comparison indicates that although the average number and duration of low-flow events remain similar, the frequency of low-flow days increases in the more recent period, particularly for FDC70. Substantial differences between the two periods and thresholds (FDC90 and FDC70) are particularly evident in statistically significant trends. The implications of this data-driven period selection for trend detection are noted, as the shorter period (1981–2019) may exclude some early historical variability while ensuring broader station coverage for a robust analysis of recent trends. A greater number of statistically significant trends was detected for 1981–2019. This may be partly explained by the higher number of gauging stations included in the shorter period. Taking into account only stations that are common to both periods, most low-flow events occurred in 1981–2019, accounting for 55% to 87% of all recorded events, depending on the station, compared to the years 1961–2019. This suggests a higher concentration of low-flow events in the more recent decades. The lower number of low-flow events in 1961–1980 likely attenuated the overall trend magnitude in the longer time series. These findings are consistent with observed regional warming, reflected in a statistically significant increase in mean annual air temperature over recent decades [48].

The impact of human influence cannot be entirely excluded. Although stations with a near-natural regime were selected, some uncertainty remains. Potential human influences, such as small reservoirs and local water abstractions, cannot be fully ruled out, even in small- and medium-sized catchments. Between 1961 and 2019, some catchment areas may have experienced changes in groundwater or surface water abstraction that were not fully captured in official records. The lack of detailed quantitative data limits the ability to completely distinguish anthropogenic influences. A comparative analysis of minimum annual flows for stations located in the Upper Vistula River Basin indicates spatial variation in this characteristic. For stations in the southern part of the area (Central Western Carpathians), increasing trends and tendencies were recorded, while for stations in the Western Beskids, decreasing trends and tendencies were observed. Similar relationships with regard to Q7_min in southern Poland were shown by [9].

Seasonal patterns of low flows

Finally, seasonal patterns of low-flow events were examined to highlight intra-annual variability and potential implications for water management. Seasonal analysis indicates a predominance of summer low flows, consistent with previous studies conducted in Poland [35,47]. Although such events occur in both summer and winter, the long-term analysis (1961–2019) shows a clear summer dominance. This pattern is primarily linked to increased evapotranspiration during the warm season, reduced effective rainfall, and longer dry spells. Despite high-intensity summer precipitation, its short duration limits groundwater recharge and enhances rapid runoff. Together with the observed rise in air temperature [48] and seasonal redistribution of precipitation [47], these factors increase the likelihood of soil moisture depletion and hydrological drought development during summer.

5. Conclusions

This article analyzes low-flow events, both shallow and deep, in rivers of the Upper Vistula River Basin. The analysis was conducted for two datasets: 25 gauging stations with 58-year-long daily discharge records (1961–2019) and 41 stations with 38-year-long records (1981–2019). Both shallow (FDC70) and deep (FDC90) low-flow events occurred at all analyzed cross-sections. Deep low-flow events have been observed almost every year across many cross-sections since 2012. The average duration of deep low-flow events was similar for both periods. Seasonal analysis revealed that summer low flows were more frequent and intense than winter low flows. Most rivers showed increasing trends in low-flow events, with several of these being statistically significant.

These findings highlight that analyzing low-flow characteristics in the Upper Vistula River Basin is crucial for predicting and mitigating the negative effects of low flows, planning water resources management, and preparing for potential water crises. This knowledge can help identify catchments particularly vulnerable to frequent or prolonged low flows and guide the implementation of water management strategies during low-flow periods, including measures to reduce impacts over short-term, seasonal, and long-term timescales.