Maximum River Runoff in Poland Under Climate Warming Conditions

A nonparametric Mann–Kendall test, which is used to detect a trend in a time series, was applied to assess multiyear trends in monthly, seasonal and annual discharge. The test was conducted using Microsoft Excel software with the MAKeSeNS overlay, which is an extended version of the Mann–Kendall test developed by researchers at the Finnish Meteorological Institute (Salmi et al. 2002).

The Mann–Kendall test is used when the given values of x_i in a time series can be described according to the following equation: 1xi=f(t)+εi{x_i} = f(t) + {\varepsilon _i} where is a continuous, decreasing or increasing function of time, and the residuals can be treated as coming from the same distribution with mean = 0. With this, the deviation from the distribution can be considered invariant over time. The S statistic of the Mann–Kendall test was calculated based on the following formula: 2S=∑k=1n−1∑j=k+1nsgn(xj−xk)S = \sum\nolimits_{k = 1}^{n - 1} {\sum\nolimits_{j = k + 1}^n {sgn\left( {{x_j} - {x_k}} \right)} } where x_j and x_k are sets of values of monthly, seasonal or annual water levels arranged as a time series at the corresponding time instants j and k, with j > k: 3sgn(xj−xk)={ 1 if xj−xk>00 if xj−xk=0−1 if xj−xk<0sgn\left( {{x_j} - {x_k}} \right) = \left\{ {\matrix{ {1{\rm{if}}{x_j} - {x_k} > 0} \hfill \cr {0{\rm{if}}{x_j} - {x_k} = 0} \hfill \cr { - 1{\rm{if}}{x_j} - {x_k} < 0} \hfill \cr } } \right.

Declining or rising trends are determined by a negative or positive Z value. To calculate it, the VAR(S) should be calculated first using the following formula: 4VAR(S)=118[ n(n−1)(2n+5)−∑p=1tp(tp−1)(2tp+5) ]VAR(S) = {1 \over {18}}\left[ {n(n - 1)(2n + 5) - \sum\nolimits_{p = 1} {{t_p}\left( {{t_p} - 1} \right)\left( {2{t_p} + 5} \right)} } \right] where q is the number of water level values, and t_p is the number of values in the p-th group. Based on the values of S and VAR(S), Z can be calculated using the following formula: 5Z={ S−1VAR(S) if S>00 if S=0S+1VAR(S) if S<0{\rm{Z}} = \left\{ {\matrix{ {{{S - 1} \over {\sqrt {VAR(S)} }}{\rm{if}}S > 0} \hfill \cr {0{\rm{if}}S = 0} \hfill \cr {{{S + 1} \over {\sqrt {VAR(S)} }}{\rm{if}}S < 0} \hfill \cr } } \right.

This procedure allows verification of the null hypothesis H₀ assuming the absence of trends. Chronologically ordered xi observations are analysed, and the alternative H1 hypothesis is the existence of a monotonically rising or falling trend. The Z test has a normal distribution, allowing the absolute value of Z to be compared with a normal distribution to assess whether there is a monotonic trend. If a trend is found, its statistical significance is determined. The study used four levels of statistical significance: p < 0.001, p < 0.01, p < 0.05 and p > 0.05. For p > 0.05, there is no statistical significance of the changes in discharge that were observed.

A rate of change was calculated to determine changes in average maximum river-specific runoff (MHq) during the warming period of 1988– 2020 relative to the period of 1951–1988: 6SX¯1988−2020−X¯1951−1988=X¯1988−2020−X¯1951−1988X¯1951−1988×100{S_{{{{\rm{\bar X}}}_{1988 - 2020}}}} - {{{\rm{\bar X}}}_{1951 - 1988}} = {{{{{\rm{\bar X}}}_{1988 - 2020}} - {{{\rm{\bar X}}}_{1951 - 1988}}} \over {{{{\rm{\bar X}}}_{1951 - 1988}}}} \times 100 where are average runoff values in the sub-periods of the multi-annual period 1951–2020. The rate that was calculated shows the percentage increase or decrease in runoff in the period after the climate change (1988–2020) compared to MHq in the period before the climate change (1951–1988).

Differences in monthly, seasonal and annual MHq were calculated between the years 1988– 2020 and 1951–1988. The statistical significance of these differences was tested using the T-test for independent samples. Each time, the hypothesis H₀ : μ₁ = μ₂ of equality of expected values was tested against the hypothesis H₁ : μ₁ ≠ μ₂. Rejection of the hypothesis indicates that there are significant differences in MHq observed after and before the climate change. The T-statistics has the Student’s distribution, with n₁ + n₂ and 2 degrees of freedom: 7T=X¯1−X¯2SX¯1−X¯2T = {{{{{\rm{\bar X}}}_1} - {{{\rm{\bar X}}}_2}} \over {{S_{{{{\rm{\bar X}}}_1} - {{{\rm{\bar X}}}_2}}}}} where SX¯1−X¯2{S_{{{{\rm{\bar X}}}_1} - {{{\rm{\bar X}}}_2}}} is 8SX¯1−X¯2=(n1−1)×S12+(n2−1)×S22n1+n2−2(1n1+1n2){S_{{{{\rm{\bar X}}}_1} - {{{\rm{\bar X}}}_2}}} = \sqrt {{{\left( {{n_1} - 1} \right) \times S_1^2 + \left( {{n_2} - 1} \right) \times S_2^2} \over {{n_1} + {n_2} - 2}}\left( {{1 \over {{n_1}}} + {1 \over {{n_2}}}} \right)} where n₁, n₂ are the sample sizes, are the variances of both samples and are the averages of both samples.

In a study of the spatial regularity of changes in average maximum runoff during the warming period after 1988, water-gauge stations were clustered using the Ward’s method by the values of 12-month MHq differences. The clustering results are presented in the form of a dendrogram that reflects the similarity structure of the set of water gauges studied and was used to identify separate typological classes. In this paper, the number of classes was determined by analysing the geometry of the dendrogram and the bond distance curve.

Surfer 13 (Golden Software) and additional tools from QGIS Development Team (QGIS.org) were used for graphical processing of the results, which enabled advanced visualisation of geographical and hydrological data. On the contrary, mathematical and statistical compilations of the data were done using Excel (Microsoft) and Statistica (TIBCO Software Inc.).

The maximum daily discharge in 1951–2020 of the rivers that were studied showed a dominance of falling trends over almost the entire territory of Poland, apart from Mountain Rivers. A decrease in maximum discharge was found at >85% of the water-gauge stations, and the decrease at 45% was considered statistically significant (p < 0.05) (Fig. 4). Particularly, significant downward trends (p < 0.01) were observed in the rivers of various regions of Poland, especially in the northeastern part of the country in the Narew river basin, as well as in upland rivers (e.g. Lubaczówka, Czarna and Kamienna) and single rivers located in the Polish Lowlands (the central Warta and Bzura) and in Wda, which is in a lake district. Only the maximum discharge of most of the rivers of the mountainous areas showed rising trends, but they were usually statistically insignificant. A statistically significant positive trend (p < 0.01) was found only for the discharge of the Skawa River in Sucha Beskidzka and the Kamienica River in Barcinek.

The spatial distribution of the MHq values of the rivers that were studied varies in a very characteristic way (Fig. 3). The highest values, exceeding 100 dm³ · s⁻¹ · km⁻², were observed in the drainage areas of the mountainous tributaries of Vistula and Oder, with maximum values reaching >300 dm³ · s⁻¹ · km⁻² (in the upper Vistula drainage area up to Skoczów). High average runoff values (>200 dm³ · s⁻¹ · km⁻²) were also found in the river basins of Soła, Skawa, Raba, the upper Dunajec up to Krościenko, Biała, Wisłoka and Ropa as well as osława in the upper San River catchment. Towards the north, MHq values decrease, reaching 30–100 dm³ · s⁻¹ · km⁻² for upland river basins. Most rivers of the Polish Lowlands typically have runoff values of 10– 20 dm³ · s⁻¹ · km⁻². The lowest MHq values of <10 dm³ · s⁻¹ · km⁻² are recorded for the drainage areas of the Noteć and Wełna rivers and the Warta River basin up to Gorzów Wielkopolski. Higher runoff values (20–40 dm³ · s⁻¹ · km⁻²) were found in the catchment areas of the coastal rivers (Rega, Parsęta, Wieprza, Słupia and Łupawa) and in the northeast catchment areas of the Guber, Gołdapa, upper Biebrza, Narew and Nurzec rivers.

Fig. 3.

Trends in changes of maximum daily discharge in a hydrological year against average maximum specific runoff from 1951 to 2020.

Maximum daily river discharge in the winter season (December–February) showed a downward trend at >54% of the gauge stations analysed, mainly in central Poland, with only 10% of them being statistically significant (p < 0.05) (Fig. 4). Falling discharge values were recorded in various regions of the country, with statistically significant results (p < 0.05) in lake district rivers such as Drawa and Wda, as well as in Mała Noteć, Pilica, Raba, in the upper oder drainage basin and in the catchments of Sumina, Nysa Kłodzka and Strzegomka. By contrast, a rise in the maximum winter discharge was observed in most mountain rivers and in northern and northeastern Poland, where a statistically significant increase (p < 0.05) was observed in the rivers in Narew, in the Biebrza basin and in single mountain rivers, such as Kwisa and Nysa Kłodzka. In spring (March–May), the majority of the rivers studied (more than 87% of the gauge stations) showed falling discharge trends, of which more than 37% were statistically significant (p < 0.05), mainly in northeastern Poland, in the Narew River basin, in the central part of the country and in the Pilica River basin. Increases in discharge were observed only in a small number of rivers in southern Poland (>12% of the gauge stations), with statistically significant results (p < 0.05) observed only in the Skawa River. Negative discharge trends dominated during the summer, which was observed at more than 77% of the gauge stations analysed, of which more than 22% reached statistical significance (p < 0.05). There were particularly significant decreases in daily maximum summer discharge, with significance at p < 0.001, recorded on rivers such as Wda, Mała Noteć and Sumina. Most of the Vistula’s tributaries showed statistically insignificant trends, except for the drainage area of the Pilica, where statistically significant values were observed (p < 0.05). The autumn analysis showed that positive trends covering more than 45% of the water-gauge stations occurred mainly in the south and east of the country, while decreases in discharge, prevalent in central and western Poland (more than 54% of the gauges), were statistically significant in only 9% of cases. It is also worth noting that only the tributaries of Vistula in the Carpathian region showed statistically significant upward trends (p < 0.05).

Fig. 4.

Trends in changes of maximum daily seasonal discharge against the average maximum specific runoff in four seasons in 1951–2020.

The hydrological analysis for 1951–2020 shows significant regional variation in the average maximum winter-specific runoff in Poland. The highest values, exceeding 50 dm³ · s⁻¹ · km⁻², were found in mountainous catchments in the southern regions of the country, with MHq of 100 dm³ · s⁻¹ · km⁻² in the upper Vistula, Nysa Kłodzka and osława in the drainage area of the San River (Fig. 5). The drainage areas of upland rivers had MHq ranging 25–50 dm³ · s⁻¹ · km⁻², and in the Koszalin Coastland and Masurian Lake District they did not exceed >30 dm³ · s⁻¹ · km⁻². The lowest runoff, below 10 dm³ · s⁻¹ · km⁻², occurred mainly in western and eastern Poland, especially in the Polish Lowlands, Polesie Lubelskie and Lublin Upland. In spring, MHq was at the highest level, and it was most important for the formation of water resources, with maximum values of >100 dm³ · s⁻¹ · km⁻² in the catchments of the Nysa Kłodzka River in the mountains and of the Carpathian rivers, and even 169 dm³ · s⁻¹ · km⁻² in the drainage area of the upper Vistula. The lowest values, below 10 dm³ · s⁻¹ · km⁻², were recorded in western Poland, especially in the catchments of Noteć and the middle and lower Warta, while in eastern and northeastern Poland spring runoff exceeded 25 dm³ · s⁻¹ · km⁻². In summer, a significantly lower runoff was observed in the north of the country, where it did not exceed 10 dm³ · s⁻¹ · km⁻², while in the south it reached >200 dm³ · s⁻¹ · km⁻² in some places. The lowest values, <5 dm³ · s⁻¹ · km⁻², occurred in the drainage areas of Warta, Noteć and the eastern regions, such as the Krzna River and part of Narew, while values exceeding 150 dm³ · s⁻¹ · km⁻² were recorded in the upper Vistula and its Carpathian tributaries. In autumn, the distribution of runoff was similar to summer, with the highest values, >50 dm³ · s⁻¹ · km⁻², in the south of the country, and locally even >100 dm³ · s⁻¹ · km⁻². In central Poland, runoff did not exceed 10 dm³ · s⁻¹ · km⁻², and in the drainage basins of Warta, Noteć, Krzna and Wieprz the values decreased below 5 dm³ · s⁻¹ · km⁻². Besides the mountain regions, larger runoff values, exceeding 15 dm³ · s⁻¹ · km⁻², were found in Pomerania.

Fig. 5.

Percent share of trends with a defined statistical significance (p) in analysed series of monthly, seasonal and annual maximum discharge from 1951 to 2020.

An analysis of monthly daily maximum discharge showed prevailing downward trends in most months (Fig. 4). Particularly significant declines were observed at more than 80% of the water-gauge stations in March and April. In March, downward trends prevailed from the south to the centre of Poland, with 25% of the water-gauge stations surveyed showing statistical significance of downward trends at p < 0.05. The largest falls were observed in April, mainly in the eastern and central parts of the country, where more than 95% of the gauge stations showed a decreasing trend and 33% were statistically significant (p < 0.05). By contrast, in January and February positive trends prevailed in 66% and 70% of the cases studied, 33% and 29% were considered statistically significant, respectively. These trends were particularly prominent in northeastern Poland in the Biebrza and Narew drainage basins, where statistical significance was recorded at p < 0.05. In the spring and summer months, declining trends prevailed in central and southern Poland. However, in May, downward trends were also recorded in Pomerania and Masuria. Starting from September, there is a clear increase in maximum discharge in mountainous regions.

During the warming period of 1988–2020, the average maximum specific runoff decreased in most of the rivers studied compared to the period 1951–1988 (Fig. 6). The data show a reduction in MHq, which is particularly prominent in the northeastern and central parts of the country, where runoff has fallen by more than 30% and, in some places, by more than 40% (the Pilica, Narew and Bug catchments). In contrast to most regions, an increase in MHq was recorded in mountainous areas and the Koszalin Coastland by more than 10% and 5%, respectively. The most significant increase, exceeding 50%, was found in the Skawa River basin.

Fig. 6.

Changes in average maximum runoff values [%] during the 1988–2020 warming period relative to the 1951–1988 period and their statistical significance (p).

MHq was found to have fallen for most rivers (at more than 83% of the water-gauge stations) (Fig. 7), and statistically significant (p < 0.05) changes occurred at more than 41% of the stations. There was a particularly high concentration of changes in MHq falls in the northeast of the country. MHq increased mainly in the Łupawa River basin, where the change was considered statistically significant (p < 0.05).

Fig. 7.

Changes in seasonal average maximum runoff values [%] during the warming period of 1988–2020 relative to the 1951–1988 period and their statistical significance (p).

Seasonal changes in winter MHq during the warming period showed a decline at 78% of the water-gauge stations surveyed, with 23% of these changes being statistically significant (p < 0.05) (Fig. 7). The largest declines, by more than 30–40%, were recorded in central and southern Poland, especially in the drainage areas of the Mała Panew, Kłodnica, Prosna, Pilica, Czarna and Wisłoka rivers (Fig. 8), where statistical significance was recorded at p < 0.01. An increase in MHq was registered in the northern river basins, but only a small portion of them was statistically significant. In spring, MHq decreased at >73% of the gauge stations, of which 30% were statistically significant. The largest declines, by more than 30%, were found in the drainage areas of Warta, Wełna, Wrześnica, Narew and Bug, where declines locally exceeded 40% (Fig. 7). By contrast, increases in MHq by more than 50% were observed in the upper reaches of Vistula, particularly in the Skawa catchment, where they reached 90%. In the summer season, declines in MHq prevailed at 87% of the gauge stations, 26% of which were statistically significant (p < 0.05). The largest declines by more than 40–50% were registered in the Vistula (Narew, Biebrza, Pilica) and Noteć river basins. In autumn, 70% of the water gauges showed decreases in MHq, with 13% of the changes being statistically significant. The largest declines by more than 30% occurred in the Warta, Noteć, Narew and Biebrza river basins. In the south of the country, an increase in MHq exceeding 100% was found in the upper reaches of Vistula and its tributaries (Soła and Skawa), and there were statistically significant changes at three stations: Vistula – Skoczów, Skawa – Sucha Beskidzka and Mleczka – Gorliczyna.

Fig. 8.

Percent share of positive and negative differences in average monthly, seasonal and annual maximum discharge during the warming period of 1988–2020 relative to 1951–1988 and their statistical significance (p).

Changes in monthly MHq values after 1988 mostly showed decreases in most rivers throughout the country (Fig. 7). By contrast, a significant increase in MHq was observed in January, February, May and September. In January and February, MHq increased mainly in the northern and northeastern parts of the country, where increases in MHq ranged from 20% to as much as 40%. The largest increase of >40% was observed in the Biebrza River basin and was statistically significant (p < 0.05). In February, an increase in runoff also appeared in southern Poland, mainly in the mountains >20% and locally >30% (Dunajec, Kwisa, Czarny Potok and Kamienica). At the same time, in January and February, there were significant decreases in MHq, mainly in the upper reaches of the Vistula and Oder rivers and their tributaries. March was characterised by significant decreases in MHq >20%, mainly in the rivers in the centre and the east of the country. The largest decreases occurred in the drainage area of Bug (MHq >30%) along with its tributaries (Liwiec, Krzna, Nurzec, Narew, Supraśl and Biebrza), and equally high decreases (>30%) in MHq occurred in the drainage area of the Warta. In both cases, the changes were statistically significant (p < 0.05). By contrast, rivers in the southeast stood out in terms of their increase in MHq >40% and locally >50% (Kwisa, Bóbr and Kamienica), which was statistically significant (p < 0.05). In May and September, rivers in the southern and southeastern parts of the country stood out in terms of a significant increase in their MHq. In May, runoff increased mainly in the upper and middle reaches of Vistula and its tributaries. The largest increases (>50%) were observed in Skawa, Raba, Soła and Vistula, but the increase was statistically insignificant. on the contrary, in the drainage areas of Oder and Warta, there were significant decreases in MHq >20%, with the largest MHq >40% in the following rivers: Bóbr, Strzegomka, Bystrzyca, Nysa Kłodzka, Flinta, Mogilnica, Sama, Mała Noteć and Gąsawka, and for most of these rivers the decreases were statistically significant (p < 0.05). In September, the increase in MHq was much greater than in May. In the upper reaches of Vistula, the largest increase of more than 100% was observed in the following rivers: Raba, Skawa, Dunajec, Wisłoka, Wisłok, Mleczka and Biała. An increase in MHq >50% also occurred in the coastal rivers, which was statistically insignificant. The rivers in central Poland mainly experienced decreases in MHq. The largest decrease in MHq occurred in August. The centre, south and northeast of Poland saw the highest decreases of more than 60%, even more than 80% in some places, including the following rivers: Kamienna, Czarna, Mała Noteć, Kłodnica, Mała Panew, Narew, Narewka, Supraśl and Biebrza, where statistically significant decreases occurred in most of these rivers. Other months showed significant decreases in MHq.

Based on the clustering (grouping) by changes in the monthly MHq after 1988, eight groups were distinguished (Fig. 9). The range of changes in the parameters of the analytical characteristics in the groups of rivers that were so identified is shown in Figure 11, while the spatial picture of the results of grouping rivers by differences in the parameters of MHq is shown in Figure 10. Group 1

includes rivers and their sections in the upper part of the Warta River basin along with its tributaries (Ner, Prosna and Widawka) and the tributaries of the Vistula River (Pilica, Czarna, Nida and San) (Fig. 10). Changes in the monthly MHq mainly decreased in most of the groups that were identified (Fig. 11). During the winter and spring months, decreases in runoff were mainly observed. The summer and autumn months, on the contrary, showed a great variation but not as strong decreases as in other months. The largest decrease occurred in August (>40%), while a slight increase (>2%) was observed in May.

Fig. 9.

Dendrogram of gauges grouping based on 12 monthly values of the changes in the average maximum specific runoff and the plot of the linkage distance. Note: gauge ID codes in accordance with Appendix 1.

Fig. 10.

Locations of water gauges grouped based on changes in the monthly average maximum specific runoff during the warming period of 1988–2020.

Fig. 11.

The scope of changes in average maximum specific runoff (MHq) in the warming period after the 1988 in individual groups, as derived from the grouping presented in Figure 9.