1 Introduction

As a result of human activity and advancing climate change, especially throughout the second half of the 20th Century, an increase in water temperature and a reduction in the extent of occurrence and duration of river ice cover have been observed (e.g., Yang et. al 2020; Graf and Wrzesinski 2020; Fukś 2023). The most significant reason for the transformation of the winter regime of rivers is considered to be the increase in air temperature, which is an essential determinant of the course of surface water temperature (Caissie 2006; Whitehead 2009). Increases in river water temperature over recent decades have been recorded in many lowland and mountain areas (Webb and Nobilis 2007; Graf and Wrzesinski 2020; Kędra 2020; Kelleher 2021; Zhu et al. 2022; Niedrist 2023). The increase in air temperature and warming of river waters translates into the subsequent formation of ice cover (Magnuson et al. 2000). Winter periods are characterized by more frequent thaws, during which snow melting occurs in the catchment area, often combined with rainfall, causing surges and the premature mechanical breakup of ice cover (Prowse et al. 2002; Prowse and Bonsal 2004). Magnuson et al. (2000) estimated that, during the period 1846–1995, ice cover breakup on inland waters (rivers and lakes) occurred 0.65 days earlier each decade, corresponding to a 0.12 °C/decade increase in air temperature. In some areas, the complete disappearance of river ice cover has also been reported (Ionita 2018). As a result of later formation, earlier breakup and greater instability of the ice cover during winter, its duration has decreased. Yang et al. (2020) estimated that for every 1 °C increase in global average temperature, the average river ice duration will decrease by 6.1 days; however, it is challenging to obtain a detailed estimation of the links between air and water temperature and ice cover occurrence due to other factors influencing river characteristics. Consequently, this is still an open problem requiring further scientific research. The complexity of the relationship between the environmental variables in question is evidenced, among other things, by the significant spatial variation in trends of ice cover breakup dates in longitudinal river profiles (Cooley and Pavelsky 2016).

The temporal and spatial variability of water temperature and ice cover occurrence on rivers resulting from hydroclimatic conditions is superimposed on the variabilities resulting from human activities. The main anthropogenic factors transforming the thermal and ice regimes of rivers include pollutant emissions (including thermal), channel regulation and construction of hydroengineering structures. Dam reservoirs are an example of structures that transform both the thermal and ice regime of rivers. Depending on their climate zone, as a result of thermal stratification and the release of bottom hypolimnion waters, reservoirs cause rivers below their location to become cooler in summer and warmer in winter (Lehmkuhl 1972; Ashton 1979; Preece and Jones 2002; Olden and Naiman 2010; Maheu et al. 2016; Jiang et al. 2018). As a consequence, among other effects, the synchronization of the air and water temperature cycles in rivers below reservoirs are disrupted (Kędra and Wiejaczka 2016, 2018). Through the warming effects of reservoir operations in winter, there is a reduction in the formation and maintenance of ice cover downstream (Starosolszky 1990; Belolipetsky and Genova 1998; Takács et al. 2013; Jasek and Pryse-Phillips 2015; Takács and Kern 2015; Pawłowski 2015; Apsîte et al. 2016; Chang et al. 2016; Maheu et al. 2016). In the context of the transformation of river ice conditions by dam reservoirs, in addition to thermal changes, it is also important to transform flow dynamics in rivers below dams (Kędra 2023) and to limit the migration of mobile ice along river courses (Huokuna et al. 2020).

The temporal and spatial variability of ice cover occurrence in mountain rivers is poorly understood in comparison to larger lowland rivers. This is due to the limited number of studies based on remote sensing data and field measurements (Thellman et al. 2021). Most work focuses on relatively large lowland rivers, for which long observation series are available and remote sensing data can be used (e.g., Thellman et al. 2021; Fukś 2023). The lack of broader recognition of this problem for mountainous areas limits the ability to quantitatively estimate the impact of the observed increases in air temperature (climate change) and associated environmental changes on the ice regime of rivers at regional and global scales. This is important in the context of the likely higher rate of air temperature increase in some mountainous areas relative to lowland areas (Pepin et al. 2022). Also problematic is the lack of consideration of the effect of other geographic environmental elements (such as large reservoirs) that can transform water temperature and ice conditions. The large number of reservoirs in river ice areas (> 8,000) suggests that they can significantly transform the winter thermal and ice regime on both local and regional scales (Fukś 2023). Detailed recognition of the role of reservoirs in shaping the ice regime of rivers is further limited by the lack of methods developed to quantitatively estimate and separate the impacts of reservoirs from transformations due to climate change.

A group of methods used to quantitatively separate the effects of climate change and dam reservoir operation on water temperature and ice cover occurrence are machine learning algorithms. To some extent they can reproduce natural hydrological conditions on rivers transformed by the operation of a dam reservoir. To date, most work in this area has focused on assessing the impact of reservoirs on water temperature (Cai et al. 2018; Qiu et al. 2021; Xu et al. 2022; Yang et al. 2022). The most commonly used methods include random forests (Qiu et al. 2021), the hybrid air2stream model (Cai et al. 2018; Qiu et al. 2021; Yang et al. 2022) and various types of artificial neural networks (Qiu et al. 2021). One method which produces very good results in predicting river water temperature is the Extreme Gradient Boosting model (XGBoost; Chen and Guestrin 2016). It is a simple and efficient method (Chen and Guestrin 2016) that has been shown to predict river water temperature with accuracy similar to that obtained by algorithms based on artificial neural networks (Feigl et al. 2021). XGBoost also makes it possible to solve classification problems and has been used in predicting the occurrence of ice cover on rivers (Graf et al. 2022). Despite its promising features, the model has not yet been used to study the impact of dam reservoirs on river water temperature and ice cover occurrence.

The main objective of the article is to quantify and separate the impacts of climatic variability and the operation of dam reservoirs on temporal–spatial changes in water temperature and related changes in the occurrence of ice cover on mountain rivers. Moreover, this study aims to investigate the phase synchronization observed between air and water temperatures in two disjoint time intervals: immediately before and after the construction of a reservoir. This will enable the identification of changes in air–water temperature synchronization caused by the operation of dam reservoirs and the estimation of the size of the disturbances inherent to their natural behavior. Two Carpathian rivers and their adjacent catchments located in the upper Vistula River basin (Central Europe), namely the Ropa River with the Klimkówka reservoir operating in its course, and the Biała River, were selected for this study. The partial objectives of the analysis undertaken can be summarized as follows:

  • Recognition of temporal trends and the magnitude of changes in water temperature and number of days with ice cover on rivers with and without dam reservoirs;

  • Recognition of spatial variability of water temperature and ice cover formation on rivers with and without dam reservoirs;

  • Application of the XGBoost machine learning algorithm to estimate the magnitude of the reservoir's influence on river thermals and ice cover;

  • Use of wavelet analysis to estimate the influence of the reservoir on the phase synchronization between air and river water temperatures.

2 Study area, data and methods

2.1 Study area

The analyzed rivers – the Ropa and the Biała – are located in the Outer Western Carpathians. Together with their neighboring catchments, these rivers flow from springs in the area of the Beskid Niski near the Polish–Slovakian border and their middle course flows through the foothills to the low uplands in the northern parts of their catchments. The catchment area of the Biała River is 984 km2, with an average annual flow volume of 8.76 m3∙s−1 at its mouth (Punzet 1991). The catchment area of the Ropa River is 974 km2, and the average flow volume at the mouth is 9.43 m3∙s−1 (in the period before the construction of the Klimkówka reservoir, Punzet 1991; Soja and Hennig 2000). The Klimkówka reservoir is located in the upper reaches of the Ropa River. It was developed in 1994 as a result of the construction of a 33-m-high ground dam. During winter (November to March), the average inflow to the reservoir is 2.9 m3∙s−1, while the outflow is 2.3 m3∙s−1. At station R2 (Fig. 1), in the period 01.11.1981–31.03.1994 (13 years before the Klimkówka reservoir was built) the average flow of the Ropa River in the winter period amounted to 5.8 m3∙s−1, while in the period 01.11.1994–31.03.2007 (13 years after the Klimkówka reservoir was built) it amounted to 6.1 m3∙s−1. It has been shown that the operation of the reservoir significantly transforms the thermal regime of the river downstream of its location (Soja and Wiejaczka 2014).

Fig. 1
figure 1

Map showing the location and topography of the study area as well as the location of hydrological and meteorological stations and measurement points

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The authors’ field measurements, low population density in the catchment area and the absence of large cities along the studied rivers suggest that factors such as thermal emissions (e.g. in the form of sewage) have a minor and solely local impact on water temperature and ice cover occurrence on the studied rivers. However, due to the lack of data on thermal pollution, its impact is difficult to quantify.

2.2 Data and methods

Owing to the lack of damming structures on the Biała River, this analysis assumes that the variabilities of water temperature and ice cover occurrence on this river are mainly due to climatic conditions. In the case of the Ropa River, on the other hand, the variability of these characteristics results from both climatic conditions and the influence of the Klimkówka reservoir. It seems that other factors affecting the occurrence of ice cover do not play a significant role in the changes of water temperature and the occurrence of ice cover in the studied rivers. The similarity of the environmental characteristics of the rivers under consideration and the presence of a dam reservoir on one of them makes it possible to compare data on water temperature and the occurrence of ice cover between these rivers and to estimate the relative influences of climatic and anthropogenic factors in shaping their thermal and ice regimes. A machine learning model was used to quantitatively separate the influence of the dam reservoir from that of climatic variability on water temperature and ice cover occurrence. An analysis of the effect of reservoir operation on the phase synchronization between air and river water temperatures based on a continuous wavelet transform was also conducted. In addition, field surveys were carried out on both rivers allowing the spatial variability of the studied characteristics in their longitudinal profile to be assessed.

During the first stage, meteorological data (daily minimum, maximum, and average air temperature and precipitation sum) and data on water temperature and ice cover occurrence were obtained for both studied rivers. For air temperature and precipitation parameters, data were obtained from the Eugeniusz Gil Research Station of the Institute of Geography and Spatial Organization, Polish Academy of Sciences in Szymbark (IGSO PAS) for the period 1973–2020 (Fig. 1, T1). For the purposes of visualization, data on mean daily air temperature were also obtained for the T2 station belonging to the Polish Institute of Meteorology and Water Management—National Research Institute (IMWM-NRI) for the period 1956–1972 (Access data from the T2 station at the following address: https://danepubliczne.imgw.pl). Data on daily water temperature in the Biała River were obtained from the IMWM-NRI hydrological station (B1) for the period 1984–2016 (no data for 1987 and 1988; access to data: https://danepubliczne.imgw.pl), whereas data on daily water temperature in the Ropa River were obtained from the IGSO PAS Research Station in Szymbark (R1) for the period 1981–2016. Data on the occurrence of ice cover (border ice and total ice cover) over the period 1950–2020 at four water gauge cross sections (R1, R2, B1, B2) were obtained from the resources of IMWM-NRI (access to data: https://danepubliczne.imgw.pl), the resources of IGSO PAS, and the hydrological yearbooks of surface waters of the Polish State Hydrological and Meteorological Institute from the period 1949–1980. Due to shortages, data on the occurrence of ice cover at station R1 were created using data from two gauging stations approximately 7 km apart (from 1971 to 2020, data were available only from station R1 marked in Fig. 1). Detailed information about the gauging stations and the data obtained are listed in Table 1.

Table 1 Information about the used measurement stations and data
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The acquired air and water temperature data and ice cover occurrence were examined for trends, both for the entire winter period (November through March) and for individual months (except for ice cover, for which the trend was determined only for the entire winter period). For this purpose, the non-parametric Mann–Kendall test was used, and the Theil-Sen estimator was applied to determine the magnitude of change (Mann 1945; Theil 1950; Sen 1968; Kendall 1975). Results at p < 0.05 were accepted as statistically significant.

2.3 XGBoost model

The supervised machine learning model Extreme Gradient Boosting (XGBoost, Chen and Guestrin 2016) was used to estimate the impact of the Klimkówka reservoir on the temporal variability of water temperature and ice cover occurrence in the Ropa River. XGBoost is based on a gradient boosting algorithm for decision trees. Gradient boosting is performed by reducing the prediction bias of models created in each successive iteration based on residuals (or misclassifications) from the previous round. The objective function \(\mathcal{L}\) at step t minimized in the learning process can be defined as follows:

$${\mathcal{L}}^{t}= \sum_{i=1}^{n}l({y}_{i}, {\widehat{y}}_{i})+ \sum_{k=1}^{K}\Omega \left({f}_{k}\right)$$
(1)

where l is the loss function measuring the difference between the predicted value \({(\widehat{y}}_{i})\) and the actual value (\({y}_{i}\)) and Ω is the penalization term for the complexity of the model (Chen and Guestrin 2016; Graf et al. 2022). The XGBoost model has the ability to solve both classification and regression problems and has been successfully used to predict changes in river water temperature and ice cover occurrence (e.g., Feigl et al. 2021; Graf et al. 2022). All calculations performed used the Python programming language and the scikit-learn and xgboost libraries. In order to demonstrate the influence of the Klimkówka reservoir on water temperature and ice cover occurrence based on data obtained from hydrological (R1, R2) and meteorological (T1) stations, a regression model predicting water temperature (for station R1) and binary classification models predicting the presence (1) or absence (0) of ice cover (for stations R1, R2) were constructed. Data acquired for the period before the construction of the reservoir were used as sets for model learning. Data from meteorological station T1 – including average, minimum, and maximum daily air temperature and total precipitation – were used as explanatory variables. A 14-day lag was included for each parameter; as such, the values of the explanatory variables from the modeled day and all 14 previous days were used to predict water temperature and ice cover occurrence on a particular day. For air temperature (average, minimum, and maximum), the average of the preceding 14 days was also used, and for precipitation, the sum of the preceding 14 days was used. Preliminary analyses showed that this approach improved the predictive ability of the models (not shown). Information concerning the time of occurrence of phenomena (day of the year in the Gregorian calendar), which plays a special role in the prediction of hydrological phenomena, was also added to the model (Feigl et al. 2021). The “clock hand coordinates” technique was used to represent temporal information appropriately. Each day of the year was converted to the sine and cosine of the angle being 1/365 of a full rotation of the “clock hand”. The formally used transformation can be expressed as follows:

$$d \to \left(\text{sin}\left(\frac{2\pi d}{365}\right),\text{cos}\left(\frac{2\pi d}{365}\right)\right),$$
(2)

where d is the day of the year in the Gregorian calendar (the extra day in leap years was not included in the analysis). The use of this type of transformation made it possible to include information about the day of the year in a cyclical manner, avoiding problems caused by increases in the numerical values defining the day of the year at increasingly later dates.

River flow data were not used for the prediction due to the transformation of the flow volume downstream of the reservoir as a result of the operation of the hydroelectric power plant at the dam. The study assumes that the model predictions in the post-dam period represent the thermal and ice conditions of the Ropa River, which are not impacted by the operation of the reservoir. Consequently, it was not possible to use explanatory variables that depended on reservoir operation. Making this assumption limits the possibility of using hybrid or physical models of water temperature and ice cover formation, since in most models the discharge of the river is an important input variable.

The acquired dataset was divided into a learning set and a test set. In the case of water temperature (R1), data from the period 01.11.1981–31.10.1991 were used as the training set, and data from the winter periods (November to March) from 01.11.1991–31.03.1994 were used as the test set. This was due to the need to estimate the actual model bias for these periods. In the case of models predicting the presence of ice cover (R1, R2), the acquired data were randomly divided into training and test sets with a 70/30 ratio while maintaining the proportion of each class (ice cover/no ice cover). In this case, the database was also limited to winter periods (November to March) to reduce class imbalance.

XGBoost is a complex model in which the appropriate choice of hyperparameters can have a significant impact on the predictive capabilities of a model. Due to the large number of hyperparameters, it was not possible to use the grid search method because of limited computational resources. Therefore, the Bayesian optimization method was employed. This method, allowing global optimization of multiple hyperparameters in complex machine learning models, was originally proposed and developed by Kushner (1964), Zhilinskas (1975), and Močkus (1975, 1989). In this method, a probability model of the objective function (surrogate model) was built from the data, based on which the points used to determine the probability distribution in subsequent iterations were sampled. The most commonly used method for building the surrogate model is the Gaussian process (GP). The hyperopt library was used to perform Bayes-based optimization (Bergstra et al. 2013). Stratified cross-validation was used to separate the validation subset for the classification models (ice cover and the R1 and R2 stations), while cross-validation was used for the water temperature model. For ice cover classification models (R1 and R2 stations), the area under the receiver operating characteristic curve (ROC-AUC) was used as the objective function for optimizing hyperparameters and as a metric for model evaluation on the test set. Additionally, balanced accuracy, recall, precision, and F1 scores were also calculated to assess model quality. For the water temperature model (station R1), the mean square error (MSE) was used as the objective function for optimizing hyperparameters and as a metric for model evaluation. Metrics such as mean absolute error (MAE), root mean square error (RMSE), the Nash and Sutcliffe (1970) coefficient of efficiency (NSE), the coefficient of determination (R2), and the RMSE-observations standard deviation ratio (RSR) were also calculated to assess model quality. The hyperparameters used and the extent of their optimization are presented in the supplementary materials (Table S1).

2.4 Method to determine the impact of reservoir and climate change

Based on the developed models, the water temperature (at station R1) was predicted for the period 1981–2016 and ice cover occurrence (at stations R1 and R2) were predicted for the period 1973–2020. Analyses of the impact of the reservoir and climatic conditions on water temperature and ice cover occurrence were based on two equal periods: 01.11.1981–31.03.1994 (before the reservoir was built) and 01.11.1994–31.03.2007 (after the reservoir was built). In addition, an analysis was carried out for periods including all available data before and after the reservoir was built: 01.11.1981–31.03.1994 and 01.11.1994–31.03.2016 for water temperature, and 01.11.1972–31.03.1994 and 31.03.1994–31.03.2020 for ice cover occurrence. The total variation in water temperature and ice cover occurrence \(({\Delta }_{TOT}\)), variation due to climate change (\({\Delta }_{CLI}\)), and reservoir impact (\({\Delta }_{ANT}\)) in the post-dam period relative to the pre-dam period were determined as follows (Cai et al. 2018):

$${\Delta }_{TOT}={\Delta }_{CLI}+{\Delta }_{ANT}$$
(3)
$${\Delta }_{TOT}= {\delta }_{obs, post dam}- {\delta }_{obs, pre dam}$$
(4)
$${\Delta }_{CLI}= {\delta }_{sim, post dam}- {\delta }_{sim, pre dam}$$
(5)

where \(\delta\) is the model-predicted (sim) or observed (obs) average water temperature or average number of days with ice cover in the period before (pre dam) and after (post dam) construction of the dam reservoir, \({\Delta }_{TOT}\) is defined as the difference between observed values after and before reservoir construction, and \({\Delta }_{CLI}\) is defined as the difference between values predicted by the model after and before reservoir construction. Model bias (\(\upvarepsilon\)) was defined as follows:

$$\upvarepsilon ={\delta }_{obs, pre dam }- {\delta }_{sim, pre dam}$$
(6)

where ε is the difference between the observed (\({\delta }_{obs}\)) and modeled (\({\delta }_{sim}\)) average water temperature or the average annual number of days with ice cover determined from the test set in the period before reservoir construction. Transforming formula (3), we obtain the following:

$${\Delta }_{ANT}={\Delta }_{TOT}-{\Delta }_{CLI}$$
(7)

By substituting formula (4) and (5) for \({\Delta }_{TOT}\) and \({\Delta }_{CLI}\) in this formula (7), we get:

$${\Delta }_{ANT}={\delta }_{obs, post dam}- {\delta }_{obs, pre dam}-\left({\delta }_{sim, post dam}- {\delta }_{sim, pre dam}\right)$$
(8)

After simple transformation we get:

$${\Delta }_{ANT}={\delta }_{obs, post dam}-{\delta }_{sim, post dam} -\left({\delta }_{obs, pre dam}- {\delta }_{sim, pre dam}\right)$$
(9)

Taking into account formula (6) for the model bias, we get:

$${\Delta }_{ANT}= {\delta }_{obs, post dam}- {\delta }_{sim, post dam}-\upvarepsilon$$
(10)

where \({\Delta }_{ANT}\) is defined as the difference between the observed and model-predicted values after reservoir construction from which model bias (ε) was subtracted. It should be pointed out that \({\Delta }_{ANT}\) is an indicator representing not only the impact of the reservoir, but also changes in other potential factors influencing water temperature and ice cover occurrence that took place between the study periods (e.g. changes in sewage emissions or changes in land use and cover). However, due to the fact that in the case of the studied rivers changes in other factors are probably small or even negligible, in this work we relate \({\Delta }_{ANT}\) mainly to the impact of the reservoir. The impact indicators \({(\Delta }_{TOT}\), \({\Delta }_{CLI}\), \({\Delta }_{ANT}\)) were calculated both for the entire winter period (November to March) and for individual months. For both water temperature and ice cover, the bias was determined and included in the calculations for the entire winter period and for individual months (November to March).

2.5 Analysis of phase synchronization between water and air temperatures

Next, the water and air temperature data were analyzed in the time-scale domain based on a continuous wavelet transform (CWT, stations R1 and B1). The mean values of the signals were removed. The continuous wavelet transform of a time series xn sampled at discrete time intervals δt is defined as the convolution of xn with a scaled and translated version of the so-called mother-wavelet \({\psi }_{0}\left(t\right)\):

$${W}_{n}\left(s\right)=\sum_{{n}{\prime}=0}^{N-1}{x}_{{n}{\prime}}{\psi }^{*}\left(\frac{\left({n}{\prime}-n\right)\delta t}{s}\right),$$
(11)

where the asterisk denotes the complex conjugate (Torrence and Compo 1998) and N is the number of elements in xn. The normalized wavelet \(\psi \left(\frac{\left({n}{\prime}-n\right)\delta t}{s}\right)={\left(\frac{\delta t}{s}\right)}^{1/2}{\psi }_{0}\left(\frac{\left({n}{\prime}-n\right)\delta t}{s}\right)\) is translated along the localized time index n such that its width corresponds to the time scale s (Torrence and Compo 1998). The Morlet wavelet consisting of a complex exponential modulated by a Gaussian function \({\psi }_{0}\left(t\right)={\pi }^{-1/4}{e}^{i2\pi t}{e}^{-{t}^{2}/2}\) was used as a mother-wavelet function. The wavelet energy spectrum \({\left|{W}_{n}\left(s\right)\right|}^{2}\) gives a measure of the time series variance at each scale s and at each time n. Due to the cyclic behavior of the analyzed temperature series, no zero padding was performed. The instantaneous phases \({\varphi }_{s}\left(n\right)\) of the main peak in the energy spectra were calculated using wavelet transforms, based on the real and imaginary parts of the CWT (Torrence and Compo 1998):

$${\varphi }_{s}\left(n\right)={tan}^{-1}\left(imag\left\{{W}_{n}\left(s\right)\right\}/re\left\{{W}_{n}\left(s\right)\right\}\right)$$
(12)

The phase relationship between the two temperature signals was considered by examining differences in time \({\Delta \varphi }_{s}\left(n\right)={\varphi }_{s}^{A}\left(n\right)-{\varphi }_{s}^{W}\left(n\right)\) between the instantaneous phases \({\varphi }_{s}^{A}\left(n\right)\) and \({\varphi }_{s}^{W}\left(n\right)\) of the air and water time series, respectively, for the scale s. In the classical case of periodic oscillators, phase synchronization is defined as phase locking, i.e., the phase difference is constant. In the case of complex systems, phase difference fluctuations typically occur; thus, for phase synchronization, the weak locking condition \(\left|{\Delta \varphi }_{s}\left(n\right)\right|<const\) should be satisfied (Rosenblum et al. 1996), which means that phase deviations in time are bounded by a constant. When the instantaneous phases are not represented as cyclic functions in the interval \(\left[0 \left.2\pi \right)\right.\), but rather as monotonically increasing functions on the real number line, then the instantaneous phase difference \({\Delta \varphi }_{s}\left(n\right)\) is also defined on the real number line and is a bounded function of time for synchronous states of systems (Paluš et al. 2007).

2.6 Field research

To identify the spatial variability of water temperature and the occurrence of ice cover on the studied rivers, water temperature measurements (12 points in the case of the Ropa and 13 in the case of the Biała) and observations of the occurrence of ice phenomena were carried out on 29.12.2021. The day of measurements was chosen due to the persistence of very low air temperatures in the period preceding it (at station T1, the average air temperature in the period 19.12.2021–28.12.2021 was − 4.3 °C, and at times below − 15 °C). Based on archival data, it was determined that prior to the reservoir's construction, such air temperatures were sufficient to cause a significant drop in temperature and overcooling of water leading to the formation and maintenance of ice cover on these rivers. The observations consisted of visual determination of the type of phenomenon (total ice cover, border ice, and initial ice forms) and the percentage of the water surface covered by ice. The raw data from the field measurements are available at the link: https://zenodo.org/records/11143878.

3 Results

3.1 Assessing the impact of reservoir operation and climate change on water temperature

The average air temperature during the winter period (November to March) at station T1 in the 1973–2020 period was 0.6 °C. The coldest month during this period was January, with an average temperature of − 2.1 °C, while the warmest (considering only the winter period) was November with an average temperature of 3.74 °C. As shown in Fig. 2, the average air temperature in winter (November–March) in 1972–1994 (before the reservoir was built) was 0.31 °C, whereas it was 0.95 °C during the period 1994–2020 (after the reservoir was built). In the thirteen-year period before the construction of the reservoir (1981–1994), the average winter air temperature was 0.1 °C, rising to 0.45 °C in the thirteen-year period after construction (1994–2007).

Fig. 2
figure 2

Average air temperature for each month. For visualization purposes, data at two stations were used: T1 (1973–2020) and T2 (1957–1972)

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Analysis of trends in average air temperature over the period 1973–2020 period showed that a statistically significant increase occurs only in November (Table 2), reaching 0.7 °C per decade. Statistically significant trends were not observed either for the other months or for the entire winter period. The increase in air temperature in November was particularly significant after 2000, when most months were anomalously warm (Fig. 2).

Table 2 Trends (Theil-Sen slope) in air temperature and water temperature (°C/10 years)
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The average winter water temperature (November–March) in the Biała River (station B1, without the influence of the dam reservoir) over the period 1984–2016 was 1.48 °C. The month with the lowest water temperature was February (0.5 °C) and the month with the highest was November (3.1 °C, considering only the winter period). During the 1984–1994 period, the average winter water temperature at station B1 (without reservoir influence) was 1.29 °C, whereas in the 1994–2016 period it was 1.56 °C. During the 1994–2007 period (the thirteen-year period following the construction of the reservoir on the Ropa River), the average winter water temperature at station B1 was 1.39 °C. Statistically significant increases in water temperature were recorded in November (0.6 °C/decade), February (0.2 °C/decade), and for the entire winter period (0.3 °C/decade). During the study period, the increase in water temperature at station B1 was similar to the increase observed in air temperature over the same period (Table 2).

The applied predictive model of water temperature at station R1 (under the influence of dam reservoir operation) showed relatively high accuracy. During the test period (winter period only), the mean square error (MSE) was 0.78, the root mean square error (RMSE) was 0.88, and the Nash–Sutcliff efficiency coefficient (NSE) of the model was 0.83 (Fig. 3). Ritter and Muñoz-Carpena (2013) defined the threshold at which a hydrological model yields acceptable predictions at NSE ≥ 0.65, whereas models achieving NSE in the range of 0.8–0.9 were defined as good. Moriasi et al. (2007), on the other hand, suggested values of NSE > 0.5 and RSR ≤ 0.7 as satisfactory for hydrological models, such that the predictions of the built regression model can be described as very good.

Fig. 3
figure 3

Comparison between modeled and observed water temperature values in the test set. Graph (a) shows values and metrics from the entire test set, whereas the values in graph (b) are limited to the winter period in the test set

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At station R1 (under the influence of the reservoir), the average winter water temperature during the 1982–2016 period was 3.72 °C. In all analyzed months, there was a statistically significant increase in water temperature varying from 0.5 °C/decade to 1.2 °C/decade. The most significant increasing trend was observed in November (1.2 °C/decade, Table 2), which translated into an overall increase in mean water temperature (ΔTOT) of 2.03 °C between 1994 and 2007 compared to 1981–1994 (Table 3). At station R1, only for November and February was the increase in water temperature of the 1994–2007 period compared to 1981–1994 due more to climatic conditions than to the operation of the dam reservoir.

Table 3 Total changes in water temperature (ΔTOT), and contributions from climatic conditions (ΔCLI) and reservoir construction (ΔANT), for the periods 1994–2007 and 1994–2016 relative to the period 1981–1994 at station R1
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In the other months, the influence of the operation of the dam reservoir was primarily responsible for the observed increase in water temperature (\({\Delta }_{ANT}\), Fig. 4).

Fig. 4
figure 4

Observed and model-predicted water temperature (RWT) at station R1 during the period of construction (1990–2000, a), before construction (1981–1994, b), and after construction of Klimkówka Reservoir (1994–2007, c). Graphs in b) and c) show the annual average values for each day of the year

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The largest transformation of water temperature during the period 1994–2007 compared to 1981–1994 resulting from the operation of the reservoir occurred in January. No increase in water temperature due to climatic conditions was observed in this month; instead, the entire increase in average water temperature was due to the warming role of the reservoir (by an average of 0.79 °C). For the entire winter period (November to March), the total increase in the average water temperature (ΔTOT) during the 1994–2007 period compared to the 1981–1994 period was 1.05 °C. This included increases of approximately 0.33 °C due to climatic variability and approximately 0.61 °C due to reservoir operation. Based on these results, it can be assumed that, at the R1 station, the operation of the dam reservoir was responsible for approximately 64.9% of the observed increase in water temperature during this period, while climatic conditions were responsible for approximately 35.1% of the increase.

A CWT of the air and water temperature series revealed that the scale (s = 365.25 days) corresponding to the annual cycle contains most of the spectral energy (not shown), thereby explaining most of the temperature variation. The linear phase difference for this scale between the respective air and water temperature series is bounded by a constant (Fig. 5). For Szymbark (stations T1 and R1), the phase difference between air and water temperature was generally below 0.257 rad (14.9 days) over the entire study period (1981–2007), whereas for the post-dam period (1994–2007), this difference increases 3.6-fold relative to the pre-dam period (on average: 0.215 and 0.059 rad, or 12.5 and 3.4 days, respectively). In contrast, although the phase difference between the air temperature at station T1 and the water temperature at station B1 (approximately 12 km away) is generally below 0.181 rad (10.5 days), its behavior is both more dynamic and diverse (Fig. 5b).

Fig. 5
figure 5

Linear phase difference [rad] for the main scale (s = 365.25 days) between the air and water temperature studied at: a measuring stations T1 and R1 in the same locality (Szymbark); b measuring stations T1 and B1 approximately 12 km away

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3.2 Evaluating the impact of reservoir operations and climate change on ice cover occurrence

On the Biała River (without the dam reservoir), the average annual number of days with ice cover (total ice and border ice) during the period 1950–2020 were 57.6 (station B1) and 45.7 (station B2). A statistically significant decreasing trend in the number of days with ice cover was noted over the period 1994–2020, reaching nine days per decade (Table 4). At station B1, a decrease in the average annual number of days with ice cover by 5.9 days was observed during the 1994–2007 period compared to the 1981–1994 period. For station B2, the average number of days with ice cover during the 1994–2007 period was 4.9 days lower than that of the 1981–1994 period.

Table 4 The average number of days with ice cover and its trends at the studied stations during each period
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In the case of the Ropa, a statistically significant decrease in the number of days with ice cover was observed, reaching 4.3 days per decade (station R1) during the period 1950–2020. In the period 1950–1994 at station R1, a significant increasing trend in the number of days with ice cover was also observed (7.7 days per decade), whereas the period 1994–2020 was characterized by a decreasing trend reaching 15 days per decade. At this station, the post-dam period (1994–2007) saw a decrease in the frequency of ice cover of 27.3 days compared to the earlier period (1981–1994). For station R2, no statistically significant decrease in the average number of days with ice cover was observed. For the 1994–2007 period, the average annual number of days with ice cover was 2.1 days lower than that during the 1981–1994 period.

The prediction accuracy and predictive ability of ice cover occurrence classification models at stations R1 and R2 were relatively high. At station R1, the balanced accuracy of prediction on the test set was 0.9, and the value under the receiver operating characteristic curve (ROC) indicated that the model exhibited very good predictive abilities (0.97, Fig. 6).

Fig. 6
figure 6

ROC curve and model evaluation indices at stations R1 and R2 developed from the test set

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It is generally accepted that values of the area under the ROC curve greater than 0.9 indicate that the model exhibits excellent predictive abilities, whereas values in the range of 0.8–0.89 indicate very good predictive abilities (e.g., Carter et al. 2016). Similar values were obtained for station R2 where the balanced accuracy was 0.87 and the value under the ROC curve was 0.95. At station R1 during the 1973–1994 period (before the reservoir was built), the observed and model-predicted number of days with ice cover were very similar (65.4 and 65.8, respectively, Fig. 7). For station R2, the observed and model-predicted annual average number of days with ice cover in the 1973–1994 period was 42. At station R1, during the post-reservoir period (1994–2020), a significant discrepancy was observed between the observed (32.8) and model-predicted (57.7) number of days with ice cover (Fig. 7). Different results were obtained for station R2 where, during the post-reservoir construction period (1994–2020), the observed and modeled values were very similar, at 36.7 and 34, respectively.

Fig. 7
figure 7

Observed (stations R1, R2, B1, B2) and model-predicted (stations R1 and R2) numbers of days with river ice cover (tiled graph) and total annual number of days with river ice cover (line graphs) at each station

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In the case of station R1, the average annual number of days with ice cover (ΔTOT) decreased by 27.3 days during the 1994–2007 period compared to the 1981–1994 period (Table 5). The operation of the dam reservoir (ΔANT) was responsible for approximately 77.5% of the observed decrease (− 21.1 days), while climatic conditions (ΔCLI) were responsible for about 22.5% (− 6.1 days). The influence of climatic conditions on the decrease in the number of days with ice cover was greater than that of the operation of the dam reservoir only in November and March. For the other months, the operation of the dam reservoir played a greater role in reducing the duration of ice cover.

Table 5 Total changes (ΔTOT) and changes due to climatic conditions (ΔCLI) and reservoir construction (ΔANT) in the annual average number of days with ice cover at stations R1 and R2 during the periods 1994–2007 and 1994–2016 compared to the period 1981–1994 and 1971–1994
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At station R2, during the period after the construction of the Klimkówka reservoir, the total decrease in the number of days with ice cover (ΔTOT) was 2.1 days. As a result of climatic conditions (ΔCLI), the number of days with ice cover decreased by 3.5 days, while as a result of the reservoir's operation it increased (ΔANT) by 1.3 days. Climatic conditions (ΔCLI) had the greatest impact on the shortening of the average duration of ice cover in February (3.8 days). In January, as a result of climatic factors (ΔCLI), the duration of ice cover increased by 4.9 days during the 1994–2007 period. The operation of the dam reservoir (ΔANT) reduced the duration of ice cover in November, December, and January by 0.57, 1.51, and 0.67, respectively. From February to March, the operation of the dam reservoir had a lengthening effect on the duration of ice cover on the river. Due to the small degree of change in the ΔANT parameter in all months at station R2 (ΔANT < 4 days), it is difficult to say how much of the ice cover duration lengthening effect in the second half of the winter period was due to the operation of the dam reservoir, and how much was due to other potential factors, such as model error and the influence of other phenomena unrelated to the operation of the dam reservoir.

During the 1994–2020 period, the structure of the occurring ice phenomena was transformed at all studied stations compared to the earlier period (1950–1994, Fig. 8). During the period 1950–1994, stations R1, B1, and B2 observed a similar share of the number of days with total ice cover and border ice out of the total number of days with ice. During the 1994–2020 period, these stations saw a decrease in the share of total ice cover (by approximately 20 percentage points) and an increase in the share of border ice. At station R2, total ice cover was relatively infrequent throughout the study period; in the 1950–1994 period it accounted for an average of 20% of total ice, whereas it formed during only three winters during the 1994–2020 period.

Fig. 8
figure 8

Contribution of border ice and total ice cover to the sum of days with ice cover in each year at the studied stations

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3.3 Spatial variability of water temperature and ice cover occurrence

The average water temperature in the Biała River on the day of measurements (29.12.2021) was 0.5 °C. No significant fluctuations in water temperature were observed throughout the river's longitudinal profile (> 90 km). The upper part of the catchment was characterized by complete ice cover, whereas the middle and lower parts of the catchment border ice covering more than half of the width of the channel was recorded (Fig. 9).

Fig. 9
figure 9

Water temperature and ice cover in the longitudinal profile of the Ropa and Biała rivers on 29.12.2021

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The average water temperature in the Ropa on the day of measurements was 1 °C. At the measurement points upstream of the Klimkówka reservoir (points Tr1–Tr4), the average water temperature was 0.6 °C, whereas at the points downstream of the reservoir (Tr5–Tr12) it was 1.3 °C. Immediately downstream of the reservoir, there was a sharp increase in water temperature up to 3 °C. With increasing distance from the reservoir, the water temperature dropped to approximately 0.6 °C. There was total ice cover in the section of the river immediately upstream of the reservoir. In the section reaching approximately 5 km downstream of the reservoir on the day of the survey, ice phenomena did not occur, and from 5 to 20 km downstream of the reservoir there were only initial ice forms and local border ice occupying less than 20% of the channel. More than 20 km downstream of the reservoir, there was an ice cover covering 20–80% of the water surface.

4 Discussion

The analyses conducted showed that, in the analyzed years, the climatic conditions in the study area transformed winter water temperatures and the frequency of river ice cover. A statistically significant increase in average air temperature over the period 1973–2020 was observed only in November. In the remaining months, the trend values determined by the Theil-Sen estimator showed an increasing trend, although not statistically significant (at the p < 0.05 level). Smaller trends in the air temperature of winter months compared to that of summer months in the Carpathian region were also confirmed by the results of other studies (Wypych et al. 2018; Kędra 2020; Micu et al. 2021). Wypych et al. (2018) showed that in the Polish part of the Carpathians, the magnitude of the upward trend in mean air temperature in winter was smaller than that in summer, decreasing with increasing altitude. This suggests that the impact of climate change on the water temperature of rivers in the study area may be less visible in winter than in summer.

For the Biała River (station B1, without reservoir influence), the increase in air temperature was associated with an increase in water temperature from November to March of 0.3 °C per decade during the period 1984–2016. The observed upward trends are consistent with studies indicating an increase in water temperature in European rivers over the past 40 years (Hari et al. 2006; North et al. 2013; Lepori et al. 2015; Marszelewski and Pius 2016). In the case of the Biała River, Kędra (2020) showed an increase in winter water temperature of 0.25 °C per decade over the 1989–2018 period, finding that this trend was statistically significant only in November and December. Increasing trends in winter water temperature were also recorded on other Carpathian rivers (Kędra 2020). As a result of the increase in water and air temperature, there was a decrease in the number of days with ice cover reaching nine days per decade during the period 1994–2020 at station B2, and a decrease in the proportion of total ice cover occurrence by approximately 20 percentage points in the sum of days with ice cover. This decline in the number of days with ice cover is a common trend observed in many areas of Europe, Asia, and North America (e.g., Magnuson et al. 2000; Yang et al. 2020; Newton and Mullan 2021). The occurrence of a statistically significant trend in the average winter water temperature at station B1 during the period 1984–2016 and in the number of days with ice cover in the period 1994–2020 at station B2, while there is no statistically significant trend in the average air temperature over the entire winter period, may be due to the simultaneous influence of increasing air temperature on many physical processes. In addition to directly influencing the heat balance at the surface of the water and ice (e.g., through an increase in incoming longwave radiation), an increase in air temperature can affect, among other things, the flow regime of rivers and the mechanism of flood generation (e.g., Smith et al. 2007; Bard et al. 2015; Blöschl et al. 2019), which also affects river ice processes (Prowse et al. 2002; Beltaos 2003) and water temperature. An important process associated with the disappearance (or decrease in thickness) of ice cover may also be due to the increase in shortwave radiation reaching the water surface, which results from a decrease in the amount of radiation reflected by the ice. Increases in air temperature can also influence increases in ground and groundwater temperatures, which can translate into river water temperatures (e.g., Jonsell et al. 2013; Hemmerle and Bayer 2020). The statistically significant increase in air and water temperature in the Biała River in November and the associated disappearance of ice cover occurrence suggests that the observed climatic changes in November have transformed the thermal and ice regime of this river most significantly (Szczerbińska 2023).

In Ropa (stations R1 and R2), transformations in water temperature and ice cover occurrence resulted from both climatic conditions and the operation of the Klimkówka dam reservoir. The study showed that the impact of the operation of the dam reservoir at station R1 (16.6 km downstream of the reservoir) exacerbated the impact resulting from climatic conditions, increasing water temperatures during the winter period by an average of 0.61 °C, which accounted for 64.9% of the increase in the 1994–2007 period relative to the 1981–1994 period. The topic of the impact of dam reservoir operations on river water temperature has been addressed many times in the scientific literature and is relatively well understood (Maheu et al. 2016; Kędra and Wiejaczka 2016, 2018; Cai et al. 2018; Xiao et al. 2022). In temperate climate zones, dammed reservoirs cause the river downstream to warm by up to several degrees during the winter (Kędra and Wiejaczka 2018) due to the release of warm hypolimnion waters and the high thermal inertia of water (Cai et al. 2018). A number of methods have been presented in the literature to separate the effects of reservoir operations and climatic conditions on river water temperature based on machine learning models (Qiu et al. 2021; Xu et al. 2022) and hybrid models (Cai et al. 2018; Xiao et al. 2022; Yang et al. 2022). For example, Cai et al. (2018) showed that the impact of human activities (mainly attributed to the Three Gorges Dam) resulted in the cooling of river waters during spring and summer (by an average of 1.03 °C) and warming during the rest of the year (by an average of 2.41 °C). The dam operation was 94% responsible for the warming observed on the Yangtze River downstream of the reservoir during the winter (December-February). Similar results were obtained by Xu et al. (2022) indicating a 2.1 °C increase in water temperature during autumn and winter due to the operation of the Three Gorges Dam.

The predictive ability of the XGBoost model obtained in this study, determined from the test set, is comparable to the results of other models used in studies of the impact of dam reservoirs on river water temperature (Table 6). However, it is not possible to directly infer the quality of models based on a comparison of results from a number of scientific studies due to the varying quality of input data, the way the data are prepared (feature engineering), or different hyperparameter optimization techniques.

Table 6 Comparison between the accuracies of models based on different metrics in studies on the impact of dam reservoirs on river water temperature
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It should be mentioned that in this study, the XGBoost model achieved very good predictive ability despite the lack of river discharge data in its explanatory variables, which is important variable influencing water temperature. This demonstrates the usefulness of the XGBoost model in predicting water temperature in situations where flow data cannot be used.

As a result of reservoir operation, the natural synchronization between air and water temperatures was disrupted at station R1, resulting in a 12.5-day lag in water temperature relative to air temperature during the 1994–2007 period. On the river not influenced by the reservoir (station B1), there was no analogous disruption in the synchronization between air and water temperatures. Similar results were obtained for other rivers influenced by the dam reservoir. For example, Kędra and Wiejaczka (2016, 2018) showed a two- to five-fold increase in the linear phase difference between air and water temperature series in several rivers in the Carpathian region in the period after reservoir construction. These results suggest that the operation of reservoirs weakens the direct relationship between water temperature and meteorological conditions.

The long-term impact of dam reservoirs on the occurrence of ice cover has been considered in many studies (e.g., Starosolszky 1990; Takács et al. 2013; Pawlowski 2015, Apsîte et al. 2016; Chang et al. 2016), but the mechanism leading to the disappearance of ice cover below reservoirs is not well understood (Fukś 2023). Available studies mainly focus on qualitative approaches, whereas quantitative approaches aimed at separating the impact of reservoir operations and climatic conditions on the process of river freezing have not been addressed. Also problematic is the lack of studies simultaneously presenting the impacts of dam reservoirs on both water temperature and the occurrence of ice cover. The methodology presented in this paper makes it possible to show that the impact of the operation of dam reservoirs on the occurrence of ice cover at site R1 (16.6 km downstream of the reservoir) exacerbated the changes resulting from climatic conditions, resulting in a greater decrease in the frequency of ice cover on the river under the influence of the reservoir. The modeling results and field observations presented in this study suggest that one of the most significant reasons for the disappearance of ice downstream of the reservoir under study was an increase in water temperature limiting the occurrence of phase transformation and consequently limiting the development of ice cover. The transformation of the hydrograph downstream of the reservoir and the capture of mobile ice forms by the reservoir may also have played a role (Huokuna et al. 2020). Previous studies of transformations in the river ice regime confirm these findings. Pawlowski (2015) showed that the construction of the Wloclawek Reservoir on the Vistula River (central Europe) resulted in a 46% decrease in the occurrence of ice cover downstream of the reservoir, but this study was limited only to periods with similar thermal conditions before and after the construction of the reservoir. Takács et al. (2013) used a similar methodology to show that the construction of small reservoirs on the Raba River (central Europe) was followed by an 8% decrease in ice cover incidence, whereas Chang et al. (2016) showed that the operation of reservoirs on the Yellow River resulted in a reduction in the duration of days with ice phenomena by up to 33 days, depending on the station considered. Fukś (2024), on the other hand, showed that the operation of two dam reservoirs resulted in a significant reduction in the occurrence of ice cover on mountain rivers in Central Europe (exceeding 80% immediately downstream of the reservoirs). Another example is the Williston Reservoir on the Peace River. As a result of its operation, ice cover does not form between 100 and 300 km downstream of the reservoir (Jasek and Pryse-Phillips 2015).

To date, the XGBoost model has been used relatively infrequently to predict ice phenomena on rivers. Previous attempts include predictions of the type of ice phenomena on the Warta River (central Europe, Graf et al. 2022) or the breakup of ice cover on many rivers in North America (De Coste et al. 2023). The results obtained in this study suggest that the model is capable of predicting the occurrence of ice cover on relatively small mountain rivers as evidenced by its high predictive ability. A particular advantage of the XGBoost model is its ability to solve both classification and regression problems, allowing simultaneous modeling of the effects of dam reservoirs on water temperature and the occurrence of ice phenomena.

As the main limitations of the presented method, it is important to point out that other potential factors that can affect water temperature and ice cover occurrence were not included in the analysis (e.g. changes in catchment land cover or thermal pollution emissions). In the study area these factors most likely did not play a significant role, however in many areas they are crucial in shaping the thermal-ice regime of rivers and should be included in the analysis.

The results presented here suggest that consideration of the potential influence of reservoirs is important in studies of changes in the thermal and ice regime of rivers. This is due to the fact that dam reservoirs exacerbate changes due to climatic conditions in the winter period, both in the case of water temperature and the occurrence of river ice cover. This is particularly important given the large number of reservoirs (> 8,000) in areas of river ice cover (mainly central North America, central Europe, and eastern Asia; Fukś 2023).

5 Conclusions

This study has presented the influence of climatic and anthropogenic conditions on water temperature and ice cover occurrence in Carpathian rivers. The main conclusions of the presented research include:

  1. 1.

    In the study area, a statistically significant increase in air temperature was observed in November, reaching 1.2 °C per decade from 1984 to 2016. In the other months, the trends determined by the Theil-Sen estimator also showed an increase, but were not statistically significant.

  2. 2.

    The Biała River (stations B1 and B2) was characterized by a statistically significant increase in the average winter water temperature, reaching 0.3 °C per decade (in the period 1984–2016) due to the increase in air temperature. The increase in water and air temperature translated into a decrease in the annual average number of days with ice cover by nine days per decade during the 1994–2020 period. A decrease in the frequency of the proportion of total ice cover in the sum of days with ice cover was also observed.

  3. 3.

    On the Ropa River (station R1, 16.6 km downstream of the reservoir), water temperatures were influenced both by climatic conditions and reservoir operations. At station R1, the 1994–2007 period saw a 1.05 °C increase in water temperature compared to the 1981–1994 period. The operation of the dam reservoir was responsible for approximately 65% of this increase (0.61 °C) whereas climatic conditions were responsible for approximately 35% (0.33 °C). The increase due to climatic conditions (0.33 °C) on the Ropa River estimated using the XGBoost model is consistent with the trends determined on the river without the influence of the reservoir (station B1, 0.3 °C per decade). The largest increase in water temperature due to climatic conditions was recorded in November, which is consistent with observed trends in air temperature. Significant variations in water temperature between these rivers are confirmed by field-based studies.

  4. 4.

    As a result of the water temperature transformation resulting from the operation of the Klimkówka dam reservoir, the synchronization of water and air temperatures was disturbed. The phase difference between water and air temperatures during the period after the construction of the reservoir increased 3.6 times, translating into 12.5 days of phase lag of water temperature relative to air temperature. As a result, the influence of climatic conditions on water temperature was disturbed.

  5. 5.

    On the Ropa River, a decrease in the number of days with ice cover was observed as a result of rising water temperatures. At station R1 (16.6 km downstream of the reservoir), there was a decrease in the average annual number of days with ice cover (by 27.3 days) during the period 1994–2007 relative to 1981–1994. The operation of the dam reservoir was responsible for approximately 77.5% of the decrease (21.1 days) whereas climatic conditions were responsible for approximately 22.5% (6.1 days). The decrease in the annual average number of days with ice cover due to climatic conditions (6.1 days) on the Ropa River estimated from the XGBoost model was consistent with the trends determined on the river without the influence of the reservoir (a decrease at station B2 of 9 days per decade). Significant variation in the occurrence of ice cover between these rivers was confirmed by field-based studies. At station R2 (28.6 km downstream of the reservoir), the observed and model-predicted mean annual number of days with ice cover was very similar, showing that climatic conditions were mainly responsible for the observed decrease in the number of days with ice cover. This suggests a decrease in the strength of the reservoir's effect on river ice cover with increasing distance from the reservoir.

  6. 6.

    The XGBoost model is a useful tool for separating the effects of dam reservoirs and climate change on water temperature and river ice cover occurrence.