Rivers increasingly warmer: Prediction of changes in the thermal regime of rivers in Poland

Mariusz PTAK; Teerachai AMNUAYLOJAROEN; Mariusz SOJKA

doi:10.1007/s11442-025-2316-5

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Journal of Geographical Sciences ›› 2025, Vol. 35 ›› Issue (1) : 139-172. DOI: 10.1007/s11442-025-2316-5

Special Issue: Climate Change and Water Environment

Rivers increasingly warmer: Prediction of changes in the thermal regime of rivers in Poland

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Abstract

Emphasis on future environmental changes grows due to climate change, with simulations predicting rising river temperatures globally. For Poland, which has a long history of thermal studies of rivers, such an approach has not been implemented to date. This study used 9 Global Climate Models and tested three machine-learning techniques to predict river temperature changes. Random Forest performed best, with R²=0.88 and lowest error (RMSE: 2.25, MAE:1.72). The range of future water temperature changes by the end of the 21st century was based on the Shared Socioeconomic Pathway scenarios SSP2-4.5 and SSP5-8.5. It was determined that by the end of the 21st century, the average temperature will increase by 2.1°C (SSP2-4.5) and 3.7°C (SSP5-8.5). A more detailed analysis, divided by two major basins Vistula and Odra, covered about 90% of Poland’s territory. The average temperature increase, according to scenarios SSP2-4.5 and SSP5-8.5 for the Odra basin rivers, is 1.6°C and 3.2°C and for the Vistula basin rivers 2.3°C and 3.8°C, respectively. The Vistula basin’s higher warming is due to less groundwater input and continental climate influence. These findings provide a crucial basis for water management to mitigate warming effects in Poland.

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global warming / forecasting / water temperature / Poland

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Mariusz PTAK, Teerachai AMNUAYLOJAROEN, Mariusz SOJKA. Rivers increasingly warmer: Prediction of changes in the thermal regime of rivers in Poland[J]. Journal of Geographical Sciences, 2025, 35(1): 139-172 https://doi.org/10.1007/s11442-025-2316-5

1 Introduction

Due to its properties, water undergoes rapid changes that affect its biotic and abiotic parameters. Among the latter, temperature is crucial as it influences a series of interconnected processes occurring in aquatic ecosystems (Adams 1976; Ridanović et al., 2010; Ying et al., 2012; Zhang et al., 2016; Cheng et al., 2020).

The key role of water temperature in rivers has led to widespread interest in its long-term changes, especially in the context of the observed warming. Studies of the winter thermal regime of the rivers of the Debed River Basin in Armenia have shown statistically significant increases in air and water temperature between 1984 and 2018 (Margaryan et al., 2023). Statistically significant temporal trends were detected throughout the Chesapeake Bay region, which were 0.028℃ for annual values (Rice and Jastram, 2015). In the case of mountain rivers in the Polish Carpathian Mountains, an increase in water temperature for all the rivers analysed ranged from 0.33 to 0.92℃ per decade (Kędra, 2020).

As a result of atmospheric warming, the average water temperature in the upper course of the Upper Rhone has increased by approximately 1.5°C (1979-1981 in 1997-1999) (Daufresne et al., 2004). Water temperature in the Ebro River basin (Spain) was characterized by a clear increase at all stations (except those located at the head of the tributaries) (Lorenzo-González et al., 2023). In the case of the Loire basin, river temperatures in the period 1963-2019 increased in almost all areas. Increases were the greatest in spring (0.38℃ per decade) and summer (0.44℃ per decade) (Seyedhashemi et al., 2022).

Long-term changes in water temperature at three observation stations for the Danube have shown statistically significant warming trends for the annual and seasonal minimum and maximum temperatures. Notable changes were observed in the 1980s, linked to climatic patterns in the North and East Atlantic that affect the amount of heat reaching Europe (Basarin et al., 2016). Of all meteorological parameters, air temperature has the most significant impact on water temperature (Ouyang et al., 2018) and can be used in statistical models to predict water temperature fluctuations, useful for future climate forecasts (Adlam et al. 2022). Air temperature has been used in numerous studies based on model solutions for Central Europe. The results obtained for two Drava River posters indicate that the combination of wavelet transformation and artificial intelligence models yields better models than conventional predictive models for simulating water temperature (Zhu et al., 2019). The hybrid machine-learning models used to predict the water temperature at the headwaters of five rivers in Poland achieved high predictive accuracy with a Pearson correlation coefficient of 0.99, a Nash-Sutcliffe efficiency of 0.98, a root mean square error of 0.718°C and a mean absolute error of 0.599℃ (Heddam et al., 2023). Sun et al. (2024), based on 18 rivers of the Vistula River basin, compared the performance of the BO-NARX-BR model with another used in hydrological studies air-stream model. They found that the former performs better in the calibration and validation phases, and the model can better capture the seasonal pattern and peak water temperatures. The increase in air temperature is crucial for water temperature, and consequently, for the protection of water resources and ensuring their proper quality (Bačová Mitková et al., 2023). Global warming, in most cases, leads to progressive changes in the thermal regime of rivers, resulting in their ecosystem transformation. The current rate of increase in water temperature will significantly impact eutrophication, pollutant toxicity, and the decline of aquatic biodiversity (Kaushal et al., 2010).

In the case of Poland, the theme of river research has a long history and encompasses many aspects (Wiejaczka, 2007; Rajwa-Kuligiewicz et al., 2015; Kapusta et al., 2019; Kubera et al., 2021; Szatten et al., 2021; Gebler et al., 2022; Tomczyk et al., 2022; Pietruczuk et al., 2023; Szarmach et al., 2023; Kirczuk et al., 2024). One of the significant strands of research involves issues related to thermal regime, addressing daily changes (Łaszewski, 2018), the impact of hydraulic structures (Yang et al., 2022), the influence of natural lakes (Nowak et al., 2020), large-scale atmospheric circulation (Graf and Wrzesiński, 2019), or trend analysis (Ptak et al., 2022). However, to date, no more extensive studies have been undertaken in relation to the forecast of future changes, although research on the historical reconstruction of water temperature in several dozen rivers has been conducted (Sojka and Ptak, 2022; Zhu et al., 2022). The analysis of the two rivers (Biała Tarnowska, Supraśl) showed that in the period 2071-2100, the warming of the water will range from 1 to 3℃ for average monthly temperatures, depending on the river and month (Piotrowski et al., 2021). Despite a large collection of field measurements, the situation in which we still do not know in which direction and with what intensity the thermal regime of flowing waters in Poland will change must be recognized as a significant knowledge deficit, especially in the context of future changes predicted for rivers in other regions of the world.

According to the RCP8.5 scenario, an increase in the water temperature of the Jucar River (Mediterranean area) by 4℃ is predicted during the summer period (Perez-Martin et al., 2022). Further analysis of the same case showed that an increase in river shading by 10% could lower the water temperature by 1℃. In the case of the Fraser River (Canada) over a hundred years (2000-2100), water temperature is expected to rise throughout the summer season, with the maximum increase occurring in August (0.14℃/decade) (Ferrari et al., 2007). The water temperature of the Nechako River is expected to increase by a maximum of 2.57℃ in the 2041-2070 period and by an average of a maximum of 3.56℃ in the 2071-2100 period under the SSP5-8.5 scenario (Gatien et al., 2024). At the scale of the Athabasca River basin, the annual water temperature is projected to increase from 0.8 to 1.1℃ (mid-century) and 1.6 to 3.1℃ (Du et al., 2019).

The correlation between water temperature and air temperature was used to model historical water temperatures of the Tudovka River (a right tributary of the Volga) and to predict future changes (Bui et al., 2018). It was established that by the year 2099, average monthly temperatures will increase by: 0.70-1.72℃ (low scenario), 0.85-2.31℃ (medium scenario), and 0.85-2.31℃ (high scenario).

For this reason, the use of predictive models of water temperature that utilize air temperature as an input variable under various possible climate change scenarios can help us predict threats to these ecosystems (Soto, 2016). Establishing the most accurate forecasts of water warming in rivers is attracting increasing interest, which in turn is creating a basis for assessing potential consequences for a range of processes and phenomena strictly dependent on temperature. At this point, it is worth paying attention to issues concerning water quality. This is particularly significant because the Vistula and Odra basins are among the largest contributors of nitrogen and phosphorus compounds flowing into the Baltic Sea (Stålnacke et al., 1999).

The aim of the study is to forecast changes in river water temperatures (RWT) in Poland. This approach complements the global state of knowledge and is the first of its kind for a set of several dozen rivers located in the transitional climate zone of Central Europe.

2 Materials and methods

2.1 Study area

Hydrologically, the area of Poland belongs mainly to the Baltic Sea catchment (over 99%), with the remaining part draining into the Black Sea and the North Sea. The largest river basins in Poland are the Vistula (covering over 55% of the territory of Poland) and the Odra (over 33%). The remainder are rivers flowing directly into the Baltic Sea (over 7%) and those belonging to the catchments of the Pregolya (flowing into the Vistula Lagoon) and the Neman. The climate of Poland is temperate and transitional between maritime and continental variants (Okołowicz, 2000). The variation in climatic conditions from east to west is particularly noticeable during the winter period. The study included 41 rivers at 52 hydrological stations located in Poland (Figure 1). The location of those hydrological stations is listed in Table 1S. On the largest rivers, temperatures were studied at several hydrological stations. On the Vistula, Odra, Warta and Narew Rivers, the analysis was made for three hydrological stations, and on the Bóbr, Bug, and Noteć for 2. The studied rivers are located in the basins of the Vistula, Odra, and Pomeranian rivers (rivers flowing directly into the Baltic Sea) and the Vistula Bay (Figure 1). In terms of the catchment area, the largest is the Vistula River basin at the Świbno station with an area of 194,103 km² (No. 26), and the smallest is the Wieprza River catchment at the Kwisno station with an area of 95 km² (No. 20). Water temperatures in rivers are mainly linked to changes in air temperature. Therefore, in this study, they were analysed in the context of changes in air temperatures at 31 meteorological stations (Figure 1). The location of those meteorological stations is listed in Table 2S.

Figure 1 Location of studied rivers in Poland

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2.2 Historical data

Water temperatures in rivers are sourced from the dataset of the Institute of Meteorology and Water Management - National Research Institute. In the case of the Odra basin (western Poland), observations at most stations were concluded in 2014. Therefore, to rely on a uniform dataset, a period covering 30 years was adopted for all hydrological stations (1985-2014). The measurement of water temperature was conducted according to uniform standards at a depth of 0.4 m below the water surface, always at the same point. Similarly, air temperatures are derived from the database of the same institution and were measured as part of standard monitoring (meteorological cages 2 m above the ground level).

2.3 Future data and methods

A study used multi-model ensembles (MMEs) based on the Bayesian model averaging (BMA) method to gather several GCM datasets as listed in Table 1 that included both present and future climate data. The MMEs are an effective way to minimize the individual model uncertainties. To improve the reliability of climate data for observation, the bias correction method was applied to all climate datasets before being used for water temperature prediction. A prediction was conducted for each location along the river and then averaged to represent each river.

Table 1 GCMs and respective institutions used in this study

GCM	GCM institutions
NorESM2-MM	Norwegian Climate Centre (NCC)—Norway
MPI-ESM1-2-HR	Max Planck Institute for Meteorology (MPI-M)—Germany
EC-Earth3	EC-Earth-Consortium
AWI-CM-1-1-MR	Alfred Wegener Institut (AWI)—Germany
BCC-CSM2-MR	Beijing Climate Center (BCC)—China
MRI-ESM2-0	Meteorological Research Institute (MRI)—Japan
GFDL-ESM4	Geophysical Fluid Dynamics Laboratory (GFDL) of the National Oceanic and Atmospheric Administration (NOAA)—USA
CESM2-WACCM*	National Center for Atmospheric Research (NCAR)—USA
CMCC-CM2-SR5*	Euro-Mediterranean Centre on Climate Change (CMCC) Foundation—Italy

The ensemble consists of nine GCMs acquired from the CMIP6 as listed in Table 1. Each model provides its surface temperature for the future period (2015 to 2100). These predictions are then adjusted to a similar spatial resolution to maintain uniformity across the group. The regridding procedure utilizes linear interpolation to map model outputs onto a predetermined grid of latitude and longitude, enabling straightforward comparison. We employ a regridding procedure to interpolate model data onto a standardized grid.

The regridding procedure entails determining an interpolated value for each point on the target grid, which is composed of coordinates (x_t, y_t), based on a source grid with coordinates (x_s, y_s). The interpolated value ‘V’ on the target grid is calculated for a variable V specified on the source grid, using a selected interpolation method. An extensively employed technique is bilinear interpolation (Jone, 1999), which can be mathematically represented as:

V^{'} (x_{t}, y_{t}) = \underset{i = 1}{\sum^{4}} w_{i} \cdot V (x_{s}^{i} \cdot y_{s}^{i})

(1)

Where

V (x_{x}^{i} \cdot y_{x}^{i})

denotes the values of the variable at the four closest adjacent grid points to the source grid surrounding the target point (x_t, y_t). The weights, w_i, are determined by the relative distances between each of these four locations and the target point.

The weights in bilinear interpolation are calculated as follows:

w_{i} = \frac{1}{Δ x \cdot Δ y} \cdot (x_{d i s t}^{i} \cdot y_{d i s t}^{i})

(2)

where the variables Δx and Δy represent the distances between nearby points on the source grid. The variables

x_{d i s t}^{i}

and

y_{d i s t}^{i}

represent the horizontal and vertical distances, respectively, between the ith neighbouring point and the target grid point.

This study uses BMA (Hoeting et al., 1999) to combine projections from five GCMs. BMA is a statistical framework that allows for the combination of predictions made by various models using probability theory. The principle behind this approach is Bayes’ theorem, which can be mathematically formulated in the context of model averaging as follows:

p (M_{i} | y) = \frac{p (y | M_{i}) \cdot p (M_{i})}{p (y)}

(3)

where

p (M_{i} | y)

represents the posterior probability of model M_i given the data y. Similarly,

p (y | M_{i})

denotes the likelihood of the data y under model M_i. The term p(M_i) refers to the prior probability of model M_i, while p(y) represents the marginal likelihood of the data y and serves as a normalizing constant.

The BMA predictive distribution for a new observation

\tilde{y}

is calculated by taking a weighted average of the predictive distributions from each model.

p (\tilde{y} | y \underset{i = 1}{\sum^{M}} p (\tilde{y} | M_{i}) \cdot p (M_{i} | y))

(4)

The equation involves the predictive distribution,

p (\tilde{y} | M_{i})

, which represents the probability distribution of the new observation

\tilde{y}

given the model M_i. Additionally,

p (M_{i} | y)

serves as the weight for model M_i, and it is calculated as explained earlier.

The ensemble of climate models provides a combined BMA prediction for the surface temperature (T) at a specific grid point (x,y) and time (t).

T_{B M A} (x, y, t) = \underset{i = 1}{\sum^{M}} w_{i} (x, y, t) \cdot T_{i} (x, y, t)

(5)

where T_i(x,y,t) represents the forecast generated by model i, whereas w_i (x,y,t) is the BMA weight assigned to model i at grid point (x,y) and time t. This weight is determined based on the posterior probability

p (M_{i} | y)

, which is particular to the given place and time.

The quantification of uncertainty in the BMA combined prediction is determined by the standard deviation of the BMA predictive distribution.

σ_{B M A} (x, y, t) = \sqrt{\underset{i = 1}{\sum^{M}} w_{i} (x, y, t) \cdot {(T_{i} (x, y, t) - T_{i} (x, y, t))}^{2}}

(6)

where σ_BMA(x,y,t) denotes the level of uncertainty at the specific coordinates (x,y) and time t on the grid. The variability of the posterior distribution indicates the level of uncertainty in the aggregated forecast and offers understanding about the level of agreement among the models.

2.4 Machine learning (ML)

In this study, we employed three machine-learning techniques to predict the future of rivers water temperature in Poland: Random Forest (RF), Gradient Boosting Machine (GBM), and Decision Tree (DT). RF (Breiman, 2001) is a type of ensemble learning technique that employs DT principles. The method creates a DT ensemble, with each tree trained on a unique random subset of the dataset. Bagging, also known as bootstrap aggregation, is used to introduce stochasticity into the model. When creating predictions, the RF algorithm takes into account the results offered by each individual tree to reach a conclusion. One of RF’s most important characteristics is its capacity to manage big datasets with several dimensions effectively. The usage of many trees improves accuracy while reducing overfitting, which is a major problem with single Decision Trees. RF exploits spatial patterns and data linkages to provide higher-resolution forecasts during downscaling. This feature makes radio frequency (RF) a potential alternative for complex climate information. The RF algorithm’s fundamental premise is the utilization of collective intelligence, sometimes known as ‘the wisdom of crowds. The basic notion behind this technique is that an ensemble of numerous fairly independent models, known as trees, functioning as a committee outperforms any single constituent model. Equation uses training examples to represent the RF regression prediction X = {x₁, x₂, x₃, …, x_n} with matching labels Y = {y₁, y₂, y₃, …, y_n}.

f (x) = \frac{1}{B} \underset{b = 1}{\sum^{B}} f_{b} (x)

(7)

Let B represent the total number of trees in the forest, and fb(x) represent the forecast made by the bth tree.

According to Friedman (2001), gradient boosting is an ensemble technique that differs from RF in that it generates Decision Trees sequentially rather than concurrently. The primary purpose of this technique is to reduce the residuals or errors caused by previous trees, hence steadily improving forecast accuracy as each successive tree added. The Gradient Boosting Machine (GBM) may iteratively modify its predictions and respond to precise patterns in the dataset. The use of GBMs in downscaling applications allows for the collection of non-linear interactions and complex spatial relationships. This capacity enhances temperature prediction accuracy on a smaller scale. The fundamental goal of the GBM is to reduce model loss by iteratively adding weak learners using a gradient descent-like approach. Gradient Boosting prediction is expressed mathematically in the equation:

f_{m} (x) = f_{m - 1} (x) + \propto \underset{j = 1}{\sum^{J}} γ_{j} I (x ϵ R_{j m})

(8)

Let ∝ be the learning rate, R_jm the regions produced by the jth leaf of the tree, and γ_jI the coefficients that minimize the loss within R_jm. Quinlan (1986) defines DTs as crucial components in many ensemble techniques with intrinsic interpretability as models. The data are recursively partitioned into subgroups based on feature values, resulting in a DT model. Every node in the tree structure reflects a distinct trait, whereas each branch represents a decision rule that eventually leads to the expected conclusion at the leaf nodes. The benefit of single Decision Trees is that they are intuitive and can capture non-linear patterns. They are, nevertheless, prone to overfitting, particularly when dealing with complicated datasets. Nonetheless, when used judiciously in the process of lowering scale, these models can be effective tools for analysing temperature changes depending on spatial coordinates and other relevant aspects. The procedure is repeated until a hierarchical model resembling a tree structure is formed, representing several decision points. At each internal node in the tree structure, a choice is made about which child node to traverse based on the input provided. This process is repeated until a leaf node is reached, at which point a forecast is issued. A certain criterion guides the decision to divide at each node. The variance is commonly recognized as a significant component in regression difficulties. An equation mathematically expresses Decision Tree prediction:

σ^{2} (D) = \frac{1}{| D |} \sum_{i \in D} {(y_{i} - {\bar{y}}_{D})}^{2}

(9)

Let D represent the data present at the current node. D’s size is represented as |D|. The ith instance’s output value is represented as y_i, while the mean output value for the data at the current node is marked as

{\bar{y}}_{D}

Tuning hyperparameters has become an important component in the attempt to improve climate model downscaling using machine-learning methodologies. The hyperparameters for models like Random Forest (RF), Gradient Boosting Machine (GBM), and Decision Tree (DT) were chosen using a combination of early experimentation and past research guidance (Breiman, 2001). The basic methodology for hyperparameter tuning was a grid search, which is known for its rigorous investigation of various combinations (Bergstra and Bengio, 2012). The tuning procedure included a k-fold cross-validation strategy to enhance model resilience and limit the risk of overfitting (Kohavi, 1995). The effects of various hyperparameters on performance, particularly RF’s reactivity to factors such as tree count, were observed and addressed in the supplementary section. To validate the model, the dataset was separated into two subsets, each with a 70-30 split between training and testing. This strategy ensured that the models were evaluated against previously unseen data. To improve the validity of the findings, a 5-fold cross-validation technique was applied, which dramatically increased data consumption for both training and validation (Arlot and Celisse, 2010). The performance metrics employed in this study were mean squared error (MSE) and Pearson correlation. These measurements were chosen because they provide detailed information on the number of errors and the direction of predictions (Chai and Draxler, 2014). The machine-learning models outperformed the original GCM data in terms of downscaling capabilities. The employment of certain methods within models, specifically GBMs, in conjunction with the inclusion of validation sets during the training process, served as anti-overfitting measures (Hastie et al., 2009). In terms of overall repeatability, thorough documentation at all stages of the research process, including data preprocessing and model validation, has been emphasized. The study’s principal programming language was Python, with aid from modules such as Scikit-learn and xarray. McKinney (2010) described the use of exact version data to ensure replicability.

The calibration process for each model involved comprehensive hyperparameter tuning to optimize performance. For the RF model, we used GridSearchCV to fine-tune parameters such as the number of estimators, max_depth, min_samples_split, and min_samples_leaf, with the best configuration utilizing 100 estimators, a max_depth of 50, min_samples_split of 5, and min_samples_leaf of 2. The GBM was optimized using RandomizedSearchCV, focusing on learning_rate, n_estimators, max_depth, and min_samples_split, with the optimal setup having a learning_rate of 0.05, 100 estimators, max_depth of 5, and min_samples_split of 4. For the Decision Tree, GridSearchCV was employed to tune max_depth, min_samples_split, and min_samples_leaf, resulting in a best configuration of max_depth 20, min_samples_split of 5, and min_samples_leaf of 2. All tuning processes utilized 5-fold cross-validation to ensure robust parameter selection. The validation results have been performed across several metrics including R², MAE, RMSE, and SD that was expressed mathematically as follows:

R² (Coefficient of Determination):

R^{2} = 1 - \frac{\sum^{} {(y_{i} - {\bar{y}}_{i})}^{2}}{\sum^{} {(y_{i} - {\bar{y}}_{i})}^{2}}

(10)

MAE (Mean Absolute Error):

M A E = \frac{1}{n} \sum^{} | y_{i} - {\hat{y}}_{i} |

(11)

RMSE (Root Mean Square Error):

R M S E = \sqrt{\frac{1}{n} \sum^{} {(y_{i} - {\hat{y}}_{i})}^{2}}

(12)

where yᵢ are the observed values, ŷᵢ are the predicted values, and ȳ is the mean of observed values, n is the number of observations.

SD (Standard Deviation) for a sample:

S D = \sqrt{\frac{1}{N - 1} \sum^{} {(x_{i} - \bar{x})}^{2}}

(13)

For a population:

S D = \sqrt{\frac{1}{N} \sum^{} {(x_{i} - μ)}^{2}}

(14)

where x_i are the individual values in a dataset,

\bar{x} \pm s

is the sample mean, N is the population size, and μ is the population mean.

Figure 2 presents a comparative analysis of three machine-learning models: RF, Gradient Boosting and Decision Tree, applied to what appears to be a temperature prediction task. Each model is evaluated using three types of plots: R² Distribution, Learning Curve and Predicted vs Actual values. For the RF model, the R² distribution shows a relatively high median value around 0.85, indicating good overall performance. The learning curve reveals that as the training set size increases, the training score decreases while the validation score increases, suggesting the model is learning and generalizing well. There is a slight gap between training and validation scores, indicating some overfitting, but it is not severe. The predicted vs actual plot shows a strong positive correlation, with points clustered tightly around the diagonal line, further confirming good predictive performance. The GBM exhibits a slightly higher median R² value compared to RF, suggesting potentially better performance. Its learning curve shows a more pronounced convergence between training and validation scores as the training size increases, indicating good generalization. The predicted vs actual plot for Gradient Boosting appears slightly tighter around the diagonal compared to RF, possibly indicating more accurate predictions.

Figure 2 Comparative analysis of three machine learning models: Random Forest, Gradient Boosting, and Decision Tree for predicted water temperature

Full size|PPT slide

The DT model shows an R² distribution like that of the RF model. However, its learning curve reveals a larger gap between training and validation scores, suggesting more overfitting compared to the other two models. The predicted vs actual plot for the DT model shows more scatter around the diagonal line, indicating less accurate predictions compared to RF and GBM.

Table 2 presents the performance metrics for three machine-learning models - Random Forest (RF), Gradient Boosting Machine (GBM), and Decision Tree (DT) - used to predict RWTs. The input for these models is the air temperature, and the output is the predicted water temperature. The RF model is an ensemble of Decision Trees that averages predictions to reduce overfitting and improve accuracy. It achieved the highest mean R² value of 0.88, indicating its superior ability to explain variance in water temperature predictions. It also had the lowest error metrics, with an MAE of 1.72 and a RMSE of 2.25, demonstrating its reliability and precision. The GBM builds Decision Trees sequentially, each correcting the errors of the previous one. While it also performed well, with a mean R² of 0.85, it showed slightly higher variability and error metrics compared to RF, indicating a good but slightly less robust model. The DT model, while simpler and more interpretable, had the lowest mean R² of 0.84 and the highest errors among the three models. This suggests that while it can capture basic patterns in the data, it is less effective for this complex prediction task. In conclusion, the RF model is the most appropriate for predicting RWTs, offering the best balance of accuracy and consistency. The GBM also performs well, albeit with more variability, while the DT model, though useful for comparison, is less suited for this specific application.

Table 2 Performance metrics of three different machine learning models: Random forest, gradient boosting machine and decision tree

Model	Mean R²	SD R²	Mean MAE	SD MAE	Mean RMSE	SD RMSE
Random Forest	0.88	0.007	-1.72	0.022	-2.25	0.02
Gradient Boosting Machine	0.85	0.021	-2.12	0.103	-2.73	0.15
Decision Tree	0.84	0.021	-2.16	0.102	-2.78	0.15

Across all models, there is a consistent pattern in the predicted vs actual plots where the models seem to slightly underestimate higher temperatures and overestimate lower temperatures, as evidenced by the slight S-curve in the point distribution. They also show good performance, the Gradient Boosting model appears to have a slight edge in R² score and prediction accuracy. The DT model, while still performing well, shows signs of more overfitting and less accurate predictions than the ensemble methods. The RF model follows closely, offering good performance with possibly better generalization. RF has established itself as a powerful machine-learning algorithm, particularly effective in temperature prediction tasks. Its robust performance stems from several key features that address common challenges in environmental modelling. As an ensemble method, RF combines multiple Decision Trees, reducing overfitting and improving generalization (Breiman, 2001). This approach has proven effective in handling the complex, non-linear relationships often present in climate data (Rahmati et al., 2020). RF’s inherent feature selection capability allows it to focus on the most informative predictors, which is crucial when dealing with the multitude of variables that can influence temperature (Tyralis et al., 2019). The algorithm’s resistance to noise and outliers, stemming from its bagging technique, is particularly valuable in meteorological applications where data quality can vary (Biau and Scornet, 2016). Moreover, RF’s ability to balance bias and variance contributes to its consistent performance across different subsets of data, as demonstrated by Hengl et al. (2018) in their global-scale temperature and precipitation mapping study. These characteristics collectively contribute to RF strong performance in temperature prediction tasks, positioning it as a reliable and efficient tool in climate science and environmental modelling.

2.5 Wavelet analysis

Wavelet analysis is used to separate a time series into components that represent different scales, providing the study of both the frequency and timing of characteristics included in the series. Before wavelet analysis, time series data are preprocessed to maintain continuity and quality. This requires standardizing the time series, X(t), by adjusting it to have a mean of zero and a variance of one:

X_{n o r m} (t) = \frac{X (t) - μ}{σ}

(15)

where μ is the mean of X(t), and σ is the standard deviation.

The Continuous Wavelet Transform of a discrete time series X(t) is given by:

W_{n} (s) = \underset{t = 1}{\sum^{N - 1}} X (t) φ^{*} (\frac{(t - n) δ t}{s})

(16)

where W_n(s) represents the wavelet coefficient at scale s and position n, ψ(t) is the wavelet function, δt is the sampling interval, N is the total number of data points, and * denotes the complex conjugate. For this study, the Morlet wavelet was selected for its effective balance between time and frequency localization, represented by:

φ (t) = π^{- 1 / 4} e^{i ω_{0} t} e^{- t^{2} / 2}

(17)

with ω₀ being the non-dimensional frequency.

The significance of the wavelet power spectrum against a background of red noise is determined through Monte Carlo simulations being compared with the power spectrum of red noise, P_red(k), modelled as:

P_{r e d} (k) = \frac{(1 - α^{2})}{1 + α^{2} - 2 α \cos (\frac{2 π k}{N})}

(18)

where α is the lag-1 autocorrelation coefficient of X(t). This process identifies regions in the wavelet power spectrum that are statistically significant.

The cross-wavelet transform (XWT) and wavelet coherence (WTC) between two time series X(t) and Y(t) explore their phase relationship and common power:

X W T_{x y} (s) = W_{x} (s) \cdot W_{Y}^{*} (s)

(19)

W T C_{x y} (s) = \frac{S (X W T_{x y} (s))}{\sqrt{S (W_{X} {(s)}^{2}) \cdot S (W_{Y} {(s)}^{2})}}

(20)

where S denotes a smoothing operator in both time and scale, facilitating the identification of coherent structures between the series.

Edge effects are addressed through the cone of influence (COI), which delineates the region where edge artefacts are non-negligible:

C O I (t) = s \cdot \sqrt{2} \cdot δ t

(21)

2.6 Climate indices

This study used several climate-related indices to examine how climate variability and change affect water temperature. The climatic indices used in this study, such as TN10p, TX10p, TN90p and TX90p, were properly estimated using the model results from MMEs. The TN10p and TX10p indices indicate the percentage of days when the minimum and maximum temperatures decrease below the 10th percentile of the climatological daily temperature distribution. The TN90p and TX90p indices represent the percentage of days where the minimum and maximum temperatures are over the 90th percentile, indicating warmer weather conditions. The indices serve as vital for evaluating the incidence of extreme temperature events, including both cold and warm episodes, which are essential for comprehending the impact of climate change on water temperature. The indicators are selected and utilized based on the approaches established by the Expert Team on Climate Change Detection and Indicators (ETCCDI), providing a standardized framework for analysing climate variability and change (Zhang et al., 2011).

2.7 Regression analysis

Regression analysis is employed to examine the correlation between climatic extreme indices and water temperature. This study is based on Ordinary Least Squares (OLS) regression, which determines the variables of the linear regression model by eliminating the sum of the squared differences between observed and predicted values. The linear regression model is typically represented in a general form as follows:

Y = β₀ + β₁X₁ + β₂X₂ + … + β_nX_n + ε

(22)

where Y is the dependent variable, X₁, X₂,..., X_n are the independent variables, β₀ is the intercept of the regression line, β₁, β₂,..., β_n are the slopes or coefficients that represent the effect of each independent variable on Y, and ε is the error term, representing the difference between the observed and predicted values of Y.

The OLS regression model is fitted using the least squares criterion, which finds the coefficient estimates that minimize the residual sum of squares (RSS):

R S S = \underset{i = 1}{\sum^{n}} {(y_{i} - {\hat{y}}_{i})}^{2}

(23)

where y_i is the observed value and

{\hat{y}}_{i}

is the predicted value of the dependent variable for the i-th observation. The goodness of fit of the model is assessed using the R² statistic, which measures the proportion of the variance in the dependent variable that is predictable from the independent variables:

R^{2} = 1 - \frac{R S S}{T S S}

(24)

where TSS is the total sum of squares, representing the total variance in the dependent variable:

T S S = \underset{i = 1}{\sum^{n}} {(y_{i} - \bar{y})}^{2}

(25)

The statistical significance of the regression coefficients is tested using the t-statistic, calculated for each coefficient as:

t = \frac{({\hat{β}}_{j} - 0)}{S E ({\hat{β}}_{j})}

(26)

Where

{\hat{β}}_{j}

is the estimated coefficient for the j-th independent variable, and SE(

{\hat{β}}_{j}

) is the standard error of

{\hat{β}}_{j}

. A p-value is obtained from the t-distribution, which, if below a certain threshold (commonly 0.05), indicates that the effect of the independent variable on the dependent variable is statistically significant.

3 Results

3.1 Historical RWT

Mean annual water temperatures for the period 1985-2014 ranged from 7.0℃ to 11.1℃ for the Wieprza River at the Kwisno hydrological station (No.20) and the Odra River at the Połęcko hydrological station (No.2), respectively. The spatial variability of mean annual water temperatures for these rivers is shown in Figure 3. The variability of mean annual water temperatures in the studied rivers ranged from 1.5 to 4.5℃ with a mean value of 2.5℃. The lowest temperature variability occurred in the Nida River at the Pińczów station (No. 33), and the highest in the Dunajec River at the Żabno station (No. 31). The coefficient of variation of mean annual water temperatures ranged from 4.2% (Osa - Rogóźno 2, No. 48) to 10.2% (Skawa - Wadowice, No.29) with a mean value of 6.5%. Water temperatures in the rivers were analysed, with mean annual air temperatures ranging from 7.3 to 9.3℃, averaging 8.4℃. At individual weather stations, mean annual air temperatures ranged from 3.0 to 4.1℃, averaging 3.3℃. The variability of annual mean air temperatures was higher than that of RWTs. This is also confirmed by the coefficients of variation, which ranged from 9.1% to 12.4% with a mean value of 10.2%.

Figure 3 Variability of mean annual river water temperature (a) and air temperature (b) between 1985 and 2014

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In the case of water temperature changes at all stations (except for the Ner River, Dabie post), a successive warming of the water was observed. The average increase in its temperature over the analysed decades was 0.36℃ per decade, with variations for individual rivers ranging from 0.22 to 0.82℃ per decade.

For air temperature, the average increase was 0.43℃ per decade, with the range of changes for individual stations varying from 0.28 to 0.69℃ per decade.

3.2 Future RWT

Analysis of annual average water temperatures from 1985 to 2100 over the Odra basin, for historical and future projections based on different SSP2-4.5, and SSP5-8.5 is presented in Figure 4.

Figure 4 Projected water temperature changes from 1985 to 2100 at Odra basin (a) and Vistula basin (b), in comparison of historical data with future scenarios of SSP2-4.5 and SSP5-8.5

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The historical data show a variability in water temperature ranging between 9℃ and 12℃. Meanwhile, from 2015 to 2100, the water temperature is projected to increase gradually, with less year-to-year variability than the historical data, ranging between 11℃ and 13℃ under SSP2-4.5. Under SSP5-8.5, the water temperature tends to show a significant upward trend in 2015, eventually surpassing the 13℃ mark around the 2060s and reaching approximately 14.5℃ by 2100.

Figure 4b illustrates the annual average water temperatures over the Vistula basin from 1985 to 2100 for historical (1985-2014) and future projections (2015-2100) under two climate scenarios. The historical data reveal a variation, with an upward trend in water temperature, ranging between 9℃ and 12℃. The SSP2-4.5 projection suggests a modraate increase in average water temperatures, following a relatively steady course with some fluctuations. It is expected to rise gradually above historical levels, reaching between 11℃ and 13℃ by the end of the century. The SSP5-8.5 shows a similar level to the SSP2-4.5 in 2015 by indicating a steady and steep increase in water temperature, crossing the 13℃ mark in the 2060s and reaching 14.5℃ by 2100.

The distribution of water temperature across the Vistula basin for the historical and future projections for both basins is presented in Figure 5. The historical data indicate a decline in the distribution of lower temperatures, ranging between around 5℃ and 15℃, with a maximum temperature of 10℃.

Figure 5 Comparative analysis of water temperature distribution for the Odra basin (a) and Vistula basin (b) from 1985-2100 and future projections under SSP2-4.5 and SSP5-8.5 scenarios

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Under SSP2-4.5, the distribution suggests that warmer temperatures tend to be more frequent than the historical average, with the highest value between approximately 10℃ and 20℃. Under SSP5-8.5 the distribution indicates a rightward shift of the temperature, as well as a broadening and extension of the distribution towards temperatures exceeding 20℃. This comparison shows that water temperatures over the Vistula basin are likely to increase in the future, especially under SSP5-8.5.

Figure 5b shows a distribution of water temperature over the Odra basin in historical and future climate scenarios. The analysis reveals trends with the maximum water temperature at 10℃. The notable distribution is a section of the data ranging from 5℃ to 15℃. Under SSP2-4.5, the result suggests that water temperatures tend to increase by the end of the century by between 10℃ and 20℃, with a peak somewhat to the right of the historical peak. Under SSP5-8.5, this indicates a wider distribution with a density that reaches temperatures over 20℃. The distribution of water temperature is positioned to the right of both the historical and SSP2-4.5 distributions, indicating a substantial rise in higher water temperatures. These results indicate that the water temperature over the Odra basin tends to increase significantly, especially at the end of the century under SSP5-8.5.

Under the SSP2-4.5 scenario, the Vistula basin tends to experience a more significant increase in water temperatures than the Odra basin, indicating a higher level of sensitivity or factors that could lead to greater warming. Both rivers are experiencing an increase in temperatures, with the Vistula basin showing a slightly more pronounced shift, suggesting a wider array of environmental or hydrological factors affecting it. The SSP5-8.5 scenario shows a significant deviation from historical patterns for both rivers, indicating a clear trend toward increased temperatures. The Odra basin is exhibiting an expansion into higher temperature ranges that were previously rare, indicating a potential increase in extreme temperature events in the future. Both the Vistula and Odra basins are expected to warm, but the extent and characteristics of these changes vary. The average temperatures of the Vistula basin are consistently rising, whereas the Odra basin is seeing both warming trends and more frequent extreme temperature fluctuations.

3.3 Wavelet analysis

This study employed wavelet analysis to identify temporal shifts and frequency variations in water temperature precisely, expanding our understanding of climate change effects on water temperature across different temporal scales. Figures 6 and 7 show the wavelet power spectra analysing the temporal and scale-dependent aspects of temperature variability in the Vistula and Odra basins under scenarios SSP5-8.5 and SSP2-4.5 and the 95% significance contour.

Figure 6 Wavelet power spectrum of water temperature under SSP2-4.5 (a) and SSP5-8.5 (b) at Vistula River

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Figure 7 Wavelet power spectrum of water temperature under SSP2-4.5 (a) and SSP5-8.5 (b) at Odra River

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Figure 6 presents a wavelet analysis of water temperature in the Vistula River under the SSP2-4.5 climate scenario from 2000 to 2100. The wavelet power spectrum reveals the temporal evolution of different periodic components in the water temperature data. In the wavelet spectrum, high power in shorter periods (1-20 years) persists throughout the century, indicating strong annual and inter-annual variability in water temperature. During longer periods (40-80 years), there is a gradual increase in power, suggesting emerging longer-term climate oscillations influencing water temperature towards the end of the century. The global wavelet spectrum shows that the highest power is concentrated in the shortest periods, confirming the dominance of annual cycles in temperature variation. The time series plot reveals a clear warming trend, with water temperature rising from about 9℃ in 2000 to approximately 12.5℃ by 2100, an increase of about 3.5℃. This warming is not uniform, with a notable jump around 2020 and periods of relative stability interspersed with warming phases.

In comparison, the SSP5-8.5 scenario shows a similar pattern in the wavelet spectrum but with a more pronounced warming trend. The wavelet spectrum under SSP5-8.5 displays a clear shift in dominant periodicities over time. While shorter periods (1-20 years) consistently show high power throughout the entire timeframe, longer periods (40-80 years) exhibit a more significant increase in power as time progresses. This suggests that longer-term climate oscillations become more prominent in influencing water temperature towards the end of the century under SSP5-8.5. The global wavelet spectrum similarly confirms the importance of annual cycles in water temperature variation. The time series plot for SSP5-8.5 illustrates a more dramatic upward trend in water temperature over the century (Figure 4). Starting from around 9℃ in 2000, the temperature rises to approximately 15℃ by 2100, representing a significant warming of about 6℃. This trend is not linear, showing periods of more rapid warming interspersed with shorter periods of relative stability. Overall, while both scenarios show warming trends, SSP5-8.5 presents a more intense increase in temperature and more pronounced long-term oscillations compared to SSP2-4.5.

Figure 7 presents a wavelet analysis of water temperature trends in the Odra River under the SSP2-4.5 climate scenario from 1980 to 2100. The wavelet power spectrum reveals the temporal evolution of different periodic components in the water temperature data. The wavelet spectrum shows strong and persistent high power at shorter periods (1-20 years) throughout the entire timeframe, indicating robust annual and inter-annual variability in water temperature. During longer periods (40-80 years), there is a gradual increase in power as time progresses, suggesting the emergence of longer-term climate oscillations influencing water temperature towards the latter part of the century. The global wavelet spectrum confirms that the highest power is concentrated in the shortest periods, underlining the dominance of annual cycles in temperature variation. The time series plot illustrates a moderate warming trend in the Odra River. Starting from around 9℃ in 1980, the temperature rises to approximately 12℃ by 2100, representing a warming of about 3℃ over the 120-year period. This warming trend is not uniform, showing periods of more rapid warming interspersed with shorter periods of relative stability or slight cooling. Notably, the warming trend appears gradual, with an acceleration from around 2040 onwards that is visible but not dramatic.

In comparison, the SSP5-8.5 scenario shows a more pronounced warming trend and intensification of long-term oscillations. The wavelet spectrum under SSP5-8.5 displays strong and persistent high power in shorter periods (1-20 years), like SSP2-4.5. However, during longer periods (40-80 years), there is a more noticeable increase in power as time progresses, suggesting a stronger emergence of longer-term climate oscillations. The time series plot illustrates a significant warming trend in the Odra River under SSP5-8.5 (Figure 4). Starting from around 9℃ in 1980, the temperature rises to approximately 14℃ by 2100, representing a substantial warming of about 5℃ over the 120-year period. This warming trend is not uniform, showing periods of more rapid warming interspersed with shorter periods of relative stability or slight cooling. Notably, there is a marked acceleration in warming from around 2040 onwards, coinciding with the intensification of longer-period oscillations in the wavelet spectrum. This suggests that long-term climate changes become increasingly influential on river temperatures in the latter half of the century under the SSP5-8.5 scenario, to a greater extent than in the SSP2-4.5 scenario.

3.4 Regression analysis

Regression analysis was used in this study to quantify the correlation between climate extreme indices and water temperature, providing a detailed understanding of the influence of climate change on water temperature. Figures 8 and 9 show the relationship between different temperature indicators and water temperature in the Odra and Vistula basins under SSP2-4.5 and SSP5-8.5.

Figure 8 Correlation between TN10p under SSP2-4.5 (a), TN10p SSP5-8.5 (b), TN90 under SSP2-4.5 (c), TN90p under SSP5-8.5 (d), TX90p under SSP2-4.5 (e), TX90p under SSP5-8.5 (f), TX10p under SSP2-4.5 (g), TX10p under SSP5-8.5 (h), and water temperature at Odra basin

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Figure 9 Correlation between TN10p under SSP2-4.5 (a), TN10p SSP5-8.5 (b), TN90 under SSP2-4.5 (c), TN90p under SSP5-8.5 (d), TX90p under SSP2-4.5 (e), TX90p under SSP5-8.5 (f), TX10p under SSP2-4.5 (g), TX10p under SSP5-8.5 (h), and water temperature at Vistula basin

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The shaded bands around the regression lines in the scatterplots are confidence intervals, visually indicating the precision of the estimated linear relationships. A smaller band indicates more precision, which strengthens the relationship between the temperature indicators and water temperature. The indices TN10p, TN90p, TX90p, and TX10p represent various percentile thresholds for temperature over specific periods, indicating cold (TN10p, TX10p) and warm (TN90p, TX90p) extremes. The correlations for the Odra basin under SSP2-4.5 (Figures 7a, 7c, 7e, 7g) and SSP5-8.5 (Figures 7b, 7d, 7f, 7h) indicate a mostly negative association between temperature indices and water temperature. As the frequency or intensity of temperature extremes rises, water temperature tends to decrease, and vice versa. The TN10p index exhibits a significant negative relationship under both SSP2-4.5 and SSP5-8.5, suggesting that a higher frequency of cold days might be related to decreased water temperatures. The TN90p and TX90p indices exhibit negative correlations, although with a lesser relationship, indicating that warmer temperatures might not exert as significant an impact on water temperature fluctuations as colder temperatures do. The TX10p index displays a comparable trend to TN10p, confirming the negative correlation between cold extremes and water temperature. The Vistula basin shows comparable patterns in respect to the Odra basin, with the SSP2-4.5 and SSP5-8.5 scenarios reflecting similar trends. The correlations for the Vistula basin show a minor decrease in sensitivity to temperature extremes, suggesting that other factors may be influencing the relationship with water temperature. Table 3 present regression results analysing the correlation between climatic indices including TX10p, TX90p, TN90p, TN10p and water temperatures under SSP2-4.5 and SSP5-8.5 at Odra basin.

Table 3 Regression analysis results analyzing the correlation between climatic indices including TX10p, TX90p, TN90p, TN10p and water temperatures under SSP2-4.5 and SSP5-8.5 at Odra basin

Index	Scenario	R²	F-statistic	Coef. of climate index	Std. error of Coef.	t-statistic of Coef.	p-value of Coef.	95% CI of Coef.
TX10p	SSP2-4.5	0.695	241.6	‒0.42	0.028	-15.54	< 0.001	(-0.48, -0.37)
TX10p	SSP5-8.5	0.800	424.8	‒0.52	0.025	-20.61	< 0.001	(-0.57, -0.47)
TX90p	SSP2-4.5	0.734	292.7	0.21	0.013	17.10	< 0.001	(0.19, 0.24)
TX90p	SSP5-8.5	0.908	1052.	0.15	0.005	32.43	< 0.001	(0.14, 0.16)
TN90p	SSP2-4.5	0.763	341.2	0.20	0.011	18.47	< 0.001	(0.18, 0.23)
TN90p	SSP5-8.5	0.887	825.8	0.12	0.004	28.73	< 0.001	(0.11, 0.13)
TN10p	SSP2-4.5	0.763	341.2	0.20	0.011	18.47	< 0.001	(0.18, 0.23)
TN10p	SSP5-8.5	0.887	825.8	0.12	0.004	28.73	< 0.001	(0.11, 0.13)

The regression analysis for SSP2-4.5 shows a significant negative correlation between the TX10p index and water temperature (R²=0.641), indicating that colder days (lower TX10p values) are related to lower water temperatures. The negative coefficient (-0.2121) is statistically significant due to the 95% confidence interval not reaching zero and a low p-value. The model for SSP5-8.5 demonstrates a negative correlation with an R² value of 0.643 and a coefficient of ‒0.2970, suggesting that this relationship could become more pronounced with increased emission levels. A positive association exists between TX90p and water temperature (R²=0.654) under SSSP2-4.5, suggesting that higher water temperatures are related to warmer days. The positive coefficient of 0.1224 is statistically significant, indicating a strong fit for the model. The association under SSP5-8.5 is very strong with an R² value of 0.908, indicating a more significant impact of warmer days on water temperature. For SSP2-4.5, there is a substantial positive connection (R²=0.715) between TN90p and water temperature, with a value of 0.1196. Warmer evenings (higher TN90p readings) are related to increased water temperatures. SSP5-8.5 shows an even greater positive trend (R²=0.913), indicating a strong connection between warmer nights and higher water temperatures. The TN10p index demonstrates a negative correlation (R²=0.666), indicating an inverse relationship between colder nights and water temperature. The negative coefficient (R²=-0.2111) suggests that as the frequency of colder nights increases, water temperatures fall under SSP2-4.5. The SSP5-8.5 model corresponds to the findings, showing a strong inverse connection with a coefficient of -0.2892 and an R² value of 0.652. Table 4 presents regression analysis results analysing the correlation between climatic indices including TX10p, TX90p, TN90p, TN10p and water temperatures under SSP2-4.5 and SSP5-8.5 at Vistula basin.

Table 4 Regression analysis results analyzing the correlation between climatic indices including TX10p, TX90p, TN90p, TN10p and water temperatures under SSP2-4.5 and SSP5-8.5 at Vistula basin

Index	Scenario	R²	F-statistic	Prob (F statistic)	Std. error of Coef.	t-statistic of Coef.	p-value of Coef.	95% CI of Coef.
TX10p	SSP2-4.5	0.641	203.8	3.85×10²⁷	0.015	‒14.27	<0.001	(-0.24, -0.18)
TX10p	SSP5-8.5	0.643	205.7	2.77×10²⁷	0.021	‒14.34	<0.001	(-0.33, -0.25)
TX90p	SSP2-4.5	0.654	215.3	5.02×10²⁸	0.008	14.67	<0.001	(0.10, 0.13)
TX90p	SSP5-8.5	0.908	1121.0	8.05×10⁶¹	0.004	33.48	<0.001	(0.11, 0.12)
TN90p	SSP2-4.5	0.715	285.8	7.63×10³³	0.007	16.90	<0.001	(0.10, 0.13)
TN90p	SSP5-8.5	0.913	1204.0	2.00×10⁶²	0.003	34.69	<0.001	(0.09, 0.10)
TN10p	SSP2-4.5	0.666	227.1	6.68×10²⁹	0.014	‒15.07	<0.001	(-0.23, -0.18)
TN10p	SSP5-8.5	0.652	213.5	6.95×10²⁸	0.020	‒14.61	<0.001	(-0.32, -0.25)

The regression analysis in the Vistula basin indicates that 69.5% of the variance in water temperature has been determined with R² of 0.695. The negative coefficient of -0.4287 shows an inverse connection, indicating that when the TX10p index (colder days) rises, the water temperature falls. The analysis also shows a strong association with high statistical significance, as indicated by the very low p-value. According to SSP5-8.5, with an R² value of 0.800, this model suggests that 80% of the variability in water temperature can be accounted for by the index. The negative coefficient of -0.5203 is more significant than in SSP2-4.5, indicating a more prominent link in this case. The R² value of 0.734 for TX90p suggests that the regression analysis accounts for 73.4% of the variance in water temperature. The positive coefficient of 0.2167 indicates that there is a direct relationship between the TX90p index (warmer days) and water temperature, meaning that when the TX90p index spreads, the water temperature also increases. The relationship is statistically significant, indicated by a low p-value. The R² value is 0.908, meaning that 90.8% of the variability in water temperature is accounted for by the SSP5-8.5 index. The coefficient of 0.1517, although fewer than in SSP2-4.5, nonetheless suggests a robust positive correlation. The analysis also shows that 76.3% of the variance in water temperature is explained by the TN90p index, with an R² value of 0.763. The positive coefficient of 0.2082 indicates a correlation between warmer nights and higher water temperatures. The model demonstrates a high R² value of 0.887, indicating that the TN90p index significantly accounts for the variability in water temperature under SSP5-8.5. The coefficient of 0.1280, which is positive, provides additional confirmation of the association. The analysis shows that the R² value is equal to 0.763 for the TN90p index under SSP2-4.5, suggesting a substantial correlation between cooler nights and water temperature. The 0.2082 positive coefficient aligns with the TN90p index for SSP2-4.5. The model for SSP5-8.5 shows a positive coefficient of 0.1280, indicating a strong association between colder nights and water temperature, as reflected by the R² value of 0.887 for the TN90p index under SSP5-8.5.

4 Discussion

The results indicate a significant transformation in the thermal regime of rivers in Poland, where a permanent increase in water temperature is observed. Historical data confirm earlier studies conducted for other years or a different number of observation posts (Ptak et al., 2016; Ptak, 2018; Wrzesiński and Graf, 2022). The results are consistent with those for other temperate regions, where an increase in the temperature of flowing waters has been recorded. In the period 1979-2018, the water temperature of several rivers in Switzerland increased on average by 0.33℃ per decade (Michel et al., 2020). In the Baltic republics, the water temperature of rivers in the first period of the multi-decade span from 1951-2010 showed a decrease (0.003℃ per year - warm season), whereas in the second, they exhibited only a positive trend (0.04℃ per year warm season) (Jurgelenaite et al., 2018). Studies conducted in Germany in the period 1985-2010 across seven river basins showed that most stations experienced significant warming (average warming trend: 0.03℃ per year), with the fastest rate of change shown for the summer period (Arora et al., 2016). Based on research conducted in the Czech Republic covering catchments with little anthropogenic pressure, it was determined that the increase in water temperature is higher by 1.15℃ over several decades (Hrdinka et al., 2015).

However, in the era of global warming, for various reasons (both natural and economic), understanding the scale of future changes in the thermal regime of aquatic ecosystems is crucial. The results of predictions of changes in river water temperature in different regions of the world unequivocally show its gradual warming (Chen et al., 2016; Hardenbicker et al.; 2017; Fuso et al., 2023; Loerke et al., 2023) In neighbouring countries, the average increase in water temperature streams in the Czech Republic by 2050 is estimated at 1.5-3℃ (Novický et al., 2009). The assessment of changes in water temperature in the Ipel River (Slovakia) showed an increase in all scenarios considered (Bajtek et al., 2023). The maximum increase according to RCP8.5 (2071-2100) is predicted to be 4.01℃ (Slovenské Ďarmoty station). By the end of the 21st century, RWTs in Lithuania, according to the RCP8.5 scenario, may increase by 4.0-5.1℃ (Kriaučiūnienė et al., 2019). Against this backdrop, the results obtained in this study align with the increasingly common global trend in understanding potential changes in RWTs over the next few decades. Importantly, this research is the first attempt to establish such information for an area covering about 3% of Europe’s surface, located in a transitional climate zone. Generally, the results resemble those of previously mentioned studies, and depending on the scenario, the annual average water temperature of rivers in Poland will be higher by 2.1℃ (SSP2-4.5) and 3.7℃ (SSP5-8.5), respectively.

The influence of climatic conditions that determine environmental conditions specific to specific latitudes in the hydrosphere is modified by regional and local conditions of individual catchments. This is evident in a more detailed breakdown, where in both scenarios (SSP2-4.5 and SSP5-8.5), the water temperature will be higher by between 1.6℃ and 3.2℃ for the Odra basin, and by between 2.3℃ and 3.8℃ for the Vistula basin. These differences can be attributed to both geological structures and different scales of maritime and continental climate influences. Based on research by Dynowska (1971), who categorized Poland according to its share of groundwater feeding into rivers, it was determined that for the Vistula basin, this is about 28%, and for the Odra basin, it accounts for about 45%. Previous studies of the relationship between runoff and water temperature in Poland have shown a strong relationship between the two variables in the case of, among others, lakeside rivers, which had a significant share of groundwater recharge (Wrzesinski and Graf, 2022). The role of local factors in the form of underground recharge is evident in the case of the Warta River, where, among the five lowland posts, the lowest increase in water temperature (0.16°C per decade) was recorded for the one with the dominant influence of underground recharge from the dune area (Ptak et al., 2019). In the analysed work, the Ner River was the only one that did not show an upward trend during the historical period. As suggested by Ptak (2017a), this may be due to the location of the observation post and the river’s alimentation by groundwater from a wide valley filled with peat. Thus, a significant share of groundwater recharge with different thermal properties and, consequently, lower RWTs in the Odra area, confirming earlier findings regarding annual averages or a slower warming pace. Similar conclusions were drawn by Latkovska and Apsīte (2016) in their analysis of long-term changes in RWTs in Latvia, noting that lower temperatures occurred in rivers with a large share of groundwater inflow. Besides the structure of river groundwater supply, climatic conditions also need to be considered. The eastern part of Poland (the Vistula basin) is more influenced by the continental climate, hence longer and colder winters, and for inland waters, longer-lasting ice phenomena. For example, an analysis of several lakes showed that the duration of ice cover east of the Vistula basin was about 26 days longer than at lakes located west of the river (Choiński et al., 2016). A marked increase in air temperature in spring accelerated the disappearance of ice cover (Ptak and Sojka, 2019), thereby shortening the period of surface water isolation from atmospheric factors, which extended their heating period.

There has been a significant increase in the water temperature of rivers, which will substantially impact their natural characteristics and economic potential. Changes in the functioning of these ecosystems caused by climate warming, which are already visible, will continue to progress in the future. Changes in the thermal characteristics of the Rhine complicate the restoration of native ichthyofauna and facilitate the establishment of invasive species, increasing competition between them (Leuven et al., 2011). The future increase in water temperature in the Fourchue River (Canada) during the summer period (in June by 0.2-0.7℃) may favour the growth of brook trout, but there is also the potential for several days of Upper Incipient Lethal Temperature (Kwak et al., 2017). Against the backdrop of climate changes, the invasiveness of selected freshwater fish species in Poland is already noticeable and will increase with rising temperatures (Zięba et al., 2019). In the context of the recorded increase in water temperature in the coming decades, the structure of the ichthyofauna of the Warta River may change (Nowak et al., 2019), and the share of invasive species may increase. Trzebiatowski (1999), analysing the ichthyofauna of the Lower Oder Valley Landscape Park, believes that the occurrence of sun bass and Amur, chequered except for refugia in the form of a channel draining heated water, appeared sporadically in the lower Odra River. Future results indicating a successive increase in water temperature may influence the spread of these species to other rivers. Among the current effects of the presence of alien species in Polish rivers, Grabowska et al. (2010) list hybridization with native species, destruction of spawning grounds and habitats, predation on the eggs and offspring of native species, and the transmission of diseases and parasites. Further issues include matters concerning water quality, which is subject to human pressure in the form of industrial and agricultural pollutants. The inflow to the Baltic Sea from the territory of Poland is considered one of the main sources of nitrogen and phosphorus (HELCOM, 2015). Chlorophyll-a concentrations were used as an indicator of eutrophication in the Lepsämänjoki catchment (Finland), establishing its dependence on the total phosphorus concentration. Moreover, a positive synergistic interaction between total phosphorus and water temperature was found (Rankinen et al., 2019). Studies on the Ner River showed that the phosphate content of the water was characterized by a clear seasonality where there was a significant relationship between phosphates and water temperature (Jaskuła et al., 2016). Projections of further increases in water temperature will determine the deepening of the recorded relationships. Increased water temperature contributes to increased eutrophication (Ciupa, 2005). The progressive increase in water temperature required a change in the concept of action to eliminate or reduce this process in rivers in Poland.

According to research conducted in the catchment area of the Ciemięga River (southeastern Poland), it was found that neither low flow velocity nor higher water temperatures favoured the process of oxygen transfer from the atmosphere and its retention in water (Zubala, 2002). One of the key elements for water self-purification is the mineralization of sediments, and therefore the appropriate amount of dissolved oxygen in the water (Ptak and Nowak, 2016). The successive increase in water temperature will reduce the amount of dissolved oxygen in the water, consequently hindering efforts towards river rehabilitation. For example, the predicted increase in water temperature during the summer period (by the end of the 21st century) for five river basins in India is estimated to be between 3.1 and 7.8℃, which will affect the amount of dissolved oxygen. Every 1℃ increase in water temperature will cause a decrease in dissolved oxygen of about 2.3% (Rajesh and Rehana, 2022).

Further significant challenges are associated with adapting actions that utilize river water resources in energy production. Poland is undergoing a dynamic energy transformation, increasingly shifting its energy production structure from fossil fuels to renewable sources. One of the consequences of such energy production is the artificial heating of water and then its return to the natural elements of the hydrographic network, which is associated with thermal pollution. As demonstrated by the study conducted on the Danube (Kostelec, Serbia), the discharge of cooling water causes a temperature increase that extends along the river’s right bank for kilometres (Laković et al., 2018). In the case of the Vistula basin, even 40 kilometres downstream from the Kozienice Power Plant, there is a differentiation between heated water and water of natural temperature (Ciołkosz,1975). However, it should be emphasized that these results come from a single expedition during the summer period. The projected increase in water temperature taken in by power plants by the end of the century could affect changes in technological processes and, consequently, the costs of energy produced in this way.

As adverse changes in the thermal regime of rivers in Poland are predicted, it is necessary to undertake actions aimed at mitigating the potential effects of global warming. One of the most currently practised methods is the appropriate planting of vegetation in riparian zones to shade sections of the river. Garner et al. (2017), based on an analysis of the impact of tree planting on the thermal conditions of a stream in Scotland, demonstrated that even sparse but appropriately located vegetation can cause a significant reduction in the maximum temperature. Based on the analysis of several rivers in Oregon, Chang et al. (2018) found that rivers fed by surface waters lacking riparian vegetation are most vulnerable to climate change (with temperature increases up to 4℃). Riparian vegetation can lower water temperature by 1-2℃, and the removal of riparian vegetation contributes to an increase in water temperature (Trimmel et al., 2018). Forested areas were negatively correlated with the average and maximum water temperature (Horne and Hubbart, 2020), which as noted in one of the few such studies in Poland. An analysis of two rivers proved that Czerna Wielka (68.3% of its length has contact with forest) and Szprotawa (21.6% of its length has contact with forest) had a water temperature 2.6℃ lower during the warm half-year (Ptak, 2017b). Thus, taking into account the cited results and the apparent further increase in the water temperature of rivers in Poland, the adaptation of water resource management strategies should take into account of the possibility of proper management of the riverbank zone. As far as possible for natural and formal-legal reasons, buffer strips in the form of tree plantings should be created in such places. Therefore, the topic addressed in the article can serve as a starting point for water management authorities to ensure that besides ensuring an adequate quantity of water, they pay attention to the possibility of stabilizing one of the basic water parameters, which is its temperature.

5 Conclusions

Predicting global warming requires detailed knowledge of the reactions of individual environmental components, which in the case of inland waters is crucial for estimating water temperature. For rivers, many existing studies indicate that historically there has been a change in the thermal regime, and further clear warming will continue to progress in the future. In the case of Poland, simulations like these have not been conducted to date, and the research undertaken in the article aims to fill this gap. Thus, the results obtained confirm previous studies of the thermal regime of rivers conducted in many other regions, enriching the existing state of knowledge for a significant area located in Central Europe. Of the three machine-learning models used to predict water temperature - Random Forest (RF), Gradient Boosting Machine (GBM), and Decision Tree (DT), it was found that the first one achieved the highest average R² value (0.88), and the lowest error rates (RMSE: 2.25, MAE: 1.72). Based on historical data, there was a successive warming of the water, at 0.36℃ per decade. Based on wavelet analysis, there was strong annual and inter-annual variability in water temperature. The emergence of long-term climatic oscillations affecting water temperature at the end of the century is taking place over longer periods. In case of further changes, it has been determined that by the end of the 21st century, depending on the scenario adopted, the average temperature will increase by 2.1℃ (SSP2-4.5) and by 3.7℃ (SSP5-8.5). Referring the results to the main basins of the Vistula and Odra, covering a total of about 90% of the area of Poland, differences are evident, at respectively 2.3℃ and 3.8℃, and 1.6℃ and 3.2℃. This situation is caused, among other factors, by a smaller share of groundwater feeding into rivers, in the case of the Vistula basin, and the dominance of the continental climate’s influence. The results constitute an important starting point for water resource management bodies to introduce comprehensive measures as soon as possible, aimed at mitigating the negative effects of warming on river ecosystems in Poland. Based on the literature, it can be concluded that currently the most common in this regard are solutions based on the appropriate management of the coastal zone associated with the presence of trees.

Conflict of Interest Statement

The authors declare no competing interests relevant to this study.

Data Availability Statement

We would like to acknowledge the Copernicus Climate Change Service, Climate Data Store, (2021): CMIP6 climate projections. Copernicus Climate Change Service (C3S) Climate Data Store (CDS). The data is available at https://cds.climate.copernicus.eu/datasets.

Table S1 Location of hydrological stations

No	River	Station	Longitude (°)	Latitude (°)
1	Odra	Ścinawa	16.44	51.41
2	Odra	Połęcko	14.89	52.05
3	Odra	Gozdowice	14.32	52.76
4	Biała Lądecka	Żelazno	16.67	50.37
5	Ścinawka	Tłumaczów	16.44	50.55
6	Oława	Oława	17.29	50.95
7	Bystrzyca	Krasków	16.58	50.92
8	Bóbr	Dąbrowa Bolesławiecka	15.57	51.33
9	Bóbr	Żagań	15.32	51.62
10	Warta	Bobry	19.41	51.03
11	Warta	Sieradz	18.74	51.60
12	Warta	Śrem	17.02	52.09
13	Ner	Dąbie	18.82	52.08
14	Prosna	Bogusław	17.95	51.90
15	Noteć	Pakość	18.09	52.80
16	Noteć	Nowe Drezdenko	15.84	52.85
17	Gwda	Piła	16.74	53.15
18	Rega	Trzebiatów	15.26	54.06
19	Parsęta	Białogard	15.98	54.00
20	Wieprza	Kwisno	17.13	54.09
21	Grabowa	Grabowo	16.44	54.30
22	Łupawa	Smołdzino	17.21	54.66
23	Łeba	Lębork 2	17.75	54.54
24	Wisła	Skoczów	18.79	49.80
25	Wisła	Kępa Polska	19.96	52.43
26	Wisła	Gdańsk-Świbno	18.94	54.33
27	Brynica	Brynica	19.00	50.47
28	Soła	Oświęcim	19.22	50.04
29	Skawa	Wadowice	19.51	49.88
30	Raba	Stróża	19.92	49.80
31	Dunajec	Żabno	20.86	50.13
32	Poprad	Stary Sącz	20.66	49.57
33	Nida	Pińczów	20.52	50.51
34	San	Radomyśl	21.93	50.67
35	Tanew	Harasiuki	22.47	50.48
36	Wieprz	Kośmin	22.00	51.57
37	Narew	Narew	23.52	52.92
38	Narew	Nowogród	21.87	53.23
39	Narew	Zambski Kościelne	21.21	52.76
40	Biebrza	Burzyn	22.46	53.27
41	Omulew	Białobrzeg Bliższy	21.48	53.11
42	Orzyc	Maków Mazowiecki	21.11	52.86
43	Bug	Strzyżów	24.04	50.84
44	Bug	Wyszków	21.45	52.59
45	Krzna	Malowa Góra	23.47	52.10
46	Drwęca	Brodnica	19.40	53.26
47	Wda	Czarna Woda	18.09	53.84
48	Osa	Rogóźno 2	18.95	53.52
49	Wierzyca	Brody Pomorskie	18.76	53.86
50	Pasłęka	Łozy	19.95	54.19
51	Łyna	Sępopol	21.01	54.27
52	Węgorapa	Mieduniszki	21.98	54.33

Table S2 Location of meteorological stations

No	Station	Longitude (°)	Latitude (°)
I	Kłodzko	16.61	50.44
II	Wrocław	16.90	51.10
III	Legnica	16.21	51.19
IV	Leszno	16.53	51.84
V	Zielona Góra	15.52	51.93
VI	Wieluń	18.56	51.21
VII	Łódź	19.39	51.72
VIII	Kalisz	18.08	51.78
IX	Piła	16.75	53.13
X	Gorzów Wielkopolski	15.28	52.74
XI	Bielsko-Biała	19.00	49.81
XII	Katowice	19.03	50.24
XIII	Kraków-Balice	19.79	50.08
XIV	Nowy Sącz	20.69	49.63
XV	Tarnów	20.98	50.03
XVI	Kielce-Suków	20.69	50.81
XVII	Sandomierz	21.72	50.70
XVIII	Lublin-Radawiec	22.39	51.22
XIX	Warszawa	20.96	52.16
XX	Białystok	23.16	53.11
XXI	Włodawa	23.53	51.55
XXII	Mława	20.36	53.10
XXIII	Płock	19.73	52.59
XXIV	Toruń	18.60	53.04
XXV	Chojnice	17.53	53.72
XXVI	Kołobrzeg	15.58	54.18
XXVII	Koszalin	16.16	54.20
XXVIII	Łeba	17.53	54.75
XXIX	Hel	18.81	54.60
XXX	Elbląg	19.43	54.16
XXXI	Kętrzyn	21.37	54.07

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Alterations of abiotic factors (e.g., river water temperature and discharge) will definitely affect the fundamental processes of aquatic ecosystems. The purpose of this study was to examine the impact of climate change on the structure of fish assemblages in fast-flowing rivers belonging to the catchment of the major Eastern European river, the Nemunas. Five catchments of semi-natural rivers were selected for the study. Projections of abiotic factors were developed for the near (2016-2035) and far future (2081-2100) periods, according to four RCP scenarios and three climate models using the HBV hydrological modelling tool. Fish metric projections were developed based on a multiple regression using spatial data. No significant changes in projections of abiotic and biotic variables are generally expected in the near future. In the far future period, the abiotic factors are projected to change significantly, i.e., river water temperature is going to increase by 4.0-5.1 degrees C, and river discharge is projected to decrease by 16.7-40.6%, according to RCP8.5. By the end of century, the relative abundance of stenothermal fish is projected to decline from 24 to 51% in the reference period to 0-20% under RCP8.5. Eurythermal fish should benefit from climate change, and their abundance is likely to increase from 16 to 38% in the reference period to 38-65% under RCP8.5. Future alterations of river water temperature will have significantly more influence on the abundance of the analysed fish assemblages than river discharge. (C) 2019 Elsevier B.V.

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Abstract
Key words
Cite this article
1 Introduction
2 Materials and methods
2.1 Study area
Figure 1 Location of studied rivers in Poland
2.2 Historical data
2.3 Future data and methods
Table 1 GCMs and respective institutions used in this study
2.4 Machine learning (ML)
Figure 2 Comparative analysis of three machine learning models: Random Forest, Gradient Boosting, and Decision Tree for predicted water temperature
Table 2 Performance metrics of three different machine learning models: Random forest, gradient boosting machine and decision tree
2.5 Wavelet analysis
2.6 Climate indices
2.7 Regression analysis
3 Results
3.1 Historical RWT
Figure 3 Variability of mean annual river water temperature (a) and air temperature (b) between 1985 and 2014
3.2 Future RWT
Figure 4 Projected water temperature changes from 1985 to 2100 at Odra basin (a) and Vistula basin (b), in comparison of historical data with future scenarios of SSP2-4.5 and SSP5-8.5
Figure 5 Comparative analysis of water temperature distribution for the Odra basin (a) and Vistula basin (b) from 1985-2100 and future projections under SSP2-4.5 and SSP5-8.5 scenarios
3.3 Wavelet analysis
Figure 6 Wavelet power spectrum of water temperature under SSP2-4.5 (a) and SSP5-8.5 (b) at Vistula River
Figure 7 Wavelet power spectrum of water temperature under SSP2-4.5 (a) and SSP5-8.5 (b) at Odra River
3.4 Regression analysis
Figure 8 Correlation between TN10p under SSP2-4.5 (a), TN10p SSP5-8.5 (b), TN90 under SSP2-4.5 (c), TN90p under SSP5-8.5 (d), TX90p under SSP2-4.5 (e), TX90p under SSP5-8.5 (f), TX10p under SSP2-4.5 (g), TX10p under SSP5-8.5 (h), and water temperature at Odra basin
Figure 9 Correlation between TN10p under SSP2-4.5 (a), TN10p SSP5-8.5 (b), TN90 under SSP2-4.5 (c), TN90p under SSP5-8.5 (d), TX90p under SSP2-4.5 (e), TX90p under SSP5-8.5 (f), TX10p under SSP2-4.5 (g), TX10p under SSP5-8.5 (h), and water temperature at Vistula basin
Table 3 Regression analysis results analyzing the correlation between climatic indices including TX10p, TX90p, TN90p, TN10p and water temperatures under SSP2-4.5 and SSP5-8.5 at Odra basin
Table 4 Regression analysis results analyzing the correlation between climatic indices including TX10p, TX90p, TN90p, TN10p and water temperatures under SSP2-4.5 and SSP5-8.5 at Vistula basin
4 Discussion
5 Conclusions
Conflict of Interest Statement
Data Availability Statement
Table S1 Location of hydrological stations
Table S2 Location of meteorological stations
References

Received	Accepted	Published
2024-03-20	2024-09-30	2025-01-25
Issue Date
2025-01-15

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Abstract

Key words

Cite this article

1 Introduction

2 Materials and methods

2.1 Study area

Figure 1 Location of studied rivers in Poland

2.2 Historical data

2.3 Future data and methods

Table 1 GCMs and respective institutions used in this study

2.4 Machine learning (ML)

Figure 2 Comparative analysis of three machine learning models: Random Forest, Gradient Boosting, and Decision Tree for predicted water temperature

Table 2 Performance metrics of three different machine learning models: Random forest, gradient boosting machine and decision tree

2.5 Wavelet analysis

2.6 Climate indices

2.7 Regression analysis

3 Results

3.1 Historical RWT

Figure 3 Variability of mean annual river water temperature (a) and air temperature (b) between 1985 and 2014

3.2 Future RWT

Figure 4 Projected water temperature changes from 1985 to 2100 at Odra basin (a) and Vistula basin (b), in comparison of historical data with future scenarios of SSP2-4.5 and SSP5-8.5

Figure 5 Comparative analysis of water temperature distribution for the Odra basin (a) and Vistula basin (b) from 1985-2100 and future projections under SSP2-4.5 and SSP5-8.5 scenarios

3.3 Wavelet analysis

Figure 6 Wavelet power spectrum of water temperature under SSP2-4.5 (a) and SSP5-8.5 (b) at Vistula River

Figure 7 Wavelet power spectrum of water temperature under SSP2-4.5 (a) and SSP5-8.5 (b) at Odra River

3.4 Regression analysis

Figure 8 Correlation between TN10p under SSP2-4.5 (a), TN10p SSP5-8.5 (b), TN90 under SSP2-4.5 (c), TN90p under SSP5-8.5 (d), TX90p under SSP2-4.5 (e), TX90p under SSP5-8.5 (f), TX10p under SSP2-4.5 (g), TX10p under SSP5-8.5 (h), and water temperature at Odra basin

Figure 9 Correlation between TN10p under SSP2-4.5 (a), TN10p SSP5-8.5 (b), TN90 under SSP2-4.5 (c), TN90p under SSP5-8.5 (d), TX90p under SSP2-4.5 (e), TX90p under SSP5-8.5 (f), TX10p under SSP2-4.5 (g), TX10p under SSP5-8.5 (h), and water temperature at Vistula basin

Table 3 Regression analysis results analyzing the correlation between climatic indices including TX10p, TX90p, TN90p, TN10p and water temperatures under SSP2-4.5 and SSP5-8.5 at Odra basin

Table 4 Regression analysis results analyzing the correlation between climatic indices including TX10p, TX90p, TN90p, TN10p and water temperatures under SSP2-4.5 and SSP5-8.5 at Vistula basin

4 Discussion

5 Conclusions

Conflict of Interest Statement

Data Availability Statement

Table S1 Location of hydrological stations

Table S2 Location of meteorological stations

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References

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