Investigation of water temperature changes in the Hron River in the context of expected climate change

The water temperature is one of the physico – chemical indicator of water quality that plays a crucial role in affecting the biological processes in surface water. In the context of the climate changes, there are also changes in the temperature of the water in the streams. The paper presents an analysis of long-term data of the water temperature in the Hron River at two selected gauging stations: Banská Bystrica and Brehy, during the period of 1962–2020. The analysis was conducted using a long series of water temperature measurements. The aim of the study is to detect whether significant trends occur in the time series of water temperature. The first part of the paper dealt with the trend analyses of monthly and annual water temperature. The following section is focused on determination, investigation and evaluation of 1, 3-, 7-day maximum water temperatures. The impact of rising air temperatures on water temperature is critical for protecting water resources and ensuring water quality. In the last part of the study, the monthly water temperature of the Hron River at two gauging stations was modeled using air temperature. The best for Hron at B. Bystrica was the model: SARIMA(1,0,0)x(0,1,1) 12 + 1 regressor, and for Hron at Brehy the best was the model: SARIMA(1,0,0)x(1,0,2) 12 + 2 regressors, with a high correlation coefficient of 0.983 at B. Bystrica and 0.985 at Brehy. Results showed that a 1°C increase in air temperature caused the water temperature to rise by 0.35°C at Banská Bystrica and 0.57°C at Brehy, while a 3°C increase resulted in a rise of 1.05°C at Banská Bystrica and 1.75°C at Brehy. The study concludes that the SARIMA model can


Introduction
Climate change and anthropogenic activity have an impact on the components of the hydrological regime of rivers, potentially leading to negative effects on the quantity and quality of water. Therefore, monitoring changes in the quantity and quality of water in streams is essential in quantifying the potential threat to their balanced regime. Understanding and analysing the relationship between the quality and quantity of water also deserves attention. Much less attention is paid to the long-term water temperature behaviour in natural streams and rivers. Till the end of 2000, a lack of suitable data hinders such studies and, for example, relatively few analyses of detailed water temperature records covering periods of a decade or longer have been published (Vannote and Sweeney, 1980;Webb and Walling, 1985;Beschta et al. 1987;Ludwig et al., 1990). Obtaining a relatively long series of data is necessary to accurately determine the true nature of the thermal regime for a river monitoring station and to assess the response of water temperature to the potential impacts of climate change on river systems. The European Environment Agency (EEA, 2017) indicates that climate change has increased the water temperature of rivers and lakes. Water temperature is a primary parameter of physical water quality which exerts an important influence on the ecology of freshwaters, low flows in conjunction with high water temperatures can directly threaten life in rivers. It is a key abiotic variable that models the chemical composition of water and organisms in rivers and streams (St-Hilaire et al., 2012). The resulting temperature of water in rivers is influenced mainly by atmospheric temperature, as well as other factors such as the amount of water in the stream, orographic conditions of the basin (e.g., altitude of the basin, size of the basin, presence of lakes in the basin), and human activity in the basin (Liptay, 2022;Okhravi et al, 2022). The assessment of the consequences of environmental changes on the temperature regime of rivers and their impact on water quality has been a frequently discussed topic in many professional studies in recent years (Webb and Walling, 1992;Webb and Nobilis, 1997;Ptak et al., 2019). Due to the air and stream temperature relationships, increases in air temperature expected from future climatic changes are thought to raise stream temperatures. The goal of several research papers in the past was not to develop a model, but to determine how stream temperatures in general can be explained by air temperatures, and whether the relationship can be expected to be linear, particularly at high air temperatures (Mosheni and Stefan, 1999). However, the potential of these future stream temperature increases has, to date, not been systematically explored. A fundamental question still remains is, how long and detailed water temperature information provides a good ability to characterize the long-term temperature behaviour of water, investigate the occurrence of recent trends in the thermal regime, and predict likely increases in stream and river temperatures as a consequence of global warming. Webb and Walling (1992) studied the long term water temperature in catchments of England and according to their study the long term water temperature behaviour between catchments appeared primarily to reflect the influence of different land use characteristics. In Poland, the analysis of data for six gauging stations along the Warta river by Ptak et al. (2019) showed, that over the last fifty years there has been a significant transformation of the thermal regime manifesting itself in a successive increase in water temperature. In the case of the analysed gauging stations it was found that the observed changes were caused mainly by climatic factors, which is confirmed by strong relations between water temperature and air temperature. The transformation of thermal conditions of stream and river waters is particularly important in the context of global warming. The importance of thermal changes occurring in rivers start to be within a broad range of interest, subject to research in the scope of various scientific disciplines. Watercourses in Slovakia have a variable hydrological regime with relatively frequent occurrence of extreme flows, both in time and space. Their variability is determined by physical-geographic and climatic conditions. Long periods of drought are increasingly occurring, alternating with intense rainfall causing flash floods (Poórová et al., 2017;Lešková and Škoda, 2003;Martincová et al., 2011). For example, in the autumn of the extremely dry year 2003, there was a mass death of fish in the river Váh, due to the high water temperature in the river (low oxygen content in the water). Authors Martincová et al. (2011) describe the methodology for classification scheme determination of water temperature, in order to evaluate status of the surface water bodies in selected Slovakian high-mountain, highland and lowland basins. Development of the methodology was based on statistical processing of long-term water temperature trends in selected Slovak rivers and used continuous 40 yearly series (time period 1964-2003) of the daily water temperature data, from six stations, that represent several altitude positions. On 19 November, 2004, a strong wind-throw destroyed the riparian vegetation along the channel of the Bela River. Pekárová et al. (2011) attempted to point out if, and possibly to what extent, the remove riparian vegetation affected the temperature regime of the Bela River. The result is, that after the wind-throw in the Bela River watershed, the variability of daily water temperature increasedmaxima are higher, whereas minima are lower on the daily time scale. The objective of this study was to analyse changes in long-term data of the water temperature in the Hron River at two selected gauging stations, Banská Bystrica and Brehy, during the period of 1962-2020. The next objective of the study was to determine the maximum water temperatures for 1-, 3-, 7-day periods, and to analyse changes in their long-term trends. Analysis of water temperature trends can be a reliable tool for decision-makers, as it provides insight into potential threats to the aquatic ecosystem. The impact of increasing air temperatures on water temperature is critical for safeguarding water resources and maintaining water quality. Due to the strong correlation between air temperature and water temperature, the final objective of the study was to predict the effect of a hypothetical increase in average monthly air temperature (Ta) on the average monthly water temperature (To).

Study area and data
The Hron River is the second longest river in Slovakia. It is 298 km long with basin area of 5 465 km 2 . The Hron River flows only through the territory of Slovakia and feeds into the Danube near Štúrovo. The Hron springs in the Horehronie valley, connected to the Low Tatras and the Spiš-Gemer Karst and can be characterized as a nivopluvial river. The location of the selected river in area of Slovak territory illustrates Fig. 1. The Hron River at Banská Bystrica drains into a basin of 1 766.48 km². The long-term average daily flow reached 24.76 m 3 s -1 at Banská Bystrica for the period 1962-2020. The Hron River at Brehy drains into a basin of 3 821.35 km². The long-term average daily discharge reached 44.59 m 3 s -1 at Brehy for the period 1962-2020. The location of the Hron River within the Slovak territory is presented in Fig. 1, and basic location characteristics of the selected gauging stations are listed in Table 1. The analysis was conducted using a long series of water temperature measurements. The first measurements in the Hron River at Banská Bystrica started in 1925, while measurements at Brehy began in 1961. However, it should be noted that the available long-term data are incomplete. Therefore, we analysed series of daily water temperatures for period of 59-years  in this study. The course of daily water temperatures and longterm mean monthly water temperature Tom at Banská Bystrica and Hron for the period 1962-2020 are presented in Fig. 2. Table 2 lists the descriptive statistical characteristics of daily water temperature series for analysed period 1962-2020. The daily maximum temperature was measured in June 1963 (20°C, Hron: Banská Bystrica) and in August 1989 (25.5°C, Hron: Brehy). The long-term mean water temperature at the Banská Bystrica reached value 7.96°C, and at Brehy it reached value of 9.51°C. From monthly water temperature point of view, the maximum long-term water temperatures   1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 (Hamed, 2008;Gilbert, 1987). The study performs two types of statistical analyses: 1) the presence of a monotonic increasing or decreasing M-K test trend and 2) the slope of a linear trend is estimated with the nonparametric Sen's method, which uses a linear model to estimate the slope of the trend and the variance of the residuals should be constant in time. We tested the null hypothesis H0 of no trend, i.e. the observations Tom against the alternative hypothesis H1, where there is an increasing or decreasing monotonic trend. The significance of trends was assessed at the four tested significance levels. The following symbols were used in the analysis: *** if trend at α = 0.001 significance level -H0 seems to be impossible; ** if trend at α = 0.01 significance level -1% mistake if we reject the H0; * if trend at α = 0.05 significance level -5% mistake if we reject the H0; + if trend at α = 0.1 significance level -10% mistake if we reject the H0; Blank: the significance level is greater than 0.1, cannot be excluded that the H0 is true.
The most significant trend is assigned three stars (***), with a gradual decrease in importance, the number of stars also decreases (Salmi et al., 2002).

Simulation and prediction of water temperature
Multiple regression and SARIMA models were created to predict water temperature based on monthly air temperature in the Hron River. The SARIMA (Seasonal Autoregressive Integrated Moving Average) model is a time series forecasting model that incorporates both autoregressive (AR) and moving average (MA) components, as well as differencing and seasonal components. The model is designed to capture and account for patterns and trends within the time series data, including seasonality and periodicity. The seasonal component is particularly important in the SARIMA model, as it allows for the modelling of data with seasonal fluctuations or cycles. The model involves fitting a regression equation to the data, where the dependent variable is the time series data, and the independent variables are lags of the series and lagged errors. The model is typically estimated using maximum likelihood estimation, and the accuracy of the model can be evaluated using various statistical measures such as AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) (Pekárová, 2009). The general form of the SARIMA(p,d,q)x(P,D,Q)L model takes the following form: where Etindependent and normally distributed random variable with zero mean value μ=0 and variance σE 2 ; p trend autoregressive order; dtrend difference order; q trend moving average order. P seasonal autoregressive order; Dseasonal difference order; Qseasonal moving average order; Lthe number of time steps for a single seasonal period (an L of 12 for monthly data suggests a yearly seasonal cycle. Breversion shift operator defined as BYt = Yt-1; In order to identify this model it is necessary to analyse the particular components of the time series in the following sequence:  identification of a trend (differentiating of order d) and seasonality (seasonal differentiating of order D);  selection of a model type (AR, MA, ARMA) and determination of the model's order;  estimation of model parameters;  verification of the model.
Monthly air temperatures from the Banská Štiavnica station (1991-2020) were used as climatic input data for the model. To predict the increase in water temperature, two scenarios of average monthly air temperatures were created. The first scenario (SCEN+1) was created by adding 1°C to the measured monthly air temperature. The second scenario (SCEN+3) was created by adding 3°C to the measured monthly air temperature.

Long-term trends of the monthly and annual water temperatures in the Hron River
Initially, we examined the average monthly water temperatures, as well as the long-term annual water temperature fluctuation at the selected gauging stations. The average monthly water temperatures show an increase in long-term trends in all months over the analysed period 1962-2020 at both gauging stations. The increasing in long-term trends of average monthly temperatures Tom, with significance level α = 0.001 were calculated during winter months from November to February, and during spring months of March and of April, at Hron: Banská Bystrica. Additionally, significant increasing trends were observed in the summer months from June to August at Hron: Brehy. The results of long-term trends significance test of mean monthly water temperatures Tom in the Hron River at Banska Bystrica and at Brehy gauging stations during the period of 1962-2020 is listed in Table 3. The course of the mean monthly water temperatures for the Hron River at Banská Bystrica and Brehy during the period 1962-2020 is illustrated in Fig. 3 a-b. The course of long-term mean annual water temperatures for the Hron River at Banská Bystrica and at Brehy during the period 1962-2020 are illustrated in Fig. 4 a-b. The long-term mean annual water temperature Toy showed an increasing in long-term trend at α = 0.001 significance level during the analysed period 1962-2020. Table 4 lists conclusion of trend significance test of longterm mean annual water temperature Toy in the Hron River at Banská Bystrica and at Brehy gauging station during the period 1962-2020.

Long-term trends of the M-day maximum water temperatures in the Hron River
Multi-day summer heatwaves during low-flow periods cause a lack of oxygen in the water, which leads to the death of aquatic organisms. Therefore, in the next section, we focused on evaluating the long-term development of water temperature in the Hron River during several days. In our study the 1-, 3-, and 7-day maximums were taken from moving averages of the appropriate length calculated for every possible period that is completely within the year. The 1-day maximum water temperatures showed decreasing long-term trend at significance level of α = 0.001 (Fig. 5) for the Hron River at Banská Bystrica during the period 1962-2020. On the other hand, the 1-, 3-, 7-day maximum water temperatures showed a significant an increasing long-term trends with significance level of α = 0.001 (Fig. 5) for the Hron River at Brehy during the same period. The conclusion of the long-term trend significance test of M-day maximum water temperature in the Hron River at Banská Bystrica and at Brehy gauging station during the period 1962-2020 (with α = 0.001) are listed in Table 5.  Fig. 3.     Hron: Brehy the model: SARIMA(1,0,0)x(1,0,2)12 + 2 regressors (the model with the lowest value of the AIC=-0.41). The process of model selection is presented on water temperature data from gauging stations Hron: Banská Bystrica and Brehy. The resulting parameters of the model simulation SARIMA are given in Table 6. The marginal significance levels of each model parameter (P-value) were less than 0.05, so any parameter of the model has not to be excluded. Relationship between the measured monthly water temperatures at the Hron: Banská Bystrica and at the Hron: Brehy and monthly water temperatures modelled using SARIMA model are illustrated in Fig. 6. The SARIMA model performs very well in modelling the monthly water temperature values, with a high correlation coefficient of 0.983 at B. Bystrica and 0.985 at Brehy. Therefore, it can be effectively used to simulate changes in water temperature for different scenarios of changes in air temperature. The largest increase in European mean temperature was detected in winter and spring, amounting to 0.5 to 1.0°C per decade during 1977-2001(Jones and Moberg, 2003. Van der Schrier et al. (2013) note that Europe is warming faster (0.41°C per decade) than global land average (0.27°C per decade) over the period 1980-2010. These values refer to conspicuously enhanced warming in Europe at the end of the twentieth century compared with other continents. The Ministry of the Environment of the Slovak Republic (ME SR, 2018) formulates the general conclusions of the further development of the climate in Slovakia in a study. This study states, that the in comparison to the period between 1951 and 1980 the average air temperature may gradually increase by from 2°C to 4°Cthe so-far inter-annual and interseasonal weather fluctuation may remain. Therefore, two hypothetical scenarios of average monthly air temperatures were created: 1. The first scenario (SCEN+1) was created by adding 1°C to the measured monthly air temperature; 2. The second scenario (SCEN+3) was created by adding 3°C to the measured monthly air temperature (Fig. 7).

Course of monthly water temperature Tom, 7-year moving averages (red line), and long-term linear trend (black line) with confidence limits 95% (dot line) of the Hron River a) at Banská Bystrica and b) at
Comparison of the monthly increase in water temperature for scenarios (SCEN+1) and (SCEN+3) in the Hron River at Banská Bystrica and at Brehy is illustrated in Fig. 8.
According to the SARIMA model simulation results, the annual average increase in water temperature is smaller than the increase in air temperature. Results showed that a 1°C increase in air temperature caused the water temperature to rise by 0.35°C at Banská Bystrica and 0.57°C at Brehy, while a 3°C increase resulted in a rise of 1.05°C at Banská Bystrica and 1.75°C at Brehy. The differences in water temperature between selected stations is very pronounced, the difference in maximum water temperature reached in average value of 5°C during the period of 1962-2020. It may be caused by elevation and geographical location of the stations. It is interesting to note that the increase in temperature in individual months varies. The highest increase is observed in October, while for the spring months, it occurs in April (Fig. 8).   Hron-Brehy, SCEN+1