Investigation of changes and modeling the oxygen regime of the of surface water along the Váh River

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. Environmental targets are set to ensure the achievement of good surface water and groundwater status in the EU and to prevent water deterioration. The achievement of environmental goals is verified through established assessment systems, which also assess the quality of surface waters. Physico-chemical indicators, including water temperature and oxygen regime, are relevant to the ecological state of a river. First the study presents the statistical analysis of water temperature and indicators of water oxygen regime measured at four sampling points on the Váh: Komárno, nad Sereďou, Hlohovec and nad Liptovským Hrádkom. Second, the monthly concentration of dissolved oxygen of the Váh River at four sampling sites was modeled using water temperature. Autoregressive SARIMA models were created to modeling dissolved oxygen concentration based on monthly corresponding water temperature. The SARIMA model with various mathematical expressions of the regressor was tested to be the best fit model with a high correlation coefficient. Results showed that for all selected models with selected regressors the p -value values of estimated parameters were α < 0.05, and the differences in their estimated parameters as well as the simulations were not statistically significant. The study concludes that the SARIMA model can effectively simulate changes in dissolved oxygen based on changes in water temperature.


Introduction
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 that exerts an important influence on the ecology of freshwaters.The low flows in conjunction with high water temperatures can directly threaten life in rivers.It is a key abiotic variable, which 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.Anthropogenic demands provoke land use structure changes, intensification of its exploitation, deforestation, fossil fuel combustion and related carbon dioxide production.Those phenomena also changing water and energy fluxes of biosphere, and conditions for life (Novák, 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.Some studies have already pointed out that the increase in air temperature led to the warming of the water and stronger thermal stratification as important source of the vertical distribution of water quality indicators (Bajtek et al., 2022;Vyshnevskyi and Shevchuk, 2022;O'Reilly et al., 2015;Varga et al., (2023) or Woolway and Merchant, (2019)).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.Martincová et al. (2011) describe the methodology for classification scheme determination of water temperature, to evaluate status of the surface water bodies in selected Slovakian highmountain, 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 (period 1964-2003) of the daily water temperature data, from six stations that represent several altitude positions.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 windthrow in the Bela River watershed, the variability of daily water temperature increasedmaxima are higher, whereas minima are lower on the daily time scale.Within the context of mentioned changes in water temperature, there are also changes in the oxygen regime of t the streams.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.The oxygen is one of indicators of water quality that plays a crucial role in affecting physical, chemical, and biological processes that are often regulated by thermal, light, and flow conditions that define river climates (Blaszczak et al., 2019;Arroita et al., 2019;Bernhardt et al., 2018).These processes include air-water gas exchange, photosynthesis (primary production), which produces DO (dissolved oxygen), and aquatic respiration, which consumes DO.The gas exchange flux depends on the solubility of the gas of interest, the concentrations of the gas in the air and water, and the gas exchange velocity (Gualtieri and Pulci Doria, 2008;Gualtieri and Gualtieri, 2004;Wang et al., 2021;Ulseth et al., 2019;Helton et al., 2012).The concentration of DO in water affected by water temperature has a greater solubility in colder water than in warmer water.As the result of this, the concentration values of DO in the rivers during the colder seasons are higher than during the warmer seasons.However, it's essential to note that this relationship can be influenced by various factors such as flow rate, biological activity, pollutant levels, and local environmental conditions.Therefore, while it's often the case that dissolved oxygen concentrations are higher in colder seasons, it may not be universally true for all rivers or all circumstances.The concentration of the DO can be further reduced by adding oxygen-demanding organics to the river systems (e.g.sewage, agricultural waste, lawn clippings, etc.).The impact of climate change on water temperature and oxygen regime has been addressed in papers by Harvey et al., (2011);Danladi et al., (2017); Rajesh and Rehana (2022) or Demars and Manson, (2013).The effects of water pollution are complex and vary depending on the nature and concentration of contaminants (Artemiadou and Lazaridou, 2005).Understanding and analysing their interconnectedness and dependencies deserves equal attention.As was mentioned above, the climate change and anthropogenic activities affect the water quantity and quality with negative impact on hydrological regime of streams.Therefore, it is necessary to know and analyse their changes and the mutual relationship of quantitative characteristics and indicators of water quality.Such knowledge enables prevention and response to a crisis phenomenon and is one of the prerequisites for a quick and correct solution in elimination of its consequences.While the potential impacts of climate change on water availability have been widely studied in recent decades, their impact on water quality is still less researched.The objective of this study was to analyse the changes in long-term trends of the oxygen regime of surface water in the Váh River at four sampling sites: Komárno, nad Sereďou, Hlohovec and nad Liptovským Hrádkom to quantify the possible threat to his balanced regime for during the long period.The input data were monthly samples of dissolved oxygen, water temperature and the corresponding daily flows on the sampling days from selected gauging stations: Šaľa, Hlohovec, Liptovský Hrádok.In addition, water temperatures at the time of sampling for water quality were analysed.Furthermore the study is focused on the cross-correlation analysis of selected components of the hydrosphere and to model them effectively.An autoregressive model with a selected regressor was tested in the presented work.For modelling dissolved oxygen depending on water temperature, the model can capture and account for patterns and trends within time series data, including seasonality and periodicity.The ability to model the components of the hydrosphere is an essential part of water resource management.Due to the strong correlation between dissolved oxygen and water temperature, the final objective of the study was to predict the effect of a hypothetical increase in average monthly water temperature (Tw) on the average monthly concentration of dissolved oxygen (DO) in the Váh River.Our study is primarily focused on establishing a regression relationship between water temperature (Tw) and dissolved oxygen (DO) concentration, without incorporating other factors such as pollutant loading and river hydrodynamics.We recognize the significance of these additional factors in influencing DO concentration, but our current scope of the data limits us, at the moment, to examining the direct relationship between Tw and DO concentration.By focusing on the Tw-DO relationship, we aim to provide valuable insights into the dynamics of oxygen concentration in the Váh River and its implications for aquatic ecosystem health.

Study area and data
The Váh River is the biggest left-side Danube River tributary and the longest river in Slovakia.It rises in the Tatra Mountains by the confluence of the White Váh and Black Váh (Fig. 1).The Váh River flows over northern and western Slovakia and finally feeds into the Danube near Komárno.The Váh River basin accounts for about 37% of water bearing of Slovakia.The Váh has a large number of tributaries, many of which are mountain streams from the Tatra Mountains and Carpathians (e.g.Belá, Orava, Kysuca, Rajčianka, Turiec, Malý Dunaj, atc.…).Fig. 1 illustrates scheme of the main river network of Slovakia with Váh River location and scheme of Váh River basin with four selected sampling sites of water quality (Komárno, nad Sereďou, Hlohovec and nad Liptovským Hrádkom) and with three water gauging stations Šaľa, Hlohovec, Liptovský Hrádok.The basic location characteristics of all selected sites are presented in Table 1.

Development of selected indicators of the oxygen regime at Váh in selected sampling sites
The input data for analysis were monthly samples of selected water quality indicators (dissolved oxygen, water temperature, biochemical and chemical oxygen demand) and the corresponding daily flows on the sampling days.In addition, analysed water temperatures are water temperatures at the time of sampling for water quality.Daily flow values on the day of water quality sampling on the selected water gauging stations are plotted in Fig. 2. Values of basic statistical characteristics of long-term annual concentration of DO, BOD, COD and Tw at selected sites along the Váh River during the whole periods of sampling are listed in Table 2.The course of monthly values of selected oxygen concertation of the Váh at selected sampling sites are plotted in Fig. 3.At chemically sampling sites, water    1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008  2010 2012 2014 2016 2018 2020   [m 3 .s     1 quality data typically have low sampling frequency (monthly to quarterly) and some inconsistent measurement duration.To obtain basic information about water quality, monthly sampling intervals can be considered sufficient, but the case of very significant transport of substances by a flood wave may not be captured.

Trend analysis of the selected monthly and annual oxygen indicators of the surface water
The Mann-Kendall nonparametric test (M-K test) was used for determining the significant trends detection of monthly and annual confrontations of selected indicators of oxygen river regime.The nonparametric tests are more suitable for the detection of trends in hydrological time series, which are usually irregular, with many extremes (Hamed, 2008;Gilbert, 1987).MAKESENS 2-tailed test is used for four different α significance levels.The significance level of the test αis a chosen number from the interval from 0 to 1, or 100% (the smaller the better, but α=0.05 or 5% is most often used).A significance level of 0.05 means that there is a 5% probability that the values of xi are from a random distribution, and with that probability we make an error in rejecting H0 (the null hypothesis) of no trend.A significance level of 0.001 means that the existence of a monotonic trend is very likely.
We evaluated the significance of the trend in our study at selected significant levels or levels of trend significance.The most important trend is assigned three stars (***), with the gradual decrease in importance, the number of stars also decreases.Statistically, we evaluate the significance of a trend using the Z value.A positive Z value indicates an upward (growing) trend, while a negative value indicates a decreasing trend.If the absolute value of Z is less than the significance level, there is no trend.

Cross-correlation analysis of selected components of the hydrosphere
The sign of the correlation coefficient depends on the covariance, according to which we interpret the value of the coefficient: The most commonly developed models for predicting river oxygen concentrations may be computationally demanding, e.g.dynamic mass balance models (Gelda et al., 2001), models of artificial neural networks (Rounds, 2002), or extended harmonic analysis, so-called algorithm models (Abdul-Aziz et al., 2007).The computational demand of these models arises from the need to capture the complex interactions and dynamics of river ecosystems accurately.While advancements in computing power and algorithms have made these models more feasible, they still require significant resources, particularly for calibration, validation, and scenario analysis.where the dependent variable is the time series data and the independent variables are the series lags and lagged errors.The model is usually estimated using maximum likelihood estimation, and the accuracy of the model can be evaluated using various statistical criteria.To identify this model, it is necessary to analyse the individual components of the time series in the following order: • trend identification; • choosing the type of model and determining the order of the model; • estimation of model parameters; • model validation.
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 ; ptrend autoregressive order; dtrend difference order; qtrend moving average order; Pseasonal autoregressive order; Dseasonal difference order; Qseasonal moving average order; Lnumber 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;  1backwards difference operator; regular AR (auto-regressive) operator of the order p; regular SMA (moving average) operator of the order q;  D L-seasonal backwards difference operator; regular SAR (seasonal auto-regressive) operator of the order P; regular SMA (seasonal moving average) operator of the order Q.

Trend analysis of selected monthly and annual indicators of the oxygen flow regime
The first part of the paper is aimed to evaluate water temperature development and oxygen regime of the Váh River at selected sampling sites during the period 1999-2021 (resp.1999-2012 for Hlohovec).Long-term monthly concentration of selected indicators and as well as water temperature are illustrated in Fig. 4. The maximal long-term monthly concentrations of dissolved oxygen were occurred in winter months.The minimum long-term monthly concentration of dissolved oxygen was observed in August.The analysed corresponding water temperatures show long-term maximum value in summer months (July and August).In terms of long-term monthly concentration of chemical oxygen demand, the maximum values occur in July.Trend analysis of the DO concentrations in August for whole periods of sampling water quality in selected sampling sites along the Váh River is illustrated in Fig. 5 and results of M-K trend test are listed in Table 3.The development of July concentrations of DO indicates a significant increasing long-term trend at nad Sereďou sampling site (α=0.05)and at Hlohovec sampling site α=0.001.The development of July and August corresponding water temperatures indicate significant increasing long-term trends at Komárno sampling site (July, α=0.01), nad Sereďou sampling site (July, α=0.01), and Hlohovec sampling site (August, α=0.1).

Correlation analysis of the selected monthly concentrations of oxygen river regime
At sampling sites, water quality data typically had a low sampling frequency (monthly to quarterly).Due to the large time gaps in the data and the inconsistent duration of the measurements for a more detailed correlation/dependency analysis, as well as for the later modelling of the monthly concentrations of dissolved oxygen with the selected regressor by the selected model, we tried to choose a period unencumbered by significant Fig. 4.
Monthly regime of corresponding daily discharges, monthly regime concentrations of DO, BOD, COD and water temperatures Tw, for the Váh River at selected gauging stations and sampling sites during the period 1999-2021 and 1999-2012 for Hlohovec.

Fig. 5.
Long-term trends of DO concentrations and water temperatures Tw for the Váh River at selected sampling sites during the whole periods listed in Table 1.data inconsistency.Although many data on water quality have been available since seventies of the 20th century.Correlation analysis of monthly values of qualitative indicators (Qd, Tw, DO, BOD and COD) in selected sampling sites on the Váh River, we used the data from period of 1999-2021 and 1999-2012 for Hlohovec, respectively.The scatter plots of the dependencies of individual indicators shoved, that more of them does not have a linear course (Fig. 6 a-d).
From the graphical comparison of all correlation dependencies, the highest linear correlation emerged between qualitative indicators: water temperature Tw and dissolved oxygen DO where R was ranged from value -0.59 to value -0.88.The course of the dependences between the water temperature Tw and dissolved oxygen DO for selected sampling sites of the Váh River for period of 1999-2021, resp. 1999-2012 for Hlohovec is plotted also in Fig. 6.The correlation coefficients between the selected components of the hydrosphere reached values in the interval -0.88 to 0.44 (Table 4).
The p-values below 0.05 indicate statistically significant non-zero correlations at the α=0.05 confidence level.The pairs of variables have p-values below 0.05 are listed also in Table 4.

Modelling of the monthly concentration of dissolved oxygen
The next part of the study is focused on modelling the dissolved oxygen DO concentration depending on water temperature Tw in the Váh River at four selected sampling sites.An autoregressive model SARIMA with a selected regressors was tested in the presented work.For modelling dissolved oxygen depending on water temperature, the model is designed to capture and account for patterns and trends within time series data, including seasonality and periodicity.The ability to model the components of the hydrosphere is an essential part of water resource management.Due to the strong correlation between dissolved oxygen and water temperature, the final objective of the study was to model the effect of a hypothetical increase in average monthly water temperature (Tw) on the average monthly concentration of dissolved oxygen (DO) in the Váh River.Monthly dissolved oxygen concentrations and monthly corresponding water temperatures were used to calibrate an autoregression model for period 1999-2021, resp. 1999-2012 for Hlohovec.Monthly values of corresponding water temperature Tw as linear, exponential and polynomial regressors were tested.The best models of SARIMA with the lowest value of the AIC criterion, the model estimation errors and model parameters for selected sampling sites of the Váh River are presented in Table 5.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.Comparison of modelled dissolved oxygen concentrations using the SARIMA models, at recorded corresponding water temperatures and relationship between the measured monthly DO concentration and monthly DO concentration modelled using selected SARIMA model are illustrated in Fig. 7.The monthly correlation scores R estimated between observed and modelled DO using preferred SARIMA models for selected sampling sites ranged between 0.71 and 0.92 and RMSE scores were ≤ 1.46 mg l -1 DO during the testing periods.Comparison of modelled dissolved oxygen concentrations using selected SARIMA models with corresponding recorded water temperatures as regressors) in the Váh River at the selected sampling sites a) Komárno, b) nad Sereďou, c) Hlohovec and d) nad Liptovským Hrádkom (period 1999-2021, resp. 1999-2012 for Hlohovec).period 1999-2021, resp. 1999-2012 for Hlohovec sampling site.The results of the correlation analysis showed the closest relationship between monthly concentrations of dissolved oxygen DO and corresponding water temperature Tw.The relationship between dissolved oxygen and water temperature is strongly negative (Harvey et al., 2011).Johnson et al. (2016), state that the exponential model may be more suitable for modelling low dissolved oxygen concentrations at higher water temperatures such as polynomial relationship.The results of our analysis on the Váh River in selected sampling sites did not show a significant difference in the correlation coefficient of the linear, polynomial and exponential dependence of the concentrations of soluble oxygen DO and water temperature Tw below to 30 o C. Subsequently, we used an autoregressive model SARIMA with mentioned different mathematical expressions of the water temperature Tw as a regressor on data for the period 1999-2021 (period 1999-2012

Fig. 1 .
Fig. 1.Scheme of the main river network of Slovakia with Váh River location and scheme of Váh River basin.

Table 1 . Basic location characteristics at the selected gauging stations in the Váh River basin
*Hlohovec1 is corresponding daily flows from gauging station Hlohovec for sampling quality site nad Sereďou

Table 2 . Basic statistical characteristics of long-term annual concentration of dissolved oxygen DO, biochemical oxygen demand BOD, chemical oxygen demand COD and corresponding water temperature Tw at selected sites along the Váh River during the whole periods of sampling (listed in Table 1) Váh: Komárno Váh: nad Sereďou DO
AR) and moving average (MA) components, as well as differencing and seasonal components.The seasonal component is particularly important in the SARIMA model because it allows modelling data with seasonal fluctuations or cycles.The model involves fitting a regression equation to the data, The simplest model is the regression model, which indicates a linear relationship between water temperature

Table 5 . The model estimation errors of selected models and model parameters of the best SARIMA models used to model the dissolved oxygen DO concentration in at selected sampling sites in the Váh River (period 1999-2021, resp. 1999-2012 for Hlohovec)
Hlohovec and Liptovský Hrádok.The maximum long-term monthly corresponding daily discharges flows occur in spring months.The maximal long-term monthly concentrations of dissolved oxygen were occurred in winter months.The minimum long-term monthly concentration of dissolved oxygen was found in August.The analysed corresponding water temperatures show long-term maximum value in summer months (July and August).In terms of long-term monthly concentration of chemical oxygen demand, the maximum values occur in July.Long-term trend analysis of the monthly DO concentrations indicates a significant increasing long-term trend at sampling sites nad Sereďou (α=0.05) and at Hlohovec α=0.001 in month of July.The development of July and August corresponding water temperatures indicate significant increasing longterm trends at Komárno sampling site (July, α=0.01), nad Sereďou sampling site (July, α=0.01), and Hlohovec sampling site (August, α=0.1)Secondly, we determined the correlation dependence of selected components of the oxygen regime indicators, water temperature and corresponding daily flows for for Hlohovec) to model the monthly concentrations of dissolved oxygen depending on the corresponding water temperature.The result of the suitable model SARIMA types, model estimation errors and model parameters are presented in tables.Comparison of modelled dissolved oxygen concentrations using selected SARIMA models with corresponding recorded water temperatures as regressors in the Váh River at the selected sampling sites a) Komárno, b) nad Sereďou, c) Hlohovec and d) nad Liptovským Hrádkom are illustrated in figures.The ability to model the components of the hydrosphere is an essential part of water resource management.Obtaining a relatively long series of data is also necessary to accurate 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.Hydrologically gauged rivers with flow data are often chemically ungauged, without DO or any water quality measurements.Although water quality data have increased in recent decades, the identification of major factors has historically been limited by scarce, inconsistent, and disjointed data.A one of the fundamental questions still remain is, how long and detailed data provides a good ability to characterize the long-term behaviour of surface water, investigate the occurrence of recent trends in the surface or chemical regime, and predict likely effect on streams and rivers as a consequence of global warming.