Exploring the combined effects of water temperature and flow on river water quality: problems with highly variable data sets and possible solutions

<h2>Abstract</h2> Correlations between physico-chemical characteristics may be key to understanding and predicting water quality changes in large rivers as a result of climate change, however, the published results regarding these correlations are often contradictory. In this study, the dependence of water quality assessment results on the data source was demonstrated and a solution was proposed to eliminate the effects of sampling time and location, as well as random, point-like changes in water quality. The study revealed the importance of cross-sectional sampling location and the combined, long term impact of water temperature and flow on a large number of water quality characteristics based on data that vary strongly in time and space. Thirty-six water quality variables measured every two weeks for one year from different longitudinal and lateral parts of the Danube were evaluated using univariate and multivariate methods. The results showed that in the case of 130 of the 630 calculated pairwise correlations, the sign and, in many more cases, the strength of the correlations changed depending on the data sets used. Correlations based on the entire data set were mostly moderate or low, compared to those calculated from the partial data sets. Most of the strongest correlations came from data collected at the middle of the river, and the lowest ones from the sampling sites near the riverbank. Comparison of the results of multivariate assessment of annual water quality changes at each sampling location showed more similarities within the same river site types than between them. Water temperature and discharge affected the water quality at all sampling points, however, the strength of the effect and the correlations between the physico-chemical variables and the two background factors depended on the sampling location. The greatest variability of water quality was observed near the riverbank. Random, point-like changes causing high variability in water chemistry could be balanced by consensus analysis, and trend-like dependence of water quality characteristics on both water temperature and flow (or only one or neither) could be revealed. According to the results, concentrations of PO₄^3--P, NO₃⁻ and DO (with values between 6.6 and 79.2 μg/L, 3.5–11.2 mg/L and 7.4–12.5 mg/L, respectively) mostly followed the change in water temperature (the first one positively, while the two others negatively), and the turbidity (4.1–180 ntu), TOC (1.1–6.2 mg/L), Cu (0.5–7.2 μg/L) and B (10.3–58.3 μg/L) concentrations were primarily affected by the water flow (positively for the first three, while negatively for the last). The amount of SO₄³⁻ (11.7–38.4 mg/L), Na⁺ (3.4–25.0 mg/L), Ca²⁺ (28.8–89.1 mg/L) and Cl⁻ (10.2–39.8 mg/L), as well as As, V, Cr and electric conductivity (with values between 0.6 and 3.3, 0.3–1.6, 0.1–2.5 μg/L and 250–600 μS, respectively) depended on both water temperature and water flow, while some of the physico-chemical parameters showed the lack of significant influence of both background factors. The paper presents the possible reasons behind the revealed correlations and makes a thorough comparison with the literature findings. These results help to predict the long-term effects of climate change on many water quality characteristics of rivers.