# Spatio-Temporal Variability of Water Temperature of Arctic Rivers in Russia over the Past 60 Years
## 3 Results
### The Potential Impact of Climatic Changes to River Water Temperatures  
Climate-related changes in air temperature are thought to be the main factor behind the changes in river water temperature described above. For most hydrological stations before and after the change point years, the probability distribution of the significance \(p\)-values for trends in air and water temperatures in the warmer months is relatively similar (Figure 10). Consequently, for most hydrological stations, the significance of both water and air temperature trends is similar. Figure 9: Hydrological gauges with significant trends in water temperature (due to Mann–Kendall test with \(\alpha=0.05\)) in the period 1991–2021 (yellow circles) and after change point year (due to Buishand test with \(\alpha=0.05\)) to 2021 (red rhombus). The majority of hydrological stations (>80%) show a high statistical significance in the regression coefficient between the average monthly water temperature at a hydrological station and the air temperature at the closest reanalysis node, ERA5, in the period from 1961 to 2021 (Figure 11). The largest number of hydrological stations with a significant regression coefficient for the values under consideration occur in July-September. The values of the regression coefficients for water and air temperatures in the Arctic zone of Russia, according to the Mann-Kendall test (\(\alpha\) = 0.05), are mostly within the same intervals for the period 1961-2021. There is also a weak linear relationship between these two variables in July and September (see Figure 12). In May and October, there is no clear linear relationship between water and air temperatures in the Russian Arctic, as during this time, ice events are observed on significant parts of rivers, especially in the Asian region of Russian Arctic. In July and August, despite high regression coefficients for water and air  
Figure 11: Histogram of \(p\)-value of regression coefficients of air–water temperature regressions for a warm period of 1961–2021. For better visualization, \(X\)-axis is in –lg(\(p\)-value). Figure 10: Cumulative distribution function of \(p\)-value of Mann–Kendall test (\(\alpha\) = 0.05) for periods before (first per.) and after (second per.) of change point year (due to Buishand test at \(\alpha\) = 0.05) in a time period of 1961–2021. For better visualization, \(X\)-axis is in –lg(\(p\)-value) and –lg(\(p\)-value) > 3 = 3.  
temperatures, there is a large number of outliers associated with a stronger or insufficient warming of rivers each year, depending on local conditions. At the same time, as mentioned previously, for most hydrological stations, there is a strong correlation between air and water temperatures in the 1961-2020 period. The spatial distribution of the degree of correlation between changes in water temperature and air temperature is illustrated in Figure 13. The primary mechanisms for mitigating the impact of changes in air temperature on water temperature are related to the elevation of the hydrological station (in the Baltic Sea system). Its greatest influence is seen in large rivers. On these rivers, there is a tendency for the relationship between water and air temperatures to decrease from west to east within the given territory. In May and especially in October, there is also a decrease in the correlation of discussing values in rivers located north of the Arctic Circle. However, this is primarily due to ice-related climate phenomena  
Figure 12: Regression coefficients of air–water temperature relationships for a warm period (May–October) in 1961–2021. on the rivers. In the Kola Peninsula and in Karelia, one of the limiting factors in this context is the natural regulation of rivers by lakes in some cases. The values of anomalies in water flow and temperature (1991-2020) were not closely related. In 8% of cases, the value of R\({}^{2}\) was greater than 0.5 for the warm season (based on data from 89 hydrometric stations).