# Spatio-Temporal Variability of Water Temperature of Arctic Rivers in Russia over the Past 60 Years
## 3 Results
### Change Point Years in Time Series of River Water Temperature  
Finding change point years could help to identify the time when the probability distribution of the stochastic process changed. Unlike statistical homogeneity tests, for example, Student's test, the search for a change point year does not involve the presence of two samples of a given length. On the contrary, these tests determine the point of necessary separation of the sample. Analyzing long-term monthly water temperature averages for each month from May to October (for months outside of this period, no meaningful analyses of water temperature are possible as rivers are frozen) over the entire 60-year monitoring period indicated the following change point years for the different study areas in the Russian Arctic region (Table 5). The spatial distribution of change point years within large watersheds and hydrographic regions is fairly uniform. The differences between the change point years at hydrological gauges and the average change point year for the hydrographic region in most cases are less than 10 years. The most common values for the change point year also differ from the average change point year for the hydrographic region by no more than 10 years in almost all months under consideration. It is important to note that in medium-sized rivers, where the hydrological regime reflects the zonal conditions for the formation of hydrological characteristics, there are no significant differences in the change point years at hydrological stations or the average change point years in hydrographic regions. These differences do not exceed four years from May to October in all hydrographic regions except Karelia. Thus, in the period from the late 1980s to the early 2000s, a violation of homogeneity of water temperature occurred in rivers in various natural zones of the Russian Arctic. The statistical significance of these changes has been confirmed by both parametric Student's \(t\)-tests and [PERSON]'s tests, and by using the non-parametric Mann-Whitney U test. These tests showed that when dividing the series relative to the change point year using the Buishand test, the homogeneity of series is violated at 66% of gauges according to the non \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Region** & **May** & **June** & **July** & **August** & **September** & **October** \\ \hline Northeast & 1.8 & 1 & 1.2 & 1.1 & 1.3 & 2.5 \\ \hline Lena & 1.7 & 1.9 & 0.9 & 0.9 & 0.8 & 2 \\ \hline Yenisei & 1.8 & 3.4 & 0.2 & 0.2 & 0.7 & 2.2 \\ \hline North of the West Siberia & 2.4 & 2.5 & 0.3 & 0.8 & 0.8 & 2.4 \\ \hline North of the European part of Russia & 2 & 0.4 & 1.1 & 1.1 & 1.1 & 1.4 \\ \hline Karelia & 1.4 & 0.5 & 1.6 & 1.3 & 1.4 & 0.8 \\ \hline Kola Peninsula & 1.7 & 1.1 & 1.6 & 1.2 & 1.3 & 1.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Changes in air temperature [K] (on nearest to hydrometric stations points of ERA5 reanalysis) in 2000–2022 in comparison with 1961–2000 during warmer months in hydrographic regions of the Russian Arctic. parametric Mann-Whitney criterion, which revealed the highest number of violations of homogeneity of series among the three tests used. A normal distribution of data regarding the monthly water temperature series was confirmed for a number of sites using the Pearson criterion. However, using the more stringent Kolmogorov-Smirnov criterion, no data series at any of the site was found to be normally distributed. Accordingly, the use of the non-parametric criterion (Mann-Whitney test) in these analyses is more justified. Thus, when analyzing the series of water temperatures in relation to the change point year, we identified a significant number of violations of homogeneity. These changes occurred over a relatively short period of time. An analysis of the homogeneity violations in the water temperature series in relation to 1991 (for the periods 1961-1991 and 1991-2021) revealed a significantly lower number of violations, as shown by the Mann-Whitney test (see Table 6).