# Spatio-Temporal Variability of Water Temperature of Arctic Rivers in Russia over the Past 60 Years
## 3 Results
### Factors Govering River Water Temperature
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Predictor Month** & **May** & **June** & **July** & **August** & **September** & **October** \\ \hline Precipitation & \(-\)0.56 & \(-\)0.64 & \(-\)0.67 & \(-\)0.65 & \(-\)0.5 & \(-\)0.3 \\ \hline Water flow & 0.53 & \(-\)0.4 & \(-\)0.58 & \(-\)0.38 & 0.43 & 0.67 \\ \hline \end{tabular}
\end{table} 
Table 1: The maximum modulo correlation coefficients between the average monthly water temperature in rivers, as measured at 286 hydrological stations; the sum of adjusted precipitation, as calculated from the ERA-5 data; the average monthly water temperature; and the average monthly water runoff by 89 other hydrological stations. Figure 2: Coefficients of water–air temperature correlations at 286 gauging stations of rivers in the Russian Arctic during May and July based data on in the nearest cells of the ERA5 reanalysis for the period 1961–2021. Thus, heat flux contributes to an increase in water temperature during the spring flood due to the transfer of heat from the parts of the catchments located to the south from gauging stations. At low water temperatures, even a small influx of heat gives an increase in water temperature. However, during a period with a relatively high water temperature and low water flow, an increase in heat flux does not increase the water temperature. Therefore, this factor is more likely to limit changes in water temperature than to form them. Other limiting factors include topographic parameters such as geographical location, height of the hydrological post, and catchment area. The relationship between water temperature in October and geographical longitude is fairly close on average (r = \(-\)0.75) across the territory under consideration. However, topographic factors may play a more significant role in determining water temperature in certain hydrographic areas and months of the year (see Table 2). From this table, it can be seen that geographical latitude is the most significant factor in the formation of average river water temperature across the regions under consideration. This factor is particularly important in May and June, when rivers have increased water content and are heating up after ice purification. The relationship between water temperature and hydrographic parameters is generally linear throughout the observed period, although in recent decades, it has been better described by a first-degree polynomial (Figure 3). It is important to note that, even with high correlation coefficients, regression dependences between water temperature and topographic factors at the scale of hydrographic regions have poor quality. At the subregional scale, there may not be enough observations to establish reliable dependences. It should be noted that, at the level of sub-regions, especially the mountainous areas of the northeast, there are separate high-altitude zones with different conditions for water temperature formation. This is reflected in the study by [46]. The height of the hydrological station and the catchment area in the Russian Arctic are significant factors that limit the maximum possible average monthly water temperature in rivers (see Figure 4). \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Region** & **Month** & **May** & **June** & **July** & **August** & **September** & **October** \\ \hline Northeast & & & & & & & \\ \hline Lena & N & N & & & & & \\ \hline Yenisei & N & N & & & F & \\ \hline North of the West Siberia & N & N & N & N & N & N, F \\ \hline North of the European part of Russia & N & N & & & & E \\ \hline Karelia & N & N, E, H & N, E, H & & & \\ \hline Kola Peninsula & & H & H & H & & \\ \hline \end{tabular}
\end{table} 
Table 2: Hydrographic parameters of catchments that have a close relationship (\(|r|>0.7\)) with the water temperature in certain regions in some months. N is the latitude, E is the longitude, H is the height of the hydrological station (m. Baltic), and F is the area of the catchment (km\({}^{2}\)).