# Spatio-Temporal Variability of Water Temperature of Arctic Rivers in Russia over the Past 60 Years
## 2 Materials and Methods  
### Data Used  
We used data on monthly average river water temperature from 278 hydrological stations of the Roshydromet network located north of 60\({}^{\circ}\) N. The analysis was carried out for the observation period from 1961 to 2021 for the months from May to October (the period from the river break-up to the beginning of the freezing period) (Figure 1). To date, this dataset for the Arctic region is the most comprehensive one we are aware of. The most well-known set of Arctic water temperature data [35], includes information from 20 hydrological stations in 17 river basins over the period 1930-2003. We used data after 1960, as a massive assessment of the representativeness of the measurement sites took place in the 1950s, after which a significant number of measurement sites were relocated to rivers. Measurements at hydrometric stations are taken twice a day at 8:00 AM and 8:00 PM. These measurements are mainly taken offshore using a specialized mercury thermometer, which has an accuracy of 0.1 degree Celsius. The measuring instruments remained the same throughout the period under review. The measurement locations remained unchanged. Thus, the errors of measurement instruments and those associated with them can be considered constant throughout the area under consideration, regardless of varying geographical conditions. Data on the average daily water temperature are averaged over at least 8 days and are published in the form of 10-day averages in the publications of the _Hydrological Yearbooks_. Measurements begin from the time of the appearance of open water until the freezing of the river, but in some cases they are postponed or completed earlier due to the risk of ice drift, most often during spring and autumn. This study uses data on average monthly water temperatures in rivers from May to October, which is the ice-free period. Measurements at gauging stations characterize the near-bank water temperature. According to studies conducted in the 1950s, it is assumed to be a characteristic of the entire river, at least for small and medium-sized rivers. For large rivers, the difference between the water temperature measured near the bank and elsewhere on the river surface can be 1-3 Kelvin (K). In small and medium rivers, higher surface water temperatures may develop in summer relative to deeper parts of the stream [10; 49], but significant surface layer heating is only noted for relatively short periods and is likely smoothed out on a monthly scale. For all gauging stations operated from 1961 to 1990 and 1991 to 2021, there are at least 15 years of observations for each month in these periods. This temporal resolution was chosen as several studies suggest that air temperature is the leading factor determining water temperature in rivers of temperate climate zones [48]. Due to the fact that water temperatures in the editions of _Hydrological Yearbooks_ are given as 10-day averages, monthly mean water temperatures in May, June, September, and October were calculated by taking into account zero values in one or two 10-day periods. The governing factors of water temperature in rivers were analyzed using air temperature and adjusted precipitation data from 169 meteorological stations located no more than 50 km from the relevant hydrological stations and air temperature data from the ERA5 [50] reanalysis grid nodes closest to the hydrological stations. Data on the average water temperature in the catchment area of 46 hydrological stations were also used, based on data from all reanalysis points within this catchment. The impact of mean monthly streamflow on river water temperature was also assessed using data from 89 hydrological gauging stations. The heat flow was also analyzed as a factor of water temperature formation. Heat flow was calculated as  
\[W_{t}=c_{p}\rho T_{w}Q, \tag{1}\]  
Figure 1: Studying area and hydrological gauging stations analyzed.