# Projections of Climate Change Impact on Stream Temperature: A National-Scale Assessment for Poland
## 2 Materials and Methods
### SWAT Model  
The SWAT model, a widely employed semi-distributed hydrological model [28], was utilized in this study. It is a widely recognized hydrological tool and has been employed due to its computational efficiency and established performance in large-scale studies. The SWAT model employs a linear equation established by [PERSON] and [PERSON] [34] to compute the mean daily temperature for a uniformly mixed stream.  
\[T_{w}=5.0+0.75\cdot T_{air} \tag{1}\]  
where \(T_{w}\) represents the stream temperature for the day (\({}^{\circ}\)C) and \(T_{air}\) denotes the average air temperature for the day (\({}^{\circ}\)C). This equation operates under the assumption that the time delay between air and stream temperature is under 1 day.  
In this study, the SWAT2012 model setup (revision 664) was used, covering the entire territory of Poland [35; 36]. While a detailed processing and preparation of input datasets are available in [PERSON] and [PERSON]'s work [36], a concise summary of input data for the model setup is presented here. Watershed delineation utilized a 50 m resolution digital terrain model (DTM). Hydrologic response units (HRUs) were defined using an agricultural soil map (1:100,000 scale) and the refined Corine Land Cover 2018 (CLC 2018), in which an actual crop distribution acquired from the agricultural census (2010, Statistics Poland) for 2477 communes in Poland within arable lands was included. The methodology was for the distribution-preserving random scatter of eight crops (spring barley, winter wheat, corn for grain and silage, potato, sugar beet, spring canola, and vegetables) within the arable [35; 36] class of the land cover map [37]. The automatic delineation resulted in 4381 sub-basins (enclosing river reaches) covering the entire area, with an average area of 79.8 km\({}^{2}\). By overlaying soil, land cover, and slope maps, 47,725 HRUs were defined, with an average area of 7.33 km\({}^{2}\).  
Daily climate data (precipitation, temperatures, relative humidity, wind speed, and solar radiation) were obtained from a 2 km gridded daily climate dataset (G2 DC-PL+) [38] and \(\sim\)9 km resolution ERA5-Land [39]. In this study, the emphasis lies on temperature variables due to their paramount importance in the context of the research objectives. Specifically, air temperature variables in [PERSON] et al.'s work [38] were interpolated using the kriging method, capitalizing on data obtained from a robust network of 200 gauging stations with verified observations. The interpolation process underwent rigorous validation through a leave-one-out cross-validation approach conducted on a daily time step across all stations. To gauge the accuracy of the interpolated values, the root mean squared error (RMSE), normalized to the standard deviation of the observed data, was employed. The resulting normalized RMSE values were determined to be 0.52 for the minimum temperature and 0.40 for the maximum temperature. These metrics provide a quantitative measure of the interpolation errors, offering insights into the reliability and precision of the kriging method specifically in capturing daily variations in temperature across the study area.  
Figure 1: Study location with SWAT sub-basins (**A**), stream temperature gauging stations (**B**), and mean seasonal air temperatures in summer (**C**) and winter (**D**).