## 2 Materials and Methods
### Study Area
\begin{table}
\begin{tabular}{c c c c} \hline
**River-Station** **(Code)** & **River Monitoring** **Period** & **Lake (Code)** & **Meteorological Station (Code)** \\ \hline Böbr–Zagán (A) & 1987–2014 & Slawskie (57.4 km) (8) & Zielona Gó (37.6 km) (p) \\  & & & Wroclaw (124.3 km) (o) \\  & & & Gorzów Wielkopolski (125.0 km) (d) \\ \hline Drawa–Drawiny (B) & 1987–2014 & Lubie (63.8 km) (2) & Gorzów Wielkopolski (49.9 km) (d) \\  & & & Pika (58.4 km) (k) \\  & & & Poznan (78.0 km) (l) \\ \hline Drweca–Brodrica (C) & 1987–2020 & Bachotek (7.2 km) (0) & Torun (58.8 km) (n) \\  & & & Mława (66.3 km) (i) \\  & & & Olsztyn (88.5 km) (j) \\ \hline Elk–Przechody (D) & 1987–2014 & Selmet Wielki (30.7 km) (6) & Bialystok (62.9 km) (a) \\  & & & Suwalki (68.4 km) (m) \\  & & & Mikolajki (70.9 km) (h) \\ \hline Guber–Prosna (E) & 1987–2016 & Mamry (37.1 km) (4) & Ketrzyn (26.0 km) (f) \\  & & & Mikolajki (59.4 km) (h) \\  & & & Olsztyn (67.7 km) (j) \\ \hline Gwda–Pila (F) & 1987–2014 & Sepolenskie (62.4 km) (7) & Pika (2.4 km) (k) \\  & & & Poznan (82.0 km) (l) \\  & & & Chojnice (82.0 km) (b) \\ \hline Leba–Lebork 2 (G) & 1987–2020 & Lebsko (25.8 km) (3) & Leba (27.3 km) (g) \\  & & & Hel (69.1 km) (e) \\  & & & Chojnice (93.0 km) (b) \\ \hline Lyna–Sepopol (H) & 1987–2020 & Dadaj (46.8 km) (1) & Ketrzyn (32.3 km) (f) \\  & & & Mikolajki (65.4 km) (h) \\  & & & Olsztyn (67.3 km) (j) \\ \hline Pisa–Ptaki (I) & 1987–2020 & Ros (28.7 km) (5) & Mikolajki (46.1 km) (h) \\  & & & Ketrzyn (80.1 km) (f) \\  & & & Bialystok (96.8 km) (a) \\ \hline Wda–Czarna Woda (J) & 1987–2020 & Wdzydze (17.4 km) (9) & Chojnice (39.5 km) (b) \\  & & & Elblag (94.7 km) (c) \\  & & & Torun (94.9 km) (n) \\ \hline \end{tabular}
\end{table} 
Table 1: River water temperature data—Institute of Meteorology and Water Management—National Research Institute. The locations of the stations are shown in Figure 1.  
material, used for the final verification of the aforementioned research questions (Figure 2). The development of multiple regression models involved the search for an optimal set of independent data. The analysis considered all possible combinations of independent variables (water temperature in the lake and air temperature from three meteorological stations). A total of 15 multiple linear regression models was obtained for each river. The multiple linear regression models were developed based on data from the period 1987-2014. The development of multiple linear regression models employed 70% of the first data series (training sample), and the remaining 30% of data (test sample) were used for testing the models. The multiple linear regression models were developed in the programme Statistica version 13.1 [29]. An analogical procedure was applied for the multilayer perceptrone network. Multilayer perceptrone network learning was based on data from the period 1987-2014. Data from the period were divided into two analogical parts; 70% of the data were used at the stage of network learning, and 30% of data at the stage of testing and verification. Finding an optimal multilayer perceptrone network diagram involved using the automatic network search diagram. Designing the network architecture included determining the number of input and output variables (i.e., neurons in input and output layers), and determining the number of hidden layers and neurons in each hidden layer. A three-layer multilayer perceptrone network model was tested, with a hidden second layer with 3 to 20 hidden neurons. The input (independent) variables were mean monthly air temperatures (from a maximum of three meteorological stations) and mean monthly lake water temperatures (from the nearest lake). Moreover, the development of a multilayer perceptrone network employed additional qualitative data, i.e., month index (M), and the output variable was mean monthly river water temperature. The functions of activation while learning for hidden neurons and output neurons were linear, logistic, tanh, exponential, and sinus.