## 2 Materials and Methods
### Study Area
An automatic way of designing the network was applied, testing 100 different network architectures, and eventually keeping the 5 best ones. Finally, out of the five best networks, one referential network was selected based on statistical parameters describing errors obtained at the stage of model testing. The multilayer perceptrone network models were developed in the programme Statistica version 13.1 [29]. An analogical procedure was adopted for the reconstruction of water temperature in rivers by means of the random forest regression method. In this case, a single random forest regression model was built, using a full set of predictors, including water temperature from one hydrological station on a lake and air temperature from the three nearest meteorological stations. Moreover, the month index (M) was used as the auxiliary variable to maximize prediction performance. The calculations related to the random forest regression were performed using the ranger [30,31] package within statistical software R 4.1.2 [32]. The multiple linear regression, multilayer perceptrone network and random  
Figure 2: Diagram of data reconstruction and uncertainty of climate change estimation. forest regression models were tested on 30% of the data not used at the stage of model development. The statistics described in Section 2.3 were calculated for all models. This analysis was performed to show whether the obtained values of goodness-of-fit measures are significantly different from those obtained at the model development stage. Finally, as a result of the adopted procedure, 15 multiple linear regression and multilayer perceptrone network models and one random forest regression model were obtained. The following method of coding the models was adopted: multiple linear regression/A/8 dop, wherein the first part of the name signifies the type of model (multiple linear regression) the second part signifies the name of the hydrological station on a river (River-Station--code--Table 1), and the third part shows the range of used independent data (lake and meteorological station code--Table 1). In the presented example, multiple linear regression/A/8 dop means a multiple regression model used for data reconstruction on the Bobr River (No. A), developed based on independent data obtained from one hydrological station on Lake Slawskie (No. 8) and three meteorological stations Gorzow Wielkopolski (No. d), Wroclaw (No. o), and Zielona Gora (No. p). Each of the developed and tested models was used for the reconstruction of water temperature in rivers in the period from 2015 to 2020. Procedure for Testing and Validation of Multiple Linear Regression, Multilayer Perceptrone Network and Random Forest Regression Models  
The verification of the multiple linear regression, multilayer perceptrone network, and random forest regression models employed monthly data from the period from 2015 to 2020. Model validation involved the calculation of the values of the standard error (SE), maximum error (ME), root mean square error (RMSE), coefficient of determination (R\({}^{2}\)), Nash-Sutcliffe model efficiency coefficient (NSE) [33], and mean absolute percentage error (MAPE) [34]. The mathematical expressions of these statistics can be written as follows.