## 3 Results
It should be emphasised that the values of the analysed statistics describing prediction quality adopt approximate values for model groups multilayer perceptrone network/c (prediction based on lake water temperature and air temperature from one meteorological station), multilayer perceptrone network/e (prediction based on lake water temperature and air temperature from two meteorological stations), and multilayer perceptrone network/g (prediction based on lake water temperature and air temperature from three meteorological stations), significantly differing at a level of 0.05 (according to the U Mann-Whitney test). It should be emphasised, however, that the lowest values of standard error, maximum error, root mean square error, Nash-Sutcliffe model efficiency coefficient, and mean absolute percentage error statistics, and the highest coefficient of determination and Nash-Sutcliffe model efficiency coefficient values, have been shown by the multilayer perceptrone network/g model. The location of the regression line P = aM + b in reference to the regression line in the form of P = M (full compatibility of results of P with M) allows for the designation of the Mo and Po values, and drawing detailed conclusions regarding the results of the prediction (reconstruction) (Table 3). The results show that in a broader range of variability of water temperatures, multilayer perceptrone network models underestimate values. This is particularly evident in the case of the Leba and Lyna Rivers. Generally, in almost any model, underestimations primarily concern predictions of higher temperatures. The only exception pertains to the Pisa River, where the highest values are slightly overestimated. The last stage involved the validation of all multilayer perceptrone network models based on the slope values of trendlines (Sen slope, Linear slope) obtained for the original measurement data from the period 1987-2020, and data in which the period 2015-2020 was supplemented based on results from the models (Figure 5). A tendency has been generally observed in which the slope values of linear regression lines and Sen slope values are lower for the data series supplemented with results of the multilayer perceptrone network/g model. For the Leba River, such a situation occurs in each month. In the remaining cases, a similar trend has been generally observed, although in individual months the opposite situation regarding the slope value of trendlines can be seen--they are higher for data supplemented with the multilayer perceptrone network/g model. In November and December, the Sen slope and linear slope values are higher for data reconstructed by means of the multilayer perceptrone network/g model for the Drweca, Lyna, and Wda Rivers. In June, in almost every case, the slope values of trendlines are higher in the original measurement data. The results show that even the best model can generate uncertainties related to data reconstruction. Therefore, the measurement of river water temperatures should be restarted as soon as possible. Trendline slope values in reference to the values of mean annual water temperatures in rivers are presented in Figure 6. The reconstructed curves have a course compatible with that towards curves based on in situ measurements. It is worth emphasising that the deviations do not exceed 0.5 \({}^{\circ}\)C (at a minimum measurement accuracy of 0.1 \({}^{\circ}\)C). Eventually, based on knowledge pertaining to the selection of the statistical model and the selection of a data set for the supplementation of missing water temperatures, reconstruction was performed. The results for all the analysed rivers are presented in Table 4.  
The obtained results show that the greatest increase in water temperatures occurred in June, August, September, November, and December. The changes can be observed in 8 to 10 rivers, and are statistically significant at a level of 0.05. The smallest changes occurred in January, February, and March (not statistically significant).