## 3 Results and Discussion
### Uncertainty Analysis  
As part of the thermal analyses, uncertainty analyses of the results of the calculations of the concrete temperatures were also performed, where six normally distributed random variables were used to determine the dispersion of the results. Their expected values and standard deviations are given in Table 1. Thermal analysis was carried out for a typical one-month period in the summer (from 1 July 2014 at 12:00 to 1 August 2014 at 12:00), where appropriate temperatures, obtained when calculating the temperature fields of the dam during a one-year period, were considered as the initial temperatures in the analysis (Section 3.3). The concrete temperatures (at 12 selected points on and inside the dam; Figures 2 and 14, Table 5) were analyzed at the end of a period of one month. Sixty repetitions of the calculation (for 60 different combinations of values of six normally distributed random variables), which resulted in 12 different samples, were performed.  
Figure 15: The concrete temperatures at the two typical cross-sections in summer and in winter.  
The calculated values of seven statistics of selected samples of the concrete temperatures are shown in Table 6, whereas the corresponding box-and-whiskers plots are presented in Figure 16.  
The maximum average temperature of the 12 samples of populations was obtained at the point A1 (30.24 \({}^{\circ}\)C), and the minimum at the point B5 (10.40 \({}^{\circ}\)C). The maximum standard deviations were also obtained at point A1 (1.15 \({}^{\circ}\)C), whereas the minimum standard deviations were identified at points B5, C1 and C2 (0.08 \({}^{\circ}\)C). It was found that the average temperatures of 12 samples of the populations, as compared with the calculated temperatures at the selected points, without considering the point of view of uncertainty, differed by 0.1 \({}^{\circ}\)C at four points (A1, A3, A4, B1), whereas at the other eight points there was no difference. The maximum temperature of 12 samples of the populations was obtained at the point A1 (32.6 \({}^{\circ}\)C) and the minimum at the point B5 (10.3 \({}^{\circ}\)C). At point  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Point**} & \multicolumn{8}{c}{**Temperature (\({}^{\circ}\)C)**} \\ \cline{2-10}  & \(n\)1 **} & \(\overline{X}\)2  \\ \hline A1 & 60 & 30.24 & 1.15 & 28.1 & 29.20 & 30.25 & 31.03 & 32.6 \\ A2 & 60 & 20.34 & 0.37 & 19.6 & 20.10 & 20.30 & 20.60 & 21.1 \\ A3 & 60 & 18.48 & 0.22 & 18.1 & 18.30 & 18.50 & 18.60 & 18.9 \\ A4 & 60 & 18.00 & 0.17 & 17.7 & 17.90 & 18.00 & 18.10 & 18.3 \\ A5 & 60 & 15.95 & 0.19 & 15.5 & 15.80 & 15.95 & 16.10 & 16.3 \\ B1 & 60 & 23.28 & 0.60 & 22.0 & 22.90 & 23.30 & 23.70 & 24.7 \\ B2 & 60 & 15.93 & 0.14 & 15.6 & 15.80 & 15.90 & 16.00 & 16.2 \\ B3 & 60 & 12.79 & 0.17 & 12.5 & 12.68 & 12.80 & 12.90 & 13.2 \\ B4 & 60 & 11.13 & 0.13 & 10.9 & 11.00 & 11.10 & 11.20 & 11.5 \\ B5 & 60 & 10.40 & 0.08 & 10.3 & 10.30 & 10.40 & 10.40 & 10.6 \\ C1 & 60 & 17.21 & 0.08 & 17.1 & 17.20 & 17.20 & 17.23 & 17.4 \\ C2 & 60 & 14.82 & 0.08 & 14.7 & 14.80 & 14.80 & 14.90 & 15.0 \\ \hline \hline \end{tabular}  
* \(n\): sample size. \({}^{2}\)\(\overline{X}\): sample mean. \({}^{3}\)\(\sigma_{X}^{2}\): standard deviation of the sample. \({}^{4}\)\(X_{\text{mix}}\), \(X_{\text{mm}}\): minimum and maximum value of the sample elements. \({}^{5}\)\(Q_{1}\), \(Q_{2}\), \(Q_{3}\): first, second and third quartile of the sample elements.  
\end{table}
Table 6: The calculated values of 7 statistics of the concrete temperatures at 12 selected points.  
Figure 16: Box-and-whiskers plots of the concrete temperatures at 12 selected points.  
A1 the maximum interquartile range (1.83 \({}^{\circ}\)C) and the maximum range (4.5 \({}^{\circ}\)C) were also registered. The minimum interquartile range was calculated for the point C1 (0.03 \({}^{\circ}\)C), whereas the minimum range was recorded at the points B5, C1 and C2 (0.3 \({}^{\circ}\)C).