## 3 Results and Discussion
### Effect of Spillover
#### 3.2.2 One Year Period  
Figures 12 and 13 show the measured and calculated concrete temperatures at two of the downstream gauges (TC3 and TC4, located in the upper borehole), with and without the effect of water spilling over the spillway crest, and the height of spillover during the analyzed one year period, from 1 September 2013 to 1 September 2014. It can be seen from these figures that the calculated concrete temperatures at the downstream gauges TC3 and TC4, when considering the effect of spillover, are in very good agreement with the measured concrete temperatures during the whole year (RMSE is 2.50 at TC3 and 2.00 at TC4, whereas MAE is 2.20 at TC3 and 1.84 at TC4). The annual concrete temperature oscillations for the analyzed year, at gauges TC1 to TC6, as well as the corresponding air (or water) temperature oscillations are shown in Tables 2-4. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{**Temperature (\({}^{\circ}\)C)**} \\ \cline{3-10}  & **Limit** & \multicolumn{2}{c}{**Air**} & \multicolumn{2}{c}{**TCI**} & \multicolumn{2}{c}{**TC2**} & \multicolumn{2}{c}{**TC3**} & \multicolumn{2}{c}{**TC4**} \\ \cline{3-10}  & & **M \({}^{\textbf{1}}\)** & **M \({}^{\textbf{1}}\)** & **C \({}^{\textbf{2}}\)** & **M \({}^{\textbf{1}}\)** & **C \({}^{\textbf{2}}\)** & **M \({}^{\textbf{1}}\)** & **C \({}^{\textbf{2}}\)** & **M \({}^{\textbf{1}}\)** & **C \({}^{\textbf{2}}\)** \\ \hline \multirow{3}{*}{**Annual oscillations**} & T min & \(-9.5\) & \(0.9\) & \(-4.6\) & \(1.4\) & \(-2.4\) & \(2.9\) & \(1.1\) & \(4.9\) & \(3.5\) \\  & T max & \(35.6\) & \(36.2\) & \(31.3\) & \(32.1\) & \(27.0\) & \(26.9\) & \(21.7\) & \(23.3\) & \(20.4\) \\  & Diff. & \(45.1\) & \(35.3\) & \(35.9\) & \(30.7\) & \(29.4\) & \(24.0\) & \(20.6\) & \(18.4\) & \(16.9\) \\ \hline \multirow{3}{*}{**Time lag**} & T min & / & \multicolumn{2}{c}{\(3\)–\(4\)\(3\)} & \multicolumn{2}{c}{\(4\)–\(5\)\(3\)} & \multicolumn{2}{c}{\(10\)–\(12\)\(3\)} & \multicolumn{2}{c}{Several days} \\  & T max & / & \multicolumn{2}{c}{\(1\)–\(2\)\(3\)} & \multicolumn{2}{c}{\(2\)–\(3\)\(3\)} & \multicolumn{2}{c}{\(10\)–\(12\)\(3\)} & \multicolumn{2}{c}{Several days} \\ \hline \hline \end{tabular} \({}^{1}\) M: measured. \({}^{2}\) C: calculated. \({}^{3}\) Time lag in hours.  
\end{table} 
Table 2: The temperature oscillations and time lags at gauges TC1 to TC4. Figure 13: The concrete temperatures at gauge TC4 during the analyzed year. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{**Temperature (\({}^{\circ}\)C)**} \\ \cline{3-10}  & **Limit** & \multicolumn{2}{c}{**Air \({}^{\textbf{1}}\)**} & \multicolumn{2}{c}{**Water \({}^{\textbf{1}}\)**} & \multicolumn{2}{c}{**Water \({}^{\textbf{2}}\)**} & \multicolumn{2}{c}{**TC5**} \\ \cline{3-10}  & & **M \({}^{\textbf{3}}\)** & **M \({}^{\textbf{3}}\)** & **M \({}^{\textbf{3}}\)** & **M \({}^{\textbf{3}}\)** & **C \({}^{\textbf{4}}\)** \\ \hline \multirow{3}{*}{**Annual oscillations**} & T min & \(-1.8\) & \(2.7\) & \(2.9\) & \(3.8\) & \(2.0\) \\  & T max & \(32.1\) & \(19.0\) & \(16.6\) & \(17.6\) & \(18.8\) \\  & Diff. & \(33.9\) & \(16.3\) & \(13.7\) & \(13.8\) & \(16.8\) \\ \hline \multirow{3}{*}{**Time lag**} & T min & / & / & / & \multicolumn{2}{c}{\(6\)–\(8\) h} \\  & T max & / & / & / & \multicolumn{2}{c}{\(5\)–\(6\) h} \\ \hline \hline \end{tabular} \({}^{\dagger}\) At gauge TW2 (i.e., \(521\) m a. s. l). \({}^{2}\) At gauge TW1 (i.e., \(519\) m a. s. l). \({}^{3}\) M: measured. \({}^{4}\) C: calculated.  
\end{table} 
Table 3: The temperature oscillations and time lags at gauge TC5. The annual air temperature oscillations at the location of the MAWS were, for the selected period, between \(-9.5\) and \(35.6\)\({}^{\circ}\)C, so their amplitude was \(45.1\)\({}^{\circ}\)C. At gauge TC1, the analyzed annual oscillations were significantly smaller (measured \(35.3\)\({}^{\circ}\)C and calculated \(35.9\)\({}^{\circ}\)C), whereas at gauge TC2 the oscillations were \(30.7\) and \(29.4\)\({}^{\circ}\)C, respectively.