## 3 Method Validation
### River KRA
The data and values of the indicators for the time series for the average discharge \(Q^{average}\), minimal discharge \(Q^{min}\), and maximal discharge \(Q^{max}\) groups for 1947-2015 are presented in Table 3.  
The \(k^{x}\) regression model for the Krka River located at \"Skradinski bulk gornii\" was obtained as \(Y=0.0807X^{2}-0.4024X+1.5217\). It is a polynomial order-two function with \(k^{x}>1\), where the upper extreme is at \(k^{max}\) and the minimal extreme is between \(k^{average}\) and \(k^{max}\). The indicator used for the determination was \(R^{2}=1\). \(k^{x}\) is a positive real number \(R_{>0}=\{x\in R|x>0\}\) with values of \(1<k^{x}<2\). The discharge in the hydrological system was characterized by \(Q^{x}\)\({}_{average}<D(Q^{x})\). It is a hydrological system that is sensitive to climatic variations. This applies to all the \(Q^{x}\) (\(1<k^{x}<1.5\)). The highest sensitivity was for annual \(Q^{max}\), followed by a slightly lower \(Q^{min}\) and the lowest \(Q^{average}\), and \(k^{x}\) had a hierarchical trend _average_\(<min<max\). From this, it follows that the relative magnitude of the oscillations and the sensitivity of the characteristic values of annual streamflow increased in the annual maximum and minimum values. This implies that the average annual streamflow has a relatively smaller uncertainty related to input changes than the annual maximum or minimum streamflow. The area of operation of the water intake is very wide, and the forecasted variations in precipitation will be greater. This considerably affects the natural capacity of the system and increases the flooding and drought hazards. The deviation from the average in the case of annual minimum streamflow is 144%, annual average streamflow 120%, and for annual maximum streamflow, it is 154%, whereas the absolute range of operation of the system is 476.0 m\({}^{3}\)/s, and in the case of annual \(Q_{min}\), it is 15.71 m\({}^{3}\)/s, \(Q_{average}\) is 61.7 m\({}^{3}\)/s, and \(Q_{max}\) is 397.5 m\({}^{3}\)/s. As in the case of the Jadro Spring, the future variables were calculated (Table 4), and the necessary analyses were conducted to determine a comprehensive solution. The area of operation increased the least for annual flows, which were slightly higher than the average \begin{table}
\begin{tabular}{l c c c} \hline \hline \multicolumn{3}{c}{**Characteristic**} & \multicolumn{3}{c}{**Discharge Group**} \\ \cline{2-4}
**Values** & \(Q^{average}\) **(m\({}^{3}\)/s)** & \(Q^{max}\) **(m\({}^{3}\)/s)** & \(Q^{min}\) **(m\({}^{3}\)/s)** \\ \hline Average & 51.3 & 258 & 10.9 \\ Max & 84.2 & 481 & 20.7 \\ Min & 22.5 & 83.5 & 4.99 \\ D(max \(-\) min) & 61.7 & 397.5 & 15.71 \\ Indicator \(k^{x}\) & 1.20 & 1.54 & 1.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Characteristic discharges and range of fluctuations in the discharge measured at the “Skradinski Bulk gornii” station, 1947–2015 [29]. Figure 6: Hydrograph of the Krka River at Marasovine station (41 km from estuary) and Skradinski Bulk station (5 km from estuary), calendar year 2002.  
flow, and the most for annual maximum flows. Therefore, the required safety factors and design parameters must be selected accordingly. The maximal streamflow and variability (range) in streamflow (\(Q_{\textit{cloud}}\)) exhibit a major increase, whereas, in the case of minimal streamflow (\(Q_{\textit{supply}}\)), the reaction is lower with different ranges depending on the forecast precipitation change. Krka River is very sensitive to climate change, and its risk is high; therefore, higher \(\text{FOS}^{\text{X}}\) values need to be applied. The drinking water abstraction facility is located in Krka National Park, which makes it impossible to solve problems related to the water supply. The environmental constraints related to streamflow changes (\(E_{\textit{environmental}}\)) are rigid and obstruct the increase in \(Q_{\textit{distribution}}\). Therefore, a solution should be sought, mostly with the application of a water demand management approach.