## 4 Discussion  
The proposed approach is characterized by interconnected water resource system processes, input-output relationships, sensitivity, autonomous capacity and vulnerability, overlapping climate change, water supply, and infrastructure. The obtained results comprehensively show the essential difference in extreme flow reactions in the two karst hydrological systems related to the potential energy arising from rainfall in the watershed system in dry and wet periods and streamflow (water abstraction) vulnerability. The estimated vulnerability is the cumulative response of the entire river system network to the input (precipitation-evapotranspiration) variability during the considered period at the reference point for water abstraction. The coefficient \(k^{x}\) is presented as a function of \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \(Q_{\textit{historic}}\) (m\({}^{3}\)/s) & **Precipitation** & \(Q^{x}\)_average_future_ & \(k^{x}\)_future_ & \(D^{x}\)_future_ & **FOS** & \(D^{x}\)_design_ & \(Q^{x}\)_average_,_design_ \\  & **Change (\%)** & **(m\({}^{3}\)/s)** & **(m\({}^{3}\)/s)** & **(m\({}^{3}\)/s)** & **(m\({}^{3}\)/s)** & **(m\({}^{3}\)/s)** \\ \hline \multicolumn{8}{c}{Maximal change scenario for 2100 year} \\ \(Q^{\textit{average}}_{\textit{average}}\) (51.3) & Annual (\(-7\)) & 47.71 & 1.20 & 57.25 & 0.8 & 45.80 & 38.27 \\ \(Q^{\textit{max}}_{\textit{average}}\) (258) & Wet period (\(+7\)) & 276.06 & 1.90 & 523.20 & 1.2 & 627.84 & 331.27 \\ \(Q^{\textit{min}}_{\textit{average}}\) (10.9) & Dry period (\(-25\)) & 8.18 & 1.46 & 11.90 & 0.8 & 9.52 & 6.54 \\ \hline \multicolumn{8}{c}{Minimal change scenario for 2100 year} \\ \(Q^{\textit{average}}_{\textit{average}}\) (51.3) & Annual (\(-2\)) & 50.27 & 1.20 & 60.33 & 0.8 & 48.26 & 40.22 \\ \(Q^{\textit{max}}_{\textit{average}}\) (258) & Wet period (\(+2\)) & 263.16 & 1.63 & 428.04 & 1.2 & 513.64 & 315.79 \\ \(Q^{\textit{min}}_{\textit{average}}\) (10.9) & Dry period (\(-5\)) & 10.35 & 1.44 & 14.93 & 0.8 & 11.94 & 8.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Krka River at the “Skradinski Buk gornji” including estimated variables for the year 2100, first iteration. the ratio of \(\frac{Q_{average}^{x}}{Q_{average}}\). It is a relevant predictor variable (assumed non-random) for \(k^{x}\) as a response variable (assumed random) because natural river system variations follow typical average behavior in response to climate (rainfall) fluctuations and susceptibility to change. Such a predictor is the foundation for assessing vulnerability to climate streamflow hazard \(Q^{x}\) expressed by the \(k^{x}\) value, where \(k^{x}\) is an incommensurable quantity for cumulative vulnerability. Therefore, \(R^{2}\) is the coefficient of the multiple determinations (sensitivity and adaptive capacity). The coefficient of determination, \(R^{2}\), has a value of 1, indicating that the regression line perfectly fits the data. Thus, the fitted model explains all the variability in \(k^{x}\) in accordance with the features of the available streamflow time series. However, a high correlation does not provide adequate evidence that changing one variable has resulted in or may have resulted from changing other variables. Thus, the regression equation depicts the type of hydrological system, structure, and magnitude of streamflow (i.e., cumulative vulnerability) in a simplified presentation. Generally, the fitted model presents a rate function and formulates a large deviation principle for future climate periods using a continuous streamflow parameter. River systems will retain the same internal characteristics and thus present a model of the large deviation principle in the future uncertain climate period, with the variability proportional to the current ones, allowing engineers to apply appropriate FOS in relation to the (hazard) design parameters \(Q^{x}\).