## 3 Results and Discussion  
### The Data Analysis, Main Results  
From the inflow data observed, the distributions' main numerical characteristics of the annual and seasonal runoff of the cascade and all its reservoirs were obtained. In this paper, here and below, the results are given only for the Kuibyshevskoye reservoir and the cascade as a whole. The results are shown in Tables 3 and 4, respectively. Figure 5: Long-term hydrological series of observed inflows to the VKC reservoirs in period WLW and PFD. The distributions of the annual runoff and its seasonal components are not symmetrical, and at the same time, they are biased towards runoff larger values, since the skewness values for them are positive. The variance of the annual runoff is not the sum of the variances of seasonal runoff; therefore, seasonal runoffs, strictly speaking, cannot be considered as independent random variables. At least some of them may be related by some kind of correlation. In both cases, the main contribution to the annual inflow (more than 80%) comes from high water and summer-autumn low-water seasons. Figure 6 shows scatterplots (correlation fields) for the following pairs of inflows to the Kubyshevskoye reservoir: Annual-HW, Annual-SLW, Annual-WLW, and HW-WLW. For each, trend lines and their equations are shown. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Statistics** & **Annual** & **HW** & **SLW** & **WLW** & **PFD** \\ \hline Mean (mln m\({}^{3}\)) & 250,913 & 151,513 & 64,050 & 24,517 & 10,833 \\ \hline SEM & 4493 & 2980 & 2005 & 960 & 552 \\ \hline Median & 254,338 & 152,411 & 59,859 & 22,824 & 9797 \\ \hline Standard deviation \(\sigma_{B}=\sqrt{D_{B}}\) & 46,041 & 30,538 & 20,543 & 9838 & 5653 \\ \hline Sample variance \(D_{B}\) & 2,119,738,992 & 932,565,653 & 422,013,534 & 96,788,357 & 31,960,172 \\ \hline Kurtosis & 0.34 & \(-\)0.25 & 0.32 & 0.26 & 3.78 \\ \hline Skewness & 0.0039 & 0.08 & 0.65 & 0.81 & 1.63 \\ \hline Minimum (mln m\({}^{3}\)) & 141,759 & 83,444 & 28,271 & 10,486 & 3981 \\ \hline Maximum (mln m\({}^{3}\)) & 374,650 & 234,826 & 130,728 & 54,563 & 35,438 \\ \hline Sample size \(N\) & 105 & 105 & 105 & 105 & 105 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical characteristics of the inflow distributions for 1916–2020 (VKC). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Statistics** & **Annual** & **HW** & **SLW** & **WLW** & **PFD** \\ \hline Mean (mln m\({}^{3}\)) & 44,639 & 28,981 & 10,163 & 4010 & 1486 \\ \hline SEM & 1081 & 744 & 396 & 175 & 85 \\ \hline Median & 45,011 & 28,702 & 9444 & 3766 & 1295 \\ \hline Standard deviation \(\sigma_{B}=\sqrt{D_{B}}\) & 11,132 & 7657 & 4078 & 1801 & 879 \\ \hline Sample variance \(D_{B}\) & 123,926,692 & 58,637,086 & 16,629,466 & 3,244,917 & 772,173 \\ \hline Kurtosis & 1.33 & 1.42 & 0.68 & 0.87 & 13.32 \\ \hline Skewness & 0.50 & 0.67 & 0.83 & 0.96 & 3.03 \\ \hline Minimum (mln m\({}^{3}\)) & 18,928 & 12,368 & 3121 & 1234 & 592 \\ \hline Maximum (mln m\({}^{3}\)) & 84,211 & 57,698 & 23,288 & 10,149 & 6488 \\ \hline Sample size \(N\) & 105 & 105 & 105 & 105 & 105 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Numerical characteristics of the inflow distributions for 1916–2020 (Kuibyshev resor-voir). Figure 7 shows similar diagrams for the corresponding seasonal inflow pairs for the cascade as a whole. Figure 6: Scatterplots—Kuibyshevskoye reservoir. Figure 7: Scatterplots—VKC. The first three diagrams in both figures demonstrate the presence of sufficiently expressed statistical relationships between the respective series of inflows. The last diagram (HW-WLW) shows the lack of correlation between high-water inflow and winter low-water inflow. A quantitative assessment of the correlation dependences of the annual and seasonal inflows of the Kuibyshevskoe reservoir (KR) and the VKC in the form of the pairwise correlation coefficients is given in Tables 5 and 6, respectively.