## 3 Results and Discussion
### The Data Analysis, Main Results
The tables show that in both cases, the strongest correlation is between annual inflow and high water, summer-autumn low water, and winter low water, as well as between SLW and WLW. Correlation in other pairs can be characterized as weak and very weak. Figure 8 shows the difference integral curves (DICs) for the annual runoff and its intra-annual components of the Kubyshevskoye reservoir and the cascade as a whole. The curves were built in accordance with expression (1) for each hydrological series. The curves obtained again demonstrate a high degree of synchronism in the long-term changes in the low-water components of the annual runoff. Based on the difference integral curves in Figure 8, constructed for the VKC, it was concluded that for all seasons of the water management year, with the exception of the high water period, the original runoff series is not stationary and can be divided into two parts, approximately at the turn of 1973-1979, depending on the intra-annual seasons. The year 1979 was calculated as the most characteristic year of the annual runoff \"turning point\" as it was described in Section 2.2.1, and the initial hydrological series of the annual inflow of the VKC 1916-2020 was divided into two series: 1916-1978 and 1979-2020. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Annual** & **HW** & **SLW** & **WLW** & **FFD** \\ \hline
**Annual** & **1** & **0.75** & **0.75** & **0.64** & 0.24 \\ \hline
**HW** & 0.75 & **1** & 0.19 & 0.1 & \(-0.12\) \\ \hline
**SLW** & 0.75 & 0.19 & **1** & **0.69** & 0.23 \\ \hline
**WLW** & 0.64 & 0.1 & 0.69 & **1** & 0.45 \\ \hline
**FFD** & 0.24 & -0.12 & 0.23 & 0.45 & **1** \\ \hline \end{tabular}
\end{table} 
Table 6: The correlation coefficients—VKC. Figure 8: Difference integral curves. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Annual** & **HW** & **SLW** & **WLW** & **IIC** \\ \hline
**Annual** & **1** & **0.86** & **0.76** & **0.63** & 0.31 \\ \hline
**HW** & 0.86 & **1** & 0.35 & 0.23 & 0.01 \\ \hline
**SLW** & 0.76 & 0.35 & **1** & **0.72** & 0.35 \\ \hline
**WLW** & 0.63 & 0.23 & 0.72 & **1** & 0.56 \\ \hline
**PFD** & 0.31 & 0.01 & 0.35 & 0.56 & **1** \\ \hline \end{tabular}
\end{table} 
Table 5: The correlation coefficients—KR. The distributions' numerical characteristics of inflow values for these two hydrological series are given in Tables 7 and 8, respectively. The calculation results show that, indeed, at the specified year intervals for all intra-year periods of the water management year, with the exception of the high water period, the inflow average values for the corresponding periods are different, increasing noticeably in the 1979-2020 series compared to the 1916-1978 series. In addition, the share of high water in the annual runoff decreased from 64% to 55%; i.e., there was a redistribution of intra-annual inflow in favor of low-water runoff due to flood runoff. Using a two-sample Student's test, the hypotheses of a significant difference in the average inflow values given in Tables 5 and 6 for the series 1916-1978 and 1979-2020 were confirmed for the corresponding seasons of the water management year.