## 1 Introduction
In accordance with the Russian regulatory documents in the field of water relations, the parameters of hydraulic structures (HSs) during design, reconstruction, and operation significantly depend on the reliability of water resources in the basin. The tool for assessing the reliability of water is the water resources calculation (WRC). WRCs are carried out in order to assess the amount and degree of development of water resources available for use under various conditions of water content of water bodies. WRCs are carried out in the design and reconstruction of hydraulic structures, preparation of a water management justification for the schemes for the integrated use and protection of water bodies (SKIOVO) [18], and development of the rules for the use of reservoirs water resources (PIVR) [19]. WRCs determine the ratio of available water resources (volumes of surface and groundwater available for long-term guaranteed use with the existing and projected composition of the water management complex) and estimated water consumption at the predicted level of economic development. Based on the WRCs,the sufficiency of water resources is assessed to meet the volumes established for water users' allowable water resources withdrawal and the possibility of developing the water management complex in the near, planned, and long term. In engineering hydrology, the concept of \"reliability of a hydrological characteristic\" is defined as the probability that the considered value of a hydrological characteristic can be exceeded among the totality of all its possible values. As an example, the set of values can be annual, seasonal, or monthly inflow in a long-term series [20]. The reliability of water yield in water resource calculations is understood as the probability of providing the consumer with water at the appropriate rate, expressed as a percentage of uninterrupted years, seasons, and months of water supply, depending on the duration of the entire calculation period [19]. Calculation of hydraulic structure parameters for water users of various sectors of the economy is carried out on the basis of the year of the corresponding reliability. Table 1 shows the normative flow rates (annual, seasonal, interval), which are used to substantiate water use indicators for various sectors of the economy. The main indicator of the reliability of providing water users is the indicator of the calculated water yield. The estimated water yield reliability is defined as the probability of providing the consumer with water, expressed as a percentage of years without violation (seasons, months, decades), and is calculated by the formula \(m/(n+1)\) where \(m\) is the number of years without violation of the water user requirements and \(n\) is the number of years in the long-term runoff series. Figure 1: Calculation scheme of the Volga–Kama cascade of reservoirs. When developing SKIOVO and PIVR for water users of various economic sectors, the following standard reliability for ensuring normal water consumption by the number of years without violation should be met:  
* Sanitary releases--97-99%;
* Water supply (drinking, household, industrial)--95-97%;
* Hydropower--85-95%;
* Navigation (maintenance of depths)--85-90%;
* Irrigation and agriculture--75-90%;
* Fisheries--75-90%. The work is dedicated to the uninterrupted operation of the following main water VKC reservoirs users: energy, transport, agriculture and fisheries, ecology, and household services. WRCs were performed by optimization methods for both runoff series--1916-1978 and 1979-2020. The management of VKC reservoirs in water resource calculations was performed on the basis of a search for optimal releases in total for the entire Volga-Kama cascade of reservoirs (release in the outlet--Vologgradskaya HPP) in different seasons and the total volumes of reservoir drawdown by the beginning of the flood. The requirements of water users for the VKC reservoir operation mode conflict with each other.