The probability matrix method in determining the control curves of operation of the reservoirs of dams and their comparison to the SPA method

The appropriate and optimum operation of reservoir system of dams ranks among the most important issues considered by experts of water industry all over the word. In most reservoir system of the world, control curves are known as the main pattern of water operation. The curves indicate the optimum volumes of supplied water or yielding system versus various conditions of reservoirs during different month of the year. There are various methods of determining the operation pattern of water reservoirs which are classified into three simulation, optimization and probability matrix. In traditional methods, reservoir systems are designed based merely on the historical data of river currents and not using of function indices of reservoir. These methods are based on the assumption that in future there will not happen draught more severe than the recoded critical periods, an assumption the truth of which is far from being definite. The purpose of this research is to demonstrate a method to determine the control curves of reservoir dams based on their functional indices (such as time reliability, vulnerability and resiliency). To achieve this goal, we provided at first, using methods of temporal series AR(1), Valencia Schaake one thousand series of data of currents of the rivers entering the reservoir dam of Mahabad and Shahar chai in west Azarbaijan. We continued with using the improved SPA methods and Gold probability matrix, conducting the necessary analysis and providing ultimately appropriate control curves to obtain various combinations of the quantity of demand and functional indices. The obtained results display a good accordance between the results obtained by SPA and probability matrix methods. There occurred the maximum difference between the methods in minimum sustainability and the minimum difference in maximum sustainability. In the site of Mahabad the maximum difference is 13.5 MCM and the minimum difference 0.37 MCM. In the site of Shahar chai the maximum difference is 9.88 MCM and the minimum difference 0.098 MCM.