Document Type : Research Article
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Abstract
Introduction: In recent decades, with increasing the world population and demand for fresh water for various applications (drinking, agriculture and industry), planning, management and optimal utilization of surface water reservoirs, especially in arid and semi-arid regions, have become the most serious challenges faced by researchers and water industry professionals in many parts of the world. In surface water reservoirs, uncontrolled flow is stored in wet periods for use in low flow periods. Therefore, surface water storage dams are created to control and regulate the flow of rivers in order to meet demand for different uses at a certain level of performance indices. During the process of storing water in the reservoirs, the uncontrolled flows of the input into the reservoir are in three ways: yield or output adjusted to meet demand for various uses, infiltration loss and evaporation from the surface of the lake and spill of excess water in a reservoir that is part of an uncontrollable flow. The proposed methods of storage-yield-performance of the storage system are classified into two main groups, simulation and optimization methods, which are widely used to analyze the reservoirs system for storing surface water. Among two final methods of simulation i.e. the behavior analysis method and the modified Sequent Peak Algorithm (SPA) method, all the actual conditions governing the system of storage reservoirs, including control of indices of reliability and vulnerability in the storage-yield-performance, are required to apply SPA. The basic SPA simulation method has been proposed as a computational method for the mass curve, and major improvements have been made to increase its functionality and efficiency at the late 20th century. The first amendments to apply the effects of evaporation losses and performance indices; time-based reliability and vulnerability, were carried out by Lele (1987). Then, Montaseri (1999) developed the SPA method for the system of multiple storage reservoirs and used non-linear or real area-volume relationship for applying losses caused by evaporation.
Materials and Methods: Stochastic models provide the possibility of generating successive hydrological time series (such as rainfall and flow) that are likely to occur in the future. On the other hand, the analysis of long-term behavior of various water resources systems, especially the storage system, depends on the availability of expected river flow time series in the years to come. Therefore, the use of stochastic models and the production of artificial data are absolutely necessary for the accurate evaluation of the design, operation and optimal management of the storage system and the elaboration of their long-term behavior. For this purpose, using a single distributed stochastic model, 1000 series of annual and monthly flows of input into the storage reservoir were generated and then the series of monthly flows generated to simulate the storage reservoir system using the SPA-I method and the reservoir performance indices (time reliability, resiliency and vulnerability) were also used for single reservoir system.
Results and Discussion: The results show that combining two stochastic AR(1) and Valencia-Schaake models had very good performance in preserving statistical data of historical data at two monthly and annual levels. This is the advantage and necessity of using the stochastic distributions model relative to other stochastic models such as Thomas-Fiering and ARMA in analyzing the storage reservoirs systems. The behavior of the reservoir system or the critical period in addition to demand, depends on system performance indices and decreases the critical period by decreasing time-based reliability or increasing the vulnerability factor. The results also indicate nonlinear (exponential) changes in the critical period and demand at a certain level of performance indices. Moreover, evaporation loss changes for demand and a certain level of performance indices have a concave shape, with a reversing point consistent with the largest within-year storage system. With a decrease/ an increase demand and volume of storage, the amount of evaporation losses increased exponentially and accounted for a considerable percentage of the reservoir's storage capacity.
Conclusion: The results revealed that volume of storage in addition to demand is a function of evapotranspiration losses and time-based reliability and vulnerability indices and follows an exponential relation for demand. In addition, in all three variants of the modified SPAs (SPA-I, SPA-II, and SPA-III), two performance indices of the reservoir, namely time-based reliability and vulnerability, are controllable in analysis, and the storage system analysis is performed for specified values or mentioned indices. Also, in the SPA-II and SPA-III methods, it is possible to use a nonlinear or a real are-volume relationship to estimate the loss of evapotranspiration in the storage system. Control of two performance indices of the reservoir and the application of real or nonlinear area-volume relationship in the analysis of reservoir system reservoir are important advantages of the above methods to the behavior analysis method.
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