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Efficient management of limited water resources in an irrigation reservoir system is necessary to increase crop productivity. To achieve this, a reservoir release policy should be integrated with an optimal crop water allocation. Variations in hydrologic variables such as reservoir inflow, soil moisture, reservoir storage, rainfall and evapotranspiration must be considered in the reservoir operating policy model. Uncertainties due to imprecision, subjectivity, vagueness and lack of adequate data can be handled using the fuzzy set theory. A fuzzy stochastic dynamic programming (FSDP) model with reservoir storage and soil moisture of the crops as fuzzy state variables and inflow as a stochastic variable, is developed to obtain a steady state reservoir operating policy. The model integrates the reservoir operating policy with the crop water allocation decisions by maintaining the storage continuity and the soil moisture balance. The reservoir release decisions are made in the model in 10-day periods and water is allocated to the crops on a daily basis. On comparison with the classical stochastic dynamic programming (SDP) model and a conceptual operation policy model, it is observed that the FSDP model, in general, results in lower release from the reservoir while maintaining lower soil moisture stress. However the steady state reservoir operation policy obtained using the FSDP model may not perform well in a short-term reservoir simulation. A fuzzy state short-term reservoir operation policy model with storage and soil moistures of the crops as fuzzy variables, is developed to obtain a real time release policy using forecasted inflow and forecasted rainfall. The distinguishing features of the model are accounting for (a) spatial variation of soil moisture and rainfall using gridded rainfall forecasts and (b) ponding depth requirement of the Paddy. On comparison with a conceptual operation policy model, the fuzzy state real time operation model is found most suitable for the application of the short term real time operation for irrigation. The real time operation model maintains high storage in the reservoir during most of the 10-day time periods of a year and results in a slightly lower annual releases as compared to the conceptual operation policy model. The effect of inflow forecast uncertainty is examined using different sets of forecasted inflows, and it is observed that the system performance is quite sensitive to inflow forecast uncertainties. The use of the satellite based gridded soil moisture in the real time operation model shows consideration of realistic situations. Further, three performance measures, viz., fuzzy reliability, fuzzy resiliency and fuzzy vulnerability are developed to evaluate the performance of the irrigation reservoir system under a specified operating policy. A fuzzy set with an appropriate membership function is defined to describe the working and failed states to account for the system being in partly working and partly failed state. The degree of failure of the irrigation reservoir system is defined based on the evapotranspiration deficit in a period. Inclusion of fuzziness in the performance measures enables realistic representation of uncertainties in the state of the system. A case study of Bhadra reservoir system in Karnataka, India is chosen for demonstrating the model applications. |
