Fuzzy State Real-Time Reservoir Operation Model for Irrigation with Gridded Rainfall Forecasts Sangeeta Kumari 1 and P. P. Mujumdar 2 Abstract: A short-term real-time operation model with fuzzy state variables is developed for irrigation of multiple crops based on earlier work on long-term steady-state policy. The features of the model that distinguish it from the earlier work are (1) apart from inclusion of fuzziness in reservoir storage and in soil moisture of crops, spatial variations in rainfall and soil moisture of crops are included in the real-time operation model by considering gridded command area with a grid size of 0.5° latitude by 0.5° longitude; (2) the water allocation model and soil moisture balance equations are integrated with the real-time operation model with consideration of ponding water depth for Paddy crop; the model solution specifies reservoir releases for irrigation in a 10-day time period and allocations among the crops on a daily basis at each grid by maintaining soil moisture balance at the end of the day; and (3) the release policy is developed using forecasted daily rainfall data of each grid and is implemented for the current time period using actual 10-day inflow and actual daily rainfall of each grid. The real-time operation model is applied to Bhadra Reservoir in Karnataka, India. The results obtained using the real-time operation model are compared with those of the standard operating policy model. Inclusion of fuzziness in reservoir storage and soil moisture of crops captures hydrologic uncertainties in real time. Considerations of irrigation decisions on a daily basis and the gridded command area result in variations in allocat- ing water to the crops, variations in actual crop evapotranspiration, and variations in soil moisture of the crops on a daily basis for each grid of the command area. DOI: 10.1061/(ASCE)IR.1943-4774.0000956. © 2015 American Society of Civil Engineers. Introduction Earlier studies on reservoir operation for irrigation have focused on developing long-term steady-state policies (Vedula and Mujumdar 1992; Vedula and Nagesh Kumar 1996; Panigrahi and Mujumdar 2000; Tilmant et al. 2002a, b; Mousavi et al. 2004a, b; Suresh and Mujumdar 2004; Sangeeta and Mujumdar 2015). Although the steady-state models are useful in deriving long-term policies, they are not found beneficial for short-term real-time operation (Mujumdar and Ramesh 1997). The short-run yearly reservoir operation models have been developed in the literature. Rao et al. (1992) used a two-stage process model to develop irrigation oper- ation policy by maximizing crop yields and considering current seasonal changes in weather and other variables. Irrigations are planned for the entire season at weekly intervals in the first stage using historical data and optimal irrigation scheduling model, and in the second stage decisions for subsequent weeks are revised with real-time data up to that week and irrigation optimization model are solved once again for the new conditions. Mujumdar and Ramesh (1997) developed a short-term real-time operation for irrigation of multiple crops with the integration of on-farm utilization of water by crop. The model has the capability of considering interdepend- ence of crop water allocations across time periods and has the abil- ity to provide adaptive release policy. Hajilal et al. (1998) proposed two-phase (plan phase and operation phase) real-time adaptive op- eration of irrigation reservoir. In the plan phase, reservoir releases were optimized biweekly for target releases and mean inflows, and in the operation phase real-time releases were made accord- ingly for the current interval. Prasad et al. (2013) developed a real- time operation short-term policy for irrigation of multicrops in which reservoir release decisions were integrated with field irriga- tion requirement. Considerations of hydrologic uncertainty in reservoir storage and soil moisture of the crops are very effective in modeling of reservoir real-time operation for irrigation. Representation of hydrologic uncertainties can be addressed by fuzzy set theory. In classical stochastic dynamic programming (SDP), a single repre- sentative value is considered to represent storage and soil moisture (which are taken as state variables) in a particular class interval. The assumption is relaxed and treats the storage and the soil moisture in a class interval as a fuzzy variable with a membership function representing numerically a degree to which an element belongs to a set, which can be expressed as a number between 0 and 1 instead of either 1 (certainly belongs to it) or 0 (certainly does not belong to it). The transitions between fuzzy numbers instead of transitions between single representative points can be simulated without dif- ficulty in the model with the help of fuzzy arithmetic. Because evaporation from the reservoir and the water available for irrigation depend on the initial storage and final storage—which are both con- sidered as fuzzy variables—those variables are also treated as fuzzy variables. Thus, the considerations of storage and soil moistures as fuzzy variables in the real-time operation model rather than single representative points represent more accurate mappings of storage state variables and soil moisture state variables throughout the sim- ulation, which results in better modeling the real situations. Fuzzy logic has been used in reservoir operation by Dubrovin et al. (2002), Panigrahi and Mujumdar (2000), Suresh and Mujumdar (2004), Mousavi et al. (2005), and Sivapragasam et al. (2007). Fuzzy arithmetic has been applied in various optimization proc- esses of reservoir operation. Recently, Guo et al. (2010) developed a two-stage program for water resources management consider- ing randomness and fuzziness. Faybishenko (2010) did fuzzy 1 Research Student, Dept. of Civil Engineering, Indian Institute of Science, Bangalore 560012, India. 2 Professor, Dept. of Civil Engineering, Indian Institute of Science, Bangalore 560012, India (corresponding author). E-mail: pradeep@civil .iisc.ernet.in Note. This manuscript was submitted on March 7, 2015; approved on July 20, 2015; published online on September 11, 2015. Discussion period open until February 11, 2016; separate discussions must be submitted for individual papers. This paper is part of the Journal of Irrigation and Drai- nage Engineering, © ASCE, ISSN 0733-9437/04015042(14)/$25.00. © ASCE 04015042-1 J. Irrig. Drain Eng. J. Irrig. Drain Eng. Downloaded from ascelibrary.org by KUNGLIGA TEKNISKA HOGSKOLA on 09/13/15. Copyright ASCE. For personal use only; all rights reserved.