Optimal Conjunctive use of Surface and Groundwater under Fuzzy Environment

Abstract

Water has become an indispensable commodity in advancing civilization. An increase in population, which demands large scale growth and development in various fields has indicated very high stress on sectors of water resources. Water shortage controls the economic and agricultural development of a country. Scarcity of water calls for proper need of its planning, development and management, to utilize it efficiently in a sustainable manner. In conditions of water scarcity, the prime objective of water resource managers is about maximizing the use of available water resources from various sources duly taking care of environmental, ecological, socioeconomic aspects. In many cases of the reservoirs, it is noted that the inflows are not sufficient to satisfy the requirement. In such cases there is a need to explore the possibility of conjunctive use of available groundwater in the command with the surface water to meet out the scarcity. An optimal operation of a reservoir system for efficient utilization of both surface and groundwater resources conjunctively requires knowledge of reservoir process and infield process. This knowledge facilitates to arrive at decisions on reservoir operation and cropping pattern by use of optimization models which are characterized by a mathematical statement of objective function subjected to a set of constraints to give global optimum solutions.
The changing climatic conditions make the inflows to the reservoir uncertain and the poor operation of the reservoir makes the storages in the reservoir vague. Net Irrigation Requirement (NIR) of crops is stochastic in nature which contributes uncertainty in irrigation demands. Further irrigation demands, although affected by weather conditions to a large extent, are likewise affected by crop type, market conditions, period of planting and harvesting. Storage and release targets for a reservoir operation are usually determined based on factors determining the operational requirement of the reservoir system. The decision makers call for considering all these issues. In many cases, fuzzy logic may provide the most appropriate methodological tool for modeling reservoir operation.
In the present study, the pertinence of the reservoir operation model is improved by incorporating the uncertainties in model parameters and interpreting those as fuzzy sets instead of individual values. The degree of satisfaction of a certain value of the parameter within the fuzzy set is represented by a membership function. Consequently, it is proposed to build up an optimization model to provide optimal operation policies of reservoir for sustainable irrigation planning with the usage of surface and groundwater conjunctively under fuzzy environment. It includes estimating groundwater potential under the command of the reservoir based on the existing GEC-97 methodology [19] and the available data, formulating Linear Programming (LP) conjunctive use model, deriving optimal reservoir operating policies by considering the storage continuity equation of the reservoir and developing a Fuzzy Linear Programming (FLP) model that will take into consideration the uncertainties involved in the parameters related to the reservoir operation.
The developed model is applied to the study area of Jayakwadi Project Stage-I, on the Godavari River near the town Paithan in the State of Maharashtra, India by considering six different cases. The model in case-I consider surface water only without any socioeconomic constraints. To have a certain minimum yield of the crops which are left without allotment of area of the model, the social economic constraints are considered in the second case. Conjunctive use of surface and groundwater is considered in the third case without any socioeconomic constraint and in the fourth case the conjunctive use is with the socioeconomic constraints. In the fifth case a FLP model is considered to take into account the fuzziness in the resources and in sixth case a FLP model with the technological coefficients as fuzzy is considered. The model developed in the present study is applied to the above six cases by taking into account all the evaluated parameters. It is solved using Language for INteractive General Optimization (LINGO) to obtain the optimal cropping pattern and optimal release policies. Being a multipurpose reservoir, after giving first priority to the water supply for drinking and industrial use the optimal releases for the power generation and for irrigation are obtained from the model.
The global optimal solution of the LP Model obtained for the first case in which only available surface water is considered without imposing the socioeconomic constraints have not allotted area to the crops Rabi Wheat, Rabi Jowar and Hot Weather Groundnuts under both the canals. It has generated net benefits of Rs. 3563.78 million with average intensity of irrigation by 55.51%. It is, therefore, required to put socioeconomic constraints to these crops to get certain minimum yield to take care of the requirement of the local population in the second case. By imposition of such socioeconomic constraint the optimal net benefit in the second case is reduced from Rs 3563.78 million to Rs 3373.45 million as compared to the first case. With the usage of available groundwater along with the surface water conjunctively, the net benefits from the crops in third case has raised to Rs 3715.57 Million from Rs 3563.78 Million and intensity of irrigation to 60.73% from 55.51% as compared to the first case. However, there is no allotment of area under the crops Rabi Jowar and the Hot Weather Groundnut by the model. Hence, in the fourth case, socioeconomic constraints are put to these crops to take care of the requirement of the local population. Therefore, all crops have been allotted area, giving an intensity of irrigation by 60.04% with optimized net benefits of Rs 3590.02 Million. The uncertainties involved in the resources have been considered in the fifth case through a FLP model. The values of the upper and lower bounds of objective function i.e. net benefit from the crops are Rs 3590.0 Million and Rs 3279.72 Million respectively. The optimized values which meet the constraints and goal with a maximum level of satisfaction Lamda (\(\lambda\)) is obtained as 0.511. Optimal results, namely net benefits, cropping pattern, surface water releases, groundwater pumpage, storages at the end of every month and corresponding head over the turbine are also obtained in this case.