KERNEL FUNCTION AND ANN BASED PLANNING OF GROUNDWATER DEVELOPMENT FOR IRRIGATION

Abstract

The present study addresses the problem of planning cropping pattern and the associated groundwater withdrawals in agricultural areas wherein the irrigational requirements are met through groundwater development exclusively or through given canal supplies supplemented by the groundwater development. The envisaged planning optimizes the cropping pattern accommodating the most rampant concerns in respect of groundwater development viz. excessive water table depth and the stream-aquifer interflows. An indiscriminate cropping/pumping pattern may lower the water table excessively, and may reduce the base flow contribution or may induce influent seepage from hydraulically connected streams. Both such eventualities may lead to a variety of technical and socio-economic problems like increased pumping cost, dysfunctional pumps, drying up of wells, deterioration of groundwater quality etc. Two approximate simulation-optimization models are presented for arriving at the optimal cropping pattern/groundwater development plans. The envisaged planning involves arriving at such zone-wise crop areas which are optimal, and whose long term irrigation through the available canal supplies and the supplemental groundwater pumpage does not lead to excessive water table depths and stream-aquifer interflow at certain critical time. The approximate simulatorin the first model invokes the artificial neural network(ANN)functions in respect of the two state variables viz. maximum water table depth (D) and stream-aquifer interflow (Qc) under dynamic equilibrium. The second model approximates these two state variables by kernel functions. Several planned runs are conducted on a simulation model to generate arrays of the state variables corresponding to various crop-area vectors. The resulting arrays of inputs (crop areas) and the outputs (state variables) are used to develop the two approximate simulators. The proposed model optimizes a stipulated function of the crop areas subject to assigned constraints on maximum water table depth and stream-aquifer interflows by linking these approximate simulators to an optimizer. The models proposed herein are applied to the Hindon-Yamuna inter-basin which falls in command of Eastern Yamuna canal system in India. The area is divided into two zones of uniform cropping pattern (0.14 and 0.46 million hectares) - first in the central core and the second in the vicinity of the two recharge boundaries. One would expect the second zone which has more favorable discharge-drawdown characteristic to be allocated larger crop areas. The crops considered feasible in the study area arepaddy, other kharif, sugarcane, wheat and other rabi. Two ANN models of the state variables are developed. The sets of inputs and outputs necessary for training and testing of ANN models are generated by employing the simulation model. Zone wise cropping areas of feasible crops are generated randomly. State variables are generated for each feasible cropping pattern through the simulation model. In all 750 data patterns of cropping patterns (comprising five crop areas in two zones), andthe corresponding state variables Dand Qc are generated. The state variable Qc comprises Hindon-aquifer (q11) and Yamuna-aquifer (q¥) interflows at pre and post monsoon times. In all 675 data patterns are invoked to train the ANN models. Remaining 75 patterns are used for validating the trained ANN model. The training is conducted by the back-propagation learning algorithm with the mean squared error and correlation coefficient as the performance evaluation criteria. For the developing kernel models of the state variables (D and Qc) zone wise crop areas are varied in the range of 1 % to 38 % of corresponding total geographical area. The corresponding values of the state variables (D and Qc) are computed invoking an available pre-calibrated simulation model of the area. The plots of the state variables vs. the crop areas provide the necessary kernel functions. The approximate kernel function and ANN based models are invoked to maximize the total cropped area. Maximizaton is conducted to the constraints of limiting maximum depth to water table to 20m, avoiding induced recharge from the adjoining rivers, and honoring the land availability for agriculture. Optimization is conducted using Genetic algorithm (GA). The optimal solutions reached by applying the two approximate simulators are subsequently validated by computing the state variables corresponding to the optimal crop areas invoking the simulation model. The discrepancies are overcome by fine tuning the near- optimum solutions reached through the approximate simulators. The fine-tuning is accomplished using nowthe simulation-optimization model but restricting the range of variation of the crop areas around the nearoptimal solution. This strategy restricts the computational costinspite of using the otherwise expensive simulation-optimization model. The result from the kernel-GA model require far less fine-tuning then the results from ANN-GA model. ii The total cropped areas in the two zones are optimizes as 0.06 million hectares, and 0.24 million hectares respectively. The second zone which has more favorable dischargedrawdown characteristic is allotted an enhanced cropping pattern. The constraints on the maximum water table depth and on Hindon-aquifer interflow rates are activated at the optimal solution. The constraints in respect of Yamuna-aquifer interflow rates and land availability remain inactive. 111