Water resource management at Tabarkabad dam in Quchan city: Using orthogonal polynomials to solve stochastic dynamic programming problems

The lack of efficient use of water as a production input has led to wastage of a significant amount of this input, which is financed at a great cost. Most provinces of the country have been facing water crisis for decades. Symptoms of this water crisis have been observed in some plains of Khorasan Province since the early 1970s, and this crisis has intensified in the last decade due to the lack of proper management of water resources. Therefore the present study, using a dynamic approach, studies the management of water resources in the Tabarkabad Dam in Quchan.
In this paper we put forward an easy-to-implement methodology for solving deterministic or stochastic dynamic programming problems within a standard optimization package such as GAMS. We found that the use of orthogonal polynomials was especially helpful in implementing approximation methods for the iterative computation of the infinite-horizon value function, due to their superior convergence properties over standard polynomials. This method is described using the case study of Tabarkabad Dam in Quchan city. For this purpose, data related to the Tabarkabad Dam were collected through the National Dams Information System for the years 2008-2016. Also, data relating to the estimation of the agricultural water demand function in Quchan city were obtained through a questionnaire prepared by the Ministry of Jihad-e-Agriculture.
Based on the results, comparing the actual and simulated values for the dam reservoir (state variable) and water release (control variable), it is determined that the simulations performed with orthogonal polynomial Chebyshev approximation were appropriate. Finally, based on the results, the netpresent value of water allocated to agriculture at Tabarkabad Dam in the studied period is 1471205 Rials and the allocation of water is equal to 24.745 million cubic meters per year.
Considering the results obtained and the proper approximation of simulated values, we can use the proposed method of this study to solve stochastic dynamic programming problems, especially in the field of water resource management. Also, by using the annual allocation of water and taking account of other regional constraints, we can provide a suitable cropping pattern for the sustainable use of agricultural water for the coming years in the fields covered by the Tabarkabad Dam.