Stochastic control of a micro-dam irrigation scheme for dry season farming

Abstract

Micro-dams are expected to be feasible options for water resources development in semi-arid regions such as the Guinea savanna agro-ecological zone of West Africa. An optimal water management strategy in a microdam irrigation scheme supplying water from an existing reservoir to a potential command area is discussed in this paper based on the framework of stochastic control. Water intake facilities are assumed to consist of photovoltaic pumping system units and hoses. The knowledge of current states of the storage volume of the reservoir and the soil moisture in the command area is fed-back to the intake flow rate. A system of two stochastic differential equations is proposed as a model for the dynamics of the micro-dam irrigation scheme, so that temporally backward solution of the Hamilton-Jacobi-Bellman equation determines an optimal control, which represents the optimal water management strategy. A computational procedure using the finite element method is successfully implemented to provide comprehensive information on the optimal control. The results indicate that the water initially stored in the reservoir can support full irrigation for about 80 days under the optimal water management strategy, which is predominantly based on the demand-side principle. However, the volatility of the soil moisture in the command area must be reasonably small.

A multi-state Markov chain model for rainfall to be used in optimal operation of rainwater harvesting systems

“…Further review of reservoir optimization was also conducted by El-Shafie et al (2014). More comprehensive hydrological and water requirement dynamics oriented for the operation of RWH systems can be described with continuous-time Markov process models using stochastic differential equations (Unami and Mohawesh, 2018;Unami et al, 2015;Unami et al, 2013). Unami et al (2013) considered stochastic water demand in a micro-dam irrigation scheme.…”

“…More comprehensive hydrological and water requirement dynamics oriented for the operation of RWH systems can be described with continuous-time Markov process models using stochastic differential equations (Unami and Mohawesh, 2018;Unami et al, 2015;Unami et al, 2013). Unami et al (2013) considered stochastic water demand in a micro-dam irrigation scheme. Unami et al (2015) proposed to utilize the Langevin equation for representing the general water flow dynamics in RWH systems, and Unami and Mohawesh (2018) showed that the mean-reverting property of the Langevin equation plays an essential role in establishing well-posedness of optimal control problems for operating RWH systems.…”

A unique value function for an optimal control problem of irrigation water intake from a reservoir harvesting flash floods

“…The performance index to be minimized is the expected deficiency of water in the future. In the present paper, we attempt to establish well-posedness for such an optimal control problem with mathematical rigor, which is lacking in earlier practical papers on relevant topics (Unami et al 2013(Unami et al , 2015Sharifi et al 2016).…”