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

Abstract

Operation of reservoirs is a fundamental issue in water resource management. We herein investigate well-posedness of an optimal control problem for irrigation water intake from a reservoir in an irrigation scheme, the water dynamics of which is modeled with stochastic differential equations. A prototype irrigation scheme is being developed in an arid region to harvest flash floods as a source of water. The Hamilton-Jacobi-Bellman (HJB) equation governing the value function is analyzed in the framework of viscosity solutions. The uniqueness of the value function, which is a viscosity solution to the HJB equation, is demonstrated with a mathematical proof of a comparison theorem. It is also shown that there exists such a viscosity solution. Then, an approximate value function is obtained as a numerical solution to the HJB equation. The optimal control strategy derived from the approximate value function is summarized in terms of rule curves to be presented to the operator of the irrigation scheme.

Identification of nominal release policies implemented in a multi-purpose water reservoir

“…Stochastic dynamic programming (SDP) theory is the general framework to establish reservoir operation policies, as explored decades ago (Heidari et al 1971;Tejada-Guibert et al 1993, 1995Yakowitz 1982). The SDP typically provides optimal operation policies with thresholds of opening valves or switching pumps (Nop et al 2021;Unami, Mohawesh 2018;Unami et al 2019b). However, reservoir operators generally do not accept such theoretically generated policies but instead rely on their empirical knowledge to make decisions when unexpected risks are involved (El-Shafie et al 2014).…”

Bounding linear rainfall-runoff models with fractional derivatives applied to a barren catchment of the Jordan Rift Valley

“…However, developing an appropriate hydrological model is not an easy task when attempting to represent dynamic causality based on time series data with a finite sampling interval, so that the model is applicable to practical problems of risk assessment or water resources management. So far, the authors have used the zero-reverting Ornstein-Uhlenbeck process for drought risk assessment (Sharifi et al, 2016), the Langevin equation for water flow index in irrigation water management (Unami and Mohawesh, 2018), and WGEN (Richardson and Wright, 1984) for optimal reservoir operation with a continuous state variable (Fadhil, 2018). The Langevin equation can be utilized for hydrological extreme value analysis as well (Rosmann and Dominguez, 2018).…”

Statistical analysis of flash flood events for designing water harvesting systems in an extremely arid environment

“…A barren catchment area A C of 1.12 km 2 (Figure 1) yields flash floods several times a year, and hydraulic structures have been constructed at the outlet to harvest them as designed in Sharifi et al (2015). Runoff is fully collected at a gutter cutting across a 16 m wide valley bottom and then guided to an open-air reservoir of 1000 m 3 capacity through a conveyance channel 60 m long (Unami & Mohawesh, 2018). The conveyance channel is equipped with a spillway to release excess backwater from the reservoir.…”