Stochastic modelling and control of rainwater harvesting systems for irrigation during dry spells

• Rainwater harvesting systems improve agricultural productivity if properly managed.
• We propose a novel stochastic model using the Langevin equation.
• Computational methods are detailed to apply the model to real life problems.
• Rule curves are prescribed for a system to be constructed in Jordan Rift Valley.

A generic rainwater harvesting system including a catchment area and a command area is often equipped with rainwater storage tanks. The stochastic nature of precipitation dominates water balance of rainwater harvesting systems, and the theory of stochastic control better serves for determining optimal strategies for water management. A mathematical model consisting of stochastic differential equations, with few model parameters that can be identified from observed data, is developed to describe dynamics of rainwater harvesting systems for irrigation. Stochastic control problems are formulated and then solved to obtain the optimal irrigation strategies during dry spells. This procedure can be inversely applicable to designing dimensions of a system. Identification of the model parameters is demonstrated with the data observed in an experimental micro rainwater harvesting system in Japan as well as in semi-arid savanna of Ghana. Then, a real life application is discussed in the context of the Jordan Rift Valley, where a rainwater harvesting system will be developed.