Original Paper

Stochastic Environmental Research and Risk Assessment

, Volume 27, Issue 1, pp 77-89

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • Koichi UnamiAffiliated withGraduate School of Agriculture, Kyoto University Email author 
  • , Macarius YangyuoruAffiliated withInstitute of Agricultural Research, University of Ghana
  • , Abul Hasan Md. Badiul AlamAffiliated withGraduate School of Agriculture, Kyoto University
  • , Gordana Kranjac-BerisavljevicAffiliated withUDS International, University for Development Studies


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 micro-dam 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.


Micro-dam irrigation Dry season farming Stochastic control Hamilton–Jacobi–Bellman equation Finite element method