Water Resources Management

, Volume 33, Issue 1, pp 423–437 | Cite as

Improved Water Allocation under Limited Water Supplies Using Integrated Soil-Moisture Balance Calculations and Nonlinear Programming

  • Bennie GrovéEmail author


Water allocation under limited water supplies is becoming more important as water becomes scarcer. Optimization models are frequently used to provide decision support to enhance water allocation under limited water supplies. Correct modelling of the underlying soil-moisture balance calculations at the field scale, which governs optimal allocation of water is a necessity for decision-making. Research shows that the mathematical programming formulation of soil-moisture balance calculations presented by Ghahraman and Sepaskhah (2004) may malfunction under limited water supplies. A new model formulation is presented in this research that explicitly models deep percolation and evapotranspiration as a function of soil-moisture content. The new formulation also allows for the explicit modelling of inefficiencies resulting from nonuniform irrigation. Modelling inefficiencies are key to the evaluation of the economic profitability of deficit irrigation. Ignoring increasing efficiencies resulting from deficit irrigation may render deficit irrigation unprofitable. The results show that ignoring increasing efficiencies may overestimate the impact of deficit irrigation on maize yields by a maximum of 2.2 tons per hectare.


Deficit irrigation Nonlinear programming Optimization Soil-moisture balance Water allocation 



The paper is based on research being conducted as part of a solicited research project, Long-run hydrolic and economic risk simulation and optimization of water curtailments (K5/2498//4), that is initiated, managed and funded by the Water Research Commission (Water Research Commission 2015). Financial and other assistance by the Water Research Commission are gratefully acknowledged.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Agricultural EconomicsUniversity of the Free StateBloemfonteinSouth Africa

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