Characterisation of basin water allocation benefit function using a sigmoid-type S-curve logistic equation

Abstract

As water allocation (WA) is reduced due to water scarcity in a river basin, the benefit function for the domestic water users and the economic sectors declines accordingly. Using the sigmoid-type equation, which is ubiquitous in natural and man-made systems, this study shows that the S-curve behaviour can be seen in a broad range of basin WA scenarios. A questionnaire survey reveals that progressive water supply cutback results in a mild initial hassle but builds up to an elaborate inconvenience and subsequently a diminished shock to the water users. The economic benefit of water consumption based on 8-year data of states in Malaysia shows evidence of the S-curve characteristics where lesser developed states tend to benefit more as water consumption increases. The model allows the sectorial benefit (and impact) level to be approximated as a function of basin water availability. The mathematical quantification, in lieu of qualitative descriptors, is useful as an integral component in water prioritisation and WA decision-making to provide an empirical assessment of optimum basin-wide benefit. HIGHLIGHTS A sigmoid-type mathematical model for water allocation (WA) benefit is introduced.; We show that data of social and economic benefit evaluation fall into the S-curve pattern.; We identify the different zones of the S-curve with descriptive meaning.; The model can be used for the quantitative evaluation of WA benefits in decision-making.;

Keywords

• benefit function
• logistic function
• s-curve
• sigmoid function
• water allocation