An optimized spatial-temporal-sectoral allocation model for water resources

The deficiency of water resources is limiting directly and severely the social-economic development and ecological environment protection in many regions, and has been exacerbated by rapid industrial growth and national and state agriculture production objectives. Recent national, provincial and local water reform efforts are also focusing on economic efficiency in water allocation. Mathematical modeling in advance is the requirement for scientific decision-making. Water allocation may have different objectives and bases, but in market economy and on the condition of national investment, we should mainly pursue the maximization of economic objectives, except the basic water guarantee for living, ecology and assuring basic production water use. The amount of allocated water is a multi-dimensional variable and can be optimized in many contexts due to differences in the definition of industrial structure, the technical level of production among different areas and the marginal revenues of water resources. Therefore, the problem of water allocation comes down to solving problems of spatial optimization. This paper presents an equating marginal revenue theory for spatial allocation of water resources: when the marginal revenues of water in all area have the same value, the economic benefit from water for all the intake areas reaches its maximum. When the local available water resources and the marginal revenue of water for all sub-areas are given, for different total water supply from outside, we may calculate the optimized dynamic allocation scheme, the sequence of water allocation starting and the economic benefit from the water allocation for different sub-areas, as well as the integrated maximum economic benefit from water utilization. The example of the six southern districts in Hebei province of China illustrates the feasibility of the theory and models. This revised version was published online in August 2006 with corrections to the Cover Date.