中文摘要：

为了建立计算简便、规范统一和普适通用的水资源系统（包括水资源可持续利用系统、水资源承载力系统和水资源安全系统）的评价模型,基于样本之间的质量相似性和距离接近程度构建聚类量,借鉴物理学中的万有引力定律和规范对称性原理,提出水资源系统样本之间也存在与万有引力定律形式相似的聚类相互作用力的思想。在适当设定指标参照值和指标值的规范变换式,并对指标值进行规范变换的基础上,提出了水资源系统的参照级样本、规范质量、规范坐标和规范距离的概念,进一步建立了基于指标规范值的水资源系统评价的引力指数公式,并分析了指数公式的稳定性和可靠性。用若干实例对公式的合理性和实用性进行了效果检验,结果表明：基于指标规范值的水资源系统评价的引力指数公式具有物理意义明确和规范、统一、简洁和通用的特点。

英文摘要：

This study aims to set up a model of water resources systems （including sustainable utilization system, carrying capacity system and safety system of water resources） evaluation, which is simple to calcu- late, normal, unitized, universal and common. In reference to the universal gravitation law and the gauge symmetry principle in physics, it is argued that there are also the thought of interactive force of cluster among water resources system samples that are similar to the universal gravitation, based on the design of cluster amount of quality similarity and the close degree of distance between two samples. This study sets the proper reference values and normalized transformation forms as well as normalized transformations for all indexes, and proposes the concepts of ＂reference grade samples＂, ＂normalized quality＂, and ＂normal- ized coordinate＂ and ＂normalized distance＂ for samples of water resources system. Therefore, it is possible to build the gravitational index formula of water resources system evaluation, based on normalized index val- ues. Furthermore, it is analyzed for the stability and reliability of index formula. The rationality and practi- cability of the formula have been verified by some samples. The results shows that the gravitational index formula of water resources system evaluation based on normalized index values exhibits the characteristics of clear physical meaning, normalization and unity, simplicity in form as well as commonness.