Using penalty functions to evaluate aggregation models for environmental indices.

The purpose of indices is to summarize a large volume of information into a single number that is easy to understand and interpret. Environmental indices provide a composite picture of an environmental condition derived from a series of observed measurements and parameters. They are used as communication tools by regulatory agencies to characterize the state of a specific environmental system (air, water, and sediments) and to study the impact of regulatory policies on various environmental management practices. In the development of environmental indices, a few issues and problems have been encountered arising as a result of the abstraction of information and data. These problems are referred to as characteristic properties that include ambiguity, eclipsing, compensation and rigidity. These characteristic properties have long been identified and interpreted in Boolean (e.g., Yes/No) or qualitative (e.g., low, medium, high) terms. In this paper, we propose a new approach to describe the above stated characteristic properties on a continuous scale to evaluate and compare the behavior of various aggregation models. Our approach is based on developing penalty functions for each characteristic property. A water quality index example by Swamee and Tyagi (2000) is used to explain our approach. A detailed case study for a developing microbial risk index is also provided to show how the proposed approach can be extended to complex hierarchical systems. Results show that it is possible to improve aggregation models for index development. Future research directions to improve index development are also discussed. 2009 Elsevier Ltd. All rights reserved.