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THE LOGNORMAL DISTRIBUTION AND USE OF THE GEOMETRIC MEAN AND THE ARITHMETIC MEAN IN RECREATIONAL WATER QUALITY MEASUREMENT
Citation:
WYMER, L. J. AND T. J. WADE. THE LOGNORMAL DISTRIBUTION AND USE OF THE GEOMETRIC MEAN AND THE ARITHMETIC MEAN IN RECREATIONAL WATER QUALITY MEASUREMENT. Chapter 6, Larry Wymer (ed.), Statistical Framework for Recreational Water Quality Criteria and Monitoring. John Wiley and Sons, LTD, , Uk, , 91-112, (2007).
Impact/Purpose:
The objectives of this research are: (1) to evaluate rapid state-of-the-art measuement methods of pathogens that may indicate the presence of fecal pollution in recreational waters (beaches); (2) to obtain, jointly with a sister laboratory (NHEERL), a new set of water quality data and related health effects data at a variety of beaches across the U.S., in both marine and non-marine waters; (3) to analyze the research data set to evaluate the utility of the tested measurement methods, the new EMPACT monitoring protocol, and the health effects data / questionnaire, in order to establish a relationship between measured pathogens and observed health effects; and (4) to communicate the results to the Office of Water in support of their efforts to develop new state and/or federal guidelines and limits for water quality indicators of fecal contamination, so that beach managers and public health officials can alert the public about the potential health hazards before exposure to unsafe water can occur.
Description:
Since 1968 United States recreational water quality criteria have set a limit on the geometric mean for fecal indicator bacteria from a number water samples taken over a period of time (National Technical Advisory Committee, 1968; U.S. Environmental Protection Agency, 1976 and 1986). On the other hand, for purposes of determining limits on effluents, including sewage, discharged into surface waters, the U.S. EPA specifies that calculations for all limitations which require averaging of measurements shall utilize an arithmetic mean unless otherwise specified by the Director in the permit (U.S. EPA, 1980, 2003). These limits, a geometric mean criterion for beaches and arithmetic mean for discharges, both pertain to provisions of the Clean Water Act of 1977 (CWA) as amended by the Beaches Environmental Assessment and Coastal Health (BEACH) Act of 2000. In addition to this disagreement between types of means that are used in beach monitoring and those used in limiting discharges, a trio of paper published in the late 1990's evaluated uses of the geometric mean and reached conclusions such as the use of this statistic is inappropriate for characterizing risk (Haas, 1996) and geometric means should be phased out as regulatory criteria as soon as it is practical (Parkhurst, 1998a). Statements such as these serve to further create doubt about the appropriateness of geometric means in the minds of federal and state regulators and stakeholders.
This chapter examines criticisms of the use of the geometric mean in risk assessment and environmental monitoring and evaluates its relevance to risk-based recreational water monitoring. Reasons for using the geometric mean (or rather the mean of the logarithms of the indicator densities, as we shall see) in modeling risk attributable to swimming in contaminated waters are explored and alternative models examined.
In the course of this discussion, we will refer to properties of the normal and lognormal probability distributions. For reference, a comparison of some characteristics of normal and lognormal distributions is presented in Table 1. The interested reader can find more detailed information and discussions in Crow and Shimizu (1988), Aitchison and Brown (1969) or Johnson and Kotz (1970) among other works. Estimation of lognormal parameters specifically in the context of environmental monitoring is discussed in Gilbert (1987).