Stormwater Quality Descriptions using the Three Parameter Lognormal Distribution
The cumulative probability distribution used to describe the variability of stormwater pollutant concentrations has been a matter of interest in recent years. Many predictive models attempt to estimate appropriate stormwater constituent concentrations based on land use and the amount of impervious area. The most important study that characterized stormwater was the Nationwide Urban Runoff Program (NURP) (EPA 1983). NURP was conducted throughout the U.S. and included about 2300 events from 1978 through 1982. One of the conclusions of the final NURP report was that the event mean concentrations (EMCs) of stormwater constituents were described by lognormal distributions. This finding has been re-evaluated recently, with the conclusion that not all stormwater constituents are adequately described by lognormal distributions (Van Buren, 1997; Beherra, 2000).
Stormwater managers have generally accepted the assumption of lognormality of stormwater constituent concentrations between the 5th and 95th percentiles. Based on this assumption, it is common to use the log-transformed EMC values to evaluate differences between land use categories and other characteristics. Statistical inference methods, like estimation and test of hypothesis, and analysis of variance (ANOVA) require statistical information about the distribution of the EMC to evaluate these differences. The use of log-transformed data usually includes the location and scale parameter, but a lower bound parameter is usually neglected. In this chapter, a large database, the National Stormwater Quality Database v.1.1 (NSQD) (Pitt, et al. 2003), will be used to evaluate a three-parameter lognormal distribution for stormwater constituent concentrations for different land uses. The NSQD is a compilation of the phase 1 data from the stormwater permit program. This chapter will also evaluate this national data for the presence of unusual elevated values and their effect on the goodness of fit for the three parameter lognormal distribution.
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