tration in milligrams per kilograms (mg/kg) as the independent variable and the normal standard variate of the population as the dependent variable using the methods described in Section 3.1 (see URS Greiner, Inc. and CH2M Hill 2001, Fig. A-11).
On a lognormal CFD plot, a pooled data set containing both background and contaminant concentrations will ideally show two distinct populations identifiable by their distinct slopes, separated by a transition zone of rapidly escalating concentrations. The population with lower concentrations represents background, while the population to the upper right of the distribution is taken to represent contaminated sediments.
No clearer definition of what is considered background is provided; it appears from the procedures adopted that the “distinct population” with lowest concentration is assumed to be the distribution of background concentrations, and this is how we interpret the data below. It is not described how “the pooled data was identified as lognormal,” but they clearly are not for any COPC. Single lognormal distributions would plot as approximately a single straight line on the plots constructed,1 and the pooled data clearly do not fall along such single straight lines.
It appears to be implied that the observed data are necessarily a probabilistic sum of two lognormal distributions that would plot as two distinct straight lines. However, this implication is false. A probabilistic sum of two lognormal distributions does not plot as two straight lines, and there is no guarantee that there are only two component distributions, nor is there a guarantee that any component distributions are lognormal. In practice, the data on individual COPCs often show plots that approximate the description given in Step 2, and the distributions for individual COPCs often can be approximated as a sum of lognormals, but it is not necessarily possible to discern by eye on such plots how many component lognormals are necessary to fit the data adequately.
Practically, there is reason to suggest that the assumption of two populations—background and contaminated sediments—is too simplistic, especially considering the environment being modeled. These proposed sediment populations would exist in a continuum with each other and vary greatly through time as background sediments and tailings interacted in varying proportions based on the dynamic interaction of flooding events,
The “normal standard variate” described in the first paragraph of Step 1 is an approximation to the expected value of the order statistic for a normal distribution. One of the best available omnibus tests for normality makes use of the correlation coefficient calculated between (better approximations for) the expected values of these order statistics and measured data, using empirically derived curves to associate correlation coefficients with probabilities (Royston 1993, 1995).