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Evaluation of Natural Attenuation: 7500 West Eleventh Street, Tracy, CA. Page 45 <br /> stability based on changes of the distribution of the mass of analytes of concern within <br /> y the plume with time. <br /> Natural attenuation of analytes of concern within the plume can be expected to <br /> approximate a first order exponential decay if the plume is stable and analyte <br /> .:� concentrations are decreasing. However, this simple relationship can be obscured by data <br /> !` scatter related to such phenomena as variations in analyte concentrations with rise and <br /> fall of groundwater levels. It is, therefore, necessary to assess the "goodness of fit" of a <br /> regression curve drawn through the data from any given well. If the fit is poor, as <br /> characterized by a low correlation coefficient, then a data trend cannot be established <br /> with confidence. The MAROS software computes the correlation coefficient to determine <br /> whether a data trend can be established with an adequate level of confidence. The <br /> procedure used by the software is essentially similar to the trend lines used by SJC to <br /> evaluate the history of analyte concentrations in such wells as MW-3 that are illustrated <br /> on Figures 20-30. <br /> The Mann-Kendall test is a statistical procedure that is well-suited for analyzing trends in <br /> data over time (Gilbert 1987). It is a non-parametric test for the zero slope of the first- <br /> >' order regression of time-ordered concentration data vs. time. It does not require any <br /> assumptions as to the statistical distribution of the data (e.g., normal, lognormal, etc.) and <br /> 11 can be used with data sets that include irregular sampling intervals and missing data. The <br /> MAROS software applies a very conservative decision-maker for characterizing the <br /> results of the Mann-Kendall test. For example, for the «ond of an analyte in a given well <br /> to be classified as "increasing" or "decreasing," the slope of the trend must be greater <br /> than zero or less than zero with a confidence of greater than 95%. Trends are classified as <br /> "probably increasing" or "probably decreasing" if the slope of a trend line can be <br /> determined with a confidence of 90-95%. In cases where the trend line cannot be <br /> computed with a confidence of 90% or more, the data is classified as having "no trend." <br /> The results of the plume stability analysis are presented in the MAROS Plume Analysis <br /> Summary presented in Appendix A. Examination of that table shows that, for the BTEX <br /> compounds and MTBE, linear regression analysis shows that the time/concentration data <br /> are, with minor exceptions, either decreasing, stable or have no trend. When the more <br /> sophisticated Mann-Kendall results are considered, no analyte in any of the wells has a <br /> trend vs. time that is classified as "increasing," nor even "probably increasing." These <br /> results demonstrate that the primary plume emanating from the 7500 West Eleventh <br /> Street Site is stable, as SJC has previously concluded, based on conventional plume <br /> stability observations, such as those described in Section 7.1.2 of this report. <br /> To further evaluate the condition of a plume and assess whether it is stable or shrinking, <br /> the MAROS software computes the moments for each sampling event. The primary <br /> moment calculation is the calculation of the zeroth moment, an estimate of the dissolved <br /> mass of a given analyte of concern relative to the source of the released fuel (i.e., about <br /> the point of origin of the well coordinate grid). Variations of the zeroth moment of a <br /> —i given analyte over time can show high variability, largely due to fluctuating <br /> concentrations at the most contaminated wells, as well as changes in the number and <br /> sic <br /> j. <br />