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TreadwelEJUlo <br /> A LANOAN.COMPANY <br /> Attachment 5 s <br /> Regression Analysis for Benzene <br /> 420 and 423 N Madison Street' <br /> Stockton,California <br /> MW-21A MW-21A <br /> 1600 -- - 5.6 <br /> —h—Benzene <br /> 1400 In(Benzene) <br /> 1200 ------ - s 5.4 <br /> c <br /> —Theil-Sen " <br /> c Soo Trend m 5.2 <br /> 600 Line c <br /> —in(Benzene) <br /> c m - Regression <br /> m 400 —First- -c"5'0 Line <br /> 200 order <br /> 0 - Decay 4.8 <br /> Trend o 0 0 0 0 0 0 0 <br /> m m m o 0 0 <br /> N O Ol O N N ..011 N N O <br /> O O N <br /> \ \ O \ \ <br /> m \ \ v m o 0 0 0 0 <br /> 0 0 " Sample Date o o ~ Sample Date <br /> Figure 1:Plot of benzene concentrations at well MW-21A at 423 Figure 2:Log-plot of Benzene concentrations at well MW-21A. The <br /> Madison. Trend line(red)shows the decrease in concentration linear regression line was calculated using ProUCL for the log of the <br /> over time and was calculated using the Theil-Sen method in PrOUCL concentrations to determine the first-order decay rate constant <br /> (USEPA,2011). The Theil-Sen method is non-parametric and (USEPA,2002). The equation for the line shown on this figure is as <br /> robust to outliers(USEPA,2009)and was chosen in this case due follows: <br /> to the outlier of 1,500 pg/L on 2/8/2000. A curve showing first- In(Benzene)=(19.0 In(µg/L))+(-3.7 x 10-4Day')(Date) <br /> order decay is also shown on the plot(purple)and was calculated <br /> as described in Figure 2. The Theil-Sen Trend Line equation is as - - _(19.n In(µg/,))+(-1.4 x 10-'Vear')(Year) <br /> follows: <br /> The fitted concentrations were plotted on Figure 1 using the following <br /> (Benzene)=(1298ug�1)+(-0.030u9�L•Day)(Date) equation: ` 1 <br /> {tg -3.7x10-Da- (Date) <br /> (Benzene)_�19.O In( �L))+e ( Y ) <br /> MW-21A CPT-EXC-W —$—Benzene <br /> 250 — so <br /> 200 - tBe nzene 40 —Theil-Sen <br /> Trend Line <br /> 150 30 <br /> m .. —First-order <br /> w 100 -- Linear m 20 Decay <br /> m _ Regression 'm <br /> t° s0 Trend Line 10 —Linear <br /> Regression of <br /> 0 <br /> 0 - Recent Data <br /> rn m a m. in o 1D <br /> o o O o \ o o o .r ,� N m m <br /> \ ti \ \ —MCL <br /> .2 <br /> Sample Date o Sample Date o <br /> Figure 3:Plot of recent benzene concentrations beginning Figure 4:Projected decrease over time from the detected <br /> 5/10/2000 at MW-21A. This date range excludes the non-detect concentration of benzene at 420 Madison in sample CPT-EXC-W. The <br /> from 11/9/1999 and the large outlier from 2/8/2000 so an rate of decrease in benzene concentration with time was calculated <br /> ordinary least-squares linear regression can be used to estimate three different ways as described for Figures 1 through 3. A line at the <br /> the decrease of concentration with time. The resulting fitted line is MCL for benzene(1 pg/L)is also shown. The extrapolations show that <br /> shown in the following equation: the expected time for benzene to reach water quality goals for <br /> groundwater at.this Site ranges from less than two years from the date <br /> (Benzene)=(2621ugJL)-+(-0.066iag/j.Day)(Date) that the sample was collected in 2004 to approximately.28 years. <br /> References: <br /> U.S.Environmental Protection Agency(USEPA).(2002).Groundwater issue,Calculation and Use of First-Order Rate Constants for Monitored natura/Attenuation <br /> Studies:November. <br /> U.S.Environmental Protection Agency . 2009).Statistical Ana"is of Groundwater Monitoring Data at RCRA Facilities,Unified Guidance,EPA 530/R-09- <br /> 9 cY(USEPA} <br /> 007.March. <br /> U.S.Environmental Protection Agency(USEPA):(2011).PmUCL 4.1.01.12.July. <br /> htti)'//www.epa.Qovlosp/hsd/tsclsoftware.htm- <br /> Proj.No.731589001 - Page 1 of 1 24 May 2013 <br />