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OCR for page 90
Appendix C Calculation of Air Exchange Rates Air exchange rates are defined in terms of a general one-compartment model of air exchange with immediate and perfect mixing of air inside residences. For any contaminant in the assumed well-mixed pool of air in the living spaces, this leads to an expectation of simple exponential decline of air con- centrations with time: C(t) = C(O)e~kt, where C(O) is the initial concentration of the contaminant inside the house, C(t) is the concentration of the contaminant at any specific time after t = 0, and k is a rate constant in units of reciprocal time (i.e., if time is expressed in hours, k is in reciprocal hours, or, by convention, "air changes per hourly. The relationship between the rate constant k and the half-life (the time re- quired to reduce the air concentration by haTi) is easily derived by setting C(t) to one-half of C(O): C ~ t ~ , 2 ~ = . 5 C ~ O ~ = C ~ O ~ e - ~ / 2 After the cancellation of the C(O)'s, and taking the natural logarithm of both sides of the equation: In(.5) = - kit, to= In(2~/k or k = In(2~/t~,2 90

OCR for page 90
PUBLIC ACCESSMATE~ALS 9] ILLUSTRATIVE LOGNORMAL TREATMENT OF DATA FOR SELECTED OCCUPATIONAL EXPOSURES Figure A- ~ shows Tognormal probability plots of the individual data points for several groups of workers in the shallow-shank tarp method application of methyl bromide. In this type of plot, correspondence of the points to the re- Lognormal plow of adjusted 24-hr exposure data for shallow shank-brped soil fumigation workers / 3.0 - o o 2.0 l 1.5 1.0 ,'~ / it/ _' I' . by/ / ~ Add/ o,,y/,: ~~ ~7 // a,./- ~ // ~',,~W y = 2.24 ~ 0.374x R2 = 0.886 C] Copilots y= 1.91 +0.426x R2=0.977 Applicators y= 2.06 ~ 0.284x R2=0.880 ~ Shovelmen y = 2.93 ~ 0.226x R2 = 0.963 ~ Tarp removem , -2 -1 0 1 2 score FIGURE A-1

OCR for page 90
92 METHYL BROMIDE RISK CHARACTERIZA TIONIN CALIFORNIA gression line is a quick qualitative indicator of the degree to which the data points are well described by the chosen distribution. in these cases, the fits are far Mom perfect, suggesting some possible heterogeneity in the data, but the Tognormal plots in Figure AM are generally better than corresponding nor- mal distribution fits (Figure A-2~. For these same worker groups, Table A-! below compares the reported highest observed values with 95th percentile values calculated from the fitted nominal and lognormal distributions. In gen- eral, the lognor~nal fits project somewhat higher 95th percentiles than the nor- mal fits. TABLE A-1 Comparison of Observed Values with 95~ Percentile Values . Occupational Group Nu 7~7 Data Points Observed Acute Calculated Calculated from (Including (24 fir) Exposure from Normal Lognormal Fit Non-Detects) Fit 479 293 330 1820 Copilots Applicators Shovelmen Tan' Removers 7 8 10 s 518 303 515 _659 716 408 337 1990

OCR for page 90
PUBLIC ACCESS MA TERIALS 93 Dam from "MB exposure data" y = 223.71 ~ 155.22x R2 = 0.890 y = 102~49 ~ 11614x R2 = 0.933 y = 147.00 ~ 111.49x R2 = 0.605 y = 873.75 ~ 574.70x R2 = 0.911 ,' o = Q o ~ / 1000 - O - / /A Q 2 -1 0 1 2 Z-Score Figure A-2 O C - be , ... LL 8 ~ T"