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Continuous Measurements of Continuous Measurements of Indoor-Outdoor Particulate PAH Indoor-Outdoor Particulate PAH
Concentrations in 7 Homes Concentrations in 7 Homes with Application to the with Application to the
Indoor Mass-Balance Model Indoor Mass-Balance Model and and
Prediction ErrorPrediction Error
14th Annual Conference of the International Society of Exposure Analysis, Philadelphia , PA
Paper No. W2A-04October 21, 2004
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AUTHORSAUTHORSWayne OttNeil Klepeis
Paul SwitzerDon Rozenberg
CONTRIBUTORSCONTRIBUTORSGeorge AngusKaren JohnsonLee LanganPeggy McClure
Mary RozenbergPamela ShreeveLaure Yadon
Department of StatisticsStanford University
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Indoor-Outdoor ModelIndoor-Outdoor Model• Derived from Mass-Balance Equation• Theoretical Basis, Exact• Equally-Spaced Time Steps• Outdoor Concentrations as Input• Only Two Parameters Required• Predicted Indoor Concentration
Compared with Measured Indoor Concentration
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Hi Yi(1 ) H i 1
i 1,2,...
where paa k
Recursive Indoor-Outdoor Model for PMRecursive Indoor-Outdoor Model for PM
e (a k )
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Modeling ApproachModeling Approach(Piecewise-Constant Inputs and Piecewise-Exponential Outputs)(Piecewise-Constant Inputs and Piecewise-Exponential Outputs)
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Persistence Parameter Persistence Parameter for Different Combinations for Different Combinations of a and k for 1-min Time Stepof a and k for 1-min Time Step
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Indoor Persistence Parameter Indoor Persistence Parameter versus (a + k) versus (a + k) for 1-min and 5-min Time Stepsfor 1-min and 5-min Time Steps
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METHODMETHOD• Measure Continuous Outdoor and Indoor
Total Particulate PAH (< 1 m)• Combustion Sources, Little Humidity Effect • Occupied, Nonsmoking Homes• Find Optimum Values of , • Compare Predicted Indoor Concentration
with Measured Indoor Concentration• For , , Calculate Ranges of a, k, and p
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Table 1Table 1Characteristics of 7 Homes Selected for Indoor-Outdoor
Field Measurement Study (5-min time steps)No. Location County Style Size (ft2) Duration1 Corte Madera Marin 1-story, 3-bedroom
ranch style home1,300 11 days
2 SanFrancisco 1Calif. Ave.
SanFrancisco
4-story, attachedhome
6,600 11 days
3 SanFrancisco 2North Beach
" 4-story, attachedhome
1,000c 3-1/2 daysb
4 Burlingame San Mateo apartment in aretirement building
for the elderly
148 3 days
5 RedwoodCitya
" 4-bedroom, 2-storydetached home
2,100 9 months,4 Periodsb
6 Palo Alto SantaClara
efficiency apartment 460 3 days
7 San Jose " 2-story, 5-bedroomdetached home
3,800 19 days
aCentrally located test home; b1-min averages; cArea of a single level.
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Outdoor and Indoor PPAH, New Year’s Day Outdoor and Indoor PPAH, New Year’s Day San Francisco House No. 2San Francisco House No. 2
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ArbitraryParameters
OptimalParameters
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Error Surface for Indoor Model Prediction Versus Error Surface for Indoor Model Prediction Versus Indoor Measurement at San Francisco House No. 2Indoor Measurement at San Francisco House No. 2
( 1-min step time for 3.5 days)( 1-min step time for 3.5 days)
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Error Surface for Data at Redwood City HouseError Surface for Data at Redwood City House1994 - 19951994 - 1995
(17.5 days, 5-min time step)(17.5 days, 5-min time step)
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Error Surface Slices at Fixed Alpha ValuesError Surface Slices at Fixed Alpha Values
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Indoor Predicted vs. Indoor MeasuredIndoor Predicted vs. Indoor Measuredat Redwood City House, 17-1/2 Daysat Redwood City House, 17-1/2 Days
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MeasuredMeasuredOutdoor,Outdoor,
MeasuredMeasuredIndoorIndoorPPAHPPAH
Predicted Predicted Indoor,Indoor,
Measured Measured IndoorIndoor PPAH PPAH
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Table 2Table 2
Values of a,k, and p Giving Same Optimal and in Redwood City House
(a,k in hr—1 with 5-min time step)a k p
0.27 0.24 1.0 0.5343 0.9593
0.30 0.20 0.89 " "
0.35 0.15 0.76 " "
0.4 0.1 0.67 " "0.5 0.0 0.53 " "
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Table 3Table 3
Optimal Values of for Houses with1-min Sampling Times
Location Hours Mean Abs.Error, ng/m3
S.F. House 23-1/2 days
84 0.436 0.981 1.5
S.F. House 2Day 1
24 0.364 0.967 1.8
S.F. House 2Day 2
24 0.509 0.967 2.0
S.F. House 2Day 3
24 0.436 0.967 0.8
Redwood City2002-03
245 0.426 0.990 0.9
Redwood City2003-04
404 0.454 0.993 1.2
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Table 4Table 4Optimum Values of and for Houses with
5-min Sampling TimesHouse/Apt. Time Mean Abs.
Error, ng/m3
Corte Madera 9 days 0.630 0.920 10.2
S. F.House 1
11 days 0.700 0.875 3.5
Burlingame 11 days 0.857 0.932 2.3
Redwood City,1994-95
17.5 days 0.534 0.959 1.6
Redwood City,1995-96
26.7 days 0.571 0.952 1.7
Palo Alto 74 hours 0.525 0.936 1.2
San Jose 11 days 0.600 0.975 2.3
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• Predicting indoor particle concentrations of ambient origin using the mass balance model requires only two parameters, and .
• Using three parameters a, k, and p in the indoor mass balance model is algebraically redundant.
p aa k
, e (a k )
DISCUSSIONDISCUSSION
H i Yi(1 ) H i 1
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CONCLUSIONSCONCLUSIONS• Continuous Indoor-Outdoor PPAH
Measurements in 7 Occupied Homes• Field Study Covered 10 Years• Indoor Model-Predicted Agreed Well with
Indoor Measured at All Homes• Fireplaces and Wood Burning were the
Major Sources of Ambient Particulate PAH• Motor Vehicles were a Minor Source• Indoor Model with 3 Parameters
(a, k, and p) is Over-specified