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

AUTHORSAUTHORSWayne OttNeil Klepeis

Paul SwitzerDon Rozenberg

CONTRIBUTORSCONTRIBUTORSGeorge AngusKaren JohnsonLee LanganPeggy McClure

Mary RozenbergPamela ShreeveLaure Yadon

Department of StatisticsStanford University

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

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 )

Modeling ApproachModeling Approach(Piecewise-Constant Inputs and Piecewise-Exponential Outputs)(Piecewise-Constant Inputs and Piecewise-Exponential Outputs)

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

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

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

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.

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

ArbitraryParameters

OptimalParameters

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)

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)

Error Surface Slices at Fixed Alpha ValuesError Surface Slices at Fixed Alpha Values

Indoor Predicted vs. Indoor MeasuredIndoor Predicted vs. Indoor Measuredat Redwood City House, 17-1/2 Daysat Redwood City House, 17-1/2 Days

MeasuredMeasuredOutdoor,Outdoor,

MeasuredMeasuredIndoorIndoorPPAHPPAH

Predicted Predicted Indoor,Indoor,

Measured Measured IndoorIndoor PPAH PPAH

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 " "

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

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

• 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

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