Using Regional Data and Building Leakage to Assess Indoor Concentrations of Particles of Outdoor Origin

Abstract

Time-resolved fine particle concentrations of nitrate, sulfate, and black carbon were examined to assess the appropriateness of using regional data and calculated air exchange rates to model indoor concentrations of particles from outdoor sources. The data set includes simultaneous, sub-hourly aerosol composition measurements at three locations: a regional monitoring site in Fresno, California, inside of an unoccupied residence in Clovis, California, located 6 km northeast of the regional site, and immediately outside of this same residence. Indoor concentrations of PM_2.5 nitrate, sulfate, and black carbon were modeled using varying sets of inputs to determine the influence of three factors on model accuracy: the constraints of the simplified indoor-outdoor model, measured versus modeled air exchange rates, and local versus regional outdoor measurements.

Modeled indoor concentrations captured the lag and attenuation in indoor concentrations as well as the differences among chemical constituents in the indoor-outdoor concentration relationships. During periods when the house was closed and unoccupied, use of air exchange rates calculated from the LBNL infiltration model in place of those directly measured did not contribute significantly to the error in the estimated indoor concentrations. Differences between ambient concentrations at the regional monitoring site and the immediate neighborhood contributed to estimation errors for sulfate and black carbon. Evaporation was the dominant factor affecting indoor nitrate concentrations. Even when limiting the model inputs to concentrations and meteorological parameters measured at the regional monitoring station, the modeled concentrations were more highly correlated with measured indoor concentrations than were the regional measurements themselves.

INTRODUCTION

Epidemiological studies have established a positive relationship between human health effects and outdoor fine particulate matter, as measured at regional monitoring sites (Dockery et al. 1993; Pope et al. 1995). Yet the majority of people's time is spent indoors, much of that in homes (Jenkins et al. 1992; Klepeis et al. 2001). Several investigators have questioned the representativeness of central site outdoor monitoring to personal exposures (Wallace 1996). Indeed, personal exposures to ambient PM_2.5 are found to be more closely linked to indoor concentrations of ambient particles than to regional values (Liu and Nazaroff 2001, 2003; Long et al. 2000). Knowledge of the indoor concentration of PM_2.5 of outdoor origin, especially inside homes, is an important aspect of the assessment of human exposure to ambient particulate matter.

This article presents work conducted as part of an on-going effort to develop a physically based, semi-empirical model for estimating concentrations of outdoor PM_2.5 in homes using regional monitoring data and available information on housing characteristics. Mass balance relationships show that indoor concentrations of outdoor particulate matter depend on outdoor concentrations, building air exchange rates, particle penetration efficiencies, deposition losses, and for volatile compounds, phase transformations. Our approach combines estimates of air exchange rates obtained from the Lawrence Berkeley National Laboratory (LBNL) infiltration model with regional meteorology and time-resolved PM_2.5 chemical composition data to estimate indoor concentrations of PM_2.5 nitrates, sulfates, and black carbon.

The LBNL infiltration model (Sherman 1994; ASHRAE Handbook 2005), and the newer AIM2 model (Walker and Wilson 1998) describe the fundamental relationships between air exchange rates, house properties, and climatological para-meters. Houses are characterized by a “leakage area,” a parameter that has been tabulated for more than 1300 US homes (Sherman and Dickerhoff 1998). The leakage area is determined using the “blower door” method in which a blower is mounted in an outside doorway and the house is pressurized (Sherman 1994). The effective house “leakage area” is derived from the measured dependence of the air infiltration rate on the degree of pressurization. The LBNL infiltration model uses the leakage area together with a general description of the house (floor area, number of stories, height of flues) to estimate air exchange rates as a function of indoor-outdoor temperature differences and wind loading for instances when the house is closed (i.e., all doors and windows shut). In contrast to direct measurements of air exchange rates, “blower door” characterization can be accomplished relatively easily, requiring approximately two hours.

Chemically resolved monitoring of PM_2.5 has evolved dramatically since the introduction by the US EPA of an ambient air quality standard for PM_2.5, with every third day speciation monitoring occurring at approximately 60 sites throughout the United States, augmented in many of these locations by automated, semi-continuous measurements for particle mass. The introduction of many automated methods for aerosol chemical composition monitoring is likely to enrich this data set over the coming years. As demonstrated by Lunden et al. (2003a, 2006), knowledge of chemical composition is crucial because semi-volatile constituents such as ammonium nitrate and organic carbon are repartitioned when transported indoors.

An important question is whether these two types of data sets, namely regional monitoring and housing characteristics, could be combined to provide statistically representative, chemical-specific estimates of indoor concentrations of PM_2.5. In this article, we address the predictive capability of this approach for a single, well-characterized, unoccupied house. Our work is part of a controlled series of experiments in an unoccupied, single story residence in Clovis, California (hereafter termed the Clovis House Study), for which time-resolved particle chemistry, size distributions, and air exchange rates were obtained inside and immediately outside of an unoccupied home (Lunden et al. 2003b). We examine these results together with analogous, time-resolved chemical speciation measurements obtained simultaneously at the regional monitoring site in Fresno, CA, located 6 km distant, obtained as part of the US EPA Supersites program and California Air Resources Board Regional PM10–PM2.5 Air Quality Study.

To date, analyses of the Clovis House Study data set have focused on refinement of the mass balance model, using as inputs the measured air exchange rate and chemically speciated particle concentrations measured directly outside of the residence. Thatcher et al. (2003) describes the size-dependence of penetration efficiency and deposition losses. Lunden et al. (2003a) estimate the rate coefficients for evaporative losses of particulate nitrate when transported indoors. Building on this work, we address the question of how well indoor concentrations can be estimated when utilizing measurements at the central monitoring site in place of those obtained immediately outside the residence. We examine the accuracy of these predictions for the case of a closed house (all windows and doors shut) when using air exchange rates estimated from the LBNL infiltration model and local meteorology.

EXPERIMENTAL

Measurements were made inside and immediately outside a house in Clovis, CA, a suburb of Fresno, as described by Lunden et al. (2003a) and Thatcher et al. (2003). Regional monitoring data were obtained from the California Air Resources Board monitoring station and Fresno Supersite, located 6 km to the southwest of the study house as described by Watson et al. (2000). At each of these three locations, referred to respectively as “indoor,” “proximate outdoor,” and “central site,” the data set included time-resolved data for PM_2.5 nitrate, sulfate, and black carbon. Experiments at the Clovis study house were conducted in October 2000, and December 2000 through January 2001.

The study house is a 134 m², single-story wood-frame dwelling constructed in 1972, with a stucco exterior, slab foundation, single glazed aluminum frame windows, and forced air heating and cooling. The house had an attached garage that was closed off from the main part of the house. The flue damper on the one fireplace in the house was closed throughout the study period. The house leakage area was characterized by blower door measurements (ASHRAE Standard 136, 1993) wherein the air flow into the house is measured as a function of the pressure difference across the building shell. The normalized leakage area was 0.65, as defined in accordance with ASHRAE Standard 119 [see also Sherman (1995), which expresses the normalized leakage as NL = 1000(H/2.5)^.3(ELA)/(FA) where ELA is the effective leakage area, FA the house floor area and H the building height in meters]. This is lower than the average value of 1.2 for US houses, but is similar to the value of 0.55 that characterizes conventional new house construction (Sherman and Matson 1997).

Throughout the three-month study period, ventilation rates at the Clovis study house were measured using sulfur hexafluoride tracer gas, which was released continuously, and monitored by photoacoustic analysis (Breul and Kajer Model 1302). Air exchange rates were derived using a transient mass balance approach that accounts for the injection rate and time-dependent infiltration losses, as described by Thatcher et al. (2003).

At the study house, indoor and outdoor concentrations of black carbon were measured with 20-min time resolution by attenuation of light through a particle deposit on a quartz fiber filter (Hansen et al. 1984). Indoor and outdoor particulate nitrate and sulfate were measured with 10-minute time resolution using the integrated collection and vaporization method (Stolzenburg and Hering 2000; Hering et al. 2003), whereby particles are collected by humidification and impaction, and analyzed by flash-vaporization and quantification of the evolved vapor compounds. Simultaneous indoor and outdoor measurements were obtained using a multicell system that shared a common set of gas analyzers. Due to instrumental difficulties, outdoor sulfate concentrations were not obtained for the January measurement period. The sampling lines and cells for outdoor sampling were mounted within an enclosure through which outdoor air was drawn to maintain near-outdoor temperature at the point of sampling. The outdoor inlets at the residential site were located at a height midway between the house eves and the roof peak. This location was chosen to obtain samples which best represent the particle concentration at the building exterior. During the intensive sampling periods the continuous measurements were supplemented with 12-hour, integrated PM_2.5 filter samples for chemical analyses. Nitrates were measured on denuded, impregnated filters, sulfates on Teflon filters, and carbon on quartz filters.

At the central monitoring site, replicate nitrate measurements were provided by two RP8400N monitors (ThermoElectron, Albany, NY). Sulfate was measured using a pre-release RP prototype equipped with a ThermoElectron 43C sulfur dioxide detector. These commercial instruments employed the same flash vaporization method used at the Clovis study house. Black carbon was measured with a commercial Aethalometer (Magee Scientific), which uses a similar measurement principle as the LBNL black carbon instrument used at the study house. Sample inlets were mounted on the flat roof of a two-story building and extended 2.0 m above the rooftop. Filter measurements were conducted on selected days, in conjunction with the California PM-10 and PM-2.5 Regional Air Quality Study (Magliano and McDade 2001).

MODELING OF INDOOR CONCENTRATIONS

Governing Equations

For conserved, nonreactive constituents, indoor-outdoor concentration relationships are described by the mass balance model:

where C _in,j and C _out,j are the indoor and outdoor concentration of species j, P is the non-dimensional penetration factor, λ is the air exchange rate coefficient (h^{− 1}) and k _dep is the deposition rate coefficient (h^{− 1}) and t is time. For nitrate we add an evaporative loss rate term, C _{in, it NO3} ⁻ k _evap , with its rate coefficient, k _evap to the mass balance

These equations were evaluated using a forward-stepping approach. An initial value is needed for the indoor concentration, from which it evolves in accordance with the mass balance equation. In our analyses the 10-minute concentration data were smoothed using a one-hour running average, and interpolated values were used to fill in data gaps of less than 1 hour. Results depend on the time-dependent outdoor concentrations, air exchange rate, the assumed values for P, k _dep , and k _evap,NO3⁻ , and the initial value for the indoor concentration.

The value for the penetration factor depends on the size distribution of the entering aerosol as well as the flow characteristics through the entering pathways. Similarly, the deposition loss rate depends on the indoor size distribution of the aerosol as well as the flow characteristics within the residence. It is, therefore, expected that both P and k _dep will not be constants, but rather will vary over time according to changes in the size distribution of the outdoor aerosol and indoor aerosol, air-exchange rate, and indoor-outdoor temperature difference. However, there is currently not a sufficient scientific understanding of the influence of these variables to assess these changes. In this study, the model constants, P and k _dep , were taken from the particle rebound work of Thatcher et al. (2003), who measured size-dependent penetration coefficients and deposition velocities in this same house. Since we do not have species-specific size distributions, the size-distribution weighted average of these measurements, P = 0.75 and k _dep = 0.2 hr^{− 1} for the PM_2.5 size fraction are used for nitrate, sulfate and black carbon. These values are within the bounds for fine particles reported by Xu et al. (1994), Mosley et al. (2001), Thatcher et al. (2002), Liu and Nazaroff (2003), Riley et al. (2002), and Bennett and Koutrakis (2006). An estimate of the error introduced by all of the model simplifications employed, including the use of constant P and k _dep , is explored in the detailed modeling case (Model 1).

The value for k _{evap,NO3 −} was taken from the results of Lunden et al. (2003a), who evaluated ammonium nitrate evaporation at the Clovis study house using the measured particle and gas phase concentrations, temperature and relative humidity. Their data were reported for a single, one-week period of the study (January 16–23, 2001) when ammonia and nitric acid concentrations were measured indoors, and the house conditions were purposely manipulated to provide a range of air exchange rates and indoor temperatures. These results show that the driving force for the loss of particulate nitrate is its equilibrium vapor concentration, which is a strong function of temperature. This nitrate loss is further driven by the subsequent loss of gaseous nitric acid by deposition and sorption to indoor surfaces. We fit the results of Lunden et al. for this analysis by the relationship:

where T _in is the indoor temperature expressed in Kelvins, and K is the equilibrium constant for the dissociation of ammonium nitrate, in units of mbars², taken from Mozurkewich (1993). The inverse relationship with T _in facilitates the conversion from units of partial pressure to mass concentration. The values of the power n and the prefactor A are determined by a fit to the data of Lunden, yielding values of n = 0.55 and A = 121.4 (μg K m⁻³ mbar^{− 1.1}).

Modeling Approaches

Three modeling approaches are compared here, as summarized in Table 1. The “Detailed” model uses as many directly measured parameters as are available. The model is initialized using the measured indoor concentrations; the air exchange rate is taken from the SF₆ tracer measurements; outdoor concentrations are from measurements made immediately outside the house; and the nitrate evaporation term is allowed to vary with the measured indoor temperature in accordance with Equation (3). The purpose of Model 1 is to provide a base case for the accuracy of modeling indoor aerosol concentrations using a simplified model that employs all of the detailed data available for this highly instrumented study. This model provides an indication of the impact of the various simplifications needed to allow the model to be evaluated. Other modeling scenarios will be compared to the “Detailed Model” to investigate the importance of additional simplifications on model accuracy.

TABLE 1 Model for inputs to mass balance analysis

Modeling Approach	1: Detailed	2: Central Site with Measured ACH	3: Central Site Only Input Parameter
Input Parameter
P	0.75	0.75	0.75
K dep	0.2 hr^− 1	0.2 hr^− 1	0.2 hr^− 1
K evap	varies with indoor temperature	4.6 hr^− 1 for Oct 1.6 hr^− 1 for Dec-Jan	4.6 hr^− 1 for Oct 1.6 hr^− 1 for Dec-Jan
Initialization
Indoor sulfate and black carbon	Measured	50% of Central Site Concentration	50% of Central Site Concentration
Indoor nitrate	Measured	20% of Central Site Concentration	20% of Central Site Concentration
Outdoor Concentration	Measured	Equal to Central Site Concentration	Equal to Central Site Concentration
Air Exchange Rate	Measured	Measured	LBL infiltration model

The second approach, “Central Site with measured ACH,” uses the ambient concentrations measured at the Central Site in place of those measured outside of the house. Model 2 is initialized using the Central Site concentrations to estimate the initial indoor concentration. For black carbon and sulfate, which are non-volatile, the initial indoor concentration was estimated as 50% of that measured at the Central Site while for nitrate, which is volatile, a value of 20% of Central Site concentration was used as a surrogate for the initial indoor concentration. The nitrate evaporation rate is assumed constant, with values of 4.6 hr⁻¹ and 1.6 hr^{− 1}for the fall and winter periods, respectively, corresponding to the mean indoor temperatures for these periods of 28°C and 20°C. The difference between the indoor concentration predictions from Models 1 and 2 represents the impact of using regional as opposed to local outdoor aerosol data in the indoor-outdoor model.

The third approach (Model 3), labeled “Central Site only” in Table 1, uses as model inputs measurements only from the central site, with air exchange rates calculated from the LBNL infiltration model. Model 3 represents the data most likely to be available for investigating indoor exposures on a regional basis. In this instance, we used model constants (leakage area, P, k _dep , k _evap ) specific to the home we studied. If actually implementing this modeling approach, a range of values representing the housing stock and characteristic for the area would be used. Comparisons between the accuracy of Model 1 and Model 3 indicate the impact of the loss of site-specific details and measurements on the ability to predict indoor concentrations.

For a closed house, the LBNL infiltration model gives the air exchange rate (hr^{− 1}) as:

where A _leak (m²) is the leakage area of the house determined from the blower door measurement, A _floor (m²) is the floor area of the house, H (m) is its height, ΔT is the absolute value of the indoor outdoor temperature difference, and W (m/s) is the wind speed. The parameters f _s (ms⁻¹K^−1/2) and f _w (dimensionless) are the stack and wind factors that depend upon the house geometry, leakage distribution, and wind shielding, as described in Appendix A. The model is not applicable for the instance when windows or doors are open.

For the Clovis study house we assumed an equal distribution of the leakage area between the walls and ceiling, yielding a value of f _s = 0.10 m s^{− 1}K^{− 1/2}. The shielding of the house describes the presence of obstructions within a distance equal to several building heights, and was classified as “heavy” (shielding class 4) because of the immediate proximity of trees and neighboring houses. The terrain parameter, which characterizes the general surface roughness of the surrounding region, was categorized “urban” (terrain class 4), yielding a value of f _w = 0.071. The temperature difference was calculated from the Central Site temperature measurements assuming an indoor temperature equal to the averaged value of 28°C for the fall study period, and 20°C for the winter study period.

RESULTS

Representative Data

Figure 1 shows a time series for the black carbon, sulfate, and nitrate concentrations at the Central Monitoring Site, immediately outside, and inside of the Clovis study house. These data are from the fall study period when the air exchange rate inside the house was purposely increased by means of mechanical ventilation during three 12-hour time periods. The sulfate concentrations are more similar between Clovis Outdoors (i.e., immediately outside of the study house) and the Central Site than those observed for either black carbon or nitrate. The black carbon at the Central Site exhibits occasional sharp peaks, one of which (October 18 near 6 pm) is also seen in the sulfate concentrations measured at that site. This behavior likely results from the closer proximity of the Central Site to a nearby freeway and more heavily traveled surface streets. The shapes of the concentration time series for nitrate are similar for the Clovis Outdoors and Central Sites. Nitrate concentration levels tend to be higher at Clovis, a trend that is also reflected in the filter data.

FIG. 1 Indoor, outdoor, and central site concentrations of black carbon, sulfate, and nitrate, together with the air exchange rate inside the Clovis Study House, during a period when the ventilation rates were purposely manipulated.

During periods of high ventilation, the indoor black carbon and sulfate values approach the outdoor levels. During periods of low ventilation the indoor response lags behind and is attenuated with respect to changes in outdoor concentration. Nitrate behaves quite differently, with much lower indoor concentrations relative to outdoors than for either black carbon or sulfate. As shown, the indoor nitrate concentrations only increase above these low levels during periods of high ventilation.

Representative data from the winter study when the house was unoccupied with windows and doors closed are shown in Figure 2. Black carbon concentrations were elevated every evening, beginning after 6 pm, and extending until midnight. The timing of these daily maxima is consistent between the Clovis Outdoor and Central Site monitors. This evening black carbon maxima has been associated with residential heating from either wood combustion or poorly operating furnaces (Watson and Chow 2002). During this period, outdoor nitrate concentrations were high, with hourly averages exceeding 100 μ g/m³ on January 3. The particulate nitrate is formed through secondary conversion processes, much of which is believed to occur in the mixed layer aloft at night, leading to widespread spatial uniformity (Watson and Chow 2002; Pun and Siegneur 1999, 2001; Lurmann et al. 2006). The correlation coefficients between concentrations measured at the Central Site and those seen immediately outside the study house were 0.73 and 0.87 for black carbon and nitrate, respectively.

FIG. 2 Indoor, outdoor, and central site concentrations of black carbon and nitrate during the period between the Christmas and New Years holidays when the house was unoccupied with doors and windows closed.

Indoor maxima lag the outdoor daily maxima by several hours and are attenuated due to deposition coupled to the low air exchange rate as reflected by the mass balance model of Equation (1). The attenuation for sulfate and black carbon are similar, with 24-hr mean values indoors equal to 35% to 50% of the levels at the Central Monitoring Site. The low air exchange rates and moderate indoor temperatures compared to the colder temperatures outdoors resulted in large evaporative losses for nitrate indoors. The mean indoor nitrate concentrations are 20% of those measured at the Central Site. The evaporative losses of nitrate led to indoor concentrations equal to 10% on average of those found outdoors for the October measurements, which had warmer indoor temperatures.

Comparison of Central Site and Outdoor Measurements

The equivalency of the continuous measurement methods utilized at the Central Site to those at the Clovis study house is assessed by comparing the semi-continuous monitors and filter-based speciation measurements. Twenty-four hour filter measurements were available at the Fresno First Street site on nine of the days when filter data were collected at the study house. These results, summarized in Table 2, show that the ratios of concentrations measured at the central site to those measured immediately outside the house, determined by both continuous and integrated filter methods are similar for sulfate and nitrate particles, but differ for black carbon. In contrast, the differences between outdoor/indoor concentrations of nitrate and sulfate at the house are much larger than differences between outdoor concentrations measured at the two sites. The filter measurements for black carbon show a larger difference between the Clovis house and the Central monitoring site than the continuous measurements. This discrepancy may be attributable to differences in the analytical methods used for the filter analyses, which are known to yield different splits between “organic” and “black” carbon (Chow et al. 2001; Watson et al. 2005).

TABLE 2 Comparison of filter and continuous measurements ¹

	Central Site/Outdoor	Outdoor/Indoor
Black Carbon
Continuous	1.57	1.85
Filter	2.28	1.63
Sulfate
Continuous	0.96	1.92
Filter	0.97	1.79
Nitrate
Continuous	0.71	10.96
Filter	0.61	9.04

Validation of Model Constants

The values for the model constants P and k _dep were taken from the work of Thatcher et al. (2003), who evaluated these terms for this specific study house through size distribution measurements and concentration-rebound experiments. We checked these values by examining the quality of fit for time-dependent indoor concentration profiles predicted by Equation (2) for black carbon and sulfate for two periods, October 18–21 and December 12–18, 2000, both of which had alternating periods of high and low ventilation rates. These fits were performed using measured air exchange rates and outdoor concentrations determined immediately outside the house (Model 1 of Table 1). The values of 0.75 and 0.2 hr^{− 1}were found to minimize the root mean square error between measured and predicted indoor concentrations. Similarly, the value of the prefactor A for the evaporation coefficient k _evap,NO3⁻ in expression [3] is based on the work of Lunden et al. (2004a). Its value was verified through fits to the nitrate data over this same two periods of alternating high and low ventilation rates, utilizing the values of P and k _dep determined by the fits to the sulfate and black carbon data. Although the evaporation rates from Lunden et al. (2004a) were determined using data from a different time period, the root mean square error between measured and predicted values was lowest using the value of A determined by the fit of Equation (3).

Model Estimates for Closed House Conditions

Indoor concentrations were modeled using the three approaches outlined in Table 1. The “detailed” model (Model 1) used all available data, including the air exchange rates determined from the SF₆ release and species concentrations measured immediately outside the house. The nitrate evaporation term (C _in,j k _evap ) was calculated from measured indoor temperatures, which averaged 28 ± 2°C for the October measurements and 20 ± 1°C for the December–January measurements. Corresponding values of k _evap ranged from 3.1 hr^{− 1} to 8.5 hr^{− 1} for the fall, and 0.9 hr^{− 1} to 2.6 hr^{− 1} for the winter study period.

Model 2, “Central Site with Measured ACH,” calculates indoor concentrations using the measured air exchange rates (as in Model 1), but without other input from the measurements at the Study House. This approach was used to test the estimation of indoor aerosol concentrations when there are no air quality data in the vicinity of the house, but without the additional uncertainly introduced by calculated air exchange rates. Model 3, “Central Site Only,” is the same as Model 2 except that the air exchange rates are obtained from the LBNL infiltration model based on Central Site measurements of winds and temperature. This analysis was performed for two periods, October 7–16 and December 22–January 16, when the house was mostly unoccupied and doors and windows were closed.

Calculated and measured air exchange rates are shown in Figure 3. The modeled values depend on the indoor-outdoor temperature difference. The air exchange rates used in Model 3 were calculated using ambient temperature at the Central Site and the mean values for the indoor temperature (equal to 28°C for the October period and 20°C in the winter). During the October 7–16 period, the modeled air exchange rate was 0.39 ± 0.05 hr^{− 1}, compared to a measured value of 0.43 ± 0.10 hr¹. During the winter, air exchange rates were lower than the fall, ranging from 0.15 to 0.3 hr^{− 1}. These varied on a daily cycle in proportion to the indoor–outdoor temperature difference. The air exchange rates obtained from the infiltration model followed the same diurnal pattern as measured for the winter period, with a correlation coefficient of 0.81, but were approximately 35% higher.

FIG. 3 Comparison air exchange rates estimated using the LBNL infiltration model to that measured by SF₆ tracer gas methods, showing the variation with the indoor-outdoor temperature difference. (Occasional spikes in measurements coincide with opening of doors to service instruments.)

Modeled and measured indoor concentrations of black carbon are compared in the top panels of Figures 4 and 5 for two periods when the house was closed. During the fall, the black carbon concentrations measured at the Central Site were generally higher than seen immediately outside the house, likely because of the closer proximity of traffic sources. Correspondingly, the detailed model (Model 1) does a better job of reproducing the indoor concentrations. As shown in Table 3, the detailed model gives a root mean square difference between measured and modeled indoor concentrations of 0.1 μ g/m³. Models 2 and 3, which utilized the Central Site data, gave nearly identical results. The positive bias in calculated air exchange rate during the winter period (see Figure 3) is nearly inconsequential in the estimation of indoor concentration, as evidenced by the agreement between Models 2 and 3. The RMS values associated with Models 2 and 3 were higher than those of the detailed model because the Central Site concentrations were a factor of two higher than those measured immediately outside the house during the fall. In contrast, during the winter period the black carbon concentrations were more spatially uniform, as shown in Figure 2, and as seen by the mean values reported in Table 3. This uniformity is because the black carbon is dominated by the evening maxima, which have been attributed to residential heating, rather than traffic. All three modeling approaches gave similar results for this winter period, with root mean square error of approximately 1 μ g/m³, or 20% of the mean outdoor concentration.

FIG. 4 Modeled indoor concentrations of black carbon, sulfate, and nitrate calculated using the three approaches outlined in Table 1, with comparison to measured values. Results are for one week of measurements during the fall study period when doors and windows in the house were closed. For nitrate, results are also given for Model 1 when the evaporation term is set to zero.

FIG. 5 Modeled indoor concentrations of black carbon, sulfate, and nitrate obtained from the three approaches outlined in Table 1, with comparison to measured values, during wintertime closed-house measurements. For nitrate, results are also given for Model 1 when the evaporation term is set to zero.

TABLE 3 Comparison of measured and modeled concentrations from differing model inputs¹

	Fall study (μg/m^3)	Winter study (μ g/m^3)
Black Carbon
Measured Ambient and Indoor Concentrations (mean):
Central Site (ambient measurement)	1.8	5.2
Outdoors (immediately outside the study house)	0.86	4.7
Indoors	0.43	2.5
Modeled Indoor Concentrations (mean):
Model 1: Detailed	0.41	1.83
Model 2: Central Site with Measured ACH	0.87	2.18
Model 3: Central Site only (ACH from LBNL infiltration model)	0.85	2.54
RMS Error (Modeled–Measured) ^1
Model 1: Detailed	0.10	1.3
Model 2: Central Site with Measured ACH	0.56	0.84
Model 3: Central Site only (ACH from LBNL infiltration model)	0.54	0.91
Sulfate
Measured Ambient and Indoor Concentrations (mean):
Central Site	1.1	1.7
Outdoors	0.9
Indoors	0.42	0.58
Modeled Indoor Concentrations (mean):
Model 1: Detailed	0.43	—
Model 2: Central Site with Measured ACH	0.56	0.70
Model 3: Central Site only (ACH from LBNL infiltration model)	0.54	0.82
RMS Error (Modeled–Measured) ^1
Model 1: Detailed	0.12
Model 2: Central Site with Measured ACH	0.21	0.23
Model 3: Central Site only (ACH from LBNL infiltration model)	0.19	0.30
Nitrate
Measured Ambient and Indoor Concentrations (mean):
Central Site	6.2	17.
Outdoors	6.5	29.
Indoors	0.22	2.7
Modeled Indoor Concentrations (mean):
Model 1: Detailed	0.37	2.61
Model 2: Central Site with Measured ACH	0.34	1.49
Model 3: Central Site only (ACH from LBNL infiltration model)	0.31	2.05
Neglecting evaporation, but otherwise with detail input of Model 1	3.11	11.56
RMS Error (Modeled–Measured) ^1
Model 1: Detailed	0.25	1.0
Model 2: Central Site with Measured ACH, k evap varies with T in )	0.19	2.0
Model 3: Central Site only (modeled ACH, k evap constant)	0.16	1.5

The middle panels of Figures 4 and 5 compare the measured and modeled indoor sulfate concentrations. Outdoor sulfate data were missing during much of the winter period, and therefore the detailed model is only shown for the fall. Ambient sulfate levels are low, resulting in indoor levels near the detection limit of the continuous measurement methods. Within these uncertainties there is no difference among the modeling approaches. Overall, sulfate exhibits the same attenuation with respect to the outdoor levels as black carbon, with indoor levels at 30% to 50% of measured outdoor values (see Table 3).

Particulate nitrate, shown in the bottom panels of Figures 4 and 5, behaves differently from either black carbon or sulfate. During the fall study the indoor nitrate concentrations were only 3% of those measured directly outside when the Clovis study house was closed. The average indoor nitrate was 10% of that measured outside for the wintertime closed-house measurements. Under these low ventilation conditions the indoor nitrate concentration is highly dependent on the evaporation rate, which is related to the indoor temperature, and sorption of the evaporated gases continues to thermodynamically favor evaporation. Evaporation rates were higher during the fall study when indoor temperatures averaged 28°C, compared to 20°C for the winter period. When the evaporation of particulate nitrate is ignored, indoor values are overestimated by factors of 3 and 7 for the winter and fall, respectively. When the evaporation term is included, all three modeling approaches yield similar results. By comparison to the evaporation term, differences between outdoor and Central Site concentrations and measured and modeled air exchange rates are not important to the model estimates of the indoor nitrate concentrations.

Figure 6 displays the combined frequency distribution of residuals, defined as the difference between the modeled and measured hourly indoor concentrations, for both periods, October 7–17 and December 22–January 16. In general, the detailed model (Model 1) is narrowly distributed around zero, while the two models using the Central Site concentrations are slightly biased towards higher indoor values for black carbon and sulfate. There is little difference between calculations performed using the measured air exchange rates and those derived from the LBNL infiltration model for the specific case of a closed house. The dominant factor for particulate nitrate is the nitrate evaporation rate, which has been treated similarly in all three modeling approaches. Correspondingly, these three models give similar results, independent of differences in the neighborhood and Central Site concentrations and differences in the modeled and measured air exchange rates.

FIG. 6 Histograms of the difference between modeled and measured indoor concentrations of black carbon, sulfate, and nitrate for the three modeling approaches outlined in Table 1. Model (1) uses measured air exchange rates, nitrate evaporation calculated from measured indoor temperatures and ambient concentrations measured immediately outside the house; model (2) uses outdoor concentrations from the central monitoring site and measured air exchange rages and (3) using central site data only, with air exchange rates estimated from the LBNL infiltration model. Penetration = 0.75, deposition = 0.2 hr^{− 1} for all scenarios. Data are from fall and winter study periods when windows and doors to the house were closed (October 10 midnight–October 16 noon, December 22 midnight–December 29 noon, December 31 noon–January 15 midnight).

DISCUSSION

Most epidemiology studies rely on Central Monitoring Site data to assess exposures to outdoor PM2.5. Inherent is the assumption that these Central Site data are a good predictor of exposure, even though people spend the majority of their time indoors, and most of that in homes. While it is not expected that indoor levels equal those outdoors, such analyses assume a consistent correlation between the monitoring site concentrations and those to which the population is exposed. The question asked here is how to relate actual indoor concentrations to Central Site data, and what factors affect that relationship. Given the limitations of the information available to develop an indoor model, and the limitations in space and time of speciated data, we ask whether we can make reasonable estimates of indoor concentrations, and if we wished to improve these estimates, what are the key sources of error.

Figure 7 compares the results of linear fits of the Central Site concentrations, proximate outdoor concentrations, and modeling results to species-specific concentrations measured indoors. Shown is the square of the correlation coefficient (R²) and regression slope for simple linear fit to the one-hour averaged indoor measurement. These comparisons are for a one-week period in October, and two-week period in January when the house was unoccupied with windows and doors closed. The comparison between the detailed model and the indoor concentrations yields values for R² between 0.8 to 0.9, while those between the Central Site and indoors are lower, ranging from 0.5 to 0.8. For black carbon, modeled indoor concentrations are more highly correlated with the measured indoor concentrations than those measured outdoors, either immediately outside or at the Central site. The same trend is seen for sulfate and nitrate, but is not as pronounced.

FIG. 7 Comparison of regression coefficient squared (R²) and regression slope for linear fits of each of the three model calculations, the proximate outdoor concentration and the central site concentration to the hourly averaged indoor concentrations for black carbon, nitrate, and sulfate. Data are shown for black carbon, nitrate, and sulfate during a one-week period in October, and for black carbon and nitrate for a two-week period in January, when the house was unoccupied with windows and doors shut.

The indoor attenuation in particle concentrations, as indicated by the regression slopes, is dependent upon the chemical species, and in the case of nitrate, on the season. During October, when temperatures indoors were high, the indoor-outdoor nitrate concentration ratio was 1:35, while in January the ratio was 1:8. For black carbon and sulfate the regression slopes indicate that the indoor-outdoor relationship is of the order of 1:2. These results emphasize the importance of speciated data, and the need to include the effects of particle volatility. In this region, where nitrate is a significant portion of the fine particulate loading, the regression of the sum of the central site concentrations (1.375*sulfate+1.29*nitrate+BC) to those measured indoors yields an R² = 0.66, while the model results using the central site concentrations give R² = 0.83 and R² = 0.82 for Models 2 and 3, respectively. These results indicate that use of an appropriate model to predict indoor concentrations utilizing Central Site data provides a better surrogate for indoor concentrations than does the Central Site data that is so often used as a surrogate for indoor exposures.

It is important to note that the analysis presented here are for a single, well-characterized house, for which the penetration factor, deposition rate and nitrate evaporation rate were already characterized. Modeled air exchange rates were obtained for a closed house, where the LBL infiltration model was applicable. Organic carbon was not included here, as time-resolved measurements were not available, nor have indoor phase-change characteristics been evaluated.

SUMMARY

In this study we investigated the accuracy of predicting indoor concentrations of outdoor fine particles using measurements from a Central Site monitoring site for the specific case of a well-characterized, unoccupied, closed house. Comparison is made between models based on detailed measurements at the house, to those utilizing Central Site data and the LBNL infiltration model. The predicted indoor concentrations of sulfate and black carbon were within 1 μ g/m³, and nitrate was within 10% of the outdoor value for the unoccupied house. Modeling captures the lag and broadening of the local concentration maxima, and provides an accurate assessment of the peak indoor exposures to outdoor PM_2.5 relative to the Central Site.

For this well-characterized house, our results indicate that the largest error in the use of Central Site data for conserved components (black carbon and sulfate) arises from the differences in ambient concentrations between the immediate neighborhood of the study house and the Central Site. Evaporation is the dominant factor affecting indoor nitrate concentrations. Use of modeled air exchange rates from the LBNL infiltration model in place of those directly measured did not contribute significantly to the RMS error in the estimated indoor concentration during periods when the house was unoccupied, with closed doors and windows.

Comparison of hourly averaged Central Site concentrations and Model predictions to those measured indoors show that the Model predictions serve as a better surrogate for indoor concentrations than do the Central Site measurements. The best fits are found when using the detailed model with measured air exchange rates, proximate outdoor concentrations and penetration, deposition and nitrate loss rates determined for this specific study house. Yet, for a closed house the substitution of calculated air exchange rates for those measured, and the substitution of Central Site concentrations for proximate outdoor concentrations, yields a higher correlation (R² = 0.82), and hence a better surrogate for indoor concentrations than does the Central Site concentration alone (R² = 0.66). An important factor contributing to this improved correlation is the inclusion of the volatilization of particulate nitrate.

APPENDIX A. LBNL INFILTRATION MODEL

The LBNL infiltration model (Sherman and Ramrod 1980; Sherman 1994) considers the infiltration into a structure with a single, well-mixed zone. The model includes two driving forces for infiltration, stack-induced flow which results from the indoor-outdoor temperature difference, and wind-induced flow that arises from the dynamic wind pressure on the building. Over the years the LBNL model has been adapted to include several refinements if building details are known. Presented here is the simplest form, which ignores the influence of flues or ducts, and ignores the orientation of the building with respect to the wind direction.

In the regime where infiltration is dominated by the stack effect, the infiltration flow rate is proportional to the square root of the absolute value of the indoor-outdoor temperature difference. When infiltration is dominated by wind, the infiltration is directly proportional to the wind speed. The total infiltration is obtained by superimposing the pressure effect resulting from each type of infiltration. These pressure effects scale as the square of the flow rate that would arise from each effect separately, giving the combined infiltration flow, in units of m³/s, as:

where A _leak (m²) is the effective leakage area of the house determined from the blower door measurement, Δ T is the absolute value of the indoor outdoor temperature difference, W (m/s) is the wind speed. The two terms in this equation describe respectively the stack-induced infiltration and wind-induced infiltration, in accordance with the proportionality constants f _s and f _w .

The stack parameter, f _s , is defined by:

The parameter R is the fraction of the total leakage area that is in the floor and ceiling. The parameter X the difference between the fraction of the total leakage area that is in the ceiling and the fraction of the total leakage area that is in the floor. Specifically, if we define w = wall leakage area, a = ceiling leakage area and b = floor leakage area, then R = (a + b)/(a + b + w) and X = (a−b)/(a + b + w). These parameters are estimated from the construction of the house. For a slab-on-grade home, the leakage area in the floor is assumed to be zero (b = 0), and R = X. In other homes, such as those with a crawl space or basement, X < R. In Equation (A2) H is the building height at the ceiling, T _o = 298 K is the reference temperature in Kelvins, and g = 9.8 m/s² is the gravitational acceleration.

The wind factor, f _w , is given by:

C is the shielding parameter, which refers to the wind shielding resulting from obstructions immediately around the house, i.e., within a distance of two building heights. The parameters A and B depend are related to the “terrain” class, which characterizes the general neighborhood in which the home is situated, and relate the wind speed measured at a monitoring station to the free-stream wind speed at the height of the building. The values of these parameters, as a function of shielding and terrain class, are given in Table A1.

TABLE A1 Shielding and terrain class model constants

Class	C	Description
Shielding classes
I	0.34	No obstructions or local shielding whatsoever
II	0.30	Light local shielding with few obstructions
III	0.25	Moderate local shielding, some obstructions within two house heights
IV	0.19	Heavy shielding, obstructions around most of perimeter
V	0.11	Very heavy shielding, large obstructions surrounding perimeter within two house heights.
Class	A	B   Description
Terrain classes
I	1.30	0.10   Ocean or other body of water with at least 5 km of unrestricted expanse
II	1.00	0.15   Flat terrain with some isolated obstacles (buildings and/or trees well separated from each other)
III	0.85	0.20   Rural areas with low buildings and/or trees
IV	0.67	0.25   Urban, industrial or forested area
V	0.47	0.35   Center of large city (e.g., Manhattan)

Stack and wind parameters for a one-story structure (ceiling height = 2.5 m) located in an urban setting (Terrain Class IV) are tabulated in Table A2. Stack parameters are shown for several values of the leakage distribution factors R and X, and for instances of moderate to very heavy shielding. These values can be used in Equation (A1) to calculate infiltration rates, or in Equation (4) to calculate air exchange rates as a function of weather-station wind speeds and indoor-outdoor temperature differences.

TABLE A2 Stack and wind factors for terrain class IV for a one-story structure (H = 2.5 m)

	Leakage Distribution Factors
Stack factor	X	R = 0.7	R = 0.5	R = 0.3
f s	X = R	0.078	0.101	0.106
	X = 0.8 R	0.096	0.108	0.108
	X = 0.5 R	0.116	0.115	0.110
Wind factor	Shielding class
f w	III: C = .24	0.076	0.090	0.101
	IV: C = .19	0.060	0.071	0.080
	V: C = .11	0.035	0.041	0.046

The authors dedicate this article in memory of Dr. Joan Daisey, who played a key role in the initial phases of this project, and whose vision has guided our work. We thank Jennifer McWilliams and Max Sherman for their review of our use of the LBNL infiltration model. This research was supported by the Assistant Secretary for Fossil Energy, Office of Natural Gas and Petroleum Technology through the National Petroleum Technology Office under U.S. Department of Energy Contract No. DE-AC03-76SF00098, and by the Western States Petroleum Association and the American Petroleum Institute.

Notes

¹Ratio of mean values over 9, 24-hr periods during study.

¹RMS Error = Root mean square of the difference between hourly average of modeled and measured indoor concentrations. Modeling approaches are described in Table 1. Comparison is for periods when doors and windows of Study House were closed (October 10 midnight–October 16 noon, December 22 midnight–December 29 noon, December 31 noon–January 15 midnight).