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Characterizing Outdoor Infiltration and Indoor Contribution of PM2.5 with Citizen-Based Low-
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Cost Monitoring Data
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Jianzhao Bi1, Lance A. Wallace2, Jeremy A. Sarnat3, Yang Liu3,*
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1Department of Environmental & Occupational Health Sciences, School of Public Health,
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University of Washington, Seattle, WA
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2United States Environmental Protection Agency (Retired), Santa Rosa, CA
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3Gangarosa Department of Environmental Health, Rollins School of Public Health, Emory
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University, Atlanta, GA
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Corresponding Author
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*Mailing Address: Emory University, Rollins School of Public Health, 1518 Clifton Road NE,
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Atlanta, GA 30322, USA. E-mail: yang.liu@emory.edu
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Abstract
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Epidemiological research on the adverse health outcomes due to PM2.5 exposure frequently relies
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on measurements from regulatory air quality monitors to provide ambient exposure estimates,
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whereas personal PM2.5 exposure may deviate from ambient concentrations due to outdoor
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infiltration and contributions from indoor sources. Research in quantifying infiltration factors
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(Finf), the fraction of outdoor PM2.5 that infiltrates indoors, has been historically limited in space
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and time due to the high costs of monitor deployment and maintenance. Recently, the growth of
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openly accessible, citizen-based PM2.5 measurements provides an unprecedented opportunity to
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characterize Finf at large spatiotemporal scales. In this analysis, 91 consumer-grade PurpleAir
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indoor/outdoor monitor pairs were identified in California (41 residential houses and 50
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public/commercial buildings) during a 20-month period with around 650000 hours of paired
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PM2.5 measurements. An empirical method was developed based on local polynomial regression
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to estimate site-specific Finf. The estimated site-specific Finf had a mean of 0.26 (25th, 75th
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percentiles: [0.15, 0.34]) with a mean bootstrap standard deviation of 0.04. The Finf estimates
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were toward the lower end of those reported previously. A threshold of ambient PM2.5
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concentration, approximately 30 μg/m3, below which indoor sources contributed substantially to
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personal exposures, was also identified. The quantified relationship between indoor source
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contributions and ambient PM2.5 concentrations could serve as a metric of exposure errors when
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using outdoor monitors as an exposure proxy (without considering indoor-generated PM2.5),
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which may be of interest to epidemiological research. The proposed method can be generalized
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to larger geographical areas to better quantify PM2.5 outdoor infiltration and personal exposure.
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Keywords: PurpleAir; fine particulate matter; ambient-origin; indoor source; exposure
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misclassification
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1. Introduction
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Fine particulate matter with an aerodynamic diameter less than 2.5 μm (PM2.5) is a major
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environmental health risk factor, whose long- and short-term adverse health effects have been
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investigated by numerous epidemiological studies (Lu et al., 2015; Bell et al., 2004; Bell et al.,
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2013). The majority of epidemiological studies are based on ambient PM2.5 measurements as an
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exposure proxy to support the development of emissions control policies (Dominici et al., 2006;
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Miller et al., 2007; Strickland et al., 2015). However, personal exposure to PM2.5 (the
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combination of indoor and ambient PM2.5) can be greatly influenced by indoor
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microenvironments as most people spend 85-90% of their time indoors (Adgate et al., 2002;
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Klepeis et al., 2001; Jenkins et al., 1992). Indoor exposure is due partly to indoor-generated
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PM2.5 (e.g., smoking, cooking, etc.) with the remainder due to outdoor-infiltrated PM2.5. Ambient
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exposure may deviate from personal exposure due to the lack of consideration of indoor-
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generated PM2.5 (Miller et al., 2019; Ebelt et al., 2000). Differential infiltration resulting from
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differences in natural ventilation (e.g., opening windows), building envelope characteristics, and
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the use of air filtration devices may also lead to variations in outdoor-infiltrated PM2.5 in
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different buildings, resulting in additional exposure errors (Chen and Zhao, 2011; Howard-Reed
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et al., 2002). For a more accurate assessment of PM2.5 exposure, it is critical to estimate indoor-
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generated and outdoor-infiltrated PM2.5 separately.
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The infiltration factor (Finf) for PM2.5 (i.e., the fraction of ambient PM2.5 particles entering
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indoors and remaining suspended) is a characteristic parameter quantifying indoor PM2.5
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concentrations attributable to pollution originating outdoors. An accurate estimation of Finf is
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crucial for the separation of indoor-generated and outdoor-infiltrated PM2.5 to reduce exposure
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errors (Miller et al., 2019). Several experimental and modeling methodologies have been
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developed to estimate Finf (Diapouli et al., 2013; Chen and Zhao, 2011; Wallace, 1996; Shi et al.,
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2017). The use of infiltration surrogates (e.g., sulfate/sulfur, nickel, iron, etc.) is the most
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accurate method as the surrogates are mainly of outdoor origin (Ozkaynak et al., 1996; Long and
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Sarnat, 2004; Wallace and Williams, 2005; Ji et al., 2018). However, accurate chemical species
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measurements are required for this method, which are not always practical and problematic when
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the surrogate has a low concentration level in the outdoor environment (Diapouli et al., 2013).
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Identifying and removing indoor PM2.5 peaks (i.e., censored indoor concentrations) is another
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method aiming to minimize the contribution of indoor sources. An underlying assumption is that
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the observed pollution peaks mainly originate from indoors (Kearney et al., 2011; Kearney et al.,
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2014; Chan et al., 2018; Miller et al., 2019). With censored indoor PM2.5 concentrations, Finf can
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be estimated in a time-dependent and recursive manner with continuous measurements. A
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simpler method not requiring continuous measurements is the steady-state assumption, which
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assumes the mean indoor/outdoor (I/O) concentration ratio over time (e.g., a daily or weekly
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mean) will approach the equilibrium I/O ratio (Kearney et al., 2014). With censored indoor
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concentrations, the equilibrium I/O ratio is a direct estimate of Finf. Without censored indoor
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concentrations, the selection of times with low indoor activity (e.g., night-time indoor
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concentrations) can serve as an alternative way to minimize contributions from indoor sources.
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Due to its simplicity and flexibility, the steady-state assumption has been widely used in Finf
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estimation.
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Research in Finf estimation has historically been based on collocated I/O monitors deployed in
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field campaigns. Due to the high labor and capital costs of deploying and maintaining the
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monitors, this research has always been spatially and temporally limited. Recently, the growth of
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citizen-based, openly accessible air quality data provides unprecedented coverage of PM2.5
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measurements at large spatial and temporal scales. PurpleAir, specifically, is a global, citizen-
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based low-cost monitoring network providing real-time and publicly accessible indoor and
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outdoor PM2.5 measurements (https://www.purpleair.com/). The added value of the large-scale,
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non-regulatory measurements to the regulatory monitoring data on ambient PM2.5 exposure
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assessment has been well-determined (Bi et al., 2020a; Bi et al., 2020b; Huang et al., 2019; Li et
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al., 2020). However, the value of the citizen-based, non-regulatory measurements in the
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characterization of Finf remains unknown and unexplored. Applying publicly available I/O PM2.5
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measurements in Finf characterization would significantly extend the geographical scope while
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reducing costs, compared to the traditional I/O measurements collected in field campaigns.
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Given the aforementioned opportunities, this study aims to assess the potential value of openly
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accessible, citizen-based I/O PM2.5 measurements, specifically PurpleAir measurements, in
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reasonably characterizing PM2.5 Finf and supporting the analysis of indoor source contributions at
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large spatiotemporal scales. The analysis was conducted in California with I/O PM2.5 monitoring
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data from spatially dense PurpleAir monitors over a 20-month period. Owing to the use of large-
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scale PurpleAir measurements, this is the first time the Finf and indoor source contributions have
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been analyzed for multiple sites monitored over thousands of hours without a field campaign to
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deploy the monitors.
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2. Data and Methods
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2.1. PurpleAir Indoor/Outdoor PM2.5 Measurements
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The PurpleAir (PurpleAir, LLC, USA) system provides indoor and outdoor data for PM number
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densities and mass concentrations, as well as other environmental parameters (relative humidity,
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barometric pressure, and temperature), every two minutes. PM number densities are measured
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based on the Plantower PMS sensor (Beijing Plantower Co., Ltd, Beijing, China). The PMS
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sensor is a laser-based optical sensor operating at around 650 nm wavelength. This sensor
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illuminates particles crossing the sensing target volume and the scattered light is collected over a
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90-degree sector. Mie scattering theory is then applied to the measured light intensity to
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determine the number of particles per deciliter in each of six size cut-off bins (> 0.3 μm, > 0.5
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μm, > 1 μm, > 2.5 μm, > 5 μm, and > 10 μm). The mass concentrations associated with
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individual size categories are summed to provide estimates of PM1, PM2.5, and PM10. The latest
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version of the PurpleAir monitor, PA-II, has two PMS sensors (Channels A and B), providing
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two sets of readings of particle number density and mass concentration. An older version, PA-I,
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has one PMS sensor, providing single-channel readings.
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In this analysis, publicly-accessible hourly I/O PurpleAir PM2.5 measurements from dual-channel
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PA-II monitors in California were downloaded from the PurpleAir website
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(https://www.purpleair.com/), covering the period of November 2018 to June 2020. The PM2.5
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data from older single-channel monitors were excluded. The six size cut-off bins were converted
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to six size categories (0.3-0.5 μm, 0.5-1 μm, 1-2.5 μm, 2.5-5 μm, 5-10 μm, and > 10 μm) to
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reduce the potential correlations between the bins. The PM2.5 measurement samples included
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particle number densities (per deciliter) in the three smallest size categories (0.3-0.5 μm, 0.5-1
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μm, and 1-2.5 μm, to exclude counts of particles > 2.5 μm) and weather parameters (temperature
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and relative humidity). The original samples underwent mass concentration conversion, data
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cleaning and quality control, and I/O pairing following the process detailed below.
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2.2. PM2.5 Mass Concentration Conversion
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The PMS sensor provides two mass concentration conversion options: CF 1 and ATM. The
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manufacturer recommends the CF 1 series for “laboratory” PM and the ATM series for
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“atmospheric” PM. However, the detailed conversion algorithms have yet to be disclosed.
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Although the ATM was claimed to be “calibrated”, we found that the CF 1 and ATM series were
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identical below around 28 μg/m3 and then began diverging. A recently published evaluation
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study also illustrated this artificial relationship in detail (Stavroulas et al., 2020). There is no
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possible physical process that could produce the straight-line relationship observed over a strictly
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limited range of concentrations exhibited by CF 1 and ATM. Therefore, we chose to calculate
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our own estimate of PM2.5 mass concentrations from number densities (Eq. 1). The conversion
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method used was also described in Wallace et al. (2020).
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We converted particle number densities to mass concentrations in a specific size category with
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the assumption that the particles had an arithmetic mean diameter equaling the mid-point of the
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size range (e.g., 0.4 μm for the size category 0.3-0.5 μm) and a mean density of water:
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!!"# " #!"# $$
%%
&
&!"#
'
'
%$ (()*+,
(1)
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where
#!"#
is the number density (per deciliter) in a specific size category,
)!"#
is the arithmetic
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mid-point diameter of the size range,
(()*+,
is the water density (1000 kg/m3), and
!!"#
is the
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converted mass concentration in this size category. The particle mass concentrations in the
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smallest three size categories were added to provide PM2.5 mass concentrations (
!-.$.&
):
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!-.$.& " !/0%1/02345 * !/0216345 * !61'02345
(2)
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Even though the assumptions of mid-point diameter (use of arithmetic versus geometric means
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for the mid-point diameter led to marginal differences in the converted PM2.5 concentrations) and
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water density might lead to biases in the converted mass concentrations, the potential biases
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could be significantly reduced when taking the ratios of indoor and outdoor concentrations for
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Finf estimation. Our mass concentration conversion method significantly lowered the limit of
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detection (LOD) of PurpleAir PM2.5 measurements by about 35%, allowing for more meaningful
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low-level measurements to be included (Wallace et al., 2020). It should be noted that the
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converted PM2.5 mass concentration was not the true mass concentration in μg/m3 due to the
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assumption of mid-point diameter and water density. Hence, we name the unit of this converted
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concentration converted mass concentration unit hereinafter. By comparing to the collocated
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reference gravimetric PM2.5 measurements, Wallace et al. (2020) found that the converted mass
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concentration (in converted mass concentration units) for indoor PurpleAir monitors was lower
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than the true mass concentration (in μg/m3) by a (crude) factor of 3.0, and the two types of
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concentrations were linearly correlated. For outdoor PurpleAir monitors used in this analysis, we
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also observed a crude calibration factor of 3.0 (see Supplemental Section 1). The similar crude
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factors for both indoor and outdoor monitors further support that PurpleAir uncertainties could
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be significantly reduced when taking indoor/outdoor ratios. It is worth noting that for the display
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purpose in Table 1 (the row of PM2.5 concentrations in μg/m3) and Figure 3 (the outdoor PM2.5
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concentrations in the x-axis), the PM2.5 concentrations in converted mass concentration units
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were adjusted with the empirical factor of 3.0 (i.e., the converted mass concentrations were
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multiplied by 3.0) to reflect a more realistic scale of PM2.5 in μg/m3. All quantitative analyses
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were based on the original converted mass concentration units, which were not affected by this
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adjustment.
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2.3. Quality Control
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The quality control procedures started with examining particle number densities. In practice,
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there was never an occasion with zero particles in the two smallest size categories, 0.3-0.5 μm
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and 0.5-1 μm. Thus, all zero readings in these two size categories were excluded as artifacts
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(extremely limited in number). Then, the PM2.5 samples were filtered based on the agreement of
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dual-channel readings; samples with a dual-channel difference greater than 30% were removed.
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A sensitivity analysis for this agreement threshold showed that the identified outliers were
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consistent within a range of 10%-50%, indicating that the threshold of 30% was reasonable.
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Furthermore, we excluded monitors with a total operating time less than three weeks over the
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entire study period. Finally, we identified potentially mislabeled indoor and outdoor monitors
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based on temperature and humidity measures. We expected that outdoor monitors should have
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larger variations in temperature and humidity than indoor monitors, whereas five indoor
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monitors (site IDs 9200, 12719, 16785, 26655, 37213) showed significant variations in
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temperature and humidity, which were even greater than most of the outdoor monitors (the 10th
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percentile of their temperature measures was < 50 °F). Likewise, we identified three outdoor
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monitors (site IDs 17529, 18421, 36615) with a narrow range of temperature measures (with a
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minimum temperature of approximately 70 °F and a maximum temperature below 80 °F). These
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potentially mislabeled monitors were removed from the analysis.
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2.4. Indoor/Outdoor PurpleAir Monitor Pairing
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There were very few strictly collocated I/O PurpleAir monitors (< 15 pairs were identified to be
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located in the same building on satellite maps). Thus, a less stringent collocation strategy
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proposed by Bi et al. (2020b) was adopted to pair I/O monitors by matching an indoor monitor to
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its nearest outdoor monitor within a 500-m radius (Figure S1). The 500-m distance threshold had
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been examined by Bi et al. (2020b), in which a high agreement between outdoor measurements
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from PurpleAir monitors within 500 m of each other was found. In this analysis, a similar
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agreement was observed, indicating the reliability of the pairing strategy and the distance
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threshold. By adopting the pairing strategy, 97 collocated I/O monitors with 650220 paired
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hourly PM2.5 measurements were obtained over the study period. Among the monitor pairs, 91 of
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them with 627417 paired measurements were able to support Finf estimation. These paired
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monitors covered most of the major cities in California (Figure 1). According to satellite maps,
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the sites could be roughly classified as 41 residential houses and 50 public/commercial buildings.
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2.5. Analysis of Infiltration Factor Estimates
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2.5.1. The LOWESS-Based Algorithm
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Assuming that the relative indoor source contributions were less measurable when outdoor PM2.5
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concentrations were high (defined as being higher than the 95th percentile of ambient PM2.5
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concentrations during the study period), we developed an Finf estimation algorithm. The
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algorithm was based on the locally weighted scatterplot smoother (LOWESS) regression with
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hourly outdoor measurements as the independent variable and hourly I/O ratios as the dependent
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variable for each I/O monitor pair. When outdoor PM2.5 concentrations were high, for example,
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the I/O ratio was expected to be close to the true Finf, and ideally, the fitted LOWESS curve
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would be approaching the value of Finf asymptotically. In practice, we found that the LOWESS
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curve tended to fluctuate with minimal variation around a specific I/O ratio value at the high end
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of outdoor concentrations for most of the monitor pairs, and this I/O ratio might be close to the
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true Finf. More importantly, hourly-level measurements were subject to the lagging effect, i.e.,
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indoor PM2.5 lagged behind sharp variations in outdoor PM2.5. As illustrated in Figure S2, the
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Spearman’s rank correlations between indoor and lagged outdoor measurements (with 0-, 1-, 2-,
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3-, 4-, and 5-hour lags) were examined. As the outdoor measurements made an hour earlier had
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the highest correlation coefficient with indoor measurements, the indoor measurements were
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paired with outdoor measurements an hour earlier to calculate the hourly I/O ratios.
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For each I/O monitor pair, N pairs of hourly I/O measurements with the highest outdoor PM2.5
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concentrations were first selected. A bootstrap sample (with a sample size of N) was then
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obtained from these N measurements to fit a LOWESS curve. The mean value of the fitted
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LOWESS curve was treated as the Finf estimate of this bootstrap sample. Finally, the
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bootstrapping and LOWESS fitting steps were repeated M times to obtain M bootstrap Finf
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estimates. The mean value of these M estimates was treated as the final Finf estimate, and their
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standard deviation was used as an uncertainty measure.
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To ensure the reliability and robustness of Finf estimation, we excluded hourly I/O ratios greater
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than 1.2 (slightly greater than 1 to allow for some measurement uncertainty) because an I/O ratio
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approaching 1 indicated significant indoor source contributions (Kearney et al., 2011).
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Additionally, we required the maximum outdoor PM2.5 concentrations to exceed 8 converted
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mass concentration units (the 95th percentile of outdoor concentrations) to reduce the possibility
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that the associated indoor concentrations were affected by indoor sources. An outdoor
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concentration threshold that was too high or too low could increase the uncertainty in Finf
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estimation. A high threshold would also decrease the number of sites available for Finf
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estimation. The 95th percentile was found to be a reasonable value balancing the number of sites
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available for Finf estimation against Finf uncertainty. According to a sensitivity analysis, the Finf
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estimates were not sensitive for the threshold within the 90th to 98th percentiles.
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There were three important parameters in the algorithm: (1) the size of the samples with the
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highest outdoor PM2.5 concentrations (N), (2) the repetition time of bootstrap sampling (M), and
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(3) the smoother span of LOWESS. N should be determined by striking a good balance between
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the robustness of Finf estimates and the number of available I/O monitor pairs. A large N would
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result in more samples with a substantial indoor contribution being selected, but a small N would
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reduce the robustness of the Finf estimates. In this analysis, N was determined to be 20 according
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to a sensitivity analysis. An N of 20 could maximize the available monitor pairs while generating
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relatively robust Finf estimates (within the range of 10-30, the coefficient of variation of the Finf
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estimates was < 8%). The parameter M was less sensitive, which was determined to be 100 to
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guarantee sufficient bootstrap samples. As N was a relatively small number, the smoother span
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was set to be 100% to maximize the LOWESS regression samples. The smoother span was not
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sensitive either (within a range of 50%-100%, the coefficient of variation of the Finf estimates
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was < 4%).
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2.5.2. Indoor Source Contributions
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With the Finf estimates for individual sites, indoor source contributions were analyzed. The
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concentration of indoor-generated PM2.5 was calculated as
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!78 " !73 + ,"#9 $ !:
(3)
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where
!73
is the total indoor concentration,
!:
is the corresponding outdoor concentration, and
!78
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is the estimated concentration of indoor-generated PM2.5. For each site, the proportion of indoor-
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generated PM2.5 (
;'(
;') $-../
) in total indoor PM2.5 was first calculated at an hourly level based
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on the paired I/O concentrations and the site-specific Finf estimate. Then, the median value (to
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alleviate the significant influence of few outliers) of the hourly proportions was treated as the
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estimated (long-term average) proportion of indoor-generated concentrations at this site.
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The quantitative relationship between indoor source contributions and outdoor concentrations
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was then analyzed, which may be of interest to epidemiological research to better assess
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exposure errors. For this analysis, the ratios between exposure to indoor-generated PM2.5 and
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exposure to outdoor-infiltrated PM2.5 (exposure was defined to be mean concentration multiplied
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by total exposure/measurement time), a metric of exposure errors when using ambient PM2.5
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concentrations as an exposure proxy, were shown against different concentrations of outdoor
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PM2.5. We further estimated the lower bounds of outdoor PM2.5 concentrations at which the
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indoor-generated PM2.5 concentrations were negligible for individual sites (< 5% of total indoor
285
concentrations). These outdoor PM2.5 threshold values are important indicators for personal
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exposure assessment, which can help further analyze exposure misclassification at a finer scale.
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The outdoor threshold value was estimated by fitting a LOWESS curve with outdoor PM2.5
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concentrations as the independent variable and indoor source contributions (proportions) as the
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dependent variable. In theory, the indoor source contributions would be highest near the origin
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(when the outdoor concentration was close to zero) and then approach zero as an asymptote. In
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reality, we found that not all LOWESS curves showed this pattern (Figure S3). This could occur
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if there were errors in the estimated Finf, or if Finf was changing due to occupant behaviors such
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as opening windows for long periods. However, the curves that did not reach zero or sank below
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zero generally reached the points with the minimum indoor contribution at outdoor
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concentrations well below the observed maximum concentrations. Thus, our assumption of little
296
or no relative indoor contribution at the highest outdoor concentrations still appeared to be
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supported.
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3. Results
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3.1. Infiltration Factor Estimates
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Among 97 I/O monitor pairs, 91 pairs had available LOWESS-based Finf estimates (satisfying
302
the quality control criteria that there were at least 20 hourly samples with I/O ratios < 1.2 and
303
outdoor concentrations > 8 converted mass concentration units). Table 1 shows the summary
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statistics of the measurement samples from the 91 I/O monitor pairs. Table 2 and Figure 2(a)
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summarize the distribution of the Finf estimates. The Finf estimates had a mean of 0.26 and a
306
median of 0.24 (25th, 75th percentiles: [0.15, 0.34]). The bootstrap standard deviations (SD), an
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uncertainty measure of Finf, had a mean of 0.04 and a median of 0.03 (25th, 75th percentiles:
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[0.02, 0.05]). The estimates had an uncertainty level of approximately 15% (bootstrap SDs
309
divided by Finf estimates). All estimated Finf values were within the range of 0-1. Table S1 shows
310
the Finf estimates and bootstrap SDs at individual sites.
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312
We used the linear regression method widely adopted in previous studies (Ott et al., 2000) as a
313
baseline reference to the LOWESS method (refer to as linear-based Finf hereinafter). For this
314
method, total indoor PM2.5 (
!7
) was the summation of outdoor-infiltrated PM2.5 (
,"#9 $ !:
) and
315
indoor-generated PM2.5 (
!78
) (Eq. 3). A linear regression model was fitted with outdoor PM2.5
316
concentrations as the independent variable and total indoor concentrations as the dependent
317
variable, in which the fitted slope was the estimation of Finf. In this analysis, we used the same
318
hourly-level I/O measurements with a 1-hour outdoor concentration lag for the model fitting. The
319
linear-based Finf estimates had a mean of 0.25 and a median of 0.25 (25th, 75th percentiles =
320
[0.14, 0.35]), which were at a similar scale as the LOWESS-based Finf estimates (Table 2 and
321
Figure 2). The bootstrap SDs of the linear-based Finf estimates had a mean of 0.02 and a median
322
of 0.01 (25th, 75th percentiles = [0.01, 0.02]), which were slightly lower than the bootstrap SDs of
323
the LOWESS-based estimates. Two types of Finf estimates had a positive correlation with a
324
Spearman’s rank correlation coefficient of 0.87 (Figure S4). However, the linear-based Finf
325
estimates were not fully within the range of 0-1 (Table 2 and Figure 2(b)).
326
327
3.2. Indoor Source Contributions
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We followed Eq. 3 to calculate the (long-term average) proportions of indoor-generated PM2.5
329
based on the Finf estimates at individual sites. The site-specific proportions of indoor-generated
330
PM2.5 had a mean of 39.9% and a median of 41.9% (25th, 75th percentiles = [24.2%, 61.4%]),
331
indicating that the indoor source contributions were relatively substantial, which was frequently
332
above 40%. While most of the sites had an estimated indoor source contribution greater than 0,
333
there were two (2) outlier sites (site IDs 17875 and 19149) with a negative contribution < -50%
334
(Table S1). A possible reason is that the indoor PM2.5 concentrations in these two sites were so
335
low that the estimated indoor source contributions had high relative errors (i.e., low signal-to-
336
noise ratios). Specifically, the mean indoor PM2.5 concentration at all sites was 0.8 converted
337
mass concentration units (approximately 2.4 μg/m3), while the two sites had a mean indoor
338
concentration < 0.1 converted mass concentration units (< 0.3 μg/m3). The extremely low indoor
339
concentrations may indicate that the indoor measurements were unreliable at these two sites.
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Therefore, the two outlier sites were excluded from the analysis of indoor source contributions.
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Figure 3 shows the quantitative relationship between indoor source contributions and outdoor
343
concentrations. The estimated relationship showed a general pattern that the indoor source
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contributions declined with an increasing outdoor concentration, and the contributions tended to
345
approach 0 when outdoor PM2.5 concentrations > 30 μg/m3. Moreover, Table S1 shows the
346
outdoor concentrations at which indoor source contributions were negligible (< 5%) for
347
individual sites based on the LOWESS curves. 74 sites had an available 5% threshold for indoor
348
contribution. For the remaining unavailable sites, a usual case was that the LOWESS curve did
349
not have a decreasing trend (N = 5). Another case was that the LOWESS curve did not decrease
350
below 5% (N = 12). The site-specific outdoor-concentration thresholds had a mean of 42.2 μg/m3
351
and a median of 26.4 μg/m3 (25th, 75th percentiles = [16.1, 53.3 μg/m3]), indicating that for most
352
of the sites, the indoor source contributions could be negligible only when the outdoor
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concentration was greater than 30 μg/m3. The estimated relationship between indoor source
354
contributions and outdoor concentrations shown in Figure 3 also reflected the same threshold of
355
(approximately) 30 μg/m3, beyond which the indoor source contributions were close to 0.
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357
4. Discussion
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Based on the citizen-based PurpleAir I/O PM2.5 measurements, this study characterized the
359
infiltration of ambient PM2.5 and the contribution of indoor PM2.5 sources at large spatiotemporal
360
scales. There were other field campaigns applying low-cost air quality monitors, including the
361
Plantower PMS sensor, to characterize PM2.5 infiltration (Barkjohn et al., 2020; Wang et al.,
362
2020; Shrestha et al., 2019; Zusman et al., 2020a). This study was different from the previous
363
research in nature, as no field campaigns and stringent I/O monitor deployments were required to
364
obtain reasonable Finf estimates, and all analyses were based solely on indoor and outdoor
365
PurpleAir measurements accessible online.
366
367
Previous studies using different infiltration estimation methods showed a range of mean PM2.5
368
Finf generally from 0.4 to 0.8 across different countries in North America and Europe (Diapouli
369
et al., 2013). Our estimated Finf values were toward the lower end of those reported previously. A
370
potential reason is the volatilization of PM2.5 nitrate (NO3-). California has relatively high
371
concentrations of outdoor nitrate (Meng et al., 2018). Facilitated by higher indoor temperatures
372
and/or lower indoor HNO3 concentrations as compared to outdoors, PM2.5 nitrate is more volatile
373
when infiltrated indoors (Sarnat et al., 2006). The increased volatilization of indoor nitrate
374
particles and their depositional losses upon building entry might lead to a lower Finf. Another
375
potential explanation is that PurpleAir owners might pay more attention to indoor air quality (as
376
the indoor monitors could provide instantaneous air quality levels) so that there might be more
377
activities that actively reduce indoor PM2.5 concentrations (e.g., the use of air purifiers). The
378
actively reduced indoor PM2.5 concentrations could result in lower I/O PM2.5 ratios, thus a lower
379
Finf estimate. While the Finf estimated across different studies may be affected by different levels
380
of some key factors including penetration factor, air exchange rate, and deposition rate, the scale
381
of our Finf estimates still agreed with some reported in previous studies in North America. For
382
instance, Wu et al. (2012) measured I/O PM2.5 concentrations and estimated Finf for 32 small and
383
medium commercial buildings in California. They obtained a mean Finf of 0.27 with a standard
384
error of 0.08. Based on a two-year continuous dataset collected in Windsor, Ontario, MacNeill et
385
al. (2012) reported median daily Finf estimates for PM2.5 ranging from 0.26 to 0.36 across
386
seasons. Our Finf was also comparable to the reported median Finf of 0.3 for Minneapolis,
387
Minnesota in spring, summer, and fall (Adgate et al., 2003). While other studies found higher Finf
388
estimates, such as an all-season median of 0.5 for Minneapolis/St. Paul, Minnesota (Allen et al.,
389
2012), an all-season mean of 0.52 for Toronto (Clark et al., 2010), and up to a daily summer
390
median of 0.80 for Halifax, Nova Scotia (MacNeill et al., 2014), the differences in climate
391
conditions and housing stock may come into play.
392
393
Based on the Finf estimates, we observed that the indoor source contributions tended to be
394
negligible only when the ambient PM2.5 concentrations were above 30 μg/m3 (Figure 3), which is
395
the original finding of this study. While California is one of the most polluted states in terms of
396
PM2.5 in the U.S. (Hu et al., 2017; Di et al., 2016), the PM2.5 concentrations tend to be below 30
397
μg/m3 for the majority of locations and time. The non-negligible proportion of indoor-generated
398
PM2.5 at low ambient concentrations suggests the importance of considering indoor PM2.5
399
sources in personal exposure assessment in relatively clean regions such as the U.S. and
400
European countries to reduce potential exposure errors. The derived relationship between indoor
401
source contributions and ambient PM2.5 concentrations may be of interest to epidemiological
402
research to better characterize PM2.5 exposure misclassification.
403
404
A crucial feature indicating that our LOWESS-based method outperformed the linear-based
405
method was that some linear-based Finf estimates were outside the range of 0-1 (Table 2 and
406
Figure 2(b)). Naturally, there is no physical meaning of Finf being less than 0 or greater than 1.
407
We observed that the negative Finf estimates were generated when there were high-level indoor
408
PM2.5 concentrations associated with low outdoor concentrations. In this case, indoor sources
409
contributed significantly to the total indoor concentrations. As an example, Figure S5 shows the
410
hourly I/O measurements and the fitted linear relationship of the I/O monitor pair (ID 23941)
411
with an Finf estimate of -0.8. This finding indicates that the linear-based method, unlike the
412
LOWESS-based method, could not properly reduce the influence of indoor sources on Finf
413
estimation, thus was less reliable. In contrast, our LOWESS-based method showed no Finf
414
estimates falling out of a reasonable range, reflecting its capability to minimize the influence of
415
indoor source contributions. While it was impractical for this study to obtain stringently
416
collocated, research-grade I/O PM2.5 measurements at the PurpleAir sites as a reference to
417
validate the Finf estimates, we observed that the overall trend of estimated indoor source
418
contributions based on the LOWESS regression showed a general pattern approaching zero at the
419
high end of ambient PM2.5 concentrations (the red curve in Figure S3). This pattern indicates the
420
reasonability of our assumption that the indoor-generated PM2.5 was less measurable when
421
ambient concentrations were sufficiently high (i.e., higher than the 95th percentile of the ambient
422
PM2.5 concentrations during the study period).
423
424
Previous studies found that PM2.5 measurements from the Plantower PMS sensor deviated from
425
collocated “gold-standard” gravimetric measurements (Zheng et al., 2018; Levy Zamora et al.,
426
2019; Kelly et al., 2017; Jayaratne et al., 2018; Bi et al., 2020b; Gupta et al., 2018). For
427
applications requiring unbiased PM2.5 measurements, such as exposure modeling (Bi et al.,
428
2020a; Huang et al., 2019) and pollution mapping (Schneider et al., 2017), calibration is always
429
crucial. However, we found that without reliable research-grade indoor PM2.5 data, calibration
430
could not improve the accuracy of Finf estimation, which could potentially introduce additional
431
biases (see Supplemental Section 1). A previous study aiming to evaluate PurpleAir
432
measurements in indoor environments observed a crude calibration factor of 3.0 for indoor
433
PurpleAir monitors (Wallace et al., 2020), and our study also observed a crude calibration factor
434
of 3.0 for outdoor PurpleAir monitors. A similar (crude) calibration factor for both indoor and
435
outdoor PurpleAir monitors indicates that the negative influence of measurement uncertainties
436
on Finf estimation could be significantly reduced when taking indoor/outdoor ratios. In contrast to
437
previous work, after extrapolating the outdoor calibration model to indoor PurpleAir monitors,
438
we observed a (crude) calibration factor of 6.0 for indoor monitors (Supplemental Section 1),
439
indicating that it might be unreliable to calibrate indoor measurements based solely on research-
440
grade outdoor measurements. Thus, due to the lack of research-grade indoor measurements to
441
support a reliable calibration, we did not apply calibration on either indoor or outdoor PurpleAir
442
monitors in this analysis.
443
444
There were several limitations to this study. First, due to the distinct indoor and outdoor
445
environmental conditions, especially distinct temperature and humidity levels influencing the
446
PurpleAir measurement accuracy (Levy Zamora et al., 2019; Zusman et al., 2020b; Stavroulas et
447
al., 2020), the matched I/O PurpleAir monitors might have multiple uncertainties. While we
448
expect any major uncertainties in PM2.5 measurements could be removed when taking the I/O
449
ratio, differential I/O uncertainties might still result in biases in the estimated Finf to some extent.
450
This limitation highlights the importance of additional validations on the I/O PurpleAir
451
measurements. Secondly, not all LOWESS curves were shown to be approaching a constant
452
value at the high end of ambient PM2.5 concentrations, most likely due to the PM2.5
453
concentrations being insufficiently high for those PurpleAir sites during the study period. This
454
issue could potentially result in biased Finf estimates for those sites, for which additional work is
455
needed to improve the Finf estimation method. Additionally, as our analyses were based solely on
456
readily available I/O measurements from a citizen-based PM2.5 monitoring network, additional
457
studies (field campaigns) with research-grade monitors and conventional Finf measurement
458
methods are needed to further validate the proposed Finf estimation method. Moreover, indoor-
459
generated secondary organic aerosol (SOA) particles may be non-negligible when other indoor
460
and outdoor sources are trivial (Ji and Zhao, 2015), which may influence the Finf estimation. The
461
effects of SOA on Finf at the PurpleAir sites are worth additional analyses when proper
462
measurement/modeling tools for SOA are available. Finally, as the characteristics regarding the
463
housing stock and ventilation were not accessible at the PurpleAir sites, it remained unknown
464
which infiltration scenarios, e.g., opening/closed windows and the use of air purifiers, were
465
associated with the estimated Finf. If the houses/buildings with an indoor PurpleAir monitor were
466
associated with a specific infiltration scenario (e.g., the homeowner using a PurpleAir monitor
467
would also be likely to use an air purifier), the estimated Finf would not be representative of the
468
average Finf in the houses/buildings across the study domain.
469
470
5. Conclusions
471
This study demonstrated the potential value of publicly available, citizen-based low-cost I/O
472
monitoring data, specifically PurpleAir data, in providing reasonable PM2.5 infiltration estimates
473
at large spatiotemporal scales, in addition to their traditional value of large-scale ambient PM2.5
474
monitoring. A LOWESS-based Finf estimation method, which was proven to outperform the
475
traditional linear regression method and more suitable for low-cost PM2.5 measurements, was
476
proposed. Based on the infiltration estimates, an outdoor-concentration threshold of
477
(approximately) 30 μg/m3 below which indoor sources were not negligible in personal PM2.5
478
exposure was also revealed. PurpleAir is a global monitoring network with rapid growth and
479
publicly accessible data. The proposed infiltration estimation method may be generalized to
480
larger geographical regions to estimate indoor source contributions of PM2.5, which can serve as
481
an additional source of information to epidemiological research seeking to assess the health
482
effects of personal exposure to PM2.5.
483
484
Acknowledgments
485
The work was supported by the Multi-Angle Imager for Aerosols (MAIA) science team and the
486
Multi-angle Imaging SpectroRadiometer (MISR) science team, both at the Jet Propulsion
487
Laboratory (JPL), California Institute of Technology, led by D. Diner (Subcontract # 1588347
488
and 1363692). We acknowledge Nelsha Athauda at Emory University for assisting in manuscript
489
reviewing and editing.
490
491
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717
718
Table 1: Summary statistics of the measurement samples from 91 indoor/outdoor PurpleAir monitor pairs.
719
Indoor PurpleAir Measurements
Outdoor PurpleAir Measurements
N of
Samples
Mean
Median
SD*
Min
Max
N of
Samples
Mean
Median
SD
Min
Max
PM2.5 Concentrations
PM2.5 (converted mass
concentration unit)
627417
1.52
0.70
5.01
0
432.05
627417
2.54
1.55
3.78
0.01
260.91
PM2.5 (μg/m3)**
627417
4.55
2.09
15.02
0
1296.14
627417
7.63
4.65
11.34
0.02
782.72
Environmental
Parameters
Temp (°F)
627417
79.43
79.52
5.22
9.75
109.77
627417
67.82
66.03
11.28
6.12
122.10
RH (%)
627417
34.41
35.00
7.88
1.00
77.72
627417
49.62
51.65
15.83
0
100.00
Operating Time (day)
627034
328.27
311.00
216.35
0
1065.00
627242
350.60
331.00
224.79
0
1081.00
* SD: standard deviation
720
** Multiplied by the empirical calibration factor of 3.0 for display purpose
721
Table 2: Summary statistics of the Finf estimates generated by the LOWESS-based and linear-
722
based methods (the latter one was adopted as a baseline reference).
723
N of Monitor Pairs
Mean
Median
25th, 75th Percentiles
Min
Max
LOWESS-Based
91
0.26 (0.04*)
0.24 (0.03)
0.15, 0.34
0.02
0.85
Linear-Based
91
0.25 (0.02*)
0.25 (0.01)
0.14, 0.35
-0.80
0.77
* Bootstrap standard deviation (SD)
724
725
Figure 1: Locations of paired indoor/outdoor PurpleAir monitors in California during the study
726
period.
727
728
729
730
Figure 2: Distributions of the (a) LOWESS-based and (b) linear-based Finf estimates.
731
732
733
734
Figure 3: The mean PM2.5 exposure levels (mean concentration times number of hours) for the
735
estimated outdoor-infiltrated PM2.5 exposure (blue bars) and indoor-generated PM2.5 exposure
736
(red bars), as a function of outdoor PM2.5 concentrations. The line in purple shows the ratio of
737
indoor-generated (i.e., total indoor minus outdoor-infiltrated) exposure and outdoor-infiltrated
738
exposure as a function of outdoor PM2.5 concentrations, a metric of exposure errors when using
739
ambient PM2.5 concentrations as an exposure proxy (without considering indoor-generated
740
PM2.5).
741
742
