Evaluation of Variability in the Ambient PM 2.5 Concentrations from FEM and FRM-like Measurements for Exposure Estimates

This study aims to evaluate the variability in ambient fine particulate matter (PM 2.5 ) concentrations obtained from the federal equivalent method (FEM) and federal reference method (FRM)-like measurements at the national air quality monitoring stations (AQMSs) for exposure estimates and to examine the effect of environmental factors and sampling site characteristics affecting the spatial and temporal variations in PM 2.5 concentrations. A mixed-effects model was used to evaluate the temporal and spatial variability in daily and annual PM 2.5 concentrations during 2014–2017 at 16 AQMSs in the Big Taipei City, Taiwan. The mean FEM PM 2.5 concentrations were ~ 30% higher than the FRM-like PM 2.5 concentrations. The FRM-like PM 2.5 concentrations obtained by applying the calibration procedures presented a negligible between-site variability. The daily FEM PM 2.5 concentrations were dominated by the within-site variability ( ~ 90%), whereas the annual concentrations were reasonably attributable to the between-site variability (47.8%). Ambient PM 2.5 was mainly affected by the gaseous pollutants (such as NO 2 , O 3 , and SO 2 ), accounting for 45.8% and 26.8% of the within-site and between-site variability in concentrations, respectively. The FEM measurements rather than the FRM-like measurements at the AQMSs could provide a higher between-site variability for exposure estimates of PM 2.5 in the epidemiological studies.


INTRODUCTION
The elevated levels of fine particulate matter (PM2.5) are associated with adverse health effects, such as respiratory and cardiovascular morbidity and mortality, which have been reported in many studies (Beelen et al., 2014;Cai et al., 2016;Kaufman et al., 2016).The World Health Organization (WHO, 2014) has indicated that outdoor PM2.5 accounts for 7 million deaths worldwide every year.Recent literature has documented that exposure to even low levels of PM2.5 can significantly increase all-cause mortality (Shi et al., 2016).National ambient air quality standards (NAAQS) are usually regulated in many countries to limit air pollution (such as ambient PM2.5 levels) and protect public health.For instance, the annual (15 µg m -3 ) and daily (35 µg m -3 ) standards of PM2.5 have been set by Taiwan EPA while lower guideline limits for outdoor PM2.5 (annual = 10 µg m -3 , daily = 25 µg m -3 ) have been suggested by WHO.The filter-based instruments such as BGI PQ200 and RAAS2.5 single and multi-day samplers are usually used for consistent

Data Sources and Calibration Process
In this study, we selected Taipei and New Taipei cities, (together known as Big Taipei City), having a population of 7 million in 2,225 km 2 of land, as our study area because it has a highdensity of national AQMSs.There are 19 national AQMSs (Fig. 1), including one national park AQMS (Yangming mountain), three traffic AQMS (Sanchong, Yonghe, and Datong), one background AQMS (FugueiCape), and 14 general AQMSs (Tu-cheng (TC), Shi-lin (SL), Zhong-shan (ZS), Gu-ting (GT), Xi-zhi (XiZ), Song-shan (SS), Ban-qiao (BQ), Lin-kou (LK), Tam-sui (TS), Cai-liao (CL), Xin-dian (XD), Xin-zhuang (XinZ), Wanli (WL), and Wan-hua (WH)).Out of these 14 general stations, one is the background station (WL) for the specific purpose of air quality monitoring.After excluding national park and background monitoring stations, the air quality monitoring data from a total of 13 general stations (except WL), and 3 traffic stations in Big Taipei City along with the meteorological observations and site specifications were included for analysis.
Briefly, the FRM calibration procedure has been implemented by the contractors of Taiwan EPA across Taiwan since 2014.Due to limited resources, filter-based FRM measurements at only 5 AQMSs in big Taipei were conducted once every three days.In the analysis, 16 AQMSs shared five FRM measurements of PM2.5 simultaneously.As a result, 16 resultant calibration equations by the station were generated for every year (Tables S1-S4).
The regression model for the calibration of FRM-like PM2.5 measurements from 2014 to 2017 in Big Taipei City is shown in the supplementary data.The measurement data, including ambient temperature, relative humidity, wind speed, rainfall, CO, NO, NO2, NOx, O3, SO2, CH4, Nonmethane hydrocarbon (NMHC), and total hydrocarbon (THC), were obtained from the Taiwan Air Quality Monitoring Network database for 16 stations.Station profiles such as the station types (ambient/traffic), the height of sampling ports (3.5-13.5 m/17.5 m/19.5-21.5 m), the distance to the nearest main road (1-5.6 m/10-15 m/20-100 m), the types of automatic sampling instruments (VEREWA F701/MetOne 1020) were also collected.Moreover, we incorporated the concurrent atmospheric pressure measurements obtained from the weather bureau stations selected based on the distance to the nearest AQMS.As a lot of meteorological information from AQMSs was missing, all the missing data were imputed by the concurrent measurements from the nearest weather bureau station.

Statistical Analysis
The SPSS software was used to evaluate temporal (within-site) and spatial (between-site) variability in PM2.5 concentrations from FEM and FRM-like measurements at 16 stations.The temporal variation of PM2.5 is defined as the variability in PM2.5 over time at each AQMS, whereas the spatial variation is defined as the variability in PM2.5 across sites at any time.Both FEM and FRM-like PM2.5 concentrations had skewed distribution and were normalized by logarithmic transformation.The measurements at daily and yearly time resolutions were evaluated to explore the trends in spatial and temporal variations at short-term and long-term scales.
Pearson's correlation coefficient (r) was used to evaluate the correlations between the variables.Among the variable pairs having r > 0.7, only the determinants considered more logically related to PM2.5 and/or more consistently and reliably available throughout the duration of the study across selected AQMSs were retained for modeling.The mixed-effects model based on a restricted maximum likelihood estimation procedure was used to examine the relationship between each variable and the log-transformed daily and annual PM2.5.The determinants were treated as fixed effects in the model.The AQMSs were treated as random effects to account for potential correlation within repeated measurements at the same AQMS.For PM2.5, the mixed-effects model was specified as (Peretz et al., 2002): For i = 1, …, k (AQMSs) and j = 1, …, ni (the repeated day or year of the i th AQMS), where Yij is the log-transformed PM2.5 concentration; β0 is an overall intercept for the study area that corresponds to mean background PM2.5 (log-transformed) when all factors equal zero; β1, …, βp are fixed effects; Xij1, …, Xijp are values of the variables for the i th AQMS on the j th day or year; b1, …, bk are AQMSs' random effects; bi is the i th AQMS random effect, which corresponds to the discrepancy between its intercept and the group intercept β0; and z1, …, zk are AQMSs' indicators.εij is the residual error associated with i th AQMS on the j th day or year.bi and εij were assumed to be independent and normally distributed, with a mean of 0, and the variances of σ 2 B (betweensite) and σ 2 w (within-site), respectively.Exponential beta [exp(β)] value of determinants strengthens the correlation of variables with PM2.5 in the model.The statistical significance was set at p < 0.05 based on a two-tailed analysis.We created univariate and multivariate models to evaluate the selective variables statistically affecting PM2.5.The fitness of each mixed-effects model with selected variables was estimated by the Akaike information criterion (AIC).A lower AIC indicates a better model fit.

PM2.5 Concentrations from the Calibrated and Uncalibrated Measurements
Table 1 shows the descriptive statistics of PM2.5 concentrations from the FRM-like (calibrated) and FEM (uncalibrated) measurements in the Big Taipei City at 16 AQMSs during 2014-2017.The annual mean concentrations of FRM-like PM2.5 were 21.5, 18.5, 17.5, and 16.6 µg m -3 in 2014,  2015, 2016, and 2017, respectively, with all the concentrations exceeding the annual standard (15.0 µg m -3 ) set by Taiwan EPA.In general, the mean PM2.5 concentrations from the FEM measurements were approximately 30% significantly (p < 0.001) higher than that from the FRMlike measurements at all the stations during 2014-2017.The ZS and LK stations had the highest mean PM2.5 concentrations from the FEM and FRM-like measurements, respectively, throughout the duration of the study.The traffic stations, including SC, DT, and YH, did not show higher PM2.5 concentrations compared with the concentrations observed at the ambient stations.As shown in Fig. S1, the annual mean concentrations of PM2.5 from both the FEM and FRM-like measurements significantly decreased by approximately 22% from 2014 to 2017 at all the AQMSs.The improvement in the air quality in terms of PM2.5 is likely attributed to several effective policies implemented by the Taiwan EPA and Environmental Protection Bureau of Taipei.Few of the policies implemented include eliminating two-stroke motorcycles and old-generation diesel vehicles, promoting electric buses and electric motorbikes, emission control measures for the catering industry, stricter standards for boiler emissions, and implementing low-sulfur jet fuel.As shown in Fig. S1, the PM2.5 concentrations at CL (31.9 µg m -3 in 2014 to 20.5 µg m -3 in 2017) from FEM measurements In addition, the lowest decline in PM2.5 concentrations was observed at LK (12.5%) and XD (7%) from the FEM and FRM-like measurements, respectively.The FEM and FRM-like measurements presenting such a dissimilarity in the reduction of PM2.5 levels measured at the stations may mask information on the effectiveness of region-specific ambient air quality management.

Variations in PM2.5 Concentrations from the FEM and FRM-like Measurements
Table 2 shows σB 2 , σW 2 , and total variance (σTotal 2 ) of daily and annual FEM and FRM-like PM2.5 concentrations at 16 AQMSs during 2014-2017.The daily FEM PM2.5 concentrations were dominated by the within-site variability (> 90% of σTotal 2 ) rather than the between-site variability.When the daily FRM-like data was analyzed in the null model (all factors of fixed effects equal zero), the between-site variability (σB 2 = 0.004; 1.29% of σTotal 2 ) in PM2.5 concentrations decreased by ~8% of total variance compared with FEM data (σB 2 = 0.027; 9.84% of σTotal 2 ) as shown in Table 2.The increase of σW 2 (=0.339; 98.7% of σTotal 2 ) in FRM-like PM2.5 could be also observed compared with that in FEM PM2.5 (σW 2 = 0.245; 90.2% of σTotal 2 ).While fitting such linear regression models, the calibration procedure limits the inherent variation in PM2.5 concentrations obtained from the AQMSs at various locations, which may reduce spatial variation in PM2.5 concentrations.Basically, the FRM measurements of PM2.5 at five AQMSs (SL, WH, XZ, BQ, and Taoyuan) were used to calibrate single or multiple FEM measurements at the corresponding AQMSs through linear regression models and coefficient of determination (R 2 , mean = 0.92, range = 0.83-0.97)during 2014-2017 (Tables S1-S4).For instance, the FRM measurement at one station (WH) was shared by the FEM measurements at a maximum of 8 AQMSs for calibration, where R 2 ranged from 0.86 to 0.97 in 2014 (Table S1).When we compared daily variations in PM2.5 concentrations from the FRM and FEM measurements during 2014-2017, σTotal 2 and coefficient of variation (CV) and σW 2 of PM2.5 concentrations from the FRM measurements were larger than those from the FEM measurements (Table S5).Hence, it can be stated that the calibration approach of FRM-like PM2.5 measurements directly decreases the spatial heterogeneity in PM2.5 concentrations across sites.
For annual PM2.5, the within-site (σW 2 = 0.016) and between-site (σB 2 = 0.014) variance in the FEM measurements were similar.However, the between-site variance in the FRM-like measurements became negligible (σB 2 = 0%) after the calibration process.The within-site variation (σW 2 = 0.245, accounting for 90.2% of σTotal 2 ) in daily PM2.5 concentrations was much higher than that (σW 2 = 0.016, accounting for 52.3% of σTotal 2 ) in annual PM2.5 concentrations, indicating the importance of temporal variation in PM2.5 concentrations for studying short-term PM2.5 exposure.Che et al. (2015) indicated that the within-group exposure variability is larger than the between-group variability for the daily exposure of children to PM2.5.Our recent study also reported that the within-subject variability (81.3% of σTotal 2 ) in personal exposure concentrations of PM2.5 was higher than the between-subject variability in concentrations (18.7% of σTotal 2 ) for university students (Hsu et al., 2020).In contrast, long-term (annual) concentrations of PM2.5 were fairly attributable to the between-site or between-group variability (47.8%).As a result, some advanced exposure models with the spatial variables have been used to estimate PM2.5 exposure.For instance, the land-use regression model incorporating annual PM2.5 levels from the monitoring stations and geographic information has been successfully developed to predict ambient PM2.5 concentrations for exposure estimates in epidemiological studies (Eeftens et al., 2012;Wu et al., 2017).However, PM2.5 concentrations from FEM measurements are more reliable to be incorporated in geographic-based prediction models, while the annual FRM-like PM2.5 data has almost zero between-site variability (i.e., σB 2 = 0).To minimize the measurement error, the calibration of FRM-like PM2.5 is still suggested after the exposure estimates in the health risk analysis have been done.

Factors Determining Variability in PM2.5 Concentrations
Table 3 shows the definition of variables for 16 AQMSs.The information about these variables was obtained from the Taiwan EPA site and the nearest weather bureau.FEM PM2.5 concentrations and 12 variables associated with meteorology, gaseous air pollutants, and sampling site characteristics were included in the models.Since FRM-like PM2.5 concentrations presented an extremely low σB 2 , this data was not evaluated in the mixed-effects model.
Table 4 shows the model coefficients for the selected variables correlated with daily FEM PM2.5 determined by the univariate and multivariate analysis.By performing the univariate analysis in the model, we found that the PM2.5 concentrations decreased significantly from 2014 to 2017,  when compared with the reference concentration in 2017.The meteorological factors including ambient temperature, relative humidity, wind speed, and rainfall were negatively correlated (p < 0.001) with ambient PM2.5, which explained 18.3% [(0.246-0.201)/0.246] of the within-site variability and 6.63% [(0.027-0.025)/0.027] of the between-site variability (Table S6).The ambient pressure was not included in the model for daily PM2.5 estimates because of its high correlation with ambient temperature.The factors such as gaseous air pollutants (NO2, O3, and SO2) were positively correlated (p < 0.001) with ambient PM2.5, explaining 45.8% [(0.246-0.133)/0.246] of the within-site variability and 26.8% [(0.027-0.020)/0.027] of the between-site variability (Table S6).Among sampling site factors, the only variable significantly affecting PM2.5 concentrations was the type of instrument used for measurement, explaining 0% of the withinsite variability but 19.5% [(0.027-0.021)/0.027] of the between-site variability (Table S6).It was observed that the VEREWA F701 sampler presented a higher value of 17% than the MetOne 1020 sampler.By performing the multivariate analysis in the model, we found that all the factors significantly affected concentration variability, explaining 50.2% [(0.245-0.122)/0.245] of the within-site variability and 15.3% [(0.027-0.023)/0.027] of the between-site variability (Table S6).
The AIC scores from each mixed-effects model were shown in Fig. 2. We found that the selective model considering all the significant variables can predict 55% of ambient PM2.5 concentrations.Among all the variables, NO2, O3, and SO2 were the predominant variables, explaining 22.1%, 13.5%, and 16.1% of σTotal 2 of PM2.5, respectively.The meteorological factors have a strong influence on the pollutants, leading to daily fluctuations in the pollutant levels.These factors have been shown to explain 50-60% of σTotal 2 of winter concentrations in China in a previous study by Zhang et al. (2015).The elevated PM2.5 concentrations with lower temperature and higher atmospheric pressure are usually observed because the lower mixing layer and higher frequency of thermal inversion in winter can restrict atmospheric dispersion and thereby trap organic and inorganic matter in the particles.It was observed that the decrease in wind speed due to unfavorable atmospheric diffusion could lead to an increase in PM2.5 concentrations (Liao et al., 2018).The long-range transport usually observed in Taipei during the cold season may be, in part, attributable to the elevated PM2.5 concentrations (Kuo et al., 2013;Hsu et al., 2019).The positive correlation of PM2.5 with gaseous air pollutants in our study confirmed the enhanced levels of PM2.5 due to the chemical reactions in the atmosphere involving precursor gases of NO2 and SO2.O3 was significantly and positively correlated with PM2.5, which probably could be explained by the covariance of VOCs.However, the precursor formation and meteorological conditions can add complexity to the relationship between both the air pollutants.Ito et al. (2007) have reported that the correlation between O3 and PM2.5 changed with the season (positive in summer and negative in winter).In a previous study by Liu et al. (2013), it was highlighted that the use of different aerosol samplers (MetOne 1020 vs VEREWA-F701) for measuring PM2.5 concentrations might result in a potential bias of exposure variability.It was not surprising that the height of the sample port, distance to the nearest main road, and station type were not significantly associated with ambient PM2.5 because the inherent confounders were not available for adjustment.Quang et al. (2012) indicated that Fig. 2. AIC scores for the selected variables associated PM2.5 concentrations using mixed-effect models.the PM2.5 concentrations decreased with the increase in the height of the office building; however, the vehicle emissions, particle formation, flow patterns around the building envelope, and street profile were the important determinants that should be taken into account for comparison.In addition, the differences in the aerosol instruments (MetOne 1020 and VEREWA F701) used in our study and the variations in the sampling factors (i.e., height of the sample port, distance to the nearest main road, and station type) led to variations in PM2.5 concentrations.For annual PM2.5, SO2 was significantly correlated with PM2.5 in addition to ambient temperature and time (in years) (Table S7).In the population-based study associated with exposure to PM2.5, meteorological conditions (i.e., temperature) are often adjusted in the model (Luo et al., 2016).Our results showed SO2 as an important factor showing a significant positive correlation with both daily and annual PM2.5.We suggest that SO2 should be taken into account in the future for health risk analysis associated with PM2.5 exposure for adjustment.

CONCLUSIONS
In this study, we highlighted that the FRM-like PM2.5 measurements with negligible betweensite variability might lead to non-differential misclassification of exposure.The gaseous pollutants (such as NO2, O3, and SO2) are significant factors affecting the spatial and temporal variations in ambient PM2.5 concentrations, which should be incorporated in the health risk assessment model.We indicated that the FEM measurements of PM2.5, rather than the FRM-like measurements, at the AQMSs are mainly applicable for exposure estimates in epidemiological studies.Then, the resultant exposure estimates of PM2.5 are further calibrated with the FRM measurements to minimize the measurement errors.

ACKNOWLEDGMENTS
We appreciate the measurement data supported from the Environmental Protection Administration Executive Yuan, Taiwan.The authors gratefully acknowledge funding received

Table 1 .
The descriptive statistics of PM2.5 concentrations (µg m -3 ) with calibrated and un-calibrated measures in Big Taipei city among 16 AQMS for 2014-2017.µg m -3 in 2014 to 14.0 µg m -3 in 2017) from FRM-like measurements drastically reduced by 35-40% owing to the operation of Taipei mass rapid transit (MRT) for the Xinzhuang reduced by 35-40% owing to the operation of Taipei mass rapid transit (MRT) for the Xinzhuang line in 2014.

Table 3 .
Definition of variables for 16 AQMS obtained from Taiwan EPA site and Weather Bureau.

Table 4 .
Model coefficients for meteorological, air pollutant and sampling site factors associated with daily ambient PM2.5 with FEM measurements.