1. Introduction

2. Methodology

3. Results and Discussions

3.1. Observed PurpleAir and Regulatory PM_2.5

It was imperative to evaluate and validate PurpleAir PM_2.5 with observed PM_2.5 at regulatory sites. Figure 1 also shows FEM/FRM and non-FEM/FRM monitored PM_2.5 sites in California during 2016 and 2023. Details of these sites are in Table 1, , with AQS ID, site name, PurpleAir monitor ID, and dates of monitoring. It also shows approximate distance calculated between PurpleAir monitor and regulatory site. Regulatory sites data were downloaded from EPA AQS Datamart from 2016 to 2022 [30]. The most recent PM_2.5 data are available till Oct 2022 and used for the analysis. PurpleAir monitored PM_2.5 was graphically and statistically evaluated for both FEM/FRM and non-FEM/FRM monitored PM_2.5. All regulatory sites with PurpleAir monitor within 20 meters were analysed. Time-series and scatter plots are shown only for four FEM/FRM and four non-FEM/FRM sites were selected covering North to South of California for discussions.

Table 1. Statistical assessment of hourly average PurpleAir PM_2.5 at selected sites for the years 2016 and 2022 at FEM/FRM and non-FEM/FRM sites.

Table 1. Statistical assessment of hourly average PurpleAir PM_2.5 at selected sites for the years 2016 and 2022 at FEM/FRM and non-FEM/FRM sites.

Site Name and AQS ID, POC	PurpleAir Sensor Index	Distance, mts	Dates Duration	Num. of Paired Observation (#)	R2	Mean Bias (µg/m3)	RMSE
FEM/FRM
El Rio-Rio Mesa Schl. 061113001, 3	9594	0.18	4/2/18 to 8/31/22	30,798	0.50	3.5	7.85
Fresno-Garland 060190011, 3	2358	1.87	7/31/17 to 12/9/19	17,194	0.83	5.7	11.85
Goleta-Fairview 060832011, 1	16705	0	9/29/18 to 6/30/22	28,532	0.56	3.4	6.93
Lompoc 060832004, 1	16703	0	9/29/18 to 6/30/22	28,482	0.60	2.1	6.21
Non-FEM/FRM
Bakersfield 060290014, 3	2350	0.6	7/31/17 to 3/8/22	34,583	0.73	4.3	11.70
Calexico-Ethel Street 060250005, 3	1174	0.0	10/24/17 to 2/19/18	2,486	0.89	3.5	11.60
Sacramento-T Street 060670010, 3	8440	2.1	2/2/19 to 12/11/20	14,797	0.86	4.2	10.20
Riverside 060658001, 9	1854	8.5	7/10/17 to 12/31/19	14,604	0.69	5.7	9.70

Table 2. Sensor Data summary over different regions in California.

Table 2. Sensor Data summary over different regions in California.

PM2.5 (µg/m3)	Bay Area	Sac Metro	San Diego	SJV	South Coast	Bay Area	Sac Metro	San Diego	SJV	South Coast
	2019						2018
Count	184,668	8,918	5,240	4,497	115,764	31,203	2,255	2,355	11,242	103,248
Maximum	201	101	217	155	185	251	300	73	277	306
Mean	7	10	11	13	13	15	23	13	20	15
Median	5	6	9	8	10	7	11	11	13	12
Std. Deviation	8	12	9	15	11	26	41	10	21	12
Standard Error	0.02	0.13	0.13	0.1	0.03	0.15	0.86	0.2	0.2	4
Q1	2	3	5	4	5	3	4	6	6	7
Q3	9	11	14	14	17	15	25	18	29	21
Inter Quartile Range	7	8	9	10	12	12	21	12	23	14

Figure 3 and Figure 4 show hourly average PM_2.5, in black lines, at four FEM/FRM and four non-FEM/FRM sites and PurpleAir PM_2.5 in purple dots. From these figures, it is very clear that PurpleAir monitors captured the trend of PM_2.5 at regulatory monitors from 2016 to 2022. PurpleAir observed higher PM_2.5 concentrations for both FEM/FRM and non-FEM/FRM regulatory monitors. They also captured the PM_2.5 events due to forest fires along with regulatory monitors. PurpleAir PM_2.5 followed the trends of regulatory monitors for both less than 100 µg/m³ and greater than 100 µg/m³ PM_2.5 concentrations. PM_2.5 above 200 µg/m³ were captured by PurpleAir at Fresno-Garland (Figure 3(c)) and all non-FEM/FRM sites with an exception of one day spike at El Rio-El Rio Mesa School (Figure 3(d)). Spikes in PM_2.5 concentrations at Sacramento-T Street (Figure 4(c)) were observed due to forest fire and the trend can be seen by both regulatory and PurpleAir monitors. PM_2.5 episodic events from windblown dust at Calexico-Ethel Street (Figure 4(a)) were also captured by both regulatory and PurpleAir monitors. Thus, the sensors have been able to capture local as well as regional episodic events.

Figure 5 shows scatter plots with hourly average PurpleAir PM_2.5 concentrations on y-axis and regulatory monitored PM_2.5 concentrations on x-axis. These plots show PurpleAir monitored higher concentrations than regulatory monitors for most of the times. Scatter plots also show +/- 25% dotted lines and for majority of times the scatter dots were out of +/- 25% range with higher number of dots towards y-axis or PurpleAir PM_2.5. The linear fit line for all sites is on the positive side of +25%. Only El Rio School site (Figure 5(b)) site has shown one-to-one linear fit.

PurpleAir monitored PM_2.5 were mostly higher than the regulatory monitored PM_2.5. It may be due to since PurpleAir monitors were calibrated by the manufacturer using particles with properties completely different than particulate matter in the ambient air [31] and the conversion of particle counts to mass is also unknown [15]. Besides that, it was found that the ambient air also includes water droplets with aerodynamic particle size. Traditionally, both FEM/FRM and non-FEM/FRM monitors measure PM_2.5 by removing water content in the sample inlet. This was achieved by heating the sample air in the inlet pipe. However, on contrary PurpleAir sensors measure PM_2.5 concentrations without removing moisture content in aerosols. It is the water content in the ambient air that makes PM_2.5 measured by PurpleAir as an “Absolute PM_2.5” or with context to regulatory monitors as “Wet PM_2.5”. The adjustment of water content in the PurpleAir measured PM_2.5 during the conversion from particle count to mass is unknown. Therefore, even before the comparison between PurpleAir PM_2.5 with FEM/FRM and non-FEM/FRM monitored PM_2.5, the PurpleAir PM_2.5 concentrations will be greater than regulatory monitors for most of the times.

Table 1 shows statistical evaluation of PurpleAir monitors in comparison with regulatory monitors. For statistical evaluation of the PM_2.5 corelation coefficient (R²), mean bias (MB), and root mean square error (RMSE) were performed. Mean bias is primarily used to estimate the average bias between two variables. The coefficient of determination, R-squared (R²) determines how well data fit regression model to observation data. The Root Mean Square Error (RMSE) is a frequently used measure of the difference between two values. RMSE measures how much error there is between two variables. Equations of the evaluation indices are shown below:

$$\mathrm{M}\mathrm{B}=\frac{1}{\mathrm{n}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{R}}_{\mathrm{i}}\right)$$

(2)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{\mathrm{n}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{R}}_{\mathrm{i}}\right)}^2}$$

(3)

$${\mathrm{R}}^2={\left[\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{i}}{\mathrm{R}}_{\mathrm{i}}-\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{i}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{R}}_{\mathrm{i}}}{\sqrt{\left[\mathrm{n}\sum _{\mathrm{i}=1}^{\mathrm{n}}{{\mathrm{P}}_{\mathrm{i}}}^2-{(\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{i}})}^2\right]\left[\mathrm{n}\sum _{\mathrm{i}=1}^{\mathrm{n}}{{\mathrm{R}}_{\mathrm{i}}}^2-{(\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{R}}_{\mathrm{i}})}^2\right]}}\right]}^2$$

(4)

where, Pi is PurpleAir PM_2.5 concentrations, Ri is regulatory PM_2.5 concentrations, $\overline{R}$is mean of Ri, $\overline{P}$is mean of Pi, and n is the number of hourly samples.

For all FEM/FRM (Table 1 and Table S1), coefficient of determination, R² values were between 0.23 and 0.9 with an average of 0.62 and for all non-FEM/FRM (Table 1 and Table S2), R² values were between 0.27 and 0.92 with an average of 0.74 which were lower than reported studies conducted for shorter durations (SCAQMD, 2020; LRAPA, 2021; Gupta et al., 2018). The coefficient of determination, R², of Goleta, El Rio-El Rio School, and Lompoc-H Street has shown lowest values of 0.56, 0.5, and 0.6 respectively. These three sites are along the coastlines of Southern California. It is expected that moisture content in the coastal air will be higher than the inland area. This affirms that moisture content plays a significant role in PurpleAir PM_2.5 monitoring. Moisture in the air attracts PM due to its hygroscopic characteristics and results in presenting higher concentrations. As of now PurpleAir monitors do not heat inlet air compared to regulatory monitors. Rest of the sites, located inland, have shown higher R² of greater than 0.70. The mean bias is highest at Fresno-Garland of 9.62 µg/m³ followed by 6.93 µg/m³ at Sacramento-T Street as shown in Supplement Tables S1 and S2. Mean bias for all sites were positive showing higher PM_2.5 from PurpleAir than FEM/FRM and Non-FEM/FRM.

After validation of performance of purple air sensors with observed data the sensor data was used to perform detailed summary statistics across different regions of California Bay Area Air Quality Management District (AQMD) (Bay Area), Sacramento Metropolitan AQMD (Sac Metro), San Diego Air Pollution Control District (APCD) (San Diego), San Joaquin Valley APCD (SJV), and South Coast AQMD (South Coast) according to the availability of data from years 2016-2019. After excluding poorly performing sensors (around 4%) all the purple air sensors were used in this statistical analysis. Table 2 represents statistical data analysis for two more recent years 2018 and 2019.

A wide range of PM_2.5 concentrations was seen across the sensor dataset with a maximum 24-hour average of around 300 μg/m³ measured in South Coast area near Los Angeles, with maximum concentrations in northern California showing impact of wildfires. Overall, the median PM_2.5 concentration of the dataset was between 5-13 μg/m³ (interquartile range: 7 to 23 μg/m³, For the individual counties the standard deviation ranged from 8 to 40 μg/m³ across the entire state of California.

It is seen that in Bay Area the average daily mean across sensors varied between15 µg/m³ 2018 to 7 µg/m³ in 2019. The standard deviation was also lower in 2019 (8 µg/m³) in comparison to values of 15 µg/m³ in 2018). The number of sensors has also increased significantly from around 369 in 2018 to around 773 sensors in 2019 in Bay Area, a growth of a huge 110 percent. The interquartile range also decreased in 2019 (around 6 µg/m³) significantly lower than that of 2018 (around 12 µg/m³). The other two areas Sac Metro and San Deigo exhibit a more modest growth of sensors (18 percent in San Diego and 94 percent in Sac Metro) in comparison to Bay Area. The southern part of California (South Coast) also has sensors over 450 in 2019.

Overall, the PM_2.5 values exhibit less magnitude and variability over the state of California showing improving trends in PM2.5 concentrations. The wildfires were more intense in 2018 than in 2019 as seen in the maxima values and standard deviation values in Bay Area.

The ANOVA (Analysis of Variance) test was performed to determine whether daily mean PM_2.5 levels as measured by the sensors across the state of California were identical to each other and show any significant difference amongst them during the study period (2017-2019). The ANOVA test indicated that there was a significant difference amongst the variances of the daily averages at the 95% significance level (p=0.00) and F statistic >0 for the different years and for the different regions. The ANOVA and Tukey test results from Bay Area have been displayed below for the years 2017, 2018 and 2019 as a representative result in Table 3.

Since the variances of the daily means were different, then the Post-Hoc test (Tukey Post Hoc test) was performed for multiple detailed comparisons. According to Tukey test, , the highest daily means of PM_2.5 levels were observed in 2018 for Bay Area (Table 4). However, there was no significant differences in variances of daily mean concentrations for Bay Area between the years 2017 and 2018 (p>.0.05), although the differences were significant with respect to 2019 (Table 4). In case of San Diego San Diego differences in variances daily mean concentrations for all years were significant (p=0.00). For South Coast and SJV the highest daily means were observed in 2016. For South Coast there were no significant differences in variances of daily mean concentrations of PM_2.5 between 2016 and 2018 ((p>.0.05), but significantly different from 2017 and 2019 (p=0.00). For SJV the differences in variances of daily means were minimal for the years 2016 and 2017 (p>0.05) and significant for other two years 2018 and 2019 (p=0.00). Therefore 2016, 2017 and 2018 may be considered the period of the highest daily PM_2.5 concentrations measured in California.

These results for these other areas have been included in supplementary material. According to the ANOVA and muti -comparison Tukey test, the lowest daily mean PM_2.5 levels was measured in 2019, disclosing a decreasing trend of daily PM_2.5 concentrations in the study area. The results are also corroborated in Table 4.

A region wise inter-comparison (Bay Area, San Diego, San Mateo, SJV and South Coast) in State of California of daily means of sensor data for the year 2018 (California had the highest number of wildfires in that year) using ANOVA (Table 5) and Tukey’s multi comparison post hoc test (Table 6) revealed highest daily mean concentrations in Bay Area (probably due to forest fires) followed closely by South Coast which is located in more polluted due to proximity to Los Angeles. The differences between Bay Area and South Coast were not significant (p>0.05). However, the differences between these two regions and the others (San Mateo, San Diego and SJV) were significant (p=0.00) and F statistic >0.

4. Conclusion

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