The first measurement campaign in the low-concentration region was on the rooftop of the Fitzpatrick Center, a three-story building located on the Duke University West Campus in Durham, NC (latitude 36.003350, longitude -78.940259). The sampling location lies in close proximity to the 28.5 km2 Duke Forest and approximately 3.5 km from the Durham downtown and 4.5 km from the Durham National Guard Armory monitoring station (latitude 36.0330, longitude -78.9043). This study location is also about 950 m southwest of the Durham Freeway, which had an annual average daily traffic of 43 000 vehicles as of 2015 (North Carolina Department of Transportation, 2015). No known principle point source emissions are located in the surrounding area. The 3-year average (2013–2015) for PM2.5 concentrations reported by the Durham National Guard Armory monitoring station was 12 µg m-3, and the reported 98th percentile daily average from 2013 to 2015 was 18 µg m-3 (North Carolina Department of Environmental Quality, 2017). At the Duke site, five Plantower PMS3003 sensors (labeled PMS3003-1 through PMS3003-5) were compared to a collocated environmental β attenuation monitor E-BAM-9800 (Met One Instruments). Unlike its more advanced counterpart BAM-1020 (Met One Instruments), the E-BAM-9800 is not currently a U.S. EPA-designated FEM for PM2.5 mass concentration continuous monitoring, although it is ideal for rapid deployment because of its portability and its ability to accurately track FRM or FEM results with proper operation and regular maintenance (Met One Instruments, 2008). The hourly values reported by the E-BAM (mg m-3) were used in the analyses. The E-BAM's sporadic negative values caused by low actual ambient concentrations (such as below 3 µg m-3) were replaced with 0 µg m-3 in this study. The sensor packages were strapped to the E-BAM tripod and operated in a collocated manner for a period of 50 days from 1 February to 31 March 2017 (all the sensor packages and the E-BAM were shut down between 3 and 12 March for maintenance). Over the course of the deployment, PMS3003-1 was disconnected between 14 and 21 February because of power supply issues, and this situation rendered PMS3003-1 data 86 % complete.

The second ambient test in the low-concentration region was performed at the U.S. EPA's Ambient Air Innovation Research Site (AIRS) on its RTP campus, NC (latitude 35.882816, longitude -78.874471) about 16 km southeast of the Duke site. The ambient PM2.5 mass concentrations in the RTP region are normally well under 12 µg m-3 (Williams et al., 2003). A Thermo Scientific 5030 SHARP (synchronized hybrid ambient real-time particulate monitor) monitor (U.S. EPA PM2.5 FEM) was operated by the U.S. EPA Office of Research and Development (ORD) and two Teledyne API T640 PM mass monitors (U.S. EPA PM2.5 FEM) were operated by the U.S. EPA Office of Air Quality Planning and Standards (OAQPS). The SHARP monitor is a hybrid of a high-sensitivity nephelometer using 880 nm infrared light-emitting diodes (IREDs) and a BAM. The SHARP continuously calculates the ratios of dynamically time-averaged beta concentrations to dynamically time-averaged nephelometer concentrations and continuously employs these ratios as correction factors to adjust the raw 1 min averaged nephelometer readings. The corrected nephelometric concentrations are reported as 1 min SHARP measurements in micrograms per cubic meter (Thermo Fisher Scientific, 2007). The T640 monitor, first introduced in 2016, is one of the latest additions to the list of approved U.S. EPA PM2.5 FEM monitors. The T640 is essentially an optical aerosol spectrometer that uses light scattering to measure particle diameters in 256 particle size classes over the 0.18–20 µm range at the single-particle level. The 256 size classes are subsequently combined into 64 channels for mass calculation with proprietary algorithms. The light source used by the T640 monitor is polychromatic (broadband) light. Compared to traditional monochromatic laser scattering approaches, the polychromatic light approach provides more robust and accurate measurements with significantly less noise, especially over the particle size range of 1 to 10 µm (Teledyne Advanced Pollution Instrumentation, 2016). The T640 reports 1 min resolution results in micrograms per cubic meter. The SHARP and one of the T640 units (T640_Shelter) were installed inside an ORD mobile laboratory and an OAQPS shelter, respectively, with roof penetration while the other T640 unit (T640_Roof) was installed inside an outdoor enclosure with heating, ventilation, and air conditioning (HVAC) control on the rooftop of the OAQPS shelter. Three PMS3003 sensor packages from the Duke site (labeled PMS3003-1 through PMS3003-3) were attached to the rail on top of the ORD mobile laboratory approximately 3 to 4 m above the ground. The SHARP inlet and the sensor packages' inlets were only about a meter apart. The two T640 inlets were situated on the rooftop of the OAQPS shelter, within about 30 m of the sensor packages' inlets. The inlets of these instruments were positioned roughly at the same height above ground. Over the course of the 32-day field project (30 June to 31 July 2017), all the instruments' data completeness was 100 % except that of SHARP (99 %). The slightly incomplete SHARP data stemmed from the removal of midnight concentration spikes (at approximately 01:00 to 01:10 EDT, eastern daylight time) due to the daily filter tape advancement.

Identical to the setup at the Duke site, the third field evaluation involving two PMS3003 sensors (labeled PMS3003-6 and PMS3003-7) alongside an E-BAM was carried out on the rooftop of the Center for Environmental Science and Engineering inside the campus of IIT Kanpur (latitude 26.515818, longitude 80.234337). The center is a two-story building (roughly 12 m above the ground level) that lies approximately 15 km northwest of downtown Kanpur. The institute is located upwind of Kanpur and away from major roadways, industrial sites, and dense residential communities; therefore it has comparatively low PM2.5 concentrations (Villalobos et al., 2015). Kanpur is a heavily polluted industrial city on the Indo-Gangetic Plain with a large urban area of dense population (approximately 2.7 million) (Villalobos et al., 2015). Various small-scale industries, a coal-fired power plant (Panki Thermal Power Station), indoor and outdoor biomass burning, heavy vehicles on the Grand Trunk Road (a major national highway) running through Kanpur, fertilizer plants, and refineries are the prime contributors to air pollution (Shamjad et al., 2015; Villalobos et al., 2015). The local climate is primarily defined as humid subtropical with extremely hot summers and cold winters (Ghosh et al., 2014). The monsoon season (June to September) is documented to have lower PM2.5 concentrations than the post-monsoon season (October and November) (Bran and Srivastava, 2017). The two sensor packages were first deployed at the study site on 8 June 2017 for approximately 22 days (early monsoon), and then on 23 October 2017 for approximately 25 days (post-monsoon). Since these two sensor units were not embedded with temperature and RH sensors, the temperature and RH data (available as 15 min averages) were simultaneously collected from an automatic weather station, roughly 500 m away from the study site and 2 to 3 m above the ground. Throughout the sampling periods, error-flagged E-BAM measurements (including delta temperature set point exceeded, flow failure, abnormal flow rate, beta count failure) during the operation were excluded from the analyses for quality assurance purposes, and this caused the E-BAM data to be 85 % and 93 % complete for monsoon and post-monsoon seasons, respectively. The two sensor packages had data completeness close to 100 % for both monsoon and post-monsoon seasons. The temperature and RH data from the automatic weather station were only occasionally missing due to power supply issues with an overall 93 % and 99 % completeness for monsoon and post-monsoon seasons, respectively.

FEMs and research-grade PM analyzers typically control for RH by dynamically heating the sample air inlet. Our sensor packages, similar to many low-cost designs, are not equipped with any heaters or conditioners to reduce RH impact. Therefore, the RH can significantly bias the PM2.5 mass concentrations reported by our sensor packages. The effect of RH on the mass of atmospheric aerosol particles has been well documented for decades. Sinclair et al. (1974) showed that there was a 2- to 6-fold increase in the mass of particles, depending on the properties of the particles, as the RH reached 100 %. Waggoner et al. (1981) also showed that RH above roughly 70 % can enhance scattering coefficients of hygroscopic or deliquescent particles in various locations in the western and midwestern US due to the growth of these particles associated with water uptake. Zhang et al. (1994) described the calculated scattering efficiencies of ammonium sulfate in the Grand Canyon as a function of RH with empirical Eq. (1). This equation was later employed by Chakrabarti et al. (2004) to predict the effect of RH on the relationship between the nephelometric personal monitors' PM2.5 mass concentration measurements and the results of a reference monitor (BAM). They found that the model agreed quite well with the field data collected from both their study and a previous study (Day and Malm, 2001). An identical equation was also among a wide variety of approaches assessed by Soneja et al. (2014) to adjust nephelometric personal monitor PM2.5 readings for the RH impact. We believe lessons learned from these previous studies can be directly applied to RH adjustments for low-cost nephelometric sensors' PM2.5 measurements in the present study by using Eq. (1): RHcorrectionfactor=scatteringefficiency(foragivenRH)scatteringefficiency(RH=30%)=rawPMS3003PM2.5conc.(foragivenRH)referencePM2.5conc.(foragivenRH)=a+b×RH21-RH. Ordinary least-squares (OLS) regressions were conducted to obtain the empirical regression parameters a and b in Eq. (1), where the dependent variable was the RH correction factors calculated as the ratio of PMS3003 PM2.5 mass concentrations averaged across all the sensor package units to the corresponding reference monitor concentrations at each point in time at a sampling location, and the independent variable was the entire RH2/(1-RH) term. The RH was the measurements averaged across all the embedded Sparkfun SHT15 RH and temperature sensors at each point in time for the calibration models of Duke University and EPA RTP study sites, and the measurements from the automatic weather station for the models of the IIT Kanpur study site. The empirical equations derived were used to compute the RH correction factor for a given RH at the sampling sites. The RH interferences were compensated for by dividing each individual raw PMS3003 PM2.5 mass concentration for a given RH by the RH correction factor yielded for that RH (Eq. 2): RHadjustedPMS3003PM2.5conc.=rawPMS3003PM2.5conc.(foragivenRH)RHcorrectionfactor(foragivenRH). We only performed the RH adjustments when the fitted models for any of the sampling locations over any time-averaging interval had at least a moderate coefficient of determination (R2≥0.40). The slightly high correlation cutoff value was implemented in this study to ensure that the RH corrections can effectively lower the error of the low-cost sensor PM2.5 measurements. Despite the similarity of the general shape of correction factor curves in different studies, the detailed behaviors of aerosols diverged greatly due to considerable difference in particle chemical composition and diameter (Waggoner et al., 1981; Zhang et al., 1994; Day and Malm, 2001; Chakrabarti et al., 2004; Soneja et al., 2014). In a previous study (Day and Malm, 2001), aerosol mass at some locations increased continuously above a relatively low RH (such as 20 %), whereas at other locations it exhibited a distinct deliquescent behavior (i.e., aerosol water uptake occurred at a relatively high RH). Even for aerosols showing deliquescent behavior, the observed deliquescence RH (RH threshold) varies from study to study. Soneja et al. (2014) also found underestimation of PM concentrations (correction factors less than 1) below 40 % RH. Because of these uncertainties, we conducted RH adjustments across the entire range of recorded RH without incorporating an RH threshold. Additionally, the RH adjustments in this study were always performed separately from and prior to either temperature adjustments or reference monitor adjustments.

The Akaike's information criterion (AIC) is a widely used tool for model selection to address the fact that including additional predictors may overfit the data (Crawley, 2017). It was used to determine the significance of the temperature term in the PMS3003 calibration models for all the study locations at various averaging times. The AIC penalizes more complex models based on the number of parameters fit in that model. A lower AIC when comparing two models for the same data set indicates a better fitting model. In a linear regression model, an AIC difference between two models of less than or equal to 2 indicates that the more complex model does not improve predictive performance. Therefore, the simpler model should be adopted. We specifically compared the AIC value of a multiple linear regression model, which included both the reference monitor measurement and temperature as predictor variables and without considering an interaction term (i.e., Eq. 3) to the value of a univariate linear regression model with only the reference monitor measurement as a predictor variable (i.e., Eq. 4). We performed the temperature adjustments using Eq. (5) only when the AIC indicated that the temperature predictor was significant in the calibration model (i.e., AICEq.(4)-AICEq.(3)>2). [raw(orRHadjusted)PMS3003PM2.5conc.]=β0+β1referencePM2.5conc.+β2temperature[raw(orRHadjusted)PMS3003PM2.5conc.]=β0+β1referencePM2.5conc.temperatureandreferencemonitor(andRH)adjustedPMS3003PM2.5conc.=[raw(orRHadjusted)PMS3003PM2.5conc.]-β0-β2temperatureβ1 The temperature was the measurements averaged across all the embedded Sparkfun SHT15 RH and temperature sensors at each point in time for the models of Duke University and EPA RTP study sites and the measurements from the automatic weather station for the models of the IIT Kanpur study site. Since the RH adjustments in this study were always performed first, the PMS3003 PM2.5 concentration in Eqs. (3) and (4) were RH-adjusted PMS3003 PM concentrations when RH adjustments were significant and were otherwise raw PMS3003 PM2.5 concentrations. Additionally, temperature adjustments and reference monitor adjustments were always conducted simultaneously when the temperature predictor was significant because Eq. (3) consists of both the reference monitor concentration and temperature terms as independent variables. The AIC values for models with 24 h data are not reported in the present study as 24 h observations generally have limited statistical power to determine the significance of temperature in the models.

The most basic calibration is a direct comparison with reference monitor measurements. We derived reference instrument calibration equations (Eq. 4) by fitting a linear least-squares regression model to each pair of PMS3003 (dependent variable) and collocated reference instrument's PM2.5 mass concentrations (independent variable). The PMS3003 PM2.5 values were RH-adjusted concentrations when RH adjustments were significant and were otherwise raw concentrations. Each PMS3003 measurement was subsequently calibrated using Eq. (6).

When the relationship between PM2.5 mass concentrations of reference monitors and PMS3003 sensors was nonlinear, PM2.5 sensor calibration equations based on reference monitor values in a quadratic form (Eq. 7) were used to describe the nonlinear performance and each PMS3003 measurement was subsequently calibrated using Eq. (8) since calibrated values should always be on the left side of the axis of symmetry of the parabola with a2<0. The AIC values (discussed in Sect. 2.3.2), and the root-mean-square errors (RMSEs) (Eq. 9) were used in combination to assess the goodness of fit and accuracy of the two model approaches (i.e., univariate linear and quadratic models) as a function of integration times. [referencemonitor(andRH)adjustedPMS3003PM2.5conc.]=[raw(orRHadjusted)PMS3003PM2.5conc.]-β0β1[raw(orRHadjusted)PMS3003PM2.5conc.]=a0+a1×referencePM2.5conc.+a2×referencePM2.5conc.2referencemonitor(andRH)adjustedPMS3003PM2.5conc.=-a1+a12-4a2×a0-[raw(orRHadjusted)PMS3003PM2.5conc.]2a2RMSE=1n∑i=1ny^i-yi2 Here n is the number of observations, y^i is the calibrated PMS3003 PM2.5 mass concentrations, and yi is the reference monitor PM2.5 mass concentrations.

Table 1 shows the summary statistics for 1 h averaged measurements at Duke University from 1 February to 31 March 2017. The 1 h E-BAM PM2.5 measurements averaged 9±9 µg m-3. The hourly PM2.5 averages of the uncalibrated sensors were close to those of the E-BAM and had little intra-sensor variability. We calculated the coefficient of variation (defined as the ratio of the SD and the mean of the PM2.5 readings from the five replicate PMS3003 sensors) as an indicator of sensor precision, which yielded 10 %, indicating the relatively high precision of the PMS3003 model. RH and temperature averaged 45±19 % and 15±8 ∘C, respectively. Figure 3 compares the 1 h E-BAM PM2.5 mass concentrations to the results of the five uncalibrated sensors. Overall, the uncalibrated PMS3003 measurements followed the trend in ambient PM2.5 concentrations and were very responsive to most sudden spikes in concentrations. However, the sensors tended not to track the E-BAM well below ∼10 µg m-3.

Correlations among the five uncalibrated PMS3003 units were high (R2=0.98–1.00) on a 1 h timescale even under low ambient PM2.5 concentrations with slopes averaging 1±0.1 and negligible intercepts averaging 0.3±0.3 (Fig. S1 in the Supplement), suggesting excellent intra-PMS3003 precision. Regressions of the uncalibrated 1 and 24 h PM2.5 measurements from the five PMS3003 units versus the corresponding E-BAM PM2.5 values indicate that different PMS3003 sensor units generally had similar calibration factors (i.e., intercept and slope values) on the same timescale (Fig. 4). Comparing across the time-averaging interval spectrum (Table 2), the calibration factors on different timescales were consistent, with the exception of 1 h results. Raw 1 h aggregated PMS3003 PM2.5 concentration measurements correlated only moderately with the corresponding E-BAM data, with a mean R2 of 0.40 (range: 0.36–0.41). When the averaging time increased from 1 to 6 h, the R2 showed a marked improvement (mean: 0.80, range: 0.77–0.82). When the averaging time further rose to 12 h and from 12 to 24 h, although still accompanied by improvements in R2 (mean: 0.84 and 0.93, respectively), the magnitudes of the improvements were considerably smaller than the one seen from 1 to 6 h.

The SCAQMD (2017a) also field-tested three Plantower PMS3003 units (Laser Egg sensors) alongside an FEM (BAM-1020, Met One Instruments) over a study period of similar length (roughly 2 months) with similar ambient PM2.5 concentrations (1 h PM2.5 range: 0–40 µg m-3) in Riverside, CA, although the data were presented differently (with reference and sensor measurements on the y and x axes, respectively) and thus the values of calibration factors cannot be directly compared to our study. The SCAQMD study demonstrated the calibration factors on a 1 h scale (intercept: 5.9–6.3, slope: 0.50–0.57) were virtually the same as the values on a 24 h scale (intercept: 6.0–6.3, slope: 0.48–0.57). This observation is in contrast to our finding in which 1 h results (intercept: 3.2–4.1, slope: 0.64–0.79) differed dramatically from the 24 h values (intercept: -4.6 to -3.6, slope: 1.5–1.8). This discrepancy might stem from the use of different reference instruments in the two studies. While both instruments use beta attenuation as the measurement principle, the accuracy of BAM-1020 (FEM) for 1 h measurements in the SCAQMD study is significantly better than that of the E-BAM-9800 (research grade) in our study. This may also account for the higher R2 on a 1 h scale in the SCAQMD study (around 0.58).

Table 2 shows that the pattern of errors was aligned with our expectation, with each of the four time integration values having successively more accurate post-calibration PMS3003 PM2.5 concentrations than all the previous time integration values (i.e., the error decreased as the averaging time increased). Furthermore, the steep gradient at which the mean error reduced over averaging time (from 201 % for 1 h to 15 % for 24 h) was unusual and most likely caused by E-BAM's poor signal-to-noise ratio at low concentrations with short real-time average periods. This finding points out that the precision of reference monitors is a critical factor in sensor evaluation, as discussed in detail in Sect. 3.2.2. It should be noted that the strong correlation on a 6 h scale (R2 mean = 0.8) did not translate into a low error (mean: 53 %). This observation emphasizes the downside of overreliance on the correlation in the examination of sensor performance.

Figure S2 displays the relationship between the PMS3003-to-E-BAM PM2.5 ratio and RH on a 1 h scale at Duke University. There was no apparent pattern of fractional increase in PM2.5 weight measured by uncalibrated PMS3003 sensors with RH. Fitting the empirical RH correction factor model (i.e., Eq. 1 in Sect. 2.3.1) to these field data resulted in an R2 close to 0. Examination of patterns and model fitting at longer averaging time intervals (i.e., 6, 12, and 24 h) yielded comparable results (not shown). These findings are indicative of the negligible impact of RH on PMS3003 PM2.5 responses at Duke University. This lack of RH interference is believed to stem from a combination of infrequently high RH conditions during the winter months (only 12.5 % and 4.0 % of the entire time greater than 70 % and 80 %, respectively) and large measurement error inherent in the E-BAM under low PM2.5 concentrations.

Table S1 demonstrates that the AIC differences between the calibration models with only a true PM2.5 concentration term and the models incorporating an additional temperature term were greater than 2 for only the 1 h aggregated data, implying the calibration model with an added temperature term was significantly better than its simpler counterpart only on the 1 h scale. Therefore, the temperature adjustment was performed only for 1 h averaged PMS3003 responses at the Duke University study site. Counterintuitively, Table 2 shows that the temperature correction worsened the sensor performance by bringing the mean of ratios down from 0.97 to 0.90 and by bringing the error up from 201 % to 207 %. The deterioration in performance was likely to arise from large measurement error inherent in the E-BAM under low PM2.5 concentrations.

Figure 5a shows 1 h time series data from all the reference monitors including the SHARP's embedded nephelometer and Fig. 5b juxtaposes the T640_Roof and the three uncalibrated PMS3003 units' PM2.5 measurements at 1 h time resolution. Table 1 indicates that the 1 h averaged ambient PM2.5 levels at the U.S. EPA RTP (9–10 µg m-3) matched those at Duke University (9 µg m-3). However, Fig. 5a depicts smaller ranges of ambient PM2.5 concentrations than were measured at Duke University. Table 1 indicates that the SD (less than 4 µg m-3) and maximum PM2.5 concentration (less than 20 µg m-3) at the EPA RTP were significantly lower than at Duke University (9 and 62 µg m-3 for SD and maximum, respectively). These comparisons imply that the RTP sampling location had overall lower ambient PM2.5 concentrations and was consequently more challenging for low-cost sensors than the Duke University sampling site. During the measurement period, the mean RH and temperature were 64±22 % and 30±7 ∘C, respectively. The higher average RH level at the EPA RTP than at Duke University (45±19 %) accentuated the RH interference in the PMS3003 PM2.5 measurements, as seen in Sect. 3.2.3.

Figure 6a–b graphically and statistically summarize the pairwise correlations among all the instruments' 1 min aggregated and 1 h aggregated PM2.5 mass concentrations, respectively. The R2 and calibration factors among all the instruments on 1 min and 1 h scales were similar. The PMS3003 sensors were well correlated with one another (R2=0.97), the two T640 sensors (R2≥0.63), and the SHARP's embedded nephelometer (R2≥0.49) even for 1 min aggregated data at exceptionally low ambient PM2.5 levels. In contrast, the 1 min or 1 h PMS3003–SHARP correlations (R2≥0.25) were poor and worse than the 1 h PMS3003–E-BAM correlations (R2≥0.36) at the Duke site. Additionally, the SHARP had only moderate correlations with the two T640 sensors (R2≤0.58) or the SHARP's embedded nephelometer (R2=0.59) even though both the SHARP and T640 are US-designated PM2.5 FEMs and the SHARP readings take into account its raw nephelometer values.

While the common optically based principles of operation shared by T640 (and nephelometer) and PMS3003 could partially explain the stark performance contrast between the SHARP and T640 (and nephelometer), the lower reported precision of the beta-attenuation-based approach with a 24 h average of ±2 µg m-3 for SHARP than the T640 with a 1 h average of ±0.5 µg m-3 in low ambient PM2.5 concentration environments appears to be the root cause (Thermo Fisher Scientific, 2007; Teledyne Advanced Pollution Instrumentation, 2016). A previous study by Holstius et al. (2014) demonstrated the poor performance of BAM-1020 in a comparably low-concentration environment in Oakland, CA. They used both statistical simulation based on the true ambient PM2.5 distribution and the measurement uncertainty of BAM-1020 (1 h average: ±2.0–2.4 µg m-3) provided by the manufacturer (Met One Instruments) and field test results to show that an R2 of ∼0.59 is as correlated as one would expect from the 1 h measurements of a pair of collocated BAM-1020 sensors. In contrast to the moderate intra-BAM-1020 correlation (∼0.59) reported by Holstius et al. (2014), the two collocated T640 instruments yielded an ideal R2 of 0.95 (Fig. 6), which suggests a significantly smaller measurement error in the T640 than in the BAM-1020. The SHARP is known to derive its reported values by dynamically adjusting its embedded nephelometer readings based on its BAM measurements. In other words, the SHARP performance was adversely affected by the low precision of its embedded BAM at low ambient PM2.5 levels. All these observations seem to imply that beta-attenuation-based monitors might be unfavorable for low-cost particle sensor evaluation at the low concentrations typically present in the US. U.S. EPA FEMs are valid for 24 h PM2.5 measurements rather than for 1 h measurements (Jiao et al., 2016). An inappropriate selection of reference monitors might prejudice the overall performance of low-cost sensors, particularly for time resolutions finer than 24 h.

The T640 sitting on the roof (T640_Roof) was chosen over the SHARP and the other T640 unit (T640_Shelter) as the reference monitor because (1) the T640 as a US-designated PM2.5 FEM is better for sensor evaluation at low concentrations than a SHARP and (2) the T640_Roof had slightly lower correlations with the sensors than the T640_Shelter, therefore giving conservative estimates of PMS3003 performance. Similar to the Duke University results, comparisons of the data using regression between the same set of instruments in Fig. 7a–d present similar calibration factors across the sensors on the same timescale, therefore indicating the excellent precision of the PMS3003 model. Unlike the analysis of the Duke University data, the calibration factors (prior to adjustments for meteorological parameters) varied little from one averaging timescale to another (Table 3). Despite an appreciable improvement in R2 compared to the Duke University site being found only on the 1 h scale, the accuracy of the T640 calibrated PMS3003 units substantially outperformed their E-BAM calibrated counterparts across the entire averaging time spectrum (Table 3) with the most pronounced difference on the 1 h scale (27 % vs. 201 %). A less dramatic mean error drop from the 1 to 24 h scale at the EPA RTP (27 % to 9 %) compared to what was seen at the Duke University site (201 % to 15 %) highlights the inferior precision of the E-BAM and further undermines its credibility as a reference sensor at low PM2.5 concentrations. It should be noted that the non-normally distributed residuals on 1 min, 1 h, and 6 h scales in Fig. 7a–c indicate that the true ambient PM2.5 concentration term alone was not sufficient to explain the variation in PMS3003 measurements, therefore revealing the likely existence of RH or temperature impacts.

Figure 7e–g display the regressions of PM2.5 measurements from the RH-adjusted PMS3003 units versus the T640_Roof on 1 min to 6 h timescales. The empirical equations of the RH correction factors (i.e., Eq. 1) on the corresponding timescales are shown in Fig. 8 and they fitted well with the 1 min to 6 h aggregated data (R2≥0.48). The RH adjustment was not implemented to the 12 and 24 h aggregated data because the equation regression fit statistics degraded when evaluating these data, likely because of an insufficient number of observations and stronger smoothing effects at longer averaging time intervals. Aerosols at the EPA RTP generally exhibited smooth and continuous growth above the lowest collected RH rather than distinct deliquescence behavior (Fig. 8). The RH correction factors were roughly 20 % to 30 % above 1 even at the lowest RH (below 30 %), which justifies the decision of conducting RH adjustments across the entire range of recorded RH without incorporating an RH threshold. Despite the promising descriptions of correction factors as a function of RH, wide divergence in the magnitude of correction factors for a given RH exists. This divergence is likely the result of substantial day-to-day variation in the chemical composition of the aerosols (Day and Malm, 2001). A higher fraction of soluble inorganic compounds can contribute to a larger magnitude of RH correction factors (Day and Malm, 2001).

The RH corrections brought the PMS–T640 correlations to above 0.90 for all 1 min, 1 h, and 6 h aggregated data (see Fig. 7e–g). This significant improvement in R2 implies a major RH influence that can explain up to nearly 30 % of the variance in 1 min and 1 h PMS3003 PM2.5 measurements in addition to the true ambient PM2.5 concentration variable. Figure S3 demonstrates that the PMS3003-to-T640 ratios after the RH corrections were also considerably closer to a strict normal distribution than those with only the FEM corrections (Fig. S4). However, Fig. 7e–g suggest that the PMS3003 PM2.5 measurements were still not in complete agreement with the T640 readings even after the RH adjustments. This discrepancy might stem from variations in aerosol composition described previously or impacts of particle size biases (Chakrabarti et al., 2004), therefore warranting a further step of FEM conversion (adjustment). According to Table 3, the combination of RH and FEM corrections were able to substantially improve the accuracy of PMS3003 PM2.5 measurements by reducing the mean errors to within 12 % even for data at a 1 min time resolution. The ideal normal distribution of PMS3003-to-T640 ratios in combination with the high accuracy and precision of the most finely grained data proves especially beneficial for minimization of exposure measurement errors in short-term PM2.5 health effect studies (Breen et al., 2015) or mapping of intra-urban PM2.5 exposure gradients (Zimmerman et al., 2018).

The decision to conduct the temperature adjustments to 1 min, 1 h, 6 h, and 12 h aggregated PMS3003 PM2.5 measurements was based on the AIC results in Table S1. Table S1 demonstrates that the AIC values of the calibration models incorporating an additional temperature term were substantially lower than those of the models including only a true PM2.5 concentration term at these levels of temporal resolution, therefore indicating the significance of the temperature variable in the calibration models. The 24 h AIC values are not reported as 24 h observations generally have limited statistical power to determine the significance of temperature in the models.

As shown in Table 3, the temperature corrections (when available) could further reduce the mean PMS3003 PM2.5 measurement errors by no more than 4 %, with the largest reduction in mean errors found in the 12 h averaged data. This marginal improvement stands in marked contrast to that brought about by the RH corrections (up to 17 %), suggesting the triviality of temperature adjustments in the entire suite of calibrations. Nevertheless, the addition of the temperature adjustments succeeded in lowering the mean errors to within 10 % at 1 min, 1 h, and 6 h time resolutions, which were comparable to the value at 24 h time resolution (9 %). Figure S5d also depicts the PMS3003-to-T640 ratios at a 12 h averaging interval after the temperature corrections and shows that these ratios were slightly more normally distributed than those with only the FEM corrections (Fig. S4). As a result, whether to conduct temperature adjustments is contingent upon the error targets, which are further dependent on the performance goals for the desired applications.

Table 1 shows that Kanpur had significantly higher ambient PM2.5 levels for a 1 h averaging period during the post-monsoon season (116±57 µg m-3) than during the monsoon season (36±17 µg m-3). This seasonal increase in ambient PM2.5 concentrations is aligned with our expectation and can be attributed to diminished wet scavenging by precipitation, a shallow boundary layer (mixing height), and lower ventilation coefficients (wind speed) during the post-monsoon season (Gaur et al., 2014). While only moderately high ambient PM2.5 levels were found during the Kanpur monsoon season, they were substantially higher than those measured at the Duke University site (9±9 µg m-3). The field tests in this study provided a wide range of ambient PM2.5 levels spanning from high (Kanpur post-monsoon season), moderate (Kanpur monsoon season), to low (Duke University site). This PM2.5 concentration range coupled with the same type of reference monitor (E-BAM) is ideal for constructing empirical error curves to investigate the sensor performance within each individual concentration class as a function of averaging time period (as discussed in Sect. 3.3.4). The RH values during the monsoon season (62±15 %) were comparable to those during the post-monsoon season (63±16 %). These RH values measured in Kanpur were also similar to those at the EPA RTP site (64±22 %). The temperature during the monsoon season (33±5 ∘C) was considerably higher than that during the post-monsoon season (22±4 ∘C).

As with the two field tests in the low-concentration region, the two PMS3003 units were highly correlated with each other during both the monsoon (R2=0.99) and post-monsoon seasons (R2=0.93) in Kanpur (Fig. S6). This good agreement is also reflected in Fig. 9, which shows that the two sensors were in sync and tracked reasonably well with the E-BAM. However, there was a minor decrease in the intra-sensor correlation from the monsoon to post-monsoon seasons that might signal a performance change of the two PMS3003 sensors due to either minor deterioration or a change in the pollutant source. Figure S6 illustrates that the magnitude of the deviation from the regression line during the monsoon season was likely irrelevant to the deployment time (measured by the number of hours past the beginning of the Kanpur study, i.e., 8 June 2017 00:00 Indian Standard Time, IST). In contrast, the extent of the divergence was somewhat larger for the longer deployment time near the high end of the PM2.5 range over the post-monsoon period. One plausible explanation for the distinguishable post-monsoon (but not monsoon season) change is the routine exposure (for nearly a month) of the sensors to high concentrations of accumulation-mode aerosols. This may be especially detrimental to PM sensors; all the more so because the foggy conditions during post-monsoon and winter over Kanpur may further exacerbate the accumulation of aerosol particles at lower surfaces and therefore the deposition of particles within the sensors (Li et al., 2015; Bran and Srivastava, 2017). This constant exposure possibly caused disproportionately large detection errors primarily near the upper end of the PM2.5 range. The effect of PM deposition on the low-cost PM sensor performance and calibration, particularly in areas of high ambient PM concentrations (e.g., Kanpur), was not evaluated as part of this work. Future studies will present how preventive maintenance of low-cost sensors including periodic cleaning can benefit their performance. Another possible explanation is the change of dominant pollutant source from the early stage of the monsoon season (long-range transport of mineral dust from Iran, Afghanistan, Pakistan, and the Thar Desert) to the post-monsoon (local impact of biomass burning emissions) season (Ram et al., 2010). Sensors are likely to respond differently to different varieties of aerosols and the change in sensor responses might be most pronounced near the upper end of the PM2.5 range. Figure 9b substantiates the potential change by showing that the two uncalibrated PMS3003 sensors were unable to match the local minima of the E-BAM (even local minima below 40 µg m-3) throughout the post-monsoon season as they were able to during the monsoon season in Fig. 9a.

Despite the slight potential change, higher PMS3003–E-BAM correlations were found in the post-monsoon season than the monsoon season over all time-averaging intervals (Table 4). Figure 10 displays the 1 and 24 h average regression plots for the two uncalibrated sensors against the E-BAM during the monsoon and post-monsoon seasons. Similar to the Durham and EPA RTP field tests, different PMS3003 units had similar calibration factors over the same averaging timescales during both seasons. Comparable to the EPA RTP evaluation, the sensor units at or in the same study location or season were roughly similar in sensitivity and baseline regardless of averaging time periods (Fig. 10 and Table 4). Figure 10 also shows a distinct baseline drift of the PMS3003 sensors from the monsoon to the post-monsoon season regime. This appreciable drift in baseline agreed with the sensors being incapable of reaching the local minima of true ambient PM2.5 concentrations. This may also suggest a performance change or may be a reflection of a different calibration regime.

Figure 11 depicts a heat map of mean errors in calibrated PMS3003 PM2.5 measurements with respect to averaging timescales and calibration methods across varied sampling locations or seasons. Even though the EPA RTP sampling location had the lowest ambient PM2.5 level among the three study locations, it achieved the highest accuracy over each averaging time period, therefore reiterating the vital role the precision of reference instruments plays in evaluating sensor performance. For the remaining two sampling sites with an E-BAM as the reference monitor, lower errors were generally found in higher PM2.5 concentration environments. The exceptions to this rule were observed at 12 h (Kanpur post-monsoon error > monsoon error) and 24 h (Kanpur monsoon error > Duke University site error) time intervals. The occurrence of these anomalies can be explained by stronger smoothing effects than PM2.5 concentration effects over longer averaging times. Table 4 details the errors in calibrated PMS3003 PM2.5 measurements during the monsoon and post-monsoon seasons in Kanpur. The appreciably narrower reductions in mean errors from the 1 to 24 h scale during both seasons in Kanpur (monsoon: 46 % to 17 %, post-monsoon: 35 % to 11 %) compared to the reduction at the Duke University site (201 % to 15 %) underscore the inferior precision of E-BAM at low ambient PM2.5 concentrations.

The lack of requirement for RH corrections during both testing seasons in Kanpur paralleled the outcomes of the Duke University field test. Figure S7 shows that the empirical RH correction equation fitted poorly with the widely scattered data from both monsoon (R2≤0.13) and post-monsoon seasons (R2≤0.03). We speculate that the E-BAM's low precision might be responsible for the failure to establish the impact of RH on PMS3003 responses, considering that the T640 measurements resulted in a significant RH relationship under similar conditions. We attempted to apply the empirical RH adjustment equations derived at the EPA RTP testing site to the Kanpur and Duke University data sets. However, no improvements in correlations or errors were found, indicating the RH correction function appears to be highly specific to study sites because of its great reliance on particle chemical, microphysical, and optical properties (Laulainen, 1993). The temperature variable was found to be statistically significant and therefore incorporated in the calibration models at time resolutions finer than 6 h for the Kanpur monsoon data and finer than 12 h for the post-monsoon data (Table S1). Overall, the temperature adjustments can scale the PMS3003 PM2.5 measurement errors down by no more than 7 %, with the 6 h averaged data during the post-monsoon season marking the greatest improvement (Table 4). These marginal improvements were comparable to those observed at the EPA RTP testing site (within 4 %).

We observed a relatively pronounced nonlinear relationship between the raw PMS3003 and the E-BAM PM2.5 responses over the full concentration range examined during the post-monsoon season at IIT Kanpur (Fig. 10). In previous research, similar nonlinearity was ubiquitously characterized by attenuated responses towards the upper end of low-cost sensors' operation range in both field campaigns (Gao et al., 2015; Kelly et al., 2017; Johnson et al., 2018) and laboratory settings (Austin et al., 2015; Wang et al., 2015). The shape of calibration curves is dependent on varied factors such as type of low-cost sensor, range of true ambient PM2.5 concentrations, particle size, and particle composition (Wang et al., 2015). Without additional information, we are unable to parse out the exact reasons for the occurrence of this nonlinearity in our data during the Indian post-monsoon season. Nevertheless, we speculate that the comparatively high concentration range along with the prevalence of small particles encountered during the post-monsoon season might account for this nonlinearity (Kelly et al., 2017). In the present study, the PMS3003 responses were well characterized by a linear model below ∼125 µg m-3, which was close to the highest 1 h PM2.5 concentration during the monsoon season. This threshold was around 3 times greater than that reported by Kelly et al. (2017), who field-tested PMS1003 sensors under an ammonium-nitrate-dominated, moderately high PM2.5 concentration condition (1 h PM2.5 mean: up to 20 µg m-3, range: 10–70.6 µg m-3).

Researchers have used higher-order polynomial (Austin et al., 2015; Gao et al., 2015), penalized spline (Austin et al., 2015), and exponential functions (Kelly et al., 2017) to capture nonlinear responses of low-cost sensors. In this study, we explored the quadratic model to describe the full range response of the PMS3003 sensors during the Kanpur post-monsoon season. The quadratic model was chosen because it is straightforward to understand, interpret, disseminate, and use. The time series of the 1 and 24 h averages of the calibrated PMS3003 PM2.5 responses using the two calibration models (i.e., simple linear and quadratic models) can be found in Fig. S8. Figure S8 shows that the quadratic model might suit the post-monsoon 1 h aggregated data better than the simple linear model as the simple linear model failed to capture the local minima of the E-BAM throughout the post-monsoon period. The two models only differed little for the 24 h aggregated data. This is expected as Figs. 10 and S9 show that the strength of nonlinearity declined as the averaging times increased because longer averaging times reduced the number of relatively low-concentration observations (such as below ∼100 µg m-3). Table S2 summarizes the goodness of fit and accuracy estimates for the two model types as a function of time-averaging intervals during the post-monsoon season. Table S2 indicates that the quadratic fit appeared to have better goodness of fit and accuracy estimates for the current post-monsoon data set than the simple linear fit with both lower AIC and RMSE values at all time resolutions. Compared to the simple linear model, the quadratic model could further improve the mean accuracy of PMS3003 PM2.5 responses by up to 11 % (Table 4). Even when the nonlinearity was not strong enough to make the simple linear fit statistically different from the quadratic fit (i.e., the quadratic term a2 in the quadratic fit (Eq. 7) not significantly different from 0 with p>0.1) at 24 h integration time, the quadratic fit can still reduce the mean error and the range of RMSEs by 2 % (Table 4) and 3 µg m-3 (Table S2), respectively. This might also shed some light on the choice of calibration methods for PMS3003 PM2.5 responses in future deployments. The quadratic model should be chosen over the simple linear model as the starting point (default approach) to PMS3003 PM2.5 response calibration since the quadratic model can always be of larger benefit to the accuracy of PMS3003 measurements than the simple linear model even when the nonlinearity is weak at low ambient PM2.5 concentrations or at longer time-averaging intervals.

Empirical error curves for PMS3003 PM2.5 measurements by calibration method and averaging time are presented in Fig. 12 by combining the results of all the field tests with E-BAM as the reference monitor (i.e., Duke University and IIT Kanpur data sets). These curves are useful for easy reference to the magnitude of errors for a given concentration range at a given temporal resolution. Overall, regardless of the averaging times, the largest errors were found below 20 µg m-3, particularly in the range of 0 to 10 µg m-3. Although further work is required to improve the error curves by collecting more data points, especially near the upper end of the PM2.5 distributions, we would presume calibrated PMS3003 PM2.5 responses to be relatively stable and consistent above ∼70 µg m-3 for 1 h aggregated data and above ∼50 µg m-3 for 6 to 24 h aggregated data with uncertainties roughly confined within 25 %, particularly when the quadratic calibration models are employed.

Given the broad range in PM2.5 concentrations, Fig. 12 seems to demonstrate that the quadratic calibration method performed better than their simple linear counterpart at all time intervals with steadier mean of ratio lines (remaining more constantly at 1 regardless of concentration classes) and relatively low uncertainties. The quadratic model outperformed the simple linear model, particularly over the moderately high concentration range (i.e., ∼60–140 µg m-3). Although a lesser improvement than over the moderately high concentration range, the quadratic fit still managed to slightly tighten the shaded uncertainty region over the range of ∼30–60 µg m-3, in which few differences existed between the two calibration curves. Table S3 shows that the quadratic fit had smaller AIC and RMSE values than the simple linear fit at all time intervals. Figure S10 further shows that the quadratic models fitted remarkably better than the simple linear model to the data. These observations support using the quadratic rather than the simple linear method as the general approach in calibrating PMS3003 PM2.5 responses.