All of the sites in this study, other than the volcanic Nicaraguan site, are classed as urban background with respect to their respective cities. We have focused on PM2.5 mass concentrations in this study, as this particle size fraction was measured by reference instrumentation at all study sites. We also note that we used a different OPC-N2 sensor at each site. Previous work has shown that co-located multiple OPC-N2 sensors have an inter-unit precision of 22±13 % for PM10 mass concentrations (Crilley et al., 2018). A summary of the measurement locations is provided in Table 1.

The methodology for the correction factor applied has previously been described in detail by Crilley et al. (2018). Briefly, the correction factor uses κ-Köhler theory to relate the particle mass to hygroscopicity for a given RH (Pope, 2010), according to Eq. (1): 1aw=mmo-1mmo-1+ρwρpκ, where aw is the water activity (aw=RH/100); m and mo are the wet and dry (RH=0 %) particle mass respectively; and ρw and ρp are the density of the dry particles and water respectively. The value for κ, which relates the bulk aerosol composition to hygroscopicity, can be determined by the non-linear curve fitting of a humidogram, calculated using the ratio of wet/dry particle mass as a function of water activity (aw, RH/100). We have used the raw mass concentrations as reported by the OPC-N2. We utilized the reference instrument measurements (TEOM-FDMS and GRIMM, as indicated in Sect. 2.2) as the dry particle mass, whereas the raw OPC-N2 measurements were the wet particle mass concentration. The TEOM-FDMS employs a Nafion dryer and, therefore, measures the dry particle mass concentration (Grover et al., 2006). Equation (1) can be rearranged to calculate the correction factor C as follows: 2C=1+κρp-1+1aw. To calculate the particle mass concentration from the measured particle number size distribution, spherical particles of a uniform density and shape are assumed by the OPC; this is not strictly true for airborne particles in an urban atmosphere but is considered to be a standard approximation. For full details, see Crilley et al. (2018). The OPC-N2 assumes the ambient particle density to be 1.65 g cm-3 across all size bins to derive the particle mass concentrations from the measured particle number concentrations (Crilley et al., 2018); therefore, we used this density for the dry particles (ρp) in Eq. (2). We assume that the particle density is uniform across the particle size distribution measured by the OPC-N2. Furthermore, we assume that both the OPC-N2 and the reference instrument respond to dry aerosol mass in the same way for all particles below the size cut-off on the reference instrument. We also note that we assume that both the OPC-N2 and the reference instrument responses are linear over the range of measured concentrations at each site. The raw particle mass concentrations derived by the OPC-N2 are corrected according to Eq. (3): 3PMcorr=PMrawC.

To explore if there was evidence of an artefact in the OPC-N2-derived PM2.5 mass concentrations due to RH, we plotted the reported PM2.5 mass concentrations from the OPC-N2 as a function of RH (Fig. 1 and Fig. S1 in the Supplement). From Fig. 1, there is clear influence of RH on the measurements performed in Delhi and Birmingham, which is evidenced by the observed exponential increase in particle mass with RH (Fig. 1a, d). In Beijing, the observed stepwise increase in the derived measured particle mass between a RH of 40 % and 50 % may point to deliquescence of a predominant PM component (Fig. 1c), which is explored further in later sections. What was evident from these three sites (Beijing, Birmingham and Delhi) was that there was a large spread in the derived PM2.5 mass concentrations at high RH, which likely reflects the heterogeneous nature of the particle composition and, hence, hygroscopicity.

Meanwhile at Nairobi, the derived concentrations from the OPC-N2 appeared to be independent of RH. Typically, during the dry season in Nairobi, airborne mineral dust comprises a large fraction of PM2.5 (35 % annual mean; Gaita et al., 2014), which is known to have low hygroscopicity. Furthermore, we note that the measurements in Nairobi were performed during the dry season and, as a result, the ambient RH was typically less than 85 %: this was the threshold RH value identified in Crilley et al. (2018) at which the OPC-N2 becomes significantly sensitive to RH. Lower humidity levels combined with the low hygroscopicity of the aerosol in Nairobi was the likely reason why there was little evidence of a RH artefact observed in the OPC-N2 measurements (Pope et al., 2018). Therefore, a simple calibration against gravimetric measurements is likely to be sufficient in locations with low RH and a low proportion of hygroscopic aerosols, such as Nairobi.

As posited in Crilley et al. (2018), the RH artefact in the OPC-N2 measurements was likely related to the ambient aerosol bulk hygroscopicity. Therefore, in Fig. 2 we plotted humidograms for the sites from Fig. 1 that showed evidence of a RH effect, where reference particle mass concentration data were available (i.e. Birmingham, Delhi and Beijing; Table 2). In Beijing, there were insufficient data at high RH levels due to the short sampling period (4 d). The factors affecting the response of the OPC-N2 in Beijing are explored in more detail in Sect. 3.2.1. A quasi-exponential increase in the ratio the OPC-N2 to reference instrument concentrations at high RH levels was observed in Birmingham and Delhi, as would be expected if the aerosols were undergoing hygroscopic growth (Fig. 2). Using κ-Köhler theory (Petters and Kreidenweis, 2007), the calculated κ values were 0.1 and 0.16 for Birmingham and Delhi respectively. These κ values are typical of continental regions with high organic loadings (Pringle et al., 2010). While high organic loadings would be expected for Delhi during winter, there are also significant loadings of hygroscopic aerosols such as sulfate and nitrate (Gani et al., 2019), which is explored in more detail in the following. Differences in aerosol composition would likely explain why the calculated κ value at Bham BAQS (0.1) was lower than that observed at Bham Tyburn (0.38–0.41; Crilley et al., 2018). Previous work in Birmingham has demonstrated that the proportion of ammonium sulfate and nitrate decreases in winter compared with summer (Yin et al., 2010), which may explain the observed lower κ value over winter. What becomes evident from Fig. 2 is that different κ values were observed at each site. If the aerosol composition was broadly similar at each site, we would expect the same κ value. This suggests that the aerosol composition varies significantly over the different measurement sites. The scatter in the OPC / TEOM observed in Fig. 2 as a function of RH was likely due to temporal variability in the aerosol composition due to changing sources and sinks (both local and regional).

During the measurements in Delhi, the OPC-N2 typically over-reported the PM2.5 mass concentrations relative to the reference (Fig. 6a). The OPC-N2 assumes a uniform particle density of 1.65 g cm-3 in the particle counts to mass conversion, and this density may be inappropriate for Delhi aerosol during winter. Previous measurements of aerosol density during winter in Delhi at midday were 1.28±0.12 g cm-3 on average (Sarangi et al., 2016), which is lower than that applied by the OPC-N2. Generally, the OPC / TEOM ratio was below 1 (Fig. 2a) and would not fully explain this discrepancy. Is can be noted from Fig. 6a that higher PM2.5 mass concentrations relative to the reference were reported by the OPC-N2 towards the start of the measurement period (Fig. 6a), generally during periods of high RH (e.g. 25–29 January, Fig. 6b). We also note that the reported concentrations from the OPC-N2 towards the end of the measurements in Delhi (11 February onwards, Fig. 6a) were in better agreement with reference. The cause of this change in performance is unclear, but it could reflect lower RH values or changes in the aerosol composition.

As the reported OPC-N2 concentrations in Birmingham and Delhi demonstrated an artefact due to RH (Fig. 2), we applied the correction factor from Crilley et al. (2018), using the in situ locally derived κ values. In addition, the κ value for ammonium sulfate (0.61) was also used, as Di Antonio et al. (2018) suggested it may be more representative for urban aerosols. The results for the correction factors relative to the co-located reference instruments are summarized in Table 3. Compared with the uncorrected OPC-N2 concentrations, the application of a correction factor with both κ values resulted in improved performance of the reported concentrations relative to the reference. However, the use of the locally derived κ resulted in the best correction of the OPC-N2 (to within 33 % of the reference measurements) compared with using the ammonium sulfate κ value (Table 3).

We also observed that the ratio of OPC-N2 / GRIMM concentrations was low at high RH at Bham BAQS (Fig. 2c). The spread in OPC / GRIMM ratios observed at high RH at Bham BAQS is indicative of a diverse aerosol composition with differing hygroscopicity over the 4 months. With respect to the calculated κ value for each month in Birmingham, very little variability (0.1–0.12) was found from October to January which suggests that the bulk hygroscopicity of the aerosols was consistent on average, although within a large range (as indicated by the large spread in the OPC / TEOM ratio in Fig. 2c).

The results so far point to the need to establish the aerosol composition in order to accurately apply a suitable correction factor, which is in agreement with previous work (Di Antonio et al., 2018; Crilley et al., 2018). However, the determination of the aerosol composition at the necessary time resolution would require expensive co-located equipment to measure the aerosol composition (e.g. an aerosol mass spectrometer), and this would somewhat negate the USPs of a low-cost monitor. Di Antonio et al. (2018) suggested that the air mass origin (determined using HYSPLIT) could provide compositional information in order to determine the appropriate κ value to use in the correction. Therefore, we examined the long-term Birmingham dataset for times when the correction factor that was applied over/under-corrected the OPC-N2 mass concentrations relative to reference instrument. However, unlike Di Antonio et al. (2018), we could not find any consistent patterns with respect to air mass origin and the performance of the correction factor. Furthermore, the application of a correction factor using this approach would require significant post-processing time. This raises the question of whether the method would then remain a “low-cost” option or not.

To remain a low-cost option, a simple correction that can be applied to the OPC-N2 irrespective of aerosol composition changes is needed, although this may decrease the accuracy of the correction factor. For many locations around the world, ambient PM2.5 mass concentrations are measured using gravimetric-based techniques (e.g. filters or TEOM) for regulatory purposes. Consequently, we focused on developing a simple correction factor using TEOM data as a reference. To explore if this was viable, we plotted the OPC / TEOM ratio for all sites where it was available (Bham Tyburn, Delhi and Beijing) on one plot (Fig. 8). Note we used the two-stage correction for the OPC-N2 measurements in Delhi, as described in Sect. 3.3.1, for Fig. 8. We did not apply this correction to the Bham Tyburn data as the RH was higher than 60 %.

From Fig. 8, a κ value of 0.33 (assuming a uniform particle density of 1.65 for all sites) was calculated, which is slightly higher than the average of 0.3 suggested for continental regions (Pringle et al., 2010). Consequently, we refer to the calculated κ value from Fig. 8 as global κ, but we note that it was calculated from three urban background sites on two continents. We applied this κ (0.33) to correct the OPC-N2 data at all sites as well as the average for continental regions (0.3), and the results are summarized in Table 4. Variation in the κ values generally resulted in changes in the slope, while the correlation co-efficient remained similar. While the κ value that was derived in situ resulted in a reasonable correction of the OPC-N2 relative to the reference (±10 %–30 %, Table 4), using the κ from Fig. 8 (0.33) was comparable. Correcting the datasets using the global κ of 0.33 resulted in an agreement with the reference instruments of within 50 % at all sites, with the Beijing, Delhi and some of the Bham Tyburn corrected OPC-N2 values being within 20 % of the reference (Table 4). The only site with a notably poorer agreement using the global compared with the in situ κ value was Bham BAQS, and this may be because the locally derived κ value for the Bham BAQS measurements (0.1) was different from the other sites. This notwithstanding, we do note that using a κ value of 0.33 resulted in a significant improvement in accuracy compared with the uncorrected OPC-N2-derived particle mass concentrations at Bham BAQS (slope of 3.5, Table 3). Overall, when considering the most appropriate correction or κ value, the results from Table 3 suggest that a locally derived κ value, based on an in situ calibration with reference instrumentation, is preferable. However, the global κ value derived using data from the three urban background locations in this study (0.33, Fig. 8) gave comparable results to the correction that was derived in situ (Table 4). Therefore, this suggests that using this κ value or a suitable value from the literature for urban background sites may be acceptable should there be no reference instruments available for calibration.