The Allan variance analysis is presented in Fig. 5. The Allan standard deviation for the 450 nm extinction measurement increases with integration time after 40 s. This is due to the σext baseline being assumed to remain constant by the A2S2 over the signal-to-noise experiment period, but the actual contribution of the ambient gas-phase species (mainly NO2) absorption to the total extinction varies with extinction time (Massoli et al., 2010). The uncertainty should be less during ambient measurements if the baseline is characterised more frequently than once per hour in operation. Nonetheless, the previous study by Pfeifer et al. (2020) shows that the variation in the gas-phase σext baseline at 450 nm for the CAPS-PMex may lead to an uncertainty up to around 0.8 Mm-1min-1 for the ambient σext characterisations. To minimise the uncertainty of the baseline variation in CAPS-based instruments, a frequent baseline characterisation is needed. In this study, measurements were conducted at locations distant from the emission sources, and baseline values were measured every 2 min to reduce the influence from the background signal. The Allan standard deviation for the 630 nm extinction and scattering measurements is smaller compared to the 450 nm measurements, and the extinction measurement at 630 nm is less influenced by baseline drift issues. The minimum detection limit (MDL) involves a calculation derived from 3 times the Allan standard deviation, and the detection limit at integration times of 1, 10 and 30 s is presented in Table 3. Our laboratory results show that, at a measurement frequency of 1 Hz, the MDL is 1.89 Mm-1 for σext and 2.25 Mm-1 for σsca at 450 nm. At 630 nm, the MDL is 0.69 Mm-1 for σext and 1.08 Mm-1 for σsca. With the increase in integration time to 10 s, the limits are reduced to 0.69 and 0.21 Mm-1 for σext at 450 and 630 nm, respectively, and to 0.45 and 0.12 Mm-1 for σsca at 450 and 630 nm, respectively. The Allan analysis indicates that the limit of detection reaches its minimum value at an integration time of 30 s. Nevertheless, in the case of ACROSS airborne measurements, there is a requirement for high-frequency results to effectively characterise aerosol optical properties, especially during instances when the research aircraft intercepted with urban plumes or conducted altitude profile measurements. The minimum σext and σsca observed during the ACROSS campaign are both ∼ 1.35 Mm-1 at 450 nm and both ∼ 0.32 Mm-1 at 630 nm. Hence, the detection limit achieved with a 10 s integration time is deemed satisfactory to fulfil the requirements of the ACROSS project measurement.

Figure 6 presents the results of the chamber measurements made at various controlled pressure levels, and the temperature of the modified CAPS-PMSSA increased slowly to 315 K after the injection of the ammonium sulfate. The dilution- and STP-corrected σext measured by the original CAPS-PMex unit agrees well with the σext from the modified CAPS-PMSSA at a constant pressure of ∼ 1013.25 and ∼ 900 hPa. However, our original CAPS-PMex unit is unable to deliver an accurate measurement when the pressure within the chamber drops to 800 hPa or less. The σext and σsca reported by the modified CAPS-PMSSA showed minimal impact until the pressure reached ∼ 550 hPa. When the pressure drops further to ∼ 400 hPa, the signal noise level increases. The chamber experiment results validate that our modification to the CAPS-PMSSA can provide accurate measurements with ambient pressures as low as 550 hPa and instrument temperatures as high as 315 K.

Figure 7 presents the data collected to determine the truncation of the A2S2 instrument at 450 and 630 nm wavelengths. The truncation measured and simulated by Onasch et al. (2015) and Modini et al. (2021) are also included for comparison. Compared to the simulation reported by Onasch et al. (2015) (MieAmigo), Modini et al. (2021) account for the reflection of scattering light from the inner surface of the glass sampling tube within the integrating nephelometer, and this reflection phenomenon is simulated for a path length range of 0 to 4.7 cm. Hence the two simulation methods are referred to as simulation with and without reflection. At both 450 and 630 nm wavelengths, the AAC-selected PSL particle results show that the truncation for particles with Dp up to 200 nm is insignificant, and the truncation uncertainty is less than 10 % for particles with Dp up to 400 nm. For larger submicron particle size (Dp between 400 and 1000 nm), the truncation of 630 nm wavelengths is around 10 %, while the truncation of 450 nm is greater and is around 20 %. This observation is consistent with observations in the Rayleigh scattering regime, where larger particles exhibit near-forward scattering that is not captured by the CAPS-PMSSA. The average truncation error for particles with Dp between 200 and 1000 nm is 0.86 and 0.94 at 450 and 630 nm, respectively.

Compared to the truncation results for the CAPS-PMSSA presented in previous studies, the truncation results of A2S2 in this study at 450 and 630 nm wavelengths are greater than the values reported by Onasch et al. (2015) but are closer to the values reported by Modini et al. (2021). Modini et al. (2021) suggested that the experiments done by Onasch et al. (2015) may be affected by multiply-charged particles, while the AAC source is not influenced by the multi-charging issues since particles are sized by an aerodynamic method. Another possible explanation for the differences could be the slight variations in the configurations of CAPS-PMSSA sample cells from one instrument to another, and our truncation results presented in this study may solely reflect the potential measurement error of our A2S2. The simulated truncation from different methods is also presented in Fig. 7. The truncation simulation of Onasch et al. (2015) shows the smallest correction, which is less than 10 %. However, the simulation that includes reflection done by Modini et al. (2021) shows a larger truncation correction of around 15 %. Though the simulation results of Modini et al. (2021) indicate that the self-reflection of the sampling tube may be another source of the uncertainty, there is no clear evidence that this will lead to significant measurement error, and the largest uncertainty is expected to arise from truncation itself. Overall, our truncation experiment results show a trend similar to the simulated results. The findings indicate that the A2S2 is less affected by truncation for the fine-mode particle measurements. However, for the studies where contributions from coarse-mode particles are present, larger measurement errors from the A2S2 are expected, especially for the 450 nm wavelength.

Based on the characterisation results reported here, we introduce a simplified correction algorithm as a function of measured uncorrected scattering Ångström exponent (SAE) to apply to ambient measurement results. The correction function is presented in Fig. 7c. Derived from the average truncation calculated above, the average correction factors are 1.13 and 1.05 at the wavelengths of 450 and 630 nm, respectively. Subsequently, the truncation is corrected based on the time-resolved measured uncorrected SAE between 450 and 630 nm observed by A2S2: when the SAE falls below 1, indicating the dominance of larger particles, the correction function is applied to the measurement results. Conversely, in situations dominated by fine particles (SAE > 1), there is no need to apply the correction due to the minimal truncation observed during characterisation experiments.

Figure 8 shows comparisons between A2S2 and the performance-validated instruments. Panels (a) and (b) are for the CAPS-PMex (σext), panels (c) and (d) use the NEPH (σsca), and panels (e) and (f) use the AE33 (σabs). Each point shown in Fig. 8 represents the average value computed over each measurement period with constant conditions. For the experiments with pure ammonium sulfate and pure Aquadag, the intercomparisons are performed under high (> 200 Mm-1 at 450 nm and > 150 Mm-1 at 630 nm), moderate (∼ 100– ∼ 200 Mm-1 at 450 nm and ∼ 50– ∼ 150 Mm-1 at 630 nm) and low (∼ 50 Mm-1 at 450 nm and < 50 Mm-1 at 630 nm) levels of σext through regulation of the dilution system. In the case of the external mixture of Aquadag and ammonium sulfate, the measurements were conducted under different SSA mixture conditions. The average SSA values determined with the A2S2 are ∼ 0.71 (high SSA), ∼ 0.67 (moderate SSA) and ∼ 0.59 (low SSA) at 450 nm and ∼ 0.66 (high SSA), ∼ 0.65 (moderate SSA) and ∼ 0.52 (low SSA) at 630 nm. The average normalised size distributions measured by SMPS are presented in Fig. 9 (normalised to the total aerosol number concentration for each SMPS scan). The size distribution results show that the median mobility diameter is smaller than 200 nm for all the groups; therefore the truncation correction for the A2S2 data can be ignored. The σext values and EAE measured by the A2S2 agree well with the results measured by two CAPS-PMex instruments, as expected, since they incorporate the same CAPS-based technique. This also confirms that our modified A2S2 monitor has equivalent performances to the currently available commercial CAPS monitors for the aerosol σext measurements. The A2S2 and NEPH instruments also show good agreement in measuring the σsca and SAE across different conditions (differences within 10 %). These results indicate that the measurements obtained from both instruments agree well and that the A2S2 provides consistent results for σsca values under varying temperature and pressure conditions. On the other hand, the average difference of σabs measured by AE33 and CAPS-PMSSA is within 10 %. Large variance was observed for the AAE, which could be attributed to the variation in the contribution of Aquadag. Previous measurements performed by Foster et al. (2019) demonstrated that when Aquadag or standard black carbon (BC) loading drops, the variance in AAE becomes more pronounced from CAPS-PMSSA results. However, the average AAE derived from both A2S2 and AE33 was close to 0.4, which is the expected AAE of the standard Aquadag particles. Our results agree with the findings found in previous laboratory experiments involving the CAPS-PMSSA, for example, where Perim De Faria et al. (2021) demonstrate that the CAPS-PMSSA can achieve measurements of σext and σsca at 630 nm with uncertainties within 10 %, but the measurement of σabs has uncertainties of 4 %–16 %. Our results also agree well with the results from Weber et al. (2022), who found that the relative uncertainties for the σext, σsca and σabs from CAPS-PMSSA at 450 and 630 nm are within 20 %, as suggested by Laj et al. (2020) for the ambient aerosol optical property measurements. In addition, Corbin et al. (2022) also demonstrated good agreement between black carbon (BC) mass concentrations and σabs from CAPS-PMSSA at 660 nm in an engine emission experiment.

The overview of the AOD values retrieved from AERONET observations at 440 and 675 nm during the ACROSS airborne flight campaign period, as measured at a Paris urban site and at a rural site (in the Rambouillet forest), and the AOD measured by the A2S2 as determined by integrating the altitude profile of σext at 450 and 630 nm are presented in Fig. 10a. Figure 10b and c display the SSA and SAE measured by the A2S2 at 450 and 630 nm within the boundary layer for each flight. According to the AERONET reanalysis of AOD results over the same area as the aircraft flight operations, there are two periods during the campaign period: a heavily polluted period with AOD values up to 0.8 between 18 (Flight A025) and 23 June (Flight A028) and light pollution periods with AOD values around 0.2 for the remainder of the flights. The AERONET AOD values at 440 nm retrieved from the Paris urban site are higher than the results from the Rambouillet forest site, whereas the AOD at 675 nm exhibits similar values at both sites. This could be attributed to the elevated concentration of non-refractory particulate matter in the urban area of Paris compared to the rural region. Comparing the AOD integrated from the altitude profiles of σext to the AERONET AOD results, the in situ measured AOD result was lower than the AOD retrieved at the Paris urban AERONET site due to lower pollution levels but is close to the results at the Rambouillet forest site.

The average SSA within the boundary layer at 450 and 630 nm varied between 0.8 and 0.9 for the entire campaign, and the average SSA during the heavily polluted period (0.82 at 450 nm and 0.85 at 630 nm) is slightly lower than the average SSA during the lightly polluted period (0.87 at 450 nm and 0.90 at 630 nm). Due to the extremely low aerosol levels during the lightly polluted period, the σext and σsca are close to the detection limits of the instrument, which leads to relatively large uncertainties. The measured SSA observed in this study is close to the average SSA reported above the Greater London area in summer (0.89 and 0.88 at 467 and 652 nm, respectively) (Davies et al., 2019). During most flights, the average SAE values range between approximately 1 and 2. However, for flights A025, A029, A032 and A033, the SAE dropped to around 1 due to the influence of larger-sized particles. The average AAE varied between 0 and 3, and this is potentially due to both the complicated emission sources and the low aerosol loading. Previous research has suggested that the stronger absorption at shorter wavelengths (average AAE > 1.5) could arise from either dust events (average SAE < 1.5) or a substantial contribution from brown carbon (BrC) (average SAE > 1.5) (Cappa et al., 2016). Our measurements indicate that dust particles contributed to the overall aerosol loading during flights A025 and A032, while BrC appears to have played a significant role in aerosol absorption during flights A026, A027, A028 and A036.

The altitude profile results of flights A025, A026, A028 and A030, and the aerosol optical properties above both the marine and continental background environments, are presented in Fig. 11. The results at 450 nm for A028 are not available due to the technical issues. Flight A025 had the highest aerosol extinction and scattering coefficients among the four cases. The sharp decrease in SAE between 1500 and 2500 m indicates the presence of a dust layer, which contributed to the increase in aerosol extinction and scattering at both wavelengths. The SSA is also observed to decrease within the dust layer, which could be caused by the mixture of dust with absorbing carbonaceous components and by the truncation correction errors. Due to the variation in boundary layer conditions, the profile of Flight A026 consists of two separate aerosol layers. One is within the boundary layer up to 1500 m, and the other one is at altitudes above 2000 m. The SAE at the upper layer is slightly less than the SAE at lower layer, and this indicates that the aerosols in the upper layer may be larger than the aerosols in the lower layer. For flights A028 and A030, the σext and σsca values decreased with increasing altitude, and the relatively low σext indicates a relative clean background profile. The increase in SAE from ∼ 1 to ∼ 3 at altitudes above 1200 m for Flight A030 indicates that only fine-mode particles are present at the upper level. The SSA of all the flights varies between 0.8 and 0.9 across the whole column, and there is a slight increase at the top for each flight indicating the reduction in the absorbing aerosols at the top.

The comparisons of measured σsca by A2S2 and NEPH at 450 and 630 nm are presented in Figs. 12 and 13, respectively. For better comparison, the normalised probability density functions (PDFs) of A2S2 and NEPH results for each flight are presented in the Supplement. As discussed previously, there were dust (coarse-mode particles) events present during flights A025, A029, A032 and A033. During flight A025 the poorest agreement (12 % differences) between the A2S2 and the NEPH among all the ACROSS flights was observed, and this could possibly be attributed to the important contributions from dust particles, as indicated by the SAE and AAE results shown in Fig. 10. This agrees with the lab results of the truncation characterisation which indicate that there are larger measurement errors for the A2S2 when measuring σsca at larger particle sizes. After implementing the simple truncation corrections described previously, the discrepancies between the A2S2 and the NEPH results at both wavelengths are reduced to approximately 10 %. For the airborne measurements during the lightly polluted periods, the uncertainty in A2S2-measured σsca increases slightly because even a small change in baseline becomes significant as the σext approaches the detection limit. The relevance of this issue is particularly pronounced at the 450 nm wavelength due to the contribution from gas-phase absorption as described previously. Overall, the A2S2 shows good agreement with the NEPH overall during the entire ACROSS campaign, and this confirmed that the A2S2 can adequately replace the NEPH to obtain reliable measurements of σsca under polluted conditions.