Evaluation and Correction of the Ambient Particle Spectral Light Absorption Measured Using a Filter-based Aethalometer

Spectral light-absorption properties measured with an Aethalometer (AE; Model AE33; Magee Scientific) are widely used in radiative forcing studies and source appointment in China. However, considerable uncertainty regarding the measured absorption coefficient (σabs) exists because of the multiple-scattering effects, loading effects, and differences in filter tape. This study evaluated σabs by comparing the values measured with an AE33 using Tape 8050, an AE33 using Tape 8060 (which differs from Tape 8050 in material), and a three-wavelength photoacoustic soot spectrometer (PASS-3) during two field campaigns in eastern China. The results indicated that the AE33-measured σabs using either tape exceeded the PASS3-measured value by approximately three times, mainly owing to the multiple-scattering effect. A wavelength-independent multiple-scattering compensation factor (2.90), which varies slightly (± 0.04) for eastern China, is recommended for these regions. When σabs was measured with the AE33 using Tape 8050, the value highly depended on the loading on the tape, which led to significant uncertainty and discontinuity in the absorption Å ngström exponent compared to using Tape 8060. A method was proposed to effectively correct the historical datasets of σabs and the absorption Å ngström exponent by using the AE33 with Tape 8050. This work provides insight into the quality of measured absorption data when filter-based measurement technology is applied.


INTRODUCTION
Light-absorbing particles exert considerable effects on aerosol radiative force by absorbing radiation, changing the aerosol single-scattering albedo and interacting with clouds (Koch and Del Genio, 2010;Bond et al., 2013). Black carbon (BC) dominates the light absorption of atmospheric particles (Saturno et al., 2017). Ice and snow albedos can be markedly changed when BC particles are deposited on them (Bond et al., 2013), which leads to great uncertainty when estimating aerosol climate effects. Absorbing aerosols can also influence the environment by suppressing turbulence in the atmospheric boundary layer (Wilcox et al., 2016).
Considerable uncertainty may also arise regarding radiative effects when the light-absorbing ability is measured at one wavelength or over a limited range because ambient aerosol light absorption is dependent on wavelength. The absorption Å ngström exponent (α abs ) (Å ngström, 1929) is used to describe the ae rosol light-absorption property as follows: where σ abs (λ 1 ) and σ abs (λ 2 ) are the absorption coefficient at wavelength λ 1 and λ 2 respectively. Different characteristics of wavelength dependence are observed for different aerosol types (Schmid et al., 2006). The theoretical α abs values of BC from the fuel is 1.0 (Martinsson et al., 2017) whereas some organic absorption classes have α abs values spanning a wide range between 3.5 and 7.0 (Schmid et al., 2006). Thus, spectral light-absorption information can provide knowledge regarding the source and aging process of ambient aerosols (Zotter et al., 2017).
Many methods have been developed to measure spectral light-absorbing properties, and these methods have been well summarized and described by Bond et al. (2013) and Petzold et al. (2013). Filter-based instruments, such as Aethalometers (AEs) (Hansen et al., 1984), Particle Soot Absorption Photometers (Bond et al., 1999) and Multi-Angle Absorption Photometers (Petzold and Schönlinner, 2004), are widely used for both ground measurements and airborne studies because they are easy to operate (Coen et al., 2010). The σ abs at different wavelengths is obtained by measuring the attenuation of light when it passes through an aerosolladen filter. AEs are the most frequently used commercial instruments to measure ambient aerosol σ abs . However, it is necessary to post-process AE-measured data to compensate for the well-known multiple-scattering effects and loading effects (Bond et al., 1999;Coen et al., 2010). Ample effort has been devoted to the methods of correcting measured σ abs (Coen et al., 2010;Virkkula et al., 2015;Saturno et al., 2017). Recently, a new dual-spot Aethalometer (AE33), which measures σ abs at seven different wavelengths from 370 nm to 950 nm with real-time loading effects compensation, was developed (Drinovec et al., 2015).
The official filter tape of AE33 has been changed from Model 8050 to 8060 because the nonlinear filter-loading effect from Tape 8050 causes dysfunction in the compensation process. Although AE33 with Tape 8050 has long been used for measurement worldwide, the performance of measured σ abs is not well characterized. It is widely accepted that the uncorrected σ abs data from AE33 is too high and that correction of the multiple-scattering effect is necessary (Moosmüller et al., 1998;Saturno et al., 2017;Sharma et al., 2017). Moreover, the σ abs measured with Tape 8050 is unstable, and the loading effects of the measured σ abs are not satisfactorily corrected, which was confirmed in this study. Furthermore, there have been more than 30 AE33 instruments employed to measure ambient σ abs in China since 2015 (personal communication), and these data are used to infer information regarding BC emissions in China. However, these data require reconstruction to accurately reveal the light-absorption properties of ambient aerosol.
In this study, we evaluated measured σ abs by using AE33 with Tape 8050 and Tape 8060 from two field measurements in eastern China. Based on the inter-comparison of the measured σ abs from AE33 and a three-wavelength photoacoustic soot spectrometer (PASS-3), a wavelength-independent multiple-scattering correction factor (C f ) value was recommended for eastern China. Using the same correction factor of 2.9 for eastern China makes it easier to reconstruct the historical observation data measured by AE33.

Measurement Sites
The field measurements were conducted at two sites: Peking University (PKU) and Taizhou. The suburban measurement at site Taizhou (119°57ʹE, 32°35ʹN), as shown in Fig. 1(a), lies at the south end of the Jianghuai Plain in eastern China. It is located approximately 118 km southeast of the megacity Nanjing and approximately 200 km northeast of another megacity, Shanghai. The industrial area between Nanjing and Shanghai has experienced severe pollution over the past 30 years. The average aerosol optical depth at the wavelength of 550 nm during 2017, as measured by the Moderate Resolution Imaging Spectroradiometer, indicates that the measurement site is more polluted than the surrounding area ( Fig. 1(b)). Taizhou is a representative location polluted mainly by secondary organic aerosol and biomass burning in eastern China (Zhao et al., 2019a). The PKU site is located northwest of Beijing, between the Fourth and Fifth Ring Road. It is 11 km away from the center of the Beijing, which is surrounded by Hebei Province and the megacity Tianjin. The Beijing-Tianjin-Hebei region suffers from heavy air pollution due to various industrial activities. As revealed in Fig. 1(b), the PKU site is on the edge of the heavily polluted area of the North China Plain. Datasets for this location are representative of the urban aerosol pollution in the North China Plain (Guo et al., 2012;Guo et al., 2013;Tang et al., 2018;Zhao et al., 2018;Zhao et al., 2019b).
Measurements at the PKU site were recorded in the spring (March 20-April 30) and in the autumn (October 10-19) of 2018, whereas observations at the Taizhou site took place in the summer (May 22-June 17) in 2018. For both sites, all of the instruments were placed in a container, in which the temperature was well controlled within 24 ± 2°C. The sample air was collected using a PM 10 impactor (Model SSI2.5; Mesa Labs) mounted on top of the container. Next, the sample air was passed through a Nafion dryer tube. The relative humidity of the sample particles measured with each instrument was controlled below 30%.

Instruments
The instruments used for the two field measurements are listed in Table S1. The corresponding time periods when data were available are marked in blue. The σ abs was measured by the PASS-3 at three wavelengths (405, 532, and 781 nm) and by two AE33s with different types of filter tape at seven wavelengths (370,470,520,590,660,880, and 950 nm). The two AE33s had the serial numbers 0345 and 0582 and were labeled as AE33-345 and AE33-582, respectively. The aerosol scattering coefficient (σ sca ) was measured using an Aurora 3000 nephelometer (Müller et al., 2011) at wavelengths of 450, 525, and 635 nm. Data correction was performed following Müller et al. (2011). The aerosol particle number size distribution (PNSD), ranging from 20 nm to 10 μm, was measured by using the Scanning Mobility Particle Size spectrometer (SMPS; Model 3936; TSI Inc.) and Aerodynamic Particle Sizer (APS; Model 3321; TSI Inc.).
Because the SMPS and APS provided the aerosol PNSD data every 5 minutes, all σ abs and σ sca data were averaged with the same time resolution of 5 minutes for further study.

PASS-3
The principle of PASS-3 has been described elsewhere (Terhune and Anderson, 1977;Utry et al., 2014;Nakayama et al., 2015;Cremer et al., 2017;Davies et al., 2018), and thus only a brief introduction is presented here. First, the PASS-3 continuously pumps the sample aerosol into an acoustic resonator, and these absorbing aerosols are irradiated by laser lights at 405, 532 and 781 nm. The laser is an amplitudemodulated square wave with a frequency of 1500 Hz. The absorbing aerosols absorb light energy and then generate periodic pressure waves in the resonator. Finally, σ abs is retrieved from the amplitude of the pressure wave by using a microphone. The PASS-3 installs a scattering integrating sphere to measure the aerosol σ sca concurrently with the σ abs .
The PASS-3 is capable of measuring the σ sca , σ abs , and the extinction coefficient (σ ext ) independently for high aerosol concentrations, which makes it easy to calibrate (Terhune and Anderson, 1977;Davies et al., 2018). In our study, σ sca of the integrating sphere was calibrated using pure scattering aerosol ammonium sulfate, and σ abs was calibrated using Aquadag soot particles by subtracting σ ext from σ sca . The PASS-3 can provide σ abs data with high accuracy if it is properly calibrated (Davies et al., 2018). The uncertainty of the absorption measurements was estimated to be 4%, 8%, and 11% from 405, 532, and 781 nm, respectively (Nakayama et al., 2015). Several studies have used σ abs data measured by a PASS as reference to evaluate the σ abs measured by a filter-based instrument (Arnott et al., 2005;Schmid et al., 2006;Lack et al., 2014;Utry et al., 2014).
Here, calibration of the PASS-3 was conducted at the beginning of field observations at the PKU site, and at the beginning and near the end of the observations at the Taizhou site. The status of the instrument did not exhibit considerable change, and the variations of the calibrated parameters were within 3%. Thus, the calibration results at the beginning of the measurement were used to derive the observations for each site.

AE
The AE is a well-designed instrument that is used to measure the light intensity transmitted through a fiber filter on which the aerosols are deposited (Masey et al., 2020). The filter attenuation (ATN) is calculated as: where I and I 0 are the concurrently measured light intensities that pass through the fiber with and without aerosol loading, respectively. The aerosol attenuation coefficient σ ATN,0 can be calculated as follows: ,0 where ΔATN is the change in ATN over time period ∆t; A is the sample spot area, and F is the aerosol flow rate. The σ ATN,0 values are corrected as σ ATN after filter-loading correction. The AE33 model succeeds in correcting the loading effects by performing real-time measurements of two parallel spots at different flow rates. More details on correcting the loading effects by using AE33 are provided by Drinovec et al. (2015). In this study, the corrected attenuation coefficient σ ATN from the AE33 was compared with the σ abs measured using the PASS-3.

Measurement and Model of the Aerosol Scattering Coefficient
The PASS-3 is capable of measuring aerosol σ sca and σ abs concurrently. We first proved the reliability of the measured σ sca by using the PASS-3, after which the reliability of the measured σ abs by the PASS-3 was guaranteed. The σ sca values measured by the PASS-3, measured by a nephelometer and calculated using the scattering model with measured aerosol PNSD were compared first. The data used were obtained from the measurements at the PKU site. Comparison within the Taizhou site yielded results that were almost the same. The Mie scattering model (Bohren and Huffman, 2007) was employed to calculate the σ sca at different wavelengths. When running the Mie scattering model, the aerosol PNSD and BC mass concentration were required. The BC mass concentrations were calculated using the corrected σ abs from the AE33 at a wavelength of 880 nm, with the assumption that the mass absorption coefficient was 7.77 m 2 g −1 . All of the BC particles were also assumed to have mixed internally with other aerosol components. The refractive indices of BC and non-light-absorbing aerosols are 1.8 + 0.54i (Wex et al., 2002;Kuang et al., 2015) and 1.53 + 10 −7 i (Wex et al., 2002) respectively. With this information, σ sca at different wavelengths can be calculated. More details regarding this calculation process can be found in Zhao et al. (2018).
The results of inter-comparisons between the σ sca values measured by the nephelometer and those calculated using the Mie scattering model are shown in Fig. S1. We observed strong consistency between the measured and calculated σ sca values (R 2 = 0.99 for different wavelengths), which indicated that the aerosol PNSD and σ sca measurements by the nephelometer were reliable. Because the σ sca values measured using the nephelometer in the present study were raw measured data, and truncation error corrections were not conducted, the calculated σ sca values were always slightly larger than the measured values, with regressed larger regression slope than unity for each wavelength.
The measured σ sca values using the PASS-3 and the nephelometer at similar wavelengths were compared. The measured σ sca were adjusted to the same wavelength using the scattering Å ngström exponent. Our findings are presented in Fig. S2 and show that great consistency was achieved between σ sca values at 525 nm from the nephelometer and σ sca from the PASS-3. The slope (1.06) was slightly higher than 1.0, which was mainly caused by the different truncation errors between nephelometer and PASS-3. The σ sca values measured at other wavelengths had almost the same trends (R 2 > 0.99). Our inter-comparison of the σ sca values measured by the PASS-3 and nephelometer demonstrated that the measurements of both instruments were reliable.
Finally, σ sca values were measured by PASS-3 and calculated using the Mie scattering model at wavelengths of 405, 532, and 781 nm; the results were compared and presented in Fig. 2. Notably, the measured and calculated σ sca values exhibited strong consistency. The relative difference between them was primarily less than 20%.
Overall, the closures achieved between the measured σ sca values by the PASS-3, the measured σ sca values by the nephelometer and the calculated σ sca values by the Mie scattering model demonstrated that the PASS-3 provided σ sca values with high accuracy. Therefore, the measured σ abs by the PASS-3 was reliable. We thus used the measured σ abs by the PASS-3 as a reference for the other instruments.

σATN Properties of Different Filter Tapes in AE33 Instruments
Two AE33 instruments (AE33-345 and AE33-582) were used to measure σ ATN using Filter Tapes 8050 and 8060, respectively. Notably, the σ ATN values obtained from the AE33 used in the present study were different from the σ abs values by a factor of C f . As shown in Table S1, four intercomparisons were conducted to evaluate the performance of Filter Tapes 8050 and 8060. The σ ATN values measured from the AE33-345 and AE33-582 were compared using (1) Table S1 at 880 nm for Groups (1), (2), (3), and (4), respectively. According to Fig. 3(a), the σ ATN values from the two instruments with Tape 8060 exhibited strong agreement (R 2 = 0.99, slope = 1.08). Moreover, almost all of the σ ATN values from the two instruments had a relative difference of less than 20%. However, the consistency between σ ATN values from the two instruments decreased when one of the instruments switched to Tape 8050 (R 2 = 0.95 and 0.97 for Test Groups [2] and [3], respectively). The slopes of 1.13 and 1.12 demonstrate that the σ ATN values measured by the AE33-582 is about 1.1 times that of measured value by the AE33-345. However, when both instruments switched to Tape 8050, the consistency between σ ATN values worsened (R 2 = 0.87); in many cases, the relative difference between the measured σ ATN values was greater than 20%. Overall, the relative difference in σ ATN values between the two instruments did not indicate a clear relationship with the ATN values. Thus, the stability of the measured σ ATN values were not improved by changing the tape more frequently.
Our inter-comparison results suggested that the σ ATN values measured by Tape 8060 was more stable than that measured by Tape 8050. Nonetheless, a relative difference of 10% still existed among different AE instruments.
The α abs value was calculated using Eq. (1) with the σ ATN values at 470 nm and 950 nm measured using the AE33, which can be used as the source attribution for traffic and wood burning (Martinsson et al., 2017;Zotter et al., 2017).  The discussion in Section 3.3 reveals that the calculated α abs values from σ ATN and σ abs were the same. The measured α abs values at different accumulated ATNs and on different days using Tape 8050 and Tape 8060 are shown in Figs. 4(a) and 4(b), respectively. The calculated α abs values from Tape 8060 ( Fig. 4(b)) did not exhibit a clear relationship with accumulated ATN, and the variations in α abs were mainly a result of the diversity in ambient aerosol absorption properties. However, the α abs from Tape 8050 was highly correlated with the ATN values shown in Fig. 4(a). When the ATN changed from 22-60 to 120, the mean α abs values changed from 1.6-1.8 to 2.0, respectively. However, the variation in α abs was approximately 0.6, which is almost the same degree of α abs variation caused by different ATNs when using Tape 8050. Therefore, the α abs value measured using the AE33 using Tape 8050 was associated with great uncertainty.
The α abs at the Taizhou site had almost the same properties as that at the PKU site, as shown in Fig. S3. The results indicated that α abs changed significantly with the ATN for Tape 8050, but that there were no clear variations with the increased accumulation of ATN for Tape 8060.

Multiple-scattering Correction Factor
The PASS-3 estimated the instrument noise and recorded the value in its reported data. The statistical results for noise during the measurement are shown in Fig. S4. The mean and standard deviation of σ abs for instrument noise were 0.34 and 0.066, respectively, with a 95.5% possibility (sum of the mean and double the standard deviation) that the noise was less than 0.473. To confirm that the measured σ abs noise comprised a small partition of the measured σ abs , we compared these data when the surrounding σ abs was larger than 10.50 Mm −1 [0.473/(1 − 95.5%)], under which condition the noise would account for less than 4.5% of the measured σ abs value.
Figs. 5(a), 5(b), and 5(c) present a comparison of the σ abs values measured using the PASS-3 and the σ ATN values by the AE33 at wavelengths of 405, 532, and 781 nm, respectively, at the PKU site. Section 3.2 reveals that the measured results of the AE33 with Tape 8060 were more reliable and stable than those from the AE33 with Tape 8050. Thus, the σ ATN value from the AE33 with Tape 8060 was used for comparison. The σ ATN value at 405 nm was calculated using the α ATN value that had been previously calculated using the σ ATN values at 370 nm and 470 nm. The corresponding σ ATN values of AE33 at 532 and 781 nm were calculated using the σ ATN values at the wavelength pairs of 520 and 590 nm, and 660 and 880 nm, respectively. σ abs can be derived by dividing σ ATN by C f .
Here, C f was determined by calculating the ratio of the σ ATN values measured using the AE33 and the σ abs values measured using the PASS-3. As revealed in Fig. 5, C f was determined to be 2.91, 2.94 and 2.94 at 405, 532, and 781 nm, respectively, by using the linear regression forcing the intercept to zero. C f did not exhibit obvious variations with changes in wavelength. The comparison was conducted for the Taizhou site and the corresponding C f values were 2.88, 2.88 and 2.86 at 405, 532, and 781 nm, respectively, as shown in Fig. S5. The C f value is smaller than that of 4.35 in central Oregon, USA (Laing et al., 2020).
Therefore, the C f was recommended to be 2.90 (± 0.04) for both sites, which is an average of all the ratios. Notably, this value was the same for different wavelengths.

Correction Method of σATN
According to the findings presented in Section 3.3, it is clear that the AE33 with Tape 8060 provided a reliable σ abs measurement with a C f value of 2.90. By contrast, the σ ATN and α abs values measured with Tape 8050 were related to the accumulation of ATN (see Section 3.2). Moreover, the σ ATN values measured with Tape 8060 was relatively stable and unrelated to the accumulation of ATN. However, because the AE33 with Tape 8050 has long been used worldwide for measuring ambient BC mass loadings, historical observation data from the AE33 with Tape 8050 should be corrected. We propose a straightforward method to correct σ ATN Fig. 6 shows the correction factors at different wavelengths and ATN values, revealing that the correction factors varied significantly with the amount of ATN. When the ATN was less than 80, the correction factors did not exhibit clear differences among different wavelengths. They did, however, become increasingly diverse across different wavelengths as ATN increased. The σ ATN values measured with Tape 8050 were slightly lower than those measured with Tape 8060 when the ATN was less than 90 across the seven wavelengths.
Because the correction factors were different for different wavelengths, we calculated the difference in α abs values at the wavelengths of 470 nm and 950 nm. The results, presented in Fig. 6, indicated that corrections of σ ATN can lead to variations in α abs from 0.02-0.15 to 0.23 when ATN increased from 30-60 to 130. The variations in α abs were consistent with the results presented in Section 3.2, namely that the measured α abs values first decreased and then increased with the increase in ATN. This suggests that the correction factors can provide a more reliable σ ATN and α abs values for Tape 8050. using the respective wavelengths of 470 and 950 nm. The location at which the tape was switched can be recognized directly when the ATN decreased from higher than 135 to less than 40, as shown in Figs. 7(c) and 7(d). Figs. 7(a) and 7(c) reveal that both σ ATN and α abs exhibited large discrepancies when the tape was switched for the raw measured σ ATN . However, the situation improved when σ ATN was corrected using the factors shown in Fig. 6, resulting in more continuous σ ATN and α abs values than before.
In conclusion, two steps of correction should be applied   for σ ATN values measured with Tape 8050. The first step is to correct the measured σ ATN values by the factor shown in Fig. 6 for different ATNs and wavelengths. The second step is the same as that used for correction for Tape 8060: correcting the multiple-scattering effects by using a recommended factor of 2.9 for each wavelength.

CONCLUSIONS
In this study, we evaluated the reliability of σ abs values measured with an AE33 during two field campaigns in Taizhou and at PKU. Comparing the values measured with two different AE33s, one using Tape 8050 and the other using Tape 8060, we found that using Tape 8060 produced more stable σ ATN values.
As no clear relationship between the α abs and the ATN was observed, the loading effects were apparently sufficiently corrected for Tape 8060; thus, only the multiple-scattering correction should be applied when measuring σ ATN values with this tape. However, since the loading effects were not adequately corrected for Tape 8050, both the loading effect and multiple-scattering corrections for σ ATN should be considered when using this tape.
Based on the comparison between the σ abs values measured with the PASS-3 and the σ ATN values measured with the AE33 using Tape 8060, we recommend a mean C f value of 2.9 ± 0.4 to correct the measured σ ATN independent of wavelength. We also obtained a correction factor for the σ ATN measured using Tape 8050 by regressing values measured using Tape 8060 against those measured using Tape 8050 for different ATNs and wavelengths. This factor corrected the discrepancy in the measured σ ATN between the tape sampling values and the raw data, thereby resolving α abs 's variation with the ATN.
This study can serve as a reference for σ abs measurements and for source appointments. Using one correction factor for the North and East China Plain offered the advantage of increasing the inter-comparability of the measurements from different sites and facilitating the reconstruction of the AE33-measured historical observation data.

DATA AVAILABILITY
The measurement data involved in this study are available upon request.