Multiple scattering correction factor estimation for aethalometer aerosol absorption coefficient measurement

Abstract

We estimate the multiple scattering correction factor ($C_{ref}$), which is an empirical constant required to correct aerosol absorption coefficient (${\sigma }_{ap}$) measurements for the multiple scattering artifacts of aethalometer, using a multiplier derived from a linear regression method ($C_{ref}^{LRL}$). Estimated $C_{ref}^{LRL}$ values during the Cheju ABC Plume Monsoon EXperiment (CAPMEX) are 3.99 (405 nm), 4.48 (532 nm), and 5.46 (781 nm) using aethalometer and 3-wavelength PhotoAcoustic Soot Spectrometer (PASS-3). The difference between these $C_{ref}^{LRL}$ values and those of a previous study ($C_{ref}^{W03}$) are ˗8.0% (405 nm), 20.1% (532 nm), and 30.2% (781 nm); the difference is greater at larger wavelengths because the linear regression line intercept is larger. $C_{ref}^{W03}$ varies by up to 121% with increasing aerosol absorption coefficient (${\sigma }_{ap}$) at 532 and 781 nm, whereas $C_{ref}^{LRL}$ varies by only 36.8%. $C_{ref}^{W03}$ and $C_{ref}^{LRL}$ determined during CAPMEX were applied to year-round aethalometer ${\sigma }_{ap}$ measurements (${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{LRL}$, respectively) at Gosan (GSN), Lulin (LLN), and Alert (ALT) stations. ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{LRL}$ were compared to concurrent ${\sigma }_{ap}$ measurements from Continuous Light Absorption Photometer (CLAP; ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$). At GSN, the bias difference and root mean square difference of ${\sigma }_{ap}^{W03}$ from ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ are ˗23.1 and 25.8%; however, those of ${\sigma }_{ap}^{LRL}$ from ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ are ˗9.0 and 17.9%, respectively. LLN and ALT both exhibit a greater difference between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ than between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$. This suggests that $C_{ref}^{LRL}$can be applied to year-round aethalometer measurements. Furthermore, ${\sigma }_{ap}^{LRL}$ agrees better with ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ than ${\sigma }_{ap}^{W03}$ in all three environments.

Copyright © 2019 American Association for Aerosol Research

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1. Introduction

Filter-based optical instruments, such as aethalometer (Hansen, Rosen, and Novakov 1984), particle soot absorption photometer (PSAP; Bond, Anderson, and Campbell 1999), and multi-angle absorption photometer (MAAP; Petzold and Schönlinner 2004), measure the change in light attenuation (ATN) across an aerosol-laden filter to retrieve the aerosol absorption coefficient (${\sigma }_{ap}$). Filter-based optical instruments have been widely used to measure ${\sigma }_{ap}$; however, they typically suffer from measurement artifacts. Specifically, the multiple scattering effect (MSE) is one of the largest sources of uncertainty in filter-based optical instruments (Bond, Anderson, and Campbell 1999; Petzold and Schönlinner 2004; Sheridan et al. 2005; Subramanian et al. 2007; Virkkula et al. 2007; Lack et al. 2008; Kondo et al. 2009; Moosmüller, Charkrabarty, and Arnott 2009; Müller et al. 2011; Di Biagio et al. 2017; Ogren et al. 2017). Many previous studies have suggested MSE correction methods for aethalometer by applying a multiple scattering correction factor ($C_{ref}$). Weingartner et al. (2003; hereafter, W03) suggested a ${\sigma }_{ap}$ correction scheme that determined $C_{ref}$ based on ${\sigma }_{ap}$ measured by aethalometer relative to that measured by a reference instrument. Arnott et al. (2005; hereafter, A05) suggested subtracting a portion of related aerosol light scattering measurements to correct for particle scattering, based on experiments with laboratory-generated aerosols and ambient aerosols. Schmid et al. (2006; hereafter, S06) modified the W03 scheme by adopting the single scattering albedo (SSA) to correct for the particle scattering artifact using ambient aerosols. Collaud Coen et al. (2010; hereafter, C10) suggested a ${\sigma }_{ap}$ correction scheme for ambient aerosols. Despite the various improvements made by many studies, the basis of $C_{ref}$ determination has not been changed substantially from W03. It is still necessary to reduce the effect of any measurement artifact induced during the $C_{ref}$ determination procedure because not only the aethalometer but also the reference instruments include their own measurement artifacts (Arnott et al. 1999, 2003; Petzold and Schönlinner 2004; Ajtai et al. 2010; Nakayama et al. 2015).

In this study, we propose a $C_{ref}$ determination method and validate its effects on accompanying aerosol optical properties, including ${\sigma }_{ap}$, SSA, and the absorption Ångström exponent (AAE). Our determination method uses a linear regression line (LRL) method outlined in Section 3.1. Estimated $C_{ref}$ values are then validated by applying them to year-round continuous aethalometer measurements and comparing our values to simultaneous measurements from other filter-based optical instruments in Section 3.2.

2. Methodology

2.1. Measurements and stations

A summary of the measurement setup is shown in Table 1. Multi-year measurement data from Gosan (GSN; 33.29°N, 126.17°E, 72 m a.s.l.; maritime), Lulin (LLN; 23.47°N, 120.87°E, 2862 m a.s.l.; high altitude), and Alert (ALT; 82.49°N, 62.51°W, 190 m a.s.l.; Arctic) stations were analyzed. An identical measurement protocol (WMO 2016) was implemented at all three stations. A brief description of the location, environment and measurements is given in Schmeisser et al. (2017) and Andrews et al. (2018). From August to September, 2008, the Cheju ABC plume monsoon experiment (CAPMEX) field campaign was performed at GSN (Flowers et al. 2010; Ramana et al. 2010).

Table 1. Instrument setup for ${\sigma }_{ap}$ measurements during CAPMEX and at GSN, LLN, and ALT.

Station	Period	Aethalometer^a (Filter-based optical)	PASS-3^b (Photoacoustic)	CLAP^c (Filter-based optical)
GSN (CAPMEX)	Aug.–Sep. 2008	No imposed RH, size cut	No imposed RH, size cut	NA^d
GSN	Jan. 2012–Dec., 2014	No imposed size cut RH < 40%	NA	10 μm size cut RH < 40%
LLN	Jan.–Dec., 2013
ALT	Sep. 2014–May, 2015

^a Aethalometer: 370, 470, 520, 590, 660, 880, and 950 nm.

^b PASS-3: 405, 532, and 781 nm.

^c CLAP: 467, 528, and 652 nm.

^d NA: Not Available.

2.2. Instrumentation

2.2.1. Aethalometer

A 7-wavelength aethalometer (AE-31, Magee Scientific Corp., Berkeley, CA, USA) measures the change of ATN and reports it as an equivalent black carbon mass concentration (M_ebc). During CAPMEX and at GSN, the aethalometer was operated without any imposed size cut, with a flow rate of 3.9 L min⁻¹, using an extended-range spot size (1.67 cm²) and a temporal resolution of 5 min. At LLN, the aethalometer was operated with a flow rate of 4.0 L min⁻¹, using a high-sensitivity spot size (0.5 cm²). At ALT, the aethalometer was operated with a flow rate of 3.9 L min⁻¹, using a high-sensitivity spot size (0.5 cm²). Müller et al. (2011) reported that the noise level is 0.8 Mm⁻¹ within 470–880 nm over a 3-min average. Aethalometer ${\sigma }_{ap}$ values were retrieved using the W03 scheme in this study, which is discussed more in Section 2.3.

2.2.2. Photoacoustic soot spectrometer (PASS-3)

A 3-wavelength Photoacoustic soot spectrometer (PASS-3, Droplet Measurement Technologies Inc., Longmont, CO, USA) (Flowers et al. 2010) was operated to obtain ${\sigma }_{ap}$ at 1 L min⁻¹ and a 10 min time-base during CAPMEX. Even though PASS-3 measurement precision can be influenced by factors such as acoustic noise and RH, PASS-3 was set as the reference instrument of CAPMEX in this study because it is free from filter-induced measurement artifacts (Arnott et al. 2000; 2003; Lack et al. 2008). The manufacturer reported that the detection limit of PASS-3 is 10, 10, and 3 Mm⁻¹ (2 second-averaged) at 405, 532, and 781 nm, respectively (http://www.dropletmeasurement.com/photoacoustic-soot-spectrometer-three-wavelength-pass-3-0). Using Equation (S4) (Supplementary Information C), this corresponds to 0.58, 0.58, and 0.17 Mm⁻¹ for 10-min averages at 405, 532, and 781 nm, respectively. Flowers et al. (2010) provide a more detailed description of PASS-3 measurements during CAPMEX.

2.2.3. Continuous light absorption photometer (CLAP)

The continuous light absorption photometer (CLAP) is a mechanically and electronically improved version of PSAP; the LRL slope of CLAP ${\sigma }_{ap}$ (${\sigma }_{ap}^{\mathit{\text{CLAP}}}$) to PSAP ${\sigma }_{ap}$ is 0.94 (standard deviation: 0.08) and the intercept is small (mean: 0.1) for three wavelengths (Ogren et al. 2017). CLAP is operated at GSN, LLN, and ALT with ∼1 L min⁻¹ and 1-min time-based measurements. ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ was retrieved using corrections derived by Bond, Anderson, and Campbell (1999) and Ogren (2010).

CLAP cannot strictly be the reference instrument for a comparison of aethalometer $C_{ref}$ because CLAP is another filter-based optical instrument. Nevertheless, CLAP was employed as the reference for comparison of multi-year measurements at GSN, LLN, and ALT because CLAP exhibits lower uncertainties than aethalometer for spot area size (aethalometer ∼8%, CLAP 2%), instrumental noise (aethalometer ∼0.42 Mm⁻¹, CLAP ∼0.07 Mm⁻¹), and unit-to-unit variability (aethalometer ∼20%, CLAP ∼4%) (Müller et al. 2011; Ogren et al. 2017). Ogren et al. (2017) reported that the noise level of the CLAP attenuation coefficient (i.e., raw absorption coefficient without any correction) is approximately 0.2 Mm⁻¹ for a 1-min average. Although simultaneous observations of CLAP and PASS are not available in this study, it is worth noting that ${\sigma }_{ap}$ from PSAP and PASS were well matched (e.g., Lack et al. 2008). Aerosols were sampled by the CLAP with both a PM₁ and PM₁₀ size cut; however, PM₁ data were not analyzed in this study because of the comparison with aethalometer, which have no imposed size cut.

2.3. Data processing and quality assurance

Measurement data were averaged to an hourly resolution for the comparison, then a standard temperature and pressure (STP; 0 °C and 1013.25 hPa) correction was applied. During CAPMEX, ${\sigma }_{ap}$ values with high nephelometer RH (> 70%) were excluded from the analysis to avoid hygroscopic effects of the measurement (Arnott et al. 2003; Kim et al. 2006; Fierz-Schmidhauser et al. 2010).

2.3.1. Retrieval of ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}$ from aethalometer measurement

Equations (1)–(3) show the aethalometer ${\sigma }_{ap}$ retrieval scheme suggested by W03. (1) $${ATN}_i=\mathrm{}-100·\mathrm{l}\mathrm{n}\left(\frac{I_i}{I_{o,i}}\right)$$(1) (2) $${\sigma }_{atn,i}=\frac{A_i}{Q_i}·\left(\frac{{\Delta \text{ATN}}_{i-(i-1)}}{{\Delta \mathrm{t}}_{i-(i-1)}}\right)$$(2) (3) $${\sigma }_{ap,i}=\mathrm{}\frac{{\sigma }_{atn,i}}{C_{ref}·R\left({ATN}_i\right)}=\mathrm{}\frac{{\sigma }_{atn,i}}{C_{ref}·\left[\left(\frac{1}{f-1}\right)\frac{ln\left({ATN}_i\right)-ln\left(10\right)}{ln\left(50\right)-ln\left(10\right)}+1\right]}$$(3)

where ATN is the light attenuation by filter-deposited aerosols, $I_o$ and $I$ are emitted and particle attenuated light intensity, respectively. Q, $t$ and A are flow rate, time and spot size area, respectively. ${\sigma }_{atn}$ is the attenuation coefficient, which is the raw aethalometer absorption coefficient without any correction applied, R(ATN) is the filter-loading correction, and $f$ is the shadowing factor. i represent the i^th data point. Supplementary Information (A) Table S1 summarizes the notations used in this study (subscripts indicate the type of parameter; superscripts indicate the method or instrument used to retrieve the parameter). Although S06 and C10 schemes are improved versions of W03, C10 reported that the W03 scheme agrees well with reference instruments and does not modify the spectral characteristics of ${\sigma }_{ap}$ for all aerosol types in a comparison among several existing schemes including W03, A05, and S06. Therefore, the W03 scheme, which has the simplest multiple scattering compensation, was selected to retrieve aethalometer ${\sigma }_{ap}$ in this study.

2.3.2. Determination method of ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}$

$C_{ref}^{W03}$ is determined using Equation (4)(4) $$C_{ref}^{W03}\mathrm{}=\mathrm{}\frac{1}{N}\sum _i^N\frac{{\sigma }_{atn,i}/R\left({ATN}_i\right)}{{\sigma }_{ap,i}^{ref}}\mathrm{}=\frac{1}{N}\sum _i^N\frac{{\sigma }_{ap,i}^{flc}}{{\sigma }_{ap,i}^{ref}}$$(4) . (4) $$C_{ref}^{W03}\mathrm{}=\mathrm{}\frac{1}{N}\sum _i^N\frac{{\sigma }_{atn,i}/R\left({ATN}_i\right)}{{\sigma }_{ap,i}^{ref}}\mathrm{}=\frac{1}{N}\sum _i^N\frac{{\sigma }_{ap,i}^{flc}}{{\sigma }_{ap,i}^{ref}}$$(4) where ${\sigma }_{ap}^{flc}$ is ${\sigma }_{atn}$ with the filter-loading effect corrected by dividing by R(ATN) and N represents the number of total data points. ${\sigma }_{ap}^{ref}$ is the ${\sigma }_{ap}$ measured by the reference instrument (PASS-3 during CAPMEX; CLAP at GSN, LLN, and ALT). $C_{ref}^{W03}$ is determined by dividing ${\sigma }_{ap}^{flc}$ by ${\sigma }_{ap}^{ref}$, but partly corrected only for the filter-loading effect to extend the sample number. Moreover, the ratio between ${\mathrm{\sigma }}_{ap}^{flc}$ and ${\sigma }_{ap}^{ref}$ can also be retrieved by the slope of the least-square LRL between the two measurements, assuming that they are linearly correlated (Wilkinson and Rogers 1973). Ideally, the LRL between ${\sigma }_{atn}$ and ${\sigma }_{ap}^{ref}$ does not have an intercept; however, it is possible that the LRL intercept is non-zero and is large enough to have a non-negligible impact on the determination of $C_{ref}$. $C_{ref}$ determined by the least-square linear regression method ($C_{ref}^{LRL}$) is defined in Equation (5)(5) $$C_{ref}^{LRL}=\mathrm{}a\mathrm{}=\mathrm{}\frac{1}{N}\sum _i^N\frac{\left\{{\sigma }_{atn,i}/R\left({ATN}_i\right)\right\}-b}{{\sigma }_{ap,i}^{ref}}=\mathrm{}\frac{1}{N}\sum _i^N\frac{{\sigma }_{ap,i}^{flc}-b}{{\sigma }_{ap,i}^{ref}}$$(5) . (5) $$C_{ref}^{LRL}=\mathrm{}a\mathrm{}=\mathrm{}\frac{1}{N}\sum _i^N\frac{\left\{{\sigma }_{atn,i}/R\left({ATN}_i\right)\right\}-b}{{\sigma }_{ap,i}^{ref}}=\mathrm{}\frac{1}{N}\sum _i^N\frac{{\sigma }_{ap,i}^{flc}-b}{{\sigma }_{ap,i}^{ref}}$$(5) $\text{where}a$ is the slope and $b$ is the intercept, when the LRL equation between ${\sigma }_{ap}^{flc}$ and ${\sigma }_{ap}^{ref}$ is $y=ax+b$. Assuming b is zero or negligible, Equation (5)(5) $$C_{ref}^{LRL}=\mathrm{}a\mathrm{}=\mathrm{}\frac{1}{N}\sum _i^N\frac{\left\{{\sigma }_{atn,i}/R\left({ATN}_i\right)\right\}-b}{{\sigma }_{ap,i}^{ref}}=\mathrm{}\frac{1}{N}\sum _i^N\frac{{\sigma }_{ap,i}^{flc}-b}{{\sigma }_{ap,i}^{ref}}$$(5) will be the same as Equation (4)(4) $$C_{ref}^{W03}\mathrm{}=\mathrm{}\frac{1}{N}\sum _i^N\frac{{\sigma }_{atn,i}/R\left({ATN}_i\right)}{{\sigma }_{ap,i}^{ref}}\mathrm{}=\frac{1}{N}\sum _i^N\frac{{\sigma }_{ap,i}^{flc}}{{\sigma }_{ap,i}^{ref}}$$(4) . Otherwise, the LRL method, which is forced through the origin, will produce equal results to those of Equation (4)(4) $$C_{ref}^{W03}\mathrm{}=\mathrm{}\frac{1}{N}\sum _i^N\frac{{\sigma }_{atn,i}/R\left({ATN}_i\right)}{{\sigma }_{ap,i}^{ref}}\mathrm{}=\frac{1}{N}\sum _i^N\frac{{\sigma }_{ap,i}^{flc}}{{\sigma }_{ap,i}^{ref}}$$(4) . Hence, b is the factor that induces the difference between $C_{ref}^{W03}$ and $C_{ref}^{LRL}$ (see Supplementary Information B for more details).

3. Results and discussion

3.1. Determination of ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}$ during CAPMEX

Figure 1 shows a comparison between ${\sigma }_{ap}^{flc}$ and ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$ during CAPMEX. The $C_{ref}$ determination results during CAPMEX are summarized in Table 2.

Figure 1. Comparison between ${\sigma }_{ap}^{flc}$ and ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$ during CAPMEX (dashed line (black) is the LRL; color scale indicates the occurrence).

Table 2. Results of $C_{ref}$ determination during CAPMEX.

	405 nm	532 nm	781 nm
LRL	$y=3.99x-2.07$	$y=4.48x+6.92$	$y=5.46x+6.22$
SEa^a	0.04	0.07	0.05
SEb^b	0.48	0.46	0.18
$C_{ref}^{W03}$	3.67 ± 1.25^c	5.38 ± 2.73	7.11 ± 1.82
$C_{ref}^{LRL}$	3.99 ± 1.33	4.48 ± 2.32	5.46 ± 1.66
N		1102

^a SE_a: Standard Error of LRL slope.

^b SE_b: Standard Error of LRL intercept.

^c Mean ± standard deviation.

It was observed that ${\sigma }_{ap}^{flc}$ and PASS-3 (${\sigma }_{ap}^{\mathit{\text{PASS}}3}$) are linearly correlated with each other (R² ∼ 0.76–0.90). The LRL between ${\sigma }_{ap}^{flc}$ and ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$ is y = 3.99x–2.07 (405 nm), y = 4.48x + 6.92 (532 nm), and y = 5.46x + 6.22 (781 nm). $C_{ref}^{LRL}$ was determined using the slope (a) of the LRL (3.99, 4.48, and 5.46 at 405, 532, and 781 nm, respectively) and $C_{ref}^{W03}$ was determined using Equation (4)(4) $$C_{ref}^{W03}\mathrm{}=\mathrm{}\frac{1}{N}\sum _i^N\frac{{\sigma }_{atn,i}/R\left({ATN}_i\right)}{{\sigma }_{ap,i}^{ref}}\mathrm{}=\frac{1}{N}\sum _i^N\frac{{\sigma }_{ap,i}^{flc}}{{\sigma }_{ap,i}^{ref}}$$(4) . The difference between $C_{ref}^{LRL}$ and $C_{ref}^{W03}$ is statistically significant at all three wavelengths after considering that the difference is larger than the standard error of a (SE_a; see Supplementary Information C). Likewise, b is statistically significant at all wavelengths considering the standard error of b (SE_b). The percentage differences of $C_{ref}^{W03}$ from $C_{ref}^{LRL}$ are –8.0 (405 nm), 20.1 (532 nm), and 30.2% (781 nm); they are relatively large at 532 and 781 nm because the LRL intercept is larger at 532 and 781 nm than at 405 nm. Considering Equations (1)–(3), it can be inferred that the difference between $C_{ref}$ is propagated to ${\sigma }_{ap}$ and that ${\sigma }_{ap}^{W03}$ is smaller than ${\sigma }_{ap}^{LRL}$ by approximately –8% (405 nm), 21% (532 nm), and 25% (781 nm).

The box-whisker plot in Figure 2 shows $C_{ref}^{W03}$ and $C_{ref}^{LRL}$ values segmented by the 10^th percentile interval of ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$. The maximum ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$ values are 32.05 (405 nm), 18.92 (532 nm), and 11.19 Mm⁻¹ (781 nm). At 405 nm, both $C_{ref}^{W03}$ and $C_{ref}^{LRL}$ are relatively stable with increasing ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$ percentile. In contrast, segmented $C_{ref}^{W03}$ varies with increasing ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$ percentile at 532 and 781 nm. The 0–10^th percentile whisker plot of $C_{ref}^{W03}$ reaches up to 19.8 (532 nm) and 26.2 (781 nm). Table 3 shows the average segmented $C_{ref}$ value and its difference from the total $C_{ref}\mathrm{}$value (unsegmented). In the 0–10^th percentile bin, the average $C_{ref}^{W03}$ is larger than that of $C_{ref}^{LRL}$ by a factor of 0.71 (405 nm), 1.94 (532 nm), and 2.15 (781 nm). However, in the 90–100^th percentile of ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$, the segment bin-averaged $C_{ref}^{W03}$ is larger than that of $C_{ref}^{LRL}$ by a factor of 1.01 (405 nm), 0.91 (532 nm), and 0.92 (781 nm). $C_{ref}^{W03}$ and $C_{ref}^{LRL}$ values become closer in the 90–100^th percentile.

Figure 2. Box-whisker plot of (a) ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}^{\mathit{W}03}$ and (b) ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}^{\mathit{L}\mathit{R}\mathit{L}}$ segmented by percentiles of ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{P}\mathit{A}\mathit{S}\mathit{S}3}$ (bottom and top whiskers represent the 5^th and 95^th percentiles; horizontal lines of the box represent the 25^th, 50^th, and 75^th percentiles of ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}$; dashed line (green) represents ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}$; cross (red) represents the average value of each percentile of ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{P}\mathit{A}\mathit{S}\mathit{S}3}$; 0–10 on the x-axis represents the interval between the 0 and 10^th percentile of ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{P}\mathit{A}\mathit{S}\mathit{S}3}$). Numbers in parentheses in x-axis are the range of ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}$ in each bin (unit in Mm⁻¹).

Table 3. ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$-segmented $C_{ref}$ and their percentage difference from the unsegmented average of $C_{ref}$ during CAPMEX.

Percentile of ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$		0–10	10–20	20–30	30–40	40–50	50–60	60–70	70–80	80–90	90–100	Total $C_{ref}$ (0–100)
Segmented $C_{ref}^{W03}$	405 nm	2.92	3.29	3.28	3.42	3.70	3.83	3.93	3.92	4.06	4.15	3.67
	532 nm	11.89	6.38	5.69	4.69	5.04	5.06	4.76	4.57	4.34	3.96	5.38
	781 nm	14.68	10.47	8.19	7.23	6.43	5.83	5.86	5.51	5.27	5.25	7.11
Difference from total $C_{ref}^{W03}$ [%]	405 nm	˗20.4	˗10.4	˗10.6	˗6.8	0.8	4.4	7.1	6.8	10.6	13.1	NA^a
	532 nm	121.0	18.6	5.9	˗12.8	˗6.2	˗5.8	˗11.3	˗14.9	˗19.3	˗26.5	NA
	781 nm	106.5	47.2	15.2	1.7	˗9.5	˗18.0	˗17.5	˗22.5	˗25.9	˗26.1	NA
Segmented $C_{ref}^{LRL}$	405 nm	4.11	3.72	3.72	3.73	3.78	3.82	3.79	3.91	3.95	4.11	3.99
	532 nm	6.13	3.92	4.16	3.61	4.31	4.62	4.53	4.54	4.50	4.35	4.48
	781 nm	6.83	5.71	5.05	5.18	5.13	4.96	5.34	5.34	5.37	5.69	5.46
Difference from total $C_{ref}^{LRL}$ [%]	405 nm	3.0	˗6.7	˗6.8	˗6.6	˗5.3	˗4.3	˗5.0	˗1.9	˗0.8	3.0	NA
	532 nm	36.8	˗12.5	˗7.14	˗19.4	˗3.8	3.1	1.1	1.3	0.4	˗2.9	NA
	781 nm	25.1	4.6	˗7.5	˗5.1	˗6.0	˗9.2	˗2.2	˗2.2	˗1.6	4.2	NA

^a NA: Not Available.

Notably, the percentage difference between segmented $C_{ref}^{W03}$ and total $C_{ref}^{W03}$ varies by ±121.0% at all wavelengths; i.e. 13.1 (405 nm), –26.5 (532 nm), and –26.1% (781 nm) in the 90–100^th percentile. The minimum percentage difference between segmented $C_{ref}^{W03}$ and total $C_{ref}^{W03}$ occurs in the 30–60^th percentile. Conversely, the segmented average of $C_{ref}^{LRL}$ lies between ±36.8% at all wavelengths; i.e. 3.0 (405 nm), –2.9 (532 nm), and 4.2 (781 nm) in the 90–100^th percentile. The minimum percentage difference of segmented $C_{ref}^{LRL}$ from total $C_{ref}^{LRL}$ occurs during the 90–100^th percentile. $C_{ref}^{LRL}$ does not change with increasing ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$ relative to $C_{ref}^{W03}$. This suggests that $C_{ref}^{LRL}$ produces less extreme values and is less affected by low signal-to-noise ratio (SNR).

$C_{ref}^{W03}$ and $C_{ref}^{LRL}$ are compared to values derived in previous studies in Figure 3. Even though their measurement environment and wavelengths are not equal, $C_{ref}$ values from previous studies range from approximately 2–5. $C_{ref}$ can be separated into two groups by aerosol type: fresh soot (black) and ambient (coated/mixed) soot aerosols. Pure diesel soot and pure PALAS soot of W03 and kerosene soot of A05, which were laboratory-generated fresh soot aerosols, are relatively lower and their $C_{ref}$ values agree closely with other aerosol types with values of approximately 2, regardless of the reference instrument type. For ambient aerosols (including coated/mixed), unlike fresh aerosols, $C_{ref}$ exhibits increased values and a more dispersed distribution. This is likely because ambient aerosols consist of a more complex mixture of various aerosol species than fresh soot aerosols. Higher $C_{ref}$ values of approximately 2.8–5.4 were observed for ambient aerosols. Coating/mixing during the ambient aging procedure increases particle absorption efficiency, as well as the MSE, resulting in high $C_{ref}$ (Fuller, Malm, and Kreidenweis 1999; Lack et al. 2008; Gyawali et al. 2009; Knox et al. 2009; Cappa et al. 2012; Bond et al. 2013; Wang et al. 2014).

Figure 3. ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}$ values from previous studies and those determined in this study (black: ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}$ using a filter-free instrument and laboratory-generated/fresh soot; blue: ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}$ using a filter-based optical instrument and ambient/coated aerosols; red: ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}$ using a filter-free instrument and ambient/coated aerosols).

The $C_{ref}$ of ambient aerosols can be divided into two groups according to the reference instrument type: filter-free reference instruments (red) and filter-based optical instruments (blue). The $C_{ref}$ of W03, A05, and S06 were determined using a filter-free reference instrument and are distributed around 3.7–5.4. $C_{ref}^{LRL}$ values during CAPMEX lie between the $C_{ref}$ values of A05 and S06. This is reasonable considering the type of reference instrument and the measurement environment. $C_{ref}^{LRL}$ during CAPMEX was determined using PASS-3 (A05: difference between extinction and scattering; S06: PhotoAcoustic Spectrometer, PAS) and the polluted maritime environment (A05: suburban; S06: remote area of Amazon basin). $C_{ref}$ values of C10 and Backman et al. (2017) range from 2.8 to 4.1. Backman et al. (2017) reported a $C_{ref}$ value of 3.1 using PSAP, CLAP, and MAAP at six Arctic stations. Saturno et al. (2017) also reported $C_{ref}$ of 4.9–6.3 (637 nm) in Amazon region. In this study, $C_{ref}^{LRL}$ was determined by setting PASS-3 as the reference instrument (CAPMEX) and by setting CLAP as an arbitrary reference (GSN, LLN, ALT). As shown in the next section, the estimated $C_{ref}^{LRL}$ values (528 nm) using CLAP are 3.67 (GSN), 3.85 (LLN), and 3.71 (ALT). Even though the measurement periods do not correlate, $C_{ref}^{LRL}$ values during CAPMEX are higher than $C_{ref}^{LRL}$ values at GSN. Furthermore, they are lower than those determined using the reference instrument, including those measured during CAPMEX. These results also lie within the range of previous research results using a filter-based optical reference instrument. Many comparison studies have reported that the ${\sigma }_{ap}$ of a filter-based optical instrument is larger than that of a filter-free instrument by a factor of 1.1–4.1 (Arnott et al. 2003; Virkkula et al. 2005; Torres et al. 2016). Specifically, liquid phase coating, organic aerosol fraction, organic gases, and their modification by filter media induce this difference (Subramanian et al. 2007; Lack et al. 2008; Lim et al. 2014; Shrestha et al. 2014; Vecchi et al. 2014). Therefore, it is likely that the organic (or liquid) portion of the aerosols increases the difference of ${\sigma }_{ap}$ between filter-based optical and filter-free instruments. This difference is then propagated into the difference of $C_{ref}$. It is likely that both the aerosol and instrument type affects the determination of $C_{ref}$.

On the other hand, $C_{ref}$ values generally increase with increasing wavelength. The Ångström exponent of $C_{ref}^{W03}$ (–1.01) and $C_{ref}^{LRL}$ (–0.47) was much larger than those from previous works. The Ångström exponent for pure PALAS soot and pure diesel soot of W03 was estimated to be –0.06 and –0.18, respectively, whereas that for coated PALAS soot and coated diesel soot of W03 was –0.18 and –0.23, respectively. The laboratory-generated kerosene soot of A05 was estimated to be –0.15.

Finally, it is worth to noting that we did not find any significant change of $C_{ref}^{LRL}$ with increasing ATN. Also, there was no special relationship among scattering coefficient, backscattering fraction, and $C_{ref}^{LRL}$.

3.2. Validation of ${\mathit{C}}_{\mathit{r}\mathit{e}\mathit{f}}^{\mathit{L}\mathit{R}\mathit{L}}$ by application to year-round measurements

$C_{ref}^{W03}$ and $C_{ref}^{LRL}$ values determined during CAPMEX were applied to continuous aethalometer measurements at GSN, LLN, and ALT for the validation. $C_{ref}^{W03}$ and $C_{ref}^{LRL}$ of PASS-3 wavelengths (405, 532, 781 nm) were adjusted to CLAP wavelengths using Ångström exponent interpolation. Adjusted $C_{ref}^{W03}$ values are 4.24 (467 nm), 4.79 (528 nm), and 5.93 (652 nm). Adjusted $C_{ref}^{LRL}$ values are 4.27 (467 nm), 4.53 (528 nm), and 5.01 (652 nm). Retrieved ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{LRL}$ values were then compared to simultaneous ${\sigma }_{ap}$ measurements of CLAP (${\sigma }_{ap}^{\mathit{\text{CLAP}}}$).

Period-averaged measurements of ${\sigma }_{ap}^{W03}$, ${\sigma }_{ap}^{LRL}$, and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ at GSN, LLN, and ALT are presented in Table 4, and the accompanying null hypothesis probability result of the student t-test is presented in Supplementary Information (D) Table S2. At GSN, ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{LRL}$ are smaller than ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ at all three wavelengths. The bias differences (BD) of ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{LRL}$ vary with increasing wavelength, from –0.3 to –1.2 Mm⁻¹ and –0.3 to –0.4 Mm⁻¹, respectively. However, considering the student t-test result, the difference of ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{LRL}$ from ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ at all three wavelengths are statistically significant (p-value >.05) except at 467 nm at ALT (because the ${\sigma }_{ap}$ level and BD are small). BD of ${\sigma }_{ap}^{W03}$ is –3.2 (467 nm), –12.0 (532 nm), and –23.1% (652 nm) from ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$. BD of ${\sigma }_{ap}^{LRL}$ is –3.9% (467 nm), –6.8% (532 nm), and –9.0% (652 nm) from ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$. The BD/RMSD ratio of ${\sigma }_{ap}^{W03}$ ranges from 0.19 to 0.90, but that of ${\sigma }_{ap}^{W03}$ ranges from 0.22 to 0.50. This shows that the difference between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is less than that between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ at 528 and 652 nm. Moreover, at LLN and ALT, the comparison result is consistent in that the difference between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is less than that between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ at 528 and 652 nm. It is suggested that ${\sigma }_{ap}^{LRL}$ agrees better with ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ than ${\sigma }_{ap}^{W03}$ not only at GSN, but in all three environments. This result suggests that a more accurate estimation of ${\sigma }_{ap}$ not only improves the accuracy of the light absorption parameter such as SSA, but also reduces the uncertainty of the estimation of the direct radiative forcing, especially atmospheric heating by light-absorbing aerosols.

Table 4. Results of the comparison between ${\sigma }_{ap}^{W03}$, ${\sigma }_{ap}^{LRL}$, and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ at GSN, LLN, and ALT.

		${\sigma }_{ap}$ [Mm^-1]^a			BD [Mm^-1]^b			RMSD [Mm^-1]^c			N
		467 nm	528 nm	652 nm	467 nm	528 nm	652 nm	467 nm	528 nm	652 nm
GSN	${\sigma }_{ap}^{W03}$	7.51 ± 5.49	5.92 ± 4.35	4.00 ± 2.91	˗ 0.25	˗ 0.81	˗ 1.20	1.35	1.27	1.34	13,662
	${\sigma }_{ap}^{LRL}$	7.45 ± 5.44	6.27 ± 4.60	4.73 ± 3.44	˗ 0.31	˗ 0.46	˗ 0.47	1.35	1.17	0.93
	${\sigma }_{ap}^{\mathit{\text{CLAP}}}$	7.76 ± 6.11	6.73 ± 5.28	5.20 ± 4.07	NA^d	NA	NA	NA	NA	NA
LLN	${\sigma }_{ap}^{W03}$	3.61 ± 5.13	2.84 ± 4.10	2.07 ± 2.81	˗ 0.07	˗ 0.34	˗ 0.51	0.65	0.64	0.69	4,151
	${\sigma }_{ap}^{LRL}$	3.58 ± 5.09	3.00 ± 4.33	2.38 ± 3.19	˗ 0.10	˗ 0.18	˗ 0.20	0.66	0.59	0.52
	${\sigma }_{ap}^{\mathit{\text{CLAP}}}$	3.68 ± 5.60	3.18 ± 4.91	2.58 ± 3.82	NA	NA	NA	NA	NA	NA
ALT	${\sigma }_{ap}^{W03}$	0.57 ± 0.41	0.45 ± 0.32	0.31 ± 0.22	˗ 0.01	˗ 0.07	˗ 0.10	0.10	0.09	0.12	4,431
	${\sigma }_{ap}^{LRL}$	0.56 ± 0.41	0.47 ± 0.34	0.36 ± 0.26	˗ 0.02	˗ 0.04	˗ 0.05	0.11	0.09	0.08
	${\sigma }_{ap}^{\mathit{\text{CLAP}}}$	0.58 ± 0.46	0.52 ± 0.40	0.40 ± 0.32	NA	NA	NA	NA	NA	NA

^aMean ± standard deviation.

^bBD = $\frac{1}{N}$.${\sum }_i^N\left({\sigma }_{ap,i}-{\sigma }_{ap,i}^{\mathit{\text{CLAP}}}\right)$

^cRMSD = $\frac{1}{N}$.${\sum }_i^N\sqrt{{\left({\sigma }_{ap}-{\sigma }_{ap}^{\mathit{\text{CLAP}}}\right)}^2}$

^dNA: Not Available.

A linear regression of ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{LRL}$ to ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ at GSN, LLN, and ALT is shown in Figure 4, indicating a linear correlation (R² ∼0.87-0.96). At GSN (Figure 4a and b), all LRL slopes are less than 0.84. LRL slopes between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ depend on the wavelength (0.84 to 0.66); however, those between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ remain relatively steady with varying wavelength (0.83 to 0.80) and lie closer to the 1:1 line. The ratio between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ changes less with increasing wavelength than that between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$. Moreover, the same trend is observed at LLN and ALT, in which the slope of ${\sigma }_{ap}^{LRL}$ is steady relative to that of ${\sigma }_{ap}^{W03}$.

Figure 4. Comparisons of aethalometer ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}$ with ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{C}\mathit{L}\mathit{A}\mathit{P}}$. (a) ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{W}03}$ and (b) ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{L}\mathit{R}\mathit{L}}$ at GSN, (c) ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{W}03}$ and (d) ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{L}\mathit{R}\mathit{L}}$ at LLN, and (e) ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{W}03}$ and (f) ${\mathit{\sigma }}_{\mathit{a}\mathit{p}}^{\mathit{L}\mathit{R}\mathit{L}}$ at ALT (black and gray dashed lines are the LRL and 1:1 line, respectively; color scale represents the occurrence).

The frequency distribution of $\Delta {\sigma }_{ap}$ (= ${\sigma }_{ap}-{\sigma }_{ap}^{\mathit{\text{CLAP}}}$) is shown in Figure 5. At GSN, the peak of the $\Delta {\sigma }_{ap}^{W03}$ distribution ranges between -0.5 and 0 Mm⁻¹ with increasing wavelength, whereas that of $\Delta {\sigma }_{ap}^{LRL}$ remains at approximately 0 Mm⁻¹. The period average of $\Delta {\sigma }_{ap}$ (vertical dashed line) equals BD in Table 4. The frequency of the negative $\Delta {\sigma }_{ap}^{W03}$ value shows a greater increase with wavelength than that of $\Delta {\sigma }_{ap}^{LRL}$. Even though the ${\sigma }_{ap}$ level is low, the trend is consistent at LLN and ALT in that the negative portion of the frequency distribution of $\Delta {\sigma }_{ap}^{W03}$ also increases with increasing wavelength (Figure 5b and c).

Figure 5. Frequency distributions of $\Delta {\sigma }_{ap}$ [= aethalometer ${\sigma }_{ap}-{\sigma }_{ap}^{\mathit{\text{CLAP}}}$] at (a) GSN, (b) LLN, and (c) ALT. Solid lines indicate the distributions of $\Delta {\sigma }_{ap}$ (${\sigma }_{ap}^{W03}$ is black; ${\sigma }_{ap}^{LRL}$ is red; vertical dashed line is the period average).

The SSA at each station using ${\sigma }_{ap}^{W03}$, ${\sigma }_{ap}^{LRL}$, and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is shown in Figure 6. Note that identical ${\sigma }_{sp}$ values were used to calculate SSA at each site. At GSN, the difference of SSA between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is 0.22% (467 nm), 0.83% (528 nm), and 1.58% (652 nm). The difference of SSA between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is 0.28% (467 nm), 0.47% (528 nm), and 0.61% (652 nm). The SSA derived using ${\sigma }_{ap}^{LRL}$ is closer to that using ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ in magnitude and in spectral dependency at 528 and 652 nm; this is also true at LLN and ALT. The difference of SSA between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is as much as ∼2.29% (652 nm) at LLN.

Figure 6. SSA retrieved at GSN, LLN, and ALT. SSA using ${\sigma }_{ap}^{W03}$, ${\sigma }_{ap}^{LRL}$, and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ are denoted as black, red, and green, respectively (${\sigma }_{sp}$ is identical at each station).

Figure 7 shows the AAE (467/652 nm) frequency distributions of ${\sigma }_{ap}^{W03}$, ${\sigma }_{ap}^{LRL}$, and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ at GSN, LLN, and ALT. At GSN, the AAE values of ${\sigma }_{ap}^{W03}$, ${\sigma }_{ap}^{LRL}$, and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ are 1.89 ± 0.35, 1.36 ± 0.35, and 1.20 ± 0.31 (Figure 7a). The difference of AAE values between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is 13.3%, while, that between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is 57.5%. This indicates that the spectral dependence of ${\sigma }_{ap}^{LRL}$ (and $C_{ref}^{LRL}$) agrees better with ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ than ${\sigma }_{ap}^{W03}$ (and $C_{ref}^{W03}$). The difference between AAE values of ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{LRL}$ propagates from $C_{ref}$ because the spectral dependence of $C_{ref}$ acts as a shift in AAE (Supplementary Information E). The AAE difference between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is also smaller than that between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ at LLN and ALT (Figure 7b and c).

Figure 7. Frequency distributions of AÅE at (a) GSN, (b) LLN, and (c) ALT. Solid line is the distribution of ${\sigma }_{ap}^{W03}$ (black/right), ${\sigma }_{ap}^{LRL}$ (red/center), and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ (green/left). Vertical dashed line is the average value.

Overall, $C_{ref}^{LRL}$ (i.e., LRL method) adequately reproduces year-round aethalometer measurements and the accompanying aerosol optical properties (${\sigma }_{ap}^{LRL}$, SSA, and AAE) are comparable to ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$. ${\sigma }_{ap}^{LRL}$ agrees better with ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ than ${\sigma }_{ap}^{W03}$ for all three environments and aerosol types. Schmeisser et al. (2017) compared aerosol characteristics from 24 global aerosol observation stations and classified the observed aerosol types (Table 4 and Figure 2). They also classified the environments of each station in this study as “marine polluted (GSN),” “other (LLN),” and “Arctic (ALT)” and aerosol types as “black carbon (BC) dominated (GSN),” “BC dominated (LLN),” and “small particles and low absorption (ALT),” respectively. The difference between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ is greatest (∼23.1% at GSN) at 652 nm, and is propagated from b (LRL intercept induced by the measurement artifact) because b is large at longer wavelengths (532 and 781 nm) when $C_{ref}$ is determined during CAPMEX. It is also inferred that $C_{ref}^{LRL}$ is less affected by measurement artifacts at all locations and for all aerosol types than $C_{ref}^{W03}$.

4. Summary and conclusions

The multiple scattering correction factor ($C_{ref}$) is one of the most uncertain parameters when retrieving the aerosol light absorption coefficient (${\sigma }_{ap}$) from an aethalometer. In previous studies, $C_{ref}$ ($C_{ref}^{W03}$) was determined as the ratio between the aethalometer ${\sigma }_{ap}^{flc}$ (uncorrected raw ${\sigma }_{ap}$) and the reference instrument ${\sigma }_{\mathrm{a}p}$. In this study, $C_{ref}$ ($C_{ref}^{LRL}$) was determined using the linear regression line (LRL), which reduced the measurement artifact effect. The results of this study are summarized as follows.

• $C_{ref}^{LRL}$ values determined using aethalometer and PASS-3 were 3.99 (405 nm), 4.48 (532 nm), and 5.46 (781 nm) during CAPMEX. The difference between $C_{ref}$ values of a previous study ($C_{ref}^{W03};\mathrm{}$Weingartner et al. 2003) and $C_{ref}^{LRL}$ was -8.0% (405 nm), 20.1% (532 nm), and 30.2% (781 nm). This difference was larger at 532 and 781 nm because the LRL intercept was larger at these wavelengths (6.92 and 6.22, respectively) than at 405 nm (-2.07). $C_{ref}^{LRL}$ varied by ∼36.8% with increasing percentile of ${\sigma }_{ap}^{\mathit{\text{PASS}}3}$, while $C_{ref}^{W03}$ varied by up to ∼121%. $C_{ref}^{LRL}$ was less affected by the LRL intercept (induced by measurement artifacts) and showed better agreement with the results reported in previous studies. $C_{ref}$ can also be associated with the type of reference instrument. According to previous studies and this study, $C_{ref}$ values determined using filter-based optical instruments were lower (2.8–4.1) than those using filter-free instruments (3.7–5.4).

• $C_{ref}$ values during CAPMEX were applied to aethalometer measurements at GSN (Gosan), LLN (Lulin), and ALT (Alert) stations and compared to CLAP measurements. The difference between aethalometer ${\sigma }_{ap}$ derived using $C_{ref}^{LRL}$ (${\sigma }_{ap}^{LRL}$) and ${\sigma }_{ap}$ derived using CLAP (${\sigma }_{ap}^{\mathit{\text{CLAP}}}$) was ∼9.0% whereas the difference with ${\sigma }_{ap}$ derived using $C_{ref}^{W03}$ (${\sigma }_{ap}^{W03}$) was ∼23.1% at GSN. The SSA difference between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ was ∼0.61%, while that between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ was 1.58%. Furthermore, the AAE difference between ${\sigma }_{ap}^{LRL}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ was 13.3%, while that between ${\sigma }_{ap}^{W03}$ and ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ was 57.5%. $C_{ref}^{LRL}$ was also deemed appropriate to apply to year-round aethalometer measurements at LLN and ALT, and ${\sigma }_{ap}^{LRL}$ agreed better with ${\sigma }_{ap}^{\mathit{\text{CLAP}}}$ than ${\sigma }_{ap}^{W03}$ for all environments and aerosol types.

In our procedure of $C_{ref}$ determination, the LRL intercept (induced by measurement artifacts) can be sufficiently large to change $C_{ref}$. Moreover, it is also possible that either aethalometer or other reference instrument have their own measurement artifacts. Thus, the measurement artifact effect on $C_{ref}$ determination can be reduced by applying $C_{ref}^{LRL}$.

Acknowledgments

The authors are thankful to technicians and operators at Gosan, Lulin and Alert stations for maintenance and calibrations of instruments. We also acknowledge Canadian Forest Service for maintain the operations of the Alert station. The authors thank Dr. M. K. Dubey for providing PASS-3 data at Gosan during the CAPMEX campaign.

Disclosure statement

No potential conflict of interests was reported by the authors.

Additional information

Funding

This research was funded by the Korea Meteorological Administration Research and Development Program under Grant KMI2018-01111.