For measuring BC with the filter-based optical technique, the optical ATN is defined as ATN=-100⋅ln⁡II0 where I0 and I are the intensities of light transmitted through a reference blank spot and a spot of aerosol on the filter, respectively. The factor 100 is introduced for convenience. The ATN change in a time interval (dATN/dt) is used to estimate the BC concentration as follows: BC=dATNdt⋅AQ⋅1σATN where A is the area of the sample spot, Q is the sampling flow rate, and σATN is the black carbon optical mass cross section.

Drinovec et al. (2014) showed that the loading effect on BC can be corrected by using the following equation, which is similar to that proposed by Virkkula et al. (2007): BCc=BC(1-k⋅ATN) where BCc and BC represent the corrected and measured black carbon concentration, respectively, and k is a correction factor. On the basis of the same principle as Eq. (), the average BC (BC‾) from initial time t0 (t0=0) to time t can be expressed as BC‾=ΔATNΔt⋅AQ⋅1σATN=ATNt-t0⋅AQ⋅1σATN Then, Eq. () can be written as ATNc=ATN(1-k⋅ATN) where ATNc and ATN represent corrected and measured light ATN values, respectively.

In practice, if the true ATN value can be found, then the artifact effect on the BC measurement can be corrected from the true ATN change rate (dATN/dt). Therefore, determining the true ATN value was the main objective of this study. According to the definition of light ATN, the ATN value is dependent on the amount of BC aerosol deposition. That is, different BC aerosol deposition rates can correspond to different ATN increasing rates. Nevertheless, the loading effect is a cumulative property of the cumulative deposit of aerosol on the filter, and it also directly influences the ATN measurement results. Therefore, different aerosol sampling flow rates in the same deposition area could lead to different loading effects on ATN measurement results.

According to Eq. (), the ATN correction equation at different flow rates can be expressed as ATNF1,c=ATNF1(1-k⋅ATNF1)ATNF2,c=ATNF2(1-k⋅ATNF2) where ATNF1 and ATNF2 represent the ATN measured at sampling flow rates QF1 and QF2, respectively. In the absence of the artifact effect, the ratio of true ATN values measured at two different flow rates should be equal to the ratio of the two different sampling flow rates: ATNF2,cATNF1,c=mBC,F2mBC,F1=BC⋅QF2⋅tBC⋅QF1⋅t=QF2QF1 where mBC,F1 and mBC,F2 represent the mass of black carbon aerosol deposited on the filter at sampling flow rates QF1 and QF2, respectively.

In this model, the correction factor k is assumed to be fixed for an ATN/Q value. Then, k can be solved using Eqs. ()–(): k=QF1⋅ATNF2-QF2⋅ATNF1QF1⋅ATNF1⋅ATNF2-QF2⋅ATNF1⋅ATNF2 Therefore, the temporal variation of k can be determined on the basis of two measured ATN values for different sampling flow rates. Subsequently, the true ATN value can be obtained from Eq. (). Moreover, the actual BC concentration can be determined from the true ATN change rate by using Eq. ().

In this study, BC (or ATN) was measured using two aethalometers (AE31; Magee Scientific); one aethalometer was operated at a sampling flow rate of 6 Lm-3 (QF6), whereas the other was operated at a sampling flow rate of 2 Lm-3 (QF2). The filter tape in these two aethalometers was shifted automatically to expose a pristine spot on the filter at the same time every eight hours to ensure that the two sampling spots had a fixed starting and ending time of the sampling for internal comparison. The internal timer and sampling flow rate of the aethalometer were checked every week. The sampling site was located on the campus of Ming Chi University of Technology at Taishan, New Taipei City, Taiwan. The main source of BC at this sampling site was traffic. Sometimes, wood combustion could be observed on the campus for waste wood disposal. During the sampling periods, the two aethalometers were positioned adjacent to each other in a sampling cabin and the inlets of both aethalometers were approximately 2 m above the ground level outside the sampling cabin. The aethalometers were operated between 21 December 2013, and 24 January 2014 (winter season), and between 5 July 2014, and 26 September 2014 (summer season). The logging interval for all measurements was set at 5 min. The filter tape used was a quartz material filter (Pallflex Q250F), which was suggested by the aethalometer manufacturer. To avoid water vapor condensing on the deposited aerosols in the summer season, a diffusion dryer with silica gel was installed on the sampling line. The silica gel was replaced every two days during sampling periods. When the diffusion dryer was not used, negative values could be observed in BC data sets at noon under conditions of high temperature and high relative humidity. Negative values were also recorded in BC data sets when sampling was performed at very low ambient concentrations at midnight and early morning hours, especially at low sampling flow rates. If negative values appeared in the data set of a sampling spot, the entire data for the sampling spot was excluded from further treatment. Local meteorological data such as temperature and relative humidity were recorded using a Vantage Pro 2TM weather station (Davis Instruments). Table 1 shows the ambient temperature and relative humidity during the sampling periods. The average temperature during the summer season was significantly higher than that during the winter season by approximately 15 ∘C (p<0.001). The average relative humidity did not differ significantly between the summer and the winter seasons (p=0.086).

Before beginning field sampling, the performance of the two aethalometers was compared at the sampling site for two sampling flow rates, 6 and 2 Lmin-1, for 2–3 days. The hourly measured results obtained using the two aethalometers are shown in Fig. 1. The hourly average BC mass concentrations in units of nanogram per cubic meter were calculated using 5 min raw data. Statistical results indicated that the intercepts were -30.751 (95 % confidence interval (CI): -56.091 to -5.411) and -18.119 (95 % CI: -43.841–7.603) for the sampling flow rates of 6 and 2 Lmin-1, respectively, and the intercepts were not considerably different from zero (p=0.019 for 6 Lmin-1 and p=0.163 for 2 Lmin-1). The slopes determined for these two flow rates were 0.991 (95 % CI: 0.985–0.997) and 0.988 (95 % CI: 0.980–0.997), respectively, and the slopes were significantly different from 1.0 (p<0.001 for both). These comparison results indicated that the performance of both aethalometers used in this study could be considered to be similar to each other.

Figure 2 shows the relationships between ATN values for sampling flow rates of 6 and 2 Lmin-1 before and after correction in the summer and winter seasons. Before ATN correction, the ATNF6 value was smaller than the value of 3 × ATNF2, indicating the presence of the artifact effect on the ATN measurement result. When the ATNF6 value increased, it deviated considerably from the value of 3 × ATNF2, especially for the 370 nm wavelength. The measurement results demonstrated that the loading effect on the ATN value at short wavelengths was stronger than that at long wavelengths. After ATN correction using Eqs. ()–(), the ratio of the ATNF6 value to the ATNF2 value could fall to 3:1. That is, the true ATN values could be determined using the algorithms proposed in this study. Subsequently, the actual BC mass concentration could be estimated from the true ATN change rate. Before BC correction, the measured BCF6 was significantly smaller than the measured BCF2 by approximately 13 and 9 % in the summer and winter seasons (p<0.001 for both), respectively. After BC correction by using the true ATN value, the corrected BCF6 could be exactly equal to the corrected BCF2. Figure 3 presents a comparison of BC corrected using the proposed model and that corrected using the correction model of Drinovec et al. (2014). The correction model of Drinovec et al. (2014) is presented in Eq. (), and the correction factor in this model can be easily estimated from the following equation on the basis of the measurement results of BC and ATN at sampling flow rates of 6 and 2 Lmin-1: k=BCF2-BCF6BCF2⋅ATNF6-BCF6⋅ATNF2 The corrected BC estimated using the model proposed in this study was comparable with that obtained using the correction model of Drinovec et al. (2014) (p=0.307 for summer; p=0.915 for winter). The k value estimated using the model of Drinovec et al. (2014) exhibited significant variations between negative and positive values for the entire data set. By contrast, the k value determined using the proposed model approached a constant value steadily when the ATN value increased. The steady variation of the k value in the proposed model was due to k being determined from a cumulative ATN value, rather than an instant differential ATN value.

The relationship between measured ATNF6 and ATNF2 is shown in Fig. 2, and it can be expressed as a power law relationship through measurement data fitting. On the basis of analytical results, the relationship between k and ATN/Q could be determined using Eq. () and the relationship between measured ATNF6 and ATNF2, as shown in Fig. 4. Analytical results showed that the relationship between k and ATN/Q for sampling flow rates of 6 and 2 Lmin-1 was similar, especially for long wavelengths. This result indicated that the assumption of the k value being fixed for an ATN/Q value in the proposed model was reasonable. Analytical results indicated that the k value was negative at extremely small ATN/Q values. The k value increased rapidly as ATN/Q increased, and then approached a constant value. Weingartner et al. (2003) noted that multiple scattering in the nearly unloaded fiber filter could enhance light absorption. Therefore, a negative k value could be observed at small ATN/Q values, which was reasonable in terms of the light scattering behavior of the nearly unloaded filter at a new sampling spot, especially at short wavelengths in the winter season. In this study, it was found that with increasing aerosol load on the filter, the influence of the light scattering behavior of the filter matrix could be eliminated. When a sufficient amount of aerosol was sampled on the filter, k initially increased as a positive value and then decreased gradually and steadily to a constant value. These observation results indicated that the proposed model could overcome the problem of enhanced light ATN resulting from light scattering at a new sampling spot, without using any light scattering coefficient.

The absorption Ångström exponent α can be used as an index to determine the type of BC emission sources (Sandradewi et al., 2008), and it is computed from the aerosol light absorption between 470 and 950 nm wavelengths as follows: α=ln⁡babs,λ=470/babs,λ=950ln⁡950/470 where babs,λ=470 and babs,λ=950 are the absorption coefficients of aerosol at 470 and 950 nm wavelengths, respectively. The absorption coefficient of aerosol can be determined from the change rate of ATN: babs=dATNdt⋅AQ⋅1C where C is a light enhancement parameter. It is associated with multiple scattering of the light beam at the filter fibers in the unloaded filter, and it is strongly dependent on the filter material (Weingartner et al., 2003). In this study, C was set as 2.14 for the quartz filter (Weingartner et al., 2003; Drinovec et al., 2014).

Kirchstetter and Novakov (2004) noted that the absorption Ångström exponent value ranged between 0.8 and 1.1 for diesel soot. Day et al. (2006) showed that the absorption Ångström exponent values were between 0.9 and 2.2 for fresh wood smoke aerosol, which strongly depended on the type of wood and burning conditions. Sandradewi et al. (2008) also demonstrated that the absorption Ångström exponent values were 1.1 and 1.8–1.9 for traffic and wood burning, respectively. A high absorption Ångström exponent value could be observed for wood combustion aerosol that is due to the compounds of the aerosol with strong absorption in the UV. However, the filter loading effect also strongly influences the calculation of the absorption Ångström exponent value. Table 2 shows the absorption Ångström exponent values calculated from measured ATNF6 and ATNF2 and from corrected ATN in the summer and winter seasons. Analytical results showed that the absorption Ångström exponent value could be improved from 1.01±0.22 (estimated from measured ATNF6) and 1.11±0.33 (estimated from measured ATNF2) to 1.17±0.44 (estimated from corrected ATN) in the summer season. In the winter season, the absorption Ångström exponent value could be increased from 1.01±0.18 (estimated from measured ATNF6) and 1.10±0.20 (estimated from measured ATNF2) to 1.15±0.24 (estimated from corrected ATN). The absorption Ångström exponent values computed using the ATN measured at the sampling flow rates of 6 and 2 Lmin-1 were relatively lower than those estimated from the corrected ATN (p<0.001 for both), indicating that the absorption Ångström exponent value could be significantly underestimated because of the filter loading effect. According to the estimated absorption Ångström exponent values, the primary emission source of BC at the sampling site was traffic.

Despite the negative k value for small ATN/Q, the k value showed a power law relationship with ATN/Q for ATN/Q >3 and 10 in the summer and winter seasons, respectively (Fig. 5). Analytical results indicated that the k values could be predicted using the empirical equations presented in Table 3. Furthermore, the existed data sets of aethalometer AE31 could be post-corrected using these empirical equations for different sampling flow rates. First, the ATN values in existed data sets of aethalometer AE31 were divided by the sampling flow rate, and k was then estimated using the proposed empirical equations in Table 3. Second, the corrected ATN was determined from Eq. () by using the determined k and measured ATN. Finally, the corrected BC could be estimated from the change rate of the corrected ATN. It should be noted that the light scattering effect on the unloaded filer was neglected in the post-processing model.

Figure 6 shows the relationship between (1-k× ATN) and ATN at different sampling flow rates. Analytical results showed that the value of (1-k× ATN) was significantly affected by the ATN and sampling flow rate. When the ATN was very small, the value of (1-k× ATN) approached 1.0. For different sampling flow rates, the (1-k× ATN) value differed significantly for the same ATN conditions because of different aerosol deposition rates, indicating that the aerosol deposition density on the filter could influence the extent of the aerosol loading effect on BC measurement results. Moreover, the aerosol loading effect on BC measurement results in the summer season was greater than that in the winter season by approximately 1–6 %, and it depended on the sampling flow rate. This difference between seasons could be because of differences in the composition, source, and age of aerosols, in addition to the different weather conditions.

Figure 7 presents the results of a comparison between 5 min BC concentrations measured at sampling flow rates of 6 and 2 Lmin-1 before and after correction. The BC was corrected using the proposed post-processing model. Results showed that the corrected BCF6 mass concentrations were not significantly different from the corrected BCF2 mass concentrations (p=0.734 for summer; p=0.594 for winter), indicating that the post-processing model could be effectively used to correct BC data for the loading effect.

Figure 8 presents the results of a comparison of BC corrected using the proposed post-processing model and the correction model of Weingartner et al. (2003). The correction model developed by Weingartner et al. (2003) is widely used to correct BC data on the basis of the measured ATN value, and it can be expressed as BCc=BCRATNRATN=1f-1ln⁡ATN-ln⁡10ln⁡50-ln⁡10+1 where f is a fit parameter dependent on the aerosol type. BC corrected using the post-processing model was comparable with that corrected using the correction model of Weingartner et al. (2003) for f=1.21 and 1.14 in the summer and winter seasons, respectively, at the sampling flow rate of 6 Lmin-1. For the sampling flow rate of 2 Lmin-1, BC corrected using the post-processing model was comparable with that corrected using the correction model of Weingartner et al. (2003) for f=1.25 and 1.15 in the summer and winter seasons, respectively. However, BC corrected using the post-processing model was slightly higher than that corrected using the correction model of Weingartner et al. (2003) (p≤0.019), except for the sampling flow rate of 6 Lmin-1 in the winter season (p=0.123). BC corrected using the correction model of Weingartner et al. (2003) was significantly lower than that corrected using the post-processing model when ATN was small, and this is possibly because the function R(ATN) in the correction model of Weingartner et al. (2003) was larger than 1.0 for ATN <10. In other words, the corrected BC was smaller than that corrected using the post-processing model for R(ATN) >1.0. Otherwise, the BC corrected using the correction model of Weingartner et al. (2003) was higher than that corrected using the post-processing model for ATN >20, especially for ATN >50. Moreover, the parameter f in the correction model of Weingartner et al. (2003) is significantly dependent on the aerosol type, and it was difficult to determine from field sampling data.