Development of a Universal Correction Algorithm for Filter-Based Absorption Photometers

7 Among the various measurement approaches to quantify light absorption coefficient (Babs), filter8 based absorption photometers are dominant in monitoring networks around the globe. Numerous 9 correction algorithms have been introduced to minimize the artifacts due to the presence of the 10 filter in these instruments. However, from our recent studies conducted during the Fire Influence 11 on Regional and Global Environments Experiment (FIREX) laboratory campaign, corrected filter12 based Babs remains biased high by roughly a factor of 2.5 when compared to a reference value 13 using a photoacoustic instrument for biomass burning emissions. Similar over-estimations of Babs 14 from filter-based instruments exist when implementing the algorithms on six months of ambient 15 data from the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) 16 Southern Great Plains (SGP) user facility from 2013 (factor of roughly 3). In both datasets, we 17 observed an apparent dependency on single scattering albedo (SSA) and absorption Ångström 18 exponent (AAE) in the agreement between Babs based on existing correction factors and the 19 reference Babs. Consequently, we developed a new correction approach that is applicable to any 20 filter-based absorption photometer that includes light transmission from the filter-based instrument 21 as well as the derived AAE and SSA. For the FIREX and SGP datasets, our algorithm results in 22 good agreement between all corrected filter-based Babs values from different filter-based 23 instruments and the reference (slopes ≈ 1 and R2 ≈ 0.98 for biomass burning aerosols and slopes 24 ≈ 1.05 and R2 ≈ 0.65 for ambient aerosols). Moreover, for both the corrected Babs and the derived 25 optical properties (SSA and AAE), our new algorithms work better or at least as well as the two 26 common PSAP-based correction algorithms. The uncertainty of the new correction algorithm is 27 estimated to be ~10%, considering the measurement uncertainties of the operated instruments. 28 Therefore, our correction algorithm is universally applicable to any filter-based absorption 29 photometer and has the potential to “standardize” reported results across any filter-based 30 instrument. 31


Introduction
Light-absorbing atmospheric aerosols directly affect the Earth's energy budget by absorbing solar radiation, leading to a warming effect when they are suspended in the atmosphere and to the melting of snow and ice following deposition (Bond and Bergstrom, 2006;Boucher, 2015;Horvath, 1993).For decades, scientists have conducted field experiments around the globe to investigate how absorbing aerosols influence the atmospheric radiative balance and interact with clouds (e.g., Andrews et al. (2011); Cappa et al. (2016); Lack et al. (2008b); Rajesh and Ramachandran (2018); Schwarz et al. (2008)).These experiments may be performed at fixed stations (e.g. and the scattering coefficient (Bscat).Correction equations are developed by comparing data between the filter-based instrument and the reference instrument, where the equations often contain one term that accounts for filter loading effects and another that accounts for multiplescattering effects.Consequently, the correction equations frequently incorporate both Tr and either Bscat or the single-scattering albedo (SSA) to account for these effects.However, even when the correction algorithms are applied, potential issues can remain such as: 1. Corrected filter-based Babs may remain biased high relative to a reference value of Babs (e.g., (Arnott et al., 2003;Davies et al., 2019;Lack et al., 2008a;Li et al., 2019;Müller et al., 2011a)).
5. The agreement between measurements of Babs and estimates of Babs by chemistry-climate models may vary based on the implemented correction algorithm (e.g., (Alvarado et al., 2016)).
The first three issues in this list may arise due to differences in aerosol optical properties between those used in deriving the correction equation and those associated with a given aerosol sample, and these issues can propagate through to the fourth issue.The final issue is arguably most important because evaluation of chemistry-climate models may be severely affected by the differences between different correction algorithms, which may inhibit the modeling community from providing accurate projections of future temperature and precipitation response.
In this work, we seek to address some of these issues.First, we evaluate the CLAP, TAP, and PSAP using two common PSAP-based correction algorithms, namely Bond et al. (1999) as updated by Ogren (2010) and Virkkula et al. (2005) as updated by Virkkula (2010).For brevity, we refer to these corrections as "B1999" and "V2005" for Bond et al. (1999) and Virkkula et al. (2005), respectively, incorporating their respective updates.In addition, we propose "universal" correction algorithms that are applicable to any filter-based absorption photometer (e.g., CLAP, TAP, PSAP, and AETH) across multiple wavelengths by combining observed filter-based Babs with Bscat (e.g., from a co-located nephelometer (NEPH)) and reference Babs (e.g., from a colocated photoacoustic instrument).However, in reality (e.g., at long-term observatories), reference values of Babs are rare, and in some cases, complementary Bscat measurements may not exist; consequently, we also provide methods to correct filter-based Babs data in these scenarios.To our knowledge, this is the first study to simultaneously evaluate B1999 and V2005 corrections on PSAP "successors" (i.e., CLAP and TAP) and to present a correction algorithm that is broadly applicable to any filter-based absorption photometer.Regarding the latter, even if our correction algorithm has its own limitations, its use can nevertheless standardize the reporting of Babs in longterm datasets.

Methodology
We developed the general form for our correction algorithms using CLAP and TAP measurements collected from biomass burning (65 fires in total) during the Fire Influence on Regional to Global Environments Experiment (FIREX) laboratory campaign in 2016.By using biomass burning emissions, we considered a dataset spanning a broader range of aerosol optical properties (SSA at 652 nm: 0.14-0.98;AAE: 1.25-4.73)than has traditionally been used in developing these correction algorithms.We then conducted further evaluation and validation of the model using ambient data, specifically using CLAP measurements from the DOE ARM Southern Great Plains (SGP) user facility in Lamont, OK, USA (02/01/13 to 07/09/13).Our algorithms were then extended to the AETH data from the FIREX laboratory campaign and the PSAP data collected at the SGP site to verify the "universal" nature of the algorithms.

Experimental setup
In October and November of 2016, we participated in the laboratory portion of the FIREX campaign to investigate the wildfire smoke and their impact on the atmosphere.During the campaign, over 100 burns took place at the U.S. Forest Service's combustion facility at the Fire Sciences Laboratory (FSL).The fuels burned in this study are representative of western US ecosystems, such as spruce, fir, various pines, and "chaparral" biome (e.g., manzanita, chamise).
A typical burn lasted for 1-3 hours depending on the smoke sampling strategies (e.g., stack burns versus room burns).During each burn, one or multiple "snapshots" of smoke (typical Babs at 652 nm ranged from 100 to 1200 Mm -1 ) were transferred from the combustion room at FSL into a mixing chamber (210 L) through a long transfer duct (30 m in length, 8" in diameter).The smoke was then diluted by filter air (~230 LPM) in the chamber.Once the concentration in the chamber was stable (detected by the Photoacoustic Extinctiometer (PAX) which was operated continuously through all fires), the smoke was passed to a suite of instruments to obtain aerosol and gas phase parameters.This chamber also served as an intermediate between the transfer duct and the instrumentation to minimize potential biases that arose due to different sample flow rates and sample locations of the instruments.A more detailed description of our experiments can be found in Li et al. (2019).

Measurements of aerosol optical properties
During the campaign, five instruments provided measurements of Babs (CLAP, NOAA GMD; TAP, Brechtel Manufacturing Inc. (BMI); Aethalometer (Model AETH-31), Magee Scientific; and two PAXs (Model PAX-870 and PAX-405), Droplet Measurement Technologies) and two instruments provided measurements of Bscat (PAX-870 and PAX-405).The instruments included in the present work are summarized in Table 1.
Both CLAP and TAP provide Babs measurements of the particles deposited on a filter, similar to PSAP.Different from PSAP, there are multiple filter spots (8 sample spots and 2 reference spots) cycling of one filter in CLAP and TAP, enabling the instruments to run continuously through two or three burns without changing filter.In the CLAP and TAP, sample illumination is provided by LEDs operated at three wavelengths (467, 528, and 652 nm).Here, we apply both B1999 and V2005 to CLAP and TAP data, similar to previous work (e.g., (Backman et al., 2014;Davies et al., 2019)).
The key differences between the CLAP and TAP during the FIREX campaign include: 2. The spot area, flow rate, and LED-detected wavelengths differed slightly (Table 1).
3. The CLAP recorded Babs every one minute, while the TAP recorded Babs every ten seconds.To enable the following analysis, we compute the 1-minute averages of TAP-derived parameters.
4. For the first portion of the campaign (the first 17 days of the 45-day campaign), Pallflex E70-2075S filters were used in the CLAP while Azumi filters (model 371M, Azumi Filter Paper Co., Japan) were used in the second portion of the campaign (due to a lack of availability of the Pallflex filters).The TAP was equipped exclusively with the Azumi filters throughout the campaign.We apply the filter correction recommended in Ogren et al. (2017) to the CLAP and convert from Pallflex to Azumi filters.
5. BMI substantially re-engineered the CLAP in their development of the TAP.These differences resulted in variable agreement between the CLAP and TAP during FIREX; however, the two instruments did largely agree within experimental uncertainty (e.g., see Fig. S8 and Fig. S13 in Li et al. ( 2019)).
A PAX measures Babs and Bscat simultaneously for suspended particles using a modulated diode laser.We use these photoacoustic absorption measurements as the reference to evaluate the filterbased Babs and develop our correction algorithms.To enable the evaluation of CLAP and TAP which operate at different wavelengths than the PAXs, we interpolate the measurements of Babs and Bscat to the wavelengths of 467, 528, and 652 nm using the values of AAE and scattering Ångström exponents (SAE), similar to Backman et al. (2014) and Virkkula et al. (2005).
Theoretically, AAE and SAE fit absorption and scattering as power law functions of wavelength (Bergstrom et al., 2007).
Due to the numerous correction algorithms for the Aethalometer (e.g.(Arnott et al., 2005;Collaud Coen et al., 2010;Kirchstetter and Novakov, 2007;Saturno et al., 2017;Schmid et al., 2006;Virkkula et al., 2007;Weingartner et al., 2003)), we do not evaluate these in the present work to limit the scope.In fact, the majority of our focus is the B1999 and V2005 corrections to TAP and CLAP.However, we still test the performance of the new algorithms on the AETH to explore its applicability to that instrument.

Measurements of aerosol optical properties at the SGP observatory
The ambient data used in this manuscript are the ground-based aerosol data measured at the SGP observatory from 02/01/13 to 07/09/13 (archived at https://www.archive.arm.gov/discovery/).For evaluation purposes, we randomly selected a range of dates during which the observations are valid (without incorrect, suspect, and missing data).This time period was also subsequent to an upgrade to the 532 nm laser in the three-wavelength photoacoustic soot spectrometer (PASS-3).
At the site, an impactor was used to switch the sampling between two cutoffs (particle diameter <10 μm (PM10) in the first 30 minutes of each hour and <1 μm (PM1) in the latter 30 minutes of each hour).The aerosols exiting from the impactor were dried to RH less than 40% and passed to a CLAP, a PSAP, and two NEPHs.The PASS-3 operated at the site and also provides Babs and Bscat for aerosols, but these samples did not pass through the impactor (e.g., characterizing total suspended particles (TSP)).Typical Babs and Bscat reported at the site ranged from 0 to 10 Mm -1 and 0 to 50 Mm -1 at 550 nm, respectively (e.g., (Sherman et al., 2015)).Although the site is rural (clean background air), long-term transport aerosols (such as mineral dust, absorbing organic aerosols, and secondary organic aerosols (SOA)) may affect the local aerosol properties (Andrews et al., 2019).
We preprocess the SGP data in three steps.First, due to the systematic difference of aerosol sizes between PASS-derived and filter-based absorption, we only include the PM10 observations, inherently assuming that any differences in the optical properties of PM10 and TSP are negligible.
Then, we smooth the 1-second data into 10-minute averages.Thirdly, we estimate the detection limits at each of the three wavelengths in the PASS-3 using the data measured during the "background zero" periods (Allan, 1966) and discard the observations which are below the detection limits.With a 10-min-averaging-time, the detection limits (3σ) for the PASS-3 are 0.78 Mm -1 (405 nm), 2.01 Mm -1 (532 nm), and 0.30 Mm -1 (781 nm).For the filter-based instruments, the detection limits are based on previous studies (See Table 1).Moreover, we only retain the observations that satisfy Babs (405 nm) > Babs (532 nm) > Babs (781 nm) (or AAE>0), similar to Fischer and Smith (2018).As with the PAX data from the laboratory, we adjust the PASS-derived Babs to 467, 528, and 652 nm using the inferred AAE values for each 10-minute average.BATN and Tr (370,470,520,590,660,880,and (Bond et al., 1999) 0.3 (Springston, 2016) a The detection limits of PAX and PASS-3 are determined by Allan deviation analysis (Allan, 1966) of Babs during "background zero".

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b During the analysis of the data collected at the SGP, we use Babs derived by the PASS and Bscat derived by the NEPH to yield the coefficients in the algorithms.a The operating wavelengths are based on the manufacturer specifications.

b
The coefficients provided in Table 2 are the values presented in Ogren (2010) and Virkkula (2010), which are updated from Bond et al. (1999)

The correction algorithms
In filter-based instruments, the light intensities transmitted through the sample spot and blank spot of the filter are recorded as Is and Ib, respectively.The logarithmic ratio of the two intensities at time t is defined as ATN using the Beer-Lambert law: where ATN = 0 when beginning a new filter spot (t = 0).
The ATN can be related to Tr by normalizing Is/Ib at time t relative to Is/Ib at the start of a new filter spot (t = 0): The change of ATN over a time interval (Δt) for the instrument operated at a volume flow rate of Q and spot area of A yields the attenuation coefficient (BATN) for that time interval: BATN is finally converted to Babs by applying correction algorithms.The general form of the correction algorithms presented for the PSAP in Bond et al. (1999) and Virkkula et al. (2005) can be summarized as: where f(Tr) is some function of Tr (that may vary between approaches), correcting for the filter loading effect.C1 is a constant that may vary with wavelength; specifically, it is a penalty for the light scattering by the particles collected on the filter which may contribute to the quantification of ATN.In most atmospheric and laboratory studies, Bscat is measured independently, typically using a co-located NEPH.
2.3.1.The B1999 correction Bond et al. (1999) was the first study to present the correction algorithm for filter-based instruments.This empirical correction was originally developed for the PSAP operated at 550 nm using various mixtures of laboratory-generated nigrosin (SSA ≈ 0.5) and ammonium sulfate (SSA ≈ 1) with Babs ranged from 0 to 800 Mm -1 .
The equation parameters were further clarified in Ogren (2010) who adjusted the B1999-measured spot area (A = 20.43 mm 2 ) to be consistent with the universal area of the PSAP (A = 17.83 mm 2 ).
Ogren (2010) also extended the correction to 574 nm using a wavelength dependence of Babs (Babs ~ λ -0.5 ).Consequently, C2 and C3 in f(Tr) were updated to 1.55 and 1.02, respectively.These are the values used in the present work (Table 2) for B1999.Moreover, Ogren (2010) stated that the correction forms of Eq. ( 4) and Eq. ( 5) were valid for any wavelength, while additional experiments were needed to establish the equation parameters for the wavelengths other than 574 nm.

The V2005 correction
Virkkula et al. ( 2005) developed a correction algorithm for both three-wavelength PSAP (467, 530, and 660 nm) and one-wavelength PSAP (574 nm) using the same functional form as Eq. ( 4).Since the operating wavelengths of the photoacoustic instruments and the NEPH were different from those of the PSAP, the measured photoacoustic Babs and Bscat was extrapolated or interpolated to 467, 530, and 660 nm, using inferred AAE and SAE respectively.In this study, the authors used various mixtures of kerosene soot, ammonium sulfate, and polystyrene latex (SSA ranged from 0.2 to 0.9) with Babs ranging from 0 to 800 Mm -1 at 530 nm.
Different from the f(Tr) in the B1999 correction which was a reciprocal function of Tr, the f(Tr) presented in V2005 was a multi-variate linear function of the natural logarithm of Tr and SSA (including an interaction term between the two): where the parameters in Eq. ( 6) vary with wavelengths.The parameters in V2005 were updated in Virkkula ( 2010) by correcting for flowmeter calibration (Table 2).
Due to the unknown values of SSA before deriving Babs, Virkkula et al. (2005) provided a solution through an iterative procedure.In the iteration, Babs is first calculated using the B1999 correction (e.g., Eq. ( 4) and Eq. ( 5)) and is then used to compute the initial guess of SSA for use in Eq. ( 6).
The Babs and SSA can be updated using Eq. ( 4) and Eq. ( 6) until convergence is reached.

The new correction
We develop a set of new correction algorithms with the same general form as Eq. ( 4) using the biomass burning emissions from 65 different burns during the FIREX laboratory study, providing a broader range of aerosol optical properties and aerosol concentrations than previous work.This was motivated by the disagreement that remained between filter-based and photoacoustic instruments, even after applying B1999 to the data (e.g., see Li et al. ( 2019) Fig. 4 and our Fig. 2 below).These differences may persist because we were effectively extrapolating the B1999 correction equation to values outside the range for which it was developed.
This new correction is developed based on multiple linear regression techniques with three dependent variables of ln(Tr), SSA, and AAE and one independent variable of Babs/BATN (Eq.( 7) -( 9)).As with other correction equations, this model takes into account the influence of scattering and weakly-absorbing materials.However, we target two additional aims: 1) extend the correction a wider range of Babs; and 2) develop a model that is applicable to any filter-based instrument.
Similar to the B1999 and V2005 corrections, this new model starts with the general form of Eq.
(4), re-written here to define Bscat in terms of SSA and Babs.
Re-arranging this equation to move all Babs terms to the left-hand side yields: where g(Tr(λ), SSA(λ)) = f(Tr(λ)) × We define the function "g" as a multivariate linear model, introducing AAE as a dependent variable and including interaction terms between SSA, AAE, and ln(Tr): Equation ( 9) suggests that different combinations of SSA, AAE and ln(Tr) can result in the same value of "g" (i.e., Babs/BATN); likewise, a given value of Babs/BATN may have infinitely many points with distinct slopes passing through it (Fig. S3).Therefore, in orderly to properly compensate for the effects of loading and aerosol optical properties, a multiple linear regression with interaction terms is required.
A detailed description of the procedure for the model development (e.g., variable transformation (from Tr to ln(Tr)), variable selection using best-subsets and stepwise approaches, and model validation) is provided in the Supplementary Material.
As in V2005, iteration is required in our algorithm because Babs is dependent on knowledge of SSA and AAE, which themselves are dependent on Babs.We propose the following iterative process to update SSA and AAE in the model. .
2. Yield an initial set of coefficients G0 through G7 for each wavelength to calculate g(Tr, SSA, AAE) in Eq. ( 9), using one of the Algorithms described in Sect.2.4.
4. Update AAE and SSA using Babs calculated in Step 3.

5.
Derive a new set of coefficient values.

Application of correction algorithms
In developing a procedure for applying our algorithm, we envision three potential scenarios: 1. Algorithm A: The filter-based instrument is co-located with a NEPH and reference instrument providing Babs.This scenario facilitates the computation of G0 through G7 in Eq. ( 9) (step 2 in the iterative process) as well as the derivation of new coefficients for existing correction algorithms.This scenario can also enable the develop of a new a set of coefficients that may be more appropriate for aerosol sources that we do not consider here.
2. Algorithm B: The filter-based instrument is co-located with a NEPH but not a reference instrument providing Babs, which is perhaps the most likely scenario (at least at many longterm monitoring sites).This scenario requires an initial guess of the coefficients; we provide sets of these in linear relationship between SSA and AAE (AAE = a + b×SSA c ) to provide an initial guess of SSA in the iterations.
To aid in decision-making between algorithms, we developed a flow chart for selecting appropriate correction algorithm for CLAP, TAP, and PSAP (Fig. 1).Furthermore, an Igor Pro (WaveMetrics, Inc.) based program for selecting and implementing our correction algorithms can be found in the Supplemental Material.Similar logic is followed for the AETH.

Application of the previous algorithms on different aerosols
We first consider the application of the B1999 and V2005 corrections on different combinations of aerosol type and filter-based absorption photometer.Specifically, we apply the two corrections to the biomass burning data from the FIREX laboratory campaign (CLAP and TAP) as well as six months of ambient data from the SGP site (CLAP and PSAP).In doing so, we use the "default" coefficients recommended in B1999 and V2005 as well as "updated" coefficients that are estimated via regression techniques.We focus on the results of the CLAP in the main text, because a CLAP is the only instrument common to deployments for both FIREX and SGP.The results of the TAP from FIREX and the PSAP from the SGP site can be found in the Supplementary Material (Table S5 and Fig. S5).
Our inter-comparison between the corrected CLAP-derived Babs and reference Babs for the FIREX and SGP data is provided in Fig. 2 and Table 3.For the FIREX measurements, both analyses (using the "default" coefficients and updating the coefficients) suggest good correlation (coefficient of determination (R 2 ) > 0.9) between the CLAP and the reference across all three wavelengths.
Nevertheless, the corrections using the "default" coefficients result in over-prediction of Babs by factors of ~2.5.If we update the coefficients in the corrections, there is an obvious improvement in the agreement (i.e., slope ≈ 1; R 2 increases).The results are generally similar for SGP, although the R 2 for ambient data is generally lower for ambient data (R 2 < 0.7).Decreased R 2 may be due to the lower aerosol concentrations measured in ambient air, which could lead to lower signal-to- noise in the instruments.Moreover, it is worth mentioning that for both datasets (FIREX and SGP), the corrected Babs from different filter-based absorption photometers using the "default" approaches does not agree with each other (slopes range from 0.69 to 1.40).However, after updating the coefficients, the slopes approach unity (Table S6).Table 3 Relationship between the CLAP-derived Babs corrected by the B1999 and V2005 algorithms (including updated coefficients) and the reference Babs at 652, 528, and 467 nm.The relationship is achieved using major axis regression (Ayers, 2001).The value in parentheses represents the coefficient of determination (R 2 ) of the linear relationship.In the FIREX data, there is an apparent dependency of the updated coefficients on the wavelength of light, but more importantly, on the aerosol optical properties, namely SSA and AAE (Tables S7-S9).However, in the ambient data from SGP, the dependency on optical properties is less obvious (Tables S10-S11).Nevertheless, all of these coefficients differ from those reported in B1999 and V2005 (again, derived for the PSAP rather than the CLAP), which highlights the potential need to use coefficient values that are appropriate for the instrument being used, its wavelength(s) of light, and optical properties that are representative of the sampled aerosols when applying correction factors to BATN.

Application of the new algorithms to the FIREX data
The co-location of the CLAP, TAP, AETH, and PAX during FIREX allows us to apply each algorithm (A, B, C) to these data.Similar to Sect.3.1, we focus our discussion on the CLAP with details on the TAP and AETH presented in the Supplementary Material (Fig. S5-S6).However, we provide the recommended initial guesses in the new algorithms and the comparison of absorption (corrected filter-based Babs versus reference Babs) for all filter-based absorption photometers in Table 4 and Table 5 to help readers quickly retrieve key information of our algorithms.
Figure 3 provides a comparison between the uncorrected BATN from the CLAP at all three wavelengths, as well as photoacoustic Babs interpolated to those wavelengths using AAE.For each wavelength, the slopes are significantly greater than one.Moreover, there is an apparent dependency on SSA and AAE in the agreement between the instruments.This is most obvious in Fig. 3a (652 nm), where data with lower SSA and lower AAE (smaller markers, "brighter" colors) fall below the best-fit line, while data with higher SSA and higher AAE (larger markers, "darker" colors) fall above the best-fit line.This phenomenon is less clear in Fig. 3b-3c, but an apparent dependancy on SSA and AAE remains, which highlights the need to include both of these aerosol optical properties (and appropriate interaction terms) when correcting BATN values.We first apply "Algorithm A" to the CLAP BATN data in Fig. 3. Using the reference Babs values from the PAX (in addition to Bscat values), we are able to derive a set of coefficients that enable the correction of the data (Table 4).Corrected CLAP values are presented in Fig. 4 with the linear relationships presented in Table 5.The slope for each wavelength is very close to the 1:1 line, suggesting that our approach works well in correcting these data.Moreover, the heteroscedasticity that exists in Fig. 3 has been minimized after correction, and there are no apparent trends in how the data are organized in Fig. 4 due to the aerosol optical properties.
Table 4 Coefficient values for Eq. ( 9) derived using "Algorithm A".We recommend these as the initial guesses when implementing "Algorithm B".   similarly, we define SSA using interpolated Bscat from the PAX and BATN from the CLAP (The rationale for using BATN is that if "Algorithm C" were to be implemented in practice, only BATN would be available).In Fig. 6, the data points are colored by "prediction error", effectively a metric to quantify how well the power function reproduces the individual data points.Although there is a fair amount of error in some of these points, we still obtain an SSA-AAE relationship required to initialize "Algorithm C".
Figure 6.AAE plotted against SSA for the FIREX data.In the figures, AAE was computed using a power-law fit across all three wavelengths, and SSA was computed using the interpolated Bscat from the two PAX and the reported BATN from the CLAP.The data points are colored by their prediction error (("true" AAE -"calculated" AAE)/ "calculated" AAE).Even though there is uncertainty in the SSA vs. AAE relationship used in "Algorithm C", after corrections have been applied, the filter-based Babs for the CLAP agrees well with the independent reference Babs; the slopes for all wavelengths are slightly greater than 1 (1.03-1.05)and the R 2 values are all high (0.97-0.98).However, even though the absorption measurements are corrected well, there still remains large uncertainties in values of inferred scattering.Examples of this are provided in Fig. 7, where we compare the SSA inferred from the PAX to the SSA inferred from "Algorithm C" as well as Bscat for each wavelength.Generally speaking, data that are better represented by the SSA vs. AAE relationship (i.e., smaller prediction error) results in better agreement with the reference for both SSA and Bscat, but there is also a clear divergence from the 1:1 line in Fig. 7a-c as SSA decreases.Therefore, even though "Algorithm C" performs well at correcting filter-based BATN to agree with the reference Babs, estimates of final SSA values should be considered to be uncertain.4 and Table 5, as well as Fig. S5-S6).
Moreover, the corrected Babs from the three filter-based instruments agrees with each other for all three wavelengths (Table 6), confirming the universal nature of our algorithm.

Application of the new algorithms to ambient data
To test our algorithms further, we extended our work to ambient data collected the DOE SGP site during the time period which the PASS-3 was operational.From the SGP data, we derived a different set of coefficients for ambient data using "Algorithm A", which differ from those derived for FIREX (Table 4).The results presented in Fig. 8 and Table 5 suggest that our new algorithm works at least as well as B1999 and V2005 on this dataset (both with updated coefficients).The repeatability of the coefficient values in "Algorithm A" is confirmed for the SGP measurements using the same procedure as described in Sect.3.2 (see results in Fig. S7 and Table S12).On the SGP data, we see similar performance to the FIREX data when we apply "Algorithm B", where we again sampled half of the CLAP data, used the initial guesses derived in "Algorithm A", and repeated this process 1000 times.Although the slopes tend to be larger than 1 (i.e., the corrected CLAP Babs remains high relative to the PASS Babs), the results still represent an improvement over B1999 and V2005 using their recommended coefficients for their correction equations.
Implementing "Algorithm C" is challenging for ambient data, because there is no distinct power function relationship in AAE vs. SSA (Fig. 9); this is consistent with other field studies reporting both SSA and AAE (e.g., Backman et al. (2014) and Lim et al. (2018)).Our approach described here is only appropriate for ambient aerosols that follow a power function, such as sites impacted by biomass burning.Nevertheless, we did apply this to a subset of the SGP data where the AAE-SSA prediction error is within 30% (N = 86), and for this subset of data, "Algorithm C" works fairly well (slopes ≈ 0.95; see Fig. S8).Therefore, while "Algorithm C" may have utility for ambient data, we advise caution when using this algorithm since the aerosols influencing the site may not be represented by a clear AAE-SSA power function (e.g., when biomass burning and coarse aerosols are equally prevalent at a long-term monitoring site).These new algorithms are also applicable to the PSAP deployed at the SGP site.The results of the correction for the PSAP are presented in Table 5 and Fig. S5, and the recommended initial guesses when implementing "Algorithm B" to PSAP-BATN at ambient environments are given in Table 4.
As expected, there is good agreement between corrected PSAP-and CLAP-Babs (Table 6).

Impact of the implemented correction algorithm on aerosol optical properties
In addition to the direct comparisons of Babs between the filter-based and photoacoustic measurements, we compare derived optical properties (AAE and SSA) from different instruments to assess the algorithms' performance on derived aerosol optical properties.For example, we have discussed the discrepancy of SSA between the filter-based and photoacoustic measurements when implementing "Algorithm C" in Sect.3.2.In this section we will more broadly discuss the impact of different correction algorithms on AAE and SSA.
In Fig. 10, we present the frequency distribution of AAE for both FIREX and SGP data generated from different campaign/instrument pairs using different correction approaches.For the FIREX data (Fig. 10a-b), most corrections (with the exception of the "default" B1999) are consistent with the photoacoustic data, while for the SGP data (Fig. 10c-d), most corrections (with the exception of "default" V2005) are consistent with the photoacoustic data.However, updating the coefficients for B1999 and V2005 improves the agreement with the photoacoustic data.The 50% difference that exists between the B1999 and V2005 algorithms in all panels in Fig. 10 are consistent with previous studies.For example, both Backman et al. (2014) and Davies et al. (2019) found that the V2005-derived AAE is greater than B1999-derived AAE by 33% to 50% for ambient aerosols.
Therefore, we highlight that the default coefficients in B1999 and V2005 may have some limitations when deriving AAE using the corrected Babs; instead, updating the coefficients or using the new algorithm proposed in this work may yield more robust AAE results.Similar to Fig. 10, we also investigate the distribution of SSA computed by using corrected Babs along with Bscat.We provide the results at 652 nm as an example in the main text (Fig. 11); figures for 528 nm and 467 nm can be found in the Supplementary Material (Fig. S9 and S10).For both FIREX and SGP data, the SSA obtained using the new algorithm agree very well with the B1999 and V2005 but only when their coefficients have been updated.Calculations of SSA using B1999 and V2005 with their recommended coefficients suggest that these values may be biased low, which follows the over-estimation of corrected Babs demonstrated in Fig. 2. the use of "Algorithm C" results in some obvious discrepancies compared to the photoacoustic reference, again highlighting the potential for large uncertainty using this algorithm.
In Fig. 12, we directly compare the distributions of both AAE and SSA at 652 nm for all of the filter-based absorption photometers considered here, using our "Algorithm A" to correct the BATN data.For both datasets, after the corrections have been applied, there are only marginal differences of the AAE (Fig. 10a and 10b) derived by different instruments.Similarly, there is good agreement among the SSA values when using corrected-Babs from different instruments (Fig. 10c and 10d).
Overall, the derived properties using the new correction are consistent across all instruments, suggesting its universality.

Figure 12
The probability density of AAE and SSA (652 nm) derived by different filter-based photometers Babs (corrected by "Algorithm A" in the present work).Note that the number of total observations vary across instruments.

Uncertainty of the new algorithms
In this section, we estimate the uncertainty of the new algorithms due to both measurement uncertainties of the instruments and the uncertainties of parameter computation.We then simulate the propagated uncertainty in the corrected filter-based Babs reported in this paper.
Measurement uncertainties of the instruments considered here have been reported in previous work (e.g., (Anderson et al., 1996;Nakayama et al., 2015;Ogren et al., 2017;Sherman et al., 2015)) and are summarized in Table 1.The typical sources of measurement uncertainty of the aerosol instruments include: 1) instrument noise (often associated with the averaging time); 2) calibration uncertainties (such as the accuracy of the operating wavelengths and the properties of the calibration materials); 3) standard temperature and pressure (STP) correction uncertainties (Sherman et al., 2015); and 4) flow rate uncertainties.Additional uncertainties that are specific to filter-based absorption photometers include spot size and filter medium corrections (Bond et al., 1999;Ogren et al., 2017).Regardless, these values all tend to be ≤ 30%, which is consistent with other commonly-used aerosol instrumentation.Because correction algorithms for filter-based absorption instruments also require aerosol optical properties, the algorithms' performance will be affected by these values as well.For example, uncertainties in SSA are directly related to uncertainties associated with Babs and Bscat, which are both included in our simulations.However, capturing uncertainties in AAE is more complex, as AAE can be computed by either "2λ fit" (a linear fit using Babs at two wavelengths) or "3λ fit" (same as the power fit used in the present work).Davies et al. (2019) used the 3λ fit to calculate AAE and compared this to calculations using 662 nm and 785 nm (i.e., AAE662/785), finding that the 3λ results was about 50% greater.Moreover, similar differences (-35% to 85%) can exist comparing two different 2λ combinations (AAE440/870 and AAE675/870), depending on the contribution of brown carbon to absorption at 440 nm (Wang et al., 2016).However, based on Fig.
S12 and S13, we demonstrate small ( < ~10%) differences in the calculated values of AAE using our Algorithm A using different 2λ combinations for linear fits and the 3λ power-law fit, when considering both FIREX and SGP data.Consequently, we do not include AAE calculation uncertainty in our simulation.
In our simulations, the propagated uncertainty of corrected Babs is estimated by implementing the new algorithm to datasets in which filter-based BATN, reference Babs, and Bscat are subject to measurement uncertainties.The full procedure is outlined in the Supplementary Material, but we provide a brief overview of our Monte Carlo approach here.First, we create a synthetic dataset (n = 500 records) that defines Babs at 652 nm and AAE that is intended to represent biomass burning.
Values of BATN and SSA are then computed using the relationships presented in Fig. 3 and Fig. 6, respectively.Respective uncertainties associated with each of these values are applied following Table 1, assuming that these follow a normal distribution.We then applied "Algorithm B" to the BATN dataset, repeated 1000 times, to quantify overall uncertainty associated with our correction algorithm.
Figure 13 provides a graphical summary of our uncertainty simulation results, which was derived by fitting linear equations to the "true" Babs value (that we defined) and the "corrected" Babs values (outputs of each iteration).Considering the slopes (Fig. 12a), our algorithm can generally reproduce the "true" value within 10% at 652 nm and 528 nm, but the performance is slightly degraded at 467 nm.The median intercept for our simulations is close to zero, but the interquartile range increases with decreasing wavelength (Fig. 12b), suggesting that the uncertainty may increase at shorter wavelengths.The coefficients of determination (Fig. 12c) range from 0.47 (652 nm) to 0.68 (467 nm), showing that the algorithm may be less precise if large measurement uncertainties exist.Even though these sources of uncertainty exist when implementing our correction algorithms and propagate through to the corrected values, we argue that our new algorithm will "standardize" uncertainties across corrected Babs values from filter-based absorption photometers.Moreover, the new algorithms perform, at least, better than the previous algorithms with "default" coefficients, or as well as the previous algorithms with updated coefficients.when the instruments are co-located.This study provides a systematic evaluation of the previous correction algorithms (B1999 and V2005 corrections) on the CLAP and similar instruments (TAP and PSAP) using both laboratory-generated biomass burning emissions and ambient aerosols.We also developed "universal" correction algorithms that are applicable to any filter-based absorption photometer (e.g., PSAP, CLAP, TAP, AETH), which will have utility for any historic or future filter-based absorption measurements and which have the potential to standardize absorption coefficients across all filter-based instruments.This latter point is demonstrated in Table 6 and Fig.
12 in that there is good agreement across all filter-based absorption photometers when applying our corrections to both biomass burning and ambient data.In practice, we anticipate that our Algorithm B will be most common, because at long-term monitoring sites, filter-based absorption photometers are typically co-located with a nephelometer.
Using the existing corrections on our CLAP measurements, we find that the corrected Babs overestimate photoacoustic Babs by factors of ~2.6 (biomass burning aerosols) and ~3.2 (ambient aerosols).Similar overestimations of absorption by filter-based instruments are seen in the results of TAP from the FIREX study and PSAP deployed at the SGP.Comparing between B1999 and V2005, Babs corrected by the two corrections differ by -6% to 18%.These discrepancies in our results are consistent with those reported for the inter-comparisons between filter-based and photoacoustic absorption instruments (e.g., (Arnott et al., 2003;Davies et al., 2019;Li et al., 2019;Müller et al., 2011a)).and ambient measurements.Our work suggests that if the filter-based instrument is co-operated with a reference absorption instrument and a NEPH at field for a period, researchers can compute site-specific initial guesses (same as "Algorithm A" in the present work).Otherwise, either "Algorithm B" or "Algorithm C" proposed in this paper can be used to correct the filter-based measurements.In "Algorithm B" when a filter-based absorption photometer is co-located with a NEPH but without a reference instrument, the set of coefficients yield in this work (Table 4) can be used as initial guesses to implement the algorithm.In "Algorithm C" when a filter-based absorption photometer is operated by itself, a "representative" relationship between AAE and SSA can be used to estimate SSA from AAE at each step in the iterative process, but we advise caution if this relationship is not monotonic (e.g., as in the ambient data from SGP and from Backman et al. (2014) and Lim et al. (2018)).The only scenario not included in the present work is that the filter-based absorption photometer is co-located with a reference absorption instrument, but no instrument for scattering.However, under this scenario, one could simply use the photoacoustic Babs data because no filter-induced biases exist for those instruments.
In terms of the aerosol optical properties (AAE and SSA) computed by different corrections, the new algorithm suggests no bias of AAE and SSA when compared to that derived by updated-B1999and updated-V2005 for both aerosol datasets.
However, the new algorithm is not without limitations.First, we used the photoacoustic Babs as the reference to develop the algorithm and the initial guess of the coefficients; meanwhile, some studies argue that photoacoustic absorption is not a "ground truth" (e.g., (Lack et al., 2006;Lewis et al., 2008)).Thus, we simulate the propagated uncertainty of our algorithms considering the measurement uncertainties due to the photoacoustic Babs (as well as BATN and Bscat) and find that the corrected Babs can be biased by -17% to 5%, depending on the operated wavelength.Although potential bias due to the precision of photoacoustic Babs cannot be excluded, using the universal algorithm to correct the filter-based Babs will at least eliminate correction-related biases among different filter-based instruments.Second, we only tested the algorithms with data from biomass burning and ambient measurements.It is unclear how the algorithms will work for other absorbing aerosols (e.g., dominated by fossil fuel emissions or mineral dust).Further evaluation of the performance of the new algorithm on other aerosol sources may help to address this issue.
Regardless, we argue that our approach can standardize reported absorption coefficients at longterm monitoring sites, which has the potential to yield a better data set with which to evaluate chemistry-climate models.
, observation sites maintained by the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program or the National Oceanic and Atmospheric Administration (NOAA) Global Monitoring https://doi.org/10.5194/amt-2019-336Preprint.Discussion started: 4 November 2019 c Author(s) 2019.CC BY 4.0 License.
https://doi.org/10.5194/amt-2019-336Preprint.Discussion started: 4 November 2019 c Author(s) 2019.CC BY 4.0 License. 1.The spot change of the CLAP was manually performed when Tr reached approximately 0.5 (or ATN decreased to ~69), while the TAP advanced to a new spot automatically with a Tr threshold set to be 0.5.

Figure 1 .
Figure 1.The flow-chart for the application of correction algorithms on PSAP, CLAP, and TAP.

Figure 2 .
Figure 2. Inter-comparison between the CLAP-derived Babs corrected by the B1999 and V2005 algorithms and the reference Babs at 652, 528, and 467 nm for both FIREX and SGP data.The solid lines represent linear regressions, while the dashed line is a 1:1 line.

Figure 3 .
Figure 3.Comparison of the uncorrected CLAP-derived BATN and the reference Babs at 652, 528, and 467 nm for the FIREX data.The data points are colored by the corresponding SSA.The size of data points reflects their AAE quantified by the two PAX.The solid line represents the linear regression, while the dashed line is a 1:1 line.

Figure 4 .
Figure 4.As in Fig. 3, but the CLAP-based BATN values have been corrected using our "Algorithm A".

Figure 5 .
Figure 5.The box-and-whisker plots for the slope, intercept, and R 2 of the relationship between the CLAP-derived Babs (corrected by "Algorithm B" in the present work) and PAX-derived Babs for all three wavelengths.For details on how these values were generated, please refer to the text.Lastly, we apply "Algorithm C" to the data in Fig.3.However, we first require a functional relationship between AAE and SSA, because in this scenario, the CLAP BATN values are the only data input to the algorithm (and therefore, SSA is unknown).Liu et al. (2014) proposed that a power function can describe this relationship (AAE = a + b×SSA c ); we present these data from FIREX along with power function fits (and associated prediction intervals) in Fig.6.To define AAE in this figure, we fit a power-law relationship to the three BATN values from the CLAP; https://doi.org/10.5194/amt-2019-336Preprint.Discussion started: 4 November 2019 c Author(s) 2019.CC BY 4.0 License.

Figure 7 .
Figure 7.Comparison of SSA (a-c) and Bscat (d-f) at the three wavelengths for the FIREX data.Vertical axis: values output from "Algorithm C"; horizontal axis: values calculated using the photoacoustic Babs and Bscat.In addition to the CLAP, we apply the new algorithms to the other filter-based absorption photometers operated during the FIREX study (TAP and AETH).Consistent with what we observed for the CLAP results, the corrected TAP-and AETH-derived Babs is in good agreement with the photoacoustic Babs (as demonstrated in Table4 and Table 5, as well as Fig.S5-S6).

Figure 8 .
Figure 8. Inter-comparison between the CLAP-derived Babs corrected by "Algorithm A" in the present work and reference Babs at 652, 528, and 467 nm for the ambient data at the SGP study area.The solid line represents the linear regression, while the dashed line is a 1:1 line.

Figure 10 .
Figure 10.The frequency distribution of AAE calculated for different instrument/correction combinations of multi-wavelength Babs.

Figure 11 .
Figure 11.The frequency distribution of SSA (652 nm) calculated for different instrument/correction combinations of Babs and Bscat.Moreover, we plot similar figures as Fig.10-11 using all algorithms (A, B, and C).As shown in Fig.S11, the results using "Algorithm B" agrees very well with those using "Algorithm A", but https://doi.org/10.5194/amt-2019-336Preprint.Discussion started: 4 November 2019 c Author(s) 2019.CC BY 4.0 License.

Figure 13 .
Figure 13.The box-and-whisker plots (slope, intercept, and R 2 ) for the Monte Carlo simulation of the relationship between the CLAP-derived Babs (corrected by "Algorithm B" in the present work) and "true" Babs for all three wavelengths.4. Conclusions Filter-based absorption instruments are widely used at global observational sites due to their relatively low cost, fast response, and easy operation.Despite the existence of different correction algorithms to correct the filter-based Babs measurements, these are not "standardized" as differences in corrected Babs values exist across different instrument/correction combinations, even Overall, our new developed algorithms (A, B, and C) perform well on correcting Babs for different filter-based absorption photometers (CLAP, TAP, PSAP, and AETH) from both biomass burning https://doi.org/10.5194/amt-2019-336Preprint.Discussion started: 4 November 2019 c Author(s) 2019.CC BY 4.0 License.

Table 1
Summary of specifications for instruments relevant to this work.

Table 2
Overview of the studies of B1999 and V2005 and the description of our experiments.

Table 6
Inter-comparison between different filter-based Babs corrected by "Algorithm A" in the present work.The value in the parentheses represents the coefficient of determination (R 2 ) of the linear relationship.