Correction of the Calibration of the 3-wavelength Particle Soot Absorption Photometer (3λ PSAP)

Abstract

During the Reno Aerosol Optics Study (RAOS) in June 2002, the prototype of the 3-wavelength Particle Soot Absorption Photometer (3λ PSAP) was calibrated and a correction scheme was subsequently published (Virkkula, A., Ahlquist, N. C., Covert, D. S., Arnott, W. P., Sheridan, P. J., Quinn, P. K., and Coffman, D. J. (2005). Modification, Calibration and a Field Test of an Instrument for Measuring Light Absorption by Particles. Aerosol. Sci. Technol., 39:68–83). Unfortunately, the 3 λ PSAP flow rate had not been corrected during that analysis. The factors in the transmittance correction change after reanalysis with flow-corrected data. Reanalysis of the data also resolves an apparent discrepancy between the 1 λ PSAP and the 3 λ PSAP, and the two instruments now agree well.

INTRODUCTION

The Particle Soot Absorption Photometer (PSAP), manufactured by Radiance Research, Seattle (WA), is a filter-based instrument for measuring light absorption by particles. It has been available both as a one-wavelength version (Bond et al. 1999 (B1999)) and as a 3-wavelength version (Virkkula, A., Ahlquist, N. C., Covert, D. S., Arnott, W. P., Sheridan, P. J., Quinn, P. K., and Coffman, D. J. (2005). Modification, Calibration and a Field Test of an Instrument for Measuring Light Absorption by Particles. Aerosol. Sci. Technol., 39:68–83) (V2005). Calibration of an absorption photometer based on light transmittance measurement requires measurements with some absorption standard and simultaneous scattering measurements, because scattering aerosols also result in a transmittance decrease that gets erroneously interpreted as light absorption if not taken into account. During the Reno Aerosol Optics Study (RAOS) in June 2002 (Sheridan et al. 2005) several aerosol absorption photometers were calibrated, among others the prototype of the 3-wavelength PSAP (3λ PSAP). Since then it has been available commercially and it is in widespread use.

The experimental setup used for the analysis here was described in detail by Sheridan et al. (2005) and Virkkula et al. (2005). In brief, the instruments used for the present work were the prototype 3λ PSAP, a 1λ PSAP, a 3λ TSI nephelometer, a 3λ optical extinction cell, and a 2λ photoacoustic instrument. The generated aerosols were primarily simple external mixtures of black (kerosene soot) and white (ammonium sulfate) particles sampled at low relative humidity, although several other aerosol types were investigated. In these experiments there were neither any condensing material, such as organics nor high or variable relative humidities that have been shown to disturb filter-based absorption measurements (e.g., Arnott et al. 2003; Cappa et al. 2008; Lack et al. 2008). Therefore, if good agreement were ever to be obtained between different PSAPs or between PSAPs and “reference” absorption measurements, they should be observed in this experiment.

Here, I report an error I made in the analysis of the RAOS data that was discovered when comparing the RAOS logbooks with raw and processed data files in 2009. The error was that the raw 3λ PSAP data had not been corrected for the flowmeter calibration before doing the analyses. The purpose of this note is to present the reanalysis of the data and the corrected transmittance correction functions. Some of the formulas presented in the earlier article are repeated here to make reading easier.

DATA ANALYSIS

If in a filter-based absorption measurement method only light absorbing particles reduced light transmittance, and if the method were artefact free, the absorption coefficient could be calculated from

where A is the area of the sample spot, Q is the flow rate of air drawn through the spot area during a given time period Δ t and I_{t - Δ t}and I_t the filter transmittances before and after the time period. However, this relationship changes as the filter gets loaded, and scattering particles also affect the result. The absorption coefficient given by the PSAP (σ_AP(PSAP)) takes the loading correction into account in the firmware. The combined loading correction and the spot size correction according to B1999 yields

The origin of the constant 0.873 was also explained by Sheridan et al. (2005) and in more detail by Ogren (2010) (O2010), who also reasoned that the above formula should be multiplied by a wavelength adjustment factor of 0.97. In the B1999 correction σ_AP is further calculated by subtracting a fraction of the total scattering coefficient σ_SP measured with a nephelometer at 550 nm, without truncation correction, and dividing by 1.22 so that the full correction becomes

In principle this is of the form

If a reference absorption σ_AP,ref and σ_SP are available, the measured loading correction function can be obtained by rearranging (4) as

At RAOS, σ_AP,ref was the average of absorption measured with the photoacoustic method and that measured as the difference of extinction and scattering. The scattering coefficient σ_SP in (5) was measured at 450, 550, and 700 nm with the TSI nephelometer, truncation-corrected and interpolated to the PSAP wavelengths 467, 530, and 660 nm. Fitting (5) to the data was done earlier by Virkkula et al. (2005). A good fit was found with the logarithmic formula

where ω₀ is the single-scattering albedo.

It is clear from (1) and (5) that an error in flow results in an error in the factors in (6). During RAOS, the 3λ PSAP flow (Q_PSAP) was calibrated by using a BIOS DryCal flow meter that reported flow at standard temperature and pressure (273.15K, 1013 mbar). This flow calibration was done three times during the experiment, and all data points fit to the same line. The relationship was highly linear, yielding Q_BIOS = 1.03*Q_PSAP+ 0.13 LPM, R² = 0.999 (Figure 1).

FIG. 1 Flow calibration of the 3λ PSAP at RAOS.

As a result of applying this calibration, the flow-corrected absorption coefficients become lower than the non-corrected ones when all other factors are kept unchanged. If the PSAP had been operated at one constant flow in all experiments the correction of the then reported factors of (6) would be very simple. However, the flow was not the same in every experiment and therefore the calculations to derive values for the factors had to be re-done.

At first the change due to the flow calibration appears to be insignificant because the slope is only 1.03. However, the offset leads to clear changes. During the black aerosol experiments flow was set low in order to avoid the need of filter change in the middle of an experiment. The flow in the black aerosol experiments was on the average 0.785 LPM according to the PSAP flow meter. Corrected with the flow regression formula Q_TRUE = 0.936 LPM which is ∼ 20% higher than that given by the PSAP.

RESULTS AND DISCUSSION

The first result is that the prototype 3λ PSAP and the 1λ PSAP run by NOAA agreed well during the campaign. The B1999 correction includes multiplication with the f(Tr) and subtraction of σ_SP. Both of these increase the uncertainty of the comparison. Therefore, to make the most direct instrumental comparison of only the two PSAPs and not the loading correction method, the simplest absorption coefficients σ₀ calculated from (1) were compared. The 3λ PSAP data were interpolated logarithmically to the same wavelength as the 1λ PSAP according to σ_0,574 = σ_0,530(530/574)^{α (530,660)}, where α (530,660) is the Ångström exponent calculated from the σ_0,530 and σ_0,660. In Figure 2 the data of both PSAPs are plotted against each other in two size ranges: all black and grey experiment data and only data where σ₀ < 100 Mm^–1.

FIG. 2 Comparison of σ₀ of the two PSAPs calculated according to Equation (1). a) all data, b) data where both σ₀ < 100 Mm^–1. The 3λ PSAP data were interpolated to 574 nm. The grey symbols present data with all transmittance differences and all aerosol types: white, grey, and black. The black symbols present those grey and black aerosol data where the absolute difference of the transmittances of the two PSAPs was < 0.05.

Most data are very close to the 1:1 line and the regression lines show that the instruments agreed within about 2%. Some points deviate clearly, however. These can clearly be explained by the different loading of the two PSAPs, because there were some experiments where the filters had not been changed at the same time and the flows were not identical. For the range σ₀ < 100 Mm^–1, the linear regression yields σ_0(1λ) = (0.931 ± 0.004) σ_0(3λ)+ (3.4 ± 0.2) Mm^–1, where the uncertainties are the standard errors of the slope and offset given by the fitting function. This regression line does not really support that the two instruments agree well. However, in the same range, if only those grey and black aerosol data are used where the transmittances of the two instruments are within 0.05 of each other, the linear regression yields σ_0(1λ) = (1.023 ± 0.004) σ_0(3λ) – (0.1 ± 0.2) Mm^–1.

In the white aerosol experiments the differences were big for reasons that could not be unambiguously resolved either from the data or from the logbook. Some of the differences can be explained: the largest ones, about 30–40% were in three white aerosol experiments where the 3λ PSAP filter was kept without changing whereas the 1λ PSAP filter was changed into a clean pristine filter. However, there were 10–20% differences also in some other white aerosol experiments. In theory one explanation could be that the flows of the two PSAPs were different and therefore the penetration depths of the particles into the filters were different. This is not an explanation, however, because in some of the white aerosol experiments the 3λ PSAP flow was set lower than that of the 1λ PSAP and in some higher but there was no dependency of the σ₀ difference on this. Similar flow differences were also in the grey and black aerosol experiments but in these both PSAPs agreed very well as shown above. Nevertheless, the differences in the white aerosol experiments are not the main objective of this paper so they will not be analyzed further.

The second result of the reanalysis is that by using the O2010 corrections the pure soot experiment data have only a few points at the 1:1 line and the rest below it whereas for the grey aerosols the points are close to the 1:1 line (Figure 3). Now the scatter plots of σ_AP(PSAP) vs. σ_AP(Ref) are very similar to those of the 1λ PSAP in the V2005 plot 2a.

FIG. 3 σ_AP(PSAP) vs. σ_AP(ref) by using the f(Tr,O2010) for all wavelengths. Upper plots: black symbols: pure soot experiments, grey symbols: mixed soot and scattering aerosol; regressions with and without the experiment with highest absorption coefficient. Lower plots: grey aerosol data where σ_AP(467) < 60 Mm^–1.

It has to be noted that here the σ_SP were first corrected for truncation and then interpolated to the PSAP wavelengths. Therefore it is not exactly the same as the B1999 and O2010 correction where non-truncation-corrected σ_SP at 550 nm are used for the scattering correction. An estimate of the difference of the two approaches can be given by assuming the Ångström exponent α = 2. The truncation correction factor (Anderson and Ogren 1998) for submicron aerosols becomes C ≈ 1.064. When interpolating from 550 to 530 nm σ_SP(550 nm) is to be multiplied by the factor (550/530)^α ≈ 1.077. Multiplied these two factors yield about 1.146. In other words, the corrected scattering coefficient σ_SP(530 nm) is about 15% larger than the non-corrected σ_SP(550 nm). However, when σ_SP is multiplied by the factor s = 0.0164 of Equation (4) the absolute difference is not very big. For example at σ_SP = 100 Mm^–1 and α = 2 the non-truncation-corrected s · σ_SP = 1.6 Mm^{− 1} and the truncation-corrected and to 530 nm interpolated s · σ_SP = 1.9 Mm^–1.

The third main result is that the logarithmic loading correction function constants changed. The measured loading correction function f _M (Tr), calculated from (5) is plotted in Figure 4 for the three wavelengths at four different single-scattering albedo ranges: for pure soot and different mixtures of soot and ammonium sulfate. Also the loading correction function (1.5557Tr + 1.0227)^–1 of Ogren (2010) (Equation (3)) is plotted in Figure 4 for comparison. This function is referred to as f(Tr, O2010).

FIG. 4 The measured transmission correction function at the three wavelengths and four single-scattering albedo ranges. f(Tr,O2010) is shown for comparison in all graphs. < SSA > = average single-scattering albedo of the data in the respective SSA range.

Qualitatively the observations made in V2005 are still valid. For dark aerosols (ω₀ < 0.7) the shape of f _M (Tr) is clearly different from that of f(Tr, B1999) or f(Tr, O2010), a function of the form f(Tr) = k₀ + k₁ ln(Tr) fits better with the data (Figure 4). The whiter the aerosol becomes the closer f _M (Tr) becomes to f(Tr, O2010). When using the logarithmic function above the change is mainly due to the change in the factor k₁. The factors k₀ shown in the fits of each wavelength and ω₀ range do not have any clear trend whereas the absolute value of k₁ decreases clearly as function of ω₀. At ω₀ > 0.8 f _M (Tr) is very noisy because of the noise in the reference absorption σ_AP,ref in formula (5). The data suggest that the k₀ and k₁ factors are wavelength dependent (Figure 5) even though this wavelength dependency is not very strong. To follow the procedure of V2005 a linear function h₀ + h₁ω₀ was fitted to the k₁(ω₀) data obtained from subplots of Figure 4. In the fittings the ω₀'s were the averages of the respective ω₀ range. Due to the high noise of the f _M (Tr) and so high uncertainty of the k₁ in the highest ω₀ range that was omitted from the fitting.

FIG. 5 The factors k₀, k₁, and s of σ_AP = (k₀ + k₁ ln(Tr))σ₀ – sσ_SP. The central values and error bars of k₀ are the averages and standard deviations of the k₀values taken from the fittings in Figure 4. The k₁ and ω₀ values are taken from Figure 4. The central value of s is obtained from fitting to all ammonium sulfate experiments. The s error bar minima and maxima are discussed in the text.

The scattering correction factors s changed very little. Figures 7 and 8 in the V2005 paper are essentially identical to those plotted after the flow corrections so the plots will not be repeated here. The same observations apply: (1) s is wavelength dependent so that the sensitivity to scattering and thus the correction increases with increasing wavelength, and (2) one single s value is not enough even for one wavelength, it varies with loading. A range for s was estimated. The maximum s in each wavelength is the value that results in zero apparent absorption in the data point where σ_AP,PSAP/σ_SP was largest and the minimum s is the value that results in zero apparent absorption in the data point where σ_AP,PSAP/σ_SP was smallest.

The resulting factors of Equation (6) are presented in Table 1 and Figure 5. When using the factors in Table 1 the linear regressions yield slopes of 1.00 ± 0.02 for all wavelengths (Figure 6). A relevant question is whether the average values of the constants in Table 1 could be used. If the average values in Table 1 are used for all wavelengths, the regression lines become σ_AP,PSAP = 0.940 × σ_AP,REF + 1.6 Mm^–1, σ_AP,PSAP = 1.024 × σ_AP,REF + 1.0 Mm^–1 and σ_AP,PSAP = 1.031 × σ_AP,REF + 1.1 Mm^–1 for λ = 467 nm, 530 nm, and 660 nm, respectively, in the range < 60 Mm^–1, slightly worse than using the constants derived for the individual wavelengths.

FIG. 6 σ_AP(PSAP) vs. σ_AP(ref) by using the logarithmic f(Tr,ω₀)) with the values presented in Table 1. Upper plots: all data and separated into black and grey aerosol experiments. Lower plots: grey aerosol data where σ_AP(467) < 60 Mm^–1.

TABLE 1 Constants for the equation σ_AP = (k₀ + k₁ (h₀ + h₁ω₀) ln(Tr))σ₀ – sσ_SP derived from the flow-corrected PSAP data. k₀: the averages and standard deviations of the k₀values taken from the fittings in Figure 4; k₁: from fitting to black aerosol experiments; h₀ and h₁ obtained from fittings to the k₁ and ω₀ values in Figure 4; the uncertainties of: k₁, h₀, and h₁: standard error of the factors obtained from linear regression by using the LINEST function of MS Excel. The central value of s is obtained from fitting to all ammonium sulfate experiments. The s minima and maxima are discussed in the text.

	467 nm	530 nm	660 nm	Ave ± std
k0	0.377 ± 0.013	0.358 ± 0.011	0.352 ± 0.013	0.362 ± 0.010
k1	–0.640 ± 0.007	–0.640 ± 0.007	–0.674 ± 0.006	–0.651 ± 0.016
h0	1.16 ± 0.05	1.17 ± 0.03	1.14 ± 0.11	1.159 ± 0.011
h1	–0.63 ± 0.09	–0.71 ± 0.05	–0.72 ± 0.16	–0.687 ± 0.041
s	0.015(0.009, 0.020)	0.017(0.012, 0.023)	0.022(0.016, 0.028)	0.018± 0.003

CONCLUSIONS

I had not corrected the prototype 3λ PSAP flows before doing the analyses of the RAOS PSAP paper (Virkkula et al. 2005). The flow correction was now done by using the flow calibrations written down in the experiment logbook. The derivation of loading correction function was repeated with the corrected flows. The main conclusions of the reanalysis are that

1.	The 1λ and the prototype 3λ PSAPs did agree well during RAOS when the loading of the filters was close to equal. This reanalysis supports logbook notes and observations suggesting better agreement between PSAP instrument during the RAOS experiment than was reported in Virkkula et al. (2005).
2.	The new logarithmic loading correction function results in about 20% higher absorption coefficients than the old one.
3.	As in Virkkula et al. (2005) for black aerosols the absorption coefficients σAP calculated by using the Bond et al. (1999) correction deviated clearly from the absorption standard. The σAP calculated by using the alternative logarithmic loading correction function agreed clearly better.
4.	For grey aerosols both the logarithmic loading correction and the B1999 correction agreed well with the reference absorption. It has to be noted that here the σSP were first corrected for truncation and then interpolated to the PSAP wavelengths. Therefore it is not exactly the same as the B1999 and O2010 correction where non-truncation-corrected σSP at 550 nm are used for the scattering correction.
5.	The important observation made also in the V2005 is that the scattering correction factor s should be a function of transmission, s =    s(Tr). Since the loading correction function obviously is a function of single-scattering albedo, the whole issue needs a more theory-based approach, for instance radiative transfer modeling.
6.	The last but not the least conclusion is that saving logbooks is important.

Acknowledgments

This work was supported by the EU FP6 Integrated Infrastructures Initiatives (I3) project EUSAAR (European Supersites for Atmospheric Aerosol Research Project FP6-026140) and by the Academy of Finland as part of the Centre of Excellence Program (project no. 1118615). The RAOS experiment was supported by the U.S. Department of Energy Atomic Radiation Measurement (ARM) and the NOAA Aerosol-Climate Interactions Program.