Uncertainty in Light Scattering Measurements by TSI Nephelometer: Results from Laboratory Studies and Implications for Ambient Measurements

ABSTRACT

We performed a series of laboratory studies to assess uncertainties in aerosol optical property measurements. We used a pulsed cavity ring-down spectrometer (CRD) to measure the aerosol light extinction coefficient, a photo-acoustic absorption spectrometer (PAS) for light absorption, and a commercial integrating nephelometer (TSI, model 3563) for the scattering coefficient. The test aerosols generated for the study consisted of both non-absorbing and slightly-to-highly absorbing polydisperse submicron particles, delivered to the systems as pure compounds or mixtures. For aerosols with single scattering albedo (ω) > 0.7, we found that the ω values calculated by combining the three instruments agreed within expected uncertainty. For aerosols with ω < 0.7, the discrepancy was outside of the boundaries of existing uncertainties. Mie theory calculations of the nephelometer correction factors indicate that the current literature expressions for nephelometer truncation correction are not adequate at ω < 0.7 due to the large real part of the refractive index (n) of absorbing particles. New corrections are given for the case when n is known. Based on our instrumental capabilities we conclude that the lowest uncertainty in ω is obtained by combining CRD and PAS data. The implications for the uncertainty of aerosol optical properties when using nephelometer-based scattering coefficient in the case of, e.g., highly absorbing aerosols, coarse mode particles, and measurements at high relative humidity are discussed.

1. INTRODUCTION

Aerosol particles are known to exert a critical role in the Earth's energy balance both directly and indirectly, yet the overall magnitude of such processes is poorly quantified. Current uncertainties in aerosol direct radiative effect (DRE) are comparable to the effect itself (0.5 ± 0.4 W/m²) with a medium-to-low level of understanding on a regional-to-global spatial scale (IPCC 2007). Reducing the uncertainty of aerosol optical properties, i.e., light extinction (σ_ep), light scattering (σ_sp), and light absorption (σ_ap), is key to improve global aerosol forcing estimates. In particular, errors associated to measurements of the aerosol single scattering albedo ω (where ω=σ_sp/σ_ep) need to be lowered by a meaningful degree (Schwartz 2004). Limitations in instrumental precision and accuracy can represent major sources of error for aerosol optical property estimates. Several studies so far have looked at the agreement between measurement techniques to assess the overall uncertainty of both extensive and intensive optical quantities (Quinn et al. 1996; Sheridan et al. 2005 and references therein; Hallar et al. 2006; Lack et al. 2008). All these studies have pointed out the existence of systematic instrument biases leading to varying degree of unsatisfactory optical property measurement closure.

Cavity ring-down spectroscopy (Baynard et al. 2007 and references therein) is an accurate and sensitive technique for measurements of σ_ep. Values of σ_ap have been measured mostly by filter-based techniques (Bond et al. 1999; Weingartner et al. 2003). Recently developed photo-acoustic systems (Arnott et al. 1999; Lack et al. 2006) offer a potentially more accurate measure of σ_ap. Values of σ_sp are historically measured by commercial nephelometers (Heintzenberg and Charlson, 1996 and references therein). An important measurement limitation with the nephelometer optical design is that light scattered at angles smaller than ∼7° and larger than ∼170° is neglected, leading to so-called truncation errors. Truncation and other systematic errors such as wavelength sensitivities can lead to uncertainties in the nephelometer σ_sp coefficient varying from 5% to 50% depending on particle size (Anderson et al. 1996; Anderson and Ogren 1998). Both angular non-idealities and wavelength sensitivities have been thoroughly quantified for commercial nephelometers manufactured by TSI¹ Inc. (St. Paul, MN), and a correction scheme has been developed to reduce such errors (Anderson and Ogren 1998). High uncertainties are to be expected for integrating nephelometer designs with poorly characterized truncation characteristics (Heintzenberg et al. 2006) and for applications at high relative humidity (Heintzenberg and Erfurt 2000). Calibration errors can also be a significant source of uncertainty in nephelometer-based measurements (Müller et al. 2009). Furthermore, theoretical calculations by Moosmüller and Arnott (2003) suggest higher than expected errors in nephelometer-derived σ_sp coefficients for absorbing aerosols due to changes in the scattering phase function. This effect may significantly influence the accuracy of ω estimates for atmospheric aerosols when using nephelometers coupled with other measurements such as the CRD-based σ_ep coefficients. Recently, integrating spheres to measure σ_sp with minimal angular truncation have been developed (Varma et al. 2002; Abu-Rahmah et al. 2006) and cosine-weighted scattering sensors have been coupled to instruments that also measure σ_ep (Strawa et al. 2003). Both these methods have the potential to reduce the uncertainties in scattering measurements, although neither is in widespread use.

In this study we present the results of experiments performed with both absorbing and non-absorbing laboratory submicrometer aerosol particles to examine instrumental closure in aerosol optical property measurements. We detect aerosol light extinction by using two custom-built cavity ring-down aerosol spectrometers, CRD (Baynard et al. 2007), light scattering by a commercial three wavelength integrating TSI nephelometer (model 3563), and light absorption coefficient by a custom photo-acoustic absorption spectrometer, PAS (Lack et al. 2006). The paper is organized as follows: Section 2 describes the methodology and experimental set-up for aerosol generation, delivery and detection, and instrument calibrations. In Section 3 we report the experimental results for purely scattering aerosols, highly absorbing aerosols, and their mixtures. Calculations based upon Mie theory are performed to investigate the adequacy of the literature expressions for nephelometer truncation corrections for absorbing particles and provide new corrections for scattering measured by nephelometers (Section 4). We assess the uncertainty boundaries for ω values obtained by using nephelometry. The implications for the overall uncertainty of aerosol optical property measurements and for specific problems, e.g., determining aerosol absorption by subtracting the extinction and scattering measurements, are discussed.

2. EXPERIMENTAL SET-UP: PARTICLE GENERATION, TRANSPORT, AND DETECTION

Particles were generated using custom built constant rate Collison-type atomizers (Collison 1935). To generate scattering polydisperse aerosols, we atomized inorganic salts such as ammonium sulphate (AS) and sodium chloride (NaCl), and organic compounds such as dioctyl sebacate (DOS) and water-soluble di-carboxilyc acids (SUCCINIC and ADIPIC). DOS is commonly used as test aerosol because it forms spherical particles upon atomization, whereas di-carboxylic organic acids, common components of ambient aerosols, were selected to investigate possible instrument biases due to volatility losses. A water soluble black pigment, nigrosin dye (NSN), was used to generate polydisperse absorbing aerosols (Lack et al. 2006). Mixtures of ammonium sulphate and humic acid (AS/HUMIC) and a complex mixture of inorganic salts and organics, MIXPO (Svenningsson et al. 2006) were used as proxies for rural and continental polluted aerosols, respectively. Table 1 lists the generated aerosol types and their characteristics.

TABLE 1 Property summary of sub-1 micron aerosols generated for the study. For polydisperse particles, the size is the number mean diameter obtained from size distribution tests. DOS is a Fluka, Inc. product; the other compounds are commercially available at Sigma-Aldrich Inc.

	Type, Size
	(nm) for
Compound	1% vol.	Optical	Refractive
name	solutions	characteristics	index (RI)
Ammonium sulphate (AS)	Polydisperse, d = 100 nm	Non-absorbing	1.53+0.0i
Sodium chloride (NaCl)	Polydisperse, d = 110 nm	Non-absorbing	1.54+0.0i
Dioctyl sebacate (DOS)	Polydisperse, d = 120 nm	Non-absorbing	1.45+0.0i
Di-carboxylic acids (ORG)	Polydisperse, d = 110 nm	Non-absorbing	n/a
Nigrosin Dye (NSN)	Polydisperse, d = 90 nm	Absorbing	1.7+0.3i
MIXPO	Polydisperse, d = 100 nm	Slightly absorbing	n/a
Humic Acid	Polydisperse, d = 100 nm	Slightly absorbing	n/a

Figure 1 depicts a schematic of the aerosol generation apparatus and delivery setup. Two atomizers were used to produce internal and external aerosol mixtures by atomizing already mixed solutions (internal mixture) or by combining the output of two atomizers (external mixture). After atomization, all aerosols were dried to ∼5% relative humidity (RH) in a pyrex glass horizontal tube half-filled with molecular sieve; the residence time of aerosol in the tube was approximately 180 s. The aerosol flow exiting the sieve was diluted with filtered room air (RH < 15%) to reach a total flow of ∼32 lpm, and passed through a Berner-type impactor to ensure exclusion of particles with aerodynamic diameters >1 μm. Several tests performed using a custom-built differential mobility analyzer (DMA) serially connected with a condensation particle counter (CPC¹, Model 3022A, TSI, St. Paul, MN) ruled out the presence of supermicron particles in the generated samples. For 1% solutions, the typical number median particle diameter (d_p) was approximately 100 nm and the geometric standard deviation (σ_g) was 2.1 for AS, whereas for NSN d_p was 90 nm and σ_g was 1.9. For the other mixtures, we observed similar particle diameter and width of the number size distribution values, in agreement with those obtained in previous laboratory studies performed by using the same solutions, size selection instrumentation, and atomizing technique (Pettersson et al. 2004; Baynard et al. 2007).

FIG. 1 Schematic diagram of the experimental setup used in this study.

A computer-controlled valve was placed after the impactor to allow switching between sample flow and particle-free air to perform routine zeroing procedure of all instruments. Aerosols were delivered to the instruments through two sample flow lines. A CRD instrument (CRD #1) and the TSI nephelometer sampled at 28 lpm from one line. A second CRD cavity (CRD #2) with the PAS serially connected downstream sampled at 1.5 lpm. Based on CPC monitoring, differences in particle number concentrations downstream of the two lines were <1%, indicating minimal differential particle losses between the flow systems. Differences between the σ_ep coefficients measured by the two independent CRD cavities were <0.5% throughout the entire experiment. A third CRD cavity constantly measured filtered air at 1.5 lpm to account for the fraction of gas phase absorption (mainly NO₂ at 532 nm) to the total aerosol σ_ep and σ_ap signals. Gas phase absorption artifacts can be significant in polluted environments (Baynard et al. 2007); for the present study, their contribution in the sample flow was <0.1% of the total σ_ep coefficient. Corrections to σ_ep accounting for purge flow dilution, Rayleigh scattering and pressure drops were <1% of σ_ep. The resulting absolute uncertainty in the CRD extinction at 532 nm (hereafter δσ_ep) is 1% for signal levels ⩾5 Mm⁻¹ and averaging intervals ⩾3 s (Baynard et al. 2007).

The TSI nephelometer was calibrated following the procedure suggested by the manufacturer and reported by Anderson et al. (1996). The calibration terms were found to be almost identical to original values provided by the manufacturer, with differences varying between 1% and 3% depending on the wavelength channel. While the CRD instrument uses a pulsed 532 nm laser, the TSI nephelometer uses a broadband light source with three optical filters. The instrument scattering response is centered at ±2–4 nm off the nominal wavelengths due to a non-perfectly Lambertian nature of the light source illumination intensity, leading to so-called “wavelength non-idealities” (Anderson et al. 2006). The errors in the TSI nephelometer scattering coefficient (δσ_sp) due to truncation and wavelength non-idealities are reported to be a few to 10% for submicron particles, signal levels >10 Mm^–1 and averaging intervals ⩾60 s (Anderson et al. 1996). In the case of submicron aerosols, wavelength non-idealities can be a significant fraction of such errors (Anderson and Ogren 1998). For this study we used the σ_sp measured at the nominal 550 nm band, for which the center wavelength is at approximately 554 nm (Anderson et al. 1996). The 550 nm σ_sp coefficients were corrected for angular non-idealities using the scheme reported in Anderson and Ogren (1998) for polydisperse aerosols (hereafter AO98) and converted to 532 nm to match the CRD and PAS wavelengths using the Ångstrom exponent (Ångstrom 1929) and solving the equation for σ_sp,532. The å term is calculated using the σ_sp coefficients measured at the nominal 450 nm and 700 nm and the actual center wavelength values of 453 nm and 698 nm.

The PAS system measured the σ_ap coefficient at 532 nm using a continuous wave (CW) laser with a Δλ= 0.1 nm, and it was routinely calibrated with O₃ following the procedure reported by Lack et al. (2006). The uncertainty associated with light absorption, hereafter δσ_ap, is ∼5% (instrument accuracy) for signal levels ⩾3 Mm^–1 and averaging intervals ⩾3 s. The CRD, PAS and TSI nephelometer data used in the study were averaged to 60 s time resolution.

We calculated three values of ω using different instrument combinations, and directly compared the ω₁, ω₂, and ω₃ values to assess the level of method agreement in the optical property measurements. Since neither the CRD nor PAS present significant angular biases, the comparison of ω₂ and ω₃ against ω₁ gives the possibility to assess the effectiveness of the AO98 expression in correcting the nephelometer-based scattering coefficients for angular and wavelength non idealities in the case of submicron aerosols.

3. RESULTS

3.1. Non Absorbing Polydisperse Aerosol Particles

Direct comparison of CRD σ_ep and TSI nephelometer σ_sp was performed with non absorbing polydisperse particles. In the absence of aerosol absorption, we use the CRD as an independent measurement of σ_sp with insignificant angular biases, low uncertainty and well quantified accuracy and precision (Baynard et al. 2007). Values of σ_ep measured by the CRD and σ_sp measured by the TSI nephelometer (corrected with the AO98 expression and converted to 532 nm according to Equation (1) for dry, sub-1 μm AS particles agree within expected uncertainties, with a least-squares linear regression slope of 0.998 ± 0.001 and R² of 0.999 (Figure 2a)).

FIG. 2 (a) σ_sp measured by the TSI nephelometer (corrected using the AO98 expression, and converted to 532 nm) displayed versus the σ_ep measured by the CRD for sub-1 micron dry AS particles (slope = 0.998, R²= 0.999). (b) TSI nephelometer submicron correction factors determined by the AO98 correction plus wavelength conversion (C_λ,AO98, solid line) and fit to the experimental data plus wavelength conversion (C_λ,EXP, dashed line) for polydisperse AS, NaCl, and DOS particles. Error bars are ±3.0% (1-σ uncertainty).

Several non-absorbing polydisperse aerosols were generated from solutions of AS, NaCl, and DOS to further examine the robustness of the literature angular truncation correction for a wide range of particle shapes, submicron sizes, and refractive indexes (RI). By varying either solute concentration or atomizer flow settings, we produced σ_sp signal levels from ∼5 Mm⁻¹ to 800 Mm⁻¹. The å values (Equation [1]) varied from 0.35 to 1.65 for DOS, 1.15 to 3.15 for NaCl, and 1.05 to 3.15 for AS. Figure 2b shows the comparison between the σ_sp submicron correction factor for the nominal 550 nm σ_sp coefficients obtained (a) using the literature AO98 scheme plus wavelength conversion (hereafter C_λ,AO98) and (b) as ratio of the experimental 532 nm σ_ep to 550 nm σ_sp plus wavelength conversion (hereafter C_λ,EXP). Both C_λ,AO98 and C_λ,EXP are plotted as a function of å. The fit to the experimental points, C_λ,EXP= 1.1536–0.007å (dashed line) is in good agreement with the AO98-based expression, C_λ,AO98= 1.1542–0.003å (solid line). Few outliers, mostly NaCl data, can explain the small observed discrepancy. These results confirm that the AO98 correction for TSI nephelometer angular non-idealities is satisfying in the case of polydisperse, non-absorbing, submicron dry aerosols of different shape, size and RI. Following such normalization to the CRD using non-absorbing aerosols, the 1-σ uncertainty obtained for the σ_sp coefficients corrected with AO98 and converted to 532 nm is δσ_sp= 3.0%.

3.2. Absorbing Polydisperse Aerosols and Mixtures

The effectiveness of the AO98 angular truncation correction was tested for absorbing aerosols generated as solutions of polydisperse pure compounds as well as their external and internal mixtures. For practical purposes, we report only the results from internal mixtures AS/NSN, SUCCINIC/NSN, ADIPIC/NSN, AS/HUMIC, and MIXPO. These mixtures provided a range of ω values from 0.39 to 0.999. As before, the nephelometer σ_sp coefficients were corrected using the AO98 scheme and converted to 532 nm according to Equation (1).

The results are summarized in Figure 3, where the parameter R= (σ_ep–σ_ap)/σ_sp (i.e., the ratio of scattering obtained by difference of extinction minus absorption and scattering directly measured by nephelometer) is reported as a function of ω₁. R highlights the level of instrument agreement between estimates of the σ_sp coefficient obtained directly and indirectly (difference method). In the absence of instrumental biases R should be always equal to 1. We observe instead a deviation from the ideal behavior, with R values decreasing as particle albedo decreases as evidenced by the exponential fit through the experimental points (solid black line). The error bars show that for ω₁< 0.7 the discrepancy exceeds the experimental uncertainty determined by propagating the errors used for the optical coefficients i.e., δσ_ep= 1%, δσ_sp= 3%, and δσ_ap= 5%. Given the reasonable assumption of no artifacts in the CRD and PAS measurements, the R< 1 values suggest that the nephelometer values (already corrected following AO98) are too high of roughly 25, 15, 10, 4, and 2% for ω values of 0.4, 0.5, 0.6, 0.7, and 0.8, respectively.

FIG. 3 Ratio (R) of scattering values obtained by difference (σ_ep minus σ_ap) and directly measured by TSI nephelometer (σ_sp) plotted as a function of ω₁. Data are for AS/NSN internal mixtures. The σ_sp coefficients are corrected using the AO98 scheme and converted to 532 nm. Error bars are calculated by propagating the absolute uncertainties of the optical coefficients (δσ_ep= 1%; δσ_ap= 5%; δσ_sp= 3% following normalization with the CRD).

We investigated potential sources of biases in the nephelometric σ_sp measurements. From the raw experimental σ_sp data, we recalculated the correction term C for each test aerosol, following the AO98 procedure (note that differently from C_λ, the term C does not include the wavelength conversion). We find that our C values increase proportionally with the absorbing fraction (C= 1.1 for AS, NaCl, DOS, and ORG; C= 1.2 for NSN) as opposed to the constant C value of approximately 1.1 as provided by AO98 for all submicron sizes. We also explored the dependence of the å values on ω, since å is used to calculate C in the AO98 correction. Comparison of the å values of non-absorbing and absorbing particles with the same number median diameter d_p showed that å did not change significantly with ω.

To further investigate these results, Mie theory calculations were performed for obtaining theoretical ω values of the internal AS/NSN mixtures (hereafter ω_Mie) to compare with the experimental ω₁, ω₂, and ω₃ values. To perform such calculations, we needed to estimate complex RI for each mixture (RI_mixture), and we adopted the volume linear mixing rule described by Bohren and Huffman (1983) to do so. This rule assumes that particles are homogeneously mixed and that contribution of each component depends on its volume fraction in the mixture, where M_i, ρ_i, and M_i are the concentration, density, and RI of the i component (Schkolnik et al. 2007). In our case, the RI values of the single components are reported in literature, 1.53 + 0.0i for AS, and 1.7 + 0.3i (Lack et al. 2006) for NSN. The M_i values were computed based on the NSN percentages, i.e., 8, 15, 27, 54, and 75%. The density of AS is ρ = 1.77 g/cm³. The density of NSN is not published; we measured a ρ of 1.37 ± 0.2 g/cm³ for a macroscale NSN sample. The RI_mixture values obtained from these calculations are reported in Table 2.

TABLE 2 Input parameters for Mie code calculations to estimate ω values for the internally mixed AS/NSN particles. From left to right columns are: NSN percentage in the mixture; RI calculated by the linear mixing rule (Equation [3]); size calculated for the internally mixed particles; single scattering albedo values from Mie code (ω_Mie); and the experimental ω data, i.e., ω₁, ω₂, and ω₃

% NSN	RI	D (nm)	ωMie	ω1	ω2	ω3
0%	1.53+0.0i	100	1	0.99	1.002	0.99
8%	1.548+0.03i	95	0.82	0.89	0.90	0.90
15%	1.56+0.06i	90	0.70	0.83	0.84	0.83
27%	1.57+0.09i	90.3	0.58	0.68	0.71	0.71
54%	1.63+0.18i	100	0.49	0.55	0.60	0.58
75%	1.66+0.24i	95	0.43	0.47	0.52	0.51
100%	1.7+0.3i	90	0.39	0.41	0.48	0.47

Figure 4 shows ω₁, ω₂, ω₃, and ω_Mie as a function of the mass percentage of AS in the mixture (0 to 100%). We find that ω_Mie is lower than all the experimental ω values particularly for mixtures with 46, 73, and 85% AS (or 54, 27, and 15% NSN), with the only exception for pure AS and NSN. For pure NSN, ω_Mie is in good agreement with ω₁ but not with ω₂ and ω₃, ω₂ and ω₃ being higher than predicted by Mie theory. We investigated such mismatch observed between experimental and theoretical ω for the internal AS/NSN mixtures. Tests performed on both ρ and RI values for AS and NSN as well as on the size distribution parameters used in the computations show that the observed discrepancies cannot be explained by Mie calculations sensitivity to these terms. The difficulty in simulating the observations may be due to inadequate assumptions of complete, homogeneous mixing of the absorbing and non-absorbing components that in turn might provide inadequate RI_mixture values. Other commonly used mixing rules (e.g., Maxwell-Garnett, molar refraction and absorption, extended effective medium approximation or EEMA) produced similar RI_mixture values. Contrasting evidence exist on the validity of such methods: early studies have indicated that the volume mixing rule might be less adequate compared to, e.g., the Maxwell-Garnett scheme (Chylek et al. 1998) whereas other comparisons of measured and modeled optical properties of internally mixed absorbing and non-absorbing components (e.g., Abo-Riziq et al. 2006) have shown that all mixing rules are unable to produce model-measurement agreement, and that the level of agreement depends on the percentage of absorbing matter.

FIG. 4 Experimental (ω₁, ω₂, ω₃) and theoretical (ω_Mie) single scattering albedo values for internal mixtures AS/NSN, reported versus the mass percentage of AS in the mixture.

4. DISCUSSION

4.1. TSI Nephelometer Truncation for Absorbing Particles

New correction factors for spherical particles in the TSI 3563 nephelometer were calculated using Mie theory. To match the range of RI values of the experimental data, the values used in the calculations for the real part of the refractive indices (n) were 1.33, 1.38, 1.43, 1.48, 1.53, 1.59, and 1.7; for the imaginary part of the refractive index (k) we chose 0.0, 0.001, 0.002, 0.005, 0.1, and 0.3. This is a much larger range of (n, k) values compared to those previously used to determine the AO98 correction scheme, which was obtained for almost purely scattering aerosols using 1.40 ⩽n⩽ 1.52 for the real part and 0.0 ⩽k⩽ 0.01 for the imaginary part. Our calculations were done at the actual nephelometer center wavelengths of 453, 554, and 698 nm using the full angular response rather than a nominal 0–7 degree forward truncation (Anderson and Ogren 1998; T. Anderson, private communication, 2008). The nephelometer response accounted for the factor of 1.022 that arises from including the truncation error of Rayleigh scattering in the calibration procedure. We calculated the nephelometer response to 52 size distributions with logarithmically spaced number median diameters between 70 nm and 2 μm and σ_g of 1.6 (for 26 distributions) and 2.2 (for the others 26 distributions). The nephelometer response to the same size distributions was also calculated with a nominal 1 μm aerodynamic diameter impactor, modeled as a hyperbolic tangent function with 50% geometric diameter cut point at 0.85 μm and 10% and 90% transmission 0.05 μm above and below the cut point. The impactor cut point was moved to 0.9 μm for cases with n of 1.38 because in the atmosphere these would correspond to wet particles with lower density (and lower n) compared to the dry case. Size distributions with a median diameter larger than 0.75 μm were eliminated from the simulated sub 1 μm impactor subset because of the skewed distributions that result from convolving a large median diameter with the impactor cut at 0.85 μm. Some of the less atmospherically relevant regimes were also eliminated from the RI matrix; for example, wet particles with n of 1.38 were considered to have maximum k of 0.01, whereas particles with n> 1.59 were considered to have some absorbing material in them, i.e., a k value of at least 0.05.

Figure 5 shows the correction factors C calculated for the full angular response at 554 nm with and without sub-1 micron impactor, color coded by both n and ω. The C values are reported as a function of å calculated between the nominal 450 nm and 700 nm wavelengths. The spread of the C values shows that for each å (i.e., particle size) more than one C value can exist depending on the complex RI (i.e., particle composition). Comparisons of Figures 5a and b (submicron case) shows that the variation of C with n (5a) is stronger than with ω (5b). The NSN particles have low values of C mostly because of their high n. The curvature as a function of å is determined by their absorbing nature (k). Common atmospheric absorbers such as soot also have very high n values, so their behavior will be qualitatively similar to NSN.

FIG. 5 TSI 3563 nephelometer correction factors C calculated using Mie theory for various RI values, for submicron aerosols (panels a and b) and for sizes up to 2 μm (panels c and d). Points are color coded either by n (panels a and c) or ω (panels b and d). The thin solid lines of panel a show a correction calculated as a function of n only. The dashed line is the C from AO98; the solid lines are the C values from Equations (4) and (5). Circles are calculations for NSN (n= 1.7, k=0.3).

In Figure 5a, the thin solid lines show a correction calculated as a function of n for situations where there is independent information available about n. This correction is given by where C'(n) is an optional correction for submicron distributions. C'(n) is equal to 0 for å ⩾2.8, and to for å < 2.8. The ν₁, ν₂, and ν₃ coefficients are given in Table 3 for the nephelometer center wavelengths of 453, 554, and 698 nm for situations with and without submicron impactor. The dashed black line is the AO98 expression. For cases where RI is unknown, these calculations confirm that AO98 is a very good approximation for the common atmospheric situation with n≈ 1.5 for submicron aerosols.

TABLE 3 Coefficients ν₀, ν₁, ν₂, and ν₃ for Equations (4) and (5) given for the TSI 3563 nephelometer center wavelengths of 453, 554, and 698 nm for situations with and without submicron impactor

	ν0	ν1	ν2	ν3
698 nm sub-μm	0.8627	0.1423	0.1816	0.0306
554 nm sub-μm	0.8511	0.1589	0.2153	0.0439
453 nm sub-μm	0.8863	0.1327	0.2758	0.0610
698 nm all	0.9868	0.0182	0.7980
554 nm all	0.9948	0.0152	0.8951
453 nm all	1.0072	0.0118	1.0036

Figures 5c and 5d show the C values calculated for the full distribution up to 2 μm. For coarse particles, no single expression can reduce the nephelometer truncation errors to less than about 0.1 due to the strong curvature of C at å < 0. For situations where a nephelometer is used without an impactor the solid black curves on Figures 5c and d are fits weighted toward the less absorbing particles given by Equation (4) for C′ (n) = 0. Therefore, this expression does not account for the effect of n on C for supermicron aerosols.

We tested these new C values calculated from Mie theory on the experimental submicron data. Figure 6 shows the R values for AS/NSN mixtures with NSN amounts of 27, 54, 75, and 100% (i.e., the mixtures with ω< 0.7) obtained with the experimental σ_sp data now calculated using the C values from Equations (4) and (5). There is an improvement in the scattering closure (cf. Figure 3), especially for the AS/NSN mixtures with 75% and 100% NSN. This is notable because the only change to C is to make it a function of n; no correction for k (i.e., ω) is included in C.

FIG. 6 Ratio (R) of scattering values obtained by difference (σ_ep minus σ_ap) and directly measured by TSI nephelometer (σ_sp) plotted as a function of ω₁ for the AS/NSN mixtures with 27%, 54%, 75%, and 100% NSN. Theσ_sp coefficients are corrected using the real-refractive index dependent correction term C from Equations (4) and (5).

After these corrections were calculated, we became aware of a parallel set of nephelometer corrections (Bond et al. 2009). They point out the possibility of using size distributions to improve TSI nephelometer measurements whereas we show the importance of the real part of the refractive index for determining accurate C values. We emphasize that C is not the truncation error per se but rather the correction for truncation error as a function of å. The imaginary part of the refractive index k does also affect truncation errors (Moosmuller and Arnott 2003). However, we find that for submicron particles the relationship between truncation and Angstrom exponent is a stronger and much more systematic function of the real index than the imaginary index.

4.2. Truncation Corrections for TSI Nephelometer Measurements at High Relative Humidity

The refractive-index-dependent truncation correction affects the accuracy of estimates of the RH dependence of light scattering fσ_sp(RH) by a TSI 3563 nephelometer. In principle, a humidified particle will have lower n than when measured dry, because of the low n of water (≈1.33). As particles grow, the truncation corrections become larger not only because the particles are larger in size, as is commonly accounted for in AO98, but also because their RI decreases. This would tend to increase the measured fσ_sp(RH) values compared to making no correction for RI.

As an example, we can consider a lognormal aerosol distribution with number median diameter of 150 nm and a geometric standard deviation of 1.6. If the initial RI is n= 1.5, k= 0.002 and all particles grow under increased RH by a diameter factor of 1.5, then using a volume mixing rule the final RI would be n= 1.38, k= 0.0006. After a 1 μm impactor the true increase in scattering fσ_sp(RH) is a factor of 2.94. Because of increased truncation errors from the larger particles, the nephelometer would measure a factor of 2.82, or 96% of the correct value. The å value would decrease from 2.01 to 1.59. Using the AO98 equation for truncation, the fσ_sp(RH) factor would be corrected to 98% of the true value. Using Equation (4) for both truncation and index of refraction, fσ_sp(RH) would be corrected to within 0.2% of the true value. However, the 2% error from AO98 is within the experimental error for realistic accuracy of the humidity control.

4.3. Uncertainty in Scattering in TSI Nephelometer and in Single Scattering Albedo Estimates

The uncertainty in the σ_sp coefficients was recalculated on the basis of the experimental results. Figure 7a shows the percentage uncertainty of the σ_sp coefficient corrected with AO98 (δσ_sp) plotted as a function of ω. The δσ_sp points are best fitted through a power function where y₀= 3.0%. For ω> 0.8, the δσ_sp is equal to 3.0%. For lower ω, the uncertainties are much higher and reach ∼30% at ω=0.4. We use these new δσ_sp values to calculate the percentage uncertainties in ω calculated by combining CRD and TSI nephelometer measurements. Figure 7b shows estimates of both δω₁ from CRD and PAS (circles) and δω₂ from CRD and TSI nephelometer (triangles) obtained using δσ_ep= 1%, δσ_sp= 3.0 + 210^(–4.88*ω) from (6) and δσ_ap= 5%. Compared to early ω uncertainty analysis based on normalization of the TSI nephelometer to the CRD for which δσ_sp is held constant (Baynard et al. 2007), these δω₂ values are much higher. The δω₁ values, derived from CRD and PAS, are <5% throughout most of the ω spectrum and reach 9% for ω⩽ 0.4. At this ω value, δω₁ is still three times lower than δω₂. Both δσ_sp and δω₂ can be reduced up to 10% if the real refractive-index-dependent truncation expression is applied (squares in Figure 7a and b, respectively); even so, the ω₁ from CRD and PAS still provides the lowest uncertainty over the entire ω range, giving more accurate estimates of ω than the values calculated from the CRD and TSI nephelometer.

FIG. 7 (a) Percentage uncertainty inσ_sp from TSI nephelometer (δσ_sp) calculated using the AO98 scheme (triangles) and corrected using Equations (4) and (5) (squares), and (b) percentage uncertainties of single scattering albedo δω₁ (CRD and PAS) and δω₂ (CRD and TSI nephelometer). δω₁ is calculated using δσ_ep= 1% and δσ_ap = 5%. δω₂ is calculated combining δσ_ep=1% with either δσ_sp AO98 (triangles) or δσ_sp Equations (4) and (5) (squares).

The implications of these findings are significant considering the widespread use of nephelometry for climate studies (e.g., Quinn et al. 2004; Doherty et al. 2005; Sierau et al. 2006) and air quality assessment applications (e.g., Hand and Malm 2007). Furthermore, the nephelometer is often combined with absorption measurement techniques such as PSAP, which are highly uncertain (Lack et al. 2008; Cappa et al. 2008). The refractive-index-dependent truncation expression proposed in this study improves upon AO98 equation for applications where the RI of the aerosol is known or can be accurately estimated. For cases where small σ_sp uncertainties errors are needed, it might be more effective to apply CRD and PAS technologies or physically reducing truncation errors in the nephelometer body, e.g., by adding a forward scattering fiber optic, rather than refining the nephelometer correction factors. In fact, recent instrument developments (Sanford et al. 2009) have shown that significant improvements in correcting angular non-idealities in optical cavities can be obtained from even modest and imperfect information about light scattered within 8 degrees in the forward direction.

Extinction techniques (which have trivial angular truncation errors compared to the nephelometer) currently appear as the best way to measure the optical properties coarse mode aerosol particles, e.g., mineral dust, which are important for climate and air quality issues. One remaining problem with this approach is separating out the absorption component of the extinction, which could be done by direct absorption measurements rather than estimating the coarse mode absorption as the difference of extinction and nephelometer-determined scattering. However both PAS and filter based absorption techniques may have biases for measurements of coarse mode absorption. For the PAS technique, loss of sensitivity due to internal heat equilibration of particles (Raspet et al. 2003) could become problematic, while filter based techniques appear to underestimate absorption by particles larger than 400 nm (Lack et al. 2009).

5. SUMMARY AND CONCLUSIONS

We designed a laboratory study to evaluate the performance and current uncertainties of instruments for optical property measurements. Single scattering albedo values ω obtained from different instrument combinations were compared for a wide range of polydisperse laboratory-generated aerosols with absorbing and non-absorbing components. The experimental data revealed a clear trend toward increasing discrepancies between the determined ω values as particle ω decreased. We find that for aerosols with ω< 0.7 the discrepancies between ω values were larger than that expected based on the adopted instrument uncertainties. The data indicate the existence of uncorrected biases in the scattering measurements by nephelometers. Re-evaluation of the nephelometer correction factors based upon Mie theory confirms that the AO98 expressions for correcting nephelometer truncation errors are not effective for highly absorbing particles; surprisingly, this is mostly due to the high real index n of absorbing materials. We have determined new corrections for the TSI nephelometer for cases when the refractive index RI is known, and have shown that the new refractive-index-dependent truncation expression is effective in improving the instrument closure with laboratory-generated submicron aerosols. However, the applicability of such correction expression will have limitations if the RI of the bulk aerosol can only be approximately known. The large and highly variable correction factors found for supermicron particles confirms that the nephelometer is not suited for precisely measuring the scattering from such aerosols (Anderson et al. 1996; Moosmuller and Arnott 2003; Marshall et al. 2005). Determination of hygroscopic growth using nephelometers is also affected by these results; even though the RI values of the ambient aerosols are not known precisely, a variable C value would have to be used for hygroscopic growth experiments since most wet particles will have systematically lower n than when measured dry.

We define more realistic error boundaries for ω values determined using the extinction from CRD combined with the nephelometer data corrected following the AO98 scheme. Compared to previous estimates, uncertainties in ω using nephelometer data are larger and are most significant for ω< 0.7; this will be important for particular episodes or specific measurement environments, such as fresh combustion or biomass burning plumes. In general, any aerosol characteristic that changes the ratio of forward to total scattering relative to that from ideal laboratory aerosols (e.g., non spherical and coarse particles) will only increase uncertainty in ω estimates derived from nephelometry.

Acknowledgments

This work was funded by the NOAA Climate Program. Drs. Adam Wollny, John Ogren, and Tad Anderson provided helpful discussions. Dr. Ranajit Talukhdar helped prepare laboratory aerosol samples.

Notes

Notes

1 Certain commercial equipment, instruments, or materials are identified in this article in order to adequately specify the experimental procedure. Such identification does not imply recognition or endorsement by the National Oceanic and Atmospheric Administration, nor does it imply that the material or equipment identified are necessarily the best available for the purpose.