Correlated IR spectroscopy and visible light scattering measurements of mineral dust aerosol

Authors


Abstract

[1] A combined infrared spectroscopy and visible light scattering study of the optical properties of quartz aerosol, a major component of atmospheric dust, is reported. Scattering phase function and polarization measurements for quartz dust at three visible wavelengths (470, 550, 660 nm) are compared with results from T-matrix theory simulations using a uniform spheroid model for particle shape. Aerosol size distributions were measured simultaneously with light scattering. Particle shape distributions were determined in two ways: (1) analysis of electron microscope images of the dust, and (2) spectral fitting of infrared resonance extinction features. Since the aerosol size and shape distributions were measured, experimental scattering data could be directly compared with T-matrix simulations with no adjustable parameters. χ2 analysis suggests that T-matrix simulations based on a uniform spheroid approximation can be used to model the optical properties of irregularly shaped dust particles in the accumulation mode size range, provided the particle shape distribution can be reliably determined. Particle shape distributions derived from electron microscope image analysis give poor fits, indicating that two-dimensional images may not give an accurate representation of the shape distribution for three-dimensional particles. However, simulations based on particle shape models inferred from IR spectral analysis give excellent fits to the experimental data. Our work suggests that correlated IR spectral and visible light scattering measurements, together with the use of theoretical light scattering models, may offer a more accurate method for characterizing atmospheric dust loading, and aerosol composition, size, and shape distributions, which are of great importance in climate modeling.

1. Introduction

[2] Mineral dust aerosol is an important component of the Earth's atmosphere. Dust affects the Earth's radiation balance through direct absorption and scattering of light [Ramaswamy et al., 2001; Satheesh and Moorthy, 2005; Sokolik and Toon, 1996]. Atmospheric dust particles also serve as nucleation sites for cloud formation [DeMott et al., 2003] and provide reactive surfaces for heterogeneous chemistry that can alter the chemical balance for key atmospheric species such as SO2, thus indirectly affecting radiative forcing [Dentener et al., 1996]. Modeling the full impact of dust on climate and atmospheric chemistry requires accurate information about aerosol loading and dust particle composition, size, and shape distributions. This information is often derived from optically based remote sensor measurements using satellite or ground-based instruments [Chowdhary et al., 2001; Sokolik, 2002; Schepanski et al., 2007; Kalashnikova et al., 2005; Koven and Fung, 2006; Cattrall et al., 2005; DeSouza-Machado et al., 2006], but these methods require accurate modeling of dust optical properties [Dubovik et al., 2006; Mishchenko et al., 2003; Thomas and Gauthier, 2009].

[3] It is well established that light scattering and absorption by aerosol can be strongly influenced by particle shape [Bohren and Huffman, 1983], and this constitutes a major source of uncertainty in aerosol retrievals from remote sensor measurements [Kalashnikova and Sokolik, 2002; Dubovik et al., 2006; Baran, 2009; Kahnert and Kylling, 2004]. There has been great progress in modeling the effect of particle nonsphericity through the use of advanced light scattering theories such as T-matrix theory, discrete dipole approximation (DDA), finite-difference time domain (FDTD), or geometrical optics methods (GOM), and for weak scattering, Rayleigh-Debye-Gans (RDG) theory [Draine and Flatau, 1994; Kalashnikova and Sokolik, 2004; Mishchenko et al., 1997; Yang and Liou, 1996a; Yang and Liou, 1996b; Wang and Sorenson, 2002]. For recent reviews of progress in light scattering from nonspherical particles see, for example, Mishchenko et al. [1996], Nousiainen [2009], Baran [2009], and Yang et al. [2007]. Such methods, however, still involve significant approximations and uncertainties. DDA or RDG approaches, for instance, allow tremendous flexibility in constructing model particles that are inhomogeneous and irregularly shaped, but are restricted to smaller particles [Kalashnikova and Sokolik, 2004; Wang and Sorenson, 2002].

[4] The T-matrix approach, based on a distribution of randomly oriented, homogeneous spheroids, has been one of the most broadly tested and applied methods, in part because of its computational efficiency [Mishchenko et al., 1997; Dubovik et al., 2006; Mishchenko et al., 2003]. A spheroid is an ellipse of revolution about a symmetry axis whose shape can be characterized by a single parameter, the axial ratio (AR), the ratio of major-to-minor axis lengths. While the T-matrix approach has proven extremely useful, it remains an open question whether calculations based on a uniform spheroid approximation can accurately model the optical properties of real atmospheric mineral dust, which generally consists of inhomogeneous mixtures of particles with highly irregular shapes.

[5] In addition, all theoretical models require assumptions about the range of particle sizes, shapes, and refractive index values that may best approximate “real” atmospheric dust. Indeed, one of the primary challenges to modeling the optical properties of atmospheric dust in any theoretical approach is to determine an effective particle shape distribution for use in the simulations. For the most part, modelers have assumed particle shape distributions inferred from electron microscope images of dust [Mishchenko et al., 1997; Kalashnikova and Sokolik, 2004]. For example, a particle shape model commonly used in T-matrix simulations is based on electron microscope image analysis of field samples of dust from collected from various source regions; this model assumes a uniform (flat) distribution of oblate and prolate spheroids with a range of moderate axial ratio parameters, AR ≤ 2.4 [Mishchenko et al., 1997; Dubovik et al., 2006].

[6] Recently, however, it has been suggested that it may be necessary to include more highly eccentric particles in the simulations. For example, Veihelmann et al. [2004] have used T-matrix methods to model particle shape effects on both laboratory scattering measurements from mineral dust, and on simulated satellite observational data. Their results suggest that accurate modeling of polarimetric observations of light scattered by irregular dust may require particle shape models that include extreme axis ratios, corresponding to highly eccentric spheroids. Dubovik et al. [2006] have also employed T-matrix-based methods to model both laboratory scattering data of mineral dust and dust retrievals from AERONET observations [http://aeronet.gsfc.nasa.gov/]. They find good fits for retrievals of aerosol scattering phase function and polarization data for particle shape distributions with moderate axis ratios. However, it is interesting to note that the shape distributions inferred from their data also show extended tails that extrapolate to more extreme axial ratios, AR > 3.

[7] Highly eccentric particles present a special challenge for T-matrix-based theoretical simulations because the calculations can fail to converge for larger and more asymmetric particles. For example, even the most advanced T-matrix code can fail to converge for a particle aspect ratio of AR = 3 with dimensionless size parameters X = 2πD/λ > ∼50, where D is the particle diameter and λ the wavelength of light [Mishchenko and Travis, 1998]. For particle size and shape distributions that include large and highly asymmetric particles, GOM, or hybrid approaches that combine T-matrix theory with GOM may prove useful [Yang and Liou, 1996b; Dubovik et al., 2006].

[8] Particle shape effects can also lead to significant changes in IR resonance spectral line shapes, even for particles that fall in the Rayleigh regime, D ≪ λ [Bohren and Huffman, 1983; Hudson et al., 2008a, 2008b]. These spectral shifts arise primarily from enhancements in the IR extinction cross section that result from surface scattering resonances and are very sensitive to particle shape [Bohren and Huffman, 1983]. Neglecting particle shape effects in spectral modeling could lead to errors in atmospheric dust loading or composition measurements that are based on spectral analysis of IR extinction data [Hudson et al., 2008a, 2008b; Thomas and Gauthier, 2009].

[9] In recent experiments, we explored these issues by collecting aerosol IR extinction spectra for a range of important components of atmospheric mineral dust, while simultaneously measuring the full aerosol size distributions [Hudson et al., 2007, 2008a, 2008b]. We could then directly compare experimental spectra with different theoretical model simulations [Hudson et al., 2008a, 2008b; Kleiber et al., 2009]. For example, in Kleiber et al. [2009], we explored the use of T-matrix theory to analyze IR spectral resonance line profiles for a series of well-characterized mineral aerosol samples. In particular, we investigated the “inverse problem,” i.e., whether IR spectral line profiles could be used, in conjunction with T-matrix theory, to infer the general characteristics of the aerosol particle shape distribution. Our results showed that accurately modeling IR resonance line profiles for mineral dust often required particle shape distributions that include highly eccentric spheroids, with axial ratio parameters, AR > 3. These results raise the question whether shape distributions based on analyses of two-dimensional electron microscope images are truly representative of the actual shape distributions for three-dimensional particles.

[10] Of course, it is a valid question whether a shape distribution derived from fitting the IR spectra has any broader significance or usefulness. In this paper, we explore this question for the case of quartz dust aerosol; specifically, do the particle shape distributions derived from analysis of IR resonance spectra provide for more accurate simulations of visible light scattering phase function and polarimetry data for the sample? These results serve as an additional internal consistency check on the shape distributions inferred from IR spectral data. We also compare the experimental results with model simulations based on particle shape distributions determined directly from electron microscope images of our quartz dust samples.

[11] Light scattering from irregularly shaped particles has been studied experimentally for many years. Previous laboratory studies have often been limited by uncertainties in the particle size distribution, shape distribution, or optical constants [Jaggard et al., 1981; Hill et al., 1984; West et al., 1997; Volten et al., 2001]. Our experimental approach enables a rigorous test of the validity of the uniform spheroid approximation in modeling the optical properties of quartz dust. Since the quartz optical constants are known and the particle size and shape distributions have been determined, simulations of the light scattering can be directly and quantitatively compared with experiment with few adjustable parameters.

[12] The work we present here is restricted to quartz dust particles that fall in the accumulation mode size range, with particle diameters in the range ∼0.1–3 μm. This mode is characteristic of particles with long atmospheric lifetimes that can undergo long-range transport. Field studies have shown that the mass median size for mineral dust aerosol over the oceans is typically in the 2–3 μm diameter range [Prospero, 1999]. Further, recent studies have estimated that up to 30% of submicron aerosol may be associated with mineral dust in a dust event [Arimoto et al., 2006].

2. Experimental Methods

[13] The experimental arrangement and methods have been previously described in Curtis et al. [2007]. Briefly, a suspension of quartz dust in water was aerosolized by means of a constant output atomizer and passed through a set of diffusion dryers to remove excess water vapor and dry the aerosol particles. The aerosol flow was then directed through a nozzle. A collection tube placed slightly below the nozzle gave a windowless light scattering region with a length of ∼1 cm. Monochromatic, polarized light from a Nd:YAG pumped tunable optical parametric oscillator (OPO) crossed the aerosol stream in the scattering zone directly below the nozzle. The crossing was located at the first focus of an elliptical mirror; the mirror collected scattered laser light from near-forward to near-backward angles (∼15°–172°), and refocused it to an aperture at the second mirror focal point. The aperture served as a field stop to limit the detector field of view. A charge-coupled device (CCD) array, located behind the aperture, recorded images of the scattering to give a measure of signal vs. scattering angle, θ, relative to the incident beam direction. The scattered light was measured for both perpendicular and parallel polarizations of the incident laser light field.

[14] The scattering phase function is proportional to the total scattered light intensity as a function of angle. The total scattered intensity was then normalized as described by Curtis et al. [2008] to obtain the normalized scattering phase function (equal to the scattering matrix element S11 in the notation of Bohren and Huffman [1983]) for direct comparison to the theoretical simulations. We also measured the linear polarization (equal to the ratio of scattering matrix elements −S12/S11) as a function of angle. Here we report the scattering phase function and linear polarization for quartz dust aerosol at three wavelengths, (λ = 470, 550, and 660 nm), chosen to overlap selected satellite observation bands. The results were typically averaged over several (∼3–6) data runs carried out over a period of several days.

[15] Simultaneous with the scattered light measurements, particle sizing instruments were used to measure the aerosol size distribution. Below the nozzle, the particle flow was pulled into a collection tube, where the flow was directed to an aerodynamic particle sizing instrument (APS) to monitor the size distribution in real time. The APS covers the size range ∼0.5–20 μm. APS size distributions were fit to a log normal distribution function as discussed in our previous work [Curtis et al., 2007, 2008]. The log normal mode diameter was constrained by independent ex situ measurements under similar flow conditions using an APS in tandem with a scanning mobility particle sizer (SMPS), which directly measured particle mobility diameters in the range of 50–500 nm [Hudson et al., 2007]. This approach results in some uncertainty in the aerosol size distribution. The effect of these uncertainties on the scattering, however, is relatively small, since the scattering is dominated by the large particle part of the distribution, which is directly measured with the APS. These issues are discussed in more detail in Curtis et al. [2007, 2008]. The theoretical model results shown in the Results section include estimates of the errors associated with these uncertainties in the particle size distribution.

[16] Typical log normal fit parameters for the size distribution correspond to a mode diameter of DMode = 0.22 μm with a width parameter σ = 1.69. This yields a mass weighted mean particle diameter (MMD) for the quartz dust sample in these studies of MMD ∼ 1.6 μm, corresponding to particles in the accumulation mode size range. However, the log normal distribution fit to the APS data has an unphysical tail that extends to very large diameters. While the APS can measure particles up to ∼20 μm in diameter, we see no particle counts (above background) in any size bin with D > 2.7 μm. This is expected because the particle size in the flow is limited by the droplet size from the atomizer to diameters less than ∼3 μm. To avoid introducing unphysical artifacts in the simulation results from very large particles that are not present in the experiment, we truncate the log normal size distribution function at a diameter of Dmax = 2.7 μm.

[17] Scanning electron micrographs (SEM) were also collected for the quartz sample used in these studies (Figure 1). A mica SEM stub was placed in the aerosol flow path for approximately 20 min. This allowed for the accumulation of enough particles to give an accurate representation of the particle shape distribution through subsequent image analysis. All SEM images were collected using a Hitachi S-4000.

Figure 1.

SEM image of dust with best-fit ellipses determined using the ImageJ software package.

3. Model Simulations

[18] In these and earlier studies, we have used the extended precision T-matrix code of Mishchenko et al., publicly available through the NASA web site [Mishchenko et al., 1996; Mishchenko and Travis, 1998; http://www.giss.nasa.gov/staff/mmishchenko/t_matrix.html]. The code can be used to calculate the full scattering matrix as well as characteristic dust optical properties such as total extinction and scattering albedo for a randomly oriented distribution of particles of specified shape. Required input includes the particle index of refraction (the optical constants) and information about the particle size and shape distributions. Optical constants for quartz at the wavelengths 470, 550, and 660 nm have been interpolated from values given in the published literature [Ivlev and Popova, 1973; Longtin et al., 1988]. The wavelength dependence of the refractive index over this range is small with an average value n = 1.55 + i (1 × 10−4). Particle sizing instruments were used to directly measure the particle size distribution simultaneously with the light scattering measurements as described above in the Experimental Methods section.

[19] The T-matrix code of Mishchenko and co-workers [Mishchenko and Travis, 1998] is written to handle a range of different model particle shapes. Here we have adopted the most common choice, which is to assume a distribution of spheroids of specified axial ratio (AR). For a given log normal size distribution (mode diameter and width parameters), T-matrix theory calculations were carried out for a distribution of randomly oriented oblate or prolate spheroids of fixed AR value. These calculations were then repeated for a range of both oblate and prolate AR values. An assumed particle shape distribution was then used to generate weighted average phase function and linear polarization curves for comparison to the experimental data. As noted above, the T-matrix code can fail to converge for large and highly eccentric particles. This does not present a major difficulty here because, for our sample, convergence errors are negligible as discussed below in the Results section.

[20] Two different model shape distributions were considered in this study. The first distribution is based on analysis of the SEM images collected for our particular quartz sample as shown in Figure 1. The distribution of axial ratio parameters was determined directly from the image using the publicly available ImageJ software package [http://rsbweb.nih.gov/ij/] to approximate all particle shapes with ellipses. The best-fit ellipses are shown as outlines in Figure 1. Since the image is two-dimensional, it is not possible to directly determine the AR value for a three-dimensional particle. We have assumed that prolate and oblate particles are equally represented in the shape distribution; thus we have simply reflected the measured AR histogram about 1.0 (circles) to generate the full shape distribution shown in Figure 2a. The analysis of two-dimensional images may not accurately measure highly eccentric particles in the distribution. For example, a very thin sheetlike particle lying at an angle to the surface may project an image that could range from circular to needlelike, depending on the viewing angle. It is difficult to correct for this effect as the inferred shape distribution will depend in detail on how particles are deposited onto the surface. As can be seen in Figure 2a, the SEM-based shape distribution is dominated by moderate axial ratio parameters with AR < 2.6 and a mean AR ∼ 1.4.

Figure 2.

The different particle shape distributions used in the modeling (left). (a) the moderate SEM-based shape distribution as determined from Figure 1 using the ImageJ software package. (b) The extreme IR-based distribution. The corresponding comparison of the T-matrix simulation results (dashed lines) with experimental IR resonance extinction spectrum (solid with circles) (right).

[21] Our previous spectroscopic work studying particle shape effects on IR spectral line profiles suggests that more extreme particle shapes with AR > 3 are often needed to accurately model IR resonance line shifts and line profiles for mineral dust particles. For example, IR resonance line profiles for clay particles are well fit by assuming them to be thin sheetlike particles [Hudson et al., 2008a]. In a recent paper, we proposed that IR line profiles might be used with T-matrix theory to infer the general characteristics of mineral dust aerosol shape distributions. The details of the fitting procedure are described in Kleiber et al. [2009]. Briefly, simulated IR spectra were calculated using the NASA T-matrix codes [Mishchenko and Travis, 1998]. Simulations were based on measured size distributions and known mineral optical constants. For each dust, IR extinction calculations were carried out for a range of spheroid AR parameters. These results served as “spectral basis functions.” We then employed a least squares fitting procedure to find the best fit linear combination of basis functions (AR shape parameters) to fit the observed IR line spectra. The second shape distribution model considered in this study is determined from this IR spectral modeling procedure and includes more extreme AR values as shown in Figure 2b. It consists of a uniform (flat) distribution of oblate and prolate spheroids ranging from AR = 4 (prolate) to AR = 6 (oblate). (This corresponds to the so-called “Window” model distribution of [Kleiber et al., 2009]).

[22] Figure 2 shows the results from IR extinction studies for quartz dust in comparison to simulations based on these different particle shape models. In each case, the left side shows the shape histogram and the right side shows the corresponding spectral fit to the Si-O stretch resonance absorption line for quartz dust. The spectral fit using the moderate shape distribution model of Figure 2a is quite poor. Clearly, fitting the IR spectral line profile for our quartz dust sample requires extreme particle shape parameters with AR > 3 as shown in Figure 2b.

[23] In the next section, we use these shape distributions to compare T-matrix theory simulations with experimental light scattering data at several visible wavelengths. We assume a specific particle shape distribution (SEM-based or IR-based) as noted above and use the known optical constants and measured size distributions to calculate the visible scattering phase function and linear polarization profiles. This comparison allows an important internal consistency check on the particle shape distributions inferred from the IR spectral data. It may not be obvious why IR extinction profiles associated with specific vibrational resonance modes should be correlated with particle shape effects on visible light scattering. However, the influence of particle shape on IR extinction line profiles is largely a consequence of surface resonance enhanced IR scattering (rather than absorption), making a correlation with visible light scattering results less surprising [Bohren and Huffman, 1983].

4. Results

[24] Results at different scattering wavelengths are summarized in Figures 35, where phase function and linear polarization data are compared with different model simulations at scattering wavelengths of 470, 550, and 660 nm, respectively. At each wavelength, two different model simulations are presented: the moderate SEM-based and the more extreme IR-based shape distributions shown in Figure 2.

Figure 3.

Comparison of (a) experimental scattering phase function and (b) polarization profiles at 470 nm with T-matrix simulations based on different particle shape models: the moderate SEM-based and the extreme IR-based model. Phase functions in Figure 3a for different shape models are offset by factors of 10 for clarity.

Figure 4.

Caption as in Figure 3 but at a scattering wavelength of 550 nm.

Figure 5.

Caption as in Figure 3 but at a scattering wavelength of 660 nm.

[25] The experimental and theoretical phase functions, F(θ), are each normalized according to the condition:

equation image

Results for the different shape models in Figures 35a are offset by a factor of 10 for clarity. Because the experimental and simulated phase functions are normalized, and since the simulations are based on known optical constants and measured particle size and shape distributions, the results shown in Figures 35 are absolute fits of experiment to theory with no adjustable parameters. While the T-matrix phase function simulations based on the different particle shape distributions appear roughly similar to one another in quality, a χ2 analysis (Table 1) shows that the IR-based shape distribution gives a much better overall fit at all three wavelengths.

Table 1. Reduced χ2 Values for Comparison of the Experimental Phase Functions with Simulations Based on Different Particle Shape Models, the Moderate SEM-Based and the Extreme IR-Based Model
Wavelength (nm)Full Angle RangeBackscattering Angles (θ > 150°)
SEM-BasedIR-BasedSEM-BasedIR-Based
4707.31.116.50.1
55010.61.062.21.0
66012.20.631.93.7

[26] To quantify the goodness of fit between the theoretical model results and experimental phase function data, we calculated a reduced χ2 factor:

equation image

In (2)Xi is the measured phase function, Ti the corresponding model prediction, σi is the estimated experimental uncertainty, all at a given scattering angle θi, and N is the number of angle data points. The reduced χ2 values for the different model simulations are shown in Table 1. It is apparent that the IR-based model (or indeed any of the extreme model shape distributions based on the IR spectroscopic analysis described in Kleiber et al. [2009]) offers a much better fit to the data than the more moderate SEM-based shape distribution. The IR-based model shows excellent agreement with the experimental phase function data and very good agreement with the polarization data for all three wavelengths.

[27] For radiative balance calculations and remote sensing dust retrievals, particle backscattering is an important scattering property. It is clear from Figures 35 that errors associated with particle shape effects are most pronounced at large (near back-) scattering angles. Table 1 also gives the χ2 comparison between different particle shape models for scattering angles θ > 150°, where the model differences are much more significant. The SEM-based shape model significantly overestimates the degree of backscattering; the extreme shape model derived from the IR spectral analysis gives much better agreement with the data at backscattering angles.

[28] Polarimetric data is significantly more sensitive to extreme particle shape effects than the phase function. The polarization profiles in Figures 35b show even more dramatic differences between the model shape distributions. At each wavelength, simulations based on the moderate SEM-based shape distribution show extremely poor agreement with experiment, while agreement between experiment and the T-matrix simulation based on the extreme IR-based shape distribution is excellent.

[29] Over the spectral range covered in these experiments, 470–660 nm, spectral differences in the polarization profiles are observable. In particular, it should be noted that the observed linear polarization for near right-angle scattering, θ ∼ 90°, increases from P = +17% to +28% as the scattering wavelength is varied from 470 to 660 nm. This variation is very well modeled in the T-matrix simulation for the extreme IR-based particle shape model, which predicts a polarization increase from +18% to + 27% over this spectral range.

[30] There are uncertainties in both the experimental and simulation results as indicated by the reported error bars in Figures 35. Experimental uncertainties include both random and systematic errors. The random errors are obtained from the range of scatter in the measurements from run-to-run and week-to-week; systematic errors are associated with possible system calibration and phase function normalization errors. These uncertainties have been discussed in detail in Curtis et al. [2007, 2008]. Because the polarization data involve a relative rather than an absolute measurement, possible systematic errors in the polarization profiles are less significant.

[31] The error bars shown in the theoretical model simulation results of Figures 35 include an estimate of the possible systematic errors associated with both residual uncertainties in the input size distribution and with possible convergence errors associated with the large diameter cutoff parameter in the numerical integration over the size distribution. These theoretical uncertainties are relatively small, especially for the phase function data. To estimate possible errors in the scattering associated with the input size distribution, we have carried out theoretical simulations for a range of log normal distribution fit parameters that cover the range of uncertainties in the experimental sizing results [Curtis et al., 2007, 2008]. These errors are relatively small because scattering is dominated by the large particle part of the distribution, which is directly measured with the APS.

[32] Additional uncertainties in the T-matrix simulations are associated with possible convergence limitations in the code. The simulations include an integration over the particle size distribution, requiring minimum and maximum diameter cutoff values. Because small particles do not scatter efficiently, the results are relatively insensitive to the choice of minimum cutoff diameter. As noted in the Experimental Methods section, the largest particles in the aerosol flow have a maximum diameter Dmax ∼ 2.7 μm. Model calculations for the moderate SEM-based shape distribution converge over the full range of particle diameters out to this maximum. However, for the most extreme particle eccentricities in the IR-based distribution (AR > 5), the T-matrix code failed to converge over the full size distribution to Dmax. In these cases, a slightly lower cutoff value (corresponding to Dcutoff ∼ 2.2 μm) was necessary to ensure code convergence. To estimate the error associated with this convergence limitation, we note that as the cutoff diameter in the calculation is increased, the simulations for the phase function and polarization profiles each converge. This is because the number of particles in the larger size bins is rapidly decreasing. By comparing differences in the simulation profiles for successive cutoff values, Dcutoff, we can estimate the rate of convergence and thereby place an upper limit on the resulting convergence error. On the basis of this analysis, we find an upper limit on the convergence error that is roughly an order of magnitude smaller than the errors associated with the uncertainty in the size distribution itself. We note in passing that for more extremely shaped or larger particles than those in this study, convergence difficulties can present a more serious limitation on the use of the T-matrix method. The error bars shown in the theoretical simulations of Figures 35 include both the size distribution and convergence limit uncertainties.

[33] Other particle shape models have been explored as well. In earlier work, we quantitatively investigated the errors associated with the use of Mie theory for spherical particles in modeling the optical properties of mineral dust aerosols in both IR extinction and visible light scattering experiments [Hudson et al., 2007, 2008a, 2008b; Curtis et al., 2007, 2008]. We also evaluated a shape model that has often been used in the past as a model for generic atmospheric dust [Mishchenko et al., 1997], consisting of a uniform distribution of oblate and prolate spheroids with AR ≤ 2.4. Because this generic distribution has a slightly higher average AR value (mean AR = 1.8), it gives slightly better results than the SEM-based model for our quartz sample described here; however, the fits to both the experimental IR resonance spectra and the visible scattering phase function and polarization data are still quite poor [Kleiber et al., 2009] with this model.

5. Discussion and Conclusions

[34] There has been significant work in modeling the optical properties of irregularly shaped dust particles through the use of advanced light scattering theories, including T-matrix theory, DDA, FDTD, and GOM methods [Draine and Flateau, 1994; Kalashnikova and Sokolik, 2004; Mishchenko et al., 1997; Dubovik et al., 2006; Yang and Liou, 1996a; Yang and Liou, 1996b]. These approaches each involve different approximations and have different limitations. However, all require assumptions about the dust particle shape distribution to use as input.

[35] T-matrix theory with the uniform spheroid approximation has been used here because of its computational efficiency and because it is readily adapted to the range of particle sizes important in these experiments. While the T-matrix approach has been commonly applied to model atmospheric dust, it remains an open question whether calculations based on a uniform spheroid approximation can accurately model the optical properties of real atmospheric mineral dust, which often consists of mixtures of particles with highly irregular shapes that may include sharp edges, points, and internal voids. For example, some work has suggested that the neglect of sharp edges inherent in the assumption that particles can be treated as smooth spheroids may lead to errors that could be appreciable in some cases [Kalashnikova and Sokolik, 2002]. Other workers have argued that the errors in the scattering phase function resulting from the spheroidal particle assumption may not be large [Kahnert and Kylling, 2004].

[36] Our light scattering results for quartz dust aerosol in the accumulation mode size range show quantitative agreement at all three wavelengths (470, 550, and 660 nm) between experimental light scattering data and T-matrix simulations based on the extreme shape distributions derived earlier through analysis of IR spectral line profiles. Since the optical constants for quartz are known, the size distributions were measured, and the shape distributions were previously determined, the comparison between experiment and theory is absolute, with no adjustable parameters. χ2 analysis suggests that the T-matrix model based on the uniform spheroid approximation can be used with confidence to model the optical properties of highly irregular quartz dust aerosol particles in the accumulation mode size range, provided the shape distribution includes spheroids with extreme axial ratios (AR > 3).

[37] Particle shape distributions derived from electron microscope image analysis, however, give poor fits to the data. Our work suggests that two-dimensional images of dust may not give an accurate representation of the shape distribution for three-dimensional particles. This is significant because all modeling approaches require some assumption about the dust particle shape distribution to use as input. Errors in these input distributions can compromise the conclusions from any theoretical scattering model. However, simulations based on particle shape models inferred from IR spectral analysis give excellent fits to the experimental data, both the scattering phase function and the polarization profiles. These results offer compelling evidence to support the suggestion that IR spectral line shapes may be useful for inferring the general characteristics of aerosol particle shape distributions [Kleiber et al., 2009].

[38] Our spectral modeling shows that the mineral dust samples we have investigated manifest shape distributions that often include particles with very high eccentricities [Kleiber et al., 2009]. Quartz dust, studied here, is a major component of atmospheric aerosol. If these laboratory results can be generalized more broadly to real atmospheric dusts, then modeling the optical properties of mineral aerosol for climate forcing and remote sensing data retrievals may require similarly broad shape distribution models that include highly asymmetric particles as suggested by others [Veihelmann et al., 2004].

[39] These studies also point the direction toward developing algorithms that use correlated IR extinction and visible polarimetry data from satellite- or ground-based field instruments, together with theoretical light scattering simulations, to more accurately characterize atmospheric dust composition, size, and shape distributions. Such information is critical for determining dust burdens in the atmosphere and for modeling the radiative transfer effects of atmospheric dust.

[40] The results presented here are for mineral aerosols in the accumulation mode size range, with D < 3 μm, corresponding to the size range important for long-range atmospheric transport [Prospero, 1999]. In major dust events, a large fraction of the aerosol will fall in the coarse mode size range with D > 3 μm. Furthermore, this dust will generally consist of a complex, inhomogeneous mix of different minerals. Silicate clays are dominant in dust samples from many regions [Sokolik and Toon, 1999] and have very different shape properties [Kleiber et al., 2009] and may also have iron-containing inclusions that can significantly alter the visible optical properties. In future work, we plan to extend this approach to more complex authentic dust samples and samples that include larger particles to determine whether the results presented here can be generalized. As noted, larger and more highly eccentric particles can present a special challenge for T-matrix theory because of convergence limitations in the code. However, it is important to point out that the IR analysis for particle shapes can be extended to much larger particle diameters because of the longer wavelengths in the IR. (The same dimensionless size parameter, X = 2πD/λ, corresponds to a much larger particle diameter in the infrared.) It is also important to note that this general approach does not require the use of T-matrix theory. In principle, any light scattering theory for nonspherical particles could be used in the visible scattering analysis. In future work, we will explore the use of GOM or hybrid T-matrix + GOM methods for treating larger particles [Yang and Liou, 1996b; Dubovik et al., 2006].

[41] While the discussion here has been restricted to particles in the accumulation size mode, the conclusions drawn above are significant nonetheless: The use of particle shape distributions based on analysis of electron microscope images may lead to serious errors in calculating the IR extinction and visible light scattering properties of mineral aerosols; in favorable cases, IR spectral measurements, combined with visible light scattering and polarimetry, may offer a useful alternative method for determining the general characteristics of the aerosol shape distribution.

Acknowledgments

[42] This research was supported in part by the National Science Foundation under grant ATM-042589. One of the authors (BM) was supported in this project through a NASA Earth and Space Science Fellowship (NESSF).

Ancillary