Experimental infrared resonance absorption line profiles are compared with results from T-matrix theory calculations for several mineral components of atmospheric dust (illite, kaolinite, montmorillonite, quartz, and calcite). The model results are used to infer general characteristics of the aerosol particle shape distribution. For the silicate clays the spectral line profiles are best fit by a shape distribution of highly eccentric oblate spheroids, consistent with the expected sheet-like nature of the clay minerals. For quartz dust the spectral line profiles are best fit by a very broad distribution including both extreme oblate and prolate spheroids. For calcite a spheroid model with moderate shape parameters gives the best fit. Our results suggest that high-resolution IR extinction measurements may offer useful insight into the shape distributions of atmospheric mineral dust.
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 It is well established that the optical properties of dust particles are strongly dependent on particle shape [Bohren and Huffman, 1983; Mishchenko et al., 1997], and this constitutes a major source of uncertainty in dust retrievals from remote sensing measurements [Dubovik et al., 2006]. There has been a great deal of progress in recent years in modeling the effects of particle nonsphericity on dust retrievals from satellite data [Dubovik et al., 2006; Mishchenko et al., 2003; Kalashnikova et al., 2005]. The most common approach is to use T-matrix methods based on a spheroidal particle assumption. Spheroid shape can be characterized by a single parameter, the axis ratio (AR), given by the ratio of the lengths of major to minor axes. Important questions remain, however, regarding the possible limitations of the uniform spheroid approximation to modeling the optical properties of real atmospheric mineral dust, which can consist of inhomogeneous mixtures of highly irregular particles.
 One of the primary challenges in these efforts is to unravel the effects of particle size, shape, and composition and, in particular, to determine an effective particle shape distribution for use in the models. For example, Veihelmann et al.  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. More recently, Dubovik et al.  have used T-matrix based methods to model both laboratory scattering data of mineral dust and dust retrievals from AERONET observations. They find good fits for retrievals of aerosol scattering phase function and polarization data for particle shape distributions with moderate axis ratios (AR ≥ ∼1.44). However, it is also interesting to note that the shape distributions derived from their data show tails that appear to extrapolate to AR values much greater than ∼3.
 Particle shape effects can also lead to significant changes in IR resonance spectral line positions and line shapes, even for particles that fall in the Rayleigh regime, D ≪ λ, where D is the particle diameter and λ is the wavelength of light [Bohren and Huffman, 1983; Hudson et al., 2008a, 2008b]. Neglect of these particle shape effects in spectral modeling could lead to errors in atmospheric dust loading or composition measurements that are based on analysis of IR remote sensing data.
 In a recent series of experiments we measured aerosol IR extinction spectra for a range of important components of atmospheric mineral dust including silicate clays (illite, kaolinite, and montmorillonite) and nonclay minerals (quartz and calcite) [Hudson et al., 2007, 2008a, 2008b]. Simultaneously, with the IR spectra, we measured the full aerosol size distributions. Because the aerosol composition and size distributions were known we were able to carry out absolute comparisons between theoretical model simulations and experimental spectra with few adjustable parameters.
 In our previous work we directly compared experimental IR spectra with simulations based on Mie theory and with results from a simple analytic model for absorption by small particles of characteristic shapes (e.g., disks, needles) [Hudson et al., 2008a, 2008b]. The analytic model results were derived in the Rayleigh limit (D ≪ λ) and are described in detail by Bohren and Huffman . Some important conclusions were drawn from these studies. Overall, Mie theory gives generally poor agreement for resonance peak positions and lineshapes for mineral aerosols in the accumulation mode size range with diameters, D ∼ 0.1–3 μm. The quantitative breakdown of Mie theory in the resonance region is due to the nonspherical shape of the mineral dust particles. Our results suggest that, for mineral aerosols in the accumulation mode, IR absorption line shapes may be better fit by the crude Rayleigh model results for characteristic particle shapes [Bohren and Huffman, 1983], despite the fact that particles in this size range may not strictly satisfy the Rayleigh criteria, D ≪ λ. Specifically, we found that the prominent Si-O stretch resonance absorptions for the silicate clays near λ ∼ 9–10 μm are better fit by assuming the particles are described by a distribution of disk shapes. The disk shape model gives a better quantitative match to the resonance line peak positions, core lineshapes, and integrated line strengths for the fine clay aerosols in this study (illite, kaolinite, and montmorillonite) [Hudson et al., 2008a]. Analogous results are found as well for the nonclay mineral aerosol components that we studied (quartz and calcite), although in these cases it is found that a “continuous distribution of ellipsoids” model for particle shape gives a better overall fit [Hudson et al., 2008b]. Thus, there appears to be a systematic correlation between mineralogical composition and effective particle shape as reflected in the observed IR resonance absorption spectra.
 For accumulation mode particles the analytic model results for characteristic particle shapes give consistently better agreement with the experimental data than Mie theory for spherical particles. However, these analytic models, which are derived in the Rayleigh limit, fail badly for larger particles in the coarse mode size range (D > ∼3 μm) [Mogili et al., 2007a]. Better spectral agreement might be obtained through the use of more rigorous and advanced light scattering models such as T-matrix theory, which allows more flexibility in specifying particle shape and can be more readily extended to larger particles [Mishchenko et al., 1996, 2002]. In this paper we explore the use of T-matrix theory to analyze IR spectral line shapes for mineral aerosols. In particular we investigate whether IR spectral line profiles can be used with T-matrix theory to infer aerosol particle shape distributions. If so, then high-resolution IR satellite data from instruments such as AIRS may offer an additional check on aerosol particle shape and composition retrievals.
 The experimental results are all taken from our earlier works. The experimental methods have been fully described by Hudson et al. [2007, 2008a, 2008b]. Essentially, we used an atomizer to aerosolize well-characterized particle samples of specific minerals. The mineral dust samples were entrained in a flow that passed through a drying tube and then through long path IR extinction cell. Extinction measurements were carried out with a Thermo-Nicolet Model 670 Fourier transform infrared spectrometer. After the extinction cell the aerosol flow was split and the particle-size distributions were measured with a combination of aerodynamic particle sizing and scanning mobility particle sizing instruments that together cover the size range 20 nm to 20 μm. The particle-size measurements were converted to volume equivalent sizes as described in our earlier papers. The mass weighted mean particle diameters (MMD) for these samples fall in the range 0.4–0.7 μm.
 We have used the extended precision T-matrix code of Mishchenko and others [Mishchenko and Travis, 1994, 1998; Wielaard et al., 1997], available through the NASA Web site (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 the well-characterized single-component mineral samples used in our work are available in the published literature. In our previous work we used the experimentally measured size distributions in the theoretical modeling analyses [Hudson et al., 2008a, 2008b]. In order to facilitate the T-matrix modeling here, we have used log normal fits to the experimental size distributions. (Mie theory spectral comparisons between the results using the measured size distributions and the best fit log normal size distributions show no significant or systematic differences.)
 The NASA T-matrix code is written to handle different models for particle shapes. We limited our investigations to spheroidal particles, which, as noted in section 1, can then be characterized by a single shape parameter, the axis ratio AR = (a/b), where a is the major axis and b is the minor axis. With this definition AR = 1 for a sphere and AR > 1 for spheroids of varying eccentricity, either oblate or prolate. For prolate (oblate) spheroids a (b) refers to the rotational symmetry axis, and b (a) refers to the degenerate transverse axis. For comparison to the analytic Rayleigh model results from our previous work, distributions with AR ≫ 1 approach the “needle” shape results for prolate spheroids and the “disk” shape results for oblate spheroids. The T-matrix code can fail to converge for large and highly eccentric particles. The maximal convergent size parameter X = πD/λ (where D is the particle volume equivalent diameter and λ is the wavelength of light) depends on the AR value [Mishchenko and Travis, 1998]. It is also important to note that, because we are working at infrared wavelengths, λ ∼ 10 μm, convergence can be reached for particles with larger volume equivalent diameters for a given AR than in the visible. Our results were checked for convergence with respect to various computational parameters.
 In this project we have run the T-matrix code for each mineral dust sample to model the IR resonance region for our particle-size distributions and for a grid of different AR values, i.e., different particle shapes. The AR grid spacing depends on the particular dust sample as noted in section 4. Typical spectral line shapes for a set of different AR parameters are shown in Figure 1 for the examples of kaolinite and quartz dusts, respectively. In each plot of Figure 1 the experimental extinction profile is also shown as a dashed line. Note the significant changes in peak position and line profile as the AR parameters are varied through a range of oblate and prolate shapes.
 We use the calculated line profiles for different AR values (such as those shown in Figure 1) as “spectral basis functions” and employ a least squares fitting procedure to find the best linear combination of basis functions to model the experimentally observed line shapes. In effect we seek the best fit particle shape distribution to simulate the experimental line profile. From the results shown in Figure 1 it is evident that the best fit shape distributions for both kaolinite and quartz will need to include spectral basis functions with relatively high AR values (AR > 2) in order to fit the experimentally observed peak positions.
 In each case we have carried out an “unconstrained” least squares analysis that simply determines the best linear combination of shape parameters to fit the data without applying any predetermined model for the shape distribution. As will be seen below, these unconstrained fits give useful insight into the range of shape parameters needed to simulate the experimental line profiles. The results, however, often show unphysical structure in the shape distributions. In order to superimpose a more physically reasonable envelope onto the shape distributions, we have also carried out least squares analyses where we constrain the distribution to different models: (1) a Gaussian shape distribution function and (2) a square Window function, each with adjustable AR center and width parameters. In every case comparable agreement between experiment and simulation can be obtained between the unconstrained and different constrained model solutions. This shows that our approach does not yield a unique shape distribution. Nevertheless, there are clear and significant conclusions about the general characteristics of the particle shape distributions that can be drawn from these analyses.
 For comparison purposes we also present results from a shape distribution model that is restricted to more moderate particle shapes. This model has been commonly applied to simulate the optical properties of mineral aerosols for modeling the effects of dust in the atmosphere [Mishchenko et al., 1997]. The moderate shape distribution model assumes a uniform distribution of both oblate and prolate spheroids with AR parameters ranging from 1.2–2.4 (in steps of 0.2). This limited AR range is based on field measurements of aerosol particle shape distributions including analyses of electron microscope images of atmospheric dust carried out by several groups. This moderate shape model and its applicability will be discussed in more detail in section 5.
4.1. Silicate Clays (Illite, Kaolinite, and Montmorillonite)
 Different shape distribution model results are compared to the experimental resonance line spectra for the silicate clays in Figures 2 and 3. Clay optical constants were taken from Querry . In each case we also compare the results with simulations from the moderate shape distribution model as described in section 3 (1.2 ≤ AR ≤ 2.4). For the silicate clays it is necessary to include highly eccentric oblate ellipsoids to give the spectral shifts needed to adequately simulate the observed spectral line profiles. Because the AR range is so large, we have used a large AR grid spacing for the clay lineshape simulations, allowing the values to range up to AR = 20 for illite and montmorillonite (with a step size of 2) and up to AR = 12 (with a stepsize of 1) for kaolinite.
 The best fit shape distribution results for kaolinite are shown in Figure 2a. The unconstrained model fit shows a distribution of oblate spheroids that is peaked at AR = 5 and extends over the range AR = 1–9. The Gaussian distribution peaks at a mean AR of 5.3 with a width of 2.8, while the Window distribution covers the AR range 3–8. The spectral line profiles derived from these different “extreme” shape models are shown in Figure 2b (solid) in comparison with the experimental line profile (points) and the more restricted “moderate” shape distribution model (AR ≤ 2.4, dashed). The spectral results for the unconstrained, Gaussian, and Window models closely overlap and cannot be distinguished in Figure 2b. Similar agreement in the simulated line spectra for the different shape models (unconstrained versus Gaussian versus Window) is found for all of the silicate clay dust samples studied here.
 For illite and montmorillonite our analysis shows that even more extreme eccentricities are needed in the fits. The unconstrained fit results lie in the range AR ∼ 12–18 for both illite and montmorillonite. The best fit Gaussian and Window distributions are sharply peaked at the values of AR = 18 ± 1 for illite and AR = 14 ± 1 for montmorillonite. The spectral simulations shown in Figures 3a and 3b are for the Window model, but the unconstrained and Gaussian model distributions give essentially identical simulated spectra.
4.2. Nonclay Minerals (Calcite and Quartz)
 Results for the nonclay minerals calcite and quartz are summarized in Figures 4 and 5, respectively. Optical constants for quartz are taken from Longtin et al.  and for calcite from Lane . Results for calcite dust aerosol are shown in Figure 4. Here it appears that the moderate shape model with AR ≤ 2.4 gives a good fit to the spectral data (as does Mie theory for this dust sample). Our spectral analysis gives results consistent with the more moderate shape distribution, with the unconstrained model showing a preference for slightly prolate spheroid shapes with a maximum at AR = 1.2 (prolate). The result for the corresponding Window model fit (which ranges from 1.2 (oblate) to 2.6 (prolate)) is shown in Figure 4, but the unconstrained and Gaussian models give essentially identical profiles. From this discussion it should be clear that the spectral simulation method we employ is not extremely sensitive to small changes in the shape parameters. As a result, for a case like calcite where there is not a lot of detailed substructure in the IR spectrum and where moderate AR values suffice to fit the spectrum, it is difficult to discriminate among different plausible shape distributions. The spectral simulations for calcite shown in Figure 4 are not markedly different from the results of a Mie theory calculation.
 The shape analysis results for quartz dust are shown in Figure 5. It is evident from the “basis functions” shown in Figure 1b that highly eccentric ellipsoids must be included in the distribution in order to red shift the resonance peak position by ∼35 cm−1. In this case no single basis function (or narrow range of AR parameters) does a good job of fitting the profile; rather the best fit shape distributions cover a very broad range of both prolate and oblate spheroids. Again, because of the extended range, we have used a large grid spacing with an AR step size of 1. The best fit shape distributions are shown in Figure 5a. The unconstrained model shape model ranges from AR = 6 (prolate) to AR = 10 (oblate) and slightly favors oblate shapes. The simple Window model distribution covers the range AR = 4 (prolate) to AR = 6 (oblate), while the Gaussian peaks at AR = 2.3 (oblate). In this case there are slight differences observable in the simulated spectra for these different shape distribution models as seen in Figure 5b. These slight differences result from the use of the fairly wide grid spacing coupled with the very sharp nature of the resonance absorption peak in quartz. Nevertheless, it is clear that the moderate shape model does a poor job in fitting both the peak position and overall line profile. An extended range of extreme shape parameters is needed to adequately model the observed IR resonance line spectrum.
 We cannot uniquely determine the aerosol particle shape distribution from this spectral analysis. Nevertheless, our results suggest that we can infer some general characteristics of the shape distributions and that there appear to be systematic shape differences between the silicate clay minerals and the nonclay minerals (calcite and quartz). It seems reasonable to expect that the underlying crystalline structure of the minerals may be reflected in the shape of dust particles in the sample.
 Our analysis for the silicate clays is consistent with a shape model consisting of highly eccentric oblate spheroids, with axis ratios ranging as high as AR ∼18 for illite and ∼14 for montmorillonite. These results are consistent with the expected sheet-like mineral structure of the silicate clays. Indeed independent shape analyses by Nadeau [1985, 1987] and others [Farmer, 1974, 1998] have suggested that small clay particles consist of thin plate-like particles; in particular, Nadeau finds typical average diameters in the range 120–1900 nm with thicknesses in the range 1–10 nm, corresponding to AR ratios > 12 (and perhaps ≫ 12). Our results here also suggest why the simple analytic model for disks works so well for the clays.
 The quartz results are also interesting and show that a very broad distribution of shapes including both prolate and oblate spheroids is needed to fit the observed line profiles. In this context it may be noted that natural quartz often forms disorganized groups of crystals with complicated irregular shapes.
 Our spectral modeling results are intriguing and suggest that the mineral dust samples we have investigated manifest shape distributions that, in many cases, include particles with very high eccentricities. Similar conclusions were reached by Veihelmann et al.  through an analysis of visible scattering and polarimetric data. Indeed, if our laboratory results can be generalized to 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. However, more work needs to be done to investigate this question.
 One issue that must be addressed is whether the literature optical constants may be in error. For some dust samples there is more than one available refractive index data set (e.g., quartz [Longtin et al., 1988; Spitzer and Kleinman, 1961; Wenrich and Christensen, 1996], calcite [Lane, 1999; Long et al., 1993], and kaolinite and montmorillonite [Querry, 1987; Roush et al., 1991]). We have investigated these differences between optical constant data sets in our previous work. Variations between data sets lead to small differences in the fine details of the resonance spectral line peaks. In addition, for birefringent minerals there can be differences in the simulated spectra depending on how the birefringence effects are included [Hudson et al., 2008b]. The spectral differences associated with the use of different optical constants, however, are generally much smaller than those resulting from different assumptions about particle shape. For example, we note that the observed shifts in resonance line peak positions from the theoretical Mie-predicted values (or from the moderate shape distribution model T-matrix simulations) are often ∼30–40 cm−1, and these large shifts cannot be effected by simply choosing a different optical constant data set for the analysis; differences in resonance peak position from different refractive index data sets are typically <10 cm−1. There is a notable exception to this discussion. Optical constants derived from measurements on powder or pellet samples sometimes show better agreement with data on aerosols than optical constants from bulk crystal samples because, in effect, the particle shape information can be incorporated into the optical constants. While this might offer an empirical “out” for dealing with the difficult problem of particle shape it is important to recognize that the result will depend on the details of the powder sample such as the size distribution and preparation methodology. Furthermore, here we are specifically interested in exploring what we might learn from the particle shape effects and choose not to hide those effects in the optical constants.
 Another issue that must be addressed is whether our particle samples are truly representative of atmospheric mineral dust. The spectroscopic results analyzed here are based on studies of laboratory dust samples aerosolized in an atomizer from a slurry of mineral dust in water. This aerosol generation method gives stable aerosol flows at high particle densities, but the range of dust particle diameters is limited by droplet size. For our mineral samples the size distributions show the MMD in the range ∼0.4–0.7 μm, i.e., in the accumulation mode size range. It is important to investigate whether these shape distribution results can be generalized to larger particles that may be more atmospherically relevant.
 In this regard we note that in other work we have also studied IR spectral line shapes for these mineral aerosol samples in an atmospheric simulation chamber that allows for measurements on larger particles [Mogili et al., 2007a]. In those experiments a sample of dry mineral dust powder was blown into the chamber with a high pressure gas pulse and extinction (from the IR to the UV) was measured as a function of time as the dust settled over the course of several hours. The size distributions were not directly measured but rather were adjusted to fit the observed IR-UV scattering extinction profiles [Mogili et al., 2007b]. In those experiments, the size distributions showed MMD ranging from ∼2 to ∼20 μm, depending on mineral sample.
 To test whether our particle shape distribution results may be generalized to larger particles, we simply used the Window shape distributions derived in section 4 for the “small particle” samples to simulate the line profiles for the “large particle” samples. (The only adjustable parameters in the simulation then are the extinction peak heights, which are determined by the different particle number densities in each experiment.) Results for illite (MMD ∼2.4 μm) and kaolinite (MMD ∼3.2 μm) are shown in Figure 6. These results show that the characteristic shape distributions derived from smaller particle dust samples also work well to model the line shapes for large particle samples. Unfortunately, for the montmorillonite (MMD ∼12.0 μm) and quartz (MMD ∼14.0 μm) dust samples, where the distributions extend to both very large particle diameters and very high AR values, we were not able to achieve convergence in the T-matrix calculations over the full range of the distributions. Even in these cases, however, the results are consistent with the general conclusions that very highly eccentric particles are needed to adequately model the IR resonance line profile data. On the basis of this we believe it likely that the characteristic shape distributions we have found here can be generalized to larger particles, at least for the diameter range up to ∼5 μm.
 It is also important to ask whether our laboratory dust samples might show unique shape characteristics that are not reflective of atmospheric aerosols. Shape distributions for atmospheric mineral aerosols are commonly investigated through analysis of scanning electron microscope (SEM) images of dust samples collected on filters. The two most commonly reported shape parameters obtained from the SEM images are aspect ratio and circularity [Kalashnikova and Sokolik, 2004]. Circularity is defined as the [P2/(4πA)], where P is the perimeter and A is the area. For irregular dust particles the aspect ratio is defined as the maximum projection (length of the longest projected dimension) divided by the width (the largest length perpendicular to the maximum projection). The aspect ratio is then closely related to the axial ratio used here to define the shape for spheroidal particles. Several studies of atmospheric mineral dust samples collected on filters and imaged by electron microscopy have found aspect ratios that typically lie in the range 1.2–2.4 with the average in the range 1.4–1.8 [Nakajima et al., 1989; Okada et al., 2001; Buseck et al., 2000; Hill et al., 1984]. These results, based on field samples, have served as the basis for specifying the restricted particle shape distributions commonly used in modeling shape effects in simulations of the optical properties of dust aerosols [Mishchenko et al., 1997].
 For comparison purposes, SEM images for our silicate clay particle samples were presented in our earlier paper [Hudson et al., 2008a]. An SEM image for our quartz sample is shown here in Figure 7. In each case the samples were collected directly from the aerosol flow stream. The clay samples show aspect ratio values (determined from the two-dimensional (2-D) SEM images) that ranged up to a maximum AR of <3 with a mean value of ∼1.6, consistent with typical results from field sample measurements. Note that there is, in those images, no evidence for the extremely high AR values determined from the spectral fitting. Similarly, the quartz image shows particle AR values that range up to a maximum of <3 and a mean of ∼1.5. Again, these values are consistent with typical results from SEM images of field dust samples. It is not entirely clear why the shape parameters determined from the spectral line fitting are so markedly different from those seen in the SEM images. But this does raise an important question, namely, can shape parameters determined from 2-D images accurately reflect the shape of real 3-D particles? In this context, note that an extremely oblate spheroidal particle lying flat on a surface will present a 2-D image with an aspect ratio of AR ∼ 1.
 In order to eliminate uncertainties and to effect a rigorous quantitative test of the optical properties of mineral aerosols, we focused our laboratory experiments on well characterized samples of single component minerals. Atmospheric dusts, in contrast, often consist of inhomogeneous mixtures of different minerals. This could certainly impact the particle shape distributions. In addition, atmospheric aerosols are subject to weathering and aging. For example, images of Saharan sand shown by Volten et al.  show particles that appear much more spherical than those seen in the images of other dust samples studied in that work. This is presumed to be a result of wind erosion. In addition, chemical processing of dust can occur in the atmosphere, and this can also affect particle shape. For example, calcite is highly reactive and dust particles with significant calcite loading may be dramatically affected by atmospheric chemical processing [Grassian, 2001]. Furthermore, some of the silicate clays (such as montmorillonite) are swellable, absorbing and holding water, which might impact the particle shape distribution. It will be important to carry out similar investigations of more authentic mixed and inhomogeneous mineral dust samples and to investigate the effects of physical and chemical processing of the particles, and we plan such experiments in the near future.
 This research was supported in part by the National Science Foundation under grant ATM-042589.