Optical properties, including infrared (IR) extinction and visible light scattering of mineral dust aerosol, are measured experimentally and compared to modeling results using T-matrix theory. The work includes studies of complex, authentic field samples of Saharan sand, Iowa loess, and Arizona road dust (ARD). Particle size distributions and aerosol optical properties are measured simultaneously. These authentic dust samples are treated as external mixtures of mineral components. The mineral compositions for the Saharan sand and Iowa loess samples have been reported by Laskina et al. , and the mineralogy for ARD is derived here using a similar method. T-matrix-based simulations, using measured particle size distributions and a priori particle shape models, are carried out for each mineral component of the authentic samples. The simulated optical properties for the complex dust mixtures are obtained by a weighted average of the properties of the mineral components, based on a given sample mineralogy. T-matrix simulations are then directly compared with the measured IR extinction spectra and visible light scattering phase function and linear polarization profiles for each sample. Generally good agreement between experiment and theory is obtained. Model simulations that account for differences in particle shape with mineralogy and include a broad range of eccentric spheroid shape parameters offer a significant improvement over more commonly applied models that ignore variations in particle shape with size or mineralogy and include only a moderate range of shape parameters.
 Atmospheric dust aerosol greatly affects the Earth's climate [Forster et al., 2007]. In particular, atmospheric aerosol directly affects radiative forcing by scattering and absorbing both incoming solar radiation and outgoing terrestrial infrared (IR) radiation. Mineral dust can also indirectly affect the climate, for example, by serving as ice and cloud nucleation sites or providing surfaces for heterogeneous chemistry. It is estimated that every year, on the order of 1000–2150 Tg of dust is blown into the atmosphere through wind action [Zender et al., 2004]. North Africa, the Middle East, Central Asia, and the Indian subcontinent are the largest contributors to the global mineral dust load [Prospero et al., 2002]. The most significant source of the total atmospheric dust load is North Africa, including the Sahara desert, which is estimated to contribute 62–73% of the global atmospheric dust load [Tanaka and Chiba, 2006; Luo et al., 2003]. Dust from the Sahara desert can be transported long distances, including to Northern Europe [Ansmann et al., 2003], the Mediterranean [Moulin et al., 1998], the Middle East [Ganor, 1994], and across the Atlantic to Barbados [Chiapello et al., 2005], South America [Prospero et al., 1981; Swap et al., 1992], and the eastern United States [Perry et al., 1997; Prospero, 1999; Yin et al., 2005]. Although not a major global source, the southwestern United States also periodically produces dust storms, resulting in mineral dust as a significant source of particulate matter pollution on regional scales [Prospero et al., 2002; Yin et al., 2005].
 In order to accurately model dust radiative transfer effects, information regarding aerosol concentration, composition, and particle size and shape distributions is needed. While much of these data can be inferred from satellite- or ground-based remote sensing measurements, the retrieval algorithms depend on accurate a priori estimates of the aerosol optical properties [Mishchenko et al., 2003; Kalashnikova et al., 2005; Koven and Fung, 2006]. Unfortunately, modeling the absorption and scattering properties of dust is complicated because atmospheric dust aerosol typically includes complex internal and external mixtures of different minerals that are often irregular in shape [Claquin et al., 1999; Okada et al., 2001; Durant et al., 2009; Nousiainen, 2009]. It has been shown that significant errors in remote sensing algorithms and climate forcing calculations can occur when Mie theory is used to model aerosol light scattering owing to the neglect of particle shape effects [Kahnert et al., 2005; Dubovik et al., 2002; Mishchenko et al., 1997; Hudson et al., 2008, 2008, Haapanala et al., 2012].
 Although many different theoretical approaches have been developed to simulate the absorption and scattering properties of irregularly shaped particles, significant challenges remain in applying these methods to light scattering by atmospheric mineral aerosol. For example, both discrete dipole approximation [Lindqvist et al., 2011; Nousiainen et al., 2009; Veihelmann et al., 2006] and finite difference time domain [Yang et al., 2000; Ishimoto et al., 2010] methods have been used to model the scattering properties of nonspherical, inhomogeneous particles, including the effects of fine scale surface features. However, these methods require significant computational resources, which limit their application to relatively small particles. Another approach, useful for modeling the light scattering of larger nonspherical particles, is based on a geometric ray optics approximation, which can also account for surface roughness. This method has been used to model light scattering from dust by approximating irregularly shaped particles as a distribution of Gaussian random shapes, triaxial ellipsoids, or nonsymmetric hexahedral prisms [Volten et al., 2001; Nousiainen et al., 2003; Muñoz et al., 2007; Bi et al., 2009, 2010; Meng et al., 2010; Nousiainen et al., 2011].
 T-matrix theory-based techniques, often coupled with the uniform spheroid approximation, have also been widely used to simulate atmospheric dust-scattering properties [Mishchenko et al., 1997; Nousiainen and Vermeulen, 2003; Nousiainen et al., 2006]. Spheroids are ellipses of revolution where the particle asphericity can be specified by the shape parameter, ξ, defined as shown in equation (1):
where ε is the major-to-minor axial ratio for oblate spheroids (ε ≥ 1) and its inverse for prolate spheroids (ε<1). While not essential to the theory, the spheroid approximation is often applied in T-matrix calculations because the orientational averaging is greatly simplified, making the method computationally efficient. Although the spheroid approximation may seem unrealistic, given the highly irregular shapes that often characterize natural mineral dust particles, it has been shown that spheroids can provide more flexibility in simulating the scattering properties than polyhedral prisms, and the spheroid approximation performs well compared to many other modeling approaches in fitting light scattering data [Nousiainen et al., 2006]. T-matrix methods, under the spheroid approximation, have been applied in both dust retrieval algorithms and climate forcing calculations [Dubovik et al., 2006; Mishchenko et al., 2004].
 These different theoretical methods provide important tools for modeling aerosol radiative transfer effects. However, determining an appropriate distribution of particle shapes as input to these models remains a significant challenge. Efforts using T-matrix theory have been devoted to finding spheroidal particle shape distributions that can reliably simulate the absorption and scattering properties of real mineral dust. Most of the prior research has been focused on fitting either the visible light scattering [Kahnert, 2004; Kahnert et al., 2005; Merikallio et al., 2011] or the IR extinction spectra [Kleiber et al., 2009; Hudson et al., 2008, 2008] of single-component minerals.
 Recently, our group has focused on understanding particle shape effects from both IR extinction and visible light scattering measurements for atmospherically relevant mineral dust components in the accumulation size mode, which is representative of long-range transport [Meland et al., 2010, 2012]. This work includes studies of silicate clays (illite, kaolinite, and montmorillonite), as well as nonclays, such as calcite and quartz [Curtis et al., 2008; Hudson et al., 2008, 2008; Kleiber et al., 2009]. For example, in studies of quartz aerosol, Meland et al.  showed that T-matrix-based simulations using a broad, equiprobable (flat-top) distribution of spheroids with shape factors in the range −3 ≤ ξ ≤ +5 give good model fits to the measured quartz dust IR extinction spectrum and visible light scattering data. More recently, Meland et al.  extended this work to model the absorption and scattering properties of kaolinite and illite, two important silicate clay minerals. Interestingly, the best overall agreement with experimental data was obtained by assuming a bimodal size shape distribution for the clay particles. In this approximation, small clay particles in the distribution were treated as highly aspheric oblate spheroids, while the larger particles were modeled as an equiprobable distribution of spheroids with more moderate shape parameters.
 While distributions of spheroids can provide a flexible basis for modeling the effect of particle shape on light scattering properties, it is not clear if the shape distributions that best fit the aerosol optical properties are correlated with the actual physical shapes of the particles as determined, for example, from electron microscopy. Indeed, there is good reason to doubt such a correlation [Nousiainen et al., 2011; Meland et al., 2010]. Certainly, electron microscope images of individual dust particles rarely look like smooth spheroids. However, our studies of modeling the effects of particle shapes do suggest such a correlation for small silicate clay particles. Mineralogical studies of clay particles by Nadeau [1985, 1987] have shown that small, base-unit clay particles are very thin flakes; this picture is consistent with the results from IR spectral analysis for silicate clays by Hudson et al.  using a Rayleigh scattering model, and more recent T-matrix results by Meland et al. .
 The goal of this work is to investigate if particle shape models, deduced in previous studies of single-component minerals, might provide a useful basis for modeling the optical properties of more complex, authentic dust samples. In this article, this approach is applied to model the optical properties of three such samples: Saharan sand, Iowa loess, and Arizona road dust (ARD). For each of these samples, experimental measurements of IR extinction spectra and visible light scattering profiles are compared with T-matrix simulations that account for particle shape effects and sample mineralogy.
 This article is organized as follows: In section 2, the experimental methods are described; experimental results are presented in section 3; in section 4, the general approach for the modeling analysis is outlined; in section 5, experimental results are compared with theoretical simulations using a priori particle shape models and mineral compositions that have been determined independently for each sample; and in section 6, the results are summarized and discussed.
2 Experimental Methods
 The experimental methods are described in earlier publications [Hudson et al., 2007; Curtis et al., 2007]. An atomizer is used to generate an aerosol flow of the dust. Excess water vapor is reduced by passing the aerosol through a set of drying tubes. The aerosol stream is then directed through either a long-path extinction cell of length of approximately 1 m, for Fourier transform IR (FTIR) spectroscopic measurements, or through a visible light scattering chamber for measurements of the relative scattered light intensity and linear polarization at a wavelength of 550 nm as a function of scattering angle. The scattered light profile is then normalized to give the scattering phase function using the methods described by Liu et al.  and Curtis et al. . The experimental data are limited by the physical geometry of the apparatus to an angle range of θ = 6° – 172°. For normalization purposes, the data are extended in the backward direction (θ>172°) by a linear extrapolation, and in the forward direction (θ<6°) by splicing the results of a T-matrix model simulation. The uncertainty in the phase function normalization that results from the extrapolation process is small and is included in the experimental error bars discussed below.
 Following the optical property measurements, the aerosol flow is directed to sizing instruments to monitor the particle size distribution in real time. An aerodynamic particle sizer (APS) and a scanning mobility particle sizer (SMPS) are used in parallel to measure the full particle size distribution over the range 20 nm to 20 µm. These instruments are calibrated with monodisperse polystyrene latex spheres. Because the SMPS and APS cover different ranges and measure different size-related physical properties, the measured size distributions must be combined and converted into a common diameter scale; the basic procedure for combining and scaling the sizing data from these instruments has been described in Hudson et al. . Size distribution results are reported in Table 1 as a function of the volume equivalent diameter. The aerosol size distribution also varies somewhat in time and with different aerosol flow conditions. Each of the optical properties data sets are analyzed using the size distribution measured simultaneously with the corresponding IR extinction or visible light scattering data. The same dust samples were used in both the IR extinction and visible light scattering experiments.
Table 1. Table of Log Normal Size Distribution Parameters That Best Fit the Measured (Volume Equivalent) Particle Size Distributions for Saharan Sand, Iowa Loess, and ARD in the IR Extinction and Visible Light Scattering Experiments
Visible (550 nm)
Here rm is the mode radius of the particle number size distribution, σ is the width parameter, and MWMD is the mass weighted mean particle diameter. In the visible light scattering experiments, the measured size distribution for the ARD sample showed a bimodal character and was modeled by a linear combination of two lognormal functions with the fitting parameters as given.
 Authentic surface dust samples of Saharan sand and Iowa loess were used in this work. The mineral composition of Saharan sand varies with source region [Avila et al., 1997; Caquineau et al., 2002; Thomas and Gautier, 2009; Formenti et al., 2011]; the Saharan sand sample used in this work was collected from the south central Sahara and analysis of the bulk sample (excluding particles >40 µm) has been discussed by Krueger et al. . The Iowa loess sample was obtained from the Loess Hills of western Iowa. In addition, a sample of ARD, often used as a simulant for complex authentic mineral dust mixtures, was purchased commercially from Powder Technology Inc. (Burnsville, Minn.) for this study.
 The samples of Iowa loess and ARD were used as received. However, much of the Saharan sand sample consisted of particles too large to pass through the flow system, and therefore a 100 µm sieve was used to filter out the extremely large particles from the sample prior to aerosolization. The particle size in the flow is further restricted by the atomizer to particle diameters less than ~2.5 µm, corresponding to aerosol in the accumulation size mode. A sample of each authentic dust was collected from the aerosol stream in order to measure the elemental composition using a Hitachi S-3400N Scanning Electron Microscope (SEM; Hitachi High Technologies America, Inc., Schaumburg, Ill.) coupled with an energy dispersive X-ray spectrometer (EDX).
3 Experimental Results
 Experimental IR extinction spectra and visible light scattering data for the samples of Saharan sand, Iowa loess, and ARD are shown as points in Figures 1, 2, and 3, respectively. The IR extinction spectra and the corresponding aerosol size distributions for Saharan sand and Iowa loess have been reported by Laskina et al. . The visible scattering results for all three samples, as well as the IR extinction spectra for ARD reported here, are new. Experimental error bars for the IR extinction spectra represent the typical spread in the data associated with run-to-run fluctuations. In addition, the experimental IR spectra have been corrected to eliminate a sloping baseline associated with the falling IR lamp intensity toward the low energy end of the spectrum, as discussed by Laskina et al. . The experimental error bars for the visible light scattering data include both random errors associated with day-to-day fluctuations and possible systematic errors due to uncertainties in the system calibration and response function. The random errors are obtained from the standard deviation (SD) from the mean for a series of data runs carried out over several days. The systematic uncertainties are discussed in more detail by Curtis et al. [2007, 2008] and Meland . Results from different theoretical model simulations are shown in the figures by the solid lines and will be described in the next section.
4 Modeling Analysis
 The purpose of this work is to determine if results from earlier studies on data obtained for single components of mineral dust aerosol can be used as a basis for modeling the optical properties of more complex, authentic mineral dust samples. Previous mineralogical investigations have found that wind-blown Saharan sand consists mostly of silicate clays (montmorillonite, illite, and kaolinite) and quartz, with smaller amounts of other minerals, including chlorite, feldspar, and calcite [Avila et al., 1997; Sokolik and Toon, 1999; Schütz and Sebert, 1987; Thomas and Gautier, 2009; Kandler et al., 2009; Glaccum and Prospero, 1980; Caquineau et al., 2002; Linke et al., 2006]. Studies of field samples of Iowa loess, in the fine particle mode (0.1–1.0 µm), have found that the samples consist mostly of silicate clays and minor concentrations of other minerals, such as quartz and calcite [Cuthbert, 1940; Davidson and Handy, 1953]. The mineralogy of the commercial ARD sample was not specified. For this analysis, all three samples have been modeled as external mixtures of silicate clays with possible additional amounts of quartz, amorphous silica, feldspars, calcite, and dolomite. Studies by others have shown that simulating mineral dust aerosol as an external mixture often gives good model results for dust optical properties [Köhler et al., 2011]. It has also been assumed that different mineral sample components do not mutually interact so that an independent scattering approximation may be used.
 Model IR extinction and visible light scattering phase function and polarization profiles for each mineral component are generated using publically available T-matrix codes from NASA [Mishchenko and Travis, 1998]. Required inputs to the code include parameters specifying the size distribution, refractive index data (optical constants), and a spheroid particle shape parameter.
4.1 Particle Size Distributions
 The experimental size distributions were fit to a lognormal form for the analysis. The parameters specifying the lognormal size distributions for Saharan sand, Iowa loess, and ARD were determined from least squares fits to the experimentally measured size distributions and are found in Table 1. Because the size distributions are measured concurrently with each optical properties data set, the lognormal parameters vary somewhat between the IR and visible measurements, but the differences are not large. The size distribution for ARD, measured during the scattering experiments, had a bimodal character and so it was fit by a linear combination of two lognormal functions with the parameters given in Table 1. In all other cases, the measured size distributions were fit well by single lognormal profiles. The aerosol samples have effective mass weighted mean particle diameters (MWMD) that fall in the range MWMD ~ 0.5–0.8 µm, as shown in Table 1.
 As noted above, the atomizer limits the aerosol's maximum particle size to ~2.5 µm diameter and there are no counts (above background) measured by the APS larger than ~2.5 µm. Therefore, the T-matrix calculations here use an upper limit on the particle diameter of ~2.5 µm for the numerical integration over the size distribution. The simulations converge over the full range of particle diameters and shape factors used in this analysis.
 In the analysis that follows, it is assumed that the individual mineral components all have the same size distribution, namely that of the sample as a whole. While this is probably not rigorously true, we have no means to determine the size distributions for each of the individual mineral elements in the complex samples, and this is the simplest approach for handling this difficulty. It is also important to reiterate that our experiments are limited to aerosol in the accumulation size mode (D<2.5 µm) and the mineralogy is predominantly silicate clay in this size range, so large variations in mineral composition with size are not expected.
4.2 Mineral Optical Constants
 In an external mixing model, refractive index data for the individual mineral components are needed. The index of refraction data used in these analyses have been taken from the literature and the sources are summarized in Table 2. For amorphous silica, the optical constants for glassy quartz are used. The plagioclase feldspars, albite and oligoclase, are treated together using the optical constants for albite, as IR refractive index data for oligoclase are not available. For the birefringent minerals (such as calcite, dolomite, and quartz), a weighted average of the optical constants was used, that is, the o-ray and e-ray optical constants have been combined with a 2/3:1/3 weighting because there are two ordinary and one extraordinary optical axes [Hudson et al., 2008]. This approximation greatly simplifies the analysis and shortens the calculation time. This approach has also been shown to give good agreement with the experimental spectra for the birefringent minerals considered here [Hudson et al., 2008]. Alternatively, a spectral averaging approach could be used where individual spectra are calculated separately using the o-ray and e-ray optical constants and then the resulting spectra are averaged in a 2/3:1/3 ratio. However, previous work by Hudson et al.  suggests that for broad shape distributions of particles, the spectral differences between these two approaches are relatively small.
Table 2. References for the Optical Constants of the Mineral Components Considered in This Studya
Visible (m = n + i k ) (Interpolated at 550 nm)
aFor the birefringent materials (calcite, dolomite, and quartz), the optical constants were obtained by combining the e-ray and o-ray index values with a 1/3:2/3 weighting. It should be noted that the optical constants for glassy quartz were used for amorphous silica.
bFriedrich et al.  do not report imaginary index (k) values for visible wavelengths. We use imaginary index values interpolated from data in Egan and Hilgeman , but note that the visible results are quite insensitive to the k-values for k<10–3.
4.3 Individual Mineral Component Shape Distributions
 Previous work by our group has shown that there are clear differences, which depend on dust mineralogy, in the particle shape distributions needed to best fit the aerosol optical properties [Hudson et al., 2008, 2008; Kleiber et al., 2009; Meland et al., 2010, 2012]. For the silicate clays, particle shape also varies with particle size [Meland et al., 2012]. Optimal spheroidal particle shape distributions have been derived in previous work to best fit the visible light scattering properties and/or the IR extinction spectra of several key mineral components of atmospheric dust [Kleiber et al., 2009; Nousiainen et al., 2006; Meland et al., 2010, 2011]. Here the particle shape distributions determined from those earlier studies of single mineral components are used as a basis for modeling the effects of particle shape in these complex mixtures. T-matrix calculations are carried out for a single particle shape parameter and then the results are averaged, as described in Meland et al. , to simulate the optical properties for a distribution of particle shapes. Details of the assumed particle shape distributions for each mineral component are reviewed in the Appendix, and the model parameters are summarized in Table 3 and Figure 4.
Table 3. Shape Distributions Used for Each of the Potential Mineral Components of Saharan Sand, Iowa Loess, ARDa
aA bimodal size shape distribution was used for the clay components (illite, kaolinite, and montmorillonite) and a single-mode shape distribution was used for calcite, dolomite, amorphous silica, quartz, and feldspar. Dc is the assumed cut-off diameter that separates the small and large particle modes in the bimodal clay size distributions. See Appendix for details.
Power Law: f(ξ) ~ |ξ|3 0 ≤ ξ2 ≤ +1.8
Power Law: f(ξ) ~ |ξ|3 0 ≤ ξ2 ≤ +1.8
Power Law: f(ξ) ~ |ξ|3 0 ≤ ξ2 ≤ +1.8
Equiprobable: –1.4 ≤ ξ ≤ + 1.4
Equiprobable: –1.4 ≤ ξ ≤ + 1.4
Equiprobable: –3 ≤ ξ ≤ + 5
Equiprobable: –3 ≤ ξ ≤ + 5
Power Law: f(ξ) ~ |ξ|3 –1.6 ≤ ξ ≤ +1.6
 The particle shape distributions of Table 3 are based on previous studies of the IR spectral extinction and visible light scattering properties of individual mineral components, as discussed in the Appendix. The results, however, are not extremely sensitive to the specific details of the shape models. For example, Meland et al.  showed that very similar fits to the IR and visible optical properties data for quartz could be obtained with different particle shape models (e.g., an equiprobable model distribution, as used here, or a Gaussian shape distribution model), provided the models included a very broad range of extreme shape parameters. Similarly, Meland et al.  showed that simulations of the optical data for illite and kaolinite could obtain fits of similar quality for a range of bimodal size-shape distribution parameters. Thus, these particle shape distribution models are not unique, but place reasonable limits on the range of shape parameters necessary to adequately describe the IR extinction and visible light scattering data for these mineral dust components.
4.4 Sample Mineralogy
 Mineral compositions for our samples of Saharan sand and Iowa loess have been reported by Laskina et al. . In that study, it was assumed that the samples are an external mixture of mineral components. The empirical analysis uses IR spectral data from a series of individual mineral components and adjusts the relative weighting of the components to find the best overall fit to the IR extinction spectra of the mixed sample. This analysis is repeated here for the sample of ARD. The resulting best-fit mineral compositions from these empirical fits to the IR extinction data are given in Table 4. Also included in Table 4 is a revised mineralogy that gives better overall fits to the range of optical properties data, as discussed in detail in section 5.3.
Table 4. Mineral Compositions (in Percentage of Particle Number Density) for the Authentic Samples of Saharan Sand, Iowa Loess, and ARD
 One concern with the mineralogy derived from the IR spectral analysis is that some very important minerals do not show a characteristic absorption resonance in the spectral range covered in our FTIR measurements (850–4000 cm–1). For example, hematite, a common iron oxide, can have a significant impact on the visible absorption, but does not have a characteristic absorption resonance in the measured spectral range. As a result, the IR analysis of the mineralogy is insensitive to the presence of hematite in the samples. This point is discussed in more detail below.
4.4.1 Saharan Sand
 The empirical IR spectral analysis of Laskina et al.  found that the major mineral components of the Saharan dust aerosol sample used for this study are montmorillonite (34%), illite (31%), kaolinite (16%), and smaller amounts of dolomite (9%), feldspar (9%), and amorphous silica (1%). The relatively high montmorillonite weight as a fraction of the total silicate clay is somewhat unusual for Saharan sand [Avila et al., 1997; Caquineau et al., 2002; Turner, 2008; Kandler et al., 2009], but appears consistent with other samples taken from the southern Sahara [Schütz and Sebert, 1987; Linke et al., 2006]. In this regard, it is also important to note that it is very difficult to distinguish between individual clay types on the basis of IR spectroscopy alone because there is significant overlap in the resonance absorption bands for the different clays (vide infra). This generally does not lead to a significant error in modeling since the different silicate clays tend to show similar scattering properties [Curtis et al., 2008].
 The low measured value for the quartz fraction may also seem surprising since many other studies have found quartz to be a major component of Saharan sand [Glaccum and Prospero, 1980; Caquineau et al., 2002; Avila et al., 1997; Schütz and Sebert, 1987; Sokolik and Toon, 1999; Thomas and Gautier, 2009]. This finding is, however, consistent with a recent field study by Turner , who also failed to find a significant quartz component in the mineral analysis of dust aerosol over the Sahel desert region of Niger. It should be noted that since the quartz Si-O resonance absorption band is spectrally well separated from the silicate bands of the clays (vide infra), it is unlikely that the IR spectral fitting routine has “swapped” clay for quartz. There is some spectral overlap between quartz and the feldspars, however, and this could affect the mineralogical analysis.
 It is also important to point out that bulk sand properties often differ markedly from the properties of dust aerosol. In fact, a strong quartz signature is observed in electron diffraction measurements of the bulk (not aerosolized) Saharan sand sample used in this work. Elemental analysis of the bulk sample that has been sieved to exclude particles >40 µm shows a Si:Al ratio of ~4.6 [Krueger et al., 2004], which is consistent with the presence of quartz at a level in excess of ~40%. However, this analysis of the bulk sample includes particles up to ~40 µm in diameter. The aerosol used in this study includes only the fine fraction particles (diameters<~2.5 µm) that are aerosolized and can pass through our flow system. Because quartz particles tend to be much larger than clay particles, it is not surprising that the mineralogy of the aerosolized sample here differs appreciably from that found in the bulk, or in other studies that may include a wider range of particle sizes. Glaccum and Prospero , for example, note that in the Saharan sand samples of their study, illite had the smallest particle size fraction (0.1–4.0 µm), while quartz particles were found to exceed 50 µm. In addition, a fractionation study of the elemental composition of Saharan sand as a function of particle size by Eltayeb et al.  shows a marked drop in the Si:Al ratio from >10 for bulk samples to ~2.5 for particles with diameters <2.5 µm. A Si:Al ratio of roughly 2.5 is similar to that expected for silicate clays, such as illite and montmorillonite. Therefore, this elemental analysis is consistent with a significant decrease in the overall quartz fraction in the aerosolized sample. The fractionation analysis of Eltayeb et al.  is in good agreement with the elemental analysis of the aerosolized sample collected from the flow in this experiment, which shows a much lower Si:Al ratio (~2.8) than that of the sieved bulk sample (Si:Al ~4.6), which included particles up to 40 µm. However, the possibility that the lack of quartz found in the spectral fitting by Laskina et al.  might be associated with the external mixing assumption cannot be ruled out; for example, Thomas and Gautier  found that the derived quartz fraction in Saharan sand samples increases when an internal mixing model is used to simulate the measured IR extinction spectrum of wind-blown dust. Unfortunately, we were unable to collect sufficient quantities of dust from the flow for electron diffraction studies of the aerosolized sample.
4.4.2 Iowa Loess
 The empirical IR spectral analysis of Laskina et al.  found that the major components of Iowa loess are montmorillonite (70%) and illite (18%), with a smaller amount of feldspar (11%) and calcite (1%). These results are qualitatively consistent with more detailed mineralogical analyses of other field samples of Iowa loess that find the soil to be largely silicate clay [Cuthbert, 1940; Davidson and Handy, 1953]. As with the Saharan sand sample, the IR extinction and visible scattering results are likely to be dominated by the silicate clay minerals.
 Using the empirical IR spectral fitting approach of Laskina et al. , the major mineral components of the ARD sample were found to be montmorillonite (31%), feldspar (19%), illite (18%), and amorphous silica (14%), with smaller amounts of dolomite (11%), quartz (6%), and calcite (1%). The ARD sample thus shows a more varied mineralogy than the heavily clay-rich Saharan sand and Iowa loess samples, making it a particularly interesting test case for spectral analysis.
4.4.4 Elemental Analysis
 Elemental compositions of the major crustal elements (Si, Al, Mg, Ca, Na, Fe, and K) in Saharan sand, Iowa loess, and ARD,were deduced from the empirical mineral compositions in order to further investigate their reliability. A comparison between the derived elemental compositions using the mineralogy of Laskina et al.  with those directly measured using EDX is given in Table 5. The comparison shows reasonably good agreement for all three aerosol samples; however, some discrepancies are worth noting. The mineral compositions derived by Laskina et al.  tend to underestimate the amount of Fe and overestimate the amounts of Ca and Mg. The Ca and Mg fraction is closely related to the presence of dolomite in the sample so this suggests that the amount of dolomite could be overestimated. This point will be further discussed below. The Fe content is commonly associated with Fe-rich clays or with iron oxides, such as hematite. As noted, the IR analysis of the mineralogy is insensitive to the presence of hematite in the samples.
Table 5. Elemental Composition (in Atomic %) of Complex Dust Samples Determined From the Empirical Mineralogy of Lakina et al.  and revised here, and EDX
 In comparing the elemental compositions, it is also important to recognize that the clay designations “illite” and “montmorillonite” refer to classes of clays with wide compositional variability in the trace metals [Grim et al., 1937]. Similarly, there is a wide compositional variation in different forms of feldspars. As a result, some differences in the concentrations of the trace elements are not surprising.
4.5 Cumulative Optical Properties
 For a given mineral composition, a forward simulation of the IR spectral extinction and visible light scattering data can be run for each mineral species in the sample. The IR extinction coefficient, Cext, and scattering matrix elements, Fαβ (θ), for each mineral component can then be combined through a weighted average to determine the cumulative properties of the externally mixed sample using equations (2)–(4):
where the summations are over the different mineral components, N(i) is the fractional number of particles, and C(i)scat (C(i)ext) is the average scattering (extinction) cross-section per particle for the ith mineral component [Meland et al., 2012]. The scattering phase function is then given by <F11(θ)> and the linear polarization by P = −<F12(θ)>/<F11(θ)>.
5 Results and Discussion
 T-matrix spectral simulation results for Saharan sand, Iowa loess, and ARD, based on the a priori mineral compositions (Table 4) and shape distributions (Table 3) as discussed above, are shown in red and compared with the experimental IR extinction spectra and visible light scattering data in Figures 1-3. The simulated T-matrix and measured IR extinction spectra in Figures 1-3 are each normalized to one at the peak. Due to variations in the baseline for the experimental IR spectra as noted above, all the extinction spectra have been baseline-corrected. The visible light scattering simulations are absolute comparisons with the measured phase function and polarization data, with no adjustable parameters. Also shown are model simulations based on Mie theory (blue line) and on the use of an equiprobable distribution of moderately shaped spheroids (green line) for all the mineral components of the complex samples. This equiprobable distribution of moderate spheroids, with −1.4 ≤ ξ ≤ +1.4, is based on analysis of electron microscope images of dust field samples and is commonly used to model the radiative transfer effects of atmospheric mineral dust [Mishchenko et al., 1997]. These results are discussed in detail below.
 Figure 5 shows, for illustration purposes, simulations of individual contributions to the IR extinction spectra and visible light scattering data for selected mineral components, in comparison with experimental data for the Saharan sand sample. This figure is instructive in that it shows how variations in sample mineralogy may influence the simulation results. It should be noted that there is significant IR spectral overlap of the extinction for the individual silicate clay components that make up the Si-O stretch vibrational resonance peak at ~1050 cm–1. This makes it very difficult to discriminate among individual clay types on the basis of IR spectral measurements alone. A similar caveat holds for the dolomite and calcite resonance line peaks near 1480 cm–1. On the other hand, there is relatively good spectral separation between the quartz and clay peaks in the silicate resonance region. In consideration of the visible data, it is clear that the clay and the nonclay components exhibit much different scattering behavior, with the clays showing a much stronger mid-range polarization. Scattering differences among the individual clay and nonclay minerals, however, are less pronounced.
 T-matrix simulations using the optimized particle shape distributions, as shown in Table 3, are in reasonably good overall agreement with the full range of experimental IR extinction and visible light scattering data. For most of the comparison data, these simulations fall within or near the limit of the experimental uncertainties. This approach also offers a very significant improvement over both Mie theory and T-matrix simulations using a simpler equiprobable distribution of spheroids. Chi-square analysis of the differences between the observed and simulated optical properties, as shown in Table 6a, further confirms this improvement. These results suggest that this T-matrix-based approach, based on a priori particle shape distributions determined from studies of the individual mineral components, can be used to more accurately simulate the optical properties of complex authentic dust mixtures across a broad spectral range from the IR to the visible. Closer inspection, however, reveals some noteworthy differences between the optimized T-matrix simulations and the experimental data.
Table 6. Comparison Between T-Matrix Simulations and Experiment: (a) Chi-Square Differences and (b) Scattering Asymmetry Parameters
Asymmetry Parameters (g)
5.1 Discussion of the IR Extinction Results
 In all three samples, the simulated IR extinction spectra, obtained using the optimized particle shape distributions, show significant improvement over the simulations using the equiprobable shape distributions or Mie theory. These two commonly used shape distributions result in IR silicate resonance absorption lines that are strongly blue-shifted from the experimental line positions by ~30 –40 cm–1. However, using the optimized shape distributions leads to much smaller errors of ~10 – 20 cm–1 in the silicate resonance line positions.
 It should be noted that the IR resonance peak positions for illite and kaolinite (as shown in the Appendix) are fit very well using the optimized T-matrix simulations. Because the empirical modeling approach of Laskina et al.  finds a significant montmorillonite fraction in all three samples, it is possible that the assumed particle shape distribution for montmorillonite is not optimal. It was assumed, for simplicity, that illite and montmorillonite could be described by the same particle shape distribution. Montmorillonite presents other difficulties in the analysis as well; it is a swellable clay meaning that it absorbs and retains water between the layers in the silicate framework. This might change the particle shape or refractive index depending on the degree of water uptake. Shifts of ~10 cm–1 in the montmorillonite spectral line position have been reported at higher relative humidity levels by Frinak et al. . Since the aerosol samples used in this study are atomized from a slurry of mineral dust in water, it is likely that there is an associated “water shift” in the montmorillonite peak position. Therefore, errors on the order of 10–20 cm–1 in the simulated silicate resonance absorption peak position for montmorillonite-rich samples are probably not unreasonable.
 However, it must be emphasized that by including the effects of thin clay flakes (modeled as highly eccentric oblate spheroids), the optimized shape distributions lead to a significant improvement in modeling over the results for Mie theory and the moderate equiprobable shape distribution. Simulations that ignore the shape effects associated with highly oblate clay particles show significant errors in the IR resonance peak position for these clay-rich authentic dust samples.
 The ARD sample, which shows the most varied mineralogy, also shows the most significant differences in the IR spectral fitting for the silicate resonance region. This could be related to a breakdown in the external mixing assumption. Furthermore, the empirical IR spectral fitting approach finds significant feldspar and amorphous silica contributions to the composition. As noted in section 4.2, the simulations for the feldspar components use IR optical constants for albite, only one member of the plagioclase feldspar family. As discussed in the Appendix, T-matrix simulations based on these optical constants do not accurately simulate the observed spectral fine structure in the absorption spectra for different feldspars. In addition, the same particle shape distributions are used for both quartz and amorphous silica, and this could lead to some error in the simulation.
 There are also significant differences between the simulated and experimental absorption line strengths for the carbonate peak near 1480 cm–1, associated with dolomite, in the Saharan sand and ARD results. A similar discrepancy was found in the analytic model results for Saharan sand of Laskina et al. . It is possible that there is an error in the magnitude of the dolomite optical constants that affects the absorption line strength. In this regard, it is also evident from the results shown in Table 5 that the mineralogy of Laskina et al.  significantly overestimates the Ca and Mg elemental fraction in the Saharan sand and ARD samples. Since Mg and Ca are characteristic of dolomite, this could indicate that the mineralogy of Laskina et al.  has somewhat overestimated the dolomite fraction in the analysis. This will be discussed in more detail in section 5.3.
 Despite these shortcomings, the IR simulations, based on a priori particle shape distributions suggested by our previous work on single component minerals (Table 3), show a significant improvement over both Mie theory and a commonly used equiprobable spheroidal particle shape distribution, particularly for the predominantly clay Saharan sand and Iowa loess samples. Chi-square analysis of the differences between the observed and simulated spectra confirms this, as shown in Table 6a.
5.2 Discussion of the Visible Light Scattering Results
 The simulation results for both the phase function and polarization profiles for Iowa loess at a visible wavelength of 550 nm (Figures 2b and 2c) are in excellent agreement with experimental measurements. Note that Iowa loess is the most homogeneous of the three samples (in terms of its mineralogy) and has the highest clay fraction, approaching 90%. The scattering properties of Iowa loess are well modeled by simulations based on the bimodal size shape distribution model proposed for the silicate clays.
 For Saharan sand, the phase function results are excellent, but the polarization peak is clearly too low in the simulation. Consideration of the individual mineral contributions to the scattering signal in Figure 5 suggests that this low polarization could be related, in part, to an overestimate of the nonclay fraction of the mineral composition, since the nonclay minerals (particularly dolomite) have lower polarization signals. Lowering the dolomite fraction and increasing the clay fraction in the Saharan sand sample mineralogy would improve the polarization fit, the IR extinction fit in the region near 1480 cm–1, and the fit to the measured elemental compositions in Table 5, as considered in the next section.
 As noted previously, the possible presence of hematite must also be considered. Elemental analysis places an upper limit of ~5% hematite in the mineral composition of the Saharan sand sample. However, hematite is a strong visible absorber with large real and imaginary refractive index values. Therefore, even at low concentrations, hematite can have a significant effect on the light scattering from complex dust samples. Previous experimental studies have measured low polarization in the scattered light signal from hematite aerosol at visible wavelengths [Meland et al., 2011]. In the authentic dust samples considered here, adding even a small amount of hematite to the simulated external mixture (up to ~5%) noticeably depresses the calculated polarization, further exacerbating the discrepancy. This suggests that the Fe content observed in the elemental analysis is probably primarily associated with Fe-rich clays, rather than in the form of iron oxides.
 The ARD simulation shows a reasonably good fit to the experimentally measured phase function and the polarization fit is very good. As with the Saharan sand sample, it is possible that fine-tuning the mineralogy might improve the overall quality of the fits (vide infra). Furthermore, as already suggested, these discrepancies might also result from a breakdown of the external mixing assumption for this more complex sample.
 Despite these differences, it is apparent that the visible simulations, based on a priori particle shape distributions suggested by our previous work on single-component minerals, show a significant improvement over both Mie theory and a more commonly used equiprobable spheroid shape distribution. Chi-square analyses of the differences between the observed and simulated optical properties confirm this, as shown in Table 6a.
 The asymmetry parameter, g, defined as shown in equation (5),
is an important parameter for modeling the radiative transfer effect of atmospheric dust. Relatively small errors in this parameter can lead to significant differences in the value of the radiative forcing effect [Andrews et al., 2006]. Table 6b compares the measured and simulated g-factors for each of the three samples. As found by other studies, Mie theory underestimates the asymmetry parameters, whereas the results based on the optimized shape distributions are much more accurate. The relative error in the asymmetry parameter using the optimized shape distributions is <1% for Iowa loess and Saharan sand and<4% for ARD (Table 6b).
 One additional point is worth reiterating here. There are no adjustable parameters in the comparison between experiment and the model simulations shown here for the visible scattering data. The sample mineralogies were determined independently in previous work by Laskina et al.  (or derived the same way for ARD), the particle size distributions were experimentally measured, and the particle shape distributions were fixed by previous studies of single-component mineral dust. Given the limited number of adjustable parameters and the range of experimental IR extinction and visible light scattering data, the overall agreement is remarkably good. It may be possible to improve the quality of the fits further by fine-tuning the sample mineralogy or by considering the possible effects of internal mixing. The effect of varying the mineral composition is discussed in the next section.
5.3 Revised Sample Mineralogies
 Based on the discussions above, it seems likely that the empirical mineralogy of Laskina et al.  overpredicts the dolomite fraction in the mineral compositions for both Saharan sand and ARD. To further explore this point, the empirical IR spectral analysis of the mineralogy was repeated, using the methods of Laskina et al. , but with dolomite excluded from the model. The revised mineral compositions and elemental concentrations for all three samples are shown in Tables 4 and 5 and the empirical IR extinction fits are compared in Figure 6. Note that the mineralogy of Laskina et al.  did not find any dolomite in Iowa loess, and therefore the revised mineralogy analysis is unchanged in Figure 6b. As shown in Figure 6, excluding dolomite from the analysis results in empirical extinction spectra for both Saharan sand and ARD that are nearly indistinguishable from the empirical IR fits of Laskina et al. . This furthers the idea that it is difficult to distinguish between calcite and dolomite based solely on IR analysis.
 T-matrix simulations based on the revised mineralogies are shown for Saharan sand and ARD in Figures 7 and 8. There is significant improvement in the fits to the carbonate IR resonance absorption bands near 1480 cm–1 for both Saharan sand and ARD. Note also the improved agreement with the elemental concentrations, particularly for Mg and Ca, as shown in Table 5.
 The visible polarization fit for Saharan sand, however, is only slightly improved and the predicted polarization at mid-range angles is still too low. Consideration of the individual contributions to the polarization signal from the different mineral components shown in Figure 5 suggests that errors in the mineralogy alone cannot fully explain this discrepancy. As discussed above, it is possible that the particle shape distribution used for the montmorillonite component in the sample may not be optimal, or the visible index of refraction values for montmorillonite may be in error or may be altered by water loading. Because scattered light polarization is highly sensitive to both particle size and shape distributions, these errors could also indicate that there is some variation in mineralogy with particle size in the distribution (contrary to our assumption that all the mineral components in the sample have the same size distribution). For example, the tail of the size distribution for the silicate clay part of the sample could fall off more rapidly at larger diameters than that for the nonclay fraction. In addition, we cannot rule out the possibility that the particle shape distributions for the mineral components in this field sample might differ from the a priori distributions of single mineral components, perhaps due to weathering processes. For example, the observed high degree of polarization could be explained if a larger fraction of the clay particles were included in the small particle mode (with a high oblate shape factor) of the bimodal size shape distribution. This would correspond to increasing the cut-off diameter that distinguishes between the small and large particle modes in the bimodal distribution. It is also possible that the underlying spheroid approximation may not be wholly adequate to describe the shape distributions of the Saharan sand dust sample.
 Despite these differences, it is clear from the results summarized in Table 6 that the use of a priori particle shape models for the individual mineral components of these authentic samples, which account for variations in particle shape with mineralogy and include highly eccentric spheroid shape parameters, offers a very significant improvement over commonly used particle shape models that cover a more limited shape parameter range.
 The principal goal of this work has been to determine if a priori spheroidal particle shape distribution models determined from earlier laboratory studies of single-component mineral dusts can be used as a basis for accurate T-matrix modeling of the IR extinction and visible light scattering optical properties of more complex, authentic field samples of mineral dust. T-matrix theory simulations of Saharan sand, Iowa loess, and ARD were carried out based on an external mixing assumption and the use of a priori particle shape models for the individual mineral components. The simulations rely on very few adjustable parameters. The particle size distributions were measured independently and the optical constants were taken from the literature. The particle shape distributions were fixed by results found in previous studies of well-characterized single-component mineral samples. Mineral compositions determined independently by Laskina et al.  were used for Saharan sand and Iowa loess, and the mineralogy for ARD was derived here using the same methods.
 T-matrix-based simulations, using a priori particle shape distributions determined from earlier laboratory studies of single-component mineral dust, show significant improvement over simulations based on commonly used moderately shaped particle distributions. The good overall agreement between the model simulations and experimental data generally support the conclusion that these particle shape distributions can provide a useful basis for more accurate T-matrix modeling of the IR extinction and visible light scattering optical properties of more complex, authentic field samples of mineral dust. For most of the IR and visible optical properties measurements, differences between model simulation results (based on the revised sample mineralogy) and the experimental data lie within or just marginally outside of the experimental uncertainties (1 SD). There are, however, some noteworthy exceptions to the good agreement between experimental data and model simulations.
 For the Iowa loess and Saharan sand IR extinction spectra, there is a persistent shift of 10–20 cm–1 from the experimental line position in the calculated Si-O vibrational resonance peak near 1050 cm–1. This is perhaps due to remaining errors in the detailed mineralogy, particularly in determining the relative amounts of illite and montmorillonite in the sample. It is also possible that the particle shape distribution assumed for montmorillonite is not optimal. In addition, modeling montmorillonite is complicated by possible line shifts associated with water uptake in the sample.
 In the case of ARD, the differences between experimental and simulated IR spectra are more pronounced and lie well outside the experimental uncertainties. However, ARD has the most varied mineralogy of the three samples studied and these errors could be associated with uncertainty in the mineralogy, or with a breakdown of the external mixing approximation. We will consider these possible effects in future work.
 In considering the visible light scattering results, the scattering phase function and linear polarization simulations for both Iowa loess and ARD show excellent agreement with the experimental data over the entire range of angles. Similarly, for the Saharan sand sample, the phase function simulation fits are excellent. One quantitative measure of the quality of the fit to a phase function is the scattering asymmetry parameter (g); the differences between the simulated and measured asymmetry parameters are less than 1% for Iowa loess and Saharan sand, and less than 4% for ARD. While this level of agreement may be somewhat fortuitous, the results are encouraging.
 The most serious differences occur in comparing the experimental and simulated linear polarization profiles for Saharan sand, where the deviations lie well outside the experimental uncertainties. Furthermore, these differences do not appear to be simply related to possible errors in the assumed mineralogy. It is possible that these differences are due to the use of nonoptimized particle shape distributions or optical constants for some of the mineral components, such as montmorillonite. The possible effects of internal mixing must also be considered. In addition, we cannot rule out the possibility that that there could be some variation in sample mineralogy with particle size, or that the mineral components in authentic field samples could have somewhat different particle shape distributions than those deduced from earlier laboratory work on single-component minerals, perhaps due to weathering effects. These issues will be addressed in future work. While it would certainly be possible to improve the quality of the fits by fine-tuning the particle size shape distributions for individual minerals in each sample, that effort lies beyond the scope of this article. Furthermore, it is not at all clear that such an approach would lead to results that are unique, physically meaningful, or practical for modeling the optical properties of a broad range of mineral dust samples.
 It is also important to reiterate that, despite these difficulties and uncertainties, the model simulations, using a priori optimized particle shape distributions that account for differences in particle shape with mineralogy and include a broader range of more eccentric spheroid shape parameters, offer a very significant improvement over more commonly used particle shape models that ignore variations in particle shape with size or mineralogy, and include only a moderate range of shape parameters.
 While much more work needs to be done to explore the issues raised in this work, significant improvements have been made to modeling the optical properties of complex, authentic dust. To further evaluate this modeling method, this work should be extended to more heterogeneous mineral dust samples with a wider variety of compositions. Also, these particular studies only deal with relatively small particles in the accumulation size mode, and therefore this approach should be further tested on larger particles. However, the generally good agreement shown between experiment and theory using the methodology outlined here shows promise for improving the accuracy of radiative transfer calculations for clay-rich mineral dust samples. This approach should prove useful in both climate forcing calculations and dust retrieval algorithms.
 This material is based on work supported, in part, by the National Science Foundation under Grant AGS-096824. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the view of the National Science Foundation. Two of the authors (J.M.A. and B.M.) gratefully acknowledge the support of NASA through an NESSF graduate student fellowship grant.
Appendix A: Details of Particle Shape Models
 Particle shape distributions determined from earlier studies of single mineral components are used as a basis for modeling the effects of particle shape in complex mineral dust samples. Here we review the shape models for the individual mineral components used in this work.
 Previous studies of quartz aerosol by Meland et al.  found that a very broad, flat-top shape distribution of spheroids with shape parameters in the range 3 ≤ ξ ≤ +5 gave good fits to both the IR and visible optical properties; therefore, this shape distribution was used for simulating the quartz component of the Iowa loess and ARD samples. The experimental IR Si-O vibrational stretch resonance line profile for amorphous silica is similar to that found for quartz in position and shape, although somewhat broader. Therefore, in the modeling analysis below, it is assumed that quartz and amorphous silica (glassy quartz) can be modeled using the same broad distribution of shape parameters.
 A flat-top distribution of spheroids, with more moderate shape parameters, was used for calcite, as described by Kleiber et al. . This distribution was shown to give good fits to the calcite IR extinction data. The simulations for dolomite use the same shape parameters as calcite because they are both carbonates with similar mineralogical structures, except that dolomite has alternating layers of calcium and magnesium [Klein et al., 1999].
Nousiainen et al.  investigated the particle shape effects on the scattering properties of one sample of small feldspar particles using T-matrix methods with the spheroid approximation. They found that a cubic power law shape distribution, (f(ξ) ∼ |ξ|3), accurately fit the scattering properties of the sample. Here this distribution is further investigated to test if it may also be used to model the IR spectral extinction of feldspars. Figure A1 shows a comparison between the experimental and simulated IR extinction spectrum for albite using the cubic power law shape distribution. The experimental extinction spectrum shows detailed fine structure that is not reproduced by the simulation. This discrepancy is probably due, in part, to limitations in the published index of refraction data because the data show no evidence for any such fine structure in the resonance. Nevertheless, this simple particle shape model does give a reasonably good fit to the overall peak position and width of the spectral line and was used for simulating a generic feldspar component of the authentic samples.
 For illite and kaolinite, a slight variation of the bimodal size shape distribution model proposed by Meland et al.  was used, with specific modeling parameters given in Table 3. In this approach, the clay particle size shape distribution is separated by an empirically determined cut-off diameter, Dc (with 450 nm<Dc<700 nm), into small- and large-particle modes, which are then allowed to have different shape distributions. The small-particle mode (mode 1, ξ1) consists of highly eccentric oblate spheroids (+7 ≤ ξ1 ≤ +11 for illite and +3 ≤ ξ1 ≤ +7 for kaolinite), and the large-particle mode (mode 2, ξ2) has a distribution of more moderate shape parameters (|ξ2| ≤ 1.8). These shape parameters were optimized to fit the measured optical properties; however, the best-fit results were also found to be consistent with expectations based on data from mineralogical studies of the physical shapes of individual clay particles [Nadeau, 1985, 1987]. The earlier analysis by Meland et al.  was mostly based on the visible refractive index data determined by Egan and Hilgeman . However, Meland et al.  also found that the best-fit shape parameters in the bimodal distribution are not highly sensitive to changes in the index of refraction. Here the optical constants of Friedrich et al.  are used, with n(illite) = 1.59 and n(kaolinite) = 1.56, because they appear to be more consistent with the range of refractive index values typically reported for silicate clay minerals n ~ 1.5–1.6 [Ehlers, 1987; Klein et al., 1999].
 In addition, the large-particle shape distribution (mode 2) has been changed from an equiprobable distribution, as used in Meland et al. , to a cubic power law, f(ξ) ~ |ξ|3, over a range of moderate oblate spheroids (0 ≤ ξ2 ≤ +1.8). The choice of a more oblate shape distribution for the large particles seems physically plausible as the larger particles are likely to be thicker layered structures formed by face-to-face bonding of thin oblate flakes, which may well retain an overall oblate character. The specific values for Dc (Dc = 600 nm), ξ1 (ξ1 = +7 for illite and +4 for kaolinite), and the range of ξ2 values (0 ≤ ξ2 ≤ +1.8) were empirically determined to give the best overall fit to the full range of measured IR and visible optical properties for the individual clays, illite and kaolinite. These simulations are shown in Figure A2. The combined change in optical constants and large particle shape distribution gives a slight improvement in the overall fits to the experimental data for illite and kaolinite, when compared to the model fits given by Meland et al. . The montmorillonite optical data are simulated using the same bimodal size shape distribution parameters as for illite because the minerals have a similar structure; both are 2:1 phyllosilicates with one gibbsite sheet sandwiched between two sheets of tetrahedral silica groups [Grim, 1939].
 One additional point is important to make here. The T-matrix method has well-documented convergence limitations for larger particles at more extreme shape factors. Here the small silicate clay particles have high oblate shape factors ranging up to ξ ~ +7. However in the T-matrix simulations, these large shape factors are only used for the small-particle mode of the size distribution; the larger particles in the size distribution have much more moderate shape factors ξ ≤ +2. As a result, the convergence limitations in the T-matrix code are much less problematic. The T-matrix results in this analysis are converged over the full range of particle size and shape parameters used.