To test the applicability of Mie theory in climate models and remote sensing data retrievals, we have studied the scattering phase function and linear polarization of representative mineral dust aerosol components at a wavelength of 550 nm. The mineral components investigated include the silicate clays, kaolinite, illite, and montmorillonite, and non-clay minerals, quartz, calcite, gypsum, and hematite, as well as Arizona road dust. In each case the aerosol size distribution was simultaneously monitored with an aerodynamic particle sizer. Particle diameters in this study fall in the accumulation mode size range characteristic of long-range transport aerosols. Our results show significant discrepancies between the experimental and Mie theory phase functions. The model shortcomings are due to particle shape effects for these non-spherical mineral dust particles. We find intriguing differences in the scattering between the silicate clay and non-clay components of mineral dust aerosol in this size range. For the non-clay minerals the most significant errors are found at large scattering angles where Mie theory substantially overestimates the backscattering signal. For the silicate clay minerals, there is more variability in the comparison to Mie theory. These findings have important consequences for the radiative forcing component of global climate models and remote sensing measurements that rely on Mie theory to characterize atmospheric dust. We also present experimentally based synthetic phase functions at 550 nm, for both silicate clay and non-clay mineral dust aerosols in the size parameter range X = 2–5, which may be useful for empirical models of the scattering due to particles in the accumulation mode size range.
 The use of more advanced modeling methods to treat scattering by nonspherical particles, such as T-matrix based calculations or discrete dipole approximation (DDA) methods [Mishchenko et al., 2002; Draine and Flatau, 1994] could help significantly to improve modeling accuracy. Because these theoretical methods are more numerically complex than Mie theory they have not been broadly applied, but as computer-processing power increases such calculations may become more commonplace [Dubovik et al., 2002, 2006; Kalashnikova et al., 2005]. These methods offer more accurate solutions than Mie theory, but still involve significant approximations and uncertainties.
 T-matrix based methods have been more widely explored and tested. The most advanced calculations involve averaging over polydisperse distributions of randomly oriented spheroids [Mishchenko et al., 1997; Dubovik et al., 2006] or various polyhedral particles [Kahnert et al., 2001]. However, these methods require assumptions as to what range of particle sizes and shape parameters, and average refractive index values best approximate “typical” atmospheric mineral dust. DDA methods have also been applied to model the light scattering properties of particles characteristic of atmospheric mineral dust [Kalashnikova and Sokolik, 2004; Kalashnikova et al., 2005; Kalashnikova and Kahn, 2006]. The DDA method offers more flexibility in modeling particles that are inhomogeneous and irregularly shaped, but the method is more computationally demanding, and is therefore restricted to smaller particles. Results from DDA modeling calculations have suggested that the neglect of sharp edges inherent in the assumption that particles can be treated as spheroids could lead to significant errors in some cases [Kalashnikova and Sokolik, 2004]. Other work [Kahnert and Kylling, 2004] suggests that the errors in the scattering phase function resulting from the spheroidal particle assumption may not be large. It is clear that more laboratory studies on well-characterized dust samples are needed to fully evaluate the reliability of these different theoretical approaches.
 Perhaps a more useful short-term approach to modeling the optical properties of “real” mineral dust aerosol is to use an empirical phase function based on laboratory data. Mishchenko and coworkers have recently developed an aerosol retrieval algorithm for AVHRR data [Mishchenko et al., 2003] that relies on an experimentally determined aerosol phase function. The “synthetic” phase function was generated from laboratory scattering data of quartz aerosol particles [Liu et al., 2003; Volten et al., 2001]. However, a great deal of laboratory data is needed to determine a synthetic phase function that can best approximate results for authentic atmospheric dust. This again points to the need for additional laboratory studies of light scattering from well-characterized mineral dust particles.
 Significant experimental and theoretical work has been carried out to evaluate the scattering phase function for a range of mineral dust aerosols. Quantitative analysis is often limited by uncertainties in particle composition, shape, and size distribution. We have recently developed a new laboratory apparatus for measurement of the scattering phase function and linear polarization of mineral dust aerosol samples [Curtis et al., 2007]. The apparatus includes a broadly tunable pulsed laser as the light source (a Nd:YAG pumped OPO), an elliptical mirror and CCD camera array for light detection (allowing us to measure the full angular scattering pattern on a shot-by-shot basis), and an aerodynamic particle sizer (for a real time determination of the particle size distribution in the aerosol flow). This apparatus allows for direct quantitative comparison of the observed light scattering from well-characterized dust samples with theoretical calculations based on the measured particle size distribution. In a recent paper we reported on testing and calibration of the system, and presented results for a synthetic phase function at 550 nm for quartz aerosol particles [Curtis et al., 2007]. Here we extend these measurements of aerosol light scattering properties at 550 nm to a broader range of mineral dust aerosol particles including the silicate clays, kaolinite, illite, and montmorillonite, and the non-clay minerals, quartz, calcite, gypsum, and hematite, as well as to a sample of Arizona road dust. In each case the aerosol size distribution was simultaneously monitored with an aerodynamic particle sizer. The particle samples studied generally fall in the accumulation mode size range characteristic of mineral dust aerosols that are transported over long distances [Prospero, 1999; Prospero et al., 1989]. Our results show significant discrepancies between the experimental and Mie theory-based phase functions. We also find intriguing differences in the scattering between the silicate clay components and the non-clay components of mineral dust aerosol in this particle size range. For the non-clay minerals the largest discrepancies are found at large scattering angles where Mie theory significantly overestimates the backscattering signal and, thus, underpredicts the asymmetry parameter, an important measure of aerosol light scattering. For the silicate clay minerals there is more variability in the comparison between experiment and theory.
2. Experimental Method and Results
 The experimental apparatus has been discussed in detail in a previous publication [Curtis et al., 2007]. Figure 1 schematically depicts the various experimental components. Briefly, monochromatic, polarized light from a Nd:YAG pumped tunable optical parametric oscillator (OPO) is used to irradiate a stream of mineral dust aerosol exiting from a narrow diameter nozzle. Scattered light is collected from near-forward to near-backward scattering angles by an elliptical mirror, where the dust stream-laser interaction region is at the first focus of the ellipse. The scattered light is imaged by the mirror onto an adjustable iris located at the second focus, which acts as a field stop. A charge coupled device (CCD) camera is located directly behind the iris, yielding an image of the scattered light, which can then be processed to give the phase function. More details of the apparatus and methodology are given below.
 The mineral dust components investigated in this study were obtained from commercial sources. The source information, specifications, and the literature references for the optical constants are given in Table 1 for the different mineral dust aerosol samples. With the exception of illite, all of the dusts were received as powders and used without any further modification. Illite was received as a block of material and pieces from the block were coarsely ground using a mortar and pestle before being more finely ground using a Wig-L-Bug. The mineral samples have each been characterized by X-ray powder diffraction and FTIR spectroscopy to verify the composition and mineralogy. Detailed characterization is most important for the silicate clay samples and the Arizona Road Dust sample as these show much more sample-to-sample variability than the other minerals. The clay samples used here have been characterized by Schuttlefield et al. , and the Arizona Road Dust sample by Cwiertny et al. . Elemental analysis and FTIR spectra of the Arizona Road Dust sample are consistent with a model composition consisting of a roughly equal weight mix of non-clay minerals (primarily quartz with a small amount of calcite) and clay minerals (primarily montmorillonite).
Table 1. Table of Mineral Dust Sources and Optical Constants for the Dust Samples Used in This Worka
Refractive index values are specified at λ = 550 nm.
 All aerosols are formed from a suspension of the mineral dust powder in Optima water (Fisher Scientific). A constant output atomizer (TSI Inc.) is then used to aerosolize the suspension. The resulting aerosol flow-passes through a diffusion dryer, which dries the aerosol and removes water vapor from the flow. After drying, the flow-passes through conductive tubing to a glass nozzle positioned just above the light scattering zone. A collection tube is placed immediately below the scattering zone, creating a windowless light scattering region with a length of approximately 10 mm. The particle flow from the nozzle is pulled into the collection tube of a commercial Aerodynamic Particle Sizer (APS) (TSI Inc.), for sizing measurements.
 It is possible that droplets from the atomizer may contain more than one dust particle. In such a case a composite particle could be formed as the water evaporates. Such composite or agglomerated particles are often found in authentic dust samples. However, with the exception of the Arizona Road Dust sample, each experiment measures the scattering from a specific mineral component. As a result a composite particle will simply appear and be counted as a larger particle of the same type. Of course a composite may have a somewhat different overall shape, but since we make no a priori assumptions about particle shape this would have no effect on the analysis or conclusions.
 The aerosol suspension is formed in Optima water and the effect of water impurities should be considered. We first note that atomizer experiments carried out with pure water give null results. That is, in the absence of mineral dust, no scattering is observed. Of course, impurities from the water could form a surface coating on the dust particles. This can be important in some measurements, such as cloud condensation activity, since surface coatings can have a significant impact on water uptake. However, monolayer level surface coatings will have negligible effect on the optical properties, which typically scale like particle volume or projected surface area. In addition, we note that the specified purity of the Optima water (residual impurities <1 ppm) is much better than that for any of the mineral dust samples we use (∼99.5% or lower).
 The light beam from the OPO crosses the aerosol flow just below the nozzle, defining the scattering volume. The OPO, equipped with frequency mixing capabilities, is tunable from 0.22–1.8 μm, although the wavelength is fixed at 0.550 μm in the current studies. The laser operates at a frequency of 10 Hz with a pulse width of ∼10 ns, and a typical pulse energy in the scattering region of ∼6 μJ at λ = 550 nm.
 Light scattered from the aerosol flow is collected from near forward (∼17°) to near backward (∼172°) angles by the elliptical mirror and refocused to a 1 mm aperture located at the second focus of the mirror. A CCD camera is located behind the iris to record images of the scattering, giving a measure of the signal as a function of scattering angle, θ, defined relative to the incident beam direction. The angular resolution is ∼0.1°/pixel. Each CCD image is obtained by integrating the scattered light signal from ∼600 laser pulses. The CCD image is then processed to yield the scattering phase function. Signal averaging algorithms, and corrections for dark counts, background scatter, and the nonlinear mapping of scattering angle to image pixel are implemented. Monodisperse polystyrene latex spheres were used to align, calibrate and test the system as described by Curtis et al. . Additional tests were carried out with ammonium sulfate aerosol [Curtis et al., 2007].
 The linear polarization of the incident laser light can be rotated to measure Ipara or Iperp, scattered light intensity for incident light polarized parallel or perpendicular to the scattering plane, respectively. The scattering phase function (given by the scattering matrix element S11 in the notation of Bohren and Huffman ) is proportional to the total scattered light intensity as a function of angle, obtained from:
The linear polarization as a function of angle is given by:
 The experimental method was used to measure the light scattering and linear polarization for several mineral dust aerosol samples over the useful angular range of our instrument (17° < θ < 172°). The background corrected, calibrated, and normalized experimental results are shown in Figures 2–5for several of the most abundant and important mineral components of atmospheric dust including the silicate clay minerals, illite, kaolinite, and montmorillonite, and non-clay minerals, quartz, calcite, gypsum, and hematite, as well as for a sample of Arizona Road Dust. Arizona Road Dust serves as a model for the complex mixtures that more closely represent authentic mineral dust aerosol. Possible systematic experimental errors associated with background scattered light, system calibration, the angular variation of the polarization response, or multiple scattering effects have been addressed in our previous work and are considered small relative to the statistical errors in the experiment. The experimental data in Figures 2–5 represent the average from a series of measurements (typically ∼3 for the non-clays and ∼6 for the clays where the day-to-day variations are larger), and the thin error bars indicate the range of the experimental data sets.
3. Mie Simulation
 Mie simulations for the phase function and linear polarization for light scattering were based on the experimentally measured aerosol size distributions and published optical constants for the mineral dust samples used in this work. Since the APS measurement principle produces an aerodynamic diameter, Da, the size distribution must be converted to an appropriate “particle” diameter to serve as input to the model calculations. For irregularly shaped particles there is always some ambiguity as to the most appropriate choice to describe the particle size. We have utilized the volume equivalent diameter, Dve, in our study because the conversion from aerodynamic diameter is straightforward and volume equivalent sizes are commonly reported in field studies. The aerodynamic diameter is related to volume equivalent diameter through [Hinds, 1999]:
where χ is an aerodynamic shape factor (χ = 1 for spheres) and ρ is the particle density. In (3) we have neglected additional terms associated with the Cunningham slip correction factors because the corrections are negligible for our particle size distribution [Hudson et al., 2007]. A more significant limitation in this experiment is that the APS is sensitive primarily to particles with Da > 600 nm, so that we cannot directly measure the size distribution for small particles (Da < 600 nm). In terms of particle number this means that only a small fraction of the total distribution is directly measured. However, light scattering typically scales with the particle projected surface area, and in the experiments reported here, relatively large particles (with Da > 600 nm) dominate the observed scattering signal. Consequently the modeling results are still well constrained by the measured APS size distribution.
 In order to model the effect of small particles (with Da < 600 nm), the APS data is used to generate a complete size distribution based on an assumed lognormal distribution function. First, the aerodynamic diameters are converted to volume equivalent diameters through equation (3). The bulk density (ρ) and aerodynamic shape factor (χ) are required as input parameters. Literature values are used for the bulk density. For most of our dust samples (illite, kaolinite, montmorillonite, quartz, calcite, and gypsum) the full particle size distribution functions and aerodynamic shape factors, χ, have been previously measured in a separate series of experiments in our lab using a similar atomizer and flow arrangement [Hudson et al., 2007, 2008, P. K. Hudson et al., submitted to Atmos. Environ., 2007, hereinafter referred to as P. K. Hudson et al., submitted manuscript, 2007]. For hematite and the Arizona road dust sample, a value χ = 1 is assumed, consistent with the measured values for the non-clay minerals, all of which were found to have χ < 1.05. Once the experimental data has been converted to a volume-equivalent diameter scale, a lognormal distribution is then constructed by assuming a mean particle diameter and fitting the tail of the lognormal function to the experimental size distribution for diameters larger than Da = 600 nm. The assumed mean diameters were based on data from the aforementioned measurements of the full particle size distribution [Hudson et al., 2008, P. K. Hudson et al., submitted manuscript, 2007]. The corresponding lognormal parameters are summarized in Table 2. Also shown in Table 2 for convenience are the corresponding effective radii (Reff), and the effective size parameters Xeff = (2πReff/λ) [Mishchenko et al., 1997], which are commonly used to specify a particle size distribution. The effective radius is essentially the projected surface area weighted radius and is a more appropriate measure of the light scattering properties of the distribution than the number density weighted average.
 Once the lognormal distribution parameters are determined the full lognormal distributions were used with Mie theory to generate the simulated spectrum. In order to gauge the possible errors in the simulated spectrum resulting from the uncertainty in the small particle part of the size distribution that we do not directly measure, we varied the lognormal parameters to generate a range of size distributions, and these different distributions were then used to estimate the uncertainty in the simulated spectra. Specifically, to generate a range of size distributions, the assumed mode diameter was varied (typically by a factor of 2 larger and smaller), and the fitting process was repeated to generate a range of lognormal distribution functions with varying mode diameters, but always constrained to match the measured size distribution for Da > 600 nm. Typical results are shown in Figure 6, which depicts the range of lognormal size distributions used for the Arizona Road Dust sample.
 For each dust sample in Figures 2–5 the Mie simulation results, obtained using the full lognormal size distribution as parameterized in Table 2, are shown by the dashed lines. The error bars show the range of simulation results obtained as the size distributions were varied as discussed. The Mie simulations in Figures 2–5 show relatively little difference as the lognormal parameters are varied because the scattering signals are primarily determined by the large particle part of the size distribution, which is tightly constrained by the APS measurements. The small variation in the Mie simulations shows that, as expected, the small particles have little effect on the results.
 The other major input to the Mie simulation is the particle refractive index at λ = 550 nm. These values were gleaned from the published literature, and the values used and literature references are contained in Table 1. For the birefringent materials (quartz, calcite, and hematite) we have averaged the o-ray and e-ray Mie results in a 2/3:1/3 ratio. For most of the dust samples studied here the imaginary part of the refractive index is small and the real values lie in the range n ∼ 1.4–1.6. The significant exception is, of course, hematite, which is especially important in climate forcing calculations precisely because it has a strong absorption onset in the visible and large real and imaginary index values at 550 nm.
4. Phase Function Normalization
 The experimental scattering data has been processed for presentation as an empirical, or “synthetic”, phase function in Figures 2–5 that can be directly compared with the Mie calculations. The unnormalized, experimentally measured scattered light signal (Itot = Ipara + Iperp), is converted to a normalized synthetic phase function using the methods outlined by Liu et al. . The experimental data is first extended to include the full angular scattering range. For near forward scattering angles, Mie theory is expected to be reliable and relatively insensitive to particle shape, so the theoretical Mie curve is spliced in to complete the data set at small angles (in our case for θ < 17°). At near backscattering angles (θ > 172°) the experimental data is extrapolated to 180°. The corresponding angular scattering function is then scaled to satisfy the normalization condition:
The result is the normalized synthetic phase function, P(θ), for that dust sample. We note that the small angle cutoff in our experiment (∼17°), which is limited by residual scattered light in the near forward direction, is appreciably larger than that used by Liu et al. . This could have some impact on the accuracy of our inversions; however, the effective size parameters for our particle distributions are not large (Xeff < 5), and T-matrix calculations suggest that differences in the forward scattering phase function for spherical versus nonspherical particles in this size range are relatively small (typically <10%) for θ < 20° [Mishchenko and Travis, 1994]. The synthetic phase function, shown by the solid curves in Figures 2–5 can be directly compared with the Mie simulation with no adjustable parameters.
5.1. Non-Clays (Quartz, Calcite, and Gypsum)
 Scattering results for several representative non-clay mineral components of atmospheric dust are shown in Figure 2, together with the Mie simulations. These include quartz, calcite, and gypsum. Hematite presents an unusual case and will be considered separately below. The particles span an effective (surface area weighted) size parameter range from Xeff ∼ 2.8 (for gypsum) to 4.9 (for quartz) for these data. The non-clay minerals all show a very similar behavior and the experimental phase function results are confined to a fairly narrow band as seen in Figure 7a, where the different results for this group of non-clay minerals are graphed together (dark band). The average phase function for this group of three non-clay minerals is given in Table 3. The experimental phase functions in Figure 7a appear to overlap well in the angular range θ ∼ 15–30°, but diverge at forward scattering angles as θ → 0° as indicated by the width of the corresponding band. This behavior is expected based on the range of particle size parameters in these experiments. T-matrix calculations performed by Mishchenko et al.  on distributions of randomly oriented spheroids in the size range X = 2–6 show similar behavior for small scattering angles. See Plate 5 by Mishchenko et al. . Indeed, the average synthetic scattering phase function for these non-clay minerals matches well over the full angular range with the T-matrix results presented by Mishchenko et al.  (Plate 5) for distributions of spheroids with X = 2–4. The agreement with Mie theory is, however, generally poor as seen in Figure 2. The most glaring differences are at large scattering angles where Mie theory significantly overestimates the backscattering signal, the scattered light signal near θ = 180°. There are additional systematic, but more subtle, differences that will be discussed in more detail below.
 The linear polarization results for the different non-clay samples are also shown in Figure 2b. In each case the experimental polarization is positive over most of the angular range, and peaks typically near θ ∼ 100°, with polarization values in the range +20–50%. The Mie predicted polarizations are all appreciably smaller, and tend to show a significant negative polarization at large scattering angles that is not reproduced in the experimental data.
 Results for the silicate clays are shown in Figure 3. In the clays the dimensionless particle size parameters range from Xeff ∼ 2.3 (for illite) to Xeff ∼ 3.7 (for kaolinite). Thus the range of sizes for the clay particles is comparable to that for the non-clay particles discussed above. The experimental results for the silicate clays show significantly more day-to-day and sample-to-sample variability, and the experimental uncertainties are correspondingly larger. It is known that the silicate clays represent classes of compounds with significant variation among samples obtained from different sources. This is particularly true for montmorillonite, which refers to a class of smectite clays rather than to a compound with a unique chemical composition and structure. Furthermore, montmorillonite, and to a lesser extent illite, are swellable clays that can absorb water. Since we aerosolize the samples from an aqueous solution, it is possible that the clay samples will have differing water contents, and that the water content may vary from day-to-day.
 Despite the uncertainties that arise from this variability it appears that there are qualitative differences between results for these clay samples and the non-clay samples described above. In particular, for the clays there does not appear to be such a clear systematic trend for Mie theory to significantly overpredict the scattering signal at large scattering angles in our experiment. This intriguing difference may be related to particle shape since the silicate clay particles are expected to have a sheet-like structure [Nadeau, 1985]. The experimentally determined phase functions for the silicate clay samples are all fairly similar as can be seen in Figure 7a where the normalized experimental phase function results for the different clay samples are graphed together (light band). The clay phase functions evince a slightly different band than the non-clays as discussed in more detail below. The average phase function for this group of clay minerals is also given in Table 3.
 Linear polarization results for the different silicate clay samples are shown in Figure 3b. In each case the experimental polarization is positive over most of the angular range, and peaks near θ ∼ 100° in the range +40–+60%. It appears that the average linear polarization for the clay samples tend to be somewhat higher than for the non-clay minerals. The Mie predicted polarizations are again all substantially smaller, and in kaolinite and montmorillonite show a significant range of negative polarization at large scattering angles that is not reproduced in the experimental data.
5.3. Comparison of Clay and Non-Clay Results
 The comparison in Figure 7a between the scattering phase functions for the clay and the non-clay mineral samples is interesting. Each data set is confined to a relatively narrow band but there is an apparent difference between the scattering phase functions for the clay and the non-clay minerals. The scattering intensities for the clay mineral samples tend to be slightly lower in the angular range 60–120°. This difference is probably not due to different average particle sizes; the effective size parameters for the clays range from 2.3–3.7 while the size parameters for the non-clay minerals range from 2.8–4.9. It is possible that the differences in scattering properties are related to systematic differences in particle refractive index (since the clays tend to have somewhat smaller real index values as seen in Table 1). Alternatively the differences might be related to particle shape as noted above.
Table 2. Lognormal Size Distribution Parameters: Assumed Mode Diameter (Dp) and Corresponding Best Fit Width Parameter (σ)a
Also shown is the range over which the mode diameters were varied to gauge the sensitivity of the simulation results to uncertainties in the size distribution. For convenience, the projected surface area weighted effective radius (Reff) and effective size parameter (Xeff = πReff/λ) is also given for each distribution. Results are an average for multiple data sets (∼3–6) for each sample.
Arizona road dust
1.73 ± 0.01
318 ± 4
2.11 ± 0.01
358 ± 8
1.88 ± 0.01
243 ± 5
1.75 ± 0.01
330 ± 2
1.86 ± 0.02
203 ± 8
2.18 ± 0.03
300 ± 41
1.81 ± 0.06
252 ± 24
2.10 ± 0.03
431 ± 19
 In order to factor out variations related to simple differences in particle size and refractive index it is convenient to compare results by considering the ratio of the experimental data to the Mie theory simulations. Figure 7b shows the ratio of experimental to theoretical phase functions for the non-clays (dark band) and clays (light band). This presentation also accentuates the more subtle differences between the data and Mie simulations at small and intermediate scattering angles.
 For the non-clay particle samples in this size range, Mie theory generally underestimates the scattering at small angles (θ < 20°) and at midrange angles (70° < θ < 120°), while overestimating the scattering in the angle range (20° < θ < 70°) and at large angles (θ > 120°). The average error at a scattering angle of θ = 90° is ∼10%, and the error for backscattering angles is a factor of ∼2–3. These results appear to be in qualitative agreement with predictions from T-matrix calculations for distributions of randomly oriented spheroids as depicted in Figure 1 of Mishchenko et al. .
 For the non-clays Mie theory significantly overestimates the backscattering signal for θ > 150° as predicted by theoretical calculations and observed in several other experiments on mineral aerosol particles. For example, Jaggard et al.  have measured the phase function for natural “Raft River” soil dust in the diameter size range D ∼ 2–5 μm, at a scattering wavelength of λ = 510 nm. For an assumed refractive index of n = 1.53 they find that Mie theory also overestimates the scattering phase function in the angular range θ > 150°. In the synthetic phase function for quartz particles with an effective radius of ∼2.3 μm, derived by Liu et al.  from an analysis of the experimental data of Volten et al. , the Lorenz-Mie predicted phase function is higher than the experimentally derived synthetic phase function in the angular range θ > 150°. This behavior is also clearly seen in the theoretical calculations for nonspherical particles carried out by Mishchenko et al. . (See Figure 1 of Mishchenko et al. .) A useful quantitative measure of the forward-backward asymmetry is the asymmetry parameter defined as,
where P(θ) is the phase function. The experimental and Mie predicted values for the asymmetry parameters are given in Table 4. Note that Mie theory generally underestimates the asymmetry parameter by an average of ∼0.02 (or ∼3%) for our non-clay dust samples.
 For the silicate clay samples, however, the situation is different, as there appears to be more variability in the results under our experimental conditions. At small and mid-range scattering angles the experiment-to-Mie ratio in Figure 7b agrees reasonably well with the results for the non-clay samples, though with a greater spread in the data. This suggests that the difference noted above in the phase function data of Figure 7a at mid-range angles (θ ∼ 60–120°) is consistent with expectations based on the differences in refractive index. In other words, the systematic difference apparent in Figure 7a between the clay and non-clay data at mid-range scattering angles is probably due largely to the fact that the clays have (on average) slightly lower real index of refraction values than the non-clays.
 At large scattering angles the differences between the Mie theory simulation and the experimental data are less consistent for the clays and, in the case of illite, Mie theory appears to slightly underpredict the backscattering signal as seen in Figure 3a. Asymmetry parameters for the silicate clays are also listed in the Table 4. The unusual results for the clays (particularly illite) apparent in Figure 7b could result from errors in the assumed index of refraction values. The optical constants for the clays were all taken from Egan and Hilgeman ; errors in these published values, or differences in the optical constants associated with sample-to-sample variability would affect the ratio plotted in Figure 7b since the Mie results depend on the refractive index. Alternatively, the differences in backscattering character could result from differences in particle shape. Hudson et al. [2008, P. K. Hudson et al., submitted manuscript, 2007] have shown that the clay and non-clay mineral aerosol particles show different character in their IR resonance absorption line shapes that correlate with differences in particle shape, with the clay resonance profiles being characteristic of “disk” shaped particles, and non-clay resonance profiles characteristic of a “continuous distribution of ellipsoids” shape.
 It is interesting to note that the silicate clays consist of layered sheets and particles are thought to be plate-like in structure. Studies by Nadeau  on various clay particles suggest that they consist of plates with average diameters in the range of 120 nm to 1900 nm and thicknesses in the range of ∼1 nm to 10 nm. Differences in particle shape might be related to the observed differences in scattering properties. Previous T-matrix calculations on light scattering from distributions of oblate and prolate spheroids do show some differences, although the calculated differences do not appear as significant as those observed here [Mishchenko et al., 1997]. We do not have a good explanation for this although it may be that the clay particles are actually more extreme in eccentricity than has been considered in the theoretical simulations.
 We have carried out similar experiments and analyses for hematite aerosol. Our hematite sample has an effective size parameter similar to the other minerals studied in this work, Xeff = 3.8. Hematite, however, is unique among the mineral dust samples studied here because of its strong visible absorption, with large index of refraction values (both real and imaginary parts) at 550 nm. The synthetic phase function and linear polarization are shown in Figure 4, together with the Mie theory prediction based on the hematite optical constants published by Longtin et al. . The synthetic phase function is markedly different from those for the other non-clay minerals, which may be expected based on the significant differences in optical constants. In particular the phase function is much flatter at midrange and large scattering angles. This flattened behavior in the phase function (relative to the other non-clay minerals) is also suggested in the Mie theory predictions, although the absolute agreement between Mie theory and the experimental result is fairly poor. Mie theory predicts a somewhat flatter phase function, underestimating the experimental result at small angles and overestimating it for midrange and large scattering angles. Consequently, the Mie theory asymmetry parameter is much lower than that measured for hematite. The flattening of the hematite phase function is primarily due to its strong absorption (associated with the large imaginary part of the refractive index), which smoothes out the angular signature of the light scattering. The synthetic phase function and asymmetry parameters for hematite are contained in Tables 3 and 4, respectively.
Table 3. Averaged Synthetic Phase Functions at 550 nm for the Group of Non-Clay Minerals (Quartz, Calcite, and Gypsum), the Silicate Clay Minerals (Illite, Kaolinite, and Montmorillonite), and for Hematitea
Scattering Angle θ, deg
Phase Function P(θ)
The phase function depends on particle size and these results are limited to effective particle diameters ∼1 μm, in the accumulation mode size range.
Table 4. Table of Asymmetry Parameters for the Normalized Phase Functions
Theoretical results are averages calculated using size distribution data for the range of assumed lognormal mode diameters as discussed in the text.
Experimental results are averages over multiple sample collections (∼3–6).
Arizona Road Dust
0.672 ± 0.010
0.682 ± 0.019
0.630 ± 0.003
0.659 ± 0.009
0.668 ± 0.018
0.680 ± 0.011
0.528 ± 0.073
0.643 ± 0.008
0.719 ± 0.025
0.688 ± 0.012
0.690 ± 0.008
0.726 ± 0.010
0.677 ± 0.021
0.683 ± 0.016
0.661 ± 0.003
0.688 ± 0.006
 The linear polarization data is also interesting, showing a much flatter polarization curve over most of the angular range, which also peaks at somewhat smaller angles (near θ ∼ 70°) than is typical for the other dusts studied here. The Mie theory polarization plot is also much flatter although still predicting a smaller than observed polarization over most of the angular range.
5.5. Arizona Road Dust
 Arizona Road Dust (or Arizona Test Dust) is a commercially available dust sample that can be used to represent a more authentic inhomogeneous mixture of different minerals. The effective size parameter for the Arizona Road Dust sample used here is similar to those of the other mineral samples studied, with Xeff ∼ 3.6. The synthetic phase function and linear polarization plots are shown in Figure 5, along with the Mie theory simulation. On the basis of other work in our lab, including elemental analysis of the Arizona Road Dust sample and an analysis of the aerosol IR resonance absorption spectrum, we estimate that our dust sample consists of a roughly equal weight mix of non-clay minerals (primarily quartz with a small amount of calcite) and clay minerals (primarily montmorillonite). On the basis of this analysis we have constructed a simple model that assumes a 50–50 weighted average of the quartz and montmorillonite Mie spectra to generate the simulated phase function shown in Figure 5 by the dashed lines. The use of weighted average optical constants yields essentially similar results for the Mie calculation. The experimental data and the Mie simulations shown in Figure 5 are consistent with the results discussed above for the other mineral samples. The calculated and measured asymmetry parameters for Arizona Road Dust (listed in Table 4) fall in line with the averages for the individual mineral dust components as expected. The linear polarization plot also appears very similar to that for both quartz and montmorillonite. Again, the polarization is positive over most of the angular range, peaking near ∼+40% at a scattering angle of θ ∼ 110°, whereas the Mie predicted polarization is negative over the full angular range.
 An alternative to the use of Mie theory (with weighted optical constants) to describe the scattering properties of an inhomogeneous mix of different minerals, as in the Arizona Road Dust sample, is to generate an empirical phase function based on a weighted average of the synthetic phase functions for clay and non-clay minerals as given in Table 3. In Figure 5 we also present results from such an empirically derived phase function obtained from an equal weight average of the clay and non-clay synthetic phase functions derived above (dotted line). It is clear, and not surprising, that the empirical phase function gives a much better overall fit to the experimental Arizona Road Dust sample results.
 Knowledge of the light scattering properties of mineral dust aerosols is critical in assessing their potential effect on global climate and for validating remote sensing studies of dust in the atmosphere. Utilizing a tunable pulsed Nd:YAG laser-pumped OPO and an optical imaging apparatus, the scattering properties of several components of atmospheric mineral dust have been studied in the visible wavelength range at λ = 550 nm. Our focus has been to study well-characterized, representative mineral components of atmospheric dust in the accumulation mode size range, with effective radii Reff ∼ 0.2–0.4 μm, corresponding to effective size parameters in the range Xeff ∼ 2–5.
 Note that the range of effective particle sizes studied in this work (with area weighted effective diameters D ∼ 0.6–0.8 μm) is primarily relevant for assessing the optical properties of mineral dust in the accumulation mode size range, typical of background aerosols and aerosols that have undergone long-range transport. Field studies during African dust events have shown that up to about of the total dust mass collected in the southeastern US and Caribbean was less than ∼2 μm in aerodynamic diameter [Moulin et al., 1997; Li-Jones and Prospero, 1998]. Furthermore, studies from different geographic areas have determined that the mass median diameter of mineral dust found over the oceans falls generally in the 2–3 μm range [Prospero et al., 1989; Prospero, 1999]. For comparison, the mass weighted mean diameters for our dust samples range from ∼0.73 μm for gypsum to ∼1.5 μm for quartz. Thus our experiments sample dust particles that are slightly smaller, but comparable in size to typical long-range transport aerosols. We caution that light scattering is a strong function of particle size and the results herein would not be appropriate to describe the scattering of dust during high dust events near the source, where dust particles can be much larger.
 For the non-clay mineral dust particles (quartz, calcite, and gypsum) we find evidence for significant discrepancies between measured and theoretical scattering phase functions, particularly in the backscattered direction (θ > 120°) where Mie theory significantly overestimates the backscatter cross-section. Such errors can adversely impact the accuracy of Mie based radiative transfer calculations under high dust loading conditions, affecting the reliability of both radiative forcing models and dust retrievals from satellite based instruments. Atmospheric dust data retrievals from LIDAR measurements can also be affected by significant errors in the backscatter cross-section. Smaller discrepancies are also observed at side scattering angles near 90° where Mie theory underpredicts the experimental phase functions by ∼5–15%. In addition, we find discrepancies between measured and theoretical polarizations, with the Mie predicted polarizations generally more negative than the observed results. While agreement with Mie theory is poor, the average scattering phase function for the non-clay minerals, with size parameters in the range X ∼ 2–5, appears to be in good agreement with the results from T-matrix calculations for distributions of randomly oriented spheroids as given by Mishchenko et al. . In the future we plan to carry out a detailed T-matrix based modeling analysis of our results in order to explore the effect of different shape distributions on fits to the experimental data.
 We have also observed differences between the scattering phase functions for the non-clay minerals (quartz, calcite, and gypsum) and the silicate clay minerals (illite, kaolinite, and montmorillonite) for particles in the size parameter range Xeff ∼ 2–5. Results for the clays show more variation under our experimental conditions and are less systematic. Some of the differences with the results from the non-clay mineral samples appear to be related to differences in the optical constants; the real refractive index values for the clay samples are typically smaller than for the non-clay samples we have studied. Particle shape effects may also play a role. These results are significant since a large fraction of atmospheric mineral dust in the accumulation mode size range is associated with silicate clay minerals, primarily illite, kaolinite, and montmorillonite [Prospero, 1999; Prospero et al., 1989]. Modeling the scattering properties of mineral dust in this size range using Mie theory and an average refractive index value for “typical” mineral dust n ∼ 1.53 may lead to significant errors.
 Perhaps a better alternative might be to use a synthetic phase function based on laboratory data in radiative transfer calculations. We have presented experimentally based synthetic phase functions for non-clay minerals and for silicate clay minerals in the size parameter range X ∼ 2–5. In each case the synthetic phase functions are averages over a group of several of the most abundant mineral components of atmospheric dust: quartz, calcite, and gypsum for the non-clays, and illite, kaolinite, and montmorillonite for the clay minerals. A weighted average synthetic phase function constructed to mimic the light scattering properties of Arizona road dust, which serves as a model for an inhomogeneous mix of different dust types, agrees fairly well with the observed scattering properties. However, as noted above, the light scattering phase function depends critically on particle size and our results are limited to particles in the accumulation mode size range with effective particle diameters ∼1 μm. The phase function results presented here should not be used to describe the scattering of dust during high dust events near the source, where dust particles can be much larger. In future work we will implement a different dust aerosol generator for studying larger particles.
 This material is based upon work supported by the National Science Foundation under grants ATM-042589. 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. The authors would like to gratefully acknowledge helpful discussions with Paula Hudson and Praveen Mogili, and to thank Mark Smalley for assistance with the experiment.