An investigation into particle shape effects on the light scattering properties of mineral dust aerosol

Transcription

1 University of Iowa Iowa Research Online Theses and Dissertations Spring 2011 An investigation into particle shape effects on the light scattering properties of mineral dust aerosol Brian Steven Meland University of Iowa Copyright 2011 Brian Steven Meland This dissertation is available at Iowa Research Online: Recommended Citation Meland, Brian Steven. "An investigation into particle shape effects on the light scattering properties of mineral dust aerosol." PhD (Doctor of Philosophy) thesis, University of Iowa, Follow this and additional works at: Part of the Physics Commons

2 AN INVESTIGATION INTO PARTICLE SHAPE EFFECTS ON THE LIGHT SCATTERING PROPERTIES OF MINERAL DUST AEROSOL by Brian Steven Meland An Abstract Of a thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Physics in the Graduate College of The University of Iowa May 2011 Thesis Supervisor: Professor Paul D. Kleiber

3 1 ABSTRACT Mineral dust aerosol plays an important role in determining the physical and chemical equilibrium of the atmosphere. The radiative balance of the Earth s atmosphere can be affected by mineral dust through both direct and indirect means. Mineral dust can directly scatter or absorb incoming visible solar radiation and outgoing terrestrial IR radiation. Dust particles can also serve as cloud condensation nuclei, thereby increasing albedo, or provide sites for heterogeneous reactions with trace gas species, which are indirect effects. Unfortunately, many of these processes are poorly understood due to incomplete knowledge of the physical and chemical characteristics of the particles including dust concentration and global distribution, as well as aerosol composition, mixing state, and size and shape distributions. Much of the information about mineral dust aerosol loading and spatial distribution is obtained from remote sensing measurements which often rely on measuring the scattering or absorption of light from these particles and are thus subject to errors arising from an incomplete understanding of the scattering processes. The light scattering properties of several key mineral components of atmospheric dust have been measured at three different wavelengths in the visible. In addition, measurements of the scattering were performed for several authentic mineral dust aerosols, including Saharan sand, diatomaceous earth, Iowa loess soil, and palagonite. These samples include particles that are highly irregular in shape. Using known optical constants along with measured size distributions, simulations of the light scattering process were performed using both Mie and T-Matrix theories. Particle shapes were approximated as a distribution of spheroids for the T-Matrix calculations. It was found that the theoretical model simulations differed markedly from experimental measurements of the light scattering, particularly near the mid-range and near backscattering angles. In many cases, in the near backward direction, theoretical

4 2 models predicted scattering intensities for near spherical particles that were up to 3 times higher than the experimentally measured values. It was found that better agreement between simulations and experiments could be obtained for the visible scattering by using a much wider range of more eccentric particle shapes. Abstract Approved: Thesis Supervisor Title and Department Date

5 AN INVESTIGATION INTO PARTICLE SHAPE EFFECTS ON THE LIGHT SCATTERING PROPERTIES OF MINERAL DUST AEROSOL by Brian Steven Meland A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Physics in the Graduate College of The University of Iowa May 2011 Thesis Supervisor: Professor Paul D. Kleiber

6 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL PH.D. THESIS This is to certify that the Ph.D. thesis of Brian Steven Meland has been approved by the Examining Committee for the thesis requirement for the Doctor of Philosophy degree in Physics at the May 2011 graduation. Thesis Committee: Paul D. Kleiber, Thesis Supervisor Mark A. Young Vicki H. Grassian Steven R. Spangler Frederick N. Skiff Kenneth Gayley

7 To Marit ii

8 ACKNOWLEDGMENTS Over this past six years, I have spent countless hours in a dark lab making light scattering measurements, hunched over textbooks while studying for the physics qualifying exam, and sitting in front of a computer writing thousands of lines of code or analyzing data. It has been difficult, stressful, and tiring but at the same time exciting and hugely rewarding. I will never forget the feelings of accomplishment when I received the fellowship I was hoping for, getting my first paper published, or finding out that I passed my exams. However, those feelings should not be mine alone. There have been many people throughout the years who offered their support so I could get my degree. Let this just be one more instance of me saying Thank you. First, I would like to acknowledge my fellow graduate students and colleagues at the Iowa Advanced Technology Laboratories. To Dr. Dan B. Curtis, thank you for introducing me to the workings of the lab and being patient with me as I learned the basic principles of light scattering. To Dr. Paula K. Hudson, for taking the time to answer my dn many questions on aerosol particles, and for repeatedly explaining to me. Dr. d log( D ) Juan G. Navea, thank you for always bringing a chemist s perspective to the lab and for all of your stories that started with Back when I was in grad school. Dr. Jonas Baltrusaitis, thank you for always collecting just one more set of SEMs. To Mark Smalley, for collecting so much scattering data that I was still analyzing it two years after you graduated. Finally, to my friends Murat, Eric, and Paul, the daily trips to the IMU always prepared me for the rest of the day. There have also been a number of sources of financial support which I wish to acknowledge. Through the University of Iowa, I received a Presidential Fellowship and a Graduate Student Incentive Fellowship. Through NASA, I received the NASA Earth and Space Science Fellowship. These awards have helped immensely by providing me with ability to focus all of my efforts towards my research. This research would not have been p iii

9 possible without funding received through the National Science Foundation (Grant AGS ). There have been many professors throughout my academic career that have been instrumental in my academic success. As an undergraduate student Dr. Ananda Shastri and Dr. Mathew Craig taught me the fundamentals of physics, from electromagnetic theory to quantum mechanics. You both encouraged and prepared me to continue on to graduate school. To my graduate school academic advisors Dr. Paul D. Kleiber, Dr. Mark A. Young, Dr. Vicki H. Grassian, thank you for all the help throughout the years. Between helping with revisions on manuscripts, data analysis, and asking tough questions about the latest set of measurements, I don t know where you also found the time to teach classes. It s a good thing that there were three of you. I would also like to thank all of my dissertation committee members, Dr. Paul D. Kleiber, Dr. Mark A. Young, Dr. Vicki H. Grassian, Dr. Steven R. Spangler, Dr. Frederick N. Skiff, and Dr. Kenneth Gayley. There have been many people outside of school to whom I owe thanks for their support. To my friends Steve, Ellery, Jason, and Ryan, our Wednesday night games were always a welcome break from working in the lab. To my parents, Steve and Kathy, and my sister, Melissa, you have supported my decision to spend all these years studying physics from the beginning. You knew I would pass my exams even when I was uncertain and you knew I would finish even when I couldn t see the light at the end of the tunnel. Our Saturday morning phone calls and occasional care packages always helped home seem not so far away. Most importantly, I wish to thank my wife Marit for her support and patience throughout this process. You have listened intently as I rambled on the days latest set of measurements, shared in the stress of graduate student life (especially while I studied for the qualifying exam), and dealt with the uncertainty of when I would finally finish writing. I will never be able to thank you enough. iv

10 ABSTRACT Mineral dust aerosol plays an important role in determining the physical and chemical equilibrium of the atmosphere. The radiative balance of the Earth s atmosphere can be affected by mineral dust through both direct and indirect means. Mineral dust can directly scatter or absorb incoming visible solar radiation and outgoing terrestrial IR radiation. Dust particles can also serve as cloud condensation nuclei, thereby increasing albedo, or provide sites for heterogeneous reactions with trace gas species, which are indirect effects. Unfortunately, many of these processes are poorly understood due to incomplete knowledge of the physical and chemical characteristics of the particles including dust concentration and global distribution, as well as aerosol composition, mixing state, and size and shape distributions. Much of the information about mineral dust aerosol loading and spatial distribution is obtained from remote sensing measurements which often rely on measuring the scattering or absorption of light from these particles and are thus subject to errors arising from an incomplete understanding of the scattering processes. The light scattering properties of several key mineral components of atmospheric dust have been measured at three different wavelengths in the visible. In addition, measurements of the scattering were performed for several authentic mineral dust aerosols, including Saharan sand, diatomaceous earth, Iowa loess soil, and palagonite. These samples include particles that are highly irregular in shape. Using known optical constants along with measured size distributions, simulations of the light scattering process were performed using both Mie and T-Matrix theories. Particle shapes were approximated as a distribution of spheroids for the T-Matrix calculations. It was found that the theoretical model simulations differed markedly from experimental measurements of the light scattering, particularly near the mid-range and near backscattering angles. In many cases, in the near backward direction, theoretical v

11 models predicted scattering intensities for near spherical particles that were up to 3 times higher than the experimentally measured values. It was found that better agreement between simulations and experiments could be obtained for the visible scattering by using a much wider range of more eccentric particle shapes. vi

12 TABLE OF CONTENTS LIST OF TABLES... ix LIST OF FIGURES... x LIST OF SYMBOLS... xviii CHAPTER 1 INTRODUCTION...1 Atmospheric Aerosol...1 Radiative Forcing...6 Remote Sensing...9 Chapter Overview...11 CHAPTER 2 EXPERIMENTAL SETUP...13 Light Scattering Apparatus...13 Mineral Dust Samples...16 Aerosol Size Distributions...18 System Alignment and Calibration...23 From Images to Phase Functions...29 CHAPTER 3 MODELING THE EXPERIMENTAL SCATTERING APPARATUS...49 Model of the Experimental Apparatus...49 Model Parameters...54 Model Results...55 Discussion...58 CHAPTER 4 LIGHT SCATTERING THEORY...65 Mie Theory...68 T-Matrix Theory...71 CHAPTER 5 MULTI-WAVELENGTH LIGHT SCATTERING STUDIES...77 Error Analysis...77 T-Matrix Shape Distribution...80 Asymmetry Parameter Calculations...81 Non-Clay Mineral Dust Results...81 Clay Mineral Dust Results...83 Iron Oxide Results...85 Arizona Road Dust Results...87 Discussion...89 CHAPTER 6 DETERMINING PARTICLE SHAPE DISTRIBUTIONS FROM FTIR SPECTRAL FITTING Modeling Error Analysis Results for Quartz vii

13 Discussion CHAPTER 7 AUTHENTIC MINERAL DUST LIGHT SCATTERING Particle Size Distributions T-Matrix Shape Distribution Optical Constants Error Analysis Authentic Mineral Dust Results Shape-Fitting Palagonite Data Discussion CHAPTER 8 FUTURE WORK Larger Mineral Dust Aerosol Particles Particle Shapes Used in T-Matrix Calculations Particle Coatings Expanding the Light Scattering Database APPENDIX A.1 Determining the System Calibration and Angle Mapping Functions A.1.1 Polarization Correction (Sub-function) A.1.2 Angle Mapping (Sub-function) A.1.3 Calibration Curve Fitting (Sub-function) A.2 Splicing APS and SMPS Data A.2.1 Fitting SMPS Data with a Log-normal Distribution (Subfunction) A.2.2 Optimizing Overlap Between APS and SMPS Data (Subfunction) A.3 Modeling the Experimental Apparatus A.3.1 Determining Aperture Collisions (Sub-function) A.3.2 Determining Detector Collisions (Sub-function) A.3.3 Determining Mirror Collisions (Sub-function) REFERENCES viii

14 LIST OF TABLES Table 2.1 Physical properties of mineral dust samples used in this work: volume equivalent mode diameter (D ve ), aerodynamic shape factor (χ), lognormal size distribution best fit width parameter (σ), and surface area weighted effective radius (R eff )...32 Table 2.2 Calculated characteristic size parameter ( X eff 2 R eff ) mineral dust samples used in this work Table 2.3 Table 2.4 Table 2.5 Table 5.1 Optical properties of mineral dust samples used in this work. For cases where optical constants were not available for a given wavelength, a linear extrapolation of values near that wavelength was used...34 Chemical composition of the well defined mineral dust samples used in this work Size properties for polystyrene latex spheres (PSL)...35 Reduced χ2 values for comparison of the experimental phase functions with simulations using Mie theory and using T-Matrix theory assuming a Standard shape distribution Table 5.2 Asymmetry parameter values for experimental (g Exp ), Mie theory (g Mie ), and T-Matrix theory (g TM ) phase functions for 470, 550, and 660 nm...96 Table 6.1 Table 6.2 Table 7.1 Reduced χ 2 values for comparison of the experimental phase functions with simulations based on different particle shape models, the moderate SEM-based and Standard models, and the extreme Window model Asymmetry parameter values for experimental (g Exp ) and T-Matrix theory assuming the SEM-Based (g SEM ), Standard (g Standard ), and Window (g Window ) shape model phase functions for 470, 550, and 660 nm Reduced χ 2 values for comparison of the experimental phase functions with simulations using Mie theory and using T-Matrix theory assuming a Standard shape distribution Table 7.2 Asymmetry parameter values for experimental (g Exp ), Mie theory (g Mie ), and T-Matrix theory (g TM ) phase functions for 550 nm ix

15 LIST OF FIGURES Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 2.7 Light scattering experimental apparatus. Aerosol generated by the atomizer is directed to the focal point of an elliptical mirror that acts as the scattering region. The aerosol is then collected for real time particle sizing measurements by an Aerodynamic Particle Sizer (APS) and a Scanning Mobility Particle Sizer (SMPS). A tunable Nd:Yag pumped OPO is used as the light source Detailed view of the optical setup (a) and scattering region (b) as viewed from above. Output from the OPO is directed to a telescope setup in order to decrease beam width by roughly a factor of three. A double Fresnel Rhomb prism is used to adjust the polarization of the incident laser before entering the scattering region. Scattered light reflects from the elliptical mirror and is subsequently focused through an aperture onto the CCD camera. The scattering angle is defined relative to the direction of the incident beam...37 Measured aerosol particle size distributions (open circles) using an Aerodynamic Particle Sizer. Also shown are log-normal fits to the particle size distribution for mode diameters of 110, 220, and 440 nm. The log-normal fits are used in Mie calculations to give a range of possible scattering signals to account for uncertainty in the small diameter part of the size distribution CCD image of light scattering for 771 nm diameter PSL for parallel (a) and perpendicular incident light (b) Experimental (solid line) and Mie theory (dashed line) phase functions for 771 nm diameter PSL. The experimental data has been mapped from pixels to scattering angle, but the system calibration has not been applied. Mie and experimental data has been normalized to the same amplitude at 35 o Experimental (solid line) and Mie theory (dashed line) phase functions (a) and polarizations (b) for PSL with mean particle diameter of 771 nm. Experimental data has been calibrated and properly normalized. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line Calibration curve for 771 nm mean particle diameter PSL (solid line). A fit to the calibration curve is shown as well (dashed line)...42 x

16 Figure 2.8 Figure 2.9 Figure 2.10 Figure 2.11 Experimental (solid line) and Mie theory calculations (dashed line) for phase functions (a) and polarizations (b) for 457 nm mean diameter PSL. Experimental data has been calibrated using the calibration curve generated using 771 nm mean diameter PSL. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line...43 Experimental (solid line) and Mie theory calculations (dashed line) for phase functions (a) and polarizations (b) for 1025 nm mean diameter PSL. Experimental data has been calibrated using the calibration curve generated using 771 nm mean diameter PSL. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line...44 Experimental (solid line) and Mie theory calculations (dashed line) for phase functions (a) and polarizations (b) for ammonium sulfate. Experimental data has been calibrated using the calibration curve generated using 771 nm mean diameter PSL. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line CCD image of light scattering for quartz mineral dust, (a). Direct scatter has been subtracted out in (b)...46 Figure 2.12 Integrated scattering intensity of quartz mineral dust Figure 2.13 Figure 3.1 Phase function (a) and polarization (b) for quartz mineral dust. The phase function has been calibrated and properly normalized. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line...48 Ray diagram for reflection of a ray confined to the inside of an ellipse with semi-major axis length, a, and semi-minor axis length, b. The tangent and normal lines at the point of reflection, (x 1, y 1 ), are shown as dashed lines Figure 3.2 Schematic representation of scattering setup. A ray emitted from f 1 (dashed line) passes between two solid vertical lines centered about f 2 (aperture) and intercepts the detector. The extension of the ellipse has been cut down to represent the physical dimensions of the elliptical mirror in our scattering setup. The inset depicts a close up of the scattering area which has been rotated by an angle, Figure 3.3 Top-down view of possible scattering volumes resulting from the overlap of the incoming laser (arrow) with the aerosol dust jet (circle). The cross-hatched region represents the scattering volume xi

17 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 5.1 Figure 5.2 Figure 5.3 Flow diagram of important elements of the scattering apparatus simulation code Histogram of the number of detector intercepts of rays (a), emitted from a rectangular scattering source located at f 1, as a function of location on the detector where the interception occurred. The dark solid line at the bottom of the figure represents the physical extent of the detector. The mapping of the detector intercepts to the scattering angles (gray) along with a fit (black) is given in (b)...61 Histogram of the number of detector intercepts of rays for 0 o (a), 10 o (b), 20 o (c), and 30 o (d) rotations of the scattering volume. The solid black line in each figure corresponds to the extent of the detector...62 Calibration functions for the standard rectangle scattering volume (circle markers), a rotated rectangular scattering volume (square markers), and a larger rectangular scattering volume (diamond markers) Experimentally determined calibration function (solid line) along with model calibration function for the standard rectangle scattering volume (circle markers). The scattering ellipse has been defined to cover polar angles between o and o. (This corresponds to a range of experimental scattering angles 17 o o.)...64 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for calcite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T- Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for gypsum measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for quartz measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T- Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity xii

18 Figure 5.4 Figure 5.5 Figure 5.6 Figure 5.7 Figure 5.8 Figure 5.9 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for illite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for kaolinite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for montmorillonite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity Range of ratios of experimental phase functions to theoretical phase functions generated using Mie theory (a) and T-Matrix Theory (b). Results are shown for the non-clay samples calcite, gypsum, and quartz (dark gray) and for the clay samples illite, kaolinite, and montmorillonite (light gray) Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for hematite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Optical constants used for the theoretical calculations were obtained from Longtin et al. [1988]. Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for hematite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Optical constants used for the theoretical calculations were obtained from Bedidi & Cervelle. [1993]. Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity xiii

19 Figure 5.10 Figure 5.11 Figure 5.12 Figure 5.13 Figure 6.1 Figure 6.2 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for hematite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Optical constants used for the theoretical calculations were obtained from Hematite Sokolik & Toon [1999]. Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for goethite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for Arizona Road Dust measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a) and linear polarizations (b) for Arizona Road Dust measured at 470 nm (left), 550 nm (center), and 660 nm (right). Empirical phase functions and polarizations (dashed line) were generated using a uniform weighting of clay (illite, kaolinite, and montmorillonite) and non-clay (calcite, gypsum, and quartz) samples SEM image of quartz particles with best-fit ellipses determined using the ImageJ software package The left panel shows the two different moderate particle shape distributions used in the experiment: (a) Standard shape distribution using a uniform distribution of oblate and prolate spheroids with AR 2.4; (b) SEM-based shape distribution as determined from Figure 6.1 using ImageJ software package. The right panel shows the corresponding comparison of the T-Matrix simulation results (dashed lines) with experimental IR resonance extinction spectrum (solid with circles) xiv

20 Figure 6.3 Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7 Figure 7.1 Figure 7.2 The left panel shows the different extreme particle shape distributions as determined from IR resonance spectrum of quartz in Kleiber et al. [2009]: (a) Unconstrained model; (b) Gaussian model; (c) Window model. The right panel shows the corresponding comparison of the T-Matrix simulation results (dashed lines) with experimental IR resonance extinction spectrum (solid with circles) Comparison of visible scattering phase function (a) and polarization profiles (b) at 550 nm for the three different extreme model shape distributions shown in the left panel of Figure Comparison of experimental scattering phase functions (a), ratios of experimental to theoretical phase functions (b), and polarization profiles (c) at 470 nm with T-Matrix simulations based on different particle shape models: the moderate SEM-based, and Standard models, and the extreme IR-Based model. Phase functions in (a) for different shape models are offset by factors of ten for clarity Comparison of experimental scattering phase functions (a), ratios of experimental to theoretical phase functions (b), and polarization profiles (c) at 550 nm with T-Matrix simulations based on different particle shape models: the moderate SEM-based, and Standard models, and the extreme IR-Based model. Phase functions in (a) for different shape models are offset by factors of ten for clarity Comparison of experimental scattering phase functions (a), ratios of experimental to theoretical phase functions (b), and polarization profiles (c) at 660 nm with T-Matrix simulations based on different particle shape models: the moderate SEM-based, and Standard models, and the extreme IR-Based model. Phase functions in (a) for different shape models are offset by factors of ten for clarity Measured size distributions obtained by splicing Aerodynamic Particle Sizer and Scanning Mobility Particle Sizer measurements (dotted line) along with log-normal fits to the size distributions (solid line) for the authentic mineral dusts used in this work Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for diatomaceous earth measured at 550 nm. Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity xv

21 Figure 7.3 Figure 7.4 Figure 7.5 Figure 7.6 Figure 7.7 Figure 7.8 Figure 7.9 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for Iowa loess measured at 550 nm. Optical constants used for the theoretical calculations were obtained from Cuthbert [1940].Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for Iowa loess measured at 550 nm. Kaolinite optical constants used for the calculations and were obtained from Egan & Hilgeman [1979].Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for palagonite measured at 550 nm. Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for Saharan sand measured at 550 nm. Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity Normalized phase functions (a), linear polarizations (b), and best fit shape distribution (c) for palagonite measured at 550 nm. The shape distribution was determined by optimizing the fit to the polarization IR spectral data (solid line) and T-Matrix simulations using shape distribution fits to the polarization (solid line with filled circles) and to the IR spectral data (dashed line) (a), and best fit shape distribution (b) for palagonite. The shape distribution in (b) was determined by optimizing the fit to the IR spectral data Particle shape distributions for palagonite (a) and Saharan sand (b). Processed samples were ground using a mortal and pestle followed by mechanical grinding using a Wig-L-Bug xvi

22 Figure 7.10 Scanning electron micrographs of the authentic mineral dust samples. SEMs are shown for diatomaceous earth (a), Iowa loess (b), palagonite (c), palagonite post-processing (d), Saharan sand (e), and Saharan sand post-processing (f) xvii

23 LIST OF SYMBOLS AR Axial ratio C ( ) System calibration function C S D A D p Cunningham slip correction factor Aerodynamic particle diameter Particle diameter D M Mobility particle diameter D ve Volume equivalent particle diameter f 1 f 2 First focal point of elliptical mirror (light scattering region) Second focal point of elliptical mirror (location of aperture) F ( ) Light scattering phase function g Asymmetry parameter I ( ) Scattered light intensity for parallel polarized incident light // I ( ) Scattered light intensity for perpendicular polarized incident light k m n(d p ) Wavenumber Complex refractive index Particle size distribution P ( ) Light scattering polarization profile R eff S(AR) X Effective particle radius Particle shape distribution Characteristic size parameter xviii

24 χ λ θ ρ Aerodynamic shape factor Wavelength Scattering angle Density xix

25 1 CHAPTER 1 INTRODUCTION Mineral dust aerosol plays an important role in determining the physical and chemical equilibrium of the atmosphere. Mineral dust affects climate forcing through the direct scattering and absorption of both incoming visible solar radiation and outgoing terrestrial IR radiation. Dust particles can also serve as cloud condensation nuclei and provide sites for heterogeneous chemical reactions involving important trace gas species, which, in turn, indirectly affect the earth s radiation balance. Unfortunately, many of these processes are poorly understood due to our incomplete knowledge of the physical and chemical characteristics of the particles, including dust concentration and global distribution, as well as aerosol composition, mixing state, and size and shape distributions. Field measurements of aerosol properties are often carried out by remote sensing using satellite or ground based instruments. However, dust retrieval algorithms can depend critically on the optical properties of the dust. Because of uncertainties in aerosol optical properties, dust loading and other characteristics inferred from the field data such as dust composition, and size and shape distributions can be highly uncertain. In this work, the light scattering properties of several of the major mineral components of atmospheric dust aerosol have been studied in order to gauge the accuracy of different light scattering theories in modeling the optical properties of mineral dust aerosol. Particular emphasis has been placed on the effect of particle shape on the analysis. Atmospheric Aerosol Before beginning a discussion of mineral dust aerosol, it is important to understand some of the basic principles and definitions relating to atmospheric aerosol in general. Aerosol is defined to be any solid or liquid particulate matter suspended in a gaseous medium. In many treatments of the subject, the term aerosol is also interchangeably used to refer specifically to the particle itself. The particles in a typical atmospheric aerosol generally

26 2 comprise only a small fraction of the overall mass and volume of the aerosol, on the order of 10-6 [Hinds, 1999]. Aerosol can be generated either through natural processes or through human activity. Common examples of natural aerosol include clouds of water droplets or ice particles, large salt particles generated from ocean spray, pollen, ash from volcanic eruptions, and windblown soil. Anthropogenic aerosol includes smoke and soot from industrial emissions such as carbon particles from incomplete combustion of fossil fuels, urban smog, aerosol generated during surface mining, and an increase in the emissions of windblown soil due to agricultural practices, deforestation, and the desertification of land areas. Total global emissions of natural aerosol are on the order of 3.1x10 9 metric tons per year, whereas anthropogenic aerosol emissions are about 0.46x10 9 metric tons per year [D Almeida et al., 1991; Andreae, 1995]. Anthropogenic aerosol makes up a relatively small fraction of total emitted atmospheric aerosol, ~15%, but is concentrated in the industrialized regions [Hinds, 1999; Sokolik et al., 2001; Satheesh & Moorthy, 2004]. On a regional scale these anthropogenic aerosol emissions can exceed those of natural aerosol. A number of physical properties are used to classify aerosol, or more accurately, classify the characteristics of the particulate phase of the aerosol. These properties include particle concentration, composition, shape, and size distributions. Concentration is a measure of either the mass or number density of the particles of the suspended medium, and is often expressed in units of mg/m 3 or number per m 3 respectively. Particle composition directly affects many of the secondary properties of the aerosol (such as optical properties). Depending on particle composition and the method of aerosolization (mechanical grinding, combustion, etc.), the shape of an aerosol particle can vary significantly. While liquid droplets tend to be spherical, solid aerosol particles tend to have more complicated shapes. Some, such as asbestos, exhibit long fibrous shapes. Smoke or soot resulting from incomplete combustion can also form long chain aggregates of many smaller primary particles. Many dust particles, such as quartz and silicate clays, are highly irregular in shape and can contain sharp edges, points, and internal voids.

27 3 Particle size is one of the most important aerosol properties. Atmospheric aerosol may contain particles with sizes that span many orders of magnitude, ranging from tens of nm to hundreds of µm, provided there are sufficient forces present, such as strong winds, to keep the particles suspended [Hinds, 1999]. It is useful to define a number of size ranges or modes, to describe aerosol particles that exhibit similar physical properties such as settling velocity or atmospheric residence time. The smallest mode is the nucleation mode, which includes particles with diameters of roughly nm. Nucleation mode particles tend to quickly coagulate with each other and with particles in the accumulation mode, especially near source regions where aerosol concentrations are high. This leads to relatively short atmospheric lifetimes for nucleation mode particles. The accumulation mode consists of particles with diameters between 0.1 and ~ 2.0 µm. Coagulation of accumulation mode particles is too slow for the particles to reach the coarse mode and other removal mechanisms, including rainout (where the aerosol particles serve as nucleation sites for raindrops) and washout (removal by falling rain or snow), are very weak. Particles in the accumulation mode can have atmospheric residence times on the order of weeks. During this time, the particles can be transported by wind action over intercontinental distances [Prospero, 1999]. The largest size mode, the coarse mode, consists of particles with diameters larger than ~2 µm. These particles are quickly removed from the air due to gravitational settling and impaction; atmospheric lifetimes for these particles are generally only a few hours or days. Dust particles generated during strong winds, salt particles from sea spray, and particles generated during agricultural or mining practices can fall into the coarse mode. As mentioned above, the term atmospheric aerosol covers a wide spectrum of particulate matter that is suspended in the Earth s atmosphere. Mineral dust aerosol is just one component of atmospheric aerosol, though an important one, and is the focus of this work. Mineral dust aerosol itself refers to a large class of naturally occurring elements or compounds formed by geological processes and comprised mainly of crustal minerals. Strong

28 4 mineral dust source regions exist throughout northern Africa, Middle East, and central Asia [Prospero, 1999]. On a global scale, mineral dust composition is highly inhomogeneous and depends strongly on the source region. For instance, the soil of the Gobi desert typically has less iron but more aluminum and calcium content than the global average earth crust composition [Petrov, 1976], and dust aerosol generated from the Gobi desert will share these traits. Due to relatively strong visible absorption, minerals containing high concentrations of iron minerals, such as hematite and goethite, play an especially important role in light scattering processes. In studies of the relative iron oxide content of a number of aerosol samples from northern Africa and Eastern Asia, Lafon et al. [2006] found that goethite was present in high concentrations in all samples investigated. Sokolik & Toon [1999] have compiled data of mineralogical composition of atmospheric dust collected from a number of regions. They show that samples collected near Central America can have clay compositions as high as 70% by bulk mass, which agrees with measurements of aerosol composition by Reid et al. [2003] who found that silicate clays such as illite, kaolinite, and montmorillonite make up the majority of mineral dust aerosol in that region. Samples collected near Nigeria, show a much lower clay fraction (<25%) and are composed primarily of quartz. This is due to much of the Nigerian sample originating from the nearby Saharan desert. Some of the mineral types found in abundance in ground soils include quartz, calcite, gypsum, dolomite, mica, feldspars, kaolinite, illite, montmorillonite, palygorskite, chlorite, and organic matter [Pye, 1987]. Due to long residence times in the atmosphere, mineral dust composition can also be altered through chemical aging and mixing with other atmospheric aerosol [Sokolik & Toon, 1999]. Mineral dust aerosol can play several important roles in atmospheric processes. Dust particles can serve as nucleation sites to promote cloud formation. Mineral dust can also provide a heterogeneous reaction site for reactive trace gases in the atmosphere [Dentener et al., 1996; Bates et al., 2004; Sullivan et al., 2006]. Arguably one of the most important processes, the absorption and scattering of light by mineral dust, has been the focus of

29 5 numerous investigations over the past several decades. These include experimental and theoretical studies of light scattering and absorption throughout the visible and infrared regions of the electromagnetic spectrum. Due to the irregular shape of mineral dust particles, the scattering process can be quite complex. A number of theories have been developed to model light scattering by small particles including Mie theory, discrete dipole approximation (DDA) methods, Rayleigh Debye Gans theory, geometrical optics methods (GOM), and T- Matrix theory. Mie theory is the simplest and fastest way to calculate light scattering, though it is strictly limited to spherical particles. While Mie theory can provide a good first order approximation to the scattering, significant errors can arise in using Mie theory for irregularly shaped particles, particularly for near back scattering angles. DDA methods allow a great deal of freedom in specifying particle shapes. However, the method is computationally intensive and so is restricted to relatively small particles. T-Matrix theory is computationally efficient and allows for modeling the scattering from a wider range of particle sizes and shapes. In addition to particle shape, light scattering theories also require estimates of the optical constants (refractive index), as well as the particle size, composition, and morphology. The net radiative effect of dust in the atmosphere remains highly uncertain due a number of factors. Of the natural aerosol types, mineral dust is among the most poorly characterized. Even though there have been studies which include characterization of mineral dust in the atmosphere, such as the series Aerosol Characterization Experiments (ACE) [Huebert et al., 2003; Seinfeld et al., 2004], there is still uncertainty as to how to best model mineral dust aerosol, including the composition, size, and shape distributions, mixing state, and particle morphology [West et al., 1997; Sokolik et al., 2001]. There is also limited understanding of the chemical and physical processes that govern mineral dust aerosol generation, transport, and atmospheric aging, all of which can affect global light scattering calculations [Sokolik et al., 2001].

30 6 Particle shape effects introduce particularly significant uncertainties into scattering calculations. Even for scattering theories that allow flexibility in particle shape, there is still uncertainty in how to specify a range of shapes that are truly representative of the mineral dust being modeled. Mineral dusts are made up of a number of components. Even if the refractive indices are known for each component, the best way to determine the overall average index value is not always clear as it depends strongly on the mixing state and morphology of the dust. Optical properties tend to vary nonlinearly with refractive index. This makes it difficult to estimate the magnitude of any errors that may result due to uncertainty in the optical constants. A precise understanding of the properties and behavior of aerosol is necessary for a broad range of applications. Aerosol can have a direct impact on human health. Small particles, those with diameters < 2.5 µm (respirable size range), can penetrate deeply into the lungs. Aerosol transport governs the deposition of highly fertile loess soil to regions throughout the world. Aerosol can have a both a regional and global effect on climate by scattering and absorbing incoming solar and outgoing terrestrial radiation. Satellite measurements of surface properties, such as earth surface temperatures, depend on corrections to account for the optical depth of the aerosol. The effect of mineral dust aerosol on satellite remote sensing measurements and on climate forcing as they relate to light scattering is discussed in more detail below. Radiative Forcing The main two processes that control the overall state of the Earth s climate system are heating through absorption of incoming solar radiation and cooling by terrestrial emission of long-wave infrared radiation. Radiative forcing refers to any system that alters this radiative balance. Positive forcing corresponds to heating of the atmosphere, while negative forcing corresponds to cooling. Greenhouse gases, which are largely transparent to incoming solar radiation, absorb IR radiation emitted by the Earth resulting in positive forcing. Soot, from

31 7 industrial burning of fossil fuels or volcanic eruptions, contains high levels of black carbon, and is the strongest absorbing component of atmospheric aerosol. Estimates of warming due to atmospheric soot are generally within the range W/m 2 [Haywood et al., 1997; Myhre et al., 1998]. Sea salts and sulfates, which are non-absorbing, generally lead to negative forcing by scattering incoming solar radiation back into space. The magnitude of the forcing for sulfates is roughly W/m 2 [Chuang et al., 1997; Feichter et al., 1997; Myhre et al., 1998]. Radiative forcing due to mineral dust is complicated and depends on many factors. Mineral dust can both directly and indirectly affect the radiative balance and the sign of that forcing can be positive or negative. Directly, mineral dust causes negative forcing through the scattering of incoming solar radiation and positive forcing by absorbing outgoing longwave terrestrial IR radiation. Indirectly, particles within the nucleation size mode can serve as cloud condensation nuclei. The increase in cloud cover increases the albedo (reflectivity) of the Earth s surface, having a cooling effect. Some estimates put the magnitude of the radiative forcing due to tropospheric mineral dust to levels comparable to, but opposite in sign, to that of greenhouse gases [Hansen & Lacis, 1990, Penner et al., 1994]. However, the net radiative effect of mineral dust aerosol is still highly uncertain, both in magnitude and sign [Penner et al., 2001, Forster et al. 2007]. Myhre and Stordal [2001] estimate the total forcing from mineral dust to be within the range W/m 2 based on simulations using different size and spatial distributions of dust. They found that increasing concentrations of hematite leads to higher positive forcing due to increases in absorption. A similar range of values, W/m 2, was found by Satheesh & Moorthy [2004]. Forcing from mineral dust aerosol of anthropogenic origin may be as large as W/m 2 [Tegen et al., 1996], though this number is uncertain due to difficulties separating contributions from natural sources of mineral dusts from those that are man-made since both components are highly mixed away from source regions. [Satheesh & Moorthy, 2004]

32 8 Radiative forcing calculations depend on many factors. Estimates of the aerosol temporal and 3-dimensional spatial distribution must be made on a global scale. However, data on these distributions are scarce and soil transport, production, and removal processes are poorly understood [Myhre & Stordal, 2001]. Accurate estimates for a number of key optical properties of the aerosol must also be made. These properties include the single scattering albedo (ratio of scattering to extinction), the asymmetry parameter (ratio of forward to backward scattering), and the optical depth (measure of total scattering and absorption) of the aerosol. Many of these properties can not be measured directly, and are instead estimated from other measured or modeled scattering properties such as extinction spectra or the angular distribution of scattered light (phase function). Accurately modeling the optical properties of mineral dust aerosol can be very difficult, however, and depends on accurate knowledge of aerosol size, composition, refractive index, shape, and mixing state. A large source of error in forcing calculations may come from poor knowledge of the refractive index, though the effects of improper modeling of particle shapes may be equally large [Kahnert & Nousiainen, 2006; Kahnert & Kylling, 2004]. Significant error can be introduced into forcing calculations from assumptions of how the mineral dust particles are mixed. For example, Sokolik and Toon [1999] found that for an external mixture of clays (75%), quartz (20%), and hematite (5%) that the overall forcing was negative, W/m 2. In contrast, they found that by aggregating a small (2%) amount of hematite with quartz (18%) which was then externally mixed with clays (80%), the overall forcing became positive, W/m 2. Similar results were found by Myhre et al [1998] for mixtures of sulfates with soot, W/m 2 (external mixture), compared to +0.10W/m 2 (internal mixture). Estimates of the asymmetry parameter for dry mineral dust aerosol generally fall within the range [D Almeida et al., 1991; Andrews et. al., 2006; Kahnert & Nousiainen, 2006]. It is believed that the asymmetry parameter is relatively insensitive to uncertainties in the refractive index and particle shape, and that differences in the scattering tend to average out over various angle ranges, though particle size plays a much stronger role [Mishchenko et al., 1995].

33 9 Changes in the asymmetry parameter can have significant effects on the overall forcing though, a 10% decrease in the asymmetry parameter can result in a ~20% reduction in radiative forcing [Andrews et. al., 2006]. Remote Sensing Remote sensing applications, including measurements of surface and oceanic temperatures, trace gas concentrations, and measurements of the total dust loading in the atmosphere, offer a signficant advantage in that they are able to make measurements over large areas in relatively little time. However, these applications require an accurate assessment of the optical and physical properties of atmospheric aerosol in order to make corrections to the measurements. For surface temperature measurements, detectors onboard satellites monitor the emitted terrestrial IR radiation. The raw IR data must be corrected to account for absorption and scattering of the signal as it passes through the atmosphere. Aerosol measurements, such as those performed by the Multi-angle Imaging SpectroRadiometer (MISR) and by the Moderate Resolution Imaging Spectro-radiometer (MODIS) sensors onboard the Terra and Aqua satellites rely on scattered solar radiation at numerous wavelength bands to determine concentration and composition of dust in the atmosphere [Diner et al., 1998; Ichoku et al., 2004; Bruegge et al., 2007]. Many of these measurements will later be used in climate forcing calculations. Therefore, any errors arising from the remote sensing algorithms will carry over to the forcing calculations as well. Much like the radiative forcing calculations, remote sensing measurements require some a priori knowledge of the aerosol optical properties. For instance in order to determine aerosol composition, the MISR satellite uses a predetermined lookup table of calculated optical properties for a number of different aerosol types (sulfate, sea spray, mineral dust, biogenic particles, and urban soot) and uses a linear combination of those properties to fit the observed data, thus yielding the the relative amounts of each aerosol type [Diner et al.,

34 ]. This approach requires many assumptions to first be made about average aerosol composition, shape, size, and complex refractive index values. Determining aerosol loading and composition is difficult and requires multi-angle measurements of intensity and polarization [Chowdhary et al., 2001; Veihelmann et al., 2004]. These measurements, especially of the polarization, depend strongly on particle shape however [Veihelmann et al., 2004; Dubovik et al., 2006]. For roughly spherical aerosol, such as marine sulfate aerosol, the use of Mie theory is sufficient to accurately describe light scattering [Masonis et al., 2003]. Mineral dust aerosol, however, is generally irregular in shape and requires more advanced scattering theories to calculate the scattering properties. Approximating mineral dust as spheres can lead to overestimation in predicted backscattering [Mishchenko et al., 1995; Kalishnikova & Sokolik, 2002; Curtis et al., 2008] which in turn leads to an underestimation of the optical thickness. Spherical approximations can also lead to errors in satellite IR spectral measurements. Hudson et al. [2008a, 2008b] found significant errors in both IR spectral line shape and peak position for a number of mineral dust samples when the particles shapes were approximated as spheres. The algorithm employed by MISR instead uses a distribution of spheroidal shapes for mineral dust calculations [Kahn et al., 1997]. There is still some uncertainty as to whether this approximation to the particle shapes creates appreciable errors in the scattering. Some work suggests that using a spheroidal approximation for particle shape introduces negligible errors [Kahnert & Kylling, 2004], while others have found that the neglect of sharp edges could lead to appreciable errors [Kalashnikova & Sokolik, 2002]. It is clear that there is a high level of uncertainty in the current understanding of the light scattering properties of mineral dust aerosol. Since aerosol plays a key role in so many atmospheric processes, it is important to assess and to mitigate this uncertainty with more rigorous laboratory measurements of the light scattering, and through systematic testing of the various light scattering theories as they apply to mineral dusts. That is the intent of the current work.

35 11 Chapter Overview The current work begins with a discussion of the experimental apparatus and methods used to measure light scattering from mineral dust aerosol in Chapter 2. There, key equations describing aerosol physical properties and size distributions are given. In addition, the procedure for analyzing and calibrating the data to account for the nonlinear response function of the experimental apparatus is discussed. A list of the mineral dust aerosol samples used in this work, and some of their relevant physical and optical properties, is given in Tables A mathematical model of the experimental apparatus and scattering process has been created in the Matlab computing language. This model is used to estimate the magnitude of the uncertainties in our measurements and assists in the optical alignment of the setup. A description of this model and the results of the model simulations are presented in Chapter 3. In Chapter 4 a brief overview of the two light scattering theories used in the work, Mie and T-Matrix theories, is given. The relative strengths and limitations of each theory are discussed. Experimental light scattering results are presented in Chapters 5-7. A multiwavelength investigation of the scattering from several key mineral components of atmospheric dust is is described in Chapter 5. Results are presented there for a number of clay (illite, kaolinite, montmorillonite) and non-clay minerals (calcite, gypsum, quartz), ironoxides (hematite, goethite), and for an example of an authentic, multi-component dust mixture (Arizona Road Dust). Experimental results are compared to model simulations using both T-Matrix and Mie theories. Possible uncertainties due to limitations in assumed particle shape distributions are also discussed. In Chapter 6, focus is given to one mineral dust, quartz. Extensive analysis of particle shape effects on model scattering is performed using results from scanning electron micrograph images as well as results from IR spectral fitting routines. T-Matrix results for a number of particle shape distributions are considered. In Chapter 7, scattering from a number of real-world mineral dust samples including Saharan sand, palagonite (a Martian regolith simulant), diatomaceous earth, and Iowa loess soil is

36 12 investigated. Finally, in Chapter 8, a summary of the results presented in this work is given. Possible directions for future this work are also discussed.

37 13 CHAPTER 2 EXPERIMENTAL SETUP This chapter will detail the experimental setup used to collect light scattering data for mineral dust aerosol. Information will be provided for each mineral dust sample used in these experiments including optical properties (indices of refraction) and particle size information (mode diameters, shape factors, etc.). The procedures for data analysis will also be presented, including the processing of scattered light images collected on the CCD camera, phase function normalization, and system calibration. Light Scattering Apparatus A diagram of the full scattering apparatus is given in Figures Mineral dust samples are prepared as a suspension in high purity water (Optima Water, > 99.9% purity). A constant output atomizer (Model 3076, TSI Inc.) is then used to aerosolize the sample. The aerosol is passed through a cyclone and multiple diffusion dryers (one commercial dryer, ATI Diffusion Dryer 250, and one home built dryer, each filled with silica as a desiccant) to remove excess water vapor from the flow. Next, the aerosol enters a conditioning tube where additional dry air is combined with the flow in order to adjust the total flow rate and minimize relative humidity. Relative humidity is monitored at the end of the conditioning tube via a solid state sensor (Model HIH-3602-C, Honeywell) to determine that it is within an acceptable range, typically 10-20%. The aerosol is then directed through a nozzle to a windowless scattering region located at one of the focal points of an elliptical mirror, f 1 (see Figure 2.2). The nozzle, located just above the scattering region, compresses the output aerosol stream down to a narrow jet with a diameter ~1mm. A collection cup, located below the scattering region, is connected to an auxiliary vacuum pump and two particle sizing instruments which are pulling in air at a total flow rate of 10 lpm. Since the combined flow rate from the atomizer and conditioning tube is much lower (~3.5 lpm), this keeps the collection cup at a low pressure relative to ambient. This pressure gradient helps ensure that

38 14 the aerosol flow is efficiently captured from the scattering region for size analysis and so that the mirror and other optics remain free of deposited dust. The aerosol nozzle is mounted on an x-y translation stage so fine adjustments to its alignment can be made to position it directly above f 1. Following capture in the collection tube below the scattering region, the aerosol flow is split for analysis to a pair of particle sizing instruments. A small fraction (~2%) of the total aerosol flow is directed to a Scanning Mobility Particle Sizer (SMPS, Model 3034, TSI Inc.). The SMPS measures particle diameters in the range of ~ nm. Particles from roughly one half of the aerosol flow are collected by an Aerodynamic Particle Sizer (APS, Model 3321, TSI Inc.). This instrument is capable of measuring particle diameters in the range ~ µm. The measurement principles of these instruments will be explained in detail below. The remainder of the aerosol flow is filtered (HEPA capsule Filter) and directed to an auxiliary vacuum pump (GAST Manufacturing, Inc., Model DOA-P704-AA). The tunable output of an Optical Parametric Oscillator (OPO, Continuum Sunlite EX) is used as the light source in this experiment. The OPO is pumped by the third harmonic of a Nd:YAG laser (Continuum Precision II) operating at 10 Hz with an average output power of 2.5 Watts at 355 nm. The OPO is capable of covering a wavelength range between µm. The pulsed output of the OPO is linearly polarized and highly monochromatic (bandwidth 0.08 cm -1 ). The pulse width is on the order of 7 ns. The output power of the OPO depends on wavelength; the maximum average power near 500 nm is ~ 500 mw. The output of the OPO is first attenuated by a factor of 100 using a series of neutral density filters. A Keplerian telescope arrangement of lenses, with focal lengths of 500 mm and 150 mm respectively, is used to narrow down the beam width from 5 mm to 1.5 mm. A pinhole is placed at the focal point within the telescope to act as a spatial filter in order to ensure a Gaussian beam profile. The smaller beam width results in a smaller scattering volume and therefore higher angular resolution for the measured scattered light as will be discussed further in Chapter 3. Next, the beam passes through a polarization rotator (double

39 15 Fresnel rhomb prism) in order to select the angle of the linear polarization vector of the incident beam relative to the scattering plane; in these experiments polarizations parallel or perpendicular to the scattering plane are used. A long focal length lens (f = 60 cm) is then used to focus the beam onto one of the focal points of the elliptical mirror, f 1. The intersection of the laser with the aerosol jet in the scattering region defines the scattering volume. A close up of the scattering region and CCD detector is shown in Figure 2.2b. Laser light, incident on the aerosol particles within the scattering region, will be scattered to all angles. Scattered light collected by the elliptical mirror is focused at the second focal point, f 2, of the mirror. The elliptical mirror was custom machined from a solid aluminum block by Opti-Forms, Inc. (Temecula, California). The ellipse defined by the mirror has a semi-major axis length of 60 cm and a semi-minor axis length of 30 cm. The mirror is mounted on an x-y translation stage, in the scattering plane, to assist in alignment of the setup. An aperture located at the second focal point, f 2, limits the detector s field of view of the scattering region. The scattered light is then imaged onto a CCD camera (Santa Barbara Instrument Group) located approximately 3 cm behind the aperture. The CCD camera is thermoelectrically cooled to 5 o C to reduce noise as a result of dark current. The elliptical mirror and CCD array are contained within an opaque box to limit room light from reaching the detector. Within the box, a wall separates the detector from the scattering region in order to cut down on background light scattering from the edges of the mirror. A small aperture in this wall allows scattered light from the aerosol to pass to the CCD array. This optical arrangement allows for the mapping of scattering angle to position on the detector, where a scattering angle of 0 o (forward scatter) corresponds to light scattered in the direction of the incident light and 180 o (backward scatter) is light scattered opposite the direction of the incident light. The physical dimensions of the mirror and laser beam diameter limit the range of measurable scattering angles to a continuous range of o. The forward direction is more limited due to large background signals associated with intense forward scattered light.

40 16 The CCD camera is positioned so that this range of scattering angles covers most of the active region of the detector, which has 2184 bins. Integration times of 100 seconds are typically used to collect each scattering image; corresponding to an average over ~1000 laser pulses. Mineral Dust Samples A number of mineral dust samples, both single and multi-component, have been examined in this work. Single component samples include both silicate clay and non-clay samples, including iron oxides. The clay samples include montmorillonite, kaolinite, and illite. The non-clay samples include quartz, calcite, gypsum, hematite, and goethite. All of these powdered samples were purchased from commercial vendors and used without further processing, with the exception of illite which came as a rock and needed to be broken down (see below). A number of samples that are more representative of real world mineral dusts, which can often be internally and/or externally mixed, were also used. Saharan sand and Iowa loess samples were both collected in the field by colleagues. Arizona Road Dust and Diatomaceous Earth samples were obtained commercially. Palagonite (JSC Mars-1), a complex mixture often used as a simulant for Martian soil, was obtained from NASA. A list of all samples used and the sources for each is given in Table 2.1. Certain samples, including some of the real-world samples, required further processing after they were received. The illite, Saharan sand, and palagonite samples contained particles that were too large to be aerosolized by the atomizer and/or settled out of the aerosol flow in the experimental apparatus before reaching the scattering region. These samples were first manually ground down using a mortar and pestle for 20 minutes. They were then further ground mechanically using a Wig-L-Bug for another 20 minutes. All samples were prepared by suspending 1-2 grams of the mineral dust in high purity water (Optima Water, > 99.9% purity). Depending on sample density and settling rate, these mineral dusts can stay in suspension for hours, which is sufficiently long to perform the

41 17 collection of all light scattering data. For the samples with a high settling rate, such as hematite and kaolinite, a magnetic stir bar was added to the sample in the atomizer. The entire atomizer was then placed on a magnetic stir plate. Agitation of the sample, along with the recirculation of the sample provided by the atomizer s mode of operation, was sufficient to maintain a relatively constant number density of particles throughout the experiment. Some details of the physical properties of these mineral dusts are also given in Tables 2.1 and 2.2. Optical properties used in the scattering calculations are given in Table 2.3. The chemical formulas for the well defined mineral dusts are given in Table 2.4. A full discussion of the methods used to determine the physical properties of these samples is given below. The sample optical constants given in Table 2.3 are, in most cases, obtained from measurements on bulk material samples. It is a valid question whether bulk optical constants are applicable to particles in the m size range of interest here. This question is particularly difficult to answer for irregularly shaped particles since it is difficult to unravel particle shape effects from possible effects associated with changing optical constants. However, for uniform spherical particles, where Mie theory is applicable, it is possible to probe this issue. Our work on visible scattering from uniform spherical particles in the m diameter size range, including PSL and ammonium sulfate aerosol, shows no evidence for any consistent or significant deviation in the experimental scattering results from Mie theory predictions based on bulk optical constants for these materials. (See for example Figures 2.6, below). In addition, work by Hudson, et al. [2007] measuring IR resonance extinction profiles for near spherical ammonium sulfate aerosol particles in the submicron size range also agrees quantitatively with Mie theory predictions based on bulk optical constants for ammonium sulfate. It is clear that, in some size range, bulk optical constants must become inappropriate. However, careful experiments by other groups on uniform spherical SiO 2 smoke particles suggests that bulk optical constants continue to be reliable down to particle diameters of < 100 nm as discussed in detail in Bohren and Huffman [1983].

42 18 Aerosol Size Distributions When dealing with irregularly shaped particles, such as mineral dust, careful consideration must be used when describing what is meant by the particle size. Irregularly shaped objects don t have a single dimension that adequately describes the size, as any physical measurement of the particle width would depend on the particle orientation. Fortunately, it is often possible to instead use an effective diameter when working with mineral dusts. An equivalent diameter is the diameter of a spherical particle with the same specified physical property as the irregularly shaped particle. Some examples of equivalent diameters include mobility, volume, and aerodynamic diameters. These will be fully explained below. In general, an aerosol will contain particles with sizes that span many orders of magnitude. Different types of aerosol will contain particles that cover different ranges of sizes. For example, soot particles, such as from an industrial plume, typically fall within the range of 20 nm 1 µm. Mineral dust aerosol, however, can range from tens of nm to hundreds of µm in size provided the source region produces sufficient wind force to keep the larger particles aloft [Hinds, 1999]. It is useful to define a number of size ranges or modes, to describe aerosol particles that exhibit similar physical properties such as settling velocity and atmospheric residence time. The nucleation mode includes particles with diameters in the range of about nm. Particles in the nucleation mode have short residence times in the atmosphere due to rapid coagulation with other particles. These particles can also serve as cloud condensation nuclei. The accumulation mode is made up of particles between 0.1- ~2 µm. These particles are important because they are able to stay suspended in the atmosphere for long periods of time since removal mechanisms are relatively slow. For this reason, accumulation mode particles can be transported by wind action over great distances. For example, Saharan dust particles have been identified in the Caribbean and southeastern US [Prospero, 1999]. The mineral dust studied in this work falls within the accumulation mode. The largest mode, the coarse mode, consists of particles with diameters larger than ~2 µm.

43 19 These particles are quickly removed from the air due to gravitational settling. Dust particles kicked up during strong winds and particles generated during agricultural or mining practices can fall into the coarse mode. Since we are dealing with particles that cover a large range of sizes it is convenient to use a size distribution function, n(d p ), rather than speaking in terms of individual particle diameters. Here, D p is an arbitrary equivalent particle diameter. Let N be the particle number concentration, the number of particles per unit volume of air, often expressed in units of cm -3. The size distribution function is the number of particles per unit volume of air with diameters between D p and D p + dd p. The size distribution is then just the number concentration normalized by the range of particle sizes: dn n( D p ) (2.1) dd p Since aerosol particles cover size ranges over many orders of magnitude, it is useful to instead use a logarithmic scale when expressing diameters. The logarithmic form of the size distribution function, n(log(d p )), then becomes: dn n(log( D p )) (2.2) d log( D ) p Further references to the particle size distribution will assume this log derivative form. The next step is to define an equivalent diameter that will later be used in the light scattering calculations (Chapter 4). If one assumes that the particle density is constant throughout the volume of the particle (no internal voids, etc.), it is possible to define a volume equivalent diameter, D, which is the diameter of a spherical particle with the same ve volume as the particle in question. Since the volume equivalent diameter can t be easily measured directly, alternate measurement techniques must be employed in order to get an estimate for D. ve The two equivalent diameters that are commonly measured by commercial instrumentation are the aerodynamic diameter, D, and the mobility diameter, D A M, for a

44 20 particle. The aerodynamic diameter for a particle is the diameter of a sphere with a reference density, ρ 0, of 1g/cm 3 that has the same settling velocity as the particle [Hinds, 1999]. The volume equivalent diameter can be calculated from the aerodynamic diameter using the following relation: D 0 CS ( DA) p CS ( DVE ) (2.3) VE D A where χ is the aerodynamic shape factor for the particle and is a correction to the Stoke s equation for the drag force on a nonspherical particle. With the exception of certain streamlined shapes, irregularly shaped particles will experience a greater drag force then an equivalent volume sphere, therefore χ > 1 typically. For a spherical particle, χ = 1. The reference density is ρ 0 and ρ P is the bulk density of the particle. The Cunningham slip correction factors, C S, account for non-continuum effects near the particle surface that result in a slightly faster settling rate than would be expected. The slip correction is more important for smaller particles (D << 1 µm). The mobility diameter, D M, is the diameter of a spherical particle which follows the same path as the irregularly shaped particle in a known electrical field. The volume equivalent diameter can similarly be written in terms of the mobility diameter: D C S ( DVE ) VE D M C ( D ) (2.4) S M By setting equations 2.3 and 2.4 equal to each other, a relationship between the mobility and aerodynamic diameters is obtained: D M 3 C ( ) ( ) 2 0 S DM CS DA DA 3 (2.5) 2 C ( D ) p S VE Measurements of the mobility diameter or the aerodynamic diameter are straightforward using commercially available instruments. The volume equivalent diameter can be calculated using either equation 2.3 or 2.4 provided the particle shape factors are

45 21 known and slip corrections can be calculated. These can be determined by simultaneously measuring both diameters for a given sample then using equation 2.5 to solve for the shape factor as originally outlined in Khlystov et al. [2004]. Provided the slip correction factor is relatively constant over a range of diameters, the aerodynamic and mobility diameters will have a linear relation. In that case, the shape of the size distribution will be the same for measurements of either D M or D A. If both diameters can then be measured over the same region, a least squares fitting algorithm can be used to overlap the distributions. The relative shift between the two size distributions will be the product of the shape factors and Cunningham slip correction factors. Shape factors for the clay (montmorillonite, kaolinite, and illite) and non-clay samples (calcite, quartz, and gypsum) used in our experiments were determined in independent measurements [Hudson et al., 2008a and 2008b]. It was found that the Cunningham slip corrections for the range of particle sizes studied (roughly 0.1 to 10 µm) were very close to 1 and could therefore be neglected in equation 2.5. Many of the non-clay samples were found to have shape factors near 1 ( ). The clay samples were seen to have much higher values however, with shape factors ranging between Measurement of the entire size distribution of a typical mineral dust aerosol is not possible using currently available commercial instruments based on a single physical property (e.g. aerodynamic or mobility diameter) since the dynamic range of diameters for a typical sample can span four orders of magnitude. As outlined above, our setup uses an APS to measure aerodynamic diameters within the range ~ µm. Later experiments also incorporated an SMPS which is capable of measuring mobility diameters in the range µm. For these latter experiments, the full size distribution was obtained by splicing together the APS and SMPS data. However, in our apparatus there is no region of overlap between these two instruments making it more difficult to determine the magnitude of the shape factor and hence the shift between the aerodynamic and mobility diameter distributions, as was done in the previous work of Hudson et al. [2008a and 2008b]. Instead,

46 22 the small diameter portion of the size distribution measured by the SMPS was first fit by a lognormal distribution. Using the resultant lognormal fitting parameters, it was possible to extrapolate the distribution to larger particles to overlap the data collected by the APS. The shape factor was then calculated by overlapping the APS data with the lognormal fit to the SMPS data. The raw data from the SMPS and APS were next converted to volume equivalent diameters using this calculated shape factor and equations 2.3 and 2.4. The data were then spliced together at volume equivalent diameter of 500 nm. The SMPS is a relatively recent addition to our apparatus. Prior to its addition, the full size distribution was determined in a different way. In those measurements, we were only able to measure the large particle part of the size distribution. These aerodynamic diameters were first converted to volume equivalent diameters using shape factors that were determined by Hudson et al. in separate measurements. In order to determine the contribution of small particles to the size distribution, it was necessary to extrapolate the distribution to smaller particles using a lognormal fit to the APS data. The mode diameters of the log-normal fits were constrained to agree with those measured by Hudson et al. [2008a, and 2008b] using a similar aerosolization method. In order to account for possible errors resulting from uncertainty in the small particle contribution to the light scattering calculations, separate lognormal fits of the size distribution were performed using mode diameters that were up to a factor of 2 larger or smaller than the previously measured mode diameters of these particles (See Figure 2.3). All three fits for the size distributions then could be used as inputs to light scattering calculations. The magnitude of the standard deviation between the resulting scattering predictions then served as an estimate of the errors in the theoretical scattering resulting from uncertainty in the small diameter part of the size distribution that was not directly measured. The total light scattering intensity is mainly dominated by large particles. Therefore, errors due to uncertainty in the small diameter part of the size distribution are small as will be seen below.

47 23 Before leaving the discussion of aerosol particle size, it will be useful to first define two additional commonly used methods of reporting particle size, the effective radius and the characteristic size parameter. Light scattering intensity by particles typically scales with the projected surface area of the particle. As such, it can be convenient to define an average particle size for the distribution using an effective radius, R eff, which is defined as the projected surface area weighted average, i.e. the ratio of the third moment of the size distribution to the second moment of the size distribution: R eff 0 0 R R 3 2 n( R) dr n( R) dr (2.6) where R is the radius of the particle and n(r) is the size distribution. The effective radii for the samples used in this study are included in Table 2.1 and fall in the range ~ nm. This corresponds to particles in the accumulation mode. The characteristic size parameter, X eff, is defined as: X eff 2 nr eff (2.7) where λ is the wavelength of incident radiation, and n is the refractive index of the external medium. For scattering from particles in air, n = 1 to a good approximation. Values for the size parameter are included in Table 2.2 for the samples used in this study. As will be seen in Chapter 4, the functional form of the light scattering theories used in this work depend on X rather than the D or λ individually. System Alignment and Calibration Once the experimental apparatus was roughly aligned using pinholes placed throughout the OPO beam path, it was necessary to perform a finer alignment and to generate

48 24 an angle mapping function (scattering angle to pixel number map) and a system response calibration function for the scattering apparatus. Scattering data collected by the CCD camera is a function of camera position, in pixels (Figure 2.4). It is therefore necessary to generate an angle mapping function to convert between pixels and scattering angles. In addition, the system detection efficiency as a function of angle is not flat. This will be discussed in more detail in Chapter 3. The calibration function corrects the scattering data for the angle dependent system response. System calibration and alignment is done using a sample that is both highly spherical in shape and that has a nearly monodisperse size distribution. Spherical particles are used for the system calibration since there exists an exact analytical solution to Maxwell s equations for light scattering for spheres, Mie theory. Further details of Mie theory, along with other light scattering theories will be given in Chapter 3. A monodisperse size distribution was desirable to eliminate any possible errors associated with measuring the full size distribution and to reduce computation time. Polystyrene latex spheres fit both of these requirements and are commercially available (PSL, Polysciences Inc.) in a number of different diameters in the submicron range (see Table 2.5). Since the optical constants for polystyrene are well known [Boundy and Boyer, 1952], an accurate theoretical prediction of the scattering for PSL particles was possible. System alignment was performed using PSL particles with a diameter of 771 nm. This size was chosen due to the structure of the theoretical phase functions and polarizations. The light scattering phase function is proportional to the total scattered light intensity as a function of scattering angle. The polarization is a measure of the degree of linear polarization of the scattered light as a function of angle. For 550 nm scattered light, 771 nm particles gave phase functions and polarizations with a large number of interference maxima and minima, as can be seen in Figures This proved to be helpful in the determination of the system calibration and angle mapping functions, as will be discussed below.

49 25 Prior to experimental measurements of mineral dust, light scattering for 771 nm PSL is collected for both perpendicular and parallel polarized incident light (as measured from the scattering plane). A double Fresnel rhomb prism is used to rotate the polarization of the incident light. The scattered light intensities for perpendicular, I ( ), and parallel, I // ( ), incident light polarizations are then measured. Here, θ is the scattering angle as measured from the laser axis. Multiple measurements of each polarization are taken (usually three) and averaged in order to reduce signal noise. The phase function, F ( ), and the polarization, P ( ), are determined using the following relations: F( ) I ( ) I // ( ) (2.8) P( ) I I ( ) I ( ) I // // ( ) ( ) (2.9) These measurements are compared against Mie theory predictions for the scattering. Small adjustments to the system alignment are then performed in order to get the best agreement with Mie theory. Once the system is aligned, the angle mapping function, (y), and the calibration curve, C ( ), are generated in a multi-step code written using the Matlab computing language. Relevant sections of this code are included in the appendix but the basic approach is described below. The first step is to make corrections to the relative intensity of the parallel and perpendicular polarization data sets. These data sets are generated a few minutes apart. This relative intensity correction is necessary to correct for possible fluctuations in the particle number concentration, which can change by + 2-3%, as well as variations in the output power of the OPO, which can be as large as +10%, during data collection. This is done by assuring that the polarization data goes to 0 near 0 o and 180 o. An optimization routine applies a scalar factor, a, to I until the magnitude of the polarization is minimized near the endpoints.

50 26 ai P ai I I // // (2.10) Once the scaling factor is determined, both the measured phase function and polarization are corrected. The magnitude of this correction tends to be less than ~ + 7%. Since the polarization data tend to be noisy near 0 o and 180 o due to decreased collection efficiency of the mirror, there is some uncertainty in the scalar correction factor, a. In order to gauge the magnitude of this uncertainty, for each sample three polarization profiles were generated, one for the optimal value of a (as determined by a chi squared fitting routine used to set the polarization to zero at the endpoints) and on each for a+0.07 and a The average deviation from the mean polarization profile was found to be on the order of ~4%. This uncertainty has been included in the error bars of all experimental polarization profiles presented. Next, the routine determines the angle mapping function, (y). This is done by first assuming a sinusoidal form for (y) : ( y) A B sin( Cy D) (2.11) where y is the CCD camera position in pixels and A, B, C, and D are fitting parameters. This form is chosen as a simple functional form that well describes the observed angle dependence. Simulations of the scattering apparatus geometry have resulted in similar predictions for the form of (y) (see Chapter 3). Another least squares fitting routine varies the fitting parameters, and thus varies the scattering angle mapping of the measured data, until the residual between the measured and theoretical polarization profile is minimized. Since the fit is done by varying the scattering angle mapping, it is necessary to have a polarization with a large number of peaks and valleys in order to ensure a unique solution. Once the phase function and polarization pixel data are converted to functions of scattering angle, the system calibration function is then determined. A comparison of the uncalibrated phase function for PSL as well as that determined by Mie theory is shown in

51 27 Figure 2.5. The calibration function is defined as the ratio of the theoretically calculated phase function, F ( ) Theory, to the experimentally measured phase function, F ( ) Measured : F( ) Theory C( ) (2.12) F( ) Measured As can be seen in Figure 2.7, C ( ) tends to exhibit a number of sharp peaks and valleys. These can be explained by limitations in the angular resolution of the scattering apparatus as discussed in more detail in Chapter 3. Since the location of these peaks and valleys will be different for different samples, it is not useful to use the raw calibration curve to correct for these sharp structures in the phase functions. Instead, by performing a least squares fit to C ( ) with an appropriately chosen function, many of the features due to the angular resolution can be smoothed out while retaining the important features associated with the geometry of the setup, as discussed in Chapter 3 Visual inspection of C( ) suggests a function of the following form for the fitting function, C '( ) : C' ( 2 C( D) F ( G) I ( J ) ) A Be Ee He (2.13) where A, B, C, D, E, F, G, H, I, and J are all variable parameters in the fitting routine. In addition, the fitting routine excludes scattering angles that exhibit the pronounced valleys or peaks due to angular resolution limitations, such as those occurring near 45 o and 125 o in Figure 2.7. As will be seen below, the quality of the fits to C ( ) for scattering angles below 17 o and above 172 o are not relevant since the experimental data from those regions is not used due to a high degree of background laser scatter in those regions. Since the fit to C ( ) is not perfect, there is some uncertainty in the experimental results due to this calibration procedure. The magnitude of this uncertainty, σ Cali, is estimated by calculating the average deviation of the fitting function, C '( ), from the raw calibration curve, C ( ) : 1 C( ) C' ( ) Cali (2.14) N C( )

52 28 where N is the number of points in C ( ). Uncertainties were estimated from a number of calibration functions and fits from many different days (>10) of data collection and is found to be ~10%. This uncertainty has been included in the experimental results in Chapters 5-7. Once C' ( ) has been determined, it is possible to generate the calibrated experimental phase function, F '( ) : F' ( ) C'( ) F( ) (2.15) This process of generating and applying the calibration and angle mapping functions has been thoroughly tested both in earlier work by [Curtis et al., 2007], and in the work developed for this thesis. Tests were performed using a number of samples which were also made up of spherical particles so that Mie theory could be used with confidence. Samples included PSL with particle diameters different from those used to generate the calibration function, and thus having very different phase function and polarization profiles. Diameters of 457 nm and 1025 nm were used for these tests. A solution of ammonium sulfate was also used as a test sample. This sample was prepared by adding 0.05 g of ammonium sulfate to 20 ml Optima water. Droplets of the solution formed by the atomizer have a near spherical shape. Calibration and angle mapping functions generated using 771 nm PSL were applied to the scattering data for each of these samples (see Figures 2.6 and ). Mie theory was used to generate theoretical phase functions and polarizations for the PSL and ammonium sulfate. For the PSL samples, the particle size distribution was assumed to be monodisperse with a diameter as reported by the sample manufacturer (Polysciences Inc.). Full particle size distributions were measured for the ammonium sulfate sample using both an APS and an SMPS and were found to have a mode diameter of roughly 60nm. In the Mie calculations, we used the known optical constants for ammonium sulfate, m = i(7.94x10-6 ) [Egan, 1982]. Previous measurements by Hudson et al. [2007] have found that the ammonium sulfate aerosol generated using a similar aerosolization method is very

53 29 spherical, χ = , for small particles (D ve < 200 nm). Since the particles used to test the calibration procedure were all spherical, Mie theory should give an accurate prediction for the light scattering. Comparisons of the calibrated experimental data with Mie theory is given in Figures Experimental data includes error bars representative of the day-to-day variation in measured values as well as uncertainties in the calibration curve (for the phase function profiles) and uncertainties in the relative scaling between the parallel and perpendicular intensities (for the polarization profiles). Excellent agreement between both the phase functions and polarizations over the entire range of scattering angles was obtained for all three test samples. The most significant deviations between measured and theoretical scattering tends to be near regions with very sharp dips in the data, such as near 20 o and 135 o in the 1025 nm PSL data. We believe this is mainly due to the limited angular resolution of the scattering apparatus. Attempts to model the behavior of the scattering region and elliptical mirror (Chapter 3) have shown that the extended size of the scattering volume at f 1, as well the diameter of the pinhole located at f 2, are the main factors that determine the angular resolution. Unfortunately, decreasing the pinhole diameter also has the effect of decreasing total signal intensity. For the mineral dust samples used in this work, the phase function and polarization are slowly varying functions of angle. Thus, the limits on angular resolution exhibited in these test cases are expected to play a negligible role in the mineral dust data. From Images to Phase Functions As was explained above, light scattering from mineral dust aerosol is imaged onto a CCD camera through use of an elliptical mirror with the scattering located at one focal point of the mirror. Once this scattering image is collected, there are many steps required to process the data before a comparison with theoretical predictions for the scattering are possible. A typical image for scattering from mineral dust particles is shown in Figure 2.11a.

54 30 This image was collected for quartz mineral dust with parallel polarized incident light. A background image, collected without any mineral dust present in the scattering region, has been subtracted from the image in order to eliminate light scattering from the edges of the mirror. Near the center of the scattering band (y 1000, z 800), a small bright spot can be seen at what corresponds to a scattering angle of 90 o. This is due to direct scattering that passes through the pinhole at f 2 without first being reflected by the mirror. This direct scatter is removed by subtracting out an image collected with the mineral dust present in the scattering region and with the elliptical mirror blocked. The final scattering image is shown in Figure 2.11b.These 16-bit grayscale images are next exported as text files for further processing. The image is integrated along the z-axis in order to obtain the total scattering intensity as a function of camera position. To cut down on signal noise, this integration is performed only near the scattering signal band, corresponding to pixels z = The integrated signal is shown in Figure 2.12 for parallel polarized light, I //. This entire process is then repeated for perpendicular polarized incident light in order to generate I. The polarization and phase functions are then generated using equations 2.8 and 2.9. An optimization routine is again used to determine the relative scaling factor, a, for I by minimizing the magnitude of the polarization near 0 o and 180 o. At this point, the calibration function, obtained using a fit to the ratio of the measured to Mie theory prediction for scattering from PSL (see above), is applied to the phase function. Since the polarization is defined as a ratio of the difference in the scattering intensities to the sum of scattering intensities (see Equation 2.9), the application of a calibration curve is unnecessary since it will cancel out. The angle mapping function is then used to convert the phase functions and polarizations to functions of scattering angle rather than pixels. In order to compare the measured phase function directly to theoretical phase functions, it is necessary to normalize the data. In keeping with the normalization convention presented in Bohren & Huffman, the following condition is used:

55 sin( ) F ( ) d Due to the geometry of the scattering apparatus and finite width of the laser beam, it is not possible to reliably measure the light scattering over the entire range of scattering angles and our data is limited to a practical range of o. In order to properly normalize the phase function, we must first extend the phase function in the forward and backward directions using the methods outlined by Liu et al. [2003]. At near forward scattering angles, light scattering is somewhat less sensitive to particle shape effects [Bohren & Huffman, 1983] and so we can use Mie Theory or T-Matrix theory to define the forward scattering signal. Theoretical scattering data for angles less than 17 o are first spliced onto the experimentally measured phase function. The experimental data is then extrapolated out to 180 o by using a linear fit of the data between 160 o and 172 o as the phase functions are relatively monotonic over this range of scattering angles. A plot of the final calibrated phase function and polarization for scattering from quartz dust at 550 nm is given in Figure 2.13 as an example.

56 32 Mineral Dust Source D ve (nm) χ σ R eff (nm) Illite** Kaolinite Montmorillonite Calcite Gypsum Quartz Hematite Goethite Arizona Road Dust Source Clay Repository Alfa Aesar Source Clay Repository Omya Inc. Alfa Aesar Strem Chemicals Sigma Aldrich Alfa Aesar Powder Technology Inc ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± * 1.75 ± ± ± ± ± ± ± Palagonite** NASA JSC Mars ± ± ± 7 Saharan Sand** Field Sample ± ± ± ± 9 Iowa Loess Field Sample ± ± ± 18 Diatomaceous Earth Alfa Aesar ± ± ± ± 15 Also shown is the range over which the mode diameters were varied to gauge the uncertainties in the theoretical scattering calculations. *No calculations of the shape factors were made for this sample. A shape factor of 1.0 was assumed based on similar samples. **The values given for illite, palagonite, and Saharan sand are for the post-processed sample (see text). For the diatomaceous earth and Saharan sand samples, a bi-modal log-normal distribution was required in fitting the size distribution data. Results are presented for each mode. Table 2.1 Physical properties of mineral dust samples used in this work: volume equivalent mode diameter (D ve ), aerodynamic shape factor (χ), lognormal size distribution best fit width parameter (σ), and surface area weighted effective radius (R eff ).

57 33 Mineral Dust X eff 470 nm X eff 550 nm X eff 660 nm Illite Kaolinite Montmorillonite Calcite Gypsum Quartz Hematite Goethite Arizona Road Dust Palagonite Saharan Sand Iowa Loess Diatomaceous Earth Table 2.2 Calculated characteristic size parameter ( X eff 2 R eff ) mineral dust samples used in this work.

58 34 Mineral Dust Refractive Index (470 nm) Refractive Index (550 nm) Refractive Index (660 nm) n k n k n k Reference Illite e e e-4 Egan and Hilgeman [1979] Kaolinite e e e-4 Egan and Hilgeman [1979] Montmorillonite e e e-4 Egan and Hilgeman [1979] Calcite (o-ray) e e e-4 (e-ray) e e e-4 Ivlev and Popova [1973] Gypsum e e e-4 Ivlev and Popova [1973] Quartz Hematite* e e e e e e-4 Longtin et al. [1988] Longtin et al. [1988] Bedidi & Cervelle [1993] Sokolik & Toon [1999] Goethite Bedidi and Cervelle [1993] Arizona Road Dust** e e e-4 Spectral Average Palagonite Johnson et al. [2001], Clancy et al. [1995], Saharan Sand e e e-4 Egan [1985] Iowa Loess*** e Cuthbert [1940] Volten et al. [2001] Diatomaceous Earth e e e-4 Egan [1985] PSL Boundy & Boyer, [1952] Ammonium Sulfate e e e-5 Egan [1982] *Light scattering calculations for hematite were performed using values from Longtin et al. [1988], Bedidi & Cervelle [1993], and Sokolik & Toon [1999]. ** Optical constants for Arizona Road Dust are based on an average of clay (montmorillonite) and non-clay (quartz) optical constants and will be discussed in more detail in Chapter 5 *** Optical constants for Iowa Loess are for 589 nm as presented in Cuthbert et al [1940]. Additional calculations were performed using kaolinite optical constants from Egan and Hilgeman [1979] as discussed in Chapter 7. Table 2.3 Optical properties of mineral dust samples used in this work. For cases where optical constants were not available for a given wavelength, a linear extrapolation of values near that wavelength was used.

59 35 Mineral Dust Chemical Composition Illite (KH 3 O)(AlMgFe) 2 (SiAl) 4 O 10 [(OH) 2 (H 2 0)] Kaolinite Al 2 Si 2 O 5 (OH) 4 Calcite Gypsum CaCO 3 CaSO 4 2(H 2 O) Quartz SiO 2 Hematite Goethite Diatomaceous Earth α-fe 2 O 3 Fe 3+ O(OH) SiO 2 *7H 2 O Table 2.4 Chemical composition of the well defined mineral dust samples used in this work. Particle Diameter (nm) Standard Deviation (nm) Table 2.5 Size properties for polystyrene latex spheres (PSL)

60 Figure 2.1 Light scattering experimental apparatus. Aerosol generated by the atomizer is directed to the focal point of an elliptical mirror that acts as the scattering region. The aerosol is then collected for real time particle sizing measurements by an Aerodynamic Particle Sizer (APS) and a Scanning Mobility Particle Sizer (SMPS). A tunable Nd:Yag pumped OPO is used as the light source. 36

61 Figure 2.2 Detailed view of the optical setup (a) and scattering region (b) as viewed from above. Output from the OPO is directed to a telescope setup in order to decrease beam width by roughly a factor of three. A double Fresnel Rhomb prism is used to adjust the polarization of the incident laser before entering the scattering region. Scattered light reflects from the elliptical mirror and is subsequently focused through an aperture onto the CCD camera. The scattering angle is defined relative to the direction of the incident beam. 37

62 Figure 2.3 Measured aerosol particle size distributions (open circles) using an Aerodynamic Particle Sizer. Also shown are log-normal fits to the particle size distribution for mode diameters of 110, 220, and 440 nm. The log-normal fits are used in Mie calculations to give a range of possible scattering signals to account for uncertainty in the small diameter part of the size distribution. 38

63 Figure 2.4 CCD image of light scattering for 771 nm diameter PSL for parallel (a) and perpendicular incident light (b). 39

64 Figure 2.5 Experimental (solid line) and Mie theory (dashed line) phase functions for 771 nm diameter PSL. The experimental data has been mapped from pixels to scattering angle, but the system calibration has not been applied. Mie and experimental data has been normalized to the same amplitude at 35 o. 40

65 Figure 2.6 Experimental (solid line) and Mie theory (dashed line) phase functions (a) and polarizations (b) for PSL with mean particle diameter of 771 nm. Experimental data has been calibrated and properly normalized. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line. 41

66 Figure 2.7 Calibration curve for 771 nm mean particle diameter PSL (solid line). A fit to the calibration curve is shown as well (dashed line). 42

67 Figure 2.8 Experimental (solid line) and Mie theory calculations (dashed line) for phase functions (a) and polarizations (b) for 457 nm mean diameter PSL. Experimental data has been calibrated using the calibration curve generated using 771 nm mean diameter PSL. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line. 43

68 Figure 2.9 Experimental (solid line) and Mie theory calculations (dashed line) for phase functions (a) and polarizations (b) for 1025 nm mean diameter PSL. Experimental data has been calibrated using the calibration curve generated using 771 nm mean diameter PSL. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line. 44

69 45 Figure 2.10 Experimental (solid line) and Mie theory calculations (dashed line) for phase functions (a) and polarizations (b) for ammonium sulfate. Experimental data has been calibrated using the calibration curve generated using 771 nm mean diameter PSL. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line.

70 46 Figure 2.11 CCD image of light scattering for quartz mineral dust, (a). Direct scatter has been subtracted out in (b).

71 47 Figure 2.12 Integrated scattering intensity of quartz mineral dust.

72 48 Figure 2.13 Phase function (a) and polarization (b) for quartz mineral dust. The phase function has been calibrated and properly normalized. Theoretical Mie data has been spliced to the phase function for scattering angles below 17 o and a linear extrapolation has been used for angles greater than 172 o. Those regions are denoted with the dotted line.

73 49 CHAPTER 3 MODELING THE EXPERIMENTAL SCATTERING APPARATUS The detection system used in these experiments has an instrumental response function that is angle dependent and nonlinear. The instrument response is characterized by a number of factors including lower collection efficiency for scattering near the edges of the collection mirror, loss of angular resolution due to finite imaging aperture size, and finite light scattering volume effects. In order to calibrate the instrument (i.e. determine the mapping function from scattering angle to CCD array pixel number) and to account for the angle dependence of the instrument response, calibration functions are derived each day for use in processing the experimental data. The calibration procedure is described in detail in Chapter 2. Briefly, this is done by collecting light scattering data from monodisperse polystyrene latex spheres (PSL, Polysciences Inc.). PSL was chosen due to the individual particles being spherical and because highly monodisperse samples can be obtained with precisely defined particle diameters. This allows for the use of Mie theory in calculating the expected light scattering phase function and polarization profiles. By taking the ratio of the measured phase function of the PSL to that calculated using Mie theory, it is possible to calibrate the system by determining both the angle mapping function and the angle dependent response function for the apparatus. Model of the Experimental Apparatus Early investigations into the structure of the instrument response function showed a number of features that were not easily explained, such as a distinct dip in the system response for scattering angles near 90 o. In order to understand and quantify these features, a code was written in the Matlab computing language (included as an Appendix) that attempts to model the relevant parameters of our light scattering experimental apparatus, including the geometric light scattering off of the elliptical mirror surface from an extended light scattering volume, and including the effects of transmission through the imaging aperture in the setup.

74 50 Careful measurements were taken of the physical dimensions of the experimental apparatus to ensure an accurate model of the setup was obtained. As was described in Chapter 2, a jet of aerosol particles is directed to one focal point, f 1, of an elliptical mirror. The output from a tunable Nd:YAG pumped OPO is also focused onto f 1, and crosses the dust jet at right angles. Since the scattered light from the aerosol sample originates from one focal point of the elliptical mirror, it will be refocused by the mirror to the second focal point, f 2. At f 2, the scattered light passes through an aperture, which functions as a field stop, and the light is then imaged onto a CCD array. However, finite scattering volume effects significantly alter this simple picture. In order to account for these effects we will first treat the case of a scattering source with an infinitesimal volume located at an arbitrary point (x 0, y 0 ) near the focal point, f 1 (see Figure 3.1). We define an ellipse with semi-major and semi-minor axial lengths of a and b, respectfully. We then define a coordinate system with the origin located at the center of the ellipse partially circumscribed by the elliptical mirror as shown in Figure 3.1. A point scattering source located at (x 0, y 0 ) emits a ray (for this model, each emitted ray corresponds to light scattered off an aerosol particle) at an angle θ measured from the optical axis of the elliptical mirror. In Cartesian coordinates f 1 will be located at the point ( f 1, 0) and f 2 will be located at the point (- f 2, 0), and the equation for the ellipse in parametric form will be: x a 2 2 b y The equation for the initial scattering ray will then be: (3.1) y tan( )( x x y (3.2) 0 ) 0 By letting m tan( ) and solving for x and y one can determine the intersection of the ray with the ellipse (x 1, y 1 ): 2 a x1 [ m( x0m y0 ) b( m { b 2mx0 y0 m x0 y0 } )] (3.3) b m a 1

75 51 y 1 m x1 x0 ) ( y (3.4) 0 Once the point of intersection is known, the reflected ray can be determined by reflecting the incident ray off of the tangent to the ellipse at (x 1, y 1 ): ' 2 (3.5) y tan( ')( x x1) y1 (3.6) Here θ is the angle the reflected ray makes with the x-axis and γ is the angle between the incident ray and the normal to the tangent line to the ellipse at that point (Figure 3.1). The reflection of the ray can be repeated as many times as necessary by repeated applications of equations (3.1) through (3.6). If the origin of the emitted ray were at f 1, the reflected ray would then pass through f 2. In order to make this general model of geometric scattering applicable to our apparatus, a number of additional elements must be introduced. The first of these is to limit the range of angles over which the ellipse is defined to polar angles, Θ, between o in accordance with the physical dimensions of the mirror in the experimental setup (see Figure 3.2). This is done by the condition that any ray striking the ellipse outside this angle range is discarded. This range of polar angles corresponds to scattering angles in the range o for a scattering source located exactly at f 1. Also included in the model is a simulated aperture (field stop) located at f 2. In the code, the aperture consists of two straight lines oriented parallel to the y-axis. There is a small gap between the two lines to define the aperture opening through which reflected rays may pass. Any ray that intersects either of the aperture lines is ignored. The model CCD detector is located a small distance behind the aperture. Any ray intersecting this detector line is counted as a successful hit. The initial emission (i.e., scattering) angle and the final position of the corresponding detector hit are then logged. This process is repeated many times in order to build up accurate statistics for the mapping function from scattering angle, θ, to detector position, y Det. The system response function, S(y Det ), can be determined through mapping the number of hits per unit area on the

76 52 detector from a uniform distribution of initial scattering angles. A uniform distribution of hits would imply a flat instrument response function whereas a non-uniform distribution would imply some variation in collection efficiency across the detector. The system calibration function, C(y Det ), is then just the inverse of the system response function: 1 C( y Det ) (3.7) S( y ) Det By mapping the relationship between initial scattering angles and final detector position (the angle mapping function), it is possible to rewrite this as a function of scattering angle: 1 C( ) (3.8) S( ) In the above development, it was assumed that all rays were emitted from the same point, (x 0, y 0 ). However, in our experimental apparatus, laser light scatters from a finite volume of dust particles. This scattering volume is determined by the intersection of the aerosol jet with that of the laser beam, as can be seen in Figure 3.3. Depending on the relative sizes of the jet and the laser beam profile, the cross sectional area of overlap between the two when viewed from above can take on different shapes. For example, if the aerosol jet diameter, d Jet, is much larger than that of the diameter of the laser beam profile, d Laser, the area of overlap (i.e. the two-dimensional projection of the intersection volume) would best be described as rectangular with a width approximately equal to d Laser and length on the order of d Jet. For the case of the laser beam profile having a much larger diameter than the aerosol jet, the intersecting area would be circular with a diameter equal to that of d Jet. In our current configuration the width of the aerosol jet is approximately 1.5 mm and the diameter of the beam profile is approximately 1 mm. For this arrangement, the area of intersection would best be described as rectangular. The next step is to incorporate an extended scattering volume into the model. Instead of choosing a point from which all rays are emitted, we can choose the center point of an

77 53 extended area, (x 0, y 0 ). The space within this area is then randomly populated with point emitters as above in a Monte Carlo averaging scheme. For each point within the area (where a point represents a single scattering source from a mineral dust aerosol particle), a large number of rays are then emitted, and the corresponding scattering angles and detector hits are logged. This process is repeated for all of the generated source points in the volume. As defined above, the scattering angle is measured from the center of the scattering volume. A ray emitted at an angle, from a point near the edge of the scattering volume will not necessarily intercept the detector at the same point as a ray with the same scattering angle but originating from the center of the scattering volume. By considering the range of scattering angles that map to a given detector position, a rough estimate of the uncertainty in initial scattering angle resulting from these finite scattering volume effects can be obtained, This angular uncertainty defines an effective angular resolution for the apparatus. This point will be discussed in more detail below. The angular resolution of the apparatus can be improved by decreasing the size of the aperture or by decreasing the size of the scattering volume. Doing so, however results in a decrease in overall collection efficiency. It is possible to obtain a monotonic relationship between initial scattering angle and detector position by using an appropriate best least-squares fit mapping function to the data. As with the experimental data (see Chapter 2), a sinusoidal function tends to fit the angle mapping very well: A B sin( Cy D) (3.9) Emission Det where A, B, C, and D are fitting parameters and y Det is the position of a ray terminating on the detector (See Figure 3.5 (b) below). It is convenient when comparing to experimental data to first express the detector position in terms of pixel number before performing the fit. This is done by dividing the length of the detector into a number of evenly spaced bins. The number of bins (2184) corresponds to the number of pixels that run the length of the CCD camera in the experimental setup.

78 54 Additional parameters have been included in the model to allow for rotation of the scattering volume about its center point by a set angle, (see insert to Figure 3.2). This allows for exploring the effects of laser misalignment in the setup. If the laser is incident on the scattering area at some angle, this is equivalent to simply rotating the scattering volume. In addition, parameters in the code can control the orientation of the detector. Slight rotations in the detector can help determine misalignment of the CCD camera in the experimental setup. To summarize the steps involved in modeling the experimental apparatus, a section of an ellipse is first defined between the polar angles = o. A point located near the first focal point of the ellipse is chosen as the center point for a rectangular scattering area that contains a large number of ray emitting source points. The code loops through the source points, each of which emits a large number of rays over a range of scattering angles. These rays are then reflected off of the ellipse (provided they intercept the ellipse within its defined range of polar angles, ). The reflected rays that intercept either of the aperture lines are discarded. Those that pass between the aperture lines strike the detector line. The detector position of the intercept, together with the corresponding scattering angle, is then logged for each ray. Finally, the mapping between scattering angle and detector position, and the angle dependent instrument response function can be determined. Figure 3.4 shows a flow diagram of the key steps in the simulation. Model Parameters In order to obtain statistically significant results for this model, it is necessary to track a large number of emitted rays from a large number of scattering points. For a given simulation, the number of randomly distributed points within the scattering volume is generally set to 20,000 points. For each point, the code loops through 180 emitted rays from that point. The emission angles from the particle are evenly distributed within the range of 0 o to 180 o, where 0 o corresponds to forward scattering and 180 o corresponds to backward

79 55 scattering in the experimental setup. The minor and major axes of the ellipse are set to correspond to the physical dimensions the elliptical mirror, 17.5 cm and 30 cm respectively. The detector has been placed 2.5 cm behind f 2 (i.e. the field stop aperture). By visual inspection of the scattering region in the experimental setup, it is most appropriate to choose a rectangular extended area for these simulations. The length (oriented perpendicular to the optical axis of the ellipse) is set to1.5 mm and the width is set to 1 mm. This corresponds to the case of the incoming laser beam profile having a smaller diameter than that of the aerosol jet (see Figure 3.3). Even though a large number of rays are generated in a single simulation (3.6x10 6 ), only a fraction of these will make it through the aperture to the detector. The fraction of emitted rays that finally intersect the detector is proportional to the width of the aperture opening in this two dimensional model. In the physical setup, this attenuation is proportional to the aperture area. For these simulations, a 1 mm aperture opening was used. This results in only ~10% of all emitted rays making it to the detector. Model Results Preliminary simulations were performed assuming the center of the scattering volume was located directly at the first ellipse focus, f 1. The scattering volume was oriented with its length running parallel to the y-axis. The detector was also oriented parallel to this axis. By plotting a histogram of the number of detector hits as a function of detector position, as shown in Figure 3.5 (a), we can see a symmetric buildup of hits with a distinct dip near the center. These features are the results of the finite nature of the scattering volume. Changing the shape of the scattering volume will result in slightly different peaks and dips in the histogram. For example, increasing the length of the scattering volume along the laser axis will result in a much wider dip. Alternately, increasing the width of the scattering volume along the mirror optical axis will result in a less pronounced dip. Even though the area itself

80 56 is centered directly on the focal point, scattering points away from the center do not originate from f 1 and therefore do not pass directly through f 2. A plot of the scattering angle as a function of the detector position for the corresponding hit is given in Figure 3.5 (b). Here, the detector position has been divided into a number of bins which correspond to the pixel number on the CCD array. It can be seen that this is not a one-to-one mapping. This is again due to scattered rays originating from source points in an extended volume. The width of this band is linearly dependent on the width of the aperture used in the simulation and gives a rough estimate for the angular resolution for the instrument. In this case the width of the band is ~ 7 o. Also included is a fit to the angle mapping (using equation 3.9) which will later be used to generate the system angle calibration function. Model simulations were also performed to test the effects of rotating the scattering volume and the detector. Due to the symmetry involved in the setup, rotating the scattering volume by an angle produces very similar results to rotating the detector by an angle -. For this reason, here only the effects of rotating the scattering volume will be discussed. Figure 3.6 depicts how of the number of detector hits as a function of detector position changes for a range of rotation angles. Even for angles as small as 10 o the relative width of the two peaks near the edge of the detector can be observed to change noticeably, with significantly more hits on one side of the detector. This can have a significant effect on the system calibration, as will be discussed below. As the ratio of the length to the width of the scattering volume increases, the effects due to rotation of the scattering volume become more pronounced. It is important to note that the large rotations used in this simulation would correspond to a gross misalignment of the laser in the experimental apparatus that would easily be detected by alignment pinholes in the setup and corrected. It has been included for informative purposes only and helps to highlight subtle changes which might otherwise be overlooked by limiting the model simulations to small rotations in the scattering volume.

81 57 These simulation results are used to generate a model angle-dependent instrument response function (see equations 3.7 and 3.8). Typical results are shown in Figure 3.7 for a number of different model inputs. The model calibration functions are averages over three consecutive model simulations for each set of input parameters. There will be variations in the model results from one simulation to the next due to the randomly populated scattering volume, though these variations are quite small due to the high number of scattering points that were chosen as inputs. Averaging multiple simulations together assures a more uniform distribution of scattering points within the scattering volume. Calibration curves are included for three sets of inputs; the standard rectangular scattering volume (length = 1.5 mm, width = 1.0 mm, no rotation), a rotated rectangular scattering volume (length = 1.5 mm, width = 1.0 mm, = 15 o ), and a larger rectangular scattering volume (length = 3.0 mm, width = 1.0 mm, no rotation). As the length of the scattering volume increases, the central peak in the calibration broadens significantly and increases in amplitude. Rotations in the scattering volume will result in a shift of the central peak away from 90 o towards larger or smaller scattering angles depending on the direction of the rotation. In our experimental measurements, the range of scattering angles in which reliable data can be collected is limited to the range o. This is due to strong forward and backward light scattering from optical elements along the beam path (even in the absence of aerosol particles) onto the mirror. Due to the high background signal intensities in the extreme forward and backward directions measured by the CCD, it is difficult to subtract this signal out. As a result we exclude data for scattering angles less than 17 o and greater than 172 o from the results. This is equivalent to having a mirror which is defined over a range of angles which are not symmetric about a 90 o. In order to account for this, the ellipse in the simulation was redefined to cover a range of polar angles between o and o (i.e. scattering angles in the range o for a scattering source located exactly at f 1 ). The standard rectangular scattering volume (length = 1.5 mm, width = 1.0 mm, no rotation) was again used for this simulation. An averaged experimentally determined

82 58 response calibration function, obtained using Mie theory and experimental data collected for polystyrene spheres, is included for comparison. The experimental calibration function is an average of 6 calibration functions derived from multiple days of collection. The model calibration function has been vertically scaled to the experimental calibration function in order to more accurately compare the structure between the two. It can be seen that the model calibration functions and those obtained experimentally, as described in Chapter 2, are in good agreement for all scattering angles for which we are able to reliably measure the light scattering (Figure 3.8). Discussion A model simulation has been developed, using the Matlab computing language, for the scattering and detection process in our experimental apparatus. This simulation includes inputs for the relevant parameters in the scattering including an extended scattering volume of chosen size and shape, incoming laser beam orientation relative to the elliptical mirror (rotating the scattering volume), adjustable aperture width, and CCD array (detector) position and orientation. The effects adjustments to these parameters may have on the resulting system response have been extensively explored. This has provided insight both into the workings of our experimental setup and into the structure of the system calibration and response functions that are generated experimentally. This has in turn allowed for more accurate alignment procedures to improve day-to-day reliability and accuracy in our data.

83 59 Figure 3.1 Ray diagram for reflection of a ray confined to the inside of an ellipse with semimajor axis length, a, and semi-minor axis length, b. The tangent and normal lines at the point of reflection, (x 1, y 1 ), are shown as dashed lines. Figure 3.2 Schematic representation of scattering setup. A ray emitted from f 1 (dashed line) passes between two solid vertical lines centered about f 2 (aperture) and intercepts the detector. The extension of the ellipse has been cut down to represent the physical dimensions of the elliptical mirror in our scattering setup. The inset depicts a close up of the scattering area which has been rotated by an angle,.

84 60 Figure 3.3 Top-down view of possible scattering volumes resulting from the overlap of the incoming laser (arrow) with the aerosol dust jet (circle). The cross-hatched region represents the scattering volume. Figure 3.4 Flow diagram of important elements of the scattering apparatus simulation code.

85 Figure 3.5 Histogram of the number of detector intercepts of rays (a), emitted from a rectangular scattering source located at f 1, as a function of location on the detector where the interception occurred. The dark solid line at the bottom of the figure represents the physical extent of the detector. The mapping of the detector intercepts to the scattering angles (gray) along with a fit (black) is given in (b). 61

86 Figure 3.6 Histogram of the number of detector intercepts of rays for 0 o (a), 10 o (b), 20 o (c), and 30 o (d) rotations of the scattering volume. The solid black line in each figure corresponds to the extent of the detector. 62

87 Figure 3.7 Calibration functions for the standard rectangle scattering volume (circle markers), a rotated rectangular scattering volume (square markers), and a larger rectangular scattering volume (diamond markers). 63

88 Figure 3.8 Experimentally determined calibration function (solid line) along with model calibration function for the standard rectangle scattering volume (circle markers). The scattering ellipse has been defined to cover polar angles between o and o. (This corresponds to a range of experimental scattering angles 17 o o.) 64

89 65 CHAPTER 4 LIGHT SCATTERING THEORY This chapter will focus on the theoretical background necessary to perform light scattering calculations. Emphasis will be placed on the two scattering theories used throughout this work, Mie theory and T-Matrix theory. Both theories provide classical solutions to Maxwell s equations, though they differ in their applicability to certain types of problems. Mie theory is only strictly valid for scattering from spherical shaped particles whereas a much wider range of particles shapes can be treated with T-Matrix theory. Both theories are routinely used in the calculation of light scattering from mineral dust aerosols, though T-Matrix theory has become increasingly popular as more powerful computers are able to reduce calculation times [Dubovik et al., 2002, 2006; Kalashnikova et al., 2005; Veihelmann et al., 2004; Mishchenko et al., 1997]. Both Mie theory and T-Matrix theory require a relatively small number of inputs for scattering or absorption calculations. For a given mineral dust aerosol, the complex index of refraction, the particle size, and the wavelength of incident light must all be specified. For the case of a polydisperse aerosol (i.e. one that is not defined by a single particle diameter but, rather, a distribution of particle diameters), separate calculations can be made for each range of particle diameters and the resulting scattering can be linearly combined with appropriate weighting factors based on the particle size distribution. One more important input parameter is required for T-Matrix theory; the specification of the particle shape. The functional form governing how these shapes are specified will be discussed below. Prior to an in depth discussion of either light scattering theory, it is convenient to first define the characteristic size parameter, X, as: nd p X (4.1)

90 66 where d p is the diameter of the particle, λ is the wavelength of incident radiation, and n is the refractive index of the external medium. For scattering from particles in air, n = 1 to a good approximation. As will be seen later, the functional form of both scattering theories depend on X rather than either d p or λ individually. The size parameter can also serve as a useful tool in determining the specific light scattering theory most appropriate for a given situation. When the particle is very large relative to the wavelength of incident radiation, X 1, geometric scattering will often be sufficient in modeling the scattering from that particle. While in this regime, the scattering intensity will be independent of wavelength. In the opposite limit, X 1, Rayleigh scattering is more appropriate. In this range, the scattering 4 intensity is proportional to. It is this strong wavelength dependence that is responsible for the blue color of the sky during the day and the red and orange hues near a sunset. As the particle diameter approaches that of the incident wavelength, neither Rayleigh nor geometric scattering accurately predicts the light scattering. As X 1, it is therefore necessary to turn to more robust theories such as Mie and T-Matrix theories. Though these are often used only in the region where the X 1, each theory is fully valid for a wide range of values of X, and converge in the appropriate limits to geometric or Rayleigh scattering. Both T-Matrix and Mie theories can be used to calculate a number of important light scattering properties including the angular light scattering intensity or phase function, the linear polarization of the scattered light, absorption, backscattering ratio, and others. Though the details of how these properties are calculated will differ for different scattering theories and will be discussed below, it will be helpful to first discuss some of these basic properties. The results of this work, presented in Chapters 5-7, will focus strongly on the scattering phase functions, F(θ), and the linear polarizations, P(θ). The scattering angle, θ, is measured relative the direction of the incident light. The phase function is proportional to the sum of the perpendicular and parallel polarized scattered light intensities from an unpolarized light source. Due to the symmetry in the scattering matrix, this is equivalent to the sum of the scattered light intensities from incident light polarized perpendicular to the scattering plane,

91 67 I, and incident light polarized parallel to the scattering plane, I //. The scattering plane is defined to be the plane containing both the incident and scattered light signal. F( ) I I (4.2) // The linear polarization, which is a measure of the degree of polarization of the scattered light, can then be written as follows: P( I // ) (4.3) I I I // where positive values for P(θ) correspond to scattered light that is partially polarized perpendicular to the scattering plane and negative values correspond to light which is partially polarized parallel to the scattering plane. The asymmetry parameter, g, is a measure of the degree of scattering in the forward (near 0 o ) or backward (near 180 o ) and defined as the cosine weighted average of the phase function over all scattering angles: 1 g cos( ) F ( )sin( ) d (4.4) 2 0 For particles that scatter isotropically, or in cases where the scattering is symmetric about a scattering angle of 90 o, g = 0. Strong forward scattering relative to that in the backward direction will result in positive vales of g, while stronger backward scatter will result in negative values of g. The remainder of this chapter will provide of brief overview of the mathematical framework of both Mie and T-Matrix theories. A rigorous derivation is beyond the scope of this work and is already given in a number of other sources. Bohren and Huffman [1983] provides an in depth derivation of Mie theory. For more information on T-Matrix theory, one should see Waterman [1965, 1971] and Mischenko et al. [1996]. Some of the computational methods and strengths and limitations of each theory will also be provided below.

92 68 Mie Theory Formulated by Gustav Mie in 1908, Mie theory is the solution to the wave equation for plane electromagnetic waves scattering from a sphere. Though the strict requirement of spherical particles places significant limitations on Mie theory, it is still commonly used to predict the scattering properties of aerosols which are roughly spherical, such as sea-salt or ammonium sulfate aerosols which are generally in droplet form at relevant atmospheric relative humilities [Masonis et al., 2003]. Application of Mie theory to non-spherical particles can result in significant errors in prediction of the scattering properties of those particles [Mishchenko et al., 1995; Curtis et al., 2008]. As will be seen in chapters 5-7, the mineral dust aerosol samples used in this work include particles that are highly irregular in shape. Nonetheless, Mie theory still provides a first order approximation to the scattering from such particles. Following the discussion of Bohren and Huffman [1983], we will first examine the relationship between the light incident on a particle, I i, to the light scattered from that particle, I sr, through use of the scattering matrix, S. I Sˆ (4.5) s I i Above, the subscript s denotes the scattered light and the subscript i denotes the incident light on the particle. This relationship can be expanded in terms of the standard Stoke s parameters I, Q, U, and V: I s Q U Vs s s S S S S S S S S S S S S S S S S I i Qi U i Vi (4.6) Written using the basis of the electric field vector oriented parallel, E //, or perpendicular, E, to the scattering plane the Stoke s parameters are defined as: I // E// E E E (4.7)

93 69 Q // E// E E E (4.8) U E E E (4.9) // E// V i E E E (4.10) // E// Alternately, the scattering matrix can be written using the basis of the electric field vectors: E // s 2 S3 // i E s ikr e S ikr S 4 E S1 E i (4.11) where k is the wavenumber, k= and S 1 and S 2 are given below. The distance from the scattering particle to the observation point is given by r. This formulation of the light scattering has the advantage that all of the optical properties of the scattering particle are contained within S. Each element of S is a function of the scattering angle. Therefore, once S is known for a given particle, it is relatively simple to determine the behavior of the scattered light at all scattering angles from that particle. In particular, the light scattering intensities for incident light polarized parallel and perpendicular to the scattering plane can be expressed in terms of the scattering matrix elements: I // S11 S12 S 2 2 (4.12) 2 11 S12 S1 I S (4.13) The next step is to use a suitable method to calculate the scattering coefficients. This has been done in Bohren and Huffman [1983] by first representing the scattered wave as a series of spherical harmonics. The plane wave incident on the particle is then also expanded in spherical harmonics. By choosing appropriate boundary conditions at the surface of the particle and setting the expansion coefficients equal to each other, the following relations for the scattering elements can be obtained: 2n 1 S 1 ( a n n bn n ) (4.16) n( n 1) n

94 70 2n 1 S 2 ( a n n bn n ) (4.17) n( n 1) n where the functions π n and τ n are defined as: n 1 Pn (4.14) sin 1 dp n n (4.15) d where 1 P n are the associated Legendre functions of the first kind of order 1. Also in the above, a n and b n are the scattering coefficients and represent weighting factors for each of the normal scattering modes of the sphere. For a spherical scattering particle, the scattering coefficients can be determined analytically and can be written in terms of the Riccati-Bessel functions, ψ n. a b n n ' ' m n ( mx ) n ( X ) n ( X ) n ( mx ) (4.18) ' ' m ( mx ) ( X ) ( X ) ( mx ) n n n n ' ' n ( mx ) n ( X ) m n ( X ) n ( mx ) (4.19) ' ' ( mx ) ( X ) m ( X ) ( mx ) n n n n The primes denote differentiation with respect to the argument in parentheses. Here X is the size parameter and m is the complex index of refraction: Though the mathematical form of the scattering coefficients and scattering matrix elements provide a rather abstract view of light scattering from a particle, there are a few important aspects of Mie theory that should be pointed out. Due to the behavior of the π and τ functions, as the diameter of the scattering particle increases there will be an increase in the ratio of forward to backward scattering (asymmetry parameter +1). Larger particles will also produce scattering phase functions with narrower forward scattering peaks. It has also been found that large non-spherical particles scatter similarly to area-equivalent spheres near the forward direction [Mishchenko & Travis, 1994]. As the scattering angle increases, the

95 71 difference in scattering between spherical and non-spherical particles increases. This factor is very important in our normalization procedure for experimental data (see Chapter 2). A code has been written in the Mathematica programming language, based on that of Hung & Martin [2002], to calculate the scattering phase function and polarization. As mentioned above, Mie theory calculations require the full size distribution and the complex index of refraction for the scattering particles as inputs. For cases where the size distribution is polydisperse, it is necessary to calculate the light scattering for each size range, and then add the resulting scatter contributions together using the number concentration of particles in that size range as a weighting factor. This code is able to generate scattering properties relatively quickly on a standard personal computer (Pentium GHz processor, 1.5 GB RAM,). Calculations of F(θ) and P(θ) are carried out at 75 evenly spaced scattering angles over the range of o. Processing times are on the order of 15 seconds per particle size range investigated. These low computational requirements have helped make Mie theory a popular choice for light scattering calculations when the particles are expected to be relatively spherical. T-Matrix Theory T-Matrix theory is an exact numerical solution to Maxwell s equations for scattering from an object of arbitrary shape. The use of a matrix approach to the determination of the light scattering properties was first given by Waterman [1965] for perfectly conducting spheres and later for scattering from objects of arbitrary shape and including dielectrics [1971]. This formulation of the scattering problem was based on solutions to the integral formulation of Maxwell s equations. Due to the linearity of those equations, it is possible to expand both the incident and scattered waves into spherical harmonics and then relate the scattering coefficients of those expansions through use of a transformation matrix. A full derivation of the T-Matrix approach is given in a number of sources [Waterman, 1965, 1971; Barber and Yeh, 1975; Mishchenko et al., 1996] and will not be repeated here, though a brief

96 72 summary and a few key equations will be presented below using the notation of Mishchenko et al. Let an arbitrarily shaped particle be located at the origin of a spherical coordinate system with a plane wave incident on the particle. The incident, E i, and scattered, E s, fields can than be expanded as a series of spherical harmonics: n E [ a RgM ( kr) b RgN ( kr)] (4.20) i n m n n mn mn mn mn E [ p M ( kr) q N ( kr)] (4.21) s n m n mn mn mn mn where M mn and N mn are proportional to the spherical Hankel functions as given explicitly in Mishchenko et al. [1996], and Rg denotes the regular solution. Due to the linearity of Maxwell s equations and the boundary conditions, it is possible to relate the incident field coefficients, a mn and b mn, to the scattered field coefficients, p mn and q mn, using the following relation: n' p mn [ Tmnm' n' am' n' Tmnm' n' bm' n' ] (4.22) n' 1 m' n' n' q [ T a T b (4.23) mn n' 1 m' n' or, in matrix form: p a T T q b T mnm' n' m' n' mnm' n' m' n' ] T T a b (4.24) where T is the transformation matrix (i.e. the T-Matrix). The T-Matrix does not depend on the incident or scattered fields, only on the physical (particle shape, size, and orientation) and optical (refractive index) properties of the scattering particle. Once the transformation matrix is known for a given particle, it is possible to calculate the scattered light for any orientation of incident radiation. The determination of the T-Matrix can be accomplished by use of the

97 73 extended boundary condition method [Waterman, 1965]. This is done by first expanding the internal field, E int, of the particle in terms of vector spherical functions as was done for the incident and scattered fields above (see equations 4.20 and 4.21): n E int [ cmnrgm mn ( mkr) d mnrgn mn ( mkr)] (4.25) n m n where the complex index of refraction is given by m. It is necessary to only use the part of M mn that is regular (i.e. finite), denoted by Rg in 4.25, over the scattering region being investigated. For example, as was mentioned above M mn and N mn are proportional to the spherical Hankel functions, H (1) ~ ( J n ± i N n ), where j is the spherical Bessel function, and n is the spherical Neumann function. Since N at the origin, the Neumann functions must n be excluded from M mn and N mn in that region. It is then possible to relate the expansion coefficients of the internal field to those of the incident and scattered fields through the transformation matrix Q: a Q b Q Q Q c d (4.26) p RgQ q RgQ RgQ RgQ c d The T-Matrix can then be related to Q by the following. (4.27) 1 T RgQQ (4.28) The elements of Q are integrals over the particle s surface and depend again on the physical and optical properties of that particle. In general, T and Q contain an infinite number of elements. However, for practical purposes, the summations (equations 4.20, 4.21, and 4.25) are truncated after certain convergence criteria are reached thus allowing T to be determined explicitly. In addition, the calculation of T can be greatly simplified by the assumption of an ensemble of randomly oriented particles [Mishchenko et al., 1996]. In that case, T reduces to a diagonal matrix in the indices m and m (see equation 4.22 and 4.23). This is a reasonable

98 74 assertion when dealing with aerosol particles. Particles with rotational symmetry also greatly simplify these calculations. All T-Matrix calculations of light scattering within this work were done using the extended precision T-Matrix Code of Mishchenko et al., publicly available through the NASA web site [Mishchenko & Travis, 1998; ]. This code has been used extensively to model the light scattering from aerosol particles [West et al., 1997; Nousiainen and Vermeulen, 2003; Veihelmann et al., 2004; Dubovik et al., 2006]. The T-Matrix code can be used to calculate the full scattering matrix as well as characteristic dust optical properties such as total extinction and scattering albedo for a randomly oriented distribution of particles of specified shape. Required input to the code include the wavelength of incident light, the particle s index of refraction (the optical constants), and information about the particle size and shape distributions. The size distributions are input as lognormal distribution parameters (mode diameter and width parameter) based on fits to experimental data as was discussed in Chapter 2. Particle shapes were modeled with a series of ellipsoids. A spheroid is defined here as an ellipse of revolution about the minor (oblate spheroid) or major (prolate spheroid) axis whose shape can then be characterized by a single parameter, the axial ratio (AR), the ratio of majorto-minor axis lengths. A sphere will have AR = 1. Though there are considerable limitations on the allowable particle shapes by restricting ourselves to spheroids (i.e. no edges), there is still a wide range of shapes that can be successfully modeled; from flat plate-like structures to needle shapes by using appropriate choices for the axial ratio. Separate calculations of the light scattering for each sample were made for a range of axial ratios. A shape distribution, to be discussed further in Chapters 5, 6, and 7, was then used to weight the scattering results for each particle shape together. It is important to note that there is still disagreement within the aerosol community as to whether using a spheroidal distribution to approximate the particle shape of mineral dust

99 75 aerosol, which are generally highly irregular in shape and may include sharp edges and internal voids, or carbon particles which are highly fractal in nature,can be used to accurately calculate the scattering properties of such particles. Mishchenko et al. [1997] and Veihelmann et al. [2004] have both used a uniform distribution of spheroid to model the scattering of mineral dust aerosol though the range of axial ratios differed in each case. Nousiainen and Vermeulen [2003] also found that the spheroidal approximation of particle shape resulted in good agreement to many elements of the full scattering matrix for feldspar particles provided a wide range of axial ratios were used. Alternate choices for particle shape include finite circular cylinders or spheres deformed by means of a Chebychev polynomial [Mugnai & Wiscombe, 1980] though these were not examined in this work. More advanced shape models are possible, though this greatly increases calculation time and limits the range of particle sizes that can be practically modeled [Dubovic et al., 2006]. A significant limitation of this T-Matrix code is the finite maximum particle diameter, or more appropriately the maximum size parameter, X, for which the code will converge. This value is dependent both on the axial ratio of the particle and the optical constants at the wavelength being investigated. For example, for a spheroidal particle with size parameter, X a, defined by the length of the semi-major axis, and a refractive index n = 1.31, the code will converge for X a = 17 for axial ratios of 20, but can converge for X a > 100 if the axial ratio is decreased to ~2. These values of X will decrease significantly as the value of n increases [Mishchenko & Travis, 1998]. For cases where larger axial ratios were considered, it was sometimes necessary to cut down the large diameter portion of the size distribution. Errors associated with the omission of the large diameter have been estimated for all T-Matrix calculations and will be discussed in detail in Chapter 5. The T-Matrix code is much more computationally demanding than the Mie code discussed earlier and was not able to be run on a typical personal computer due to the need for extended precision variables. Calculations were instead run on a 4-CPU IBM RS/6000 workstation (2.5 GB RAM, four 375-MHz 2-Way Power Bit Processors).

100 76 Computation times varied significantly and were largely dependent on the maximum size parameter and the axial ratios of the particles being modeled. For nearly spherical particles, computation times can be as low as a few minutes to generate the full T-Matrix and scattering matrix. For highly eccentric particles, AR > 8, computation times longer than 5 hours were observed. Results from both Mie and T-Matrix simulations will be compared with experimental data in Chapters 5 7.

101 77 CHAPTER 5 MULTI-WAVELENGTH LIGHT SCATTERING STUDIES In this chapter, phase function and polarization profiles for a number atmospherically relevant components of mineral dust aerosol including silicate clay (montmorillonite, kaolinite, and illite), non-clay (calcite, gypsum, and quartz), and iron-oxide (hematite and goethite) samples are given. In nature, mineral dust aerosol is composed of a mixture of individual minerals. Atmospheric mineral dust may be internally (aggregates of different minerals) or externally (each particle is composed of one mineral) mixed. For an external mixture, it should be possible to treat each mineral component separately in scattering calculations and then perform a weighted sum of the resulting scattering matrices assuming the relative concentrations of each are known [Sokolik & Toon, 1999]. For internally mixed samples the results can be quite different [Bohren & Huffman, 1983] Results will also be presented for Arizona Road dust, a commonly used test aerosol that is a mixture of a number of minerals and is more representative of a real world dust sample. For this sample, the applicability of using weighted-average scattering properties based on an assumed mineralogy will be investigated. Data will be presented at three visible wavelengths, 470, 550, and 660 nm, which were chosen to coincide with a number of wavelength bands used by remote sensing satellites such as MISR and MODIS. Error Analysis Since (with the exception of Arizona Road Dust) these are well characterized, single component mineral samples, wavelength dependent optical constants are available from published sources (see Table 2.3). In some cases it was necessary to linearly interpolate between tabulated values of the optical constants to the wavelengths investigated here, but the optical constants were (in most cases) slowly varying functions of wavelength and the interpolations were performed over a short wavelength range. The uncertainties in the optical constants from the interpolation result in negligible errors in the scattering calculations. The

102 78 notable exceptions to this are the iron oxides, hematite and goethite, which have optical constants that vary dramatically across the visible. The optical constants for the iron oxides should be considered as highly uncertain, with a correspondingly large uncertainty in the scattering calculations. All measurements of the light scattering from the mineral dust aerosol samples were performed simultaneously with the measurement of the aerosol size distribution as discussed in Chapter 2. The size distributions were measured using a TSI Inc. Aerodynamic Particle Sizer (APS) which is able to measure particle diameters within the range ~ µm. At the time this data was taken we did not have an integrated Scanning Mobility Particle Sizer (SMPS), which covers the small particle diameter range, in our aerosol flow system. Since the samples investigated here contain a significant number of particles with diameters below this range it was necessary to extend the distribution to smaller diameters (D < 0.5 m) by using a log-normal fit to the APS data at large diameters (D > 0.5 m). The log-normal distribution was constrained to have mode diameters consistent with those made in earlier measurements of these samples using both an APS and SMPS under similar flow conditions [Hudson et al., 2008a and 2008b]. However, this approach results in significant uncertainty in the aerosol size distribution for use in the theoretical scattering calculations for both Mie theory and T-Matrix theory. In order to gauge the magnitude of the errors in the theoretical scattering profiles resulting from uncertainty in the input size distribution, multiple log-normal fits were generated for each measured size distribution, all consistent with the APS data for D > 0.5 m but with varying mode diameters at small diameters. These fits were constrained to have mode diameters that differed by a factor of two (higher and lower) than the mode diameter measured by Hudson, D Exp, in earlier work. In some cases, the distributions using mode diameters of 2 or 1 D resulted in very poor fits to the APS data for D > 0.5 m. In Exp DExp 2 those cases, the largest and smallest values of the mode diameter that would still give good fits to the APS data were used instead. The values for the range of mode diameters used for

103 79 each sample are included in Table 2.1. Light scattering calculations for the phase functions and polarizations were then performed using Mie theory for all three size distributions. Error bars for the theoretical phase function and polarization profiles were then determined by the range of the variation between the different Mie theory simulations. We did not carry out a similar error analysis for the T-matrix theory simulations since those calculations are more computationally demanding and require a time-consuming loop over particle shape parameters as discussed below. It seems reasonable to assume that the errors resulting from variation in the input size distribution should be of comparable magnitude for the T-matrix calculations. Since light scattering intensity typically scales with the projected particle surface area, the errors in the simulated scattering that result from uncertainty in the small particle part of the distribution are often small. This is because the scattering signal is dominated by scattering from the large diameter part of the size distribution directly measured by the APS. Errors in the experimental scattering data result from day-to-day variation in the measured scattering data (random errors) and uncertainty in the instrument calibration function (systematic errors). For each day of data collection, three experimental phase function and polarization profiles were measured. The scattering phase function and polarization for each sample were measured for 3-6 days, depending on the repeatability of the measurements. Results are presented as an average over all the data sets, and the standard deviation from the mean of the different data sets gives an estimate of the measurement variability. In addition to measurement variability, error bars for the phase function also include an estimate of the systematic error resulting from uncertainty in the instrument calibration function. Error bars for the polarization profiles include estimates of the uncertainties in the relative scaling factor, a, between the parallel and perpendicular intensities. Both systematic errors are discussed in detail in Chapter 2. For the polarization profiles, the magnitude of the error bars represents the standard deviation from the mean of the different experimental data sets as well as uncertainty in the

104 80 relative intensity between the incident parallel and perpendicular polarized beams (see Eq. 2.10). The calibration error doesn t affect the polarization because the polarization involves a ratio of two measured values (see Eq. 2.9) and any systematic calibration effects would cancel. In order to quantify the goodness of fit between the theoretical and experimental phase function profiles, a reduced chi-square factor was calculated: 2 1 N 2 {[ F( ) ( )] / ( ) 2 i T i i N i 1 } (5.1) In (5.1) F is the measured phase function, T is the corresponding model prediction, i is the estimated experimental uncertainty, all at a given scattering angle i, and N is the number of angle data points. The reduced chi-square values for the Mie and T-Matrix theory simulations are given in Table 5.1 for all wavelengths investigated. T-Matrix Shape Distribution In addition to the wavelength dependent optical constants and full size distribution, T- Matrix theory also requires assumptions about the particle shape. Throughout this chapter a uniform distribution of spheroidal particle shapes will be assumed. The use of spheroids allows the particle shape to be characterized by a single parameter; the axial ratio (AR), the ratio of major-to-minor axis lengths. Separate T-Matrix calculations have been performed for ARs ranging between 1.0 AR 2.4 in steps of 0.2 for both prolate and oblate spheroids. The resulting phase function and polarization profiles were summed assuming a uniform (constant) distribution of AR values over this range. This shape distribution is a common model used for mineral dust aerosol [Mishchenko et al., 1997] and is based on electron microscope images of mineral dust aerosol particles collected in the field. This model will be referred to as the Standard shape distribution model. As will be shown in chapter 6, this range of ARs is also roughly

105 81 consistent with electron microscope images collected in the lab for the samples used in this work. Asymmetry Parameter Calculations As was discussed earlier (Chapter 4), the asymmetry parameter, g, is a measure of the relative scattering in the forward (near 0 o ) to backward (near 180 o ) directions. For mineral dust aerosol with characteristic size parameters in the range X ~ 2-5, as appropriate here (see Table 2.3), the forward scattering tends to dominate the overall scattering signal, resulting in positive values for g [Andrews et. al., 2006; Kahnert & Nousiainen, 2006]. For each sample, asymmetry parameters have been calculated using equation 4.4 for the experimental (g Exp ), Mie theory (g Mie ), and T-Matrix theory (g TM ) phase function profiles for all three wavelengths, and the results are given in Table 5.2. For the experimental asymmetry parameter, the value given is an average over consecutive days of data collection. For the Mie theory results, the asymmetry parameter is an average over the results for the three size distributions that were used in the calculations and the errors are representative of the standard deviation about the mean value of the results. As discussed above, we expect the errors in the T-Matrix and Mie results to be of comparable magnitude. Non-Clay Mineral Dust Results Shown in Figures are the scattering phase function and polarization profiles for a number of non-clay samples including calcite, gypsum, and quartz for incident light at 470 nm, 550 nm, and 660 nm. The particles span an effective (surface area weighted) size parameter range from X eff = 2.8 for gypsum to X eff = 4.9 for quartz for 550 nm incident light (see Table 2.3). For these dust samples, the imaginary part of the refractive index is small and the real part lies within the range n throughout the range of visible wavelengths investigated. The iron oxide samples differ markedly from these in that they exhibit strong absorption in the visible range and they will be discussed separately below. Calcite and quartz are both birefringent materials, which must be taken into account in the light

106 82 scattering calculations. Assuming that these particles are randomly oriented in the aerosol flow, light will scatter from each of the three optical axes (two ordinary, 1 extraordinary) with equal probability. For birefringent samples, it is therefore necessary to average the o-ray (ordinary) and e-ray (extraordinary) theoretical scattering results in a 2:1 ratio. We have found for quartz that averaging the optical constants in a 2:1 ratio prior to running the scattering calculations produced negligible changes in the resulting theoretical scattering. This is due to the very small difference between the o-ray and e-ray optical constants (~1%). In order to reduce calculation times, these averaged optical constants for quartz were used. This was not done for the calcite as the differences in the optical constants were much larger between the e-ray and o-ray axes. As can be seen for the non clay minerals in Figures (a), Mie theory tends to over predict the scattering in the backward direction, scattering near 180 o, at all three wavelengths. An better way of viewing the differences between the experimental and theoretical phase functions is to examine the ratio of the experimental phase function to that generated using either T-Matrix theory (TM Ratio) or Mie theory (Mie Ratio) as shown in Figure (b). It is easy to see in Figures (b) that the experiment-to-theory ratio for the T-Matrix simulations tend to be flatter and closer to unity than those for the Mie theory simulations, indicating significantly better agreement with experiment. The tendency for Mie theory to overestimate the backscattering signal results in theoretical asymmetry parameters, g Mie, that are slightly lower, ~ 4-6%, than those determined experimentally (see Table 5.2). Though T-Matrix theory results, assuming the Standard shape distribution, are in better agreement with the experimental phase function overall (Table 5.1), the calculated asymmetry parameters for T-Matrix theory, g TM,, are still very similar to those for Mie theory. A comparison of the polarization profiles for the non-clay samples is given in Figures (c). For all three samples, the polarization is positive over the entire range of scattering angles with a peak near 110 o. The magnitude of the experimental polarization

107 83 increases with increasing wavelength, ranging from 31-55% for quartz. In contrast, the theoretical polarization curves tend to be negative over the entire range with minimums between 150 o and 160 o. It can easily be seen that even though the quantitative agreement between the T-Matrix and experimental polarizations is poor, qualitatively, it is a significant improvement over that of Mie theory. Overall, T-Matrix theory using a commonly applied particle shape distribution model, a uniform distribution of spheroids of moderate axial ratios, gives a significant improvement over Mie theory in modeling both the phase function and polarization profiles for the nonclay mineral samples, quartz, calcite, and gypsum. However, the agreement with experiment is still not especially good, particularly for the polarization. This could indicate a limitation of the spheroid approximation in T-Matrix theory or it could result from a difference between the assumed and actual particle shape distribution function. These points will be discussed in more detail in the next chapter. Clay Mineral Dust Results Analogous results for the scattering from the silicate clay minerals, illite, kaolinite, and montmorillonite, are given in Figures For the clay samples, the effective size parameter range of X eff = 2.3 for illite and X eff = 3.4 for kaolinite for 550 nm incident light (see Table 2.3), which is very similar to that of the non-clay samples. As with the non-clay samples, the variation in the real part of the refractive index for the clays is relatively small over the visible range, n The illite sample is unique among the clays in that it exhibits a greater degree of absorption within the visible range. The imaginary part of the refractive index for illite is an order of magnitude higher than those of the other two clays (though still small, particularly when compared to hematite or goethite). The silicate clays show much greater variability in the scattering results than the nonclay samples discussed above. The observed scattering profiles are more variable from dayto-day and week-to-week, and show much greater variation between the different samples

108 84 and at different scattering wavelengths (Figures (a) and (b)). For example, Mie theory tends to over predict the scattering for scattering angles greater than ~125 o for kaolinite measured at 470 nm, but the over prediction becomes much more pronounced for the kaolinite phase function measured at 660 nm where it can be seen for all scattering angles above ~30 o. The situation is reversed for the illite sample where Mie theory actually under predicts the scattering for near backscattering angles at all three wavelengths. The overall agreement between experiment and T-Matrix theory assuming a Standard shape distribution is similar to that of Mie theory for all samples. There is a trend that the asymmetry parameters calculated for both Mie and T-Matrix theories tend to be slightly lower than those determined experimentally, i.e. a higher predicted backscatter-to-forward scatter ratio than that seen experimentally, as was also the case for the non-clays. An alternative way of viewing the differences between the clay and non-clay results is to plot the range of experiment to theory ratios for the different clay (light gray band) and non-clay (dark gray band) minerals on the same plot. This is done in Figure 5.7 for both the experiment-to-mie and the experiment-to-t-matrix ratios. As is evident from both the Mie and the TM ratios, the scattering from the clay samples seems to be inherently different from that of the non-clay samples even though both have similar size distributions and optical constants. The ratios for the non-clay samples tend to be constrained to a much narrower band indicating very similar scattering behavior for the quartz, calcite, and gypsum samples. The ratios for the clays are much more varied, corresponding to a much wider band. Possible reasons for the greater variability in the scattering results for the silicate clays are discussed below. However, it is clear that this increased variability makes it much more difficult to draw consistent and general conclusions for scattering from the silicate clays than for the non-clay mineral samples. As was seen for the non-clay samples, the experimental polarization profiles for the clays, shown in Figures (c), tend to be positive over the entire range of scattering angles, though the peak of the polarization signal tends to occur at smaller angles for these

109 85 samples; ~90 o for montmorillonite, ~95 o for illite, and ~ 100 o for kaolinite. The peak magnitude of the polarization again increases with increasing wavelength, varying from 55-70% for montmorillonite. The Mie polarization is again negative over all scattering angles for the kaolinite and montmorillonite with minimums near 160 o. For the illite sample, Mie theory comes closest to agreeing with experiment in that it is positive for scattering angles less than ~140 o and the predicted peak position near 99 o. The overall magnitude of the peak is still lower than that seen experimentally, however. T-Matrix theory performs better in predicting the peak magnitude of the polarization, but tends to place the peak of the profile at larger scattering angles. As the imaginary part of the refractive index increases, both Mie and T-Matrix theory predict a polarization that peaks at more positive values. This may explain in part why the illite polarization shows better agreement with theory. Iron Oxide Results The effective size parameters for the hematite and goethite samples are X eff = 3.8 and 2.4, respectively, for 550 nm incident light (see Table 2.3), which is similar to the other samples. These samples are treated separately from the other non-clay samples because of the relatively large index of refraction values (both real and imaginary) for both samples. The optical constants for hematite, as reported by Longtin et al. [1988], also have a stronger dependence on wavelength than is seen in any of the other samples, with the imaginary part of the index changing by nearly two orders of magnitude over the wavelength range presented here. It bears repeating that the optical constants for the iron oxide samples are highly uncertain. The indices of refraction reported by three different sources, Longtin et al. [1988], Bedidi and Cervelle [1993], and Sokolik & Toon [1999], give dramatically different values for both the real and imaginary parts (see Table 2.3) which has significant effects on the theoretical scattering calculations. For this reason, theoretical phase and polarization profiles were generated for hematite for each set of optical constants (Figures ). At 470 nm, the experimental phase function for hematite (Figure (a)) is relatively flat

110 86 for scattering angles above roughly 70 o which may be due to the large imaginary index of refraction at that wavelength. This flatness results in an asymmetry parameter that is relatively high compared to other samples investigated, g Exp Both Mie and T-Matrix theory predict this flattening of the phase function though the overall agreement with experiment for scattering angles within the range o is quite poor for any of the three sets of refractive index values. The more gently sloping phase functions predicted by theory leads to an under prediction for the asymmetry parameter, g Miey 0.68 for the Longtin optical constants, g Mie 0.66 for the Bedidi optical constants, and g Mie 0.67 for the Sokolik & Toon optical constants. As the incident wavelength increases, the experimental phase functions for hematite become more symmetric about 90 o, with a corresponding decrease in the magnitude of g. The theoretical phase functions follow this general trend though the absolute agreement with experiment does not improve and the asymmetry parameter is again underestimated at all wavelengths with the exception of the 660 nm calculations based on the Sokolik & Toon or the Bedidi refractive indices which lead to an over-prediction of the asymmetry parameter by about10% or 30% respectively. Compared to the hematite sample, the goethite experimental phase functions (Figure 5.11 (a)) tend to show a weaker wavelength dependence, the most notable variation occurring at large scattering angles (>140 o ). This may be explained because the imaginary part of the refractive index is less dependent on wavelength for goethite. These phase functions are also have much higher backscatter relative to forward scatter, and therefore have asymmetry parameter values which are lower than any of the other samples, g Exp The changes in the theoretical phase functions are more pronounced with wavelength. The most notable difference between the experimental and theoretical phase functions is for near backward scattering. These general trends are correctly predicted by the theoretical simulations. As the wavelength increases, the experimental scattering increases for scattering angles greater than 140 o. However, the theoretical phase functions decrease in this region with increasing

111 87 wavelength. The theoretical phase functions also take on a more linear form for mid-range scattering angles, o. A similar trend is hardly evident in the experimental data. The hematite, and to a lesser extent the goethite, polarizations given in Figures (c), tend to be flatter for all scattering angles then was seen for the other non-clay samples. Though the goethite polarization follows the trend of increasing peak magnitude with increasing wavelength as was seen before, the hematite actually exhibits the opposite behavior and is near zero (un-polarized scattering) for 660 nm incident light. For both samples, the theoretical polarizations are in relatively good agreement with each other, but with T-Matrix theory again giving slightly better fits to the experimental data. However, both theories predict polarization values that are too low. In addition, polarization profiles generated using the Sokolik & Toon optical constants agree with experiment much better than those generated using either the Bedidi or the Longtin optical constants. Arizona Road Dust Results Arizona Road Dust (ARD) serves as a model for the complex mixtures that more closely represent authentic mineral dust aerosol in that it is an inhomogeneous mixture of different minerals. ARD is a commercially available sample (Powder Technology Inc.) and is provided in a number of particle size ranges. For these measurements, ARD in the fine size range was used, corresponding to particles with an effective radius, R eff 320 nm (X eff = 3.6 for 550 nm) (see Tables 2.2 and 2.3). This is similar to other samples investigated. The ARD sample was characterized separately in our laboratory by Cwiertny et al. [2008]. Elemental analysis and FTIR data collected for this sample are consistent with a model composition consisting roughly equal weight mix of clays (probably primarily montmorillonite) and nonclays (primarily quartz). Based on this analysis, optical constants were generated for the ARD sample by averaging those of the quartz and montmorillonite in a 1:1 ratio (see Table 2.3). For an external mixture, it is more accurate to generate separate scattering matrices for each mineral component (i.e. each set of optical constants), then average the resulting phase

112 88 functions and polarizations [Sokolik & Toon, 1999]. However, for quartz and montmorillonite, the real and imaginary parts of the refractive index are quite close for all wavelengths examined. Since we assume the same size distribution for each constituent mineral dust, the use of optical constant average method results in a negligible error and was used to reduce computation time when running the T-Matrix simulations. The experimental and theoretical phase function and polarization profiles for ARD are given in Figure As seen for the non-clay samples, Mie theory tends to over-predict the scattering in the background direction (>120 o ) at all three wavelengths. T-Matrix theory using the Standard shape distribution does a much better job fitting the experimental phase function and agrees over the entire range of scattering angles. In contrast, the T-Matrix polarization profiles are still negative for most angles though the theory does predict a slightly positive polarization over the mid range scattering angles, o, it is still negative for most angles and again fails to properly model the polarization for this sample. As an alternative to theoretical calculations for modeling complex mixtures, it may be possible to use a set of empirically measured phase functions and polarizations as a basis set for the scattering of the mixture, provided the mineralogical composition of the mixture is known. This approach has been used previously by Mishchenko et al. [2003] using an experimentally measured quartz phase function in an aerosol retrieval algorithm for satellite data. Average scattering phase functions and polarizations were first generated for the clay samples (illite, kaolinite, and montmorillonite) and the non-clay samples (calcite, gypsum, and quartz). The average clay and average non-clay scattering data were then averaged in a 1:1 ratio (consistent with mineralogical analysis for ARD). These empirical phase functions and polarizations are shown in Figure 5.13 along with the experimentally measured ARD scattering data. Not surprisingly, the agreement between the empirically generated and the experimentally measured phase functions and polarizations is much better than that obtained using either Mie or T-Matrix theory.

113 89 Discussion As was seen for nearly all the samples studied, Mie theory fails to accurately model the scattering properties of irregularly shaped mineral dust aerosol for wavelengths throughout the visible spectral region. The failure of Mie theory is most clearly evident in the results for the non-clay minerals (calcite, gypsum, & quartz) and for the Arizona Road Dust sample. In these samples the most pronounced deviations from experimental measurements occur for scattering angles >150 o where Mie theory consistently and significantly overpredicts the phase function, by up to a factor of three. Near mid-range scattering angles, there seems to be a wavelength dependent deviation from experimental values as Mie theory under-predicts scattering in this region for the 470 nm data, but over-predicts the scattering for the 660 nm data. For the silicate clays (illite, kaolinite, & montmorillonite) and the iron oxides (hematite and goethite) the deviations between the experimental phase function and Mie theory simulations are less consistent but still appear to generally hold, particularly (and notably) for the kaolinite sample. As noted above, there is great variability in the experimental results among the clay samples and, for a given sample, at different wavelengths; this variability makes it difficult to draw general conclusions from the clay scattering data. Here it should be noted that, from a model testing perspective, the results for the non-clay minerals (particularly calcite and quartz) are much more significant than the results for the clay or iron-oxide samples. The many reasons for this will be discussed below but essentially it is due to the fact that the optical constants (the index of refractions) for quartz and calcite are known at a very high confidence level while the optical constants for the other samples have significant uncertainties. The failures of Mie theory are most consistent and most pronounced in the polarization data for all of the samples studied, where the experimental polarization is generally opposite in sign to the Mie theory predictions. This might be expected since the

114 90 scattering polarization is much more sensitive to particle shape effects than the phase function. Failure to properly model the scattering phase function for mineral dusts will ultimately result in errors in calculating the back scattering cross section, and the asymmetry parameter, which are used in a number of aerosol retrieval and climate forcing algorithms [Kahn et. al., 1997; Myhre & Stordal, 2001]. For most cases studied here, it was seen that the theoretical asymmetry parameters were consistently lower than those seen experimentally, in some cases up to ~10% lower. As noted above a 10% error in asymmetry parameter can result in a 20% error in the climate forcing effect of dust [Andrews et. al., 2006]. The use of T-Matrix theory with the assumption of a uniform distribution of oblate and prolate spheroids of moderate asymmetry parameter (AR 2.4, Standard shape model) results in a significant improvement in the agreement between the experimental and theoretical phase function and polarization profiles. This is most evident in the non-clay and ARD scattering results where the reduced chi-square factors of Table 5.1 show a dramatic and consistent improvement with T-Matrix theory. It is also readily apparent in the Figures (b) and 5.7 where the TM ratios are much flatter and closer to unity than the Mie ratios. The improvements in the model results using T-Matrix theory for the silicate clays and iron oxides are less consistent and obvious, but the general conclusion appears to hold as well, particularly for kaolinite. As noted above, from a model-testing perspective, the results for the non-clay samples are deemed to be much more significant and reliable. While T-Matrix theory offers a significant improvement over Mie theory in simulating the scattering profiles, the agreement is still not great and, for the polarization data, is quite poor for nearly all of the mineral samples and scattering wavelengths investigated. This might be a result of uncertainty in the mineral optical constants, but even for quartz and calcite where the optical constants are known very accurately, there are large discrepancies between the measured and calculated polarization profiles. It seems most likely that the discrepancy is a result of particle shape effects, and could indicate that the

115 91 Standard shape distribution model may not be appropriate for our samples. This issue will be explored in detail in the next chapter. It is also interesting to see how the theoretical simulations do in predicting the wavelength dependence in the scattering data for a given sample. The most pronounced wavelength variations are seen for hematite. In this case the curvature of the phase function increases significantly, and the polarization decreases markedly as the wavelength changes across the visible from 470 nm to 660 nm. T-Matrix theory (and to a somewhat lesser degree, Mie theory) does very well in predicting these dramatic changes with wavelength for either set of optical constants used in the calculations. We also note the significant differences in scattering properties of hematite and goethite. Iron oxides are a common constituent of mineral dust aerosol and play a critical role in determining aerosol optical properties because of their strong visible absorption bands. It has been generally assumed that iron oxide in mineral dust appears most commonly in the form of hematite. However, recent analyses by Lafon et al. [2006] call this assumption into question. The results here show that this issue is extremely important since goethite and hematite have very different scattering properties, and very different wavelength dependences. We have commented that the results for the non-clays are more significant than those of the silicate clay samples or the iron oxides for the purpose of testing theoretical models for the scattering. This is largely due to uncertainty in the optical constants used for these calculations. The optical constants for calcite and quartz have been measured by multiple groups over many years and the results are known with a high level of confidence. This is not so for the other samples under study here, particularly for the clay and iron oxide samples. For the silicate clays there is only a single data set for the visible index of refraction values, Egan and Hilgeman [1979]. The accuracy of this data set is not known. Since optical constants for the clays were all obtained from this source, any errors in those measured values would carry over into these calculations. Furthermore, the silicate clays

116 92 represent classes of compounds with significant variation in mineral form among samples obtained from different regional sources. This is especially true of montmorillonite, which refers to a broad class of smectite clays with significant mineralogical variability. In addition, many clays (and especially the smectites) often have inclusions of iron-containing impurities, which can have a very significant impact on optical constants. Thus, even if the optical constants of Egan and Hilgeman were very accurately determined for their samples, they may not be applicable to our clay mineral samples. In addition, some clays (such as montmorillonite and illite, but not kaolinite) are swellable, i.e., they absorb water with the water molecules moving into interstitial sites between the silicate layers in the clay compound, causing the particles to swell. Because the water is absorbed into the volume of the particle, it is very difficult to remove. Our dust samples are aerosolized from slurry of mineral dust in water. As a result it is very likely that the illite and montmorillonite clay samples are impregnated with water. The size and shape of the particles, and the optical constants may change from day-to-day as a result of different water loading. Interestingly, kaolinite, which shows the most consistent agreement with the scattering characteristics of the non-clay samples, as noted above, does not absorb water. The optical constants for the iron oxide samples are also highly uncertain. For hematite, one set of optical constants used were obtained from Longtin et al. [1988], who reports the refractive index for hematite to be n = i at 550 nm. However, Bedidi & Cervelle [1993] give slightly higher values for the real part and significantly higher values for the imaginary part of the refractive index values for hematite, n = i at 550 nm. A third set of optical constants was obtained from Sokolik & Toon [1999], who report the highest imaginary part of the imaginary part of the refractive index, give a value of n = i at 550 nm. The light scattering calculations, both Mie and T-Matrix, based on the Bedidi & Cervelle optical constants agree significantly better with the experimental polarization profiles than those generated using the Longtin refractive indices, but result in overall poor fits to the phase functions (particularly for the 660 nm data). The overall best fit

117 93 to the phase function and polarization profiles is obtained using the Sokolik & Toon optical constants. However, at 660 nm, both sets of results using the Bedidi & Cervelle or the Sokolik & Toon values lead to a significant over-prediction of the scattering in the backward direction. At 660 nm, better results were obtained using the Longtin refractive indices which suggests that the imaginary part of the optical constants from the other two sources is too high for this particular sample. For hematite, the T-Matrix and Mie theory simulations are in close agreement for both the polarization and phase function profiles. This degree of concurrence suggests that moderate departures from spherical shape are relatively unimportant in determining the scattering matrix for particles with high refractive index values, like hematite. This result is agreement with the earlier studies of Munoz et al. [2006]. This illustrates the degree of uncertainty in the optical constants for hematite and the significant impact that uncertainty can have on the scattering simulations. It is important to note that the optical constants used in this work [Longtin et al., 1988; Bedidi & Cervelle, 1993, Sokolik & Toon, 1999 ] were chosen because they are commonly used in many climate forcing and aerosol retrieval algorithms [Liang, 1997; Weaver et al., 2002; Nobileau & Antoine, 2005; Park et al., 2005, Balkanski et al., 2007; Otto et al., 2009]. Any errors due to uncertainties in the optical constants would also be present in those calculations. For goethite we have only a single measurement for the optical constants. The accuracy of this measurement is not known, but (based on the hematite results) we should expect that there is significant uncertainty in this value. Perhaps an even larger source of discrepancy between experiment and theory may be particle shape effects. It is well known that these mineral dusts are highly irregular in shape and may contain sharp edges, points, and internal voids. Here we have used a uniform distribution of spheroids of moderate asymmetry (AR < 2.4) to model these particles. Some sources claim that the neglect of sharp edges inherent in the spheroid approximation can result in significant errors in calculated optical properties [Kalashnikova & Sokolik, 2002]

118 94 while others assert that these edge effects have a small effect on the scattering [Kahnert & Kylling, 2004]. This remains an open question that will require more study. Another question, which will be addressed in Chapter 6, is whether or not restricting the range of aspect ratios to the relatively narrow range used here, AR 2.4, is truly representative of the shapes of these mineral dust particles. This range is based on analyses of SEM images of particles collected in the field [Mishchenko et al., 1997]. However, SEM data are two dimensional image representations of three dimensional particles. This can lead to errors; for example, a disc-shaped particle may appear circular or needle-like depending on the viewing angle. It is known that the clay particles are highly plate-like [Nadeau, 1985], so a more extreme range of aspect ratios with higher weighting of oblate shapes might be expected to give a more realistic approximation to the shapes of those particles. In contrast, goethite particles are known to be rod-like and so a more extreme range of aspect ratios with higher weighting to prolate spheroids might give better agreement. Due to the uncertainties in mineral optical constants and the difficulties in calculating the scattering properties of non-spherical particles, it has been suggested that using empirical phase function data based on experimental measurements of real dust samples may be a more reliable approach. For example, empirical scattering data could be used in climate forcing calculations and aerosol retrievals. We have seen that using average clay and average nonclay phase functions and polarizations to model the scattering for an external mixture, ARD, has worked extremely well. Of course, knowledge of the composition of the aerosol being modeled is still necessary using this method. It is particularly important to have reliable information about the iron oxide content and mineralogical form. Average scattering data for the clays, non-clays, and hematite has been provided for this purpose in Curtis et al. [2008]. Our results here supply additional input for this database. It is important to reiterate here that scattering is highly dependent on particle size. Those results were collected for particles in the accumulation size mode, corresponding to effective particle diameters 1.0 µm, and the empirical data should only be used to model particles in a similar size range.

119 95 Mineral Dust Wavelength χ 2 (Mie) χ 2 (T-Matrix) 470 nm Calcite 550 nm nm Gypsum Quartz Illite Kaolinite Montmorillonite Goethite Hematite (Longtin et al. [1988]) Hematite (Bedidi and Cervelle [1993]) Hematite (Sokolik & Toon [1999]) Arizona Road Dust 470 nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm nm Table 5.1 Reduced χ2 values for comparison of the experimental phase functions with simulations using Mie theory and using T-Matrix theory assuming a Standard shape distribution.

120 96 Mineral Dust Wavelength g Exp g Mie g TM * Calcite Gypsum Quartz Illite Kaolinite Montmorillonite Goethite 470 nm 0.65 ± ± nm 0.65 ± ± nm 0.69 ± ± nm 0.69 ± ± nm 0.68 ± ± nm 0.71 ± ± nm 0.69 ± ± nm 0.69 ± ± nm 0.72 ± ± nm 0.70 ± ± nm 0.68 ± ± nm 0.71 ± ± nm 0.74 ± ± nm 0.71 ± ± nm 0.76 ± ± nm 0.70 ± ± nm 0.68 ± ± nm 0.68 ± ± nm 0.57 ± ± nm 0.55 ± ± nm 0.55 ± ± Hematite 470 nm 0.72 ± ± (Longtin et al. 550 nm 0.64 ± ± [1988]) 660 nm 0.42 ± ± Hematite 470 nm 0.72 ± ± (Bedidi and 550 nm 0.64 ± ± Cervelle [1993]) 660 nm 0.42 ± ± Hematite (Sokolik & Toon [1999]) Arizona Road Dust 470 nm 0.72 ± ± nm 0.64 ± ± nm 0.42 ± ± nm 0.69 ± ± nm 0.68 ± ± nm 0.71 ± ± *Errors in asymmetry parameters generated using T-Matrix theory, due to uncertainties in the input size distributions, are expected to be comparable to those generated using Mie theory. Table 5.2 Asymmetry parameter values for experimental (g Exp ), Mie theory (g Mie ), and T- Matrix theory (g TM ) phase functions for 470, 550, and 660 nm.

121 Figure 5.1 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for calcite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity. 97

122 Figure 5.2 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for gypsum measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity. 98

123 Figure 5.3 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for quartz measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity. 99

124 Figure 5.4 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for illite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity. 100

125 Figure 5.5 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for kaolinite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity. 101

126 Figure 5.6 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for montmorillonite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity. 102

127 Figure 5.7 Range of ratios of experimental phase functions to theoretical phase functions generated using Mie theory (a) and T-Matrix Theory (b). Results are shown for the non-clay samples calcite, gypsum, and quartz (dark gray) and for the clay samples illite, kaolinite, and montmorillonite (light gray). 103

128 Figure 5.8 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for hematite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Optical constants used for the theoretical calculations were obtained from Longtin et al. [1988]. Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T- Matrix results in (a) have been scaled by a factor of 10 for clarity. 104

129 Figure 5.9 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for hematite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Optical constants used for the theoretical calculations were obtained from Bedidi & Cervelle. [1993]. Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity. 105

130 106 Figure 5.10 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for hematite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Optical constants used for the theoretical calculations were obtained from Hematite Sokolik & Toon [1999]. Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity.

131 107 Figure 5.11 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for goethite measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity.

132 108 Figure 5.12 Normalized phase functions (a), ratios of experimental to theoretical phase functions (b), and linear polarizations (c) for Arizona Road Dust measured at 470 nm (left), 550 nm (center), and 660 nm (right). Mie or T-Matrix results were spliced onto the experimental phase functions for scattering angles less than 17 o, the experimental phase functions were linearly extrapolated past 172 o prior to normalization (black circles). Phase functions comparing experimental data to T-Matrix results in (a) have been scaled by a factor of 10 for clarity.

133 109 Figure 5.13 Normalized phase functions (a) and linear polarizations (b) for Arizona Road Dust measured at 470 nm (left), 550 nm (center), and 660 nm (right). Empirical phase functions and polarizations (dashed line) were generated using a uniform weighting of clay (illite, kaolinite, and montmorillonite) and non-clay (calcite, gypsum, and quartz) samples.

134 110 CHAPTER 6 DETERMINING PARTICLE SHAPE DISTRIBUTIONS FROM FTIR SPECTRAL FITTING As discussed in Chapter 5, the use of T-Matrix theory for scattering calculations leads to slightly better agreement with experimental measurements of scattering phase function and polarization data for irregularly-shape mineral dust aerosol than that obtained using Mie theory, which is limited to spherical shapes. However, for the range of axial ratios used in the T-matrix simulations, AR 2.4, it was found that theoretical polarization profiles failed to agree with experiment, both in peak position and overall magnitude, over most of the scattering angles. Since the optical constants were known and the particle size distribution was measured simultaneously with measurements of the light scattering, deviations of the theoretical scattering simulations from experiment were most likely due to particle shape effects. In this chapter, a more rigorous treatment of quartz mineral dust, a major component of atmospheric aerosol, will be presented. Particle shapes will again be approximated using spheroids, though the range of aspect ratios used to define the shape distribution will be significantly expanded to include more extreme particle shapes. In addition to the Standard shape distribution considered in Chapter 5, two other particle shape distributions will be considered here, one based on ex situ analysis of electron micrographs for our particular quartz dust sample, and the other determined from spectral fits of the Si-O stretch resonance absorption line for quartz dust. Modeling As described in Chapter 5, mineral dust particle shapes can be approximated by a distribution of randomly oriented ellipsoids of specified axial ratios, AR. T-Matrix calculations were again carried out using the code of Mishchenko & Travis [1998]. The size distribution parameters and optical constants for quartz used in these calculations are given in

135 111 Tables 2.1 and 2.2 respectively. For a given log normal size distribution, T-Matrix theory calculations were carried out for a distribution of randomly oriented oblate or prolate spheroids of fixed AR value. These calculations were then repeated for a range of both oblate and prolate AR values. An assumed particle shape distribution was then used to generate weighted average phase function and linear polarization curves for comparison to the experimental data. In addition to the Standard shape model (AR 2.4 prolate and oblate spheroids with an average aspect ratio, AR = 1.7) that is based on electron microscope images of mineral dust aerosol particles collected in the field [Mishchenko et al., 1997], a number of other shape distributions are also used here. The first, the SEM-Based shape model, was determined from the results of image analysis of the SEM images collected for our particular quartz sample as seen in Figure 6.1. To determine the shape distribution from the SEMs, all particles were first approximated as ellipses using the publicly available ImageJ software [ ]. The best-fit ellipses are shown as outlines in Figure 6.1. From these ellipses, the AR is given by the ratio of the major to minor axis. Since the image is twodimensional, it is not possible to directly determine the AR value for a 3-D particle. A thin disk-like particle sitting at an angle to the surface will project an image that could range from circular to needle-like depending on the viewing angle. We have assumed that prolate and oblate particles are equally represented in the shape distribution; thus we have simply reflected the distribution of measured AR histogram about 1.0 (circles) to generate the full shape distribution. The SEM-Based model covers a similar range of aspect ratios that is seen in the Standard, but has a lower average aspect ratio, AR = 1.4. Both the Standard and the SEM-Based shape models, shown in the left panel of Figure 6.2, make up what will be referred to here as the moderate shape distributions. In earlier IR spectroscopic modeling studies in the infrared by Hudson et al. [2008a], it was found that in order to accurately predict IR resonance absorption peak position and line profiles, more extreme particle shapes must be used. In studies of clay mineral dust

136 112 particles within the fine aerosol mode ( µm), it was found that disc-like particle shapes approximated the IR resonance band better than that which was obtained using needle-like particles or particle shapes represented by a continuous distribution of ellipsoids. This is consistent with the plate-like structure of clay particles as reported by Nadeau [1985]. A similar study of non-clay particles, including quartz, found that a continuous distribution of ellipsoidal shapes gave the best agreement with IR spectral measurements [Hudson et al., 2008b]. Those model results were all developed in the Rayleigh approximation for particle diameters much smaller than the wavelength of incident light, an approximation which was not strictly satisfied for the dust samples in the work of Hudson et al. In a more recent study which used T-Matrix theory to model spectral line profiles for quartz mineral dust, Kleiber et al. [2009] suggested that fitting the IR spectrum might allow a determination of the particle shape distribution. The spectroscopic methods for determining the particle shape distribution and the corresponding results are given here for completeness. Simulated IR spectra were calculated using T-Matrix theory assuming spheroidal particle shapes for a wide range of aspect ratios. These results served as spectral basis functions. A least-squares fitting algorithm was used to find the best fit linear combination of basis functions (AR shape parameters) to the observed IR line spectra. An unconstrained least squares analysis was first performed to determine the best linear combination of shape parameters to fit the data without applying any predetermined model for the shape distribution. These unconstrained fits give useful insight into the range of AR parameters needed to simulate the experimental line profiles. These results, however, typically showed unphysical structure in the shape distributions. In order to superimpose a more physically reasonable envelope onto the shape distributions they also carried out least squares analyses where the shape distribution was constrained to fit different models, either a Gaussian shape or a square Window function, each with adjustable AR center and width parameters. In each case, comparable agreement between experiment and simulation was obtained between the unconstrained and different constrained model solutions. This shows that the approach did

137 113 not yield a unique shape distribution. Nevertheless, there are clear and significant conclusions about the general characteristics of the particle shape distributions that could be drawn from those analyses, including the range of AR values required to fit the spectra. Figures 6.2 and 6.3 show the results from IR extinction studies for quartz dust in comparison to simulations based on different particle shape models. In each case the left panel shows the shape histogram and the right panel shows the corresponding spectral fit to the Si-O stretch resonance IR absorption line. The spectral fits using the moderate shape distribution models in Figure 6.2 are quite poor. In Figures 6.3 a-c, results are shown for the different extreme shape model distributions, Unconstrained, Gaussian, and Window, respectively. Clearly, fitting the IR spectral line profile for our particular quartz dust sample requires extreme particle shape parameters with AR > 3. For the Gaussian model fit, the mean AR value is AR = 2.4 (oblate) and the range extends to AR ~ 10 for oblate spheroids. Visible scattering simulations were also generated using T-Matrix theory over the same wide range of aspect ratios. The shape distributions determined from the fits to the IR spectral data were then used as weighting functions for the visible scattering phase function and polarization calculations. The use of the three different extreme particle shape models in the visible scattering T-Matrix calculations results in phase function and polarization profiles that are very similar to one another. In Figure 6.4 scattering results are presented for all three extreme shape models at 550 nm. Similar results hold at the other wavelengths studied. For simplicity, further analysis of the visible scattering will be limited to the Window shape model as a representative extreme particle shape model. Error Analysis The comparison between experimental scattering data for quartz at different scattering wavelengths and the T-Matrix based simulations for different model shape distributions is shown in Figures The uncertainty in the experimental data was calculated as in Chapter 5 and represents day-to-day variability in the measured phase

138 114 function and polarization profiles, as well as systematic uncertainties in the phase function as a result of system calibration errors. The error bars in the theoretical T-Matrix simulations are determined from two contributing factors. The first is due to the uncertainty in the small diameter region of the size distribution. As discussed in Chapter 5, Mie calculations were run for a range of size distributions, consistent with the APS data, in order to characterize the corresponding variation in the resulting phase function and polarization profiles. The magnitude of the error in the T-Matrix calculations was assumed to be of the same magnitude as those in the Mie calculations. The estimate of this size distribution error was performed using Mie theory due to the long computation times required for the T-Matrix calculations. The second factor contributing to the errors in the T-Matrix simulations is due to convergence limitations in the T-Matrix code and is discussed in detail below. For a given particle shape parameter, the T-Matrix code carries out an integration over the particle size distribution, requiring minimum and maximum endpoint values for the assumed log normal size distribution. Since small particles do not scatter efficiently the simulations are insensitive to choice of the minimum diameter. Determining the large diameter endpoint is more problematic. The log normal size distribution has a long tail that extends to infinite diameter. However, as a practical matter our aerosol generator and flow system do not pass particles with diameters larger than ~ 3 m. Indeed for these experiments on quartz, the APS measured no particles (above background) in any size bin greater than d APS ~ 2.7 m. This represents an empirical maximum diameter endpoint for the integration. The T-Matrix code used in these studies has convergence limitations for large and/or highly eccentric particles. As a result, the calculations are limited by a maximum size parameter for which the code will converge, X Max = πd Max /λ. The value of X Max is dependent both on the optical constants and the eccentricity of the spheroids in the calculation. For example, for oblate spheroid particles with AR = 1.5 and refractive index value n = 1.311, the code will fully converge for size parameters up to ~ 160. In contrast, X Max decreases to ~17 when the aspect ratio is increased to AR = 10 [Mischenko & Travis, 1998]. For prolate

139 115 spheroids, the maximal convergent size parameter, X Max tends to be slightly lower than that for oblate spheroids with the same AR value. In our T-Matrix calculations of the visible scattering for more extremely shaped particles, there were cases where the code did not converge over the entire range of the measured size and shape distributions. This introduces some convergence error into the theoretical scattering results for the extreme shape distributions presented here. For both of the moderate shape distributions (the Standard and SEM-Based models), the T-Matrix simulations were converged for the entire measured size distribution up to the maximum observed particle diameter (d APS 2.7 µm). However, for the extreme shape models, convergence up to this diameter was not obtained for some of the more highly eccentric particle shapes. For example, for prolate shapes with AR = 6.0, convergence was only obtained out to d Max ~2.0 µm. For prolate shape of AR = 10.0, the maximum diameter for which the code would converge was d Max ~1.1 µm. In order to gauge the magnitude of the uncertainty due to this convergence limitation on the maximum diameter, a series of simulations were run for each aspect ratio where the cutoff diameter used in the T-Matrix calculations, d Cutoff, was incrementally changed. As d Cutoff was increased in a series of steps toward the convergence limit, d Max, the calculated scattering matrix elements were observed to converge. By comparing results for different cutoff values we could estimate the rate of convergence and use that to place on upper limit on the possible convergence error associated with the finite cutoff value. This error was estimated as follows: For a fixed AR value, d Max was determined by stepping the integration cutoff value d Cutoff downward from d APS in steps, Δd, of ~200 nm until code convergence was obtained. The code was then run one more time with the cutoff diameter set one step smaller, d Max - Δd. The difference in the calculated scattering matrix elements for these two runs can be used to define an incremental error associated with each step d in changing the integration cutoff diameter. An estimate for an upper limit on the resulting convergence error can then be made by assuming this difference is constant for all of the succeeding steps

140 116 between the maximal convergent diameter d Max and the maximum observed particle diameter d APS. The error, σ i (AR), is then: d APS d Max i ( AR) Pi ( d Max ) Pi ( d Max d)) (6.1) d where P i (d) is the calculated phase function or polarization value for an integration cutoff diameter d, at scattering angle i. The dimensionless prefactor in Equation 6.1 essentially gives the number of incremental steps between the maximum diameter for which convergence is obtained and the maximum observed particle size. The total error, Σ i, for the phase function and polarization profiles, weighted by the shape distribution, S(AR), is then obtained from: i S ( AR) i ( AR) (6.2) AR There are a few aspects of this convergence error that should be stressed. First, these errors are only present for the most extreme particle shapes (i.e. AR > 4.0). The final reported scattering data is a weighted sum of the results over all aspect ratios (most of which have AR < 4.0); therefore, the contribution to the total error in the data tends to be small. Second, d APS as reported above is the maximum particle diameter bin for which particle counts (above background) were observed. The number density for that bin was very low. Though scattering intensity does scale with projected surface area, the number of particles with diameters greater than 1.0 µm only made up ~7% of the total particles measured by the APS, and those with diameters greater than 2.0 µm only made up 0.05%. Therefore the total contribution to the scattering due to the larger particles will be small. As such, the errors due to the finite cutoff value tend to be much smaller than the errors due to uncertainties in the size distribution itself. The reported error bars on the simulation results in Figures include both contributions.

141 117 Results for Quartz The visible scattering phase functions and polarizations for quartz mineral dust at 470, 550, and 660 nm are given in Figures respectively. Results are presented for the SEM-Based, Standard (AR 2.4), and IR-Based shape models. As noted above, all three shape models derived from the IR spectra give very similar results (Figure 6.4); for simplicity here we use the Window shape model as the IR-Based distribution. To show more clearly the differences between the phase functions generated with each of the shape models, the ratio of the experimental to theoretical phase function is also included in each figure (Figures (b)). The phase functions were first normalized in accordance with Equation 2.13 then offset by factors of 10 for clarity. Because the experimental and simulated phase functions are normalized, and since the simulations are based on known optical constants, and measured particle size and shape distributions, the results shown in Figures are absolute fits of theory to experiment with no adjustable parameters. For all wavelengths investigated, the theoretical phase functions generated using T- Matrix theory for the different shape distributions all appear similar to one another. However, by looking at the ratio of experiment to theory, it is evident that using extreme particle shapes in the calculations ( IR-Based model) results in better agreement with experiment for midrange and large scattering angles than calculations which use the more moderate shape distributions. In order to quantitatively judge the goodness of fit to the phase function data, χ 2 fitting parameters (calculated using Equation 5.1) have been calculated for all models at all three wavelengths and are given in Table 6.1. The results of the χ 2 analysis shows that the IR-Based model gives much better overall agreement with experiment for all wavelengths investigated. Particle backscattering is an important scattering property for radiative balance calculations and remote sensing dust retrievals. The most significant deviation from experiment for the results generated with the moderate shape distributions occurs for near backscattering angles, >135 o, where the theoretical scattering intensity can be as much as

142 118 twice as large as measured values. Though the IR-Based model comes closer to predicting the magnitude of the scattering intensity for large angles, the moderate shape distributions do give slightly better agreement with the overall asymmetry parameter for the phase functions for 470 and 550 nm (see Table 6.2). The scattered light polarization is much more sensitive to particle shape effects and the theoretical polarization profiles given in Figures (c) show much more variation between the different shape models. The predicted polarizations for the SEM-based model are again negative over the entire scattering angle range and look very similar to those generated using Mie theory (Figure 5.3). This isn t surprising as a large fraction of the particle shapes for this model are very close to spheres. There is a slight improvement in going to the Standard shape distribution, yielding slightly positive peaks near 120 o, but overall agreement with experiment is still poor. Only by including extreme particle shapes, AR >> 3, does the theoretical polarization agree with experiment for all scattering angles. Spectral differences in the profiles across the range of wavelengths studied here are not large. However, it should be noted that the observed linear polarization for near rightangle scattering, ~ 90, increases from P(θ) = +17% to +28% as the scattering wavelength is varied from 470 to 660 nm. This variation is very well modeled in the T-matrix simulation for the IR-Based particle shape model, which predicts a polarization increase from +18% to +27% over this spectral range. Discussion As was discussed in Chapter 4, T-Matrix theory, and light scattering theories in general, require a number of input parameters including the particle size distribution, wavelength dependent optical constants, and particle shape distribution. In order to accurately model the scattering, it is therefore important to use input parameters that are representative of the physical and optical properties of the scattering medium. Errors in these input distributions can compromise the conclusions from any theoretical scattering model.

143 119 For this study, we have used known optical constants for quartz, measured the particle size distribution simultaneously with the light scattering measurements, and determined the particle shape distribution using ex situ analysis of quartz mineral dust at multiple wavelengths. Therefore, all results presented here are absolute comparisons of experiment with theory, with no adjustable parameters. The mode diameter of our particular quartz sample is d < 3 m, corresponding to the size range important for long-range atmospheric transport [Prospero, 1999]. T-Matrix theory has been used here because of its computational efficiency and because it is readily adapted to the range of particle sizes important in our experiments. Particle shapes were represented using a spheroidal approximation for a range of aspect ratios. The spheroid shape approximation has been previously used in a number of reported studies [Kahn et al., 1997; Nousiainen & Vermeulen, 2003;Veihelmann et al., 2004; Dubovik et al., 2006], though there is still some question as to the validity of this approximation since real mineral dust particles may have many sharp edges, points, and internal voids (see Figure 6.1). For example, some work has suggested that the neglect of sharp edges inherent in the assumption that particles can be treated as smooth spheroids may lead to errors that could be appreciable in some instances [Kalashnikova & Sokolik, 2002]. Others have argued that the errors in the scattering phase function resulting from the spheroidal particle assumption may not be large [Kahnert & Kylling, 2004]. A number of particle shape distributions have been explored in this work. Two shape distributions were based on analysis of electron micrographs of aerosol particles. The first, the SEM-Based model, was based on images of quartz particles used in this study, and included aspect ratios in the range AR < 3.0 consisting primarily of nearly spherical particles. T-Matrix results for this shape distribution were very close to those predicted by Mie theory, which is valid only for spheres, and agreed poorly with experimental phase functions and polarizations. The Standard shape model is based in image analysis of micrographs of a range of aerosol samples collected in the field [Mishchenko et al., 1997] and is a commonly

144 120 used model to represent mineral dust aerosols. Though scattering calculations using the Standard shape model agree slightly better with experiment than the SEM-based model, deviation from experiment is still large for the polarimetric data, both in term of peak position and magnitude. In Kleiber et al. [2009], particle shape distributions for quartz were also determined by spectral fitting of the Si-O resonance absorption band.. The shape and peak position of the IR spectral resonances show a strong dependence on particle shape [Hudson et al., 2008a, 2008b]. This analysis gives information on the range of aspect ratios necessary for accurately modeling the light scattering. For quartz, aspect ratios AR >> 3.0 were required to get good agreement with experiment. These IR-Based particle shape distributions that include more extremely shape particles give much better agreement with both the experimental phase functions and the experimental polarization data for all wavelengths investigated in this study, 470, 550, and 660 nm. These results suggest that using electron micrograph images of a dust sample may not give an accurate representation of the particle shape distribution and indicates the inherent limitations in using a 2D analysis to extract information on 3D particles. Quartz dust, studied here, is a major component of atmospheric aerosol [Sokolik & Toon, 1999]. If these results can be generalized to real atmospheric dust, this study also suggests that it may be possible to develop algorithms that use correlated IR extinction and visible polarimetry data from satellite or ground based field instruments, together with T-Matrix based simulations, to more accurately characterize atmospheric dust composition, size, and shape distributions Chi-square analysis suggests that the T-matrix model based on the uniform spheroid approximation can be used with confidence to model the optical properties of highly irregular quartz dust aerosol particles in the accumulation mode size range provided the shape distribution is reliably modeled. However, due to convergence limitations of the T-Matrix code, visible scattering calculations may be limited to the accumulation mode size range for particles with high aspect ratios. The IR spectral analysis for particle shapes, on the other

145 121 hand, can be extended to much larger particle diameters because of the longer wavelengths in the IR because the same dimensionless size parameter, X=2 r/, corresponds to a much larger particle diameter in the infrared. This method for determining particle shapes could then be used with other light scattering theories such as the geometric optical theory to determine visible scattering for large particles.

146 122 Wavelength (nm) Shape Model SEM-based Standard Window Table 6.1 Reduced χ 2 values for comparison of the experimental phase functions with simulations based on different particle shape models, the moderate SEM-based and Standard models, and the extreme Window model. Mineral Dust Wavelength g Exp g SEM g Standard g Window Quartz 470 nm 0.69 ± nm 0.69 ± nm 0.72 ± Table 6.2 Asymmetry parameter values for experimental (g Exp ) and T-Matrix theory assuming the SEM-Based (g SEM ), Standard (g Standard ), and Window (g Window ) shape model phase functions for 470, 550, and 660 nm.

147 Figure 6.1 SEM image of quartz particles with best-fit ellipses determined using the ImageJ software package. 123