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Optical Characterization of Complex Aerosol and Cloud Particles:

Remote Sensing and Climatological Implications

LI LIU

Submitted in partial fulfillment of the

requirements for the degree

of Doctor of Philosophy

in the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY 2004

© 2004

Li Liu

All Rights Reserved

ABSTRACT

Optical Characterization of Complex Aerosol and Cloud Particles: Remote Sensing and Climatological Implications

Li Liu

Optical characterization of aerosol and cloud particles has been a challenge to

researchers involved in a wide range of disciplines including remote sensing and climate

studies. This thesis addresses several important atmospheric radiation problems involving

cloud and aerosol particles with complex structure. We solve these problems by (i)

extensively using state-of-the-art theoretical techniques to compute radiative properties of

nonspherical and composite atmospheric particulates; (ii) combining theoretical and high-

quality laboratory data for single scattering by irregular dust-like aerosols; (iii) applying

advanced retrieval algorithms to analyze satellite observations of tropospheric aerosols;

and (iv) validating satellite retrievals with high-quality ground-based data.

In Chapter 1, the superposition T-matrix method is used to compute electromagnetic

scattering by semi-external aerosol mixtures in the form of polydisperse, randomly

oriented two-particle clusters with touching components. The results are compared with

those for composition-equivalent external aerosol mixtures. It is concluded that

aggregation had a relatively weak effect on radiative properties of composite aerosols.

In Chapter 2, scattering and absorption characteristics of water cloud droplets

containing black carbon (BC) inclusions are calculated in the visible spectral range by a

combination of ray-tracing and Monte Carlo techniques. In addition, Lorenz-Mie

calculations are performed assuming that the same amount of BC particles are mixed

with water droplets externally. It is concluded that under normal conditions the effect of

BC inclusions on the radiative properties of cloud droplets is weak.

In Chapters 3 and 4, we compare and combine the results of laboratory

measurements of the Stokes scattering matrix for nonspherical quartz aerosols at a visible

wavelength in the scattering angle range 5°–173° and the results of Lorenz-Mie

computations for projected-area-equivalent spheres with the refractive index of quartz. A

synthetic normalized phase function is constructed and then used to analyze the potential

effect of particle nonsphericity on the results of retrievals of mineral tropospheric

aerosols based on radiance observations from Advanced Very High Resolution

Radiometer (AVHRR).

Chapter 5 presents the validation results of the aerosol optical thickness retrieved

from AVHRR channel 1 and 2 radiances. The satellite retrieved optical thickness is

compared with the accumulated historical ship-borne sun-photometer measurements.

Comparisons of single-scattering albedo and Ångström exponent values retrieved from

the AVHRR data and those measured in situ at Sable Island indicate that the currently

adopted value 0.003 can be a reasonable choice for the imaginary part of the aerosol

refractive index in global satellite retrievals.

In chapter 6, we analyze existing lidar observations of polar stratospheric clouds

(PSCs) and derive several constraints on PSC particle miscrophysical properties based on

extensive T-matrix computations of light scattering by polydispersions of randomly

oriented, rotationally symmetric nonspherical particles.

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TABLE OF CONTENTS

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 1 Scattering and radiative properties of semi-external versus

external mixtures of different aerosol types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2 Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 2 The effect of black carbon on scattering and absorption of

solar radiation by cloud droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2 Optical properties of black carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4 Ray-tracing/Monte Carlo model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.5 Model computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.5.1 Internal mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.5.2 External mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.5.3 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 3 Scattering matrix of quartz aerosols: comparison and

synthesis of laboratory and Lorenz-Mie results . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Measurements and Lorenz-Mie computations . . . . . . . . . . . . . . . . . . . .

3.3 Synthetic phase function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 4 Investigation of the effects of particle nonsphericity on aerosol

retrievals from AVHRR observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 Effect of particle shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 5 Global validation of the operational two-channel AVHRR

retrieval product over the ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2 Validation of satellite aerosol optical thickness retrievals. . . . . . . . . . .

5.2.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2.2 Ship data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2.3 Primary validation results . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3 Validation of the aerosol single-scattering albedo . . . . . . . . . . . . . . . . .

5.4 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 6 Constraints on PSC particle microphysics derived from lidar

observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6.2 T-matrix computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.3 Observation data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.4 Analysis results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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LIST OF FIGURES

1.1 (a) External, (b) semi-external, and (c) internal particle mixtures . . . . . . . . . . .

1.2 Phase function versus scattering angle for dust-sulfate semi-external (solid

curves) and external (dotted curves) mixtures . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3 As in Fig. 1.2, but for sulfate-soot mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4 As in Fig. 1.2, but for scattering-matrix element ratios . . . . . . . . . . . . . . . . . . .

1.5 As in Fig. 1.3, but for scattering-matrix element ratios . . . . . . . . . . . . . . . . . . .

2.1 External (a) and internal (b) mixing of large cloud droplets and smaller

aerosol particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2 Single-scattering co-albedo ϖ−1 and asymmetry parameter g for mixtures

of cloud droplets and BC particles versus BC particle effective radius at a

wavelength of 0.55 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3 Single-scattering co-albedo ϖ−1 and asymmetry parameter g for mixtures

of cloud droplets and BC particles versus BC mass fraction . . . . . . . . . . . . . . .

2.4 Relative differences (in %) between the single-scattering co-albedo and

asymmetry parameter for external and internal mixtures of cloud droplets and

BC particles versus the BC mass fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1 Normalized distribution of the average area of the particle projection for

randomly oriented quartz aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Laboratory data for nonspherical quartz aerosols and results of Lorenz-Mie

computations for projected-area-equivalent quartz spheres . . . . . . . . . . . . . . . .

3.3 The pattern of the differences between the Lorenz-Mie phase function for

spherical quartz particles (solid curve) and the phase function for

nonspherical quartz aerosols depends on the vertical position of the

experimental )(~1 Θa profile (dashed, dotted, and dot-dashed curves) . . . . . . . .

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3.4 Synthetic and Lorenz-Mie phase functions for nonspherical quartz aerosols

and projected-area-equivalent quartz spheres, respectively . . . . . . . . . . . . . . .

4.1 Synthetic and Lorenz-Mie phase functions for nonspherical quartz aerosols

and projected-area-equivalent quartz spheres, respectively, used in the one-

channel retrieval algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 Monthly averages of the ratio τN/τS and the respective scattering angle versus

longitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1 AVHRR retrieved aerosol optical thickness τSAT versus ship measurements

τSP at λ = 0.55 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2 τSAT versus τSP for different AVHRR instrument (NOAA-7, 9, 11, 14) . . . . . .

5.3 Comparison of τSAT and τSP at λ = 0.55 µm for three increasing values of

diffuse component of surface reflection S = 0.002, 0.004, 0.005 and the

corresponding linear regression lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.4 Aerosol single-scattering albedo versus Ångström exponent for Re(m) = 1.5

and four increasing values of Im(m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5 Monthly averages of the Ångström exponent and single-scattering albedo for

July 1999 derived from two-channel AVHRR data assuming a fixed aerosol

refractive index m = 1.5 + 0.003i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.6 The annual cycle of the aerosol single-scattering albedo measured in situ at

Sable Island . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.7 The annual cycle of the aerosol optical thickness retrieved from channel–1

and –2 AVHRR data over Sable Island during the period November 1994–

December 1999 assuming that the imaginary part of the aerosol refractive

index is fixed at 0.001, 0.002, 0.003, and 0.005 . . . . . . . . . . . . . . . . . . . . . . . .

5.8 As in Fig. 5.7, but for the constrained Ångström exponent. . . . . . . . . . . . . . . .

6.1 Linear depolarization ratio )nm603(δ , backscatter color index α , and

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depolarization color index β versus effective equal-volume-sphere radius

effr for polydisperse, randomly oriented spheroids with a refractive index of

5.1=m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2 As in Fig. 6.1, but for polydisperse, randomly oriented cylinders . . . . . . . . . . .

6.3 As in Fig. 6.1, but for the refractive index m = 1.308 typical of water ice at

visible wavelengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.4 As in Fig. 6.3, but for polydisperse, randomly oriented circular cylinders . . . .

6.5 The bars depict the respective ranges of the effective radius that reproduce the

values of δ , α , and β observed for type Ia PSCs, as shown in Figs. 6.1 and

6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


values of δ and α observed for type Ib PSCs, as shown in Figs. 6.1 and 6.2 .


values of δ , α , and β observed for type II PSCs, as shown in Figs. 6.3 and

6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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LIST OF TABLES

1.1 Optical characteristics of dust-sulfate particle mixtures . . . . . . . . . . . . . . . . . .

1.2 Optical characteristics of sulfate-soot aerosol mixtures . . . . . . . . . . . . . . . . . . .

2.1 Black carbon concentration in cloud water . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2 Model parameter values used in this study . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1 Ship measurements of aerosol optical thickness in maritime areas used in this

study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2 Statistics of comparison of τSAT and τSP for three increasing values of diffuse

surface reflection S = 0.002, 0.004, 0.005 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3 Mean values of aerosol parameters retrieved from AVHRR data and

measured in situ at Sable Island . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1 Typical backscattering characteristics of PSCs observed by Browell et al. . . . .

6.2 Ranges of backscattering characteristics for different PSC types used in this

study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to all those who made this thesis

possible. My deepest appreciation is to my thesis advisor Dr. Michael I. Mishchenko. I

thank him for kindly providing supervision throughout all my years in graduate school.

His ideas, insightful advice, support, and heart-warming encouragement have been

crucial to the successful completion of my thesis. I am thankful to my other advisory

committee members, Dr. James E. Hansen and Dr. Dick Ou, who also provided very

helpful guidance in my research work. I am indebted to Dr. Andrew A. Lacis. Like my

fourth mentor, he generously gave me advice on every aspect of my research. I

gratefully acknowledge Dr. William B. Rossow for his continuous encouragements,

suggestions, and teaching us climate science and science philosophy. I am also thankful

to Dr. Anthony Del Genio for being a strict but caring professor. I have benefited a lot

from his initial “push” at an early stage of my study here. I would like to thank Dr.

Larry Travis, Dr. Brian Cairns, Dr. Surabi Menon, and Dr. Makoto Sato for their

interest and comments on my research. I owe much to Dr. Yuanchong Zhang. He has

been the expert I fall back on whenever I have questions using ISCCP DX data.

This work was finished in collaboration with many other scientists. I would like to

thank Dr. Mishchenko for many of his source codes, including the T-matrix, and

Lorenz-Mie codes, and Dr. Igor V. Geogdzhayev for helping me to get familiar with the

one- and the two-channel retrieval algorithms using AVHRR observations. I gratefully

acknowledge Dr. Andreas Macke (University of Kiel, Germany) for providing us with

his Ray-tracing/Monte Carlo model. I would like to express my appreciation to Dr. Joop

W. Hovenier (Free University and University of Amsterdam, The Netherlands), Dr.

Hester Volten (University of Amsterdam and FOM-Institute for Atomic and Molecular

Physics, The Netherlands) and Dr. Olga Muñoz (Instituto de Astrofisica de Andalucia,

Spain) for providing us the results of laboratory measurements of the Stokes scattering

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matrix for mineral aerosols and the corresponding size distributions. Sincere gratitude

also goes to Dr. John A. Ogren at NOAA/CMDL for providing us the extensive in situ

aerosol data set collected at Sable Island, to Dr. Alexander Smirnov at NASA/GSFC,

Dr. Sergey M. Sakerin and Dr. Dmitry M. Kabanov of the Institute of Atmospheric

Optics, Russia, for providing us with historically accumulated ship-borne sun

photometer aerosol data for validation purposes.

I would like to thank Nadia T. Zakharova for her expertise in computer graphics,

Zoe Wai and Josefina Mora for helping to find papers that were not readily accessible,

Sabrina Hosein, Michael Shopsin, Angel Suarez, Raymond Encarnacion, and Kenneth

Bell for technical support. I also would like to extend my thanks to department

administrators Mia Leo and Missy Pinckert for being so devoted and kind to students.

I also would like to express thanks to all my fellow students at GISS – Jacek, Ting,

Kirstie, Mike, Jiping, Junye, Radley, Peng, Max, Reha, Johnny, Joy, Duane. They have

been a source of wisdom and have had much influence on me.

Last but not least, I am grateful to my family for their love, strength, and

continuous support.

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INTRODUCTION

Aerosols are fine particles suspended in air. The impact of aerosols on the global

climate system through the direct and indirect radiative forcings is one of the major

uncertainties in present climate modeling (Hansen and Lacis, 1990; Charlson et al.,

1992; Lacis and Mishchenko, 1995; Hansen et al., 1998; Mishchenko et al., 2002).

Furthermore, aerosols play an important role in atmospheric chemistry and hence affect

the concentrations of other key-role atmospheric constituents, such as ozone. Therefore

knowledge of aerosol physical and chemical properties is critically important to climate

change and environmental studies.

Remote-sensing characterization of airborne particulates and their radiative effects

has been a challenging problem to atmospheric scientists due to the high spatial

inhomogeneity and heterogeneity and significant temporal variability of aerosols.

Furthermore, aerosol particles are often nonspherical, have a tendency to aggregate, and

can exist inside larger cloud droplets, thereby adding significantly to the complexity of

computing their scattering properties and radiative effects.

The objective of this thesis is to addresses several important atmospheric radiation

problems involving airborne particulates with complex morphology such as irregular

dust-like aerosols and polar stratospheric cloud particles, aerosol particle clusters, and

internal mixtures of aerosols and cloud droplets. These problems are solved by

(i) extensively using state-of-the-art theoretical techniques to compute radiative

properties of non spherical and composite scatterers;

(ii) combining theoretical and high-quality laboratory data for single scattering by

irregular dust-like aerosols;

(iii) applying advanced retrieval algorithms to analyze satellite observations of

tropospheric aerosols; and

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(iv) validating satellite retrievals with high-quality ground-based data.

The thesis is divided into four parts with 6 chapters.

Effect of mixing

The uncertainty in current estimates of the aerosol radiative forcing (defined as an

externally imposed perturbation in the radiative energy budget of the Earth’s climate

system (IPCC, 2001)) remains large despite significant recent progress in theoretical

understanding, model simulations, and aerosol observations. There are three major areas

of uncertainty related to (i) the atmospheric burden and its anthropogenic component,

(ii) the aerosol optical parameters, and (iii) the method of translating the optical

parameters and burden into a radiative forcing (IPCC, 2001). The optical parameters

are uncertain because of poor knowledge of the aerosol size distribution, chemical

composition, state of mixing, method of mixing, degree of agglomeration, and shape.

The problem of the degree of mixing deserves special attention (IPCC, 2001) since

global modeling studies tend to assume that aerosols are externally mixed (different

aerosol particles are separated by distances much greater than their sizes and scatter

light independently of each other), which makes modeling the sources, atmospheric

transport, and radiative properties much simpler than in the case of internal mixtures

(one or several small aerosol particles are imbedded in a larger host particle). However,

many aerosol particles appear to be mixed internally (one or more particles are

imbedded in a larger host) or semi-externally (two or more aerosol particles are in

physical contact and form an aggregate). For example, Podzimek (1990) found that in a

polluted urban-marine environment haze elements can exist as insoluble, carbonaceous

particles on or in larger nonabsorbing droplets. Buseck et al. (2000) have found soot

inter-grown with sulfates in aerosol particles collected from marine particles over the

northern Atlantic, equatorial Pacific, Southern, and Indian oceans, and from polluted

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continental regions in Europe and the United States. Significant aggregation of soot

and/or sulfate with mineral dust is common when dust from the Chinese interior mixes

with pollution plumes from major industrial cities.

Changing the mixing state and the degree of aggregation can alter aerosol optical

properties significantly. These changes may influence the results of remote sensing

studies of tropospheric aerosols and calculations of the direct aerosol forcing of climate

(e.g., Sato et al., 2003) and, therefore, must be accurately evaluated using theoretical

calculations and/or laboratory measurements. For example, uncertainties in the way

absorbing aerosols are mixed can introduce a range of a factor of two in the magnitude

of radiative forcing by black carbon (Haywood and Shine, 1995; Jacobson, 2000). The

results of Fuller et al. (1999) show that the radiative properties depend on a variety of

parameters that include particle size and shape, degree of crystallinity, type of

aggregation, density of aggregates, and type (internal or external) and extent of mixing

with non-absorbing materials such as sulfate.

Given the importance of the aerosol mixing problem, the first chapter of this thesis

will be devoted to a study of the scattering and radiative properties of semi-external

mixtures of different aerosol species, viz., sulfate, dust, and carbonaceous particles.

These three types of aerosols are believed to have a significant effect on the Earth’s

climate.

Secondly, it is well known that carbonaceous aerosols (internal or external mixtures

of organic carbon and black carbon), biomass burning aerosols in particular, are

efficient cloud condensation nuclei (e.g., Novakov and Penner, 1993; Novakov and

Corrigan, 1996). Once they are incorporated into cloud droplets, the enhanced

absorption by black carbon particles could potentially reduce the cloud albedo (Chýlek

et al., 1984), thereby causing a significant indirect forcing of climate (Charlson et al.,

1992). There have been few GCM studies evaluating the indirect forcing from

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carbonaceous aerosols, and quantitative estimates of this effect are still highly

uncertain. Therefore, the goal of Chapter 2 is to investigate the effect of internally

mixed black carbon on scattering and absorption of solar radiation by cloud droplets

using an advanced ray-tracing/Monte Carlo model.

Effect of particle shape

The second major objective of this thesis is to study particle nonsphericity and its

effect on remote sensing of mineral tropospheric aerosols. The effect of particle shape

on scattering and absorption characteristics has been discussed in the literature for

several decades (e.g., van de Hulst, 1957; Mishchenko et al., 2000a; Mishchenko et al.,

2002a). It is commonly assumed that aerosol particles are spherical in computations of

radiative transfer because both absorption and scattering can be readily evaluated for

spherical particles by applying the Lorenz-Mie theory. Many studies indicate that this

assumption does not lead to significant errors in radiation flux computations (e.g., Lacis

and Mishchenko, 1995; Mishchenko et al., 1995; Mishchenko et al., 1997). However,

the assumption of sphericity can be problematic in satellite retrievals of aerosol optical

properties since the light scattering behavior of nonspherical particles may differ

significantly from that of spherical ones, especially in backscattering directions.

Global aerosol information can only be acquired using satellite passive and/or

active remote sensing (Karl, 1995). Most current satellite remote sensing of

tropospheric aerosols relies upon radiance measurements, such as the retrievals using

Advanced Very High Resolution Radiometer (AVHRR), Total Ozone Mapping

Spectrometer (TOMS), Moderate Resolution Imaging Spectroradiometer (MODIS),

Multiangle Imaging SpectroRadiometer (MISR), and Global Imager (GLI) data. As

discussed by Wang and Gordon (1994), the retrieval of aerosol optical thickness using

satellite reflectance measurements requires an aerosol model, namely, the specification

5

of the aerosols scattering phase function and single-scattering albedo. Currently the

majority of aerosol remote-sensing retrievals still rely on the conventional Lorenz-Mie

theory, which is strictly valid only for the spherical particle shape. However, the

climatically important dust-like and sea salt aerosols are apparently nonspherical. It is

therefore important to examine the applicability of using the Lorenz-Mie theory in

retrieval algorithms when such aerosol species are present. To address this problem

requires accurate information regarding scattering properties of aerosols. Theoretical

methods for simulating the scattering of light by various nonspherical shapes have

rapidly evolved over the last two decades (c.f., Mishchenko et al., 2000b). Numerous

studies (e.g., Nakajima et al., 1989; Mishchenko et al., 1995; Mishchenko et al., 1997;

Diner et al., 2001; Dubovik et al., 2002a; Dubovik et al., 2002b) indeed indicate the

need to account for particle non-sphericity in modeling the optical properties of dust-

like aerosols. Despite the significant progress, theoretical and numerical techniques are

still limited in their ability to model electromagnetic scattering by realistic

polydispersions of irregular particles. Therefore, laboratory measurement techniques

(Hovenier et al., 2000; Gustafson et al., 2000) remain an important source of

information on scattering properties of nonspherical aerosols.

In a recent paper, Volten et al. (2001) presented an extensive dataset which

includes the results of laboratory measurements in the visible of the Stokes scattering

matrix in a wide scattering angle range for several types of polydisperse, randomly

oriented mineral aerosols and accompanying size distribution data. A traditional

limitation of such laboratory measurements is the lack of data at very small and very

large scattering angle (in this case, from 0º to 5º and from 173º to 180º), which makes

the measurements less useful in those cases when the absolute phase function values for

the entire scattering-angle range are needed (Mishchenko et al., 1995; Krotkov et al.,

1999; Diner et al., 2001; Dubovik et al., 2002a; King et al., 1999). However, based on

6

the assumption that the diffraction forward-scattering peak is the same for spherical and

nonspherical projected-area-equivalent particles (Mishchenko et al., 1996; Mishchenko

et al., 1997), we have constructed a synthetic normalized phase function and used it in a

global one-channel retrieval algorithm to study the potential effect of nonsphericity on

the aerosol optical thickness retrieved from the AVHRR data. These results will be

described in Chapters 3 and 4.

Validation of AVHRR retrievals

The important role of tropospheric aerosols in forming the Earth’s climate has

motivated several dedicated research programs (Artaxo et al., 1998; Russell et al., 1999;

Raes and Bates, 2000), including the Global Aerosol Climatology Project (GACP)

(Mishchenko et al., 2002b). A major component of the GACP is a retrospective analysis

of the AVHRR radiance data set in order to infer the long-term global distribution of

aerosols, their properties, and seasonal and interannual variations. The papers by

Mishchenko et al. (1999, 2003) and Geogdzhayev et al. (2002) outlined the

methodology of inverting channel-1 and -2 AVHRR radiance data over the oceans,

described a detailed analysis of the sensitivity of monthly averages of retrieved aerosols

parameters to the assumptions made in different retrieval algorithms, and presented a

global aerosol climatology for the period extending from July 1983 to December 1999.

In order to retrieve aerosol optical thickness and Ångström exponent (the retrieved

aerosol parameters), several unavoidable assumptions must be made in the operational

two-channel retrieval algorithm (e.g., size distribution, real and imaginary parts of the

aerosol refractive index). These assumptions together with all the uncertainties due to

the instrument itself and the measurement procedure can generate errors in the final

retrieval products.

7

An important direction of our research has been validation of the satellite retrieval

results. This effort has involved comparisons and consistency checks with other

satellite, airborne, and ground-based datasets (e.g., Haywood et al., 2001; Smirnov et

al., 2002; Zhao et al., 2003) and models (e.g., Penner et al., 2002). This is not a simple

task because of the scale differences, collocation problems, and different approaches to

cloud screening. The ground-based networks such as the Aerosol Robotic Network

(AERONET) (Holben et al., 1998; Dubovik et al., 2000) and the Multi-Filter Rotating

Shadowband Radiometer (MFRSR) network (Alexandrov et al., 2001) provide

extensive coverage over land, but have only a few coastal sites, where the atmospheric

conditions and surface albedo may be significantly different from those in the open

ocean.

In a recent paper, Smirnov et al. (2002) summarized aerosol optical thickness

measurements in maritime and coastal areas. This comprehensive survey of ship-borne

measurements published over the last 30 years has proved to be a great asset for our

validation since much of the data were collected over undisturbed open ocean areas.

Furthermore, the availability of extensive in situ measurements of the single-scattering

albedo at Sable Island as reported by Delene and Ogren (2002) have enabled us to

examine the accuracy of the choice of the imaginary part of the refractive index in the

AVHRR retrieval algorithm, at least in the Atlantic Ocean area adjacent to that location.

These results will be described in Chapter 5.

Retrievals of PSC particle microphysics using the T-matrix method

The third part of the thesis deals with the application of the T-matrix method to

retrievals of polar stratospheric cloud (PSC) particle microphysics from lidar

observations. PSCs are important because heterogeneous reactions can occur on the

surfaces of the cloud particles. Condensation onto the clouds and subsequent reactions

8

remove nitrogen from the active gas phase (process known as “denoxification”). At the

same time, other reactions also liberate active chlorine and bromine. These compounds

then catalyze ozone destruction in the presence of sunlight, resulting in ozone depletion.

Therefore, an improved understanding of PSCs is essential to predictions of future

ozone depletion. A detailed review of PSC studies has been published by Toon et al.

(2000). The traditional classification of PSC types is based on lidar observations

(Browell et al., 1990). There are two main types of PSCs. Type Ia PSCs are

characterized by low backscattering but strong depolarization, whereas type Ib PSCs

exhibit the opposite behavior. Type II PSCs demonstrate both strong backscatter and

large depolarization ratios. Note that a non-zero depolarization ratio is indicative of the

presence of non-spherical particles (Mishchenko and Sassen, 1998).

Theoretical computations are required in order to interpret these measurements

quantitatively in terms of particle size and shape. As we have mentioned earlier, the past

two decades have seen much progress in both theoretical and numerical solutions of the

electromagnetic scattering problem for nonspherical particles. Although techniques

such as the finite difference time domain method (FDTDM; Yang and Liou, 2000; Sun

et al., 1999) and the discrete dipole approximation (DDA; Draine 2000) have no

restrictions on the particle shape, their relatively low efficiency and limited size

parameter range make their application to polydispersions of randomly oriented PSC

particles problematic. Therefore, we have based our analysis of PSC lidar observations

on the highly efficient T-matrix code (Mishchenko and Travis, 1998). The details of the

computations and the analysis results will be described in Chapter 6.

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16

Chapter 1

Scattering and radiative properties of semi-external versusexternal mixtures of different aerosol types1

Michael I. Mishchenkoa, Li Liua,b, Larry D. Travisa, Andrew A. Lacisa

aNASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USAbDepartment of Earth and Environmental Sciences, Columbia University, 2880 Broadway, New

York, NY 10025, USA

Abstract

The superposition T-matrix method is used to compute the scattering of unpolarized

light by semi-external aerosol mixtures in the form of polydisperse, randomly oriented

two-particle clusters with touching components. The results are compared with those for

composition-equivalent external aerosol mixtures, in which the components are widely

separated and scatter light in isolation from each other. It is concluded that aggregation

is likely to have a relatively weak effect on scattering and radiative properties of multi-

component tropospheric aerosols and can be replaced by the much simpler external-

mixture model in remote sensing studies and atmospheric radiation balance

computations.

Keywords: Aerosols; Scattering; Optical cross sections; Single-scattering albedo;

Asymmetry parameter; Scattering matrix; Remote sensing; Atmospheric radiation

1.1 Introduction

1 Submitted to Journal of Quantitative Spectroscopy & Radiative Transfer, 2003.

17

Different kinds of tropospheric aerosols (e.g., dust, carbonaceous, and sulfate

particles) can be suspended in air both in the form of external mixtures (different

aerosol particles are separated by distances much greater than their sizes and scatter

light independently of each other), semi-external mixtures (two or more aerosol

particles are in physical contact and form an aggregate), and internal mixtures (one or

several small aerosol particles are imbedded in a larger host particle) (see Fig. 1.1). For

example, Podzimek [1] found that in a polluted urban-marine environment haze

elements can exist as insoluble, carbonaceous particles on or in larger nonabsorbing

droplets. Significant aggregation of soot and/or sulfate with mineral dust is common

when dust from the Chinese interior mixes with pollution plumes from major industrial

cities. Since aerosol particles forming an aggregate are in the near field zone of each

(a)

(b)

(c)

Figure 1.1: (a) External, (b) semi-external, and (c) internal particle mixtures.

18

other, the scattering and radiative properties of semi-external aerosol mixtures can differ

from those of composition-equivalent external mixtures. These potential differences

may influence the results of remote sensing studies of tropospheric aerosols and

calculations of the direct aerosol forcing of climate (see, e.g., [2] and references therein)

and, therefore, must be accurately evaluated using theoretical calculations and/or

laboratory measurements [3–5].

In this paper we calculate the optical cross sections and the elements of the Stokes

scattering matrix of semi-external two-component mixtures of carbonaceous, dust, and

sulfate aerosols – the three types of aerosols which are believed to have a significant

effect on the earth’s climate – and compare them with those of equivalent external

mixtures computed with the standard Lorenz-Mie theory [6,7]. This comparison is used

to derive conclusions about the likely effect of aggregation on the scattering and

radiative properties of multi-component aerosols.

1.2 Computations

Important single-scattering characteristics of randomly oriented particles with a

plane of symmetry are the ensemble-averaged scattering, Csca, and extinction, Cext, cross

sections and the elements of the normalized scattering matrix )(ΘF , where Θ is the

scattering angle [7]. In the standard {I, Q, U, V} representation of polarization, the

scattering matrix has the well-known block-diagonal form [6,7],

−

=

)()(00

)()(00

00)()(

00)()(

)(

42

23

21

11

ΘΘΘΘ

ΘΘΘΘ

Θ

ab

ba

ab

ba

F , (1.1)

so that only eight elements of )(ΘF are nonzero and only six of them are independent.

19

The (1, 1) element of the scattering matrix )(1 Θa is traditionally called the phase

function and satisfies the normalization condition

∫ =π

ΘΘΘ0

1 1)(sind21

a . (1.2)

Additional useful quantities are the ensemble-averaged absorption cross section, Cabs =

Cext – Csca, the single-scattering albedo, ϖ = Csca/Cext, and the asymmetry parameter

defined as

∫=π

ΘΘΘΘ0

1 cos)(sind21

ag . (1.3)

The computations reported here were performed at a visible wavelength of λ =

0.628 µm assuming that each aerosol mode is represented by the power law size

distribution of the following type [7,8]:

≤≤

−=−

otherwise.,0

,,2

)(21

32

12

2

22

21 rrrr

rr

rr

rn (1.4)

The effective radius reff and effective variance effv of the size distribution are defined

as

2eff )(d

1 2

1

rrrnrG

rr

rπ∫= , (1.5)

22eff2

effeff )()(d

1 2

1

rrrrnrrG

r

rπ−= ∫v , (1.6)

where

2)(d2

1

rrnrGr

rπ∫= (1.7)

is the average area of the particle geometrical projection [7,8]. Dust aerosols are usually

20

characterized by a broad range of effective radii from about 0.2 µm to greater than 5

µm. The most common dust mode occurring at a large distance from the source is

around 1 µm in radius. The effective radius of sulfate particles ranges from less than 0.1

to larger than 0.5 µm and depends on relative humidity. Soot aerosols are usually fine

particles with effective radii around 0.1 µm.

In our computations, we have used two types of aerosol particle mixture. Mixture 1

is composed of dust-like particles with an effective radius of 1 µm and an equal number

of sulfate particles. The effective radius of the sulfate component was set at the

following four representative values: 0.1, 0.2, 0.5, and 1 µm. Mixture 2 consists of equal

numbers of sulfate particles with an effective radius of 0.5 µm and soot aerosols. The

effective radius of soot particles was set at 0.05, 0.1, 0.2, and 0.5µm. We used the

following values of the relative refractive index for the three different aerosol species:

1.53 + 0.008i for dust, 1.44 for sulfates, and 1.75 + 0.435i for soot [9]. The effective

variance for all aerosol types was fixed at 0.2, thereby representing a moderately wide

size distribution. Although solid aerosol particles should be presumed to have

nonspherical shapes, our main interest here is in evaluating the potential effect of

aggregation on light scattering. Therefore, for the sake of simplicity, we have assumed

that all three aerosol species consist of spherical particles.

We calculated the scattering of unpolarized incident light by polydisperse,

randomly oriented two-sphere clusters with touching components and compared the

results with the results of Lorenz-Mie calculations assuming that the same component

particles were mixed externally and acted as independent scatterers. In our

computations for two-sphere clusters, we used a highly efficient code developed by

Mishchenko and Mackowski [10] and publicly available at

http://www.giss.nasa.gov/~crmim. This code is based on the T-matrix solution of

Maxwell’s equations and precisely computes the scattering of light by randomly

21

oriented two-sphere clusters with sizes comparable to and larger than the wavelength.

The efficiency of the methods is the result of combining the power of the superposition

approach in treating light scattering by composite particles [11,12] and the analyticity of

the T-matrix formulation in application to randomly oriented nonspherical scatterers

[13]. The main idea of the method is to employ the superposition approach to calculate

the T matrix of a bisphere in the natural coordinate system with the z-axis connecting

the centers of the component spheres and then to use this T matrix in an analytical

procedure to directly compute the orientation-averaged optical cross sections and the

elements of the scattering matrix for randomly oriented bispheres. The analytical

averaging over orientations makes this approach much faster than that based on the

standard numerical averaging and, thus, suitable for computations for realistic size

distributions. The Lorenz-Mie code used is described in [7] and is also available at

http://www.giss.nasa.gov/~crmim. The numerical data are summarized in Figs. 1.2–1.5

and Tables 1.1 and 1.2 and are discussed in the following session.

1.3 Discussion

Figures 1.2 and 1.3 illustrate the differences between the phase functions for semi-

external (solid curves) and external (dotted curves) aerosol mixtures. One can see that

the relative phase-function differences are rather small and, on average, do not exceed

20%. A notable exception is the exact forward-scattering direction, where the

interference effects result in a significant enhancement of the aggregate phase functions

[14]. The phase-function differences are especially small when the effective radius of

one component is much smaller than that of the other, in which cases the thin solid and

dotted curves are almost (or even completely) indistinguishable. This obviously

happens because the contribution of the smaller component to the total scattered signal

becomes negligibly small.

22

The differences in the other scattering-matrix elements are also surprisingly small

(Figs. 1.4 and 1.5). The only clear indications of the fact that two-sphere aggregates are

nonspherical particles are the deviation of the ratio )()( 12 ΘΘ aa from unity and the

deviation of the ratios )180()180( 13 °° aa and )180()180( 14 °° aa from –1 (cf. [7,14]).

Tables 1.1 and 1.2 demonstrate that the differences in the integral photometric

characteristics (the ensemble averaged extinction, scattering, and absorption cross

sections, the single-scattering albedo, and the asymmetry parameter) between the semi-

external and the composition-equivalent external mixtures do not exceed 15% and are

0 60 120 180Scattering angle (deg)

0.1

1

10

100

1000

a1

reff (µm)

0.1

1.0

Figure 1.2: Phase function versus scattering angle for dust-sulfate semi-external (solid curves)and external (dotted curves) mixtures. The effective radius of dust particles is fixed at 1 µm.The thin and thick curves, respectively, show the results for the smallest (reff = 0.1 µm) and thelargest (reff = 1 µm) sulfate aerosol mode considered in this paper.

23

often much smaller, particularly for Cabs, ϖ , and g. Owing to mutual shadowing, the

scattering cross sections of the semi-externally mixed aerosols are always smaller than

those of their externally mixed counterparts, whereas the absorption cross section hardly

changes.

The small differences in the single-scattering albedo and the asymmetry parameter

in combination with the small phase function and polarization differences suggest that

aggregation is likely to have a relatively weak effect on remote sensing retrievals of the

0 60 120 180

Scattering angle (deg)

0.1

1

10

100

a1

reff (µm)

0.05

0.5

Figure 1.3: As in Fig. 1.2, but for sulfate-soot mixtures. The effective radius of sulfateparticles is fixed at 0.5 µm. The thin and thick curves, respectively, show the results for thesmallest (reff = 0.05) and the largest (0.5 µm) soot aerosol mode considered in this paper.

24

aerosol physical characteristics and computations of the aerosol direct radiative forcing.

This is especially true when one of the aerosol components is much larger than the other

and, thereby, dominates the total optical characteristics of the mixture. It is also quite

obvious that the semi-external mixing does not cause as pronounced an enhancement of

the black carbon absorption as that caused by internal mixing [3]. As a consequence, it

appears to be rather safe to use the much simpler external mixture model in radiative

transfer computations irrespective of the actual form of mixing.

Table 1.1: Optical characteristics of dust-sulfate particle mixturesa

0.1 � 0.2 � � 0.5 � 1reff (µm)

SEb E � SE E � � SE E � SE E

Cext (µm2) 4.540 4.542 4.578 4.635 �� 5.319 5.794 � 8.309 9.361Csca (µm2) 3.952 3.955 3.988 4.048

��

4.727 5.207� �

7.716 8.774Cabs (µm2) 0.588 0.587 0.590 0.587

� �

0.592 0.587� �

0.593 0.5870.871 0.871 0.871 0.873

� �

0.889 0.899� �

0.929 0.937g 0.712 0.712 0.711 0.712 � � 0.716 0.715 � 0.726 0.720

a The effective radius of dust particles is fixed at 1 µm.b “SE” denotes semi-external mixing and “E” denotes external mixing.

Table 1.2: Optical characteristics of sulfate-soot aerosol mixtures a

0.05 0.1 0.2 0.5reff (µm)

SEb E SE E SE E SE E

Cext (µm2) 1.259 1.259 1.272 1.282 1.367 1.426 2.176 2.423Csca (µm2) 1.256 1.257 1.255 1.266 1.269 1.332 1.563 1.822Cabs (µm2) 0.003 0.002 0.017 0.016 0.098 0.094 0.613 0.601

0.998 0.998 0.986 0.988 0.928 0.934 0.718 0.752g 0.722 0.721 0.726 0.720 0.737 0.717 0.780 0.751

a The effective radius of sulfate particles is 0.5 µm.b “SE” denotes semi-external mixing and “E” denotes external mixing.

The analysis of this paper is limited to simple two-particle aggregates. Since more

ϖ

ϖ

25

complex aerosol aggregates can also be encountered in the atmosphere, we plan to

extend this study by performing calculations using the code described in [15] and

applicable to randomly oriented clusters with three or more components.

0

25

50

75

100

a 2 /a

1 (%

)

−100

−50

0

50

100

a 3 /a

1 (%

)

−100

−50

0

50

100

a 4 /a

1 (%

)


−100

−50

0

50

100

−b1 /a

1 (%

)


−100

−50

0

50

100

b 2 /a

1 (%

)

reff (µm)

0.1

1.0

Figure 1.4: As in Fig. 1.2, but for scattering-matrix element ratios.

26

Acknowledgement

This research was supported by the NASA Radiation Sciences Program managed

by Donald Anderson.

0

25

50

75

100

a 2 /a

1 (%

)

−100

−50

0

50

100

a 3 /a

1 (%

)

−100

−50

0

50

100

a 4 /a

1 (%

)


−100

−50

0

50

100

−b1 /a

1 (%

)


−100

−50

0

50

100

b 2 /a

1 (%

)

reff (µm)

0.05

0.5

Figure 1.5: As in Fig. 1.3, but for scattering-matrix element ratios.

27

References

[1] Podzimek J. Physical properties of coarse aerosol particles and haze elements in a

polluted urban-marine environment. J Aerosol Sci 1990;21:299–308.

[2] Sato M, Hansen J, Koch D, Lacis A, Ruedy R, Dubovik O, Holben B, Chin M,

Novakov T. Global atmospheric black carbon inferred from AERONET. Proc

Natl Acad Sci, in press.

[3] Chýlek P, Videen G, Ngo D, Pinnick RG, Klett JD. Effect of black carbon on the

optical properties and climate forcing of sulfate aerosols. J Geophys Res

1995;100:16325–32.

[4] Fuller KA. Scattering and absorption cross sections of compounded spheres. II.

Calculations for external aggregation. J Opt Soc Am A 1995;12:881–92.

[5] Fuller KA, Malm WC, Kreidenweis SM. Effects of mixing on extinction by

carbonaceous particles. J Geophys Res 1999;104:15941–54.

[6] van de Hulst HC. Light scattering by small particles. New York: Wiley, 1957.

[7] Mishchenko MI, Travis LD, Lacis AA. Scattering, absorption, and emission of

light by small particles. Cambridge: Cambridge University Press, 2002.

[8] Hansen JE, Travis LD. Light scattering in planetary atmospheres. Space Sci Rev

1974;16:527–610.

[9] d’Almeida GA, Koepke P, Shettle EP. Atmospheric aerosols. Hampton, VA:

Deepak, 1991.

[10] Mishchenko MI, Mackowski DW. Light scattering by randomly oriented

bispheres. Opt Lett 1994;15:1604–6.

28

[11] Fuller KA. Optical resonances and two-sphere systems. Appl Opt 1991;30:4716-

31.

[12] Mackowski DW. Calculation of total cross sections of multiple-sphere clusters. J

Opt Soc Am A 1994;11:2851–61.

[13] Mishchenko MI. Light scattering by randomly oriented axially symmetric

particles. J Opt Soc Am A 1991;8:871–82.

[14] Mishchenko MI, Mackowski DW, Travis LD. Scattering of light by bispheres

with touching and separated components. Appl Opt 1995;34:4589–99.

[15] Mackowski DW, Mishchenko MI. Calculation of the T matrix and the scattering

matrix for ensembles of spheres. J Opt Soc Am A 1996;13:2266–78.

29

Chapter 2

The effect of black carbon on scattering and absorption ofsolar radiation by cloud droplets1

Li Liua,b, Michael I. Mishchenkoa, Surabi Menona,b, Andreas Mackec,Andrew A. Lacisa

aNASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USAbDepartment of Earth and Environmental Sciences, Columbia University, 2880 Broadway, New

York, NY 10025, USAcInstitute for Oceanography, University of Kiel, Duesternbrooker Weg 20, D-24105 Kiel,

Germany

Abstract

Scattering and absorption characteristics of water cloud droplets containing black

carbon (BC) inclusions are calculated at a visible wavelength of 0.55 µm by a

combination of ray-tracing and Monte Carlo techniques. In addition, Lorenz-Mie

calculations are performed assuming that the same amount of BC particles are mixed

with water droplets externally. The results show that it is unlikely under normal

conditions that BC aerosols can modify scattering and absorption properties of cloud

droplets in any significant way except for geographical locations very close to major

sources of BC. The differences in the single-scattering co-albedo and asymmetry

parameter between BC-fraction-equivalent internal and external mixtures are negligibly

small for normal black carbon loadings, which makes possible the use of the much

simpler external mixing model in radiative transfer modeling irrespective of the actual

form of mixing. For a fixed amount of BC internally mixed with cloud droplets, the

absorption is maximal when the effective radius of the BC inclusions is about 0.05–0.06

1 Published in Journal of Quantitative Spectroscopy & Radiative Transfer, 74, 195-204, 2002.

30

µm.

Keywords: Black carbon; Cloud water droplets; Internal and external mixing; Single-

scattering co-albedo; Asymmetry parameter

2.1 Introduction

Black carbon (BC) has long been recognized as an important atmospheric pollutant

[1]. It plays a significant role in the absorption of solar radiation by atmospheric

aerosols and possibly also by clouds. Enhanced absorption by black carbon particles

imbedded in water droplets could potentially reduce the cloud albedo [2], thereby

causing a significant indirect forcing of climate [3].

The effect of BC impurities on the absorption of solar radiation by cloud water

droplets was considered by Danielson et al. [4] using an idealized model with an inner

sphere of an absorbing aerosol particle surrounded by a concentric shell of pure water.

Chýlek et al. [2] calculated the spectral cloud albedo using an effective medium

approximation, which substitutes a heterogeneous internal water-carbon mixture by a

fictitious homogeneous material characterized by an effective refractive index.

However, the applicability of various effective medium approximations to water

droplets containing relatively large soot inclusions remains somewhat uncertain and

requires further theoretical and experimental research [5]. Recently, the exact solution

for electromagnetic scattering by a host sphere containing one or several non-concentric

spherical inclusions has become available (e.g., [6–10]). However, the practical

implementations of this solution are still limited in terms of the maximal size parameter

of the host and the number and size of inclusions and become very time-consuming

when applied to realistic cloud water droplets with multiple randomly positioned

inclusions. Therefore, in this paper we address the problem of scattering and absorption

31

of solar radiation by cloud droplets containing BC inclusions using the ray-

tracing/Monte Carlo approach developed by Macke et al. [11–13]. This approximate

technique assumes that the size of the host particle is much larger than the wavelength

of the incident radiation and that the inclusions are randomly and sparsely distributed,

and we expect that these conditions are adequately satisfied by an average cloud water

droplet (radius ~10 µm) at visible wavelengths. The results thus obtained are compared

with those calculated with the standard Lorenz-Mie formulation and assuming that the

same amount of BC particles are mixed with water droplets externally. This

comparison is used to derive conclusions about the specific effects of internal mixing on

radiative properties of cloud droplets contaminated with soot.

2.2 Optical properties of black carbon

An important consequence of the presence of BC in the atmosphere is increased

absorption of solar radiation [14]. The magnitude of absorption depends on the BC

refractive index (especially its imaginary part) and the size, shape, and porosity of BC

particles. It also depends on whether the BC particles are mixed with cloud droplets

internally or externally and is a function of the average size of the cloud droplets and

the exact location of BC inclusions within the droplets. The external and internal

mixture models are shown schematically in Fig. 2.1. Since there is no obvious reason to

assume that BC inclusions should have a preferential location inside water droplets, the

scattering and absorption properties of contaminated water droplets should be averaged

over a random distribution of BC particle locations.

The imaginary part of the BC complex refractive index depends on the original

composition of the material that was burned and on the burning process itself.

Consequently, there are no universal well-defined optical constants of BC [15].

Following the suggestion by d’Almeida et al. [16], we have adopted for this study the

32

refractive index 1.75 + 0.44i. This refractive index was also used in recent publications

by Chýlek et al. [14,15].

(a)

(b)

Figure 2.1: External (a) and internal (b) mixing of large cloud droplets and smaller aerosolparticles.

Table 2.1: Black carbon concentration in cloud water

ReferencesMean BC

)kgµg( 1−Range of BC

)kgµg( 1− LocationDegree ofinternalmixing (%)

Twohy et al. [29] 23–79 Southern California

Chýlek et al. [23] 40 10–61Nova Scotia

(Canada)9

Kou [30] 16 8–41Nova Scotia

(Canada)6

Bahrmann and Saxena [31] 74.2 20.7–196.9 North Carolina 13

Hallberg et al. [34] 6

2.3 Observations

In order to evaluate the effect of BC on the radiation balance of the Earth’s

atmosphere, one needs global information on the distribution of BC throughout the

33

atmosphere [17,18]. Although there have been several measurements of the BC

concentration in cloud water droplets, the observational data are incomplete, and no

clear global or regional picture can be deduced. Rather than rely on a definite set of

local observations, Chýlek et al. [15] estimated the lower and upper bounds on the black

carbon mixing ratio (by mass) in cloud water for stratus type clouds to be 9104.2 −× and

6108 −× . A summary of BC concentration measurements is given in Table 2.1.

2.4 Ray-tracing/Monte Carlo model

The ray-tracing/Monte Carlo technique is a simple and efficient hybrid method

combining ray optics and Monte Carlo radiative transfer concepts. This method permits

the treatment of light scattering and absorption by arbitrarily shaped host particles

containing small, randomly positioned spherical and nonspherical inclusions and is

valid for host particles that are large compared to the wavelength of the incident

radiation. The ray-tracing program takes care of individual reflection and refraction

events at the outer boundary of the host particle, while the Monte Carlo routine

simulates the process of multiple internal scattering by the inclusions. A detailed

description of this model is provided in [11–13]. The respective computer code is

publicly available at the following URL http://www.ifm.uni-kiel.de/fb/fb1/me/research/

Projekte/RemSens/SourceCodes/codes.html.

2.5 Model computations

Since BC is found in cloud droplets in measurable amounts, it has been of interest

from the climatic standpoint to determine whether the typical BC concentrations could

cause significant excess absorption of solar radiation relative to absorption by cloud

droplets alone. This absorption would be caused by both increased single-scattering co-

34

albedo ϖ−1 and increased asymmetry parameter g of the cloud droplet/BC mixture,

where ϖ is the single-scattering albedo. To find the upper bound on the absorption

effect of BC, we consider the maximal plausible BC mixing ratio in cloud water

6108 −× (by mass) as estimated by Chýlek et al. [15]. The specific density of BC is

largely unknown and depends on the actual burning process. In this paper, we have

adopted a low BC specific density of 3cmg1 −=ρ consistent with our desire to estimate

an upper limit on the BC absorption effect. The refractive index of water at a visible

wavelength of 0.55 µm and the water specific density are taken to be i10233.1 9−×+

and 1 3cmg − , respectively. Below we will consider separately the cases of internal and

external mixing of BC and cloud water.

2.5.1 Internal mixing

First, we consider a spherical 10 µm-radius water droplet containing a 6108 −×

fraction (by mass) of polydisperse, randomly distributed, spherical BC particles. The

size distribution of the small BC inclusions was determined on only a very few

occasions (e.g., [19–22]). Most of BC particles are in the submicron size range with a

typical mode radius between 0.03 and 0.06 µm [23]. Instead of specifying a fixed

effective radius effr of the BC inclusions, we vary it from 0.01 to 0.22 µm, with effr =

0.22 µm corresponding to one inclusion per host particle under the condition that such a

composite particle contains the 6108 −× BC fraction (by mass), to see how the effective

radius of these inclusions affects the total scattering and absorption properties of cloud

droplets. We assume that the size distribution of the BC particles is given by the

standard gamma distribution [24]:

−×= −

ab

rrrn bb expconst)( )31( , (2.1)

35

where effra = and effvb = . In this study, the effective variance effv is fixed at 0.1,

representing a moderately wide size distribution. The model variable values used in this

study are summarized in Table 2.2. The scattering and absorption properties of BC-

contaminated cloud droplets at the wavelength λ = 0.55 µm (corresponding to the

maximum in the spectral distribution of the solar radiation) have been calculated by a

combination of ray-tracing and Monte Carlo techniques as mentioned above. The

single-scattering properties of BC particles have been computed assuming the spherical

particle shape and using the Lorenz-Mie code described by Mishchenko et al. [25] and

available at http://www.giss.nasa.gov/~crmim.

Table 2.2: Model parameter values used in this study a

)cmg( 3−ρ Refractive index effr (µm) veffMixingratio bymass BC W BC W BC W BC W

Relative BCRefractiveindex b

6108 −× 1 1 1.75+0.44i 910233.1 −×+ i0.01–0.22

10 0.1 – i331.0316.1 +a BC = black carbon; W = water.b The BC refractive index is divided by that of water at 0.55µm.

2.5.2 External mixing

BC particles not only can act as cloud condensation nuclei and be found inside

cloud droplets but can also exist outside the droplet as interstitial aerosols. The optical

properties of externally mixed cloud droplets and BC aerosols can be well represented

by the traditional Lorenz-Mie theory provided that the cloud and aerosol particles are

widely separated [26]. We have performed the Lorenz-Mie computation assuming the

same mass fraction of BC. Assuming independent scattering, the total single-scattering

albedo ϖ and asymmetry parameter g of the mixture are given by [27]

36

0.00 0.05 0.10 0.15 0.20 0.25Effective Radius (µm)

0.0002

0.0003

0.0004

0.0005

Sin

gle-

Sca

tterin

g C

o-A

lbed

o

Internal Mixing

External Mixing

0.00 0.05 0.10 0.15 0.20 0.25Effective Radius (µm)

0.8832

0.8833

0.8834

0.8835

0.8836

0.8837

0.8838

Asy

mm

etry

Par

amet

er

Figure 2.2: Single-scattering co-albedo ϖ−1 and asymmetry parameter g for mixtures ofcloud droplets and BC particles versus BC particle effective radius at a wavelength of 0.55 µm.The effective variance of the BC particle size distribution is fixed at 0.1, and the BC massfraction is fixed at 6108 −× . The solid curves show the results for the internal mixture, whereasthe dashed curves represent the external mixture. The dash-dotted curve depicts the asymmetryparameter of pure 10 µm-radius water droplets.

BCext,Wext,

BCsca,Wsca,

NCC

NCC

++

=ϖ , (2.2)

BCsca,Wsca,

BCsca,BCWsca,W

NCC

CNgCgg

++

= , (2.3)

where scaC and extC are the scattering and extinction cross sections per particle and N

37

is the number of BC particles per cloud droplet assuming that the BC fraction by mass

is fixed at 6108 −× . The subscripts W and BC correspond to water droplets and BC

aerosols, respectively.

2.5.3. Numerical results

Fig. 2.2 shows the single-scattering co-albedo ϖ−1 and asymmetry parameter g

of water droplets internally and externally mixed with BC aerosols at the wavelength

0.55 µm as a function of the BC particle effective radius effr computed for the BC mass

fraction 6108 −× . It is clear that internal mixing enhances absorption compared to

external mixing, which has already been pointed out in previous studies (see, e.g.,

[2,29,28]). The absorption is maximized at 05.0eff ≈r µm for internal mixing

( 4106.41 −×≈ϖ− ) and at 08.0eff ≈r µm for external mixing 4104.41 −×≈ϖ− . Since

the imbedded BC particles decrease the ray-tracing part of the total phase function of

heterogeneous droplets and thus increase the fractional contribution of the diffraction

part, the total asymmetry parameter of BC-contaminated water droplets increases

relative to that of pure water droplets [11].

Although we have adopted the upper limit on the BC mass fraction equal to

6108 −× [15], the measured BC fractions in water cloud droplets are usually two orders

of magnitude smaller [19–22]. To demonstrate the effect of varying BC amount, Fig.

2.3 depicts the single-scattering co-albedo and asymmetry parameter as a function of

the BC mass fraction at the same wavelength 0.55 µm, with effr and effv of BC

particles fixed at 0.05 µm and 0.1, respectively. We have chosen the value effr = 0.05

µm because it maximizes the absorption effect of internally mixed BC particles and

because this value appears to be quite realistic according to the measurement results

reported in [23,32,33].

38

0.001 0.01 0.1 1 10BC Mass Fraction in Units of 8 x10−6

0

0.001

0.002

0.003

0.004

0.005

Sin

gle-

Sca

tterin

g C

o-A

lbed

o

Internal Mixing

External Mixing


0.8825

0.8830

0.8835

0.8840

0.8845

Asy

mm

etry

Par

amet

er

Figure 2.3: Single-scattering co-albedo ϖ−1 and asymmetry parameter g for mixtures ofcloud droplets and BC particles versus BC mass fraction. The BC particle effective radius is0.05 µm and the effective variance is 0.1. The solid curves show the results for the internalmixture, whereas the dashed curves represent the external mixture. The dash-dotted curvedepicts the asymmetry parameter of pure 10 µm-radius water droplets.

Fig. 2.3 shows that absorption increases almost linearly with increasing BC mass

fraction. However, it is also obvious that the traditionally measured amounts of BC

cannot cause significant indirect forcing by strongly increasing cloud absorption.

39


−40

−20

0

20

40

Relative Difference in Single-Scattering Co-Albedo (%)


−0.15

−0.1

−0.05

0

0.05

Relative Difference in Asymmetry Parameter (%)

Figure 2.4: Relative differences (in %) between the single-scattering co-albedo and asymmetryparameter for external and internal mixtures of cloud droplets and BC particles versus the BCmass fraction. The BC particle effective radius and effective variance are 0.05 µm and 0.1,respectively.

The absolute difference in the single-scattering co-albedo and asymmetry

parameter results between the cases of internal and external mixing is negligible when

the BC mass fraction is less than 7108 −× . The latter value is still an order of magnitude

larger than those measured for the majority of water clouds [23,29-31]. Fig. 2.4 shows

the relative external/internal differences (in percent) in ϖ−1 and g as a function of the

BC amount at the wavelength 0.55 µm. The values of effr and effv of the BC particles

40

are 0.05 µm and 0.1, respectively. The relative differences in the asymmetry parameter

are very small, less than 0.13% in absolute value even when the BC mass fraction is as

high as 5108 −× . The relative differences in the single-scattering co-albedo are about –

13% when the BC mass fraction is greater than 7104.2 −× and reach –28% when the BC

fraction is 88 108104.2 −− ×−× (thus representing a very clean atmosphere). Taking into

account that the majority of BC particles remain outside cloud droplets ([23,29-31,34])

and that the differences in ϖ−1 and g between the internal and external mixtures are

very small, we conclude that irrespective of the actual form of mixing, one can always

use the much simpler external mixing scheme in radiative transfer modeling with great

confidence.

2.6 Discussion

Despite the use of a different approach to compute the optical properties of BC-

contaminated cloud droplets, our conclusions are in remarkable agreement with those

derived by Chýlek et al. [2] and Twohy el al. [29]. Chýlek et al. [2] found that a mass

fraction of internally mixed graphitic carbon of about 6107 −× is required to increase the

single-scattering co-albedo of droplets forming thick stratus clouds from 710− (pure

water) to 310− . Twohy et al. [19] concluded that BC mass concentrations in excess of

20,000 µg per 1 kg of cloud water are necessary to reduce the albedo of a cloud with an

optical thickness of 30 by 0.03. The observed BC mass concentrations [23,29–31] are

usually too low to reduce the cloud albedo in any significant way.

There are a number of uncertainties about the BC optical constants and their

variability with type of BC. As a result, the measured refractive indices vary

appreciably. The absorption by a small black carbon particle can be shape dependent

and may be enhanced by porosity. In this study, we have assumed that BC particles are

41

randomly distributed inside water droplets, whereas a preferential location of BC

impurities may cause an enhanced absorption. Absorption also depends on the

(variable) size of cloud droplets. Although disregarding these uncertainties may result

in a biased quantitative estimate of the effect of BC particles on cloud droplet optical

properties, it is unlikely to affect our conclusions in a significant way because the

observed BC concentrations are so small.

Acknowledgements

This research was funded by the NASA Global Aerosol Climatology Project

managed by Donald Anderson.

42

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[19] Heintzenberg J. Size-segregated measurements of particulate elemental carbon and

aerosol light absorption at remote Arctic locations. Atmos Environ 1982;16:2461–

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[20] Pueschel RF, Blake DF, Snetsinger KG, Hansen ADA, Verma S, Kato K. Black

44

carbon (soot) aerosol in the lower stratosphere and upper troposphere. Geophys

Res Lett 1992;19:1659–62.

[21] Parungo F, Nagamoto C, Zhou MY, Hanson ADA, Harris J. Aeolian transport of

aerosol black carbon from China to the ocean. Atmos Environ 1994;28:3251–60.

[22] Blake DF, Kato K. Latitudinal distribution of black carbon soot in the upper

troposphere and lower stratopshere. J Geophys Res 1995;100:7195–202.

[23] Chýlek P, Banic CM, Johnson B, Damiano PA, Isaac GA, Leaitch WR, Liu PSK,

Boudala FS, Winter B, Ngo D. Black carbon: atmospheric concentrations and

cloud water content measurements over southern Nova Scotia. J Geophys Res

1996;101:29105–10.

[24] Hansen JE, Travis LD. Light scattering in planetary atmosphere. Space Sci Rev

1974;16: 527–610.

[25] Mishchenko MI, Dlugach JM, Yanovitskij EG, Zakharova NT. Bidirectional

reflectance of flat, optically thick particulate layers: an efficient radiative transfer

solution and applications to snow and soil surfaces. JQSRT 1999;63:409–32.

[26] Mishchenko MI, Mackowski DW, Travis LD. Scattering of light by bispheres with

touching and separated components. Appl Opt 1995;34:4589–99.

[27] Mishchenko MI, Travis LD, Lacis AA. Scattering, absorption, and emission of light

by small particles. Cambridge University Press, Cambridge, 2002.

[28] Ackerman TP, Toon OB. Absorption of visible radiation in atmosphere containing

mixtures of absorbing and nonabsorbing particles. Appl Opt 1981;20:3661–8.

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material extracted from cloud droplets and its effect on cloud albedo. J Geophys

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Halifax (Canada): Dalhousie University.

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[31] Bahrmann CP, Saxena VK. Influence of air mass history on black carbon

concentrations and regional climate forcing in southeastern United States. J

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efficiency of submicron amorphous carbon particles between 2.5 and 40µm.

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IB. Phase partitioning for different aerosol species in fog. Tellus B 1992;44:545–

55.

46

Chapter 3

Scattering matrix of quartz aerosols: comparison andsynthesis of laboratory and Lorenz-Mie results1

Li Liu,a,b Michael I. Mishchenko,b,* Joop W. Hovenier,c,d Hester Volten,d,e

Olga Muñozf

aDepartment of Earth and Environmental Sciences, Columbia University, 2880 Broadway,

New York, NY 10025, USAbNASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USAcDepartment of Physics and Astronomy, Free University, De Boelelaan 1081, 1081 HV

Amsterdam, The NetherlandsdAstronomical Institute “Anton Pannekoek,” University of Amsterdam, Kruislaan 403,

1098 SJ Amsterdam, The NetherlandseFOM-Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam,

The NetherlandsfInstituto de Astrofisica de Andalucia, P.O. Box 3004, Granada 18080, Spain

Abstract

This paper compares and combines the results of laboratory measurements of the

Stokes scattering matrix for nonspherical quartz aerosols at a visible wavelength in the

scattering angle range 5°–173° and the results of Lorenz-Mie computations for

projected-area-equivalent spheres with the refractive index of quartz. A synthetic

normalized phase function is constructed based on the laboratory data and the

assumption that the diffraction forward-scattering peak is the same for spherical and

nonspherical projected-area-equivalent particles. The experimental scattering matrix for

1 Published in Journal of Quantitative Spectroscopy & Radiative Transfer, 79-80, 911-920,2003.

47

the nonspherical quartz particles is poorly represented by the Lorenz-Mie results for

most scattering angles. However, the asymmetry parameters for the synthetic phase

function and for the equivalent spherical particles are similar.

Keywords: Electromagnetic scattering; Nonspherical particles; Polarization

3.1 Introduction

Particle nonsphericity has been shown to be an important factor that must be

carefully addressed in optical characterization of mineral atmospheric aerosols [1–4].

Despite the significant recent progress [5–9], theoretical and numerical techniques are

still limited in their ability to simulate electromagnetic scattering by realistic

polydispersions of irregular particles. Therefore, laboratory measurement techniques

[10,11] remain an important source of information on scattering properties of

nonspherical aerosols.

In a recent paper, Volten et al. [12] presented an extensive dataset which includes

the results of laboratory measurements in the visible of the Stokes scattering matrix in a

wide scattering angle range for several types of polydisperse, randomly oriented mineral

aerosols and accompanying size distribution data. A traditional limitation of such

laboratory measurements is the lack of data at very small and very large scattering

angles (in this case, from 0° to 5° and from 173° to 180°), which precludes the

determination of the absolute angular dependence of the phase function )(1 Θa by using

the standard normalization condition,

1)(sind21

10

=∫ ΘΘΘπ

a , (3.1)

where Θ is the scattering angle. As a consequence, Volten et al. plotted the relative

quantity )30()()(~111 °= aaa ΘΘ rather than )(1 Θa , which makes their measurements

48

less useful in those cases when the absolute phase function values are needed [1–4,13].

The main purpose of this paper is to explore what insight and knowledge can be

gained by comparing and synthesizing an experimental and a theoretical scattering

matrix in the visible part of the spectrum. A unique opportunity to do so was provided

by a sample of randomly oriented quartz particles, because (i) its scattering matrix at a

wavelength of 441.6 nm was measured in the laboratory over a wide range of scattering

angles [12]; (ii) independently measured size distribution data are available for this

sample [12]; and (iii) independently measured values of the refractive index of quartz at

visible wavelengths are also available [14]. Consequently, in this case the experimental

scattering matrix can be contrasted with the most physically relevant theoretical Lorenz-

Mie scattering matrix, namely the one that is valid for projected-area-equivalent spheres

with the same refractive index.

The organization of this paper is as follows. First, we parallel the laboratory study

of Volten et al. [12] for the quartz particle sample by performing theoretical Lorenz-Mie

computations for projected-area-equivalent quartz spheres. Second, we construct a

synthetic phase function for the quartz particle sample using the relative angular profile

of the phase function measured by Volten et al., assuming that the forward-scattering

diffraction peak is independent of the particle shape and depends only on the

distribution of surface-equivalent-sphere radii, and using the normalization condition of

Eq. (3.1). The synthetic phase function is then used to compute the corresponding value

of the asymmetry parameter,

ΘΘΘΘΘπ

cos)(sind21

cos 10

a∫= . (3.2)

Finally, we briefly compare all elements of the scattering matrix and the asymmetry

parameter for the quartz particle sample and for projected-area-equivalent quartz

spheres.

49

3.2 Measurements and Lorenz-Mie computations

Volten et al. [12] used a laser particle sizer to measure the normalized projected

area distribution )(log rS of the quartz particle sample, where )d(log)(log rrS is the

fraction of the total projected area of the sample contributed by particles with radii in

the size range from rlog to )d(loglog rr + . The equivalent-sphere radius r of a

nonspherical particle is defined as the radius of a sphere that has a projected area equal

to the average projected area of the nonspherical particle in random orientation. This

distribution was presented in tabular form by Volten [15] and is shown in Fig. 3.1. Note

that equal areas under the curves correspond to equal contributions to the total projected

area. The effective radius effr and effective variance effv of this broad size distribution

are 2.3 µm and 2.4, respectively, where [16]

2eff )(d

1 max

min

rrrnrG

rr

rπ= ∫ , (3.3)

−1 0 1 2 logr

0

0.2

0.4

0.6

0.8

1

S(lo

gr)

Figure 3.1: Normalized distribution of the average area of the particle projection for randomlyoriented quartz aerosols. Here r is expressed in micrometers.

50

22eff2

effeff )()(d

1 max

min

rrrrnrrG

r

rπ−= ∫v , (3.4)

0.01

0.1

1

10

100

Lorenz-Mie results

Measurement results

Pha

se fu

nctio

n

−0.4

−0.2

0

0.2

−b1 /a

1

0

0.5

1

a 2 /a

1

−1

−0.5

0

0.5

1

a 3 /a

1


−0.6

−0.4

−0.2

0

0.2

b 2 /a

1


−1

−0.5

0

0.5

1

a 4 /a

1

Figure 3.2: Laboratory data for nonspherical quartz aerosols and results of Lorenz-Miecomputations for projected-area-equivalent quartz spheres. Experimental errors are shown byvertical error bars.

51

and

2)(dmax

min

rrnrGr

rπ= ∫ (3.5)

is the average area of the particle geometrical projection. Here rrn d)( is the fraction of

projected-area-equivalent spheres with radii between r and r + dr.

The open circles in Fig. 3.2 show the experimentally determined elements of the

scattering matrix versus scattering angle at a wavelength of 441.6 nm. The

measurements were performed at 5° intervals for scattering angles, Θ , in the range

from 5° to 170° and at 1° intervals for Θ from 170° to 173°. The experimental phase

function is normalized by its value at Θ = 30° and is plotted on a logarithmic scale. The

other elements are shown relative to the phase function. Within measurement errors,

the scattering matrix has the standard block-diagonal form,

− )()(00

)()(00

00)()(

00)()(

42

23

21

11

ΘΘΘΘ

ΘΘΘΘ

ab

ba

ab

ba

, (3.6)

thereby indicating that during the measurement, the quartz particles suspended in the air

jet were randomly oriented and formed a macroscopically isotropic and mirror-

symmetric scattering medium [17].

For comparison, the solid curves in Fig. 3.2 show the results for projected-area-

equivalent spheres calculated with the Lorenz-Mie code described in [18] and available

on the Internet at http://www.giss.nasa.gov/~crmim. For these computations, we

employed the number size distribution )(rn derived from the measured projected area

distribution shown in Fig. 3.1. Furthermore, we used the real part of the refractive index

1.559 as typical of quartz at wavelengths close to 440 nm [14]. Since quartz is

essentially nonabsorbing at visible wavelengths, the imaginary part of the refractive

52

index was set to zero. The theoretical Lorenz-Mie phase function is normalized

according to Eq. (3.1). Note that Volten et al. [12] use the time factor )iexp( tω rather

than the factor )iexp( tω− adopted in [18], which causes a sign difference in the

numerical values of the ratio )()( 12 ΘΘ ab . Therefore, the sign of the experimentally

measured ratio )()( 12 ΘΘ ab in Fig. 3.2 is opposite to that in [12].

3.3 Synthetic phase function

As we have already mentioned, Volten et al. [12] measured the relative phase

function )(~1 Θa rather than the actual phase function. Therefore, although the laboratory

data give the relative angular profile of the phase function in the scattering angle

interval from 5° to 173°, the exact vertical position of the experimental curve in (Θ , a1)

coordinates remains uncertain. The dashed and dot-dashed curves in Fig. 3.3 show two

extreme vertical positions of the experimental curve intended to match the phase

function values for nonspherical and projected-area-equivalent spherical quartz particles

at side- and backscattering angles, respectively. It is seen that in both cases spherical-

nonspherical phase function differences at other angles are very large and can exceed a

factor of 10. Placing the experimental curve in an intermediate position minimizes the

differences at side- and backscattering angles on average (dotted curve), but they can

still exceed a factor of 3. It is thus clear that irrespective of the actual vertical position

of the experimental curve, spherical-nonspherical phase function differences remain

very large at specific scattering angles.

In order to get a better idea of a plausible vertical position of the phase function for

nonspherical quartz particles, we did the following. It is known that the phase function

at small scattering angles for particles greater than a wavelength is mostly determined

by Fraunhofer diffraction and is largely the same for spherical and projected-area-

53

equivalent nonspherical particles with moderate aspect ratios and regular shapes (e.g.,

[19,20]). Therefore, we used the results of Lorenz-Mie computations for projected-area-

equivalent quartz spheres in the scattering angle interval from 0° to 5° and shifted the

experimental )(~1 Θa -curve in the vertical direction until its value at Θ = 5° matched the

Lorenz-Mie result. Finally, the experimental phase function was extrapolated from Θ =

173° to Θ = 180° using cubic splines.

We then evaluated the left-hand-side of Eq. (3.1) in order to check whether this

synthetic phase function satisfied the normalization condition. The result was 0.848

rather than the expected value unity. Since the contribution of the interval from Θ =


0.01

0.1

1

10

100

Pha

se fu

nctio

n

Figure 3.3: The pattern of the differences between the Lorenz-Mie phase function for sphericalquartz particles (solid curve) and the phase function for nonspherical quartz aerosols depends onthe vertical position of the experimental )(~

1 Θa profile (dashed, dotted, and dot-dashed curves).

54

173° to 180° to the integral was only 0.005, it is obvious that the use of spline

extrapolation could not explain the large discrepancy between the computed and

expected integral values.

There are several potential contributors to this discrepancy, including the

following.

• Experimental errors. These are always a potential source of complications.

However, in this case the errors (indicated by error bars in Fig. 3.2) appear to be too

small to be a likely explanation of the above discrepancy.

• The possible inaccuracy of the underlying assumption, made on the basis of

computations for regular nonspherical shapes, that the phase functions for projected-

area-equivalent spherical and nonspherical particles are the same in the forward-

scattering direction. One should not exclude the possibility that this assumption may

not be sufficiently precise for the irregular (including complicated surface structure)

quartz aerosols under consideration, especially at scattering angles as large as 5º.

• Inaccuracies in the measured size distribution of the quartz aerosols, especially for

the smallest particles. For example, we have found that truncating the measured size

distribution by leaving out all particles with equivalent-sphere radii smaller than

0.31 µm and then renormalizing the resulting size distribution improves the

normalization of the synthetic phase function significantly. Therefore, we should not

exclude the possibility that the size distribution of the quartz particles during the

scattering matrix measurements contained fewer small particles than was deduced

from the separate measurements with the particle sizer.

• Multiple scattering effects in the laboratory measurements. However, these appear

to be very unlikely, since the shape of the curves for )(~1 Θa did not show any

significant difference when the amount of scattering mineral aerosol particles was

doubled (see also [21]).

55

• Some constructive interference of light singly scattered by particles in the forward

direction [22] may have contributed to the intensity measured at small scattering

angles.

Given these uncertainties, we have decided to use, as a tentative fix, the following

simple procedure. Since it is likely that the most “vulnerable” quantity is the phase

function at the smallest scattering angle, we kept changing the experimental )5(~1 °a

value in very small increments and repeated the process of compiling the synthetic

phase function until it satisfied the normalization condition of Eq. (3.1) to better than

0.001. The result is shown in Fig. 3.4 by the dotted curve and is contrasted with the

Lorenz-Mie phase function for projected-area-equivalent quartz spheres depicted by the

solid curve. The respective asymmetry parameters evaluated using Eq. (3.2) are 0.669

and 0.698.

It is often convenient to represent a phase function by expanding it in Legendre

polynomials )(cosΘnP [17]:

∑=

Θ=Θmax

011 ).(cos)(

n

nn

n Pa α (3.7)

The expansion coefficients for the synthetic phase function were computed by

evaluating numerically the integral in the formula

∫ ΘΘΘΘ+=π

α0 11 )(cos)(sin)

2

1( n

n Padn (3.8)

and are available from the corresponding author upon request.

3.4 Discussion and conclusions

Figure 3.4 represents the main result of this paper. It closely resembles Fig. 6(a) of

Jaggard et al. [23] depicting experimental and theoretical Lorenz-Mie results for Raft

56

River soil dust. In agreement with the results of Jaggard et al. and previous theoretical

studies of light scattering by polydisperse, randomly oriented spheroids and circular

cylinders [19,20], Fig. 3.4 reveals the following three distinct regions:

nonsphere < sphere from Θ ~15°–20° to Θ ~65°;

nonsphere >> sphere from Θ ~65° to Θ ~150°;

nonsphere << sphere from Θ ~150° to Θ = 180°.

The asymmetry parameter for the nonspherical quartz particles, as determined from the

synthetic phase function, is smaller than that for the projected-area-equivalent quartz

spheres, but not by much, which also agrees well with theory [19,20].


0.1

1

10

100

1000

Pha

se fu

nctio

nLorenz-Mie phase function

Synthetic phase function

Figure 3.4: Synthetic and Lorenz-Mie phase functions for nonspherical quartz aerosols andprojected-area-equivalent quartz spheres, respectively.

57

The differences between the Lorenz-Mie and the synthetic phase function are quite

significant: they can exceed a factor of two at side-scattering angles and are even

greater in the backscattering direction. Large differences between the experimental and

Lorenz-Mie results also occur for all other scattering matrix elements (see Fig. 3.2) and

follow the general pattern discussed by Mishchenko et al. [24]. Specifically, the degree

of linear polarization for unpolarized incident light, )()( 11 ΘΘ ab− , tends to be positive

at side-scattering angles for the nonspherical particles, but shows a broad negative region

at side-scattering angles and a narrow positive feature at Θ ~ 165º caused by the primary

rainbow for the spherical aerosols. Whereas 1)()( 12 ≡ΘΘ aa for spherically symmetric

scatterers, the )()( 12 ΘΘ aa curve for the nonspherical quartz aerosols significantly

deviates from unity and exhibits strong backscattering depolarization. Similarly,

)()()()( 1413 ΘΘΘΘ aaaa ≡ for spherically symmetric particles, whereas )()( 14 ΘΘ aa

for the nonspherical quartz aerosols tends to be significantly greater than )()( 13 ΘΘ aa for

most angles, especially at backscattering directions. Furthermore, the ratios )()( 12 ΘΘ ab

for the nonspherical and spherical quartz aerosols show significant differences at scattering

angles in the range °<<° 170120 Θ . Thus our results reinforce previous indications that

for most scattering angles, the phase function and the other elements of the scattering

matrix for nonspherical aerosols are inadequately represented by Lorenz-Mie results

computed for the same size distribution and refractive index and caution against the use

of the latter in optical characterization of nonspherical particles.

The idea of compiling a synthetic phase function using a combination of

experimental and theoretical Lorenz-Mie results appears to be attractive because of its

simplicity and may be a useful practical tool in cases when experimental data are not

available in the entire scattering angle interval from 0º to 180º. Somewhat similar

procedures were described by Hill et al. [25] and Moreno et al. [26]. We have

58

mentioned, however, that there are several issues that may make the application of this

procedure less straightforward than one would like it to be. Our current research is

focused on addressing the potential complexifying factors one-by-one.

Finally, we note that Mishchenko et al. [27] used the synthetic phase function to

analyze the potential effect of nonsphericity on the results of retrievals of mineral

tropospheric aerosols based on radiance observations from earth-orbiting satellites.

Acknowledgements

It is a pleasure to thank J. F. de Haan and W. Vassen for many fruitful discussions

and two anonymous reviewers for constructive comments. This research was supported

by the NASA Radiation Sciences Program managed by Donald Anderson.

59

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nm. J Geophys Res 2001;106:17 375–401.

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aerosols from space: past, present, and future. Bull Am Meteorol Soc 1999;80:2229–

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[18] Mishchenko MI, Dlugach JM, Yanovitskij EG, Zakharova NT. Bidirectional

reflectance of flat, optically thick particulate layers: an efficient radiative transfer

solution and applications to snow and soil surfaces. J Quant Spectrosc Radiat

Transfer 1999;63:409–32.

[19] Mishchenko MI, Travis LD, Macke A. Scattering of light by polydisperse, randomly

oriented, finite circular cylinders. Appl Opt 1996;35:4927–40.

[20] Mishchenko MI, Travis LD, Kahn RA, West RA. Modeling phase functions for


polydisperse spheroids. J Geophys Res 1997;102:16 831–47.

[21] Hovenier JW, Volten H, Muñoz O, van der Zande WJ, Waters LBFM. Laboratory

studies of scattering matrices for randomly oriented particles. Potentials problems

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[22] Mishchenko MI, Mackowski DW, Travis LD. Scattering of light by bispheres with

touching and separated components. Appl Opt 1995;34:4589–99.

[23] Jaggard DL, Hill C, Shorthill RW, Stuart D, Glantz M, Rosswog F, Taggart B,

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Environ 1981;15:2511–19.

[24] Mishchenko MI, Wiscombe WJ, Hovenier JW, Travis LD. Overview of scattering

by nonspherical particles. In: Mishchenko MI, Hovenier JW, Travis LD, editors.

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San Diego: Academic Press, 2000, p. 29–60.

62

[25] Hill SC, Hill AC, Barber PW. Light scattering by size/shape distributions of soil

particles and spheroids. Appl Opt 1984;23:1025–31.

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to compute energy fluxes in cometary nuclei. Icarus 2002;156:474-84.

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63

Chapter 4

Investigation of the effects of particle nonsphericity onaerosol retrievals from AVHRR observations1

Abstract

In this paper, we use the synthetic phase function [1] to analyze the potential effect

of particle nonsphericity on the results of retrievals of mineral tropospheric aerosols

from Advanced Very High-Resolution Radiometer (AVHRR) radiance observations.

Our results reconfirm the previously reached conclusion that the nonsphericity of dusk-

like and dry sea salt aerosols can lead to very large errors in the retrieved optical

thickness if one mistakenly applies the scattering model for spherical particles.

Keywords: Atmospheric aerosols; Nonspherical particles; Remote sensing

4.1 Introduction

The important role of tropospheric aerosols in forming the Earth’s climate is now

well recognized [2–4] and has motivated several dedicated research programs [5–7],

including the Global Aerosol Climatology Project (GACP) established in 1998 as part

of the National Aeronautics and Space Administration’s Radiation Sciences Program

and the World Climate Research Programme’s Global Energy and Water Cycle

Experiment [8]. A major component of the GACP is a retrospective analysis of the

Advanced Very High Resolution Radiometer (AVHRR) radiance data set in order to

1 Published in Journal of Quantitative Spectroscopy & Radiative Transfer, 79-80, 953-972,2003.

64

infer the long-term global distribution of aerosols, their properties, and seasonal and

interannual variations.

In recent publications [9,10], Mishchenko et al. and Geogdzhayev et al. described

an advanced aerosol retrieval algorithm based on using channel–1 and –2 AVHRR data

over the oceans and applied it to the ISCCP DX radiance dataset [11]. Specifically, the

algorithm retrieves the aerosol optical thickness τ and Ångström exponent A for each

pixel by minimizing the difference between two radiances measured in the 0.65 and

0.85µm channels at the specific illumination and observation angles determined by the

satellite orbit on the one hand and the radiances computed theoretically for a realistic

atmosphere–ocean model on the other hand. The Ångström exponent is defined as

1)(ln

)]([ln

λλλλ

=

−=d

CdA ext , (4.1)

where λ1 = 0.65µm is the nominal wavelength of the AVHRR channel 1 and Cext is the

ensemble-averaged extinction cross-section per particle. With only two pieces of data

per pixel available, one can retrieve only the two model parameters and must assign

fixed global values to the remaining parameters describing the complex atmosphere–

ocean system, thereby introducing potential biases in the aerosol product. We have

performed an extensive study of the expected accuracy of the algorithm and its

sensitivity to various a priori assumptions and used it in the development of a

preliminary global climatology of the aerosol optical thickness and size for the period

extending from July 1983 to August 1994.

It is well known that the climatically-important dust-like aerosols have

nonspherical shapes, whereas the operational GACP algorithm is based on Lorenz-Mie

computations and assumes the spherical particle shape irrespective of aerosol type. It is,

therefore, important to examine how nonsphericity can affect the results of AVHRR

aerosol retrievals.

65

4.2 Effect of particle shape

Desert dust can dominate the aerosol population over large Atlantic Ocean areas off

the north-west coast of Africa, the Persian Gulf region, and large areas of the Pacific

Ocean off the coast of China. Sea salt particles are believed to be the dominant aerosol

species at high southern latitudes. It has been demonstrated recently that particle

nonsphericity is an important factor that must be carefully addressed in optical

characterization of mineral aerosols such as dust-like and dry sea salt particles [12–15].

Previous analyses of this issue were based either on semi-empirical approximate

approaches [16,17] or on theoretical computations of the phase function for simplified

model shapes [13–15,18-21]. However, theoretical and numerical techniques are still

limited in their ability to simulate electromagnetic scattering by realistic polydispersions

of irregular particles. Therefore, laboratory measurement techniques [22,23] remain an

important source of information on scattering properties of natural nonspherical

aerosols.

Recently, Volten et al. [24,25] presented an extensive dataset which includes the

results of laboratory measurements for several types of polydisperse, randomly oriented

mineral aerosols at 441.6 and 632.8 nm wavelengths. A limitation of these

measurements is the lack of data at very small and very large scattering angles (from 0°

to 5° and from 173° to 180°), which precludes the determination of the absolute angular

dependence of the phase function )(1 Θa by using the standard normalization condition,

∫ =ΘΘΘπ

0 1 1)(sin2

1ad , (4.2)

where Θ is the scattering angle. As a consequence, Volten et al. plotted the relative

quantity )30()()(~111

oaaa Θ=Θ , rather than )(1 Θa , which limits the applicability of

their results in satellite remote sensing. However, Liu et al. [1] used the relative angular

profile of the phase function measured by Volten et al. [24,25] for a quartz particle

66

sample at 441.6 nm to construct a synthetic phase function on the entire interval

]180,0[ oo∈Θ by assuming that the forward-scattering diffraction peak is independent of

the particle shape and depends only on the distribution of surface-equivalent-sphere

radii and the wavelength, and then using the normalization condition (4.2). The quartz

phase function was selected because the refractive index of quartz is rather well known

in the visible spectral range. Furthermore, the experimental angular profile of the phase

function for the quartz sample appeared to be only weakly dependent on the wavelength

and was similar to those of the other mineral aerosol samples studied by Volten et al.

irrespective of their exact size distribution and chemical composition.

Since the synthetic phase function is available only for one average particle size

relative to the wavelength, it cannot be used in the operational two-channel algorithm in

order to retrieve simultaneously the aerosol optical thickness and size. However, it can

be used in a one-channel algorithm analogous to that used by Stowe et al. [26], wherein

the average particle size (and, thus, the phase function) is assumed to be fixed globally

and the only retrieved parameter is τ . Although this approach does not generate a

product similar to that based on the two-channel algorithm [9,10], it allows us to study,

at least semi-quantitatively, the potential effect of nonsphericity on the aerosol optical

thickness retrieved from the AVHRR data. This follows, indeed, from the theoretical

observation that the spherical–nonspherical differences in the phase function should be

very similar for the two close AVHRR channels [19].

Volten et al. [24,25] defined the equivalent-sphere radius r of a nonspherical

particle as the radius of a sphere that has a projected area equal to the average projected

area of the nonspherical particle in random orientation. The effective radius reff and

effective variance veff [27] of the quartz particle sample studied in [24,25] are 2.3 µm

and 2.4, respectively. The laboratory measurements were performed at a wavelength of

441.6 nm. Therefore, the effective radius of a phase-function-equivalent size

67

distribution at the AVHRR channel–1 wavelength 650 nm is 3.39µm, thereby

representing the coarse mode of dust-like aerosols. The extrapolation of the results

obtained at 441.6 nm to 650 nm is based on the assumption that the refractive index of

quartz remains nearly constant in this spectral interval, which is indeed the case.

Fig. 4.1 depicts the synthetic phase function as well as the phase function for

projected-area-equivalent quartz spheres calculated using the Lorenz-Mie code

described in [28] and available on-line at http://www.giss.nasa.gov/~crmim. In close

agreement with previous results of Jaggard al. [29] for Raft River soil dust and the

results of theoretical studies of light scattering by polydisperse, randomly oriented


0.1

1

10

100

1000

Pha

se fu

nctio

n

Lorenz-Mie phase function

Synthetic phase function

Figure 4.1: Synthetic and Lorenz-Mie phase functions for nonspherical quartz aerosols andprojected-area-equivalent quartz spheres, respectively, used in the one-channel retrievalalgorithm (see text).

68

spheroids and circular cylinders [19,30], Fig. 4.1 exhibits the following three

conspicuous regions:

nonsphere < sphere from Θ ~ 15°–20° to Θ ~ 65°,

nonsphere >> sphere from Θ ~ 65° to Θ ~ 150°, (4.3)

nonsphere << sphere from Θ ~ 150° to Θ = 180°.

The differences between the Lorenz-Mie and the synthetic phase function are quite

significant at side-scattering angles, where they can exceed a factor of two, and are even

greater at backscattering angles.

We have used both phase functions in the one-channel retrieval algorithm and

applied the latter to AVHRR data collected in 1987 over a region often dominated by

Sahara dust aerosols and extending from Central Meridian to 60°W and from 7°S to

18°Ν. We then calculated the monthly average of the ratio of the aerosol optical

thickness τN retrieved with the phase function of the nonspherical quartz particles to the

optical thickness τS retrieved with the phase function computed for the projected-area-

equivalent spherical quartz aerosols at λ = 0.65 µm. This ratio is plotted in Fig. 4.2 as a

function of longitude for 1°-wide horizontal belts along with the corresponding monthly

averages of the scattering angle.

Fig. 4.2 is an excellent illustration of the relationships summarized by Eq. (4.3) and

shows that τN/τS > 1 for Θ > 150° and τN/τS < 1 for Θ < 150°. Owing to the specific

NOAA-9 spacecraft orbit, the scattering angle for this area is, for the most part, greater

than 150° during the four months studied. As a consequence, the algorithm based on the

Lorenz-Mie phase function tends to generate significantly smaller optical thicknesses

than that based on the phase function representative of nonspherical aerosols. The ratio

τN/τS reaches values exceeding 3.5 in April, but stays closer to unity in July.

69

Accordingly, the monthly averages of this ratio over the entire area studied are 1.545 for

January, 1.975 for April, 1.053 for July, and 1.974 for October.

0

1

2

3

4

τ(no

nsph

eric

al)/

τ(sp

heric

al) Jan 87

0

1

2

3

4

Apr 87

120o

150o

180o

Sca

tterin

g an

gle

120o

150o

180o

0

1

2

3

4

τ(no

nsph

eric

al)/

τ(sp

heric

al) 7oS−6oS

2oS−1oS

3oN−4oN

8oN−9oN

13oN−14oN

17oN−18oN

Jul 87

0

1

2

3

4

Oct 87

60oW 50oW 40oW 30oW 20oW 10oW 0o120o

150o

180o

Sca

tterin

g an

gle

Longitude60o 50oW 40oW 30oW 20oW 10oW 0o

120o

150o

180o

Longitude

Figure 4.2: Monthly averages of the ratio τN/τS and the respective scattering angle versuslongitude.

70

Our results obviously reinforce the previously reached conclusion [18] that the

nonsphericity of mineral particles can have a profound effect on the reflected intensity

and must be explicitly accounted for in aerosol retrievals based on satellite radiance

data. Unfortunately, the AVHRR data by themselves provide no means of identifying

particle type and shape. This is also true for any instrument taking reflectance data at

only one scattering geometry per pixel, such as the MODerate resolution Imaging

Spectrometer (MODIS) [31,32]. Although small values of the Ångström exponent can

be indicative of the presence of large mineral particles, this test cannot be expected to

distinguish between dry (nonspherical) and wet (spherical) sea salt particles. It thus

appears to be difficult, if not impossible, to develop a simple and reliable procedure

which improves the AVHRR retrieval algorithm by introducing the necessary

corrections when the particles happen to be nonspherical. However, this may be feasible

with multi-angle instruments such as the Multiangle Imaging Spectro-Radiometer

(MISR) [13,33], the POLarization and Directionality of Earth Reflectances (POLDER)

instrument [34,35], and the Earth Observing Scanning Photopolarimeter [36], especially

when polarization of the reflected light is also measured.

4.3 Conclusions

To summarize, we conclude the use of the phase function typical of irregular

mineral aerosols in the retrieval algorithm based on channel–1 AVHRR radiances

indicates that the nonsphericity of dust-like and dry sea salt aerosols can lead to very

large errors in the retrieved optical thickness if one mistakenly applies look-up tables

based on Lorenz-Mie computations. The errors change with season and geographical

location and cannot be corrected using AVHRR data alone since the latter do not

provide a reliable indication of aerosol type.

71

Acknowledgements

This research was supported by the NASA Radiation Sciences Program managed

by Donald Anderson.

72

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77

Chapter 5

Global validation of the operational two-channel AVHRR retrieval product over the ocean1

Abstract

In this chapter we present validation results for the aerosol optical thickness τSAT,

the Ångström exponent A, and the single-scattering albedo ϖ retrievals. These retrievals

are part of the global long-term aerosol climatology derived by applying a two-channel

algorithm to Advanced Very High Resolution Radiometer (AVHRR) data. The satellite

retrieved optical thicknesses are compared with ship-borne sun-photometer results, τSP.

The comparison of the spatial and temporal statistics of the satellite retrievals and the

ship measurements shows a strong correlation. A systematic overestimation in τSAT by

about 11% relative to τSP for average aerosol loadings was found for the initial satellite

dataset. Increasing the diffuse component of the surface reflectance from 0.002 to 0.004

produces a better match, with the ensemble average at 0.55 µm differing by only about

3.6% from the ship truth and having a small offset of 0.03. Comparisons of single-

scattering albedo and Ångström exponent values retrieved from the AVHRR data and

those measured in situ at Sable Island indicate that the currently adopted value 0.003

can be a reasonable choice for the imaginary part of the aerosol refractive index in the

global satellite retrievals.

1 Part of this work has been published in Journal of Quantitative Spectroscopy & Radiative Transfer, 79-80, 953-972, 2003; the rest is in preparation for submission.

78

5.1 Introduction

The Advanced Very High Resolution (AVHRR) radiance dataset with its two-

decade record and near global coverage is a unique potential source of information

about atmospheric aerosols. Mishchenko et al. (1999) and Geogdzhayev et al. (2002)

developed an advanced retrieval algorithm that utilizes AVHRR channels 1 and 2 to

retrieve aerosol optical thickness and Ångström exponent over the ocean and conducted

comprehensive sensitivity studies. By using the algorithm, a long-term climatology has

been created, which combines the data from several AVHRR instruments and currently

spans the period from 1983 to 2001.

Because of the ill-posed character of the inverse scattering problem, various a priori

assumptions must be made in order to retrieve aerosol properties from remotely sensed

data. Any variability in the assumed parameters leads to uncertainty in the satellite

retrievals. Therefore validation of the retrieved results is critical and has been an

important direction in our research. This chapter has two major objectives. The first one

is to validate the satellite-retrieved aerosol optical thickness. This task poses significant

problems since sun-photometer aerosol measurements over ocean are scarce. A number

of publications describe inter-comparisons of various satellite, ground-based and model

aerosol data. Kinne et al. (2001) and Penner et al. (2002) performed a comparison of

monthly statistics of aerosol satellite retrievals and model results with the AERONET-

derived (Holben et al. 1998) statistics. Kinne et al. found that the aerosol optical

thickness derived using the original algorithm described by Mishchenko et al. (1999)

for the period of NOAA-9 observations are systematically higher compared to the

averages from several coastal AERONET sites. Penner et al. used a more recent aerosol

product and found a significantly better agreement. A study by Myhre et al. (2002) uses

the most recent two-channel AVHRR retrievals and shows a much better agreement

than the paper by Kinne et al.

79

The discrepancies between the ground-based measurements and the satellite

retrievals may be associated with space and time co-location, different approaches to

cloud screening, sensor calibration error, improper assumption about ocean surface

reflectance, inconsistency between the aerosol microphysical model (such as aerosol

size distribution and refractive index) used in the retrieval algorithm and that in the real

world. In addition, higher surface albedos in the coastal regions compared to the open

ocean values assumed in the retrieval algorithm and desert particle nonsphericity may

also have contributed to the discrepancies.

In a recent paper, Smirnov et al. (2002) summarized aerosol optical thickness τ

measurements in maritime and coastal areas. The comprehensive survey of ship-borne

measurements published over the last 30 years is a great asset for our validation since

the ship data cover the same period of time as many of the AVHRR retrievals. The data

have been collected over open ocean areas, and thus we do not have to consider the

possible effects of coastline and shallow water on the satellite retrievals (e.g., Zhao et al

2003). This will be the subject of the following section.

Second, the inherent limitations of a retrieval algorithm based on utilizing only two

pieces of data per pixel (Mishchenko et al. 1999 and Geogdzhayev et al. 2002) force

one to adopt a spatially and temporally fixed value of the imaginary part of the aerosol

refractive index. The current version of the algorithm (Geogdzhayev et al. 2002) uses

the value 0.003, which is smaller than the value 0.005 used in the initial version

(Mishchenko et al. 1999), the reason being that this decrease may help to achieve a

better balance between the nonabsorbing sea salt aerosols and the absorbing

anthropogenic and dust aerosols on a global scale. Although the effect of this change on

the retrieved optical thickness and Ångström exponent was found to be relatively small,

one can expect a more significant effect on the retrieved single-scattering albedo. The

latter is not a formal operational product, but follows implicitly from the retrieved

80

Ångström exponent and the assumed shape of the aerosol size distribution and the real

and imaginary parts of the aerosol refractive index. The availability of extensive in situ

measurements of the single-scattering albedo at Sable Island as reported by Delene and

Ogren (2002) enable us to examine the accuracy of our choice of the imaginary part of

the refractive index, at least in the Atlantic Ocean area adjacent to that location. This

will be done in Section 5.3.

5.2 Validation of satellite aerosol optical thickness retrievals

5.2.1 Methodology

The space-time collocation between satellite and sun photometer observation is

an important part of the aerosol validation process (Ignatov et al. 1995; Zhao et al.

2002). Many validations performed for spaceborne and airborne aerosol retrievals can

be found in the literature (e.g., Ignatov et al. 1995; Stowe et al. 1997; Nakajima and

Higurashi 1997; Tanŕe et al. 1997; Goloub et al. 1999; Zhao et al. 2002; Remer et al.

2002; Ichoku et al. 2002), each with different validation concepts and procedures. Since

a two-channel algorithm can retrieve only two aerosol parameters and must rely on

globally fixed values of all other model parameters, and because the retrieval accuracy

can be plagued by factors such as imperfect cloud screening and calibration

uncertainties, it appears more appropriate to talk about the “calibration” of the

algorithm in terms of minimizing the difference between the actual and the retrieved

global and regional long-term averages of the aerosol properties.

Considering that ship aerosol data are relatively scarce, that each research cruise

did not last longer than a few months, and that the route of the expedition varied, it is

not realistic to perform a monthly statistics comparison. We can however calculate the

aerosol statistics over a certain geographical location and within a certain range of time

81

provided that there are space-time collocated ship measurements. In our validation, we

take into account all the satellite retrieved data points over each location considered.

5.2.2 Ship data sets

Judging from a recent review paper (Smirnov et al., 2002), there is a total of 77

known published results of aerosol optical thickness measurements in maritime and

coastal areas from 1967 to 2001. Not all the data summarized by Smirnov et al. can be

used to validate the results of the satellite observations. First, 33 records were taken

before July 1983 when our satellite climatology begins. Even for those aerosol data

collected after July 1983, still sometimes measurement accuracy was unknown

(Smirnov et al. 2002). Table 5.1 summarizes the ship measurements used in this study.

The instruments, the method, and the errors of aerosol optical thickness determination

were described in the earlier papers (c.f. Smirnov et al. 1995; Kabanov and Sakerin

1997; Moulin et al. 1997; Smirnov et al. 2000; Sakerin and Kabanov 2002 etc.). It was

estimated that the errors in these measured aerosol optical thickness were not exceeding

0.02 in the visible range compared to the 0.03-0.05 error of reconstructing aerosol

optical thickness from the satellite (Rao et al. 1989; Ignatov et al. 1995; Tanѓe et al.

1997). Thus the accuracy of the sun photometer optical thickness is accurate enough to

use as a ground truth standard for validation of our retrieval product.

5.2.3 Primary validation results

Results of the comparison of the aerosol optical thickness at wavelength λ = 0.55

µm retrieved from the AVHRR data τSAT and ship-borne sun photometer measured τSP

for 58 aerosol statistics are presented in Figure 5.1. Each data point is numbered

according to the corresponding dataset in Table 5.1. The figure indeed shows the

aerosol optical thickness spatial distribution pattern described by Smirnov et al. (2002).

The atmosphere over the Pacific Ocean is more transparent compared to that of the

82

Table 5:1: Ship measurements of aerosol optical thickness in maritime areas used in this study

Reference Datea Area τ ± στb N/H/Dc

Volgin et al. (1988) Mediterranean Sea 1. 08/13/86-08/28/86 33N-40N, 21E-27E 0.20 ± 0.07 –/25/11 2. 09/06/86-09/15/86 34N-40N, 12E-29E 0.17 ± 0.05 –/21/9 Pacific Ocean 3. 11/01/85-11/04/85 10N-20N, 145E-158E 0.05 ± 0.02 –/7/4 4. 11/05/85-11/13/85 8S-9N, 159E-175E 0.08 ± 0.02 –/5/4 5. 11/16/85-12/01/85 21S-13S, 166W-172E 0.06 ± 0.01 –/24/15 6. 12/24/85-12/29/85 10N-14N, 124E-140E 0.07 ± 0.01 –/6/4 Shifrin et al. (1989) Indian Ocean 7. 11/17/83-11/18/83 11.6N-12.4N, 45.8E-53.8E 0.14 ± 0.04 –/2/2 Sakerin et al. (1991) & Korotaev et al. (1993) Atlantic Ocean 8. 09/01/89-09/10/89 36.27N-59.45N, 9.77W-2.85E 0.20 ± 0.13 29/–/6 9. 09/22/89-10/03/89 33.34N-41.96N, 68.96W-48.60W 0.08 ± 0.07 –/–/7 10. 10/04/89-10/11/89 17.02N-28.24N, 68.81W-43.32W 0.08 ± 0.03 –/–/8 11. 10/12/89-10/26/89 6.23N-15.19N, 38.03W-16.94W 0.31 ± 0.19 –/–/9 12. 11/17/89-12/04/89 2.02N-16.42N, 21.57W-17.01W 0.30 ± 0.10 82/–/14 13. 12/05/89-12/14/89 20.96N-31.28N, 19.40W-12.37W 0.06 ± 0.03 –/–/7 Mediterranean Sea 14. 12/15/89-12/20/89 35.18N-40.22N, 6.85W-26.56E 0.07 ± 0.05 –/–/6 Sakerin et al. (1993) Atlantic Ocean 15. 07/04/91-08/03/91 24.99N-32.97N, 30.38W-16.92W 0.24 ± 0.17 125/–/2816. 08/04/91-08/09/91 33.36N-39.76N, 64.33W-34.39W 0.14 ± 0.03 –/–/6 17. 08/18/91-09/08/91 38.28N-40.30N, 68.93W-61.24W 0.23 ± 0.27 –/–/20 18. 09/19/91-09/26/91 38.32N-41.02N, 70.22W-16.30W 0.13 ± 0.08 –/–/6 19. 09/09/91-09/18/91 36.76N-39.29N, 76.55W-73.10W 0.28 ± 0.20 –/–/9 Mediterranean Sea 20. 09/29/91-09/30/91 37.23N-37.25N, 5.75E-10.48E 0.38 –/–/2 Atlantic Ocean 21. 05/01/94-05/22/94 22.82N-28.14N, 16.94W-15.21W 0.18 ± 0.16 –/–/19 Villevalde et al. (1994) Pacific Ocean 22. 12/17/88-12/27/88 39.4N-40.0N, 170.0E-170.0E 0.13 ± 0.0 –/2/1 23. 12/30/88-12/27/88 25.0N-30.0N, 154.7E-180.0E 0.094 ± 0.031 –/8/6

83

Table 5.1 (continued)

Reference Date Area τ ± στ N/H/D

24. 01/13/89-01/18/89 10.8N-22.4N, 133.8E-156.2E 0.136 ± 0.037 –/12/6 25. 01/23/89-02/03/89 1.6S-18.4N, 174.9E-180.0E 0.147 ± 0.044 –/15/9 26. 02/11/89-02/21/89 40.0S-38.5S, 157.6E-179.9E 0.127 ± 0.015 –/3/3 Indian Ocean 27. 3/13/1989-03/16/89 23.0S-9.1S, 90.0E-90.0E 0.075 ± 0.021 –/2/2 Sakerin et al. (1995) Atlantic Ocean 28. 03/01/95-03/07/95 3.70N-14.70N, 20.47W-13.09W 0.41 ± 0.10 –/–/6 29. 03/08/95-04/04/95 1.65S-0.29N, 10.92W-9.64W 0.14 ± 0.08 –/–/19 30. 04/09/95-04/13/95 20.53N-36.40N, 17.90W-12.46W 0.27 ± 0.11 –/–/4 31. 04/14/95-04/21/95 40.21N-50.16N, 11.07W-1.23W 0.13 ± 0.07 –/–/7 Smirnov et al. (1995a) Mediterranean Sea 32. 12/14/89-12/21/89 37N-40N, 1W-13E 0.04 ± 0.02 –/4/3 33. 01/25/90-01/27/90 36N-38N, 3W-4E 0.06 ± 0.03 –/4/3 34. 08/25/91-08/30/91 36N-38N, 2E-25E 0.23 ± 0.12 –/6/4 Black Sea 35. 08/19/91-08/24/91 41N-44N, 28E-38E 0.33 ± 0.06 –/6/5 Atlantic Ocean 36. 09/02/91-09/23/91 37N-48N, 64W-24W 0.14 ± 0.07 –/8/8 37. 12/29/89-01/19/90 23N-27N, 28W-18W 0.07 ± 0.03 –/20/12 38. 10/03/91-10/18/91 21N-28N, 60W-20W 0.24 ± 0.04 –/20/12 39. 01/21/90-01/24/90 28N-35N, 15W-9W 0.08 ± 0.02 –/4/3 Gibraltar Area 40. 10/26/91-10/27/91 35N-36N, 13W-9W 0.21 ± 0.05 –/3/2 Smirnov et al. (1995b) Baltic Sea 41. 05/16/84-05/18/84 56.1N-56.1N, 11.8E-19.1E 0.461 ± 0.006 –/2/2 Atlantic Ocean 42. 05/20/84-06/06/84 60.5N-65.0N, 4.8W-2.7W 0.200 ± 0.078 –/4/4 Baltic Sea 43. 07/06/84-07/07/84 59.0N-59.3N, 21.1E-23.5E 0.087 ± 0.008 –/2/2 Atlantic Ocean 44. 05/23/88-05/26/88 62.6N-64.0N, 3.3W-4.7E 0.155 ± 0.040 –/5/3 45. 06/19/88-07/03/88 67.1N-68.8N, 2.0W-0.4W 0.110 ± 0.071 –/2/2 46. 05/14/89-05/26/89 58.0N-67.3N, 6.2W-7.0E 0.098 ± 0.017 –/6/5 Kabanov et al. (1997)

84

Table 5.1 continued

Reference Date Area τ ± στ N/H/D

47. 08/25/96-08/26/96 44.03N-44.03N, 63.55W-63.55W 0.13 ± 0.11 –/–/2 48. 08/27/96-09/13/96 29.15N-41.24N, 58.24W-21.44W 0.08 ± 0.04 –/–/18 49. 09/14/96-09/15/96 44.16N-46.70N, 15.61W-10.32W 0.09 ± 0.02 –/–/2 English Channel 50. 09/16/96-09/17/97 49.55N-51.83N, 3.70W-2.76E 0.100 ± 0.021 –/–/3 Moorthy et al. (1997) Indian Ocean 51. 01/07/96-01/22/96 5S-8.83N, 60E-69E 0.186 ± 0.10d –/15/13 Moulin et al. (1997) Atlantic Ocean 52. 09/14/91-09/29/91 15.50N-27.70N, 31.15W-17.90W 0.46 ± 0.31 –/–/13 Kuśmierczyk-Michulec (1999) Baltic Sea 53. 07/02/97-07/15/97 54N-58.5N, 11E-21E 0.205 ± 0.094 145/–/12 Smirnov et al. (2000) Atlantic Ocean 54. 07/08/96-07/08/96 34.93N-37.30N, 69.95W-67.34W 0.29 ± 0.07 24/–/1 55. 07/18/96-07/18/96 32.37N-32.78N, 64.87W-64.58W 0.06 ± 0.01 8/–/1 56. 07/26/96-07/26/96 36.74N-38.17N, 70.89W-68.48W 0.16 ± 0.04 12/–/1 57. 07/27/96-07/27/96 35.82N-38.24N, 71.09W-68.30W 0.25 ± 0.13 28/–/1 58. 07/08/96-07/27/96 32.37N-40.76N, 74.01W-64.57W 0.19 ± 0.12 130/–/7 a Read xx/xx/xx as mm/dd/yy. b τ and στ are the mean value and the standard deviation of aerosol optical thickness at a wavelength 0.55 µm. c N: number of sets of data; H: number of half day averages; D: number of observation days. d The measurements were taken at a wavelength of 0.50 µm.

Atlantic Ocean, inland seas and coastal zones. There is generally a good agreement

between the satellite retrievals and the ship data. One can see that over the Pacific

Ocean the retrieved τSAT values are higher relative to the ship-measured τSP. Aerosol

optical thickness over the Atlantic Ocean shows large variability, where the systematic

bias of τSAT relative to τSP , is somewhat less obvious compared to that over the Pacific

85

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Measured τ(0.55 µm)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5A

VH

RR

ret

rieve

d τ(

0.55

µm

)

1

2

3

4

5

6 7 8

9

10

11

12

13

14

15

16

17 18

19

20

21

28

29

30

31

32

33

34

35

36

37

38

39

40

47

48

49

50

51

52

53

54

55

56

57

58

22

23

24

25

26

27

41

42

43

44

45

46

Mediterranean Sea

Pacific Ocean

Indian Ocean

Atlantic Ocean

Black Sea

Gibraltar Area

English Channel

Baltic Sea

Figure 5.1: AVHRR retrieved aerosol optical thickness τSAT versus ship measurements τSP at λ = 0.55 µm. Different sea areas are represented by different colors. The number near each data point corresponds to the aerosol data shown in Table 5.1.

86

Ocean although again we see a slight overestimation in τSAT. Since there is very little

aerosol data for the other areas except perhaps Mediterranean Sea, the comparison

results are less conclusive. Performing a linear regression analysis yields the following

relation between τSAT and τSP: τSAT = 0.047+0.836 τSP, with a high correlation coefficient

R of 0.90 and a standard error σ of 0.04.

However the ensemble average <τSAT > is 0.188, which is 11.2% higher than <τSP >.

This is more than the 3%-5% accuracy estimated in previous studies (Rao et al. 1989;

Ignatov et al. 1995; Tanŕe et al. 1997). The systematic errors of the retrieval algorithm

for low (τSP = 0), average (τSP = <τSAT >), and high (τSP = 1) aerosol loadings are found to

be 0.047, 0.019, and –0.117 respectively. This is comparable to the values reported by

Zhao et al. (2003) after the cloud and wind effects are minimized in their retrievals.

These values tell us that τSAT tends to be overestimated in low τ and underestimated in

high aerosol optical thickness.

The non-unity slope in the regression may be associated with a regional bias:

incorrect assumptions in the aerosol model of the retrieval algorithm for the sites of the

ship measurements. Due to the high aerosol inhomogeniety, this problem cannot be

easily solved by current retrieval algorithm which uses a global uniform aerosol model.

A possible improvement is to adopt regional aerosol models which take into account,

e.g., the stronger absorptivity of soot and dust-like particles (e.g., Fuller et al. 1999) and

the nonsphericity of mineral aerosols (e.g., Liou and Takano 1994; Mishchenko et al.

1997). This is a great challenge and will be our future research subject. A nonzero

intercept may be associated with sensor calibration error, improper assumption of ocean

surface reflection, and subpixel cloud contamination (Zhao et al. 2002).

In order to improve the agreement between the satellite retrievals and the ship data

we can try to reduce the positive intercept. An overestimation of τSAT at low τ can result

from either an underestimation of ocean surface reflection and/or an error in calibration

87

of satellite radiances, namely an error in the offset (deep space count) value. In order to

distinguish between the two possible causes we repeated the comparisons using data

from a single AVHRR instrument (NOAA-7, 9, 11, 14) each with its own calibrations

and the results are shown in Figure 5.2. No obvious satellite-dependent discrepancy was

found. We are thus inclined to consider the diffuse subsurface reflectance as a cause of

the overestimation.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Measured τ(0.55 µm)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

AV

HR

R r

etrie

ved

τ(0.

55 µ

m)

NOAA 7

NOAA 9

NOAA 11

NOAA 14

Figure 5.2: τSAT versus τSP for different AVHRR instrument (NOAA-7, 9, 11, 14).

88

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Measured τ(0.55 µm)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

AV

HR

R r

etrie

ved

τ(0.

55 µ

m)

S=0.002

S=0.004

S=0.005

y=0.047+0.836xR=0.899 σ=0.042

y=0.032+0.844xR=0.899 σ=0.043

y=0.021+0.850xR=0.895 σ=0.044

Figure 5.3: Comparison of τSAT and τSP at λ = 0.55 µm for three increasing values of diffuse component of surface reflection S = 0.002, 0.004, 0.005 and the corresponding linear regression lines. The dotted line depicts a 1:1 relationship.

Figure 5.3 shows τSAT versus τSP at λ = 0.55 µm and the corresponding linear

regression statistics using three increasing values of diffuse component of surface

reflectance S. Dotted line represents a 1:1 relationship. The detailed statistics are

summarized in table 5.2. Note our current two-channel retrieval algorithm uses the

value of S equals to 0.002. Although choosing S = 0.005 tends to minimize the offset,

the satellite retrievals are extremely sensitive to the selection of the surface reflectance

89

Table 5.2. Statistics of comparison of τSAT and τSP for three increasing values of diffuse surface reflection S = 0.002, 0.004, 0.005.

Intercept Slope Mean Systematic Errors (∆τ) Random Error S

a b R

τSAT τSP Minimum Mean Maximum σ 0.002 0.047 0.836 0.899 0.188 0.169 0.047 0.019 -0.117 0.042 0.004 0.032 0.844 0.899 0.175 0.169 0.032 0.006 -0.124 0.043 0.005 0.021 0.850 0.895 0.165 0.169 0.021 -0.004 -0.129 0.044

Systematic error is defined as ∆τ = τSAT – τSP (or ∆τ = a + b τSP – τSP), for minimum, mean and maximum ∆τ, τSP = 0, mean of τSP and 1 correspondingly. R is correlation coefficient between τSAT and τSP. Parameters a, b, and σ are intercept, slope, and standard deviation, respectively, of the linear regression line.

model in low τ. One cannot fail to notice that one retrieval falls to zero if S = 0.005 is

adopted in the retrieval algorithm and an underestimation of τSAT relative to τSP. Overall,

S = 0.004 is a good choice in terms of minimizing the difference between the actual and

the retrieved aerosol optical thickness, with ensemble average of τSAT differs that of τSP

only by 3.6%, within the 0.03-0.05 range estimated by previous papers (Rao et al. 1989;

Ignatov et al. 1995; Tanŕe et al. 1997). Linear regression of τSAT versus τSP produces a

good match τSAT = 0.032+0.844 τSP with a high correlation coefficient of 0.9 and a small

standard error of 0.04. This is encouraging considering that AVHRR was not specially

designed for aerosol retrievals and the sensor is less advanced and well calibrated

compared to that of the MODerate Resolution Imaging Spectrometer (MODIS) and the

Multiangle Imaging SpectroRadiometer (MISR) and considering that all the available

satellite retrievals were included in the comparisons.

90

5.3 Validation of the aerosol single-scattering albedo

Although the aerosol single-scattering albedo ϖ is not included explicitly in the

operational product generated by the two-channel retrieval algorithm (Mishchenko et al.

1999 and Geogdzhayev et al. 2002), it can be determined from the implicit relationship

between ϖ and the Ångström exponent provided that the aerosol refractive index m is

fixed. Fig. 5.4 shows this relationship computed using the Lorenz-Mie theory for Re(m)

= 1.5 and four increasing values of Im(m). As in (Mishchenko et al. 1999 and

Geogdzhayev et al. 2002), we use the simple power law distribution of aerosol radii

>

≤<

≤

=−

,,0

,,)(

,),(

),(

2

211

1

rr

rrrrrC

rrC

rnα

α

α

α (5.1)

with r1 = 0.1 µm, r2 = 10 µm, and ]5,5.2[∈α , where the normalization constant C(α) is

chosen such that

∫∞

=0

.1),( αrndr (5.2)

Obviously, the ϖ(A) dependence is always monotonic, and ϖ always decreases with

particle size. Furthermore, ϖ always decreases with increasing Im(m ).

The current version of the two-channel algorithm uses the value Im(m) = 0.003

(Geogdzhayev et al. 2002). Fig. 5.5 illustrates the single-scattering albedo for July 1999

(lower panel) determined from the retrieved constrained Ångström exponent (upper

panel). The latter means that only the Ångström exponent values falling in the interval

(0.05,1.72) are retained (Geogdzhayev et al. 2002). It is seen that ϖ varies from 0.86 to

0.98 and is indeed smaller in areas dominated by larger particles. Unfortunately, this

implicit relationship can be unphysical in that it does not allow large but weakly

absorbing particles (e.g., sea salt aerosols) to have greater single-scattering albedos than

91

0 0.5 1 1.5 2Ångström exponent

0.7

0.8

0.9

1

Sin

gle−

scat

terin

g al

bedo

at λ

= 0

.55

µm

m = 1.5 + 0.001i

m = 1.5 + 0.002i

m = 1.5 + 0.003i

m = 1.5 + 0.005i

Figure 5.4: Aerosol single-scattering albedo versus Ångström exponent for Re(m) = 1.5 and four increasing values of Im(m).

smaller but strongly absorbing particles (e.g., soot aerosols). However, the choice of a

constant Im(m) can still be optimized in such a way that it provides a realistic global

average value of the single-scattering albedo. Although the latter is not known at

present, the extensive in situ measurements of ϖ at Sable Island (43.933°N, 60.007°W)

reported by Delene and Ogren (2002) can be used to validate our choice of Im(m), at

least for that region of the Atlantic Ocean.

The measurements by Delene and Ogren cover the period from 23 November 1994

to 15 April 2000 and are summarized in Fig. 5.6. For comparison, Fig. 5.6 also depicts

the results of AVHRR retrievals averaged over a 100×100 km square centered at Sable

Island for the period from November 1994 to December 1999. In this study, we have

92

90oS

60oS

30oS

EQ

30oN

60oN

90oN

DL 120oW 60oW CM 60oE 120oE DL

ÅNGSTRÖM EXPONENT(a)

0

0.5

1

1.5

2

90oS

60oS

30oS

EQ

30oN

60oN

90oN

DL 120oW 60oW CM 60oE 120oE DL

SINGLE−SCATTERING ALBEDO(b)

0.86

0.89

0.92

0.95

0.98

Figure 5.5: Monthly averages of the Ångström exponent and single-scattering albedo for July 1999 derived from two-channel AVHRR data assuming a fixed aerosol refractive index m = 1.5 + 0.003i.

93

JAN MAR MAY JUL SEP NOV AVER Month of year

0.85

0.9

0.95

1

Sin

gle−

scat

terin

g al

bedo

at λ

= 0

.55

µmIm(m)=0.001 Im(m)=0.002 Im(m)=0.003 Im(m)=0.005

Figure 5.6: The annual cycle of the aerosol single-scattering albedo measured in situ at Sable Island (Delene and Ogren 2002). The whiskers denote the 5 and 95 percentiles, the bottom and top of the box denote the 25 and 75 percentiles, and the horizontal line within the box denotes the median value. The statistics are based on the hourly averaged data for all valid measurements obtained during the period 11/23/1994–04/15/2000. The horizontal axis shows the month of year, with the last tick mark representing the statistics for the entire study period. The circle, triangle, plus, and diamond signs represent the average monthly ϖ values retrieved from channel–1 and –2 AVHRR data during the period 11/1994–12/1999 assuming that the imaginary part of the aerosol refractive index is fixed at 0.001, 0.002, 0.003, and 0.005, respectively. The AVHRR results for March, April, and December were not computed because of the insufficient number of cloud-free pixels during these months.

94

Monthly average τ for 94/11−99/12


0

0.2

0.4

0.6A

eros

ol o

ptic

al th

ickn

ess

at λ

= 0

.55

µm

Im(m)=0.001 Im(m)=0.002 Im(m)=0.003 Im(m)=0.005

Figure 5.7: The annual cycle of the aerosol optical thickness retrieved from channel–1 and –2 AVHRR data over Sable Island during the period November 1994–December 1999 assuming that the imaginary part of the aerosol refractive index is fixed at 0.001, 0.002, 0.003, and 0.005. The horizontal axis shows the month of year, with the last tick mark representing the average results for the entire study period. The AVHRR results for December were not computed because of the insufficient number of cloud-free pixels.

95

Constrained monthly average Ångström exponent for 94/11−99/12


0

0.3

0.6

0.9

1.2

1.5Å

ngst

röm

exp

onen

t

Im(m)=0.001 Im(m)=0.002 Im(m)=0.003 Im(m)=0.005

Figure 5.8: As in Fig. 5.7, but for the constrained Ångström exponent. The AVHRR results for March, April, and December were not computed because of the insufficient number of cloud-free pixels during these months.

compared our AVHRR-retrieved single-scattering albedo ϖ with the ground-based

results and investigate its seasonal variability using several discrete values of the

imaginary part of the aerosol refractive index Im( m ) in order to accommodate the

strong variability of aerosol absorption. It is seen that the in situ ϖ results may be best

reproduced by an Im(m) value between 0.002 and 0.003. Figs. 5.7 and 5.8 show a rather

weak dependence of the retrieved aerosol optical thickness and Ångström exponent on

Im(m) for Im(m) in the range [0.002, 0.003] and suggests that the current choice

96

Im(m)=0.003 is quite consistent, at least for locations in the vicinity of Sable Island.

This conclusion is only reinforced by the inspection of Table 5.3, which suggests that an

Im(m) value close to 0.0025 is needed to reproduce the long-term mean in situ value of

the single-scattering albedo and a value close to 0.0035 could reproduce the long-term

mean in situ value of the Ångström exponent (Delene and Ogren 2002).

Table 5.3: Mean values of aerosol parameters retrieved from AVHRR data and measured in situ at Sable Island.

Im(m) ϖ τ A Retrieved values for 11/1994-12/1999 0.001 0.978 0.160 0.710 0.002 0.962 0.164 0.735 0.003 0.949 0.172 0.758 0.005 0.928 0.184 0.786 In situ values for 11/1994-04/2000 (Delene and Ogren 2002) 0.956 0.770

5.4 Discussion and conclusions

We have used ship-borne aerosol data with known accuracy estimates to validate

our global two-channel AVHRR satellite retrievals. The results of comparison statistics

for three increasing values of diffuse surface reflectance are summarized in Table 5.2.

Adjusting the diffuse component of surface reflection S from 0.002 value in the

operational algorithm to 0.004 reduces the positive offset of 0.047 to 0.032. The

positive bias in AVHRR retrieved τSAT compared to ship τSP at mean aerosol optical

thickness was reduced from 0.019 (11.2 % relative to τSP) to 0.006 (3.6% relative to τSP).

We also used AERONET sun photometer observations to evaluate our satellite

retrievals and obtained similar results to the study by Zhao et al. (2003)

97

The small systematic error at low τ and the random error may be attributed to

calibration errors, radiometric noise, and measurement instability. These sensors-related

error sources are anticipated to have less effect on the aerosol retrievals from more

advanced instruments such as MODIS and MISR. Our further research will focus on the

comparisons of AVHRR-derived aerosol properties over oceans with these new satellite

data products.

The proportional systematic error at large τ is mainly the result of improper

assumptions on the aerosol microphysical model in the retrieval algorithm. For

example, Zhao et al. (2002) have showed that the proportional systematic error at large

aerosol optical thickness can be reduced by increasing the imaginary part of the aerosol

refractive index Im(m). However one can argue that good agreement with a limited

ground-based or in situ dataset does not guarantee the global applicability of the

satellite-retrieved product. Our comparison indicated that the currently adopted value

Im(m)=0.003 can be a reasonable choice for the imaginary part of the aerosol refractive

index in the global AVHRR retrievals by comparing single-scattering albedo and

Ångström exponent values generated by the operational two-channel algorithm and

those measure in situ at Sable Island (Delene and Ogren 2002).

98

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102

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103

Chapter 6

Constraints on PSC particle microphysics derived fromlidar observations1

Li Liua, Michael I. Mishchenkob

aDepartment of Earth and Environmental Sciences, Columbia University, and NASA GISS, 2880Broadway, New York, NY 10025, USA

bGoddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USA

Abstract

Based on extensive T-matrix computations of light scattering by polydispersions of

randomly oriented, rotationally symmetric nonspherical particles, we analyze existing

lidar observations of polar stratospheric clouds (PSCs) and derive several constraints

on PSC particle miscrophysical properties. We show that sharp-edged nonspherical

particles (finite circular cylinders) exhibit less variability of lidar backscattering

characteristics with particle size and aspect ratio than particles with smooth surfaces

(spheroids). For PSC particles significantly smaller than the wavelength, the

backscatter color index α and the depolarization color index β are essentially shape-

independent. Observations for type Ia PSCs can be reproduced by spheroids with aspect

ratios larger than 1.2, oblate cylinders with diameter-to-length ratios greater than 1.6,

and prolate cylinders with length-to-diameter ratios greater than 1.4. The effective

equal-volume-sphere radius for type Ia PSCs is about m8.0 µ or larger. Type Ib PSCs

are likely to be composed of spheres or nearly spherical particles with effective radii

smaller than 0.8 µm. Observations for type II PSCs are consistent with large ice crystals

1 Published in Journal of Quantitative Spectroscopy & Radiative Transfer, 70, 817-831, 2001

104

(effective radius greater than 1 µm) modeled as cylinders or prolate spheroids.

Keywords: Scattering, Depolarization, Polar stratospheric clouds, Remote sensing,

Nonspherical particles

6.1 Introduction

Although polar stratospheric clouds (PSCs) are unlikely to cause a significant direct

radiative forcing of climate, their critical role in chemical ozone depletion is now well

recognized (e.g., [1] and references therein). A detailed review of PSC studies has

recently been published by Toon et al. [2]. The traditional classification of PSC types is

based on lidar observations [3]. Type Ia PSCs are characterized by low backscattering

but strong depolarization, whereas type Ib PSCs exhibit the opposite behavior. Type II

PSCs demonstrate both strong backscatter and large depolarization ratios. Type Ib

clouds are believed to consist of droplets of supercooled ternary solutions (STSs) of

water, nitric acid, and sulfuric acid [4], whereas type Ia PSCs are thought to form by

condensation of nitric acid tri- or dihydrate (NAT or NAD). Type II PSCs are thought

to consist of water ice crystals. Although more recent observations indicate the

occurrence of other types of PSCs (e.g., [5–9]), the traditional classification covers the

majority of PSC observations (e.g., [10]) and is, therefore, the focus of this paper.

Our aim is to derive certain constraints on PSC particle microphysics based solely

on remote-sensing lidar observations. Although these constraints may not always

provide a definitive identification of the shape, size, and composition of PSC particles,

they can significantly narrow down the plausible range of particle microphysical

parameters and can be useful in analyses of in situ physical and chemical measurements

as well as in modeling PSC particle formation and evolution.

Analyzing lidar observations of PSCs is a challenging problem because many PSCs

105

are likely to consist of nonspherical solid particles with sizes comparable to the

wavelength of the lidar light (at least for lidars operating in the visible and near-infrared

spectral ranges). Theoretical computations of lidar backscatter and depolarization by

wavelength-sized nonspherical particles may not rely on the geometrical optics

approximation [11,12] but must be based on directly solving the Maxwell equations

using an exact numerical technique [13]. Although techniques such as the finite

difference time domain method (FDTDM; [14,15]) and the discrete dipole

approximation (DDA; [16]) have no restrictions on the particle shape, their relatively

low efficiency and limited size parameter range make their application to

polydispersions of randomly oriented PSC particles problematic. Therefore, we base

our analysis on the T-matrix code [17] specifically designed for polydisperse, randomly

oriented, rotationally symmetric particles such as spheroids and finite circular cylinders.

The code takes advantage of the analytical procedure for averaging scattering and

absorption characteristics over the uniform distribution of particle orientations [18,19],

uses the matrix inversion scheme based on a special form of the LU-factorization

method [20], and extends the range of particle size parameters by employing extended-

precision floating-point FORTRAN variables [21]. Although the code is limited to

rotationally symmetric particle shapes, it is much faster and is applicable to

significantly larger size parameters than FDTDM and DDA. Furthermore, by changing

the aspect ratio of spheroids and the length-to-diameter ratio of circular cylinders one

can model a wide variety of oblate and prolate shapes with either smooth or sharp-

edged surfaces.

6.2 T-matrix computations

Assuming that the laser light is linearly polarized, we define the linear

backscattering depolarization ratio )(λδ at the lidar wavelength λ as the ratio of the

106

aerosol backscatter returns in the perpendicular, )(λβ ⊥a , and parallel, )(// λβa , planes

relative to the emitted polarization plane [22-24]:

)()(

)(// λβ

λβ=λδ ⊥

a

a (6.1)

The backscatter ratio )(λR is defined as the ratio of the total molecular, )(λβm , and

aerosol, )(λβa , backscatter returns to the molecular backscatter return [3]:

)()()(

)(λβ

λβ+λβ=λm

amR . (6.2)

Similarly, the aerosol backscatter ratio is given by

1)()()(

)( −λ=λβλβ=λ RR

m

aa . (6.3)

The color ratio ),( 12 λλS is defined as the ratio of the aerosol backscatter ratios at

wavelengths 2λ and 1λ :

)()(

),(1

212 λ

λ=λλa

a

R

RS . (6.4)

The wavelength dependence of the aerosol backscatter is often characterized by the

backscatter color index

)ln(),(ln

412

12

λλλλ−=α S

. (6.5)

Analogously, the wavelength dependence of the depolarization ratio is described by the

depolarization color index

)ln(])()(ln[

12

12

λλλδλδ−=β . (6.6)

It is thus assumed that the aerosol backscatter aβ is proportional to α−λ (given the 4−λ

dependence of the molecular backscatter) and the depolarization ratio δ is proportional

to β−λ . A positive α (β ) indicates that the aerosol backscatter (depolarization ratio)

107

decreases with increasing wavelength [25]. A large α indicates the abundance of

particles with radii smaller than the lidar wavelengths, whereas a small α indicates the

predominance of large particles [2,6]. The depolarization ratio vanishes for molecular

scattering and spherical particles. A nonzero δ usually indicates the presence of

nonspherical particles provided that the contribution of multiple scattering to the

detected signal is negligible [23,24,26]. (Note, however, that wavelength-sized

needlelike and platelike particles can generate depolarization ratios close to zero [27]).

The lidar scattering properties of particles depend upon the lidar wavelengths as

well as on the particle size distribution, shape, and refractive index. We model the

shape of nonspherical PSC particles using smooth spheroids with varying aspect ratios

and sharp-edged circular cylinders with varying length-to-diameter ratios. Previous

analyses of PSC observations assumed different analytical representations of the

particle size distribution, including gamma and log normal distributions. However, it

has been demonstrated by Hansen and Travis [28] that many size distributions can be

well represented by just two parameters, the effective radius effr and effective variance

effv . Specifically, they have shown that different size distributions but with the same

effr and effv can be expected to have similar scattering properties. In this study, we

have adopted a simple power law distribution given by

>≤≤

≤=

,for0

,for)(

,for

)(

2

213

1

1

rr

rrrrrC

rrC

rn (6.7)

where C is a normalization constant and r is the radius of the volume-equivalent

sphere. The parameters 1r and 2r are chosen such that the effective variance is fixed at

1.0 , representing a moderately wide distribution. An important advantage of the power

law distribution is that for the same effv , it has a (much) smaller value of the maximal

108

radius 2r than optically equivalent gamma and log normal distributions, thereby

significantly accelerating theoretical computations [29].

Most of our theoretical computations pertain to two typical lidar wavelengths of

603 nm and 1064 nm and assume a spectrally independent refractive index.

Measurements by Deshler et al. [30] showed that the refractive index of PSC particles at

visible and near-infrared wavelengths was close to 47.1 ± 01.0 in the lower

nondepolarizing layer of the cloud and 1.52–1.56 ± 04.0 in the upper depolarizing

layer. These values are in reasonable agreement with those reported by Middlebrook et

al. [31] and Berland et al. [32]. A typical value of the refractive index of water ice at

visible and near-infrared wavelengths is 1.308 [33]. Based on this evidence, we chose

the refractive indices 1.5 and 1.308 as typical of type I and II PSC particles,

respectively. We thus used the same refractive index for type Ia and Ib PSCs, the

reason being that their refractive indices appear to be close and that their chemical

composition remains to be somewhat uncertain. The computations have been

performed for the range 0 – 3 µm of effective radii for prolate and oblate spheroids with

aspect ratios from 1 to 2, prolate cylinders with length-to-diameter ratios from 1 to 2,

and oblate cylinders with diameter-to-length ratios from 1 to 2.

6.3 Observational data

Table 6.1 summarizes the results of lidar observations of PSCs at nm6031 =λ and

Table 6.1: Typical backscattering characteristics of PSCs observed by Browell et al. [3].

R (%)δCloud type

nm6031 =λ nm10642 =λα

nm6031 =λ nm10642 =λβ

Ia 1.2 – 1.5 2 – 5 0.4 30 – 50 30 – 50 ~0Ib 3 – 8 5 – 20 2 – 3 0.5 – 2.5 <4 No dataII >10 >20 <0.8 >10 >10 ~0

109

nm10642 =λ performed by Browell et al. [3] during the NASA/NOAA Airborne

Arctic Stratospheric Expedition in the winter of 1988–1989. Larsen et al. [34]

performed extensive balloon-borne backscatter sonde observations of type I PSCs

during the winters of 1989, 1990, 1995, and 1996 and concluded that the color ratio

)nm480,nm940(S was greater than 10 for type Ia PSCs and was in the range 5–8 for

type Ib PSCs. The range of the color ratio )nm490,nm940(S observed by Vömel et

al. [35] for type II PSCs was 11–15.

The backscatter ratio defined by Eq. (6.2) depends on the PSC particle number

concentration. Since the latter cannot be directly retrieved from lidar measurements and

is a priori unknown, we have not used the measurements of the backscatter ratio in our

analysis. Unlike R, the backscatter color index, the depolarization ratio, and the

depolarization color index are independent of the particle number concentration and can

be directly used to infer particle microphysical characteristics. We have converted the

color ratio values measured by Larsen et al. [34] and Vömel et al. [35] into the

respective backscatter color index values and combined the latter with the

measurements by Browell et al. [3]. Table 6.2 summarizes the ranges of the lidar

quantities α, δ, and β used in our analysis. Note that instead of using a constant β value

equal to zero for type Ia and II PSCs, we allowed it to vary within a narrow range [–0.4,

0.4], which seems to be a reasonable assumption given the natural variability of PSC

particles. The same approach was used to define the plausible range of variability of the

backscatter color index for type 1a PSCs.

Table 6.2: Ranges of backscattering characteristics for different PSC types used in this study.

Cloud Type α (%)nm)603(δ βIa 0 – 0.8 30 – 50 –0.4 – 0.4Ib 1 – 3 0.5 – 2.5 No dataII –0.2 – 0.8 >10 –0.4 – 0.4

110

6.4 Analysis results

Figures 6.1–6.4 summarize the results of the T-matrix computations. In general,

the curves of all backscattering characteristics versus effective equivalent-sphere radius

are (much) less aspect-ratio dependent for cylinders than for spheroids. This is not

surprising since spheroids with an aspect ratio of one are perfect spheres, whereas

cylinders with a length-to-diameter ratio of one are already distinctly nonspherical

particles. There is a rapid increase of the depolarization ratio with increasing effective

radius from 0 to about 0.5 µm. Maximal δ values for most nonspherical particles are

observed at effective equal-volume-sphere radii between 0.5 µm and 1.5 µm. The most

notable exception are nearly spherical spheroids, whose depolarization ratio increases

with particle size rather monotonically. It is obvious that there is no definitive

relationship between the magnitude of depolarization and the degree of particle

asphericity [36]. For example, prolate spheroids with as small an aspect ratio as 1.05

(Fig. 6.1) produce depolarization ratios exceeding 65%. The maximal depolarization

value (~70%) is produced by prolate ice spheroid with an aspect ratio of 1.2 (Fig. 6.3).

The fact that this maximal value is caused by wavelength-sized particles indicates that

multiple internal reflections in very large particles as discussed by Liou and Lahore [37]

are not the only mechanism generating strong depolarization and not necessarily the

mechanism producing maximal depolarization values [22].

In the large-particle limit, both α and β are expected to tend to zero for

nonabsorbing scatterers. This trend is more visible for cylinders than for spheroids.

However, both color indices exhibit a significant degree of variability in the range of

sizes studied for cylinders as well as for spheroids. In the Rayleigh limit, α must tend

to 4 and β must tend to zero. This theoretical behavior is indeed well reproduced by

our T-matrix computations.

111

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70

Line

ar D

epol

ariz

atio

n R

atio

δ(%

)Prolate Spheroids

0

10

20

30

40

50

60

70

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70Obate Spheroids

ε21.81.61.41.21.11.05

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-2

-1

0

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3

4

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-1

0

1

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3

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ε21.81.61.41.21.11.051

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Effective Equal-Volume-Sphere Radius ( µm )

-2

0

2

4

6

8

Dep

olar

izat

ion

Col

or In

dex

β

Prolate Spheroids

-2

0

2

4

6

8

ε21.81.61.41.21.11.05


-2

0

2

4

6

8Oblate Spheroids

-2

0

2

4

6

8

ε21.81.61.41.21.11.05

Figure 6.1: Linear depolarization ratio )nm603(δ , backscatter color index α , and

depolarization color index β versus effective equal-volume-sphere radius effr for polydisperse,

randomly oriented spheroids with a refractive index of 5.1=m . ε is the ratio of the largest tothe smallest semi-axes of a spheroid. The light and dark shaded areas show the observed rangesof these parameters for type Ia and Ib PSCs, respectively.

112

Figures 6.5–6.7 show the ranges of the effective equivalent-sphere radius that

reproduce the observed values of the respective backscattering characteristics for

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70Li

near

Dep

olar

izat

ion

Rat

io δ

(%)

Prolate Cylinders

L/D21.81.61.41.21

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70Obate Cylinders

D/L21.81.61.41.21

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-2

-1

0

1

2

3

4

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ksca

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or In

dex

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-1

0

1

2

3

4Oblate Cylinders

D/L21.81.61.41.21


-2

0

2

4

6

8

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or In

dex

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-2

0

2

4

6

8

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-2

0

2

4

6

8Oblate Cylinders

-2

0

2

4

6

8

D/L21.81.61.41.21

Figure 6.2: As in Fig. 6.1, but for polydisperse, randomly oriented cylinders. The shapes ofprolate and oblate cylinders are specified by length-to-diameter and diameter-to-length ratios,respectively.

113

different particle shapes and refractive indices. To represent a plausible PSC particle, a

combination of model size, shape, and refractive index must simultaneously reproduce

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70Li

near

Dep

olar

izat

ion

Rat

io δ

(%)

Prolate Spheroids

0

10

20

30

40

50

60

70

ε21.81.61.41.21.11.05

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

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20

30

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or In

dex

β

Prolate Spheroids

-2

0

2

4

6

8

ε21.81.61.41.21.11.05


-2

0

2

4

6

8Oblate Spheroids

-2

0

2

4

6

8

ε21.81.61.41.21.11.05

Figure 6.3: As in Fig. 6.1, but for the refractive index m = 1.308 typical of water ice at visiblewavelengths. The shaded areas show the respective ranges of the backscattering characteristicsobserved for type II PSCs.

114

all observed lidar characteristics.

Figure 6.5 shows that cylinders with diameter-to-length and length-to-diameter

ratios larger than about 1.5 and effective equivalent-sphere radii larger than about 0.8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70Li

near

Dep

olar

izat

ion

Rat

io δ

(%)

Prolate Cylinders

L/D21.81.61.41.21

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70Obate Cylinders

D/L21.81.61.41.21

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-2

-1

0

1

2

3

4

Bac

ksca

tter

Col

or In

dex

α

Prolate Cylinders

L/D21.81.61.41.21

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-2

-1

0

1

2

3

4Oblate Cylinders

D/L21.81.61.41.21


-2

0

2

4

6

8

Dep

olar

izat

ion

Col

or In

dex

β

Prolate Cylinders

-2

0

2

4

6

8

L/D21.81.61.41.21


-2

0

2

4

6

8Oblate Cylinders

-2

0

2

4

6

8

D/L21.81.61.41.21

Figure 6.4: As in Fig. 6.3, but for polydisperse, randomly oriented circular cylinders.

115

0 1 2 3 4

Effective Equal-Volume-Sphere Radius (µm)

Prolate Spheroids

ε=1

ε=1.05

ε=1.1

ε=1.2

ε=1.4

ε=1.6

ε=1.8

ε=2

0 1 2 3 4

Oblate Spheroids

Type Ia PSCs

ε=1

ε=1.05

ε=1.1

ε=1.2

ε=1.4

ε=1.6

ε=1.8

ε=2

0 1 2 3 4


Prolate Cylinders

L/D=1

L/D=1.2

L/D=1.4

L/D=1.6

L/D=1.8

L/D=2

δ

β

0 1 2 3 4

Oblate Cylinders

D/L=1

D/L=1.2

D/L=1.4

D/L=1.6

D/L=1.8

D/L=2

α

Figure 6.5: The bars depict the respective ranges of the effective radius that reproduce thevalues of δ , α , and β observed for type Ia PSCs, as shown in Figs. 6.1 and 6.2.

116

Figure 6.6: The bars depict the respective ranges of the effective radius that reproduce thevalues of δ and α observed for type Ib PSCs, as shown in Figs. 6.1 and 6.2.

0 1 2 3 4


Prolate Spheroids

ε=1

ε=1.05

ε=1.1

ε=1.2

ε=1.4

ε=1.6

ε=1.8

ε=2

0 1 2 3 4

Oblate Spheroids

Type Ib PSCs

ε=1

ε=1.05

ε=1.1

ε=1.2

ε=1.4

ε=1.6

ε=1.8

ε=2

0 1 2 3 4


Prolate Cylinders

L/D=1

L/D=1.2

L/D=1.4

L/D=1.6

L/D=1.8

L/D=2

δ

0 1 2 3 4

Oblate Cylinders

D/L=1

D/L=1.2

D/L=1.4

D/L=1.6

D/L=1.8

D/L=2

α

117

Figure 6.7: The bars depict the respective ranges of the effective radius that reproduce thevalues of δ , α , and β observed for type II PSCs, as shown in Figs. 6.3 and 6.4.

0 1 2 3 4


Prolate Spheroids

ε=1

ε=1.05

ε=1.1

ε=1.2

ε=1.4

ε=1.6

ε=1.8

ε=2

0 1 2 3 4

Oblate Spheroids

Type II PSCs

ε=1

ε=1.05

ε=1.1

ε=1.2

ε=1.4

ε=1.6

ε=1.8

ε=2

0 1 2 3 4


Prolate Cylinders

L/D=1

L/D=1.2

L/D=1.4

L/D=1.6

L/D=1.8

L/D=2

δ

β

0 1.0 2.0 3.0 4.0

Oblate Cylinders

D/L=1

D/L=1.2

D/L=1.4

D/L=1.6

D/L=1.8

D/L=2

α

118

µm are the likely model representatives of type Ia PSC particles. Prolate and oblate

spheroids with aspect ratios 1.2 and larger are also acceptable solutions, although the

ranges of the effective radius that reproduce all three lidar observables may be narrower

than those for the cylinders and may be too shape-dependent to be realistic.

Figure 6.6 suggests that type Ib PSC particles are likely to have effective radii less

that 0.8 µm and are best represented by spheres or spheroids with very small aspect

ratios. Spheroids with aspect ratios larger than 1.1 and cylinders may also qualify, but

must have radii smaller than a few tenths of a micrometer. Note, however, that

choosing the narrower range [2, 3] of α values observed by Browell et al. [3] would

constrain type Ib PSC particles to spheres or nearly spherical spheroids with effective

radii close to 0.5 mµ (cf. [2]).

According to Fig. 6.7, type II PSC particles are well represented by ice cylinders

and prolate spheroids ( 2.1≥ε ) with effective equivalent-sphere radii exceeding 1 µm.

Although oblate ice spheroids with 1.1=ε , 1.2, and 1.6 are also potential candidates,

the respective effective radius ranges appear to be too narrow to be realistic.

6.5 Concluding remarks

We have used the current advanced version of the T-matrix method to perform

massive computations of backscattering lidar characteristics for polydisperse, randomly

oriented spheroids and circular cylinders and analyzed the existing lidar measurements

of three predominant types of PSCs. Our analysis is an extension of that previously

published by Toon et al. [2] and determines the likely ranges of particle physical

parameters that reproduce the existing lidar data. We have not discussed the plausibility

of our results from the standpoint of the physics and chemistry of PSC formation and

evolution and hope that such a discussion will be the subject of further research.

An obvious limitation of our analysis is the use of simple, rotationally symmetric

119

shapes and a restricted range of particle sizes. Although our model shapes and the

range of effective radii from 0 to 3 µm may be relevant to many real PSCs, further

effort is obviously warranted in order to include particles with larger sizes (e.g., [38])

and more irregular shapes (e.g., [14]). Another desirable extension would be an

analysis of less frequently encountered types of PSCs potentially composed of a mixture

of different particle species [2].

Acknowledgement

This research was funded by the NASA Global Aerosol Climatology Project

managed by Donald Anderson. We thank K.H. Fricke for valuable comments on a

preliminary version of this paper.

120

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