Optical Properties of Airborne Dust: The Effect of 

Particle’s Nonsphericity on the Single-Scattering 

Properties and Downstream Applications 

Ping Yang1,2

George Kattawar,2 K. N. Liou3

1. Dept. of Atmospheric Sciences, Texas A&M Univ.

2. Dept. of Physics &Astronomy, Texas A&M Univ.

3. Dept. of Atmospheric and Oceanic Sciences, Univ. of California, Los Angeles 

With contributions by L. Bi and B. Yi
Asian Dust, MODIS RGB (0.65μm, 0.55μm, 0.47μm) Image

A major component of atmospheric aerosols is airborne dust 

that may have significant opacity (particularly over arid and 

semi-arid areas) and can thus have a substantial impact on 

atmospheric radiation budget and climate

2
3
The track of a large dust storm that was followed with the 

SeaWIFS Satellite observations in 1998

Source: R. B. Husar et al, JGR, 2001 

4
• The important role of mineral dust aerosols in the climate system

has been recognized (Haywood & Bougher, 2000).

• Modeling the effect of dust aerosols on the transfer of radiation

in the atmosphere contributes to our understanding of the climate

system (d’Almeida et al, 1991) and aerosol retrieval algorithms

(Mishchenko et al. 1995, Kahn et al. 1997).

 Determination of the sign and magnitude of direct radiative 

forcing by dust on regional and global scales remains a key 

unsolved problem (e.g. Sokolik et al., 2001). 

 The optical properties of dust particles are fundamental to the 

assessment of the radiative forcing of dust aerosols. There is a 

pressing need to reduce the substantial uncertainties in the 

current knowledge of the optical properties of dust particles. 

5
Scattering plane

Scattering Geometry

Scattering angle

E||

s

E

s

Scattering object

Amplitude scattering matrix

E||

s

E

s

e

ikr

ikr

S2S3

S4S1

E||

i

E

i

Incident beam

E

i

E||

i

6
Stokes vector-Phase matrix/Mueller 

matrix formulation

The electric field can be resolved 

into components. E// and E are 

complex oscillatory functions. E = E// l + E r

The four component Stokes vector 

(Stokes, 1852) can be defined.

They are all real numbers and 

satisfy the relation

I

2 = Q2 + U2 + V2

I

s

Q

s

U

s

V

s

M11 M12 M13 M14

M21 M22 M23 M24

M31 M32 M33 M34

M41 M42 M43 M44

Ii

Q

i

U

i

V

i

The phase matrix, P, (for a singlescattering event) or Mueller matrix, 

M, (for a multiple scattering event, 

or radiative transfer process) relates 

the incident and scattered Stokes 

vectors

I= E// E//

* + E E *

Q= E// E//

*

- E E *

U= E// E *+ E E//

*

V= i(E// E *- E E//

*

)

7
Reid et al., 2003 Volten et al., 2005

8
The Finite-Difference Time 

Domain (FDTD) Method

ABC (Absorbing Boundary 

Condition)

9

Yee, 1966

Citations: 4926 (as of 

3/10/2011)

Basic principle: Discretizatio of two time-dependent Maxwell’s curl 

equations in terms of the finite-difference technique
Purcell E. M., and C. R. Pennypacker, 

Scattering and absorption of light by nonspherical dielectric grains, Astrophys. J. 186, 

705–714, 1973. 

Discrete Dipole Approximation (DDA) method 

ApJ 333 848 (1988)

Edward Mills Purcell

Nobel Prize in Physics (1952) 10
Diagram: Z. Zhang
Yang and Liou (1996)

Yang and Liou (1997)

12

Improved Geometric Optics Method
Nonsphericity Effect of Dust Particles

• “...even moderate nonsphericity results in substantial errors 

in the retrieved aerosol optical thickness if satellite 

reflectance measurements are analyzed using Mie theory” 

(Mishchenko et al. 1995).

• “Multiple, multispectral remote sensing observations, such 

as those anticipated from the Earth Observing System 

(EOS) multiangle imaging spectroradiometer (MISR), can 

distiguish spherical and nonspherical particles over calm 

ocean for mineral-dust-like particles” (Kahn et al. 1997).

• Demonstrated of a significant impact of the nonsphericity 

of dust particles on the retrieval of dust microphysical and 

optical properties (Dubovik et al. 2002, 2006) 

13
Comparison between the phase functions computed for spherical and nonspherical

dust particles (Feng, Yang, Kattawar, Hsu, Tsay and Laszlo, 2009). The symbols

indicate laboratory measurements (Volten et al. 2001).

14

1

P1 1

Retrieval:
Elements of the kernel matrices K11(Θ, λ, n, k, p, rk) and K12(Θ, λ, n, k, p, rk) at different scattering 

angles for prolate randomly oriented spheroids ( = ~2.7, n = 1.53+i0.003). The red and blue 

curves show the results obtained with the T-matrix code [Mishchenko and Travis, 1994] and the 

Yang and Liou [1996] method, respectively. Adapted from Dubovik et al. (2006), 

15
A typical situation where utilizing the spheroid scattering assumption [Dubovik et al., 2002b] resulted in 

the removal of the false fine mode in the size distribution and false spectral dependence in the real part of 

refractive index. Size distributions and refractive indices are retrieved assuming sphere and spheroid 

models from spectral radiance measurements covering the full range of scattering angles. The size 

distribution retrieved from the aureole only (Θ < 40°, where effects of nonsphericity are minimal) and 

assuming spherical particles is also shown. Adapted from Dubovik et al. (2006).

16
Simulated solar reflectance at the top of a dusty atmosphere. 

Spherical and nonspherical (spheroidal) shapes are assumed for dust 

particles (Yang, Feng, Hong, Kattawar, Wiscombe, Mishchenko, 

Dubovik, Laszlo, and Sokolik, 2007). 

• These results indicate that the equivalent sphere approximation leads to an underestimate

of the albedo of a dusty atmosphere. This underestimate has an important implication to

the study of the effect of airborne dust on the radiation budget within the atmosphere.

17
MODIS RGB image on March 2, 2003, showing a dust plume over West Africa.

The area indicated by the small red box is used to retrieve dust AOD in the present

sensitivity study (Feng, Yang, Kattawar, Hsu, Tsay and Laszlo, 2009).

18
Upper panels: the 

retrieved dust AOD 

based on the 

nonspherical 

(spheroidal) and 

sphere models. 

Lower left panel: 

retrieved dust AOD 

based on the sphere 

model versus those 

based on the 

nonspherical model. 

Lower right panel: 

the relative 

differences of the 

retrieved AOD 

(Feng, Yang, 

Kattawar, Hsu, Tsay 

and Laszlo, 2009). 19
MODIS RGB image (05/27/2008)

Retrieved dust optical depths

(Courtesy of Q. Feng)

20
Does the particle shape have a large effect on 

radiative flux simulation?

• Yes?

– Pilinis and Li (1998) compared the model calculated single-scattering

properties with observations, and claimed that aerosol forcing could be

underestimated by a factor of 3 if particle shape effect was neglected.

– Several studies (Kahnert & Kylling, 2004; Kahnert et al, 2005; Kahnert et

al, 2007) investigated the particle shape effect on the simulation of

radiance and flux simulation and compared the uncertainties associated

with dust nonsphericity with the other important uncertainties.

 From modeling simulations, Kahnert & Kylling (2004) found that the

misrepresentation of the aerosol phase function by using the spherical

counterpart caused an overestimation of yearly averaged TOA spectral net

flux, which was five times larger than the errors due to uncertainties in

refractive index.

 Kahnert et al (2005) found that an optimal shape distribution of spheroids

could significantly reduce the errors compared with the equiprobable shape

distribution.

 The errors due to the spherical particle approximation are found to be the

same order as the errors associated with the uncertainties in the refractive

indices(Kahnert et al, 2007) 21
Does the particle shape have a large effect on 

radiative flux simulation?

• No?

– Despite the apparent differences in the phase function, Mishchenko et

al. (1995) argued that the sphere model could be a suitable

approximation for nonspherical dust in radiative flux simulation,

because the single-scattering albedo and asymmetry factor were similar

in the two cases.

– Fu et al (2009) found that the errors in reflectivity and absorptivity

resulted from the spherical particle approximation were small and

concluded that Mie-theory-based single-scattering properties were

suitable for radiative flux calculations.

• The controversy has not been resolved!

• The particle shape effect on broadband radiative flux

simulation is not yet determined. 22
Integrated net flux of dust forcing at the top of the atmosphere 

(TOA) and the surface using the spherical and nonspherical 

models under various conditions

23

(Solar spectral band: 0.3μm-4.5μm)

Difference = the nonspherical results minus the spherical counterparts
New Effort

• Objective

Use manageable and optimal particle morphological sets (or, 

the geometric parameters associated with particle shapes and 

compositions) to quantify the effect of the nonsphericity of 

dust particles on their optical and radiative properties from 

remote sensing and radiative forcing perspectives. 

• Particle shapes 

Tri-axial ellipsoid (Bi, Yang, Kattawar, and Kahn, 2008)

Non-symmetric hexahedra (Bi, Yang, Kattawar, and Kahn, 2010)

24
ELLIPSOIDS

 For size parameters from 0.5 to 30, we used the ADDA code of Yurkin and Hoekstra (2007)

to calculate the relevant quantities.

 For size parameters from 15 to 1000, we use the IGOM with the edge effect included.

 We use a numerical method to calculate the edge effect accurately for ellipsoids.

Triaxial ellipsoid 

geometry (Bi 

et al., 2009)

Qe Qe,IGOM Qe,edge Qe

Qa

g

Randomly oriented ellipsoids: m=1.53+0.008i, =0.66 m (Bi, Yang, Kattawar, and Kahn, 2009)

a:b:c=0.53 : 0.71 : 1.00 a:b:c=0.30 : 0.70 : 1.00 Qa Qa,GOM Qa,above Qa,below

25
HEXAHEDRA, PHASE MATRIX ELEMENTS 

(Bi, Yang, Kattawar, and Kahn, 2010)

Effective radius re= 2.3 m, variance =1.5 Effective radius re= 3 m, variance =12.3

26
Polluted Dust Particles

Some dust particles, after passing through high-density 

industrial regions or oceans, may be coated with soot or seasalt (Parungo et al. 1995). 

Some new efforts (e.g., 

Liou, Takano and 

Yang, 2011)

27
A Novel Geometric-optics Surface-wave Approach 

(Liou, Takano and Yang, 2011)

28
Experimental Setup

Yong-Le Pan, Kevin B. Aptowicz, Richard K. Chang, Matt Hart, and Jay D. Eversole,

Characterizing and monitoring respiratory aerosols by light scattering, Optics Letters,

Vol. 28, No. 8, p589 (2003). 29
B. D. Cameron, M. J. Rakovic, M. Mehrubeoglu, G. Kattawar, S. Rastegar, L. V. Wang, and G. L. Coté, "Measurement 

and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium," Optics Letters 23, 485-487 

(1998). 30
Mueller Image for Three Particles

m=1.34 1.0 m

0.8 m

=0.5 m

1.0 m

0.8 m

0.5 m m=1.35 = 0.532 m

1.0 m

P11 P33 P34 P44

31
Available Laboratory Measurements

The Amsterdam Light Scattering 

Database (http://www.iaa.es/scattering/) 

• Samples: feldspar, red clay, quartz, Pinatubo, Sahara...

• Wavelengths: 632.8 nm and 441.6 nm

• Scanning microscope images of the particles 

• Phase matrix: scattering angles from 5° to 173°

• Particle size distribution

32
Experimental setup at the University of Amsterdam.

http://www.astro.uva.nl/scatter 

Aerosol Generator

Mobile detector

NeHe laser

Stability monitor

33
Summary

• Nonsphericity effect of dust aerosol particles is quite important 

from remote sensing perspective. 

• The effect of the nonsphericity of dust particles on simulating 

radiative flux (i.e., radiation budget) is still controversial. 

• Efforts have been made to develop dust optical properties using 

numerical models. Follow-up effort is needed to intercompare 

the theoretical simulations.

• Laboratory data for the single-scattering properties of dust 

particles can constrain developing optimal and realistic models 

(overall shape, surface texture, and inhomogeneity) for these 

particles.

• Measurements of backscatter are extremely useful for modelers.

34