Accounting for non-sphericity of aerosol particles in photopolarimetric remote

sensing of desert dust

Oleg Dubovik (UMBC / GSFC, Code 923) Alexander Sinyuk (SSAI, Code 923)Tatyana Lapyonok ( GSFC, Code 923) Brent Holben ( GSFC, Code 923)Michael Mishchenko (NASA/GISS)Ping Yang (Texas A&M University)Anne Vermeulen (SSAI, Code 923)Tom Eck (UMBC/GSFC, Code 923)Ilya Slutsker (SSAI, Code 923)Hester Volten (Free University,Netherlands)Ben Veihelmann (SRON Space Res., Netherlands)

Outlines:Outlines:

Simulating non-spherical dust scattering Simulating non-spherical dust scattering in remote sensing retrievalsin remote sensing retrievals

Fitting laboratory polarimetric Fitting laboratory polarimetric

measurements of dust light scatteringmeasurements of dust light scattering

Sensitivity of polarimetric Sensitivity of polarimetric measurements to aerosol parametersmeasurements to aerosol parameters

Applications to AERONET polarimetric Applications to AERONET polarimetric retrievalsretrievals

Difficulties of accounting for particle Difficulties of accounting for particle non-sphericity in aerosol retrievals:non-sphericity in aerosol retrievals:

1. many limitations in simulating light scattering by non-spherical particles (on particle size, shape, refractive index, etc.)

2. Simulation are too slow for operational retrievals (much slower than Mie scattering by spherical particle)

3. Concept of choosing particle shape is unclear

4. Validation of models is ambigious

Main limitations of T-Matrix code (Mishchenko et al.):- only spheroid shape (?)- size parameter ≤ ~ 60- aspect ratio ≤ 2.4- speed (for large aspect raitos) ~ 100 times slower than Mie

Difficulties of accounting for particle non-Difficulties of accounting for particle non-sphericitysphericity

SimplestSimplest model of non-spherical model of non-spherical aerosolaerosol

Randomly orientedRandomly orientedspheroids :spheroids :

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

How to implement operationally ???

Is this correct???

0

0.02

0.04

0.06

0.08

0.1 1 10

dV/dlnR (

μm3 /μm2)

(Radius μ )m

Modeling Polydispersions

τ λ( )= Kτ(rmin

rmax

∫ k;n;r)V(r)dr≈ V(ri ) Kτ(ri −Δ/2

ri +Δ/2

∫ k;n;r)dr∑

K k;n;ri( ) - Kernel look-up table for fixed ri (22 points) (1.33 ≤ n ≤ 1.6; 0.0005 ≤ k ≤ 0.5)

0

0.02

0.04

0.06

0.08

0.1 1 10

dV/dlnR (

μm3 /μm2 )

(Radius μ )m

V(ri) V(ri)

Single Scattering using Single Scattering using spheroids:spheroids:

Model by Mishchenko et al. 1997:Model by Mishchenko et al. 1997:

particles are randomly oriented homogeneous spheroids () - size independent aspect ratio distribution

€

τ λ( )≈ Viωp Kτ ...;r;ε( )drdεΔri

∫Δεp

∫⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ i;p( )

∑

= Kip ...;n;k( )i;p( )∑ ωpVi

K - kernel matrix:

0.05 ≤ r ≤ 15 (μm)1.33 ≤ n ≤ 1.6

0.0005 ≤ k ≤ 0.50.4 ≤ ≤ 2.4

spheroidspheroid kernels data basekernels data basefor for operational modeling !!!operational modeling !!!

Basic Model by Mishchenko et al. Basic Model by Mishchenko et al. 1997:1997:randomly oriented homogeneous spheroids () - size independent shape distribution

€

τ λ( ),F11,...,F44 ≈ K ip ...;n;k( )i;p( )∑ ω p V ri( )

K - pre-computed kernel matrices:Input: n and k

Input: p (Np =11), V(ri) (Ni =22 -30)

Output: τ(λ), 0(λ),

F11(), F12(),F22(),

F33(),F34(),F44()

Time:Time: < < one sec.one sec.Accuracy:Accuracy: < < 1-3 %1-3 %

Range of applicability:Range of applicability:0.15 ≤ 20.15 ≤ 2r/r/λ λ ≤ ≤ 280 280 (26 bins)(26 bins)

0.4 ≤ 0.4 ≤ ≤ 2.4 ≤ 2.4 (11 bins)(11 bins)1.33 ≤ n ≤ 1.6 1.33 ≤ n ≤ 1.6

0.0005 ≤ k ≤ 0.50.0005 ≤ k ≤ 0.50.1

1

10

100

0 40 80 120 160

Phase Functions (0.67 μ )m

Spheres - Spheroids

1()

- Spheroids 1()

( )Scattring Angle degree

Modeling of dust light scattering by mixture of spheroids

0.1

1

10

100

0 40 80 120 160

Aspect Ratios:

0.400.480.580.690.831.01.441.201.732.072.49

Phase Function (0.34

μ )m

( )Scattering anlge degree

Single aspect raitios spheroids

0.1

1

10

100

0 40 80 120 160

Spheres

Spheroid mixture

Phase Function (0.34

μ )m

( )Scattering anlge degree

Mixture of spheroids

0

0.05

0.1

0.15

0.2

0.25

0. 1 10

Retireved size distribution

Radius (microns)

dV/dlnR (

μm3/μm

2)

() - size independent shape distribution

n(λ)k (λ)

Averaging with ()

0

0.05

0.1

0.15

0.2

0.25

0.5 1 1.5 2 2.5 3

Probability

Aspect Ratio

Modeling of dust light scattering by mixture of spheroids

0

0.05

0.1

0.15

0.2

0.25

0. 1 10

Retireved size distribution

Radius (microns)

dV/dlnR (

μm3/μm

2)

() - size independent shape distribution

n(λ)k (λ)

Averaging with ()

-0.2

0

0.2

0.4

0.6

0 40 80 120 160

Spheres

Spheroid mixture

Degree of Linear Polarization (0.44

μ )m

( )Scattering anlge degree

Mixture of spheroids

-0.2

0

0.2

0.4

0.6

0 40 80 120 160

Aspect Ratios:

0.400.480.580.690.831.01.441.201.732.072.49

Degree of Linear Polarization (0.44

μ )m

( )Scattering anlge degree

Single aspect raitios spheroids

0

0.05

0.1

0.15

0.2

0.25

0.5 1 1.5 2 2.5 3

Probability

Aspect Ratio

0

0.05

0.1

0.15

1 10 100

Kscat

(1200, x)

V(x)K

scat(1200, x) * V(x)

Kscat

(1200

,x), V(x), K

scat

(1200

,x) * V(x),

Size Parameter

0.0001

0.001

0.01

0.1

1

1 10 100

30

50

300

600

1200

30

50

300

600

1200

Kscat(

; ... )

Size Parameter

Mishchenko and Mishchenko and Travis, 1994Travis, 1994

Yang and Liou, 1996Yang and Liou, 1996 Contribution of differentContribution of differentsizes to scattering at 120sizes to scattering at 12000

Computational challenge of using Computational challenge of using spheroids (phase function)spheroids (phase function)

Mishchenko and Mishchenko and Travis, 1994Travis, 1994

Yang and Liou, 1996Yang and Liou, 1996 Contribution of differentContribution of differentsizes to scattering at 120sizes to scattering at 12000

Computational challenge of using Computational challenge of using spheroids (polarization)spheroids (polarization)

0

3.4 10-5

6.8 10-5

0.000102

0.000136

0. 1 10 100

1200

1400

1200

1400

-KF12

(,...)

Size Parameter

0

0.08

0.16

0.24

0.32

0. 1 10 100

-K12

(,...)

( )V r-K

12(,...) ( )V r

-K12F

(,...), ( ), -V r K

12F

(,...) ( ) V r

Size Parameter

name of sample feldspar

origin crushed piece of Feldspar rock from Finland

main constituents K-feldspar, plagioclase, quartz

particle size distributions measured with laser diffraction

reff =1.0 micrometer, v eff =1.0

particle shape irregular (SEM image)

refractive index estimated to be in the range:1.5-1.6 - i0.001-0.00001 

color  light pink to white powder

scattering matrix from 5-173 degrees scattering angle

wavelength 441.6 nm (figure)632.8 nm (figure)

article Scattering matrices of mineral particles at 441.6 nm and 632.8 nm.

Volten H, Muñoz O, Rol E, de Haan JF, Vassen W, Hovenier JW, Muinonen K, Nousiainen T.Journal of Geophysical Research, 106, 17375-17401,2001

Facts and Figures

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

F11λ F12 λ /F11 λ F22/F11 , F33/F11, F34/F11, F44/F11

Numerical inversion:Numerical inversion:-Accounting for uncertainty (F(F1111; -F; -F1212/F/F11 11 !!!)!!!) - Setting a priori constraints

aerosol particle sizes,aerosol particle sizes, refractive index, refractive index,

single scattering albedosingle scattering albedo,, aspect ratio distributionaspect ratio distribution

Inversion of Scattering MatricesInversion of Scattering Matrices

€

F11

,F12

,F22

,F33 ,,F34 ,,F44 , ≈ K ip λ;θ ;n;k( )

i;p( )∑ ω p V ri( )

Forward Model:Forward Model:

Fitting of Measured Scattering Matrix by spheroids model

Feldspar0.441 μm

€

I Θ;λ( ) =μ0 exp −μ0τ( ) − exp −μ1τ( )( )

μ0 + μ1ω0τ L 2P Θ;λ( )L1I0 + mult. scat.( )

Accounting for polarization in radiationAccounting for polarization in radiationtransmitted through the atmospherictransmitted through the atmospheric

L1; L2 - rotation matricesTotal:Total:

I

Q

U

V

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

I = - Stokes vectorF(λ) =

€

F11 F12 0 0

F12 F22 0 0

0 0 F33 F34

0 0 −F34 F44

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

phase matrix !!!

€

I0 =

1

0

0

0

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

€

I Θ;λ( ) ~ ω0τ F11 Θ;λ( ) + mult. scat.( )

€

P Θ;λ( ) ~ - F12 Θ;λ( ) /F11 Θ;λ( ) + mult. scat.( )

- Intensity

-Linear Polarization

Fitting of Measured Scattering Matrix by spheroids model

Fitting of Measured Scattering Matrix by spheroids model

Feldspar0.633 μm

Fitting of Measured Scattering Matrix by spheres

Feldspar0.441 μm

dV(r)/dlnrAspect ratio distribution

Size and shape distributions retrieved from Scattering Matrix

Spheroids

-0.5

0

0.5

1

0 45 90 135 180

SPHERES (Rv = 0.14μ )m

= 1.33n = 1.4n = 1.45n = 1.5n = 1.55n = 1.6n

(-Degree of Linear Plarization F

12/F11)

( )Scattering Angle degrees

-0.5

0

0.5

1

0 45 90 135 180

SPHEROIDS (Rv = 0.14μ )m

= 1.33n = 1.4n = 1.45n = 1.5n = 1.55n = 1.6n

(-Degree of Linear Plarization F

12/F11)

( )Scattering Angle degrees

Sensitivity of Linear Polarization of fine mode aerosol to real part of refractive index

Log-normal monomodal dV(r)/dlnr : v = 0.5, μ = 0.44 μm, k = 0.005

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 45 90 135 180

SPHERES (Rv = 2.0μ )m

= 1.33n = 1.4n = 1.45n = 1.5n = 1.55n = 1.6n

(-Degree of Linear Plarization F

12/F11)

( )Scattering Angle degrees

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 45 90 135 180

SPHEROIDS (Rv = 2.0μ )m

= 1.33n = 1.4n = 1.45n = 1.5n = 1.55n = 1.6n

(-Degree of Linear Plarization F

12/F11)

( )Scattering Angle degrees

Sensitivity of Linear Polarization of coarse mode

aerosol to real part of refractive index Log-normal monomodal dV(r)/dlnr : v = 0.5, μ = 0.44 μm, k = 0.005

Shape effect in presence of Multiple Scattering(Radiance)

Log-normal monomodal dV(r)/dlnr : rv= 2μm, v = 0.5, μ = 0.44 μm, n = 1.45, k = 0.005

Shape effect in presence of Multiple Scattering(Polarization)

Log-normal monomodal dV(r)/dlnr : rv= 2μm, v = 0.5, μ = 0.44 μm, n = 1.45, k = 0.005

t=1.0

ττ((λλ), I(), I(λλ),P(),P(λλ)) Numerical inversion:Numerical inversion:-Accounting for uncertainty (F(F1111; -F; -F1212/F/F11 11 !!!)!!!) - Setting a priori constraints

aerosol particle sizes,aerosol particle sizes, refractive index, refractive index,

single scattering albedosingle scattering albedo

AERONET Polarized InversionAERONET Polarized Inversion

€

P11

,P12

,P22

,P33 ,,P34 ,,P44 , ≈ K ip λ;θ ;n;k( )

i;p( )

∑ ω p V ri( )

Forward Model:Forward Model:

Single Scat:Single Scat:

Multiple Scat:Multiple Scat: DEUZE JL, HERMAN M, SANTER R, JQSRT, 1989

Successive Orders of Scattering CodeSuccessive Orders of Scattering Code

Inversions of intensity and polarization measured by AERONET

Banizombu(Africa)

Sept. 26, 2003

τ 5

Inversions of intensity and polarization measured by AERONET

Cape VerdeJuly 12,2001τ 6

Inversions TESTS of intensity and polarization measured at 4 wavelengths

Solar Vilageτ12 4

Modeling Desert Dust Lidar Ratio

0

0.05

0.1

0.15

0.2

0.1 1 10

5 channels (+ 1.637 μ )m

/ (dV dlnR

μm3 /μm

2 )

( )Particle Radius micron

21:2:24, 5:21:34, Dhabi

0.1

1

10

100

0 40 80 120 160

Spheres Spheroids

Phase Function (0.532

μ )m

( )Scattering Angle degrees

€

S(λ ) =4π

ω0 λ( ) P λ ,1800( )

Muller, et al., 2003:S(0.532μm)= 50~80sr

S=19

S=50

S=80

Dhabi Aerosol

Conclusions:Conclusions:

Kernel look-up tables seems to be Kernel look-up tables seems to be promising for remote sensing retrievalspromising for remote sensing retrievals

Spheroids may closely reproduce Spheroids may closely reproduce

laboratory polarimetric measurements laboratory polarimetric measurements of dust scatteringof dust scattering

Spheroid Spheroid model model is successfully is successfully employed inemployed in both intensity and both intensity and polarized polarized AERONET retrievalsAERONET retrievals

Sensitivity to particle Sensitivity to particle shape is a shape is a challenge forchallenge for utilizing utilizing polarizationpolarization for for aerosol retrievalsaerosol retrievals