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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
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