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Aerosol retrievals from AERONET sun/sky radiometers: Overview of - inversion principles
- aerosol retrieval products - advances and perspectives
Aerosol retrievals from AERONET sun/sky radiometers: Overview of - inversion principles
- aerosol retrieval products - advances and perspectives
The Second International Conference of Aerosol Science and Global ChangeAugust, 18-21, 2009, Hangzhou, China
O. DubovikO. Dubovik1,2, A. Sinuyk, A. Sinuyk2, B.N. Holben B.N. Holben2 and AERONET team1 - University of Lille, CNRS, France
2 - NASA/GSFC, Greebelt, USA
((), I(), I(),P(),P()) Optimized Numerical inversion:Optimized Numerical inversion:- Accounting for uncertainty (F(F1111; -F; -F1212/F/F11 11 !!!)!!!) - Setting a priori constraints
aerosol particle sizes,aerosol particle sizes, complex refractive index (complex refractive index (SSASSA)), ,
Non-spherical fractionNon-spherical fraction
AERONET InversionAERONET InversionForward Model:Forward Model:
Single Scat:Single Scat:
Multiple Scat:Multiple Scat: (scalar) Nakajima and Tanaka, 1988, or (polarized) Lenouble et al., JQSRT, 2007
ensemble of polydisperse randomly oriented spheroidsensemble of polydisperse randomly oriented spheroids(mixture of spherical and non-spherical aerosol components)
Accounting for multiple scattering effects
- cloud-free atmosphere;
- horizontal homogeneous atmosphere;
- assumed gaseous absorption and molecular scattering;
- vertically homogenous atmosphere (assumed profile of concentration !?)- bi-directional surface reflectance assumed from MODIS observations
- accounting for polarization effects !?!
ASSUMPTIONS in the retrievals:
AERONETAERONET model of aerosol model of aerosolspherical:spherical:
Randomly orientedRandomly orientedspheroids :spheroids :
(Mishchenko et al., 1997)(Mishchenko et al., 1997)
Dubovik et al., 2006
Aerosol single particle scattering:
EACH AEROSOL PARTICLE
- sphere or spheroid (!!!);
- homogeneous;
- 1.33 ≤ n ≤ 1.6 (1.7- ???)
- 0.0005 (0 - ???) ≤ k ≤ 0.5
-n and k spectrally dependent (but smooth)
ASSUMPTIONS in the retrievals:
Aerosol particle size distribution
ASSUMPTIONS:
- dV/dlnr - volume size distribution of aerosol in total atmospheric column;
- size distribution is modeled using 22 triangle size bins (0.05 ≤ R ≤ 15 m);
- size distribution is smooth
0
0.05
0.1
0.15
0.2
0.25
0.3
0.1 1 10
Size Distribtuion Approximation
Particle Radius (m)
Vtotal
(r) = (i=1,...,22)
aiV
i(r)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.1 1 10
Size Distribtuion
dV
/dln
(r)
(m3
/m2
)
Particle Radius (m)
Voriginal(r)
(Twomey 1977)
Trapezoidal approximation
Mixing of particle shapes
ASSUMPTIONS:
- dV/dlnr - volume size distribution is the same for both components;
- non-spherical - mixture of randomly oriented polydisperse spheroids;
- aspect ratio distribution N(is fixed to the retrieved by Dubovik et al. 2006
C Kspherical (
rmin
rmax
k;n;r )V(r )dr (1 C) K (k;n;r ,)
min
max
N()d
rmin
rmax
V(r )dr
retrieved
C + (1-C)
Aspect ratio distr.
0.1
1
10
100
0 40 80 120 160
Spheres Spheroids
Pha
se
Fun
ctio
n (0
.532
m
)
Scattering Angle (degrees)
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
,F11,...,F44 K ip ...; n;k i;p p V ri
K - pre-computed kernel matrices:Input: n and k
Input: p (Np =11), V(ri) (Ni =22 -26)
Output: (), 0(),
F11(), F12(),F22(),
F33(),F34(),F44()
Time:Time: < < one sec.one sec.Accuracy:Accuracy: < < 1-3 %1-3 %
Range of applicability:Range of applicability:0.012 ≤ 20.012 ≤ 2r/r/≤ ≤ 625 625 (41 bins)(41 bins)
0.3 ≤ 0.3 ≤ ≤ 3.0 ≤ 3.0 (25 bins)(25 bins)1.3 ≤ n ≤ 1.7 1.3 ≤ n ≤ 1.7
0.0005 ≤ k ≤ 0.50.0005 ≤ k ≤ 0.50.1
1
10
100
0 40 80 120 160
Phase Functions (0.67 m)
Spheres
Spheroids - 1()
Spheroids - 1()
Scattring Angle (degree)
Particle Size Distribution:0.05 m ≤ R (22 bins) ≤ 15 m
Complex Refractive Index at = 0.44; 0.67; 0.87; 1.02 m
0.01
0.02
0.04
0.05
0.07
0.1 1 10
dV
/dln
R(
m3 /
m2)
Radius (m)0.00
0.01
0.10
Wavelength (m)0.44 0.67 0.87 1.02
Imarinary PartImaginary Part
Smoke Desert Dust Maritime
AERONET retrievals are driven by 31 variables :
1.35
1.40
1.45
1.50
1.55
1.60
Wavelength (m)0.44 0.67 0.87 1.02
Real Part
dV/lnr - size distribution (22 values); n() and k() - ref. index (4 +4 values) Cspher (%) - spherical fraction (1 value)
Statistically Optimized Minimization - Fitting (Dubovik and King, 2000)
Measurements:i=1 - optical thicknessi=2 - sky radiances-their covariances(should depend on and )-lognormal error distributions
a priori restrictions on norms of derivatives of:i=3 -size distr. variability;i=4 -n spectral variability; i=5 -k spectral variability;
i=6 - limiting dV/dlnr for Rmin
Lagrange parameters
consistencyIndicator
weighting
0
2
i2 fi
fi x 2, i
02
i2 fi
a fi x 2i (N total - Nx ) ˆ 0
2
A priori restrictions on smoothness (Dubovik and King, 2000)
norms of derivatives Meaning :
m=1 -constant straight line: V(lnr)= C;m=2 -constant straight line: V(lnr)= B lnr +C; m=3 -parabola: V(lnr)= A(lnr)2 + B lnr +C;
Most unsmooth KNOWN size distribution
Strength of constraint
i
2 amax dmV (lnr)
dm ln r
r
2
d ln r
AERONET retrieval products:
Directly retrieved parameters:- dV/dlnR - size distribution; (- dynamic errors )- C(t,f,c), Rv(t,f,c), (t,f,c), Reff (t,f,c) - integral parameters of dV/dlnR - n() and k () at 0.44, 0.67, 0.8, 1.02 m; (- dynamic errors )- Cspherical - fraction of spherical particles (- dynamic errors )
- V1 - V2 - V3
Indirectly retrieved/estimated parameters:
popular: - at 0.44, 0.67, 0.8, 1.02 m; (- dynamic errors ) - P11() (- dynamic errors ) and <cos()> ; - P12() and P22() - ??? (- dynamic errors )- F
TOA() and FBOA() - down ward spectral fluxes
- FTOA() and F
BOA() - upward spectral fluxes
not well-known / under-developed:
- S() - lidar backscattering-to-extinction ratio; (- dynamic errors ) - () - lidar depolarization ratio ; (- dynamic errors ) - F
TOA and FBOA - down ward broad-band (visible) fluxes;
- FTOA and F
BOA - upward broad-band (visible) fluxes; - ∆FTOA and ∆ FBOA - radiative forcing - ∆FEff
TOA and ∆FEffBOA - radiative forcing efficiency
Fine / Coarse modes parameters:
0.1
1
10
100
0 45 90 135 180
totalfine modecoarse mode
Pha
se
Fun
ctio
n
Particle Radius (micron)
02:05:2003,09:27:51,PolarPP,Beijing,14
0
0.3
0.6
0.9
0 45 90 135 180
totalfine modecoarse mode
Line
ar
Pol
ariz
atio
n (
-F12
/F11
)Particle Radius (micron)
02:05:2003,09:27:51,PolarPP,Beijing,14
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.1 1 10
dV/d
lnR
(m
3 /m
2 )
Particle Radius (micron)
Coarse
Fine
Coarse
02:05:2003,09:27:51,PolarPP,Beijing,14
Beijing Aerosol
Flexible separation: minimum between: 0.194 and 0.576 m
0.45m
Integral parameters of dV/dlnR: t - total; f - fine ; c - coarseC(t,f,c) - Volume ConcentrationRv(t,f,c) - Mean Radius(t,f,c) - Standard DeviationReff (t,f,c) - Effective Radius
Retrieval accuracy and limitationsSensitivity tests by Dubovik et al. 2000
Real Part Imaginary PartSSA
≤ 0.05
80-100%0.05-0.07
≥ 0.02550%0.03
Size Distribution:
0.00
20.00
40.00
60.00
80.00
0.1 1 10
Err
ors
(%
)
Radius (m)
bias ∆ = ± 0.01Effective
Random errors Nonsphericitybiases
0
0.05
0.1
0.15
0.1 1 10
aureolefull almucantar
dV
/dln
R(
m3/
m2 )
Radius (m)
1.30
1.35
1.40
1.45
1.50
1.55
1.60
Wavelength (m)0.44 0.67 0.87 1.02
Real Part
wide angularcoverage
Error estimates:Error estimates:
New strategy: Errors are to be provided in each single retrievals for all retrieved parameters
Important Error Factors:- Aerosol Loading - Scattering Angle Range - Number of Angles (homogeneity)- Number of spectral channels- Aerosol Type
etc.
Rigorous ERRORS estimates:Rigorous ERRORS estimates: General caseGeneral case: : large number of unknownslarge number of unknowns and and
redundant measurementsredundant measurements
U - matrix of partial derivatives in the vicinity of solution
ˆ x i 2 ˆ x irandom 2 ˆ x i
bias 2
ˆ x
Above is valid: - in linear approximation
- for Normal Noise - strongly dependent on a priori constraints
- very challenging in most interesting cases
C ˆ x random UTC-1UU a
T Ca 1Ua -1
ˆ x bias UTC-1UU aT Ca
1Ua 1
UTC-1Ibias U aT Ca
1Iabias
Dubovik 2004
Input ERRORS and biasesInput ERRORS and biases
Random (normally distributed with 0 means):
- optical thickness: - optical thickness: 0.015 0.015 COS(SZA) COS(SZA)
- sky-radiances: - sky-radiances: skysky3% 3%
- a priori: - a priori: skysky/ / ii100 - 300 % 100 - 300 % (Dubovik and King, 2000)(Dubovik and King, 2000)
Biases (constant): - optical thickness: - optical thickness: 0.015 0.015 COS(SZA) COS(SZA)
- sky-radiances: - sky-radiances: 3% + obtained misfit3% + obtained misfit
- a priori: 100 - 300 %- a priori: 100 - 300 %
The error estimates are calculated The error estimates are calculated twice with + and - biastwice with + and - bias..
Size distribution
0
0.05
0.1
0.15
0.1 1 10
dV/d
lnR
(m
3 /m
2 )
Radius(m)
GSFC, (0.44) = 0.7
Examples of error estimates
0
0.05
0.1
0.15
0.1 1 10
dV/d
lnR
(m
3 /m
2 )
Radius(m)
GSFC, (0.44) = 0.7
1.25
1.3
1.35
1.4
1.45
0.4 0.6 0.8 1
GSFC, (0.44) = 0.7
Re
al
Pa
rt o
f R
efr
ac
tiv
e I
nde
x
Wavelength (m)
0.6
0.7
0.8
0.9
1
0.4 0.6 0.8 1
GSFC, (0.44) = 0.07
Sin
gle
Sc
att
eri
ng A
lbe
do
Wavelength (m)
0.8
0.9
1
0.4 0.6 0.8 1
GSFC, (0.44) = 0.7
Sin
gle
Sca
tter
ing
Alb
edo
Wavelength (m)
high loading
low loading
- vector of partial derivatives in the vicinity of solution
Above is valid: - in linear approximation
- for Normal Noise - strongly dependent on a priori constraints
C ˆ x random UTC-1UU a
T Ca 1Ua -1
ˆ x bias UTC-1UU aT Ca
1Ua 1
UTC-1Ibias U aT Ca
1Iabias
Dubovik 2004
0 2 u0
T Cx random (
x bias)(
x bias)T u0
ERRORS estimates for theERRORS estimates for the functions of the retrieved parameters:functions of the retrieved parameters:
00, , PPiiii((), etc.), etc.
ˆ x
u0
Statistical variability of SSA errors
A. Sinyuk
The Second International Conference of Aerosol Science and Global ChangeAugust, 18-21, 2009, Hangzhou, China
Statistical variability of errors for sphericity parameter
A. Sinyuk
The Second International Conference of Aerosol Science and Global ChangeAugust, 18-21, 2009, Hangzhou, China
Lidar Ratio
0
0.05
0.1
0.15
0.2
0.1 1 10
5 channels (+ 1.637 m)
dV/d
lnR
(m
3 /m
2 )
Particle Radius (micron)
21:02:2004, 05:21:34, Dhabi
0.1
1
10
100
0 40 80 120 160
Spheres Spheroids
Pha
se
Fun
ctio
n (0
.532
m
)
Scattering Angle (degrees)
S() 4
0 P ,1800
S=19
S=50
0
5
10
15
20
25
30
35
40
-0.005 0 0.005 0.01 0.015
CALIOP single laser pulse
Alt
itu
de,
(km
)
Attenuated backscattering coefficient, (km)-1 (sr)-1
532 nm
0
5
10
15
20
25
30
35
40
0 0.001 0.002 0.003 0.004
Along track and vertically averegedCALIOP data
Alt
itu
de,
(km
)
Attenuated backscattering coefficient, (km)-1 (sr)-1
532 nm
CALIOP Data:
() Extinction
Lidars are sensitive to:
Optics Optics Microphysics Microphysics
Volten et al.
0
0.2
0.4
0.6
0.8
1
1.2
0.1 1 10
determined by granulometryretrieved (0.44 m)retrieved (0.63 m)
dV
/dln
r (
m3/
m3)
(no
mal
ized
to
max
imu
m)
Particle Radius (m)
a
0
0.05
0.1
0.15
0.2
0.25
0.3
0.5 1
Mixture 1 (ret. 0.44m)Mixture 3 (ret. 0.63m)Mixture 3 (from modeling) ~Mishchenko et al. 1997
dn
()/
dln
(n
orm
alized
to 1
)
Axis Ratio
b
Volten et al. 2001
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2
Mixture 1 (ret. 0.44 m)Mixture 3 (ret. 0.63 m)Mixture 3 (from modeling) ~Mishchenko et al. 1997
dn
()/
dln
Aspect Ratio
Lidar Ratio from AERONET climatology
S()4
0 P ,1800
Cattrall et al., 2005
Size Dependence of Depolarization for Randomly Oriented Spheroids
Log-normal monomodal dV(r)/dlnr : v = 0.5, = 0.44 m, n = 1.4, k = 0.005
F22/ F11
0
0.2
0.4
0.6
0.8
1
0 45 90 135 180
SPHEROIDS
Rv = 0.1Rv = 0.12Rv = 0.14Rv = 0.2Rv = 0.4Rv = 0.6Rv = 1.0Rv = 2.0Rv = 3.0Rv = 5.0
F2
2/F11
Scattering Angle (degrees)
F22()/ F11()
() 1F22 1800, F11 1800,
1F22 1800, F11 1800,
Lidar signal depolarization
0
0.1
0.2
0.3
0.4
0.5
0.1 1 10
1 10 100
Dep
ola
riza
tio
n R
atio
Volume Median Radius in m (for =0.532 m)
Effective Size Parameter
AERONET estimated broad-band AERONET estimated broad-band fluxes in fluxes in solar spectrumsolar spectrum
Size distribution
FTOA and F
BOA
FTOA and F
BOA
Fbroadband F()dmin
max
Integrations details:min = 0.2 m, max = 4.0 m; more than 200 points of integration between;Aerosol: dV/dlnR - retrieved n() and k() are interpolated/extrapolated; from n(i) and k(i) retrieved;
Radiative transfer code uses 12 moments for P11()
Surface: Surface reflection is Lambertian; Values of surface refelctance are interpolated/ extrapolated from MODIS data valuesGases: Gaseous absorption is calculated using correlated k-distributions implemented by P. Dubuisson
Validation studies:Derimian et al. 2008Garcia et al. 2008( F
BOA ~ 10% agreement )
AERONET estimated aerosol AERONET estimated aerosol forcing in forcing in solar spectrumsolar spectrum
Size distribution
Radiative forcing: ∆FTOA = F0
TOA - FTOA
∆FBOA = F0BOA - F
BOA
Radiative forcing efficiency: ∆FEff
TOA = ∆FTOA/0.55 ∆FEff
BOA = ∆FBOA/0.55
Finding by Derimian et al. 2008: importance of non-sphericity: up to 10% overestimation of ∆FTOA/BOA;
Suggested improvements by Derimian and others: Use net fluxes: ∆FBOA = (F0
BOA- F0BOA) - (F
BOA- FBOA)
Estimate daily forcing Estimates of IR fluxes/forcing
0
50
100
150
200
0
0.5
1
1.5
2
1 10Wavelength, m
Gas absorption
Aerosolextinction
C440nm
=1.0
C440nm
=0.5
Sol. R
adia
nce
,mW
cm-2st
r-1m
-1
Terr. R
adia
nce
,mW
cm-2str
-1m
-1
size
Aerosol
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Water+Soluble+Insoluble++BC
n()
k()
Shuster, et al. 2005, 2009
m()= m( a1 m1(); a2 m2(); a3 m3()) ?
Perspectives:Perspectives:
1. Improving retrieval products:- releasing dynamic errors;
- polishing Flux and Forcing products (ref: Y. Derimian talk)
- providing lidar ratios;- providing depolarizations ratios;
2. Updating scattering model:- including surface roughness for spheroids- expanding ranges of n and k
3. New Inversion developments: - inversion of polarized data (ref: Z. Li talk) - AERONET/MODIS/PARASOL (ref: A. Sinuyk talk)- AERONET/CALIPSO (ref: A. Sinuyk work )- inversion of daily data, combining with PARASOL (ref: O. Dubovik talk )- deriving composition information (ref: G. Shuster work)
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The Second International Conference of Aerosol Science and Global ChangeAugust, 18-21, 2009, Hangzhou, China
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