AERONET Skylight Retrievals Using Polarimetric Measurements: Toward Physically Consistent Validation of
APS/RSP Aerosol Products
Jun WangJing Zeng, Xiaoguang Xu
Department of Earth and Atmospheric SciencesUniversity of Nebraska – Lincoln
Robert SpurrRT Solutions, Inc.
Xiong LiuThe Harvard Smithsonian Center for Astrophysics
Michael Mishchenko, Brent Holben, Aliaksandr Sinyuk NASA Goddard Space Flight Center
Qingyuan HanUniversity of Alabama - Huntsville
Motivation
The 1991 eruption of Mount Pinatubo, photo from USGS
The validation of APS aerosol product has two major challenges (Mishchenko et al., BAMS, 2007): (1)the expected accuracy … is unlikely to be matched by most ground-based and in situ instruments; (2) the lack of cross-track converge …
Physically consistent Validation: reff, veff, mr, mi , ε,
of fine & coarse aerosol
multi-angle multi-radiance + polarization
RSP algorithm
AERONET retrieval algorithm
Current AERONET retrieval algorithm
Dubovik and King (2000): designed a flexible inversion algorithms and original Nakajima and King’s algorithm was replaced.
Dubovik et al. (2000): accuracy assessment of the new algorithmDubovik et al. (2006): Spheroid consideration in the retrieval…
• Limited use of Polarization; not used in the operational retrieval • While AERONET inversion products significantly advanced our understanding
of aerosol properties, they, similar as any other retrievals, have limitations:• the inversion of aerosol refractive indices and single scattering albedo is only
reliable in conditions of high AOT (>0.4 at 0.4μm) and at high solar zenith angle (>50º).
• most products are reported at the 68% confidence level; • single scattering albedos for both the fine and coarse modes are estimated, but
they are not advised for use, since the inversion algorithms assume the same complex refractive indices for all particle size;
• this refractive index limitation can lead to large errors in retrieval of size distributions when the refractive indices for fine mode and coarse mode aerosols have large difference; and
• Other inconsistence with RPS• size distribution: bin (AERONET) vs. log-normal (RPS)
“A preliminary analysis shows that adding polarization in the inversion can reduce possible errors (notably for about 30% of our field cases) in the fine mode size distribution, real part of refractive index and particle shape parameter retrievals, especially for small particles.”
• A theoretical framework to study and retrieve the aerosol information content from ground-based polarimetric instrument is highly needed.
• AERONET collects polarization data at 870nm over many stations (primarily in Europe) since its inception in 1990s.
HITRAN &LBLRTM
GEOS-chemAtm
ospheric
Profile
LMIELTmatrix
Reff , v
eff , mr , m
i , ε, of fine
& coarse aerosol
VLIDORT
Gas Absorption
&Rayleigh
Scattering
Single scattering properties & their
Jacobian to reff, veff, mr, mi ε
M, ρ of fine & coarse aerosol
Sky radiances and polarization & their Jacobians w.r.t. reff, veff, mr, mi , , ε
AERONET sun + sky radiance & polarization
VLIDORT
flow chart of this study
Inversion(Optimal Estimation
Module)
reff, veff, mr, mi ε, of fine & coarse aerosol
Forward Model Structure
User’s Setting Inputs
- Via a simple namelist
User’s Setting Inputs
- Via a simple namelist
Load Atmospheric Profiles
- Z; P; T- Air & trace gas density
Load Atmospheric Profiles
- Z; P; T- Air & trace gas density
Trace Gas Module
- HITRAN 2008- Raman
Trace Gas Module
- HITRAN 2008- Raman
Diagnostic Module
- Output to netCDF
Diagnostic Module
- Output to netCDF
Aerosol Module
- Linearized Mie- Scale height
Aerosol Module
- Linearized Mie- Scale height
Rayleigh Module
-Bodhaine (1999)
Rayleigh Module
-Bodhaine (1999)
VLIDORT Module
- Prepare VLIDORT IOP- VLIDORT: RTM solution
VLIDORT Module
- Prepare VLIDORT IOP- VLIDORT: RTM solution An undergraduate can
play with it easily.
Now primarily focus on the shortwave spectrum
SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer), Ricchiazzi,P., 1988, BAMS. It uses LOWTRAN with spectral resolution about 5 nm in uv-visible spectrum.
Gas Absorption Lines
- Evans and Stephens (1991)
o τ = 1.0
o Upwelling at TOA
o surface ρ = 0.25
o cosθ0 = 0.8
o 8 difference θ
Average Error
I Q U
Evans and Stephens 2.1E-4 9E-5 7E-5
This Model 1.9E-4 2E-5 4E-5
Relative Error(This model) 0.05% 0.14% 0.03%
Compare with Coulson et al (1960)
I UQ
Validation: Pure Rayleigh Atmosphere
- Red: positive values- Green: Negative values
Validation: VLIDORT Jacobians w.r.t. AOT
Input parameter:
mid-latitude summerτ = 1.0 scale height: 2.0 kmλ: 550nmΘ0=30°, 45°Θ: 10°-80° with 10° intervalϕ: 90°m = 1.53 + 0.001 i
Log-normal size distributionRg = 0.1 μmσg = 1.6 μm
- Jacobian of Stokes parameters with respect to aerosol single scattering albedo (ω)
- Red: positive values- Green: Negative values
Validation: VLIDORT Jacobians w.r.t. ω
Validation: Jacobians of Stokes parameters w.r.t. real part of refractive index
I
U
Q
V
Validation: Jacobians of Stokes parameters w.r.t. imaginary part of refractive index
I
U
Q
V
Validation: Jacobians of Stokes parameters w.r.t. geometric mean radius
I
U
Q
V
Validation: Sensitivity of Stokes parameters w.r.t. geometric standard deviation
I
U
Q
V
Linear Tmatrix
LINEARIZED T-MATRIX CODE
Robert SpurrRT Solutions, Inc.Cambridge, MA 02138, USA
Jun Wang, Jing ZengUniversity of Nebraska, Lincoln, NE, 68588, USA
Michael MishchenkoNASA GISS, 2880 Broadway, New York, NY 10025, USA
GLORY STM, 10-12 August 2011, NASA-GISS
Linearized T-matrix code• Mie code was linearized several years ago by 3 groups including RT Solutions.• Macroscopic optical properties: Extinction and scattering coefficients Cext and
Csca, scattering matrix expansion coefficients k (k=1,…6) and F-matrix F()• Linearized Mie code Analytic derivatives of optical properties with respect
to r and i (refractive index components)• Also Analytic derivatives of polydispersed properties w.r.t PSD parameters
such as mode radius rg and standard deviation sg for Lognormal• From polarization measurements, you can retrieve microscopic aerosol
properties {r, i, rg, sg} instead of specifying macroscopic optical properties• Butz et al. (2009) did study for OCO measuring XCO2, much better able to
characterize aerosols in the retrieval using combination of linearized Mie code and linearized Vector RT model.
• We have developed combined Mie/VLIDORT tool for looking at ground-based Aeronet data as part of our participation in the GLORY Science Team.
• Extension to T-matrix capability has potential to extend the reach of Mie-based applications.
04/20/23 17GLORY STM, NASA-GISS, 10-12
August 2011
Linearized T-matrix code• Maxwell’s theory is linear! Should be analytically differentiable• Electromagnetic Field, vector spherical function expansion:
• T-matrix, linear relation between incident and scattered fields
where and
max
1
)()()(n
n
n
nmmnmnmnmninc kRgbkRga RNRMRE
max
1
)()()(n
n
n
nmmnmnmnmnpar kRgdkRgc RNRMRE
max
1
)()()(n
n
n
nmmnmnmnmnsca kqkp RNRMRE
1Rg QQT
b
a
TT
TT
b
aT
q
p2221
1211
d
c
b
a2221
1211
d
c
q
p2221
1211
RgRg
RgRg
04/20/23 18GLORY STM, NASA-GISS, 10-12
August 2011
Linearized T-matrix code
Linearization:
Already have T and Q from T-matrix evaluation, just need to calculate derivatives of Rg Q and Q; y is one of {r, i, }
Rg Q and Q made up of products of vector spherical functions
Here, x is particle size parameter kR, hn(x) are Hankel (Bessel) functions depend on radius R() which is function of
For internal field, argument is kR ( is the complex refractive index) need complex Bessel functions, depending on {r, i, }
C, P, B are angular functions related to Wigner spherical functions, not dependent on {r, i, }, no need to differentiate.
1][][Rg
TQT
yyy
04/20/23 19GLORY STM, NASA-GISS, 10-12
August 2011
)exp()()()1()( )1( imxhdkR mnnnm
mn CM
)exp()()(1
)()()1(
)1()( )1()1( imxxhxx
xhkR
nndkR mnnmnnn
mmn
BPN
Linearized T-matrix code• Bessel functions developed by simple recursion relations, easy to
differentiate. Applies equally to Mie and T-matrix.• Surface area integration (T-matrix). r = r Expressions such as
• Integrals of following type (no , as axially symmetric)
• Done by quadrature sums. E.g. for spheroids
• Through-differentiation / with respect to .• R~() is equivalent sphere (ES) radius (constant for volumes)
04/20/23GLORY STM, NASA-GISS, 10-12
August 201120
S nmmn
mmnnm krkrRgrdST ),,(),,()(ˆ)1(11 MMn
0
2
0
dsin),(;dsin),( rr
rGJrrFJ r
222
2
222 cossin
cossin)1()(1;
cossin
)(~
)(21
31
r
r
Rr
Linearized T-matrix code• ESAS representation (equivalent surface-area sphere)
• E. g. Prolate spheroids (a/b = < 1)
• Just need to work through the differentiation / • So far, monodisperse. For polydisperse, need only to
differentiate PSD functions n(r) with respect to their parameters such as rg and sg for Lognormal.
• Through-differentiate the PSD numerical integration. Applies equally to Mie and T-matrix.
04/20/23GLORY STM, NASA-GISS, 10-12
August 201121
213
1
4
)()(;
)()(;
)(
)(~)(
~)(
~
3400
A
EV
EE
ERSRR AV
A
V
21
31
2)(;1
1arcsin122)(;
3
4)(
2
222
2
HSaHaA
baV
Linearized T-matrix code
• Start with GISS F77 T-matrix code. Keep this. Original commentary regarding convergence issues and accuracy still applies.
• Convert to modular F90 code, implicit none, explicit Intent (in/out/inout) statements, no Common blocks or Equivalences.
• Additional PSD specifications from Meerhoff (Dutch) Mie code• Add linearization code. 2 “masters”, one just regular optical property
output, other with regular + additional linearized output.• Package has configuration-file input with new linearization flags and
additional control options (e.g. optional F-matrix).• Kept original names for the most part. Much of the original code still
intact and in use. Continue using LAPACK utility for Matrix inversion• Validation (1) optical properties against original F77 code; (2)
Jacobians by finite difference constructions.• Package (when finished) will be publicly available.
04/20/23GLORY STM, NASA-GISS, 10-12
August 201122
Example 1
04/20/23GLORY STM, NASA-GISS, 10-12
August 201123
Example 2
04/20/23GLORY STM, NASA-GISS, 10-12
August 201124
04/20/23GLORY STM, NASA-GISS, 10-12
August 201125
Bi-mode log normalSulfate (0.07, 1.8)Dust (0.4, 1.8) Fraction 0: all sulfateFraction 1: all dust
polarization is much more sensitive to the change of non-spherical large mode fraction than phase function F11, especially at 90..
Note the scale difference
Non-linear Optimal Estimation Theory
i: iteration time step; X: retrieved state vector; Xa: a priori vectorY: is the measurement vector; Ki is the Jacobian or weighting function matrix, defined as ∂F/∂Xi
Total error covariance matrix CT: = instrument + forward model error
Ca: A priori covariance matrix (Ca)
Similar as Waquet et al. (2010), we use OET by Rodgers (2000) and the cost function is:
Instrument Error Model Error
Sky radiance
5% relative error Holben et al., 1998
5% relative errorHalthore et al., 2005
LDOP 0.01 absolute errorDubovik et al., 2006
0.01 absolute error Zeng et al., 2008
the measured - the modeled difference with a priori
Non-linear Optimal Estimation Solutions
The optimal solution is:
Solution error covariance matrix for the retrieved parameters
We can also attribute the model and instrument errors to the error budget of retrieved parameters.
Theoretical retrieval of information content
In primarily plane, VZA=0, 10 at RAZ=0 and 180. Dust-like aerosols.3 wavelengths: 380, 470, and 670 nmtotal 8 retrieval parameters: rg, sigma_g, (mi, mr,) at 3 wavelengthsSurface is assumed to be well known; in this case, grassland surface.
With I only
With I, + Sunphometer tau
I, Q, U + Sunphometer tau
I, Q, U + Sunphometer tau + additional 2 angles
Adding polarization increases information content by 10%-40%, depending on SZA.
Theoretical retrieval of information content
In primarily plane, VZA=0, 10 at RAZ=0 and 180. Dust-like aerosols.Three wavelengths; total 8 retrieval parameters: rg, sigma_g, (mi, mr,) at 3 wavelengths
With I only
With I, + Sunphometer tau
I, Q, U + Sunphometer tau
I, Q, U + Sunphometer tau + additional 2 angles
The information content of refractive index, in particular, real part refractive index, can be better retrieved by adding polarization.
Theoretical retrieval of information content
In primarily plane, VZA=0, 10 at RAZ=0 and 180. Dust-like aerosols.Three wavelengths; total 8 retrieval parameters: rg, sigma_g, (mi, mr,) at 3 wavelengths
With I only
With I, + Sunphometer tau
I, Q, U + Sunphometer tau
I, Q, U + Sunphometer tau + additional 2 angles
The retrieval of refractive index, in particular, real part refractive index, can be significantly improved by adding polarization measurements at more angles.
Summary and next steps
• A modeling framework is developed to study the information content for aerosol retrievals using multispectral and multiangle sky radiance and polarization data (such as those collected by AERONET)
• A combination of VLIDORT with linearized Mie and Tmatrix codes will be a powerful tool for a formal inversion of aerosol parameters; it will be a useful tool for the retrieval community.
• Multi-angle polarization data are key for retrieval of refractive index, size, and shape of the particle.
• We plan to streamline the codes, and start the retrieval using AERONET data in fall, as well as any other sky radiance and polarization data collected from various field campaigns.
• Last but not least, we like to work with the Glory team’s research strategy (with RSP instrument) and plan well for our next steps.