AERONET Skylight Retrievals Using Polarimetric Measurements Toward Physically

AERONET Skylight Retrievals Using Polarimetric Measurements: Toward Physically Consistent Validation of APS/RSP Aerosol Products Jun Wang Jing Zeng, Xiaoguang Xu Department of Earth and Atmospheric Sciences University of Nebraska – Lincoln Robert Spurr RT Solutions, Inc. Xiong Liu The Harvard Smithsonian Center for Astrophysics Michael Mishchenko, Brent Holben, Aliaksandr Sinyuk NASA Goddard Space Flight Center Qingyuan Han University of Alabama - Huntsville

Motivation 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 groundbased and in situ instruments; (2) the lack of cross-track converge … RSP algorithm Physically consistent Validation: reff, veff, mr, mi , ε, of fine & coarse aerosol The 1991 eruption of Mount Pinatubo, photo from USGS AERONET retrieval algorithm multi-angle multi- radiance + polarization

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 algorithm Dubovik 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 870 nm over many stations (primarily in Europe) since its inception in 1990 s.

c eri h osp file m At Pro HITRAN & LBLRTM GEOS-chem M, ρ of fine & coarse aerosol VLIDORT ve & c ff , mr , oar mi , ε se aer , of fin oso e l flow chart of this study LMIE LTmatrix Iterate A-B until converge ff , Single scattering properties & their Jacobian to reff, veff, mr, mi ε, of fine & coarse aerosol VL Sky radiances and polarization & their Jacobians w. r. t. reff, veff, mr, mi , , ε ID OR T Gas Absorption & Rayleigh Scattering Re A Inversion (Optimal Estimation Module) AERONET sun + sky radiance & polarization B

Forward Model Structure User’s Setting Inputs - Via a simple namelist Load Atmospheric Profiles - Z; P; T - Air & trace gas density Rayleigh Module -Bodhaine (1999) Trace Gas Module - HITRAN 2008 - Raman Aerosol Module - Linearized Mie - Scale height VLIDORT Module - Prepare VLIDORT IOP - VLIDORT: RTM solution Diagnostic Module - Output to net. CDF An undergraduate can play with it easily. Now primarily focus on the shortwave spectrum

Gas Absorption Lines SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer), Ricchiazzi, P. , 1988, BAMS. It uses LOWTRAN with spectral resolution about 5 nm in uv-visible spectrum.

Validation: Pure Rayleigh Atmosphere - Evans and Stephens (1991) Average Error o τ = 1. 0 o Upwelling at TOA I Q U Evans and Stephens 2. 1 E-4 9 E-5 7 E-5 This Model 1. 9 E-4 2 E-5 4 E-5 Relative Error (This model) 0. 05% o surface ρ = 0. 25 o cosθ 0 = 0. 8 o 8 difference θ I Q Compare with Coulson et al (1960) U 0. 14% 0. 03%

Validation: VLIDORT Jacobians w. r. t. AOT Input parameter: mid-latitude summer τ = 1. 0 scale height: 2. 0 km λ: 550 nm Θ 0=30°, 45° Θ: 10°-80° with 10° interval ϕ: 90° m = 1. 53 + 0. 001 i Log-normal size distribution Rg = 0. 1 μm σg = 1. 6 μm - Red: positive values - Green: Negative values

Validation: VLIDORT Jacobians w. r. t. ω - Jacobian of Stokes parameters with respect to aerosol single scattering albedo (ω) - Red: positive values - Green: Negative values

Validation: Jacobians of Stokes parameters w. r. t. real part of refractive index I Q U V

Validation: Jacobians of Stokes parameters w. r. t. imaginary part of refractive index I Q U V

Validation: Jacobians of Stokes parameters w. r. t. geometric mean radius I Q U V

Validation: Sensitivity of Stokes parameters w. r. t. geometric standard deviation I Q U V

Linear Tmatrix

LINEARIZED T-MATRIX CODE Robert Spurr RT Solutions, Inc. Cambridge, MA 02138, USA Jun Wang, Jing Zeng University of Nebraska, Lincoln, NE, 68588, USA Michael Mishchenko NASA 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 ak (k=1, … 6) and F-matrix F(Q) • Linearized Mie code Analytic derivatives of optical properties with respect to rr and ri (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 {rr, ri, rg, sg} instead of specifying macroscopic optical properties • Butz et al. (2009) did study for OCO measuring XCO 2, 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 Miebased applications. 9/25/2020 GLORY STM, NASA-GISS, 10 -12 August 2011 17

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 9/25/2020 and GLORY STM, NASA-GISS, 10 -12 August 2011 18

Linearized T-matrix code Linearization: § Already have T and Q-1 from T-matrix evaluation, just need to calculate derivatives of Rg Q and Q; y is one of {rr, ri, e} § Rg Q and Q made up of products of vector spherical functions § Here, x is particle size parameter k. R, hn(x) are Hankel (Bessel) functions depend on radius R(e) which is function of e § For internal field, argument is rk. R (r is the complex refractive index) need complex Bessel functions, depending on {rr, ri, e} § C, P, B are angular functions related to Wigner spherical functions, not dependent on {rr, ri, e}, no need to differentiate. 9/25/2020 GLORY STM, NASA-GISS, 10 -12 August 2011 19

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 (q, f). Expressions such as • Integrals of following type (no f, as axially symmetric) • Done by quadrature sums. E. g. for spheroids • Through-differentiation / e with respect to e. • R~(e) is equivalent sphere (ES) radius (constant for volumes) 9/25/2020 GLORY STM, NASA-GISS, 10 -12 August 2011 20

Linearized T-matrix code • ESAS representation (equivalent surface-area sphere) • E. g. Prolate spheroids (a/b = e < 1) • Just need to work through the differentiation / e • 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. 9/25/2020 GLORY STM, NASA-GISS, 10 -12 August 2011 21

Linearized T-matrix code • Start with GISS F 77 T-matrix code. Keep this. Original commentary regarding convergence issues and accuracy still applies. • Convert to modular F 90 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 F 77 code; (2) Jacobians by finite difference constructions. • Package (when finished) will be publicly available. 9/25/2020 GLORY STM, NASA-GISS, 10 -12 August 2011 22

Example 1 9/25/2020 GLORY STM, NASA-GISS, 10 -12 August 2011 23

Example 2 9/25/2020 GLORY STM, NASA-GISS, 10 -12 August 2011 24

Bi-mode log normal Sulfate (0. 07, 1. 8) Dust (0. 4, 1. 8) Fraction 0: all sulfate Fraction 1: all dust polarization is much more sensitive to the change of non-spherical large mode fraction than phase function F 11, especially at 90. . Note the scale difference 9/25/2020 GLORY STM, NASA-GISS, 10 -12 August 2011 25

Non-linear Optimal Estimation Theory Similar as Waquet et al. (2010), we use OET by Rodgers (2000) and the cost function is: the measured - the modeled difference with a priori i: iteration time step; X: retrieved state vector; Xa: a priori vector Y: 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 Instrument Error Model Error Sky radiance 5% relative error Holben et al. , 1998 5% relative error Halthore et al. , 2005 LDOP 0. 01 absolute error Dubovik et al. , 2006 0. 01 absolute error Zeng et al. , 2008 Ca: A priori covariance matrix (Ca)

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 nm total 8 retrieval parameters: rg, sigma_g, (mi, mr, ) at 3 wavelengths Surface is assumed to be well known; in this case, grassland surface. I, Q, U + Sunphometer tau + additional 2 angles I, Q, U + Sunphometer tau With I, + Sunphometer tau With I only 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 I, Q, U + Sunphometer tau + additional 2 angles I, Q, U + Sunphometer tau With I, + Sunphometer tau With I only 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 I, Q, U + Sunphometer tau + additional 2 angles I, Q, U + Sunphometer tau With I, + Sunphometer tau With I only 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.