mie scattering this type of scattering predominates for particle sizes larger than the wavelength...

Mie scattering

This type of scattering predominates for particle sizes largerthan the wavelength λ. It is characterized by an asymmetric phase function P(θ), which produces a scattering pattern similar to an antenna lobe, with a sharper and more intense forward lobe for larger particles. This scattering is not strongly λ-dependent – the reason of the appearance of almost white glare around the sun when a lot of particular (e.g. dust, soot) material is present in the air.

Validation of the 6S Radiative Transfer Code for Atmospheric Correction of MODIS dataSvetlana Y. Kotchenova ([email protected]) & Eric F. Vermote ([email protected])

Effects of polarization

Radiative Transfer Codes Purely Molecular Atmosphere

Purely Aerosol Atmosphere

scalarcodes

v e c t o r i a l c o d e s

6S (no polarization) - Second Simulation of the Satellite Signal in the Solar SpectrumThis code is based on the method of successive orders of scattering approximations. It enables accurate simulations of satellite and plane observations, accounting for elevated targets, use of anisotropic and Lambertian surfaces, and calculation of gaseous absorption.

References – (1) The 6S User Guide; (2) Vermote et al., IEEE T. Geosci. Remote, 35(3), pp.675-686, 1997.Availability – by request from E. Vermote

SHARM-1DThis code is designed to compute monochromatic radiance / fluxesin the shortwave spectral region over Lambertian and anisotropic surfaces. The atmospheric properties can be changed arbitrarily in the vertical dimension. The code is based on the modified method of spherical harmonics.

References – (1) Manual: Code SHARM-1D; (2) Muldashev et al., J. Quant. Spectrosc. Radiat. Transfer, 61(3), pp.393-404. 1999.Availability – by request from A. Lyapustin, NASA GSFC.

Monte Carlo (with polarization)In this computation one photon at a time is followed on its three-dimensional path through the atmosphere. The various events which may happen to the photon at various heights are defined by suitable probability distributions. This code is considered a ‘benchmark’ for any other RT code, as it does not have any limitations except for large amounts of calculation time and angular space discretization.

Reference – F.-M. Bréon, J. Atmos. Sci., 49, pp.1221-1232, 1992.Availability – by request from F.-M. Bréon, CEA/DSM/LSCE Gif sur Yvette, France.

DISORT – ‘Discrete Ordinates’It is one of the most heavily tested codes available for plane-parallel atmospheric models. The simulated physical properties include thermal emission, scattering, gaseous absorption, and bidirectional reflection and emission at the lower boundary. The code is based on the discrete ordinate method for radiative transfer.

Reference – (1) The DISORT Manual; (2) Stamnes et al., Appl. Optics, 27(12), pp.2502-2509, 1988.Availability – ftp://climate1.gsfc.nasa.gov/users/ftp/wiscombe

6S (with polarization)Availability – by request from E. Vermote, UMd

• Validation of the new version of 6S which accounts for light polarization against Monte Carlo (with polarization) and K.L. Coulson’s tabulated values (Coulson et al., ‘Tables Related to Radiation ...’, 1960) for a purely molecular atmosphere.

• Testing of the new version of 6S in the scalar mode. Comparison with SHARM and DISORT for purely molecular and aerosol atmospheres under different atmospheric and surface boundary conditions.

• Demonstration of the importance of the effects of polarization

Rayleigh scattering

is the scattering from molecules. The intensity of scattered light isproportional to the (– 4) degree of the incident waveform λ – themain reason why the cloudless sky is blue. This type of scattering is characterized by a symmetric phase function:

Accurate modeling of molecular scattering is especially important for satellite monitoring of ocean color and the inversion of aerosols over land, which require measurements in the blue spectral range.

where θ is the scattering angle A polarized electromagnetic wave

is described by a set of 4 Stokes’ parameters, which are related to the amplitudes of the components ( and ) of the electric field:

If an electromagnetic wave is not polarized, then

]sin[)()(2

]cos[)()(2

)()(

)()(22

22

yxyx

yxyx

yx

yx

teteV

teteU

teteQ

teteI

no

polarization

p o l a r i z a t i o n

0 VUQ

xe ye

Experimental applications of the new version of 6S (with polarization)

Objectives

Comparison study

6S (no polarization) has been tested against SHARM for several different wavelengths over a wide range of geometrical combinations of view (VZA) and solar (SZA) zenith angles and relative azimuths (AZ). The selected values of atmospheric optical thickness included 0.1 (λ ≈ 0.53 μm), 0.3445 (λ = 0.4 μm), 0.5 (λ ≈ 0.36 μm). The ground surface was assumed to be Lambertian with reflectance ρ = 0 (black soil) and ρ = 0.25.

Some results of the comparison are presented on the right. Both codes calculated the reflectance at the top of the atmosphere as an output parameter. The relative difference was calculated using SHARM as a reference.

Results

• The maximum relative difference between the outputs of 6S (no polarization) and SHARM does not exceed 0.3%. In general, the absolute difference between the codes slightly increases with the increase of VZA or optical thickness. The use of ρ = 0.25 leads to a decrease of the maximum difference to 0.2%.

• The models difference is not of concern, as it is more than 6 times less than the 2% accuracy of raw MODIS top-of-atmosphere reflectance data

Results

• The maximum relative difference between reflectances calculated by 6S (no polarization) and SHARM does not exceed 0.35%. As in the caseof the purely molecular atmosphere, the absolute difference between the codes slightly varies in dependence of VZA and optical thickness.

• DISORT and SHARM demonstrate better agreement with the maximum difference within 0.1%, which can be explained by the equivalency of the methods for the azimuthally independent component.

• Again, the models difference is negligible compared to the 2% accuracy of raw MODIS top-of-atmosphere reflectance data

Comparison study

6S (no polarization) has been tested against SHARM at λ = 0.694 μm for a wide range of geometrical combinations of SZA, VZA and AZ. The selected aerosol model was similar to the standard continental model: 70% of dust + 30% of water-soluble particles. The aerosol phase function was calculated as in SHARM. Two valuesof optical thickness, 0.072804 and 0.72804, werechosen to simulate ‘clear’ and ‘hazy’ atmosphericconditions.

6S (no polarization) and SHARM have also been compared with DISORT to make sure of a correctuse of SHARM.

Some results of the comparison are presented onthe right. In comparison between SHARM and 6S,SHARM was used as a reference. In other cases,DISORT was the reference.

Aerosol model parameters(phase function, single scattering albedo (SSA) and

asymmetry factor (g))

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.0 20.0 40.0 60.0 80.0 100.0

VZA, degrees

Ab

so

lute

dif

fere

nc

e, %

Comparison between 6S (no polarization) and SHARMpurely aerosol atmosphere, 70% of dust + 30% of water-soluble particles, optical thickness = 0.72804, SZA = {0.0; 11.48; 23.07; 32.86; 58.67}, AZ = {0; 90.0; 180.0}

Coulson 6S with P SHARM Coulson 6S with P SHARM Coulson 6S with P SHARM0.00 0.188490 0.188259 0.17184716.26 0.187900 0.187642 0.17309643.95 0.190130 0.189740 0.18691666.42 0.219760 0.219212 0.23427978.46 0.264930 0.264259 0.291785

6S/Cou SHARM/Cou 6S/Cou SHARM/Cou 6S/Cou SHARM/Cou0.00 0.12 8.8316.26 0.14 7.8843.95 0.21 1.6966.42 0.25 -6.6178.46 0.25 -10.14

Coulson 6S with P SHARM Coulson 6S with P SHARM Coulson 6S with P SHARM0.00 0.039196 0.039093 0.037716 0.039196 0.039093 0.037716 0.039196 0.039093 0.03771616.26 0.043815 0.043702 0.041975 0.039348 0.039239 0.038001 0.035380 0.035277 0.03449843.95 0.054435 0.054291 0.052691 0.042130 0.042002 0.041679 0.033870 0.033754 0.03446766.42 0.076446 0.076244 0.075864 0.057543 0.057365 0.058791 0.050685 0.050520 0.05303378.46 0.118478 0.118176 0.119793 0.093935 0.093667 0.097389 0.093935 0.093667 0.098037

6S/Cou SHARM/Cou 6S/Cou SHARM/Cou 6S/Cou SHARM/Cou0.00 0.26 3.77 0.26 3.77 0.26 3.7716.26 0.26 4.20 0.28 3.42 0.29 2.4943.95 0.26 3.20 0.30 1.07 0.34 -1.7666.42 0.26 0.76 0.31 -2.17 0.33 -4.6378.46 0.26 -1.11 0.29 -3.68 0.29 -4.37

Coulson 6S with P SHARM Coulson 6S with P SHARM Coulson 6S with P SHARM0.00 0.196483 0.196433 0.199528 0.196483 0.196433 0.199528 0.196483 0.196433 0.19952816.26 0.241067 0.240919 0.232936 0.201067 0.201020 0.204419 0.173083 0.173071 0.18537943.95 0.362167 0.362026 0.334833 0.237950 0.237923 0.243427 0.205133 0.205165 0.22459966.42 0.532033 0.531709 0.493351 0.330983 0.330847 0.340417 0.363483 0.363403 0.37409378.46 0.676767 0.676159 0.638009 0.434850 0.434524 0.447783 0.555033 0.554672 0.550409

6S/Cou SHARM/Cou 6S/Cou SHARM/Cou 6S/Cou SHARM/Cou0.00 0.03 -1.55 0.03 -1.55 0.03 -1.5516.26 0.06 3.37 0.02 -1.67 0.01 -7.1043.95 0.04 7.55 0.01 -2.30 -0.02 -9.4966.42 0.06 7.27 0.04 -2.85 0.02 -2.9278.46 0.09 5.73 0.07 -2.97 0.07 0.83

Difference, %

VZAAZ=0 AZ=90 AZ=180

SZA = 0.0, optical thickness = 0.5

purely molecular atmosphereValidation of 6S (with polarization) against Coulson's tabulated values (example)



VZA

Difference, %




AZ=90 AZ=180

Difference, %


AZ=0

Comparison study

6S (with polarization) and SHARM have been tested against Coulson’s tabulated values (which, according to S. Chandrasekhar, represent the complete solution for the Rayleigh problem) for the case of a purely molecular atmosphere with optical thickness of 0.1 and 0.5, for a wide range of geometrical conditions. 6S (with polarization) has also been tested against Monte Carlo for a purely molecular atmosphere with optical thickness of 0.35 (λ = 0.4 μm), for SZA = {0.0, 23.0, 57.0}

0

5

10

15

20

0.0

7.3

27.3

57.0

91.8

126.

3

155.

2

174.

1

Scattering angle

Ph

ase

fun

ctio

n

SSA = 0.9398g = 0.6969

Conclusions

1. Ignorance of the effects of light polarization leads to large errors in calculated top-of-atmosphere reflectances. The maximum relative error is more than 10% for a purely molecular atmosphere and is up to 5% for a purely aerosol atmosphere.

2. The new vectorial version of 6S, which accounts for polarization, has demonstrated good agreement with Monte Carlo and Coulson’s tabulated values for a wide range of geometrical and atmospheric conditions. The agreement is better than 0.5% for Monte Carlo and 0.3% for Coulson’s.

3. The new vectorial version of 6S, used in the scalar mode, has demonstrated good agreement with the scalar code SHARM: better than 0.3% for a purely molecular atmosphere and better than 0.35% for a purely aerosol atmosphere.

4. Account for light polarization is extremely important for atmospheric correction of remotely sensed data, especially those measured over dark targets, such as ocean surface or dark dense vegetation canopies.

We would like to thank F.-M. Bréon for providing the Monte Carlo code and A. Lyapustin for providing the SHARM-1D code. We would also like to thank both of them for helpful discussions and suggestions during this study. This work was supported by NASA contract NNG04HZ17C.

How to account for light polarization?

To make a scalar code account for polarization, one needs

• to modify the molecular phase function to account for dipole moments of molecules;

• to add new components to the aerosol scattering phase function to describe the polarization state of scattered light.It means the replacement of ‘the MIE subroutine’.

• to add 3 new components ( ) describing polarization to the radiative transfer part of the code. It means the replacementof the radiative transfer part (or the core) of the code.

Ocean surface reflectance

MODIS AQUA data, collected over the Hawaii islands, have been corrected using the new version of the 6S code (with polarization) and AERONET measurements collected at Lanai island. The graph below shows the results of the comparison of surface reflectances measured by MOBY (the Marine Optical Buoy System) just above the ocean surface with AQUA estimated reflectances at λ={412; 443; 490; 530; 550; 667; 678} nm. The MOBY measurements were conducted during the year of 2003 on January 2, February 1, February 10, September 3, September 19, October 6, October 22.

The agreement between the corrected AQUA and the MOBY surface reflectances was 0.001 to 0.002 for the 400-550 nm region.

Biomass burning smoke

Surface reflectances calculated with the scalar (no polarization) and the vectorial (with polarization) versions of 6S have been compared for a ‘biomass burning smoke’ aerosol model to study the effects of polarization for an aerosol atmosphere. The selected aerosol model is a typical pattern produced by forest fires over the Amazonian tropical forest region in Brazil (O. Dubovik et al., J. Atmos. Sci., 59, pp.590-608, 1996). The comparisonwas made for λ = 0.67 μm. The results of the comparison showedthat the relative difference between the atmospheric reflectances,calculated with and without account for light polarization, can beas large as 5%.

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90

VZA, degrees

Ab

so

lute

dif

fere

nc

e, %

6S (with polarization) vs. 6S (no polarization)biomass burning aerosol model, optical thickness = 0.72804,SZA = {0.0; 11.48; 23.07; 32.86; 58.67}, AZ = {0; 90.0; 180.0}

0

0.02

0.04

0.06

0.08

0.1

0.05 0.11 0.26 0.58 1.30 2.94 6.64 15.00

Average aerosol volume size distribution(from AERONET measurements)

radius, μm

dV/d

lnr,

(μ

m3/μ

m2)

SSA = 0.9237g = 0.585

factortiondepolarizathewherePP

0279.0),cos)1(1()2(2

3)()cos1(

4

3)( 22

easy

relatively easy

VUQ ,,

not easy at all

,)cos1(4

3)( 2 P

6S no P SHARM Diff., % 6S no P SHARM Diff., % 6S no P SHARM Diff., %0.00 0.171755 0.171847 0.0516.26 0.172999 0.173096 0.0643.95 0.186778 0.186916 0.0766.42 0.234046 0.234279 0.1078.46 0.291417 0.291785 0.13

6S no P SHARM Diff., % 6S no P SHARM Diff., % 6S no P SHARM Diff., %0.00 0.037670 0.037716 0.12 0.037670 0.037716 0.12 0.037670 0.037716 0.1216.26 0.041925 0.041975 0.12 0.037951 0.038001 0.13 0.034448 0.034498 0.1443.95 0.052621 0.052691 0.13 0.041609 0.041679 0.17 0.034395 0.034467 0.2166.42 0.075725 0.075864 0.18 0.058655 0.058791 0.23 0.052894 0.053033 0.2678.46 0.119525 0.119793 0.22 0.097127 0.097389 [ 0.27 ] 0.097767 0.098037 [ 0.27 ]

6S no P SHARM Diff., % 6S no P SHARM Diff., % 6S no P SHARM Diff., %0.00 0.199325 0.199528 0.10 0.199325 0.199528 0.10 0.199325 0.199528 0.1016.26 0.232722 0.232936 0.09 0.204205 0.204419 0.11 0.185162 0.185379 0.1243.95 0.334549 0.334833 0.08 0.243129 0.243427 0.12 0.224300 0.224599 0.1366.42 0.492756 0.493351 0.12 0.339829 0.340417 0.17 0.373486 0.374093 0.1678.46 0.636885 0.638009 0.18 0.446680 0.447783 0.25 0.549265 0.550409 0.21





Validation of 6S (no polarization) against SHARM (example)purely molecular atmosphere



6S no P DISORT SHARM 6S no P DISORT SHARM 6S no P DISORT SHARM0.00 0.046585 0.046584 0.046582 0.046585 0.046584 0.046582 0.046585 0.046584 0.04658211.48 0.051380 0.051371 0.051369 0.047222 0.047218 0.047216 0.044200 0.044197 0.04419516.26 0.060293 0.060277 0.060275 0.047660 0.047653 0.047652 0.043361 0.043356 0.04335423.07 0.071673 0.071657 0.071655 0.048244 0.048231 0.048229 0.043588 0.043580 0.04357832.86 0.062714 0.062689 0.062687 0.049787 0.049761 0.049758 0.047908 0.047891 0.04788843.95 0.064584 0.064525 0.064523 0.055232 0.055183 0.055179 0.060269 0.060239 0.06023350.21 0.070228 0.070148 0.070146 0.061233 0.061165 0.061160 0.072104 0.072064 0.07205658.67 0.077234 0.077117 0.077115 0.073893 0.073795 0.073789 0.096017 0.095965 0.09595366.42 0.085523 0.085362 0.085359 0.090878 0.090745 0.090736 0.128397 0.128338 0.12832071.34 0.092051 0.091852 0.091849 0.103965 0.103805 0.103793 0.154468 0.154408 0.15438473.74 0.095277 0.095055 0.095052 0.110563 0.110386 0.110372 0.168288 0.168229 0.16820078.46 0.100223 0.099947 0.099943 0.121955 0.121740 0.121720 0.194687 0.194637 0.19459480.79 0.101000 0.100694 0.100690 0.125449 0.125215 0.125190 0.205186 0.205152 0.20509784.26 0.098413 0.098086 0.098082 0.125610 0.125385 0.125345 0.213609 0.213671 0.21358186.56 0.093541 0.093281 0.093277 0.121385 0.121266 0.121202 0.212612 0.212897 0.212748

6S/SHARM SHARM/DIS 6S/DIS 6S/SHARM SHARM/DIS 6S/DIS 6S/SHARM SHARM/DIS 6S/DIS0.00 -0.01 0.00 0.00 -0.01 0.00 0.00 -0.01 0.00 0.0011.48 -0.02 0.00 -0.02 -0.01 0.00 -0.01 -0.01 0.00 -0.0116.26 -0.03 0.00 -0.03 -0.02 0.00 -0.02 -0.02 0.00 -0.0123.07 -0.02 0.00 -0.02 -0.03 0.00 -0.03 -0.02 0.00 -0.0232.86 -0.04 0.00 -0.04 -0.06 0.01 -0.05 -0.04 0.01 -0.0343.95 -0.09 0.00 -0.09 -0.10 0.01 -0.09 -0.06 0.01 -0.0550.21 -0.12 0.00 -0.11 -0.12 0.01 -0.11 -0.07 0.01 -0.0658.67 -0.15 0.00 -0.15 -0.14 0.01 -0.13 -0.07 0.01 -0.0566.42 -0.19 0.00 -0.19 -0.16 0.01 -0.15 -0.06 0.01 -0.0571.34 -0.22 0.00 -0.22 -0.17 0.01 -0.15 -0.05 0.02 -0.0473.74 -0.24 0.00 -0.23 -0.17 0.01 -0.16 -0.05 0.02 -0.0378.46 -0.28 0.00 -0.28 -0.19 0.02 -0.18 -0.05 0.02 -0.0380.79 -0.31 0.00 -0.30 -0.21 0.02 -0.19 -0.04 0.03 -0.0284.26 [ - 0.34 ] 0.00 -0.33 -0.21 0.03 -0.18 -0.01 0.04 0.0386.56 -0.28 0.00 -0.28 -0.15 0.05 -0.10 0.06 0.07 0.13

purely aerosol atmosphere, 70% dust + 30% water soluble, optical thickness = 0.72804SZA = 23.07


Difference, %

Comparison between 6S (no polarization), SHARM and DISORT (example)


y = 1.0223x - 0.0007

R2 = 0.9868

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.01 0.02 0.03 0.04 0.05

measured reflectances

mo

dis

re

flec

tan

ce

s A

QU

A r

elfe

cta

nce

s

measured reflectances

*MOBY

larger particles

direction of incident light

direction of incident light

VZA / AZ 0 - 22.5 22.5 - 45.0 45.0 - 67.5 67.5 - 90.0 90.0 - 112.5 112.5 - 135.0 135.0 - 157.5 157.5 - 180.0

0 - 15.0 0.141392 0.140024 0.137726 0.134632 0.131336 0.128316 0.126339 0.12512715.0 - 21.4 0.149480 0.146802 0.142264 0.136045 0.130543 0.125353 0.121469 0.11931221.4 - 26.6 0.154810 0.151213 0.145188 0.137854 0.130303 0.123471 0.118742 0.11618926.6 - 31.1 0.160085 0.155630 0.148338 0.139238 0.130068 0.122724 0.117008 0.11441431.1 - 35.3 0.164071 0.159645 0.151428 0.140618 0.130927 0.122350 0.116434 0.11327835.3 - 39.2 0.168545 0.163406 0.154425 0.142627 0.131716 0.122545 0.116189 0.11302739.2 - 43.1 0.173703 0.167464 0.157287 0.144918 0.133013 0.123396 0.116943 0.11369343.1 - 46.9 0.178582 0.172319 0.161152 0.147416 0.135074 0.124935 0.118266 0.11538446.9 - 50.8 0.184905 0.177741 0.165435 0.151187 0.137976 0.127667 0.121061 0.11808850.8 - 54.7 0.191733 0.183394 0.170767 0.155666 0.141877 0.131728 0.125334 0.12257954.7 - 58.9 0.199675 0.191292 0.177453 0.161666 0.147625 0.137484 0.131519 0.12885658.9 - 63.4 0.210228 0.201577 0.186510 0.170226 0.155980 0.146217 0.141101 0.13886363.4 - 68.6 0.225009 0.215701 0.200005 0.183053 0.168814 0.160282 0.155895 0.15500268.6 - 75.0 0.249403 0.238998 0.222026 0.204574 0.191857 0.184872 0.182682 0.183046

0.132947

VZA / AZ 0 - 22.5 22.5 - 45.0 45.0 - 67.5 67.5 - 90.0 90.0 - 112.5 112.5 - 135.0 135.0 - 157.5 157.5 - 180.0

0 - 15.0 0.141419 0.140075 0.137639 0.134528 0.131255 0.128312 0.126123 0.12495515.0 - 21.4 0.149105 0.146565 0.141984 0.136225 0.130279 0.125048 0.121217 0.11920621.4 - 26.6 0.154582 0.151201 0.145145 0.137622 0.129971 0.123357 0.118591 0.11611726.6 - 31.1 0.159430 0.155325 0.148030 0.139058 0.130059 0.122408 0.116979 0.11419731.1 - 35.3 0.164043 0.159288 0.150885 0.140654 0.130533 0.122062 0.116151 0.11315935.3 - 39.2 0.168638 0.163278 0.153857 0.142500 0.131419 0.122301 0.116049 0.11292939.2 - 43.1 0.173438 0.167495 0.157115 0.144724 0.132809 0.123185 0.116716 0.11354043.1 - 46.9 0.178650 0.172137 0.160827 0.147475 0.134839 0.124842 0.118282 0.11512546.9 - 50.8 0.184495 0.177415 0.165204 0.150954 0.137711 0.127490 0.120972 0.11791750.8 - 54.7 0.191262 0.183611 0.170515 0.155436 0.141710 0.131428 0.125114 0.12225954.7 - 58.9 0.199508 0.191271 0.177291 0.161444 0.147384 0.137249 0.131347 0.12882258.9 - 63.4 0.210218 0.201358 0.186472 0.169930 0.155733 0.146044 0.140853 0.13884963.4 - 68.6 0.225337 0.215788 0.199960 0.182831 0.168828 0.160080 0.156104 0.15493668.6 - 75.0 0.249754 0.239395 0.222570 0.205114 0.191998 0.185218 0.183493 0.183812

0.13276

VZA / AZ 0 - 22.5 22.5 - 45.0 45.0 - 67.5 67.5 - 90.0 90.0 - 112.5 112.5 - 135.0 135.0 - 157.5 157.5 - 180.0

0 - 15.0 -0.02 -0.04 0.06 0.08 0.06 0.00 0.17 0.1415.0 - 21.4 0.25 0.16 0.20 -0.13 0.20 0.24 0.21 0.0921.4 - 26.6 0.15 0.01 0.03 0.17 0.25 0.09 0.13 0.0626.6 - 31.1 0.41 0.20 0.21 0.13 0.01 0.26 0.02 0.1931.1 - 35.3 0.02 0.22 0.36 -0.03 0.30 0.24 0.24 0.1135.3 - 39.2 -0.06 0.08 0.37 0.09 0.23 0.20 0.12 0.0939.2 - 43.1 0.15 -0.02 0.11 0.13 0.15 0.17 0.19 0.1343.1 - 46.9 -0.04 0.11 0.20 -0.04 0.17 0.07 -0.01 0.2246.9 - 50.8 0.22 0.18 0.14 0.15 0.19 0.14 0.07 0.1450.8 - 54.7 0.25 -0.12 0.15 0.15 0.12 0.23 0.18 0.2654.7 - 58.9 0.08 0.01 0.09 0.14 0.16 0.17 0.13 0.0358.9 - 63.4 0.00 0.11 0.02 0.17 0.16 0.12 0.18 0.0163.4 - 68.6 -0.15 -0.04 0.02 0.12 -0.01 0.13 -0.13 0.0468.6 - 75.0 -0.14 -0.17 -0.25 -0.26 -0.07 -0.19 [ -0.44 ] -0.42

0.14

Nadir viewing

Nadir viewing

Nadir viewing

Validation of 6S against Monte Carlo (example)

Monte Carlo (with polarization), 1 billion photons, SZA = 23.0

6S (with polarization), SZA = 23.0

Difference, % (reference - MC)

pure molecular atmosphere, optical thickness = 0.35

mie scattering this type of scattering predominates for particle sizes larger than the wavelength...

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