1

'SCATRD' code for calculation of multiple scattering

solar radiation in the spherical atmosphere. First

application to Omega MEX limb aerosol profiles.

Alexander V. Vasilyev,Russia, Sankt-Petersburg, Research Institute of Physics of Sankt-Petersburg State University,

Bogdan S. Mayorov,Russia, Moscow, Space Research Institute of the Russian Academy of Sciences,

Liudmila V. Zasova,Russia, Moscow, Space Research Institute of the Russian Academy of Sciences,

Jean-Pierre Bibring,France, Orsay, L'Institut d'Astrophysique Spatiale, CNRS-Universite de Paris 11,

Anna A. Fedorova,Russia, Moscow, Space Research Institute of the Russian Academy of Sciences.

2006-10-19 Russia, Moscow, Space Research Institute of the Russian Academy of Sciences.

The conference consecrate to forty years French-Russian cooperation in space science,session “Planetary studies and future missions” devoted to 75-anniversary of V. I. Moroz.

2

Goals of research

Global:

- orbital spectrometric observed data analysis with account for the sphericity of the planetary atmosphere and surface.

Local (current):

- testing of the code for calculation of scattered solar radiation in the spherical atmosphere based on Monte-Carlo method (code SCATRD);

- adaptation of base code for calculation monochromatic intensity in orbital spectrometric observations (subroutine SCATRD-OFOS);

- Omega’s limb aerosol profiles simple analyses.

3

General theoretic notes and approximations

- Scalar equation (no polarization).- Linear theory (for extinction and generation of radiation processes).- No redistribution of radiation energy on wavelengths.

Scalar radiation transfer equation (in differential form):

tzyxII ,,,,,

- Phenomenological approach

Spectral (on wavelength , monochromatic) intensity (in the Cartesian coordinate system

Cxyz):

It

I

c

n

n

I

dn

22

de de

n - index of refraction;

- coefficient of extinction;

- coefficient of emission.

- unitary vector of direction; t – time.

- Stationary field of radiation:

- , no refraction .

Scalar stationary radiation transfer equation in invariant form:

d

I

t

I

c

n

2

constn 1n

IIed ,

4

Code SCATRD: common informationAuthor: Alexander V. Vasilyev.

Reference: Vestnik Sankt-Peterburgskogo Universiteta, ser. 4., vyp. 3, 2006 (in press; in Russian)

Current version: 05.24.

Target: numerical simulation of solar multiple scattering radiation monochromatic intensity and its derivatives in spherical geometry atmosphere.

Features: - platform: Fortran-77;- detailed theory description, documentation and user guide (in Russian);- optical atmospheric parameters are piecewise linear continuous functions of altitude

(inhomogeneous layers);- derivatives with respect to input atmospheric and surface parameters;- molecular scattering (for the Earth only);- analytic (Henyey-Greenstein) or look-up table (arbitrary) phase functions;- two reflection models of radiation from surface: ideal mirror and isotropic;- single‑ and double-scattering approximations calculations by analytical formulas and

algorithm for calculations of multiple scattering radiation by Monte‑Carlo technique;- detailed settings for calculations.

5

Code SCATRD: main approximation

- Spherical shape of the planetary solid body with radius R > 0;

- Spherically-symmetrical optical atmospheric and surface properties.

C – center of the planet

Spherical symmetry:

6

Code SCATRD: geometry of observation

Based on observation point D (point of detector or observer).

Detector can not be situated inside solid planetary body ( );

- unitary external normal to the surface at D.

RCD

ne

RCDhd

7

Code SCATRD: geometry of observation

- unitary vector of direction to the Sun (Sun is infinitely far from observation region: no solar parallax).se

8

Code SCATRD: geometry of observation

- unitary vector of boresight.Four independent parameters determine geometry of observation completely.ve

9

Code SCATRD: other approximations

- stationarity;

- no refraction;

- monochromatic intensity, no redistribution of radiation energy on wavelengths;

- no polarization;

- no thermal radiation and non-LTE processes;

- incidence solar radiation: a beam of parallel-propagating photons.

10

Code SCATRD: testingSome simple, obvious tests:

Test 1: Calculated intensity is even function of azimuth ( ):v

11

Code SCATRD: testingTest 2: If the Sun in zenith ( ), intensity doesn’t depend on azimuth ( ).0zs v

12

Code SCATRD: testingTest 3: Increasing of volume absorption coefficient (for whole atmosphere or for any

atmospheric level) leads to decreasing of intensity:

13

Code SCATRD: testingTest 4: The more surface albedo of isotropic reflection model, the more intensity.

14

Code SCATRD: testingOther tests:

- the less volume scattering coefficient, the closer intensity to the single-scattering

radiation;

- tests based on other asymptotic expressions and comparisons with analytical

solutions for some special cases;

- comparison (validation) of results with SCIATRAN code

[Rozanov A., Rozanov V., Buchwitz M., et al.; Adv. in Space Research, 2005, vol. 36, N 5, pp. 1015-1019],

average deviation = 3,4 %

Many successful calculations with various atmospheric, surface and geometrical

observational parameters.

15

Adaptation for orbital spectral observations

Subroutine SCATRD-OFOS based on computer SCATRD code.

Authors: Bogdan S. Mayorov and Alexander V. Vasilyev.

Current version: 05-06.10.15

Target: numerical simulation of solar multiple scattering radiation monochromatic intensity in spherical geometry atmosphere specially for observation from

orbit.

Features:- platform: Fortran-90 (Fortran-90 subroutine interface);- description, documentation and user guide;- determination of observation geometry is adapted for orbital spacecraft;- tabular (arbitrary) phase functions;- isotropic reflection of radiation from surface model;- detailed settings for calculations;- computation act time ~ 1 second (Windows XP, Intel Pentium 4 (2.8 GHz), System memory 2 Gb).

16

SCATRD-OFOS: geometry of observationsAnalogically to Omega and PFS Mars express:

ReRssRhd cos222

eRssR

seRz

cos2

cosarccos

22v

eRssR

siRzs

cos2

coscosarccos

22

,0z 0,e ,coscoscos2sinsinsin

coscoscoscoscoscosRarccos s2222v

ieRssiRe

eisei

eRssR

es

cos2

sinarccosz

22v

Coordinate transformations:

180zs

17

SCATRD-OFOS: example of calculationThe atmosphere was divided by 101 altitudinal levels from surface (h = 0 km) to

the top boundary (h = 100 km) to determine optical properties as a piecewise

linear continuous functions.

Surface albedo = 0.25. Planetary radius = 3395 km.

18

SCATRD-OFOS: example of calculation- Pure aerosol atmosphere: total optical depth = 0.2;

exponential distribution with height scale = 10 km;

single scattering albedo = 0.9;

Henyey-Greenstein phase function with g=0.7;

101 altitudinal levels from surface (h = 0 km) to the top boundary (h = 100 km).- Surface albedo = 0.25;- Solar flux = 1.- Sun at zenith for tangent point(s); phase angle = 90 degrees.- Monte-Carlo error ≤ 0.5 %

19

SCATRD-OFOS: example of calculation

Comparison with the method: the source function is calculated by SHDOM code[Evans K. F.,1998, The spherical harmonics discrete ordinate method for three-dimensional

atmospheric radiative transfer, Journal of the Atmospheric Science, 55, 429-446]for each layer in appropriate direction.

20

Omega Mex: general informationSome characteristics of Omega – visible and infrared mapping spectrometer:

Spectral range:

VNIR channel SWIR channel

Spectral range: 0.36 ÷ 1.05 μm 0.93 ÷ 2.73 μm and 2.55 ÷ 5.1 μm

Spectral sampling: 50 Å

Spatial sampling: 0.4 mrad 1.2 mrad (Instantaneous FOV)

21

Omega Mex: limb measurementsMeasured limb aerosol profiles:

- Orbit N 0044 – first limb observation.

- Orbit N 0285.

- Orbit N 0291 (qub # 0); limb coordinates: Longitude: 13° E

Latitude: - 44° N

px; lines: 600 ÷ 1000px

22

SCATRD-OFOS: fitting to the aerosol profileOrbit N 291, qub # 0.

- λ = 1.227 μm (spectel (spectral channel): # 22).

- 54 altitudinal nodes:

from surface (h=0 km) to the top boundary (h = 53 km) to determine atmospheric optical properties.

Parameterization of aerosol: Henye-Greenstein phase function with

[Ockert-Bell M. E., Bell III J. F., Pollack J. B., McKay Ch. P. and Forget F., 1997, Absorption and scattering properties of the

Martian dust in the solar wavelengths, Journal of Geophysical Research, Vol. 102, No. E4, pp. 9039-9050].

-

-

- Radius of Mars R = 3395 km ([Allen, 1973]; equatorial).

- Monte-Carlo error ≤ 1 %.

- Don’t take into account FOV.

25.0Asurface

63.0)g(h, 95.0a 0

m

2m

W 81.57F

23

SCATRD-OFOS: fitting to the aerosol profile

km 10H0

10.0

First rough estimation: calculation for exponentially distributed aerosol:

24

SCATRD-OFOS: fitting to the aerosol profile

km 10H0

10.0

Retrieving vertical distribution of aerosol: analogically to "onion peeling" technique.

0.21

21.0

25

Results and conclusions

- Computer code SCATRD was successfully tested and it will being developing.

- SCATRD-OFOS subroutine also was successfully tested and it will be developed

simultaneously with SCATRD code.

- SCATRD-OFOS subroutine could be apply to spectrometric data analysis obtained

by orbital gauges.

26

Further workGlobal:

Development of SCATRD code and SCATRD-OFOS subroutine:

To take into account:

- molecular scattering for Venus and Mars;

- molecular (gaseous) absorption;

- device model: spectral instrument function and FOV;

- account thermal processes (based on LTE hypothesis).

Local:

- Detailed Omega aerosol limb profile analyses with account of spectral relation

of aerosol optical properties.

27

Thanks for your attention!