1. 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. 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. 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): - Phenomenological approach Spectral (on wavelength, monochromatic) intensity (in the Cartesian coordinate system Cxyz) : 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:

4. 4 Code SCATRD: common information Author: 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. 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. 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.

7. 7 Code SCATRD: geometry of observation - unitary vector of direction to the Sun (Sun is infinitely far from observation region: no solar parallax).

8. 8 Code SCATRD: geometry of observation - unitary vector of boresight. Four independent parameters determine geometry of observation completely.

9. 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. 10 Code SCATRD: testing Some simple, obvious tests: Test 1: Calculated intensity is even function of azimuth ( ):

11. 11 Code SCATRD: testing Test 2: If the Sun in zenith ( ), intensity doesn’t depend on azimuth ( ).

12. 12 Code SCATRD: testing Test 3: Increasing of volume absorption coefficient (for whole atmosphere or for any atmospheric level) leads to decreasing of intensity:

13. 13 Code SCATRD: testing Test 4: The more surface albedo of isotropic reflection model, the more intensity.

14. 14 Code SCATRD: testing Other 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. 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. 16 SCATRD-OFOS: geometry of observations Analogically to Omega and PFS Mars express: Coordinate transformations:

17. 17 SCATRD-OFOS: example of calculation The 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. 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. 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. 20 Omega Mex: general information Some 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. 21 Omega Mex: limb measurements Measured 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. 22 SCATRD-OFOS: fitting to the aerosol profile Orbit 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.

23. 23 SCATRD-OFOS: fitting to the aerosol profile First rough estimation: calculation for exponentially distributed aerosol:

24. 24 SCATRD-OFOS: fitting to the aerosol profile Retrieving vertical distribution of aerosol: analogically to "onion peeling" technique.

25. 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. 26 Further work Global: 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. 27 Thanks for your attention!