Optical depth from shadows in orbiter images of Mars

1. Optical depth from shadows in orbiter images of Mars Nick Hoekzema Oliver Stenzel Lena Petrova WojtekMarkiewicz Maya Garcia-Comas Nick Thomas Klaus Gwinner Ai Inada

2. Optical depth from shadows in orbiter images of Mars the optical depth  of the atmosphere determines the brightness of shadows  retrieve  from shadow brightness very difficult for Earth but appears to work for Mars!  >> 1 ≈ 1

3. Outline • Why develop a shadow method? • The results we will present are built on the assumption: • pressure scale height ~ scale height of optical depth • In how far is this justified? • Deriving the shadow method formula • Radiative transfer is too complicated to solve accurately • Simplify until it is more workable • Removing diffuse radiation • A surface albedo is needed, it is unknown, now what? • Simplifications introduce important errors • Correct with empirical correction factor • Check when shad ~ (constant correction factor) * • Study region with large altitude range (Valles Marineris) • Determine correction factors • Compare shadow method retrievals with the accurate measurements by the MER rovers on the surface

4. Mars and airborne dust • Typically for Mars: 0.3 <  < 1.0 • Sometimes higher (dust-storms) • Locally lower (polar regions) • Cause: aerosol haze • Mostly reddish airborne dust The haze has important effects, for example: • Absorbs insolation • Invokes strong reddish diffuse illumination onto the surface • Diminishes the contrast of orbiter images • Interpretation of such images should consider the atmospheric effects. • Quantifying atmospheric effects  need to know 

5. Retrieving from space images Earth • Compare measured TOA albedo with known surface albedo(TOA: Top Of Atmosphere) • From stereo imaging (ATSR-2, MISR) Mars •  from comparing TOA and surface albedo • TOA albedo not accurately measurable • Calibration not as good as in Earth remote sensing • Surface albedos not well known yet • Retrieving  from stereo images works! • but need high contrasts • high contrast is rare on Mars • In short: another tool would help  Learn how to retrieve  from shadows with the so called “shadow method”

6. Shadows?...Mars is quite flat • Digital Terrain Models (DTMs) from HRSC and MOLA show • slopes are gentle and hardly ever cast usable shadows when the sun is > 25°-30° above the horizon • sun below ~10°  shadow method is inaccurate because plane parallel approximation breaks down • Overall: few resolved shadows  the shadow method is of limited use • If…the spatial resolution > 10 m/px No shadow, it is merely shading No shadow These are dust devil streaks with albedo ~ 0.2

7. On smaller scales Mars is less flat HiRISE has resolution of 3-4 px/m • Frequent shadows (e.g., behind boulders, and in fresh craters) • Shadow method is quite useful for HiRISE images

8. Simple shadow method • Concept: translate brightness difference between sunlit and shadowed region into  • For doing this translation correctly one needs to know inputs that often are not available: • surface albedo • bidirectional reflection properties of the surface • distribution of diffuse illumination from the sky • local surface topography • which part of the sky is visible in the shadow • which part is visible in the sunlit comparison region • A serious attempt to solve it all: Petrova et al. 2011 • We here present a simpler version • It only requires more readily available inputs • because it makes several rough assumptions

9. Assumptions • The surface is Lambertian • Similar atmosphere above shadowed and above sunlit comparison regions • All pixels in an analyzed pair of shadowed and sunlit comparison regions receive the same amount of diffuse radiation from the sky • The albedo of the surface is approximated with the measured TOA albedo (Top Of Atmosphere albedo) The approximations introduce (systematic) errors, especially 3 and 4 are rather rough • Measure errrors • Compensate with correction factor

10. shad = correction factor * 1) estimate the correction factor • Estimate the correction factor by comparing MER measurements with shadow method retrievals from regions near the rovers • MER rovers on the surface • measured the local optical depth by looking into the sun

11. shad = correction factor *  2) Investigate if the correction factor is a constant  • shad and  must be close to proportional if shadow method retrievals shad yield an accurate scale height of the optical depth • (Obviously, proportional implies a “constant correction factor”)

12. shad and  must be close to proportional if shadow method retrievals shad yield an accurate scale height of optical depth • use shadow method to derive scale-height of optical depth in VallesMarineris • it spans > 8 km in altitude • use HRSC images • these have good co-registered DTMs

13. shad and  must be close to proportional if shadow method retrievals shad yield an accurate scale height Two assumptions • The pressure scale-height implied by the consulted Global Circulation Model (GCM) has an accuracy of a few hundred meters • http://www-mars.lmd.jussieu.fr/ • pressure scale-height ~ scale-height of optical depth

14. What about the assumption:pressure scale-height ~ scale-height of optical depth • By now, many studies confirm it • I’ll show some of my own work • Some work by others: • Jaquin et al. (1986); Kahn et al. (1981); Thomas et al. (1999); Chassefiere et al. (1995); Grassi et al. (2007); Zasova et al. (2005); Lemmon et al. (2004); …

15. Stereo method analysis of HRSC images from orbit 902 Pavonis Mons H~10.0—11.7 km(Temp range 194—227 K)(Hoekzema et al. 2007) • High contrast  here the stereo method is reasonable accurate • Implied temperature consistent with PFS temp. measurements • Value very similar to expected pressure height  • Aerosols appear well mixed into the atmosphere, here also horizontally over few * 100 km 88 km False color

16. 200 km HRSC orbit 471: stereo method retrievals on a wall of the VallesScree displays very high contrasts stereo method is pretty accurate here Hoekzema et al. 2010 Dust scale height: 14.0 km+1.3/-1.1 km similar to that of the gas pressure

17. Regions 10, 17, 18, 22, 23, 24, 25 • Here: dust scale height ≠ atmospheric scale height • Optical depth is almost independent of altitude • Probably dusty banner cloud • Thus: watch out for exceptions, especially in the Valles! Another branch of the canyon

18. Deriving the shadow method formula

19. Or for short: B(i,j) Optical depth Orbiter image I(i,j) Cosine emission angle Surface component Atmospheric component

20. Variables for deriving theshadow method formula • F direct solar flux onto the surface • Fdiff total diffuse flux onto the surface • RS surface albedo • x1fraction ofFdiff reaching shadow • x2 fraction of Fdiffreaching sunlit comparison region • atmospheric components A = Ashad = Asunlit • Bshad surface component B in shadow • Bsunlit surface component B in sunlit comparison region

21. SubtractionIsunlit-Ishadremovestheatmospheric componentA ___________________________________________________________-- • Used approximation A = Ashad = Asunlit • Quite accurate when shadowed and sunlit comparison region • are less than a few kilometers apart and around same altitude • The atmosphere rarely changes on scales < many kilometers

22. Taking x1 = x2 removes term Fdiff • x1fraction ofFdiff reaching shadow • x2 fraction of Fdiffreaching sunlit comparison region • Grave simplification, introducing a large error • One of two main reasons for large systematic differences between shadand the real optical depth • Let’s show why…

23. In shadow there is less diffuse radiation than in the sunlit comparison region • In a shadow, part of the bright aureole around the sun is obscured as well, thus: x1 < x2 • approximation x1 = x2introduces an error, the correction factor compensates for average error in validation sample • Expect error in of easily 15-20% from this approximation Gusev circus

24. The shadow method formula • Still needed: surface albedoRS • Usually unknown • Take the measured TOA albedo instead

25. surface albedo andTOA albedo ? • Approximation is not generally correct • neglects the atmospheric influence • introduces substantial error • very bad approximation for Earth • Rayleigh scattering on gas molecules and scattering on thin cloud covers yield an important radiation field that is independent of the underlying surface • this is why a shadow method is problematic for Earth • but in red colors it is better for Mars...

26. surface albedo and TOA albedo (II)…because most scattering is on reddish aerosols • Gas molecules and very small aerosols • Raleigh scattering • Similar amounts are scattered forward and backward • Aerosol size > photon wavelength • Strong forward scattering • Martian airborne dust on average 1-2 µm  • very strong forward scattering(in the visible)

27. surface albedo and TOA albedo (III) On Mars, in the rangeYELLOW - RED:average TOA albedo ≈ average surface albedo • Airborne dust: in a single scattering event 90-95% of the photons are scattered forward • The remainder is mostly absorbed • Only a small part of it is scattered to the side or backwards Result for • Atmospheric contribution A to image I is mostly a diffuse and transparent picture of the surface B • A does not brighten or darken I much because there is little absorption • Conclusion: between yellow and red Martian airborne dust • diminishes contrast • does not introduce large differences between the average surface albedo and the average TOA albedo

28. surface albedo and TOA albedo (IV) On Mars, towards the blue:average TOA albedo < average surface albedo • Airborne dust: in a single scattering event 25-30% of the photons is destroyed • The remainder is scattered forward very strongly Result for • A darkens and reddens I because there is strong absorption • Consequence for the shadow method • taking TOA albedo instead of surface albedo is not a good approximation • The introduced error will increase the shad that are retrieved from blue (and green) images.

29. At  = 1.5, atmospheric component A contributes ~2/3 to I, still… dark remains dark Observed image I with  = 1.5 Scattering angle: ~25° A is mostly a diffuse and reddened image of the surface B Surface image B 60 km R 0.90 G 0.90 B 0.90 R 0.05 G 0.05 B 0.05 R 0.63 G 0.52 B 0.28 R 0.13 G 0.09 B 0.06

30. Note: slopes can yield errors • Choose sunlit comparison region on flat terrain • Approximation Contains which is only valid for flat surface • Obviously, also choose sunlit comparison region with roughly average albedo • (sometimes hard to judge) Correct result: 0.32

31. When is the correction factor constant?For this part we use HRSC stereo images of VallesMarineris and the DTM that is derived from these

32. HRSC and the used images • HRSC: developed and built by DLR in Berlin • 9 CCD line detectors acquire superimposed image tracks. • colors: • 5 * stereo 675 ± 90 nm • blue 440 ± 45 nm • green 530 ± 45 nm • red 750 ± 20 nm • NIR 970 ± 45 nm • Valles Marineris • 9 HRSC images from orbit 1944 July 21, 2005 • Gusev • 3 stereo images from orbit 4165

33. Example of shadow method retrievals • Comparing a sunlit region (black line) and a shadowed region (white line) yields an estimate of the optical depth • The full analysis uses > 150 retrievals 100 km

34. The panchromatics shad • S1 12.8 km (12.3—13.4) • P1 12.8 km (12.3—13.4) • Nd 11.3 km (10.8—11.7) • P2 12.0 km (11.6—12.5) • S2 12.3 km (11.8—12.8) • Average: 12.2 ± 0.3 km • Implied temperature ~ 236 K • Agrees with GCM value! •  Hpressure ~ Hoptical depth • Effects from phase angle differences are limited  • No problems from Lambertian approximation for this range (58°-88°) shad shad Conclusion: shad ~ (constant correction factor) *

35. All colors shad • IR 10.6 km10.2—11.1 • Re 12.5 km12.0—13.0 • Pan 12.2 km11.9—12.5 • Gr 14.5 km14.0—15.1 • Bl 17.0 km16.4—17.7 • shad is highest in blue and green • predicted a few sheets ago • Scale-heights in blue and green are too high • In IR it may be a bit low • correction factor: no proof that it is ~constant for blue, green, or NIR shad shad

36. Clear trend from blue towards red • towards the blue, high altitude layers artificially blow up the scale height • Compare with the dust cloud over VallesMarineris in sheet14 • Towards the blue these whitish layers become much better visible and have larger impact • Aerosols on average become smaller while going up: • aerosol size ~< λ in NIR  • scattering properties may change when going up

37. Measuring correction factors

38. For Yellow-Red images: • shad = constant correction factor *  • Measure the correction factor by • Comparing the MER rover measurements with shadow method retrievals from regions near the rovers • We studied a few data-sets • Results from only two data-set here • These illustrates the accuracy • All other data-sets that we studied give similar results

39. #4165: shadows in the rim of Gusev crater sunlit comparison regions close to the shadows  similar diffuse illumination Analyzed: s1, nd, s2 panchromatic images rebinned at 125 meter/pixelSurface albedo in panchromatic 0.2-0.3 • Shadow method: τshad = 0.54 ± 0.02 • Note: corrected for altitude differences between the regions • Spirit:  = 0.76 ± 0.03 •  Correction factor = 0.71 ± (see next sheets) S 45 km

40. #4165: shadows in the rim of Gusev crater sunlit comparison regions far away from the shadowsShadow: large part of the sky is obscured by slope Sunlit comparison region: slopes are far away • Shadow method: shad = 0.41 ± 0.01 • Note: corrected for altitude differences between the regions • Spirit: real optical depth  = 0.76 ± 0.03 •  Correction factor = 0.54 ± (see next sheets) S 12 km 45 km

41. #4165: shadows in the rim of Gusev crater The range of correction factors • 0.71 Highest value • sunlit comparison regions close to shadows • 0.54 Lowest value • sunlit comparison regions far away from shadows • The correction factors increase gradually when moving the sunlit comparison regions towards shadows • Correction factors range 0.54 - 0.71  0.63 ± 0.09

42. Assigned error ±15% • arises solely from the range in measured correction factors • Technically, it should be combined with the errors from other sources • but in this case other errors are hardly significant • However, a better selection of the sunlit comparison regions will give a much smaller range of correction factors • then these other errors are important.

43. Sunlit comparison regions close to their shadows • Sunlit comparison regions close to their shadows yield 0.71 with a spread of ± 3% • combine with educated guesses of other errors • Lambertian approximation: < ± 5% • Measurements by MER rovers: ± 4% • Offset errors in HRSC’s intensity calibration: ± 4%. • From comparing different versions of the HRSC data Combining these errors yields maybe: ± 8% 

44. Result for the analyzed HRSC images of GusevIf the sunlit comparison regions are • at varying, more or less arbitrary, distances from the shadows . close to the shadows so that these see a similar sky • Now use an HiRISE image • It yields compatible values

45. HiRISE image of Victoria crater • Opportunity measured opportunity = 0.46 ± 0.02 • 0.27 meter/pixel Opportunity 750 m

46. Correction factor for the HiRISE red image • 20 retrievals yielded shad = 0.324 ± 0.016 • = 0.48 ± 0.05 • Correction factor~ (0.68 ± 0.09) * • Very similar to Gusev, even though • surface albedo is very different • spatial resolution is more than 100 times better

47. Correction factors for the HiRISENIR and blue-green images • Reminder: correction factors for NIR and for blue-green are of limited use because these may depend on optical depth • NIR: 20 retrievals yielded shad = 0.309 ± 0.014 • = 0.48 ± 0.05 • Correction factor~ (0.64 ± 0.09) *  • Blue-green: 20 retrievals yielded shad = 0.378 ± 0.016 • (Note: again higher than for yellow-red) • = 0.48 ± 0.05 • Correction factor~ (0.79 ± 0.10) * 

48. Conclusions • The shadow method is a useful tool for measuring optical depth • That is, in the rangeYELLOW - RED • It may not work very well towards the blue • We found no influence from spatial resolution or average surface albedo on these results • Phase angle influence appeared marginally significant • Range: 58°-88°

50. Note on using the shadow method:slope and wrong albedo can yield errors • Choose sunlit comparison region on flat terrain Approximation Contains which is valid for flat surface • Choose sunlit comparison region with ~average albedo • (often hard to judge) Correct result: 0.32