Optical depth from shadows in orbiter images of Mars

Nick Hoekzema Oliver Stenzel

Lena PetrovaWojtek MarkiewiczMaya Garcia-Comas

Nick Thomas Klaus Gwinner

Ai Inada

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

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

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

Retrieving from space images Earth1. Compare measured TOA albedo with known surface

albedo (TOA: Top Of Atmosphere)2. From stereo imaging (ATSR-2, MISR)

Mars3. 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

4. Retrieving from stereo images works! – but need high contrasts– high contrast is rare on Mars

5. In short: another tool would help Learn how to retrieve from shadows with the so called “shadow method”

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 shadowThese are dust devil streaks

with albedo ~ 0.2

On smaller scales Mars is less flatHiRISE 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

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

Assumptions1. The surface is Lambertian2. Similar atmosphere above shadowed and above

sunlit comparison regions3. All pixels in an analyzed pair of shadowed and

sunlit comparison regions receive the same amount of diffuse radiation from the sky

4. 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

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

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”)

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 Valles Marineris – it spans > 8 km in altitude

• use HRSC images– these have good co-registered DTMs

shad and must be close to proportional if shadow method retrievals shad yield an accurate scale height

Two assumptions 1. 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/

2. pressure scale-height ~ scale-height of optical depth

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); …

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

HRSC orbit 471: stereo method retrievals on a wall of the Valles Scree displays very high contrasts stereo method is pretty accurate here

Dust scale height: 14.0 km +1.3/-1.1 kmsimilar to that of the gas pressure

Hoekzema et al. 2010

200 km

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

Deriving the shadow method formula

Or for short:

),(),(),( jiAejiBjiI

Surface component Atmospheric component

Optical depthCosine emission angle

Orbiter image I(i,j)

B(i,j)

ABeI

Variables for deriving theshadow method formula

• F direct solar flux onto the surface • Fdiff total diffuse flux onto the surface• RS surface albedo • x1 fraction of Fdiff reaching shadow • x2 fraction of Fdiff reaching sunlit comparison region• atmospheric components A = Ashad = Asunlit

• Bshad surface component B in shadow• Bsunlit surface component B in sunlit comparison region

Sdiff

shad RxF

B 1 S

diffSsunlit Rx

FeRFB 20

0

Subtraction Isunlit-Ishad removes the atmospheric component A

eRxxF

RFeIII Sdiff

Sshadsunlit ))(( 1200

___________________________________________________________--

AeRxF

RFeI Sdiff

Ssunlit

)( 20

0

AeRxF

AeBI Sdiff

shadshadshad

1

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

ABeI

Taking x1 = x2 removes term Fdiff

• x1 fraction of Fdiff reaching shadow • x2 fraction of Fdiff reaching sunlit comparison

region

• Grave simplification, introducing a large error• One of two main reasons for large systematic

differences between shad and the real optical depth

• Let’s show why…

eRFeIII Sshadsunlit 00

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 = x2 introduces an error, the correction factor compensates for average error in validation sample

• Expect error in of easily 15-20% from this approximation

The shadow method formula

• Still needed: surface albedo RS• Usually unknown• Take the measured TOA albedo instead

eRFeIII Sshadsunlit 00

)ln(0

0

0

S

shad

RFI

surface albedo and TOA 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...

?

• 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)

surface albedo and TOA albedo (II)…because most scattering is on reddish aerosols

• 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

On Mars, in the range YELLOW - RED: average TOA albedo ≈ average surface albedo

ABeI

surface albedo and TOA albedo (III)

• 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.

On Mars, towards the blue: average TOA albedo < average surface albedo

ABeI

surface albedo and TOA albedo (IV)

At = 1.5, atmospheric component A contributes ~2/3 to I, still… dark remains dark

60 km

Surface image B

Observed image I with = 1.5Scattering angle: ~25°

R 0.90 G 0.90 B 0.90R 0.05 G 0.05 B 0.05

R 0.63 G 0.52 B 0.28R 0.13 G 0.09 B 0.06

ABeI

A is mostly a diffuse and

reddened image of the surface B

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)

FIRS 0

0

Correct result: 0.32

When is the correction factor

constant?

For this part we use HRSC stereo images of Valles Marineris and the DTM that is derived from these

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

• 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

The panchromatics• 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°)

Conclusion: shad ~ (constant correction factor) *

shad

shad

shad

All colors• IR 10.6 km 10.2—11.1• Re 12.5 km 12.0—13.0• Pan 12.2 km 11.9—12.5• Gr 14.5 km 14.0—15.1• Bl 17.0 km 16.4—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

shad

Clear trend from blue towards red

• towards the blue, high altitude layers artificially blow up the scale height – Compare with the dust cloud

over Valles Marineris in sheet 14

– 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

Measuring correction factors

For Yellow-Red images:

1. shad = constant correction factor * – Measure the correction factor by – Comparing the MER rover measurements with

shadow method retrievals from regions near the rovers

2. We studied a few data-sets3. Results from only two data-set here

– These illustrates the accuracy– All other data-sets that we studied give similar

results

#4165: shadows in the rim of Gusev crater sunlit comparison regions close to the shadows

similar diffuse illumination

• 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

Analyzed: s1, nd, s2 panchromatic images rebinned at 125 meter/pixelSurface albedo in panchromatic 0.2-0.3

#4165: shadows in the rim of Gusev crater sunlit comparison regions far away from the shadows

Shadow: 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

45 km

12 km

#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

• 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.

*0.09) ±0.63(shad

Sunlit comparison regions close to their shadows

1. Sunlit comparison regions close to their shadows yield 0.71 with a spread of ± 3%• combine with educated guesses of other errors

2. Lambertian approximation: < ± 5% 3. Measurements by MER rovers: ± 4% 4. Offset errors in HRSC’s intensity calibration: ± 4%.

• From comparing different versions of the HRSC data

Combining these errors yields maybe: ± 8% *0.06) ±0.71(shad

Result for the analyzed HRSC images of GusevIf the sunlit comparison regions are

1. at varying, more or less arbitrary, distances from the shadows

1..

2. close to the shadows so that these see a similar sky

*0.09) ±0.63(shad

*0.06) ±0.71(shad

• Now use an HiRISE image• It yields compatible values

HiRISE image of Victoria crater• Opportunity measured opportunity = 0.46 ± 0.02• 0.27 meter/pixel

Opportunity

750 m

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

Correction factors for the HiRISE NIR 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 yieldedshad = 0.378 ± 0.016

– (Note: again higher than for yellow-red)• = 0.48 ± 0.05• Correction factor ~ (0.79 ± 0.10) *

Conclusions• The shadow method is a useful

tool for measuring optical depth

• That is, in the range YELLOW - 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°

Note on using the shadow method:slope and wrong albedo can yield errors

• Choose sunlit comparison region on flat terrainApproximation

Contains which is valid for flat surface

• Choose sunlit comparison region with ~average albedo – (often hard to judge)

FIRS 0

0

Correct result: 0.32