T00fri's Titan @ Celestia

[ajtribick]

I'm amazed! Saturn and Titan are 30 times the distance from the sun as Earth. By the inverse square law, sunlight is then 900 times weaker.

Er, no.

30 times the distance from the sun as Earth is 30 AU, which is roughly where Neptune is.

Saturn is 10 AU from Sol. So actually it's getting 1/100th of the light that Earth gets, since it's 10 times further away.

Oh, the shame of it! I used to know the distance of all the planets in the solar system to 2 decimal places in AU. That's a worse mistake than my 'the moon's apparent magnitude is -18' (it's -12). How did I do that? I'll tell you how I did that. I read all 6 pages of this thread to make sure I really followed it, and filtered out the 2 or 3 sub-topics along the way, then spent ages editing my thoughts. I was so tired, that when I tried to recall Saturn's distance, the number 29.5 popped into my head. Now I realise, I confused Saturn's year with its distance. Please forgive me!

You know Bode's "Law" comes in pretty handy for these kind of things, except that the estimate it gives for Neptune is actually rather closer to Pluto IIRC...

0,3,6,12,24,48... then add four and divide by ten to get the distance in AU, and watch out for Ceres.

[granthutchison]

I looked at that Galileo link, and sorry, but I would never consider that a realistic 'visual' portrait of Venus.

Nor do I. All I said was that the image was taken in visible light - by no stretch of the imagination is it true colour. All I was hoping to point out was an albedo variation in reflected visible light (of some wavelength or another).

Yup, absorption and diffusion - two different things.

Yup.
And each of them can obscure the Sun - absorption is a complete red herring, here, and Fridger should be sternly reprimanded for introducing the concept .
If the optical depth is such that the majority of light rays reaching your eye have been scattered by several particles on their way to you (as occurs at high optical depths) then most of the light reaching you appears to come from someplace other than the direction of the light source - and I'd guess that it's easy enough to see how that effect must be independent of the brightness of the light source (since each particle and photon has no knowledge of the number of other particles and photons out there). So when diffusion reaches a critical level at which scattered light obscures the edge contrast of a bright source relative to a dark field, it has that effect for all sources against dark fields, no matter how bright or dim.
And this would apply even if there were no absorption at all - my unpleasant hiking experience involved a thin mist above snow which became diffusely illuminated by the Moon. The light was actually pretty bright but entirely ambient, with no hint of direction and no shadows on the snow by which to judge contour or slope, or even to see my own footprints.
The shower screen analogy is a good one for pointing out the differential effects of diffusion, but I'm afraid it's too optically shallow a medium to illustrate anything about bright light sources seen through very dense diffusors. (I did try to compartmentalize my discussion into "resolution of fine detail" and "obscuration of bright sources", but I guess I did a bad job.)

We might better be careful in making predictions before knowing both pretty well.

From the above, can you see why I maintain that in a high-scattering environment, low absorption might make the ambient light a little brighter, but it's not going to make distant light sources any more clearly visible?

Grant

[t00fri]

No need to travel all the way to Titan:



Anybody see the "nude in the main street" of Ny ?lesund?

Cheers,
Bye Fridger

[t00fri]

...
And each of them can obscure the Sun - absorption is a complete red herring, here, and Fridger should be sternly reprimanded for introducing the concept .

...helpless protesting ...

...that effect must be independent of the brightness of the light source (since each particle and photon has no knowledge of the number of other particles and photons out there).

But rather depending on the source's radiation integrated over the solid angle. All rays that reach your eye on Titan's surface, were emitted from the source, no matter how many scatterings have occurred on their way.

So in the case you considered, it's not the local brightness of the source that counts but instead the spacial integral over the radiated energy ...the total luminosity so to speak.

If you switch off the source ('click';-)), it's gonna be pitch dark on Titan...No doubt about that. That limiting case is clearly independent of the multiple scattering rate...

We might better be careful in making predictions before knowing both pretty well.

From the above, can you see why I maintain that in a high-scattering environment, low absorption might make the ambient light a little brighter, but it's not going to make distant light sources any more clearly visible?

Grant

Really?;-)

Bye Fridger

[granthutchison]

But rather depending on the source's radiation integrated over the solid angle. All rays that reach you eye on Titan's surface were emitted from the source, no matter how many scatterings have occurred on their way.

Um ... are we at cross purposes, here? I can't see the relevance of this at all. I've never said that you would be unable to see the Sun's light - what possible sense would that make?

Interpreting using your mathematical construction:
1) A rather moderate level of scattering will prevent you discerning the Sun's disc (the graph of surface brightness over the solid angle may show a local maximum, but no stepwise transition adequate to register as an "edge" to the human eye). At this point I'd suggest a person with no argumentative agenda would say "I can't see the Sun", while being happy to agree "I can see where the Sun is, roughly". This is what I meant when I said that (if Titan's haze has the optical depth it's reported to have) the Sun would be associated with a

very diffuse patch of luminance

rather than Spiff's

low contrast but sharp! solar disk

2) Very marked scattering will spread the Sun's light so smoothly across the sky that it will be impossible to point to its location. (At this point perhaps even you would confess to being unable to see the Sun.) The graph of surface brightness across the solid angle would now have a very flat central plateau spread over a wide central region. This might occur on Titan if the haze density were at the higher end of the range I've seen quoted. (One old estimate puts the optical depth at 10000!)
In both these cases the integrated luminous intensity over the whole sky could (as you say) turn out to be very similar to that measured in a hazeless sky with a clear solar disc, but that seems to have no relevance to the idea of seeing the Sun.

It only takes a layer of cloud (= suspended particles) ~50m thick to achieve condition 1) on Earth - that's pretty much a pure scattering effect, since the absorption is relatively trivial. You, Fridger, must have seen many bright morning mists of ~100m depth generate entirely directionless lighting during your Arctic travels - I've climbed in and out of such things in coastal valleys, and I certainly wouldn't care to try to navigate by the Sun under such conditions! So I'm a bit puzzled to find myself having to work so hard at convincing you of the simple observable fact that haze obscures the Sun.

Really?

Yes, really.

Grant

[t00fri]

But rather depending on the source's radiation integrated over the solid angle. All rays that reach you eye on Titan's surface were emitted from the source, no matter how many scatterings have occurred on their way.

Um ... are we at cross purposes, here? I can't see the relevance of this at all. I've never said that you would be unable to see the Sun's light - what possible sense would that make?

Grant,

sorry, I guess there was some misunderstanding creeping in, and it was presumably mainly my fault (I was tired and in a hurry...).

Hmm, I am again in a hurry and again tired after a long hectic day

So let me escape from that 'deadlock' by proposing a more constructive alternative approach:

Perhaps we could collect together what we really know in form of scientific data about Titan's crucial atmosphere parameters. Of course I presume that we all are aware of the "basics".

I mean rather things like

-- What is the mean free path for a photon (of a given wavelength!) entering the haze? What do we know about this ingredient which is clearly crucial for the issue of diffusion?
-- Is there any data whatsoever about the absorption of (visible) light in the haze?

-- what else is crucial?

Such a data 'collection' might be very useful as a basis for further discussions and also speculations, of course.
In case there are NO respective data, this would also allow certain conclusions

I must confess that I do not know very many 'hard' facts myself...

...
So I'm a bit puzzled to find myself having to work so hard at convincing you of the simple observable fact that haze obscures the Sun.
...
Grant

Don't worry , you will certainly succeed soon or later...

Bye Fridger

[granthutchison]

Well, we know that the optical depth of the whole atmosphere is described on theoretical grounds as being of "order 1 to order 10" (damn, lost the URL - I'll get back to you).
My favourite atmospheric physicist, Craig Bohren, gives the most intuitive definition of optical depth as being the true depth expressed as a multiple of the mean free path for photons of the relevant wavelength. So an optical depth of 1 implies that a significant proportion of photons will be able to make the double journey space->surface->space without being scattered - we'll be able to see the surface, albeit through some perceptible haze. An optical depth of 10, however, implies most (non-absorbed) photons will have >10 scattering interactions on a single journey to the surface, and therefore the surface will be effectively invisible.

The fact that we cannot see surface detail in visible wavelengths indicates that either:
a) The optical depth of the haze is greater than "order 1"; or
b) The surface has very minimal albedo variation.
We also know that minimally absorptive clouds with optical depths of order 10 are sufficient to obscure the Sun on Earth, and that such clouds are thousands of times less deep than the full thickness of Titan's atmosphere - so option a) has very strong plausibility. The fact that Titan has significant albedo variation in IR implies that the chemical constitution of its surface varies markedly from place to place, which therefore requires some remarkable coincidences for b) to be true. William of Occam therefore favours a).

We can also deduce that the atmosphere is a moderate, but not huge, absorber of visible wavelengths because:
a) It's coloured; and
b) 10% (estimated) transmission through the atmosphere and 20% (measured) reflected overall implies that 70%-80% is absorbed by the atmosphere (surface albedo between 0 and 1).

Beyond that, I cannot go. Do you have a reference for the "1000th Earth illumination" figure - that would let us look at the assumptions and measurements it was derived from.

Grant

PS: Do you think it's too late to persuade them to point Huygens' camera straight at the Sun after landing? I'll tell them it can't possibly cause any damage

[Spaceman Spiff]

This is what I meant when I said that (if Titan's haze has the optical depth it's reported to have) the Sun would be associated with a

very diffuse patch of luminance

rather than Spiff's

low contrast but sharp! solar disk

Sorry, Grant, but I feel compelled to defend my claim. I still don't think it's a foregone conclusion that the sun and Saturn are totally blurred out. I'll try and give a quick idea.

Let's dispense with absorption, as you wish. Let's also stick to optical depths of order 1-10, or even take:

A search on the optical depth of Titan's smog in visible light turns up recent estimates of around 5 - that would count as "opaque".

Optical depth is defined another way (related to mean free path, as you say), but a general equation is that illumination drops off from I0 to I1 as I1 / I0 = e ^ ( - tau ), where tau is the optical depth the light experiences. This means for tau = 1, I1 = I0 / e = 0.368 ? I0. For tau = 5, that means 1 - ( 1 / e ) ^ 5 = 99.33% of the light is scattered, but it also means that ( 1 / e ) ^ 5 = 0.67% isn't. Now, from the ground that 99.33% is scattered over 2pi steradians of sky, while that 0.67% comes from within a 0.05° = 0.000873 radians wide disc (reminding myself that Titan is only 10 AU from the sun!!!), and that disc occupies pi ? ( ? ? 0.000873 ) ^ 2 = 0.000000598 steradians. For relative surface brightnesses, compare 0.67% / 0.000000589 to 99.33% / 2pi = 0.67% / 99.33% ? 2pi / 0.000000598 = 70,871. This 0.67% must define a sharp edged disc, because it is the part of light not scattered. This diffusion from opacity does not blur edges, it merely reduces contrast until our eyes can't tell an edge any more. So, the sun can be seen as a sharp edged disc...

Yes, I admit the argument is very simplified, but am I convincing anyone?

I can make a similar argument for Saturn in Titan's night sky, but I think it would really be difficult to pick Saturn out in Titan's day sky. If you agree my argument has merit, maybe we can try to work it out.

But a banded giant with razor-edge rings, so beloved of NASA illustrators? Nah.

Yes, true it won't be spectacular, even at night

Maybe I get it all wrong again, but I'm tired again, and too rushed to check through the argument thouroughly. Hope you understand. Must go now.

Spiff.

[t00fri]

Thanks Grant,

that all looks like a productive restart of our quest...

Here is another thought that crosses my head when reading through your interesting discussion:

So far we have entirely ignored the angular distribution of the photons scattered from the haze "constituents".

Diffractive scattering is presumably quite important (all depending on the typical "droplet" size).

Why?...Here we go:

On Earth, diffraction on the irregularly arranged many droplets in the air is the basis for why the sky appears blue (Lord Rayleigh).

Well, it is a nice familiar experiment (Tyndall) to demonstrate that the spectral coloration of white in-falling light in the atmosphere depends strongly on the traversed layer thickness, starting off with blue and then shifting into orange-red with increasing thickness!
[That's why our sky turns red in the morning or evening, for example...]

Aha...Perhaps Titan's thick haze layer could be part of the reason for the apparent wavelength shift towards orange!? But clearly, the diffractive sky coloration effect refers mainly to looking up into the sky rather than looking down onto the surface from above.
Or perhaps orange is just a "natural" smog color merely related to absorption?

OK, it's too long ago that I knew these things really well but this seems worth some consideration...

Once we accept that diffraction scattering is dominant or at least important, we know that the angular distribution is strongly peaked towards small angle scattering. Then we could presumably afford considerably more scatterings before we "loose the sun's" image..

And so on....
I am too tired now, but you can probably immediately rule out these considerations?

Bye Fridger

PS: I just notice;-) : Spiff is tired, I am tired, so no chances for solutions tonight...

[granthutchison]

Sorry, Grant, but I feel compelled to defend my claim.

Cripes, don't be sorry. I enjoy this stuff.

Yes, I admit the agruments is very simplified, but am I convincing anyone?

I think there's a problem with your assumption that light is scattered over the whole sky evenly. That sort of thing occurs with the molecular-level Rayleigh scattering that gives us the blue sky, but particles of a size comparable to the wavelength of scattered light (haze, cloud, mist) cause Mie scattering which has a strong preference for the forward direction.

So your direct light is superimposed on a tight halo of single-scattered light, a more diffuse halo of double-scattered light, an even more diffuse halo of triple-scattered light ... and so on. So the scattered light forms a great, bright diffuse blob on top of the small amount of direct light, and if the change in luminance across the disc edge drops to <1%, your eyes can no longer see an edge - hence my "diffuse patch of luminance".
Admittedly, as the diagram shows, if the haze consists of very fine particles the scatter is more uniform. But figures are typically several tenths of a micron for Titan's upper haze, at least.

Grant

[granthutchison]

Once we accept that diffraction scattering is dominant or at least important, we know that the angular distribution is strongly peaked towards small angle scattering. Then we could presumably afford considerably more scatterings before we "loose the sun's" image..

I think the reverse is true if we consider obscuration of the visible disc ... see above.

Grant

[JarC]

Hi all,

Very interresting discusison here most of it is beyond me, but if I got the jist then the focal point seems to be the reason why one shouldn't be able to see the Sun/Saturn from Titan's surface if one also can not see the surface detail.

I've seen lots of things mentioned, again most of which is beyond me, although I get a pretty good indication what's it about (amount of haze and atmospheric height in relation to gravity?), how much light gets there in relation to how much reaches Earth.

However, one thing I missed in the presented arguments. I for one would find it perfectly believable that the sun would be visible from Titan's surface, yet surface detail itself would not be visible from our end. Simply because on Titan's surface, I get to experience the full intensity of what light reaches that surface, but in order for an of-world viewer to see surface detail, the reflected light *from* the surface will be even more scattered and dispersed AAR of its second trip through the atmosphere, resulting in even less light reflected back to the observer's position. So yes, I think the sun could be visible similar as we observ the moon on a hazy night (very diffused) yet we not being able to see through that same atmosphere from here

does this sound daft?

[granthutchison]

does this sound daft?

No, it's completely logical. So the fact we can't see any surface detail is a pretty weak constraint on what we might be able to see from the surface ... both for the reason you give, and because of the possibility that the surface may just not have much in the way of brightness variation for us to see.

Grant

[Spaceman Spiff]

Sorry, Grant, but I feel compelled to defend my claim.

Cripes, don't be sorry. I enjoy this stuff.

Oh, goody!

Grant, you're right: the scattering doesn't occur with uniform angular distribution, which was the simplification I had in mind. However, I was amazed when even my simplistic calculation threw up an edge contrast of 70,870 - that's about 12 magnitudes! I agree forward scattering would create a condensed 'halo' being brightest next to the sun's limb, but I still think it won't compete. I had in mind memories of the sun with a very sharp edge, even when severely faded through a cloud edge, fire smoke or fog, and even with a bright condensation some magnitudes greater than elsewhere existing around it. Even the 'silver lining' of a cloud as the sun comes out doesn't obscure the sun's limb.

This graph you got from the University of Winnipeg... it's good that you found it, but I'm trying to understand it. First, there's no specification of wavelength, so I'm assuming our climatologist chappie is integrating over the solar spectrum - 0.4µm - 0.65µm. Second, there's no indication what the scale is. What varies from 0 through 0.001 to 1000? I tried to have a look at the source but "Permission Denied"...

if I got the jist then the focal point seems to be the reason why one shouldn't be able to see the Sun/Saturn from Titan's surface if one also can not see the surface detail

I think so, JarC - well done for getting through this long thread! I think it started after t00fri posted surface textures from the new IR piccies, and someone wanted a 'cloudy' atmosphere. T00fri made a 'hazy' one, and it let Saturn and the sun show through from the surface. That started a debate about what is expected to be seen. To summarise:
1. NASA and ESA have let Saturn's visibility from Titan be popularised, possibly to keep the public interested in Titan. There are some common pictures (example http://saturn.jpl.nasa.gov/spacecraft/images/probe-dwe.jpg) showing Huygens descending underneath clouds letting rays of sunlight through. The clouds look very realistic, but Saturn is shown in the background with a dark night side and very open rings. The dark night side should have been 'filled in' by Titan's bright atmosphere, so instead Saturn looks like it's sitting inside Titan's atmosphere - whoops!
2. Objections raised are then a) Saturn's rings do not appear wide open from Titan, b) Huygens is landing on the far side of Titan from Saturn, c) the clouds assumed to be underneath Titan's haze would probably be so thick as to cover Saturn and the sun perpetually.
3. After Cassini, Titan's surface doesn't appear to be obscured by clouds after all, but only thick haze. Clouds only seem to have been seen over the South Pole.

I for one would find it perfectly believable that the sun would be visible from Titan's surface, yet surface detail itself would not be visible from our end.

Yes, I agree. The finer question I picked on is does this haze still mean the sun and Saturn can't been seen sharply in visible light from Titan's surface? I think it's not a foregone conclusion, and I'm coming more to think that if the obscuration is only because of haze and not clouds, there's a chance that the sun and even Saturn at night are visible, and can even be seen with sharp edges, though with ghostly contrast. I suspect I'm alone in this.

Anyone got any more numerical thoughts?

Spiff.

[granthutchison]

I agree forward scattering would create a condensed 'halo' being brightest next to the sun's limb, but I still think it won't compete. I had in mind memories of the sun with a very sharp edge, even when severely faded through a cloud edge, fire smoke or fog, and even with a bright condensation some magnitudes greater than elsewhere existing around it. Even the 'silver lining' of a cloud as the sun comes out doesn't obscure the sun's limb.

I agree all of this stuff happens - it just happens at optical depths <10, according to Craig Bohren in his book on atmospheric physics, What Light through Yonder Window Breaks.

This graph you got from the University of Winnipeg... it's good that you found it, but I'm trying to understand it. First, there's no specification of wavelength, so I'm assuming our climatologist chappie is integrating over the solar spectrum - 0.4µm - 0.65µm. Second, there's no indication what the scale is. What varies from 0 through 0.001 to 1000?

Mie scattering is independent of wavelength across the visible spectrum (that's why clouds are white), so wavelength doesn't require specification. The three different scales apply to the three different line styles corresponding the three different radii of scatterer, indicating that they're plotted on different scales and that the preponderance of forward scattering is very great as you move to larger radii. Quite what the units are I can't say ... I just plucked the image from the ether to illustrate the preference of Mie scattering for the forward direction, and in its original web context it has simply been scanned, uncaptioned, from a book.

Grant

[Guest]

Hi all,

after further thinking about Mie scattering and all that (remembering that I even wrote a paper about Mie scattering in my "youth";-)) , remembering the independence of Mie scattering on wavelength, I think there is an important constraint:

namely that in the near IR and in the IR we can look to Titan's surface very well!

Bye Fridger

[t00fri]

No wonder, I was not logged in in my mail above:

"Mir isch es Zuendhoelzli uffe Deppich abbe gspickt..."

Bye Fridger

[granthutchison]

... remembering the independence of Mie scattering on wavelength, I think there is an important constraint:

namely that in the near IR and in the IR we can look to Titan's surface very well!

Although Mie scattering is constant across wavelengths, the optical depth needn't be - for aerosols in the Earth's atmosphere there's a rough inverse power relationship with wavelength, so that IR encounters a lower optical depth than visible wavelengths. The value of the exponent depends on the size distribution of the particles, but it makes sense that the haze is optically thinner in IR. So the measured variation of optical depth with wavelength for Titan's haze would allow the particle size distribution to be reconstructed. You'd think that calculation must have been done already, somewhere ... which would then let us build something in the way of a Mie scattering model.

Grant

[t00fri]

Hi all,

well, as a next step to improve my Titan texture in Celestia-1.3.2 might be to start from Steve Albers' recent 2k texture, which is based in part on the texture I made for Celestia:

http://laps.fsl.noaa.gov/albers/sos/sos.html

By colorizing that improved grayscale texture with the surface color spectrum from the first colored surface image (ESA site), we get a next approximation to reality, as you may judge below.

There is a glitch, however:

The apparent surface colors strongly depend on the colors of the atmospheric haze. Yesterday's color photo from ESA

was taken in the presence of the haze, of course. In Celestia, we can exhibit Titan's surface only, after 'clicking away' the haze (i.e. toggling the I-key). So what is the appropriate color of the surface in Celestia??

I think it is most reasonable to colorize the surface texture according to realistic surface photos taken with a realistic sky coloration overhead...


The result then would look about like so in Celestia



Bye Fridger

[fsgregs]

Fridger:

Your skill in coloring Titan using more detailed surface layers is obviously excellent. I will defer to your effort over mine. I am ready to package and zip up my most recent Educational Activity, which covers the planetary spacecraft, including Huygens. I want to include the latest texture of both Titan and its clouds, and of course, Jestr's great Huygens descent add-on.

When will your new textures for Titan's surface, its clouds, and its haze be available for download? Also, will the cloud layer have any transparency, as you once suspected it might?



Frank