PDA

View Full Version : Moon color and humidity

Provocateur
2008-Mar-21, 08:05 AM
I've noticed that as humidity h increases, the color of the moon progresses as follows:

h : c
Low: White
Medium: Yellow
High: Orange
V High: Red

My question is how would I use standard theory to approximate the color of the moon from a length of atmosphere and its humidity? I'm not interested in specifics about the Earth's atmosphere. Specifically I want to know how standard color spectrum diffraction theory explains the white/yellow/orange/red progression that I've observed. Thanks

Hornblower
2008-Mar-21, 12:46 PM
I've noticed that as humidity h increases, the color of the moon progresses as follows:

h : c
Low: White
Medium: Yellow
High: Orange
V High: Red

My question is how would I use standard theory to approximate the color of the moon from a length of atmosphere and its humidity? I'm not interested in specifics about the Earth's atmosphere. Specifically I want to know how standard color spectrum diffraction theory explains the white/yellow/orange/red progression that I've observed. Thanks
The theory does not tell us much unless we apply it to specifics about the atmosphere.

The reddening is caused by preferential scattering of the light in the blue end of the spectrum by small particles of dust and similar substances. These particles are often, but not always, more numerous when the humidity is high.

I will leave it to others to explain the relation between the particle size to wavelength ratio and the amount of scattering. I have been away from college level physics for a long time and thus I am pretty rusty on the details.

George
2008-Mar-21, 04:38 PM
I've noticed that as humidity h increases, the color of the moon progresses as follows:

h : c
Low: White
Medium: Yellow
High: Orange
V High: Red
This color range looks extraordinary. It is rare to see an orange or red Moon except when it is on the horizon. Red is surprisingly rare, which applies also for the Sun. Is this range based on a given approximate altitude?

I know little of how humidity affects scattering. I think water vapor will attach itself to very small existing particles in the air. This should limit the effects of scattering.

Rayleigh Scattering is the effect that applies. Lord Rayleigh first worked a mechanical model for the scattering profile, but quickly changed it when Maxwell showed light was electromagnetic.

In general, the scattering increases as to the 4th power of light's frequency, if the scattering particle is a fair bit less than the wavelength of the light being scattered. There is some information I have read that seems to indicatae scattering may occur as the 6th power if the particles happen to be much smaller and of a certain size, but I am unclear on this view. In some cases, where the particles are larger, selective scattering can occur which will scatter the red end of the spectrum more than the blue end. This can be seen in the atmosphere of Mars and it explains the blue halo around the Sun the Mars rovers have observed.

There are other interesting things that happen in our atmosphere, too, that affect the colors we see. The Chappius Effect is quite an interesting color altering process found in our thin ozone layer.

Spaceman Spiff
2008-Mar-21, 07:34 PM
Presumably these observations of color correspond to times when the Moon lies not far above the horizon.

This article (http://homepages.wmich.edu/%7Ekorista/atmospheric_optics.pdf) by acclaimed atmospheric physicist, Craig Bohren, gives an excellent accounting of a lot of atmospheric phenomena.

Humid airmasses are notorious for carrying with them a lot of microscopic crud ("aerosols" and the like), which tend to scatter more efficiently the shorter wavelengths (just as the smaller air molecules do, although the larger particulate cross sections have a more complicated wavelength dependence).

George - I think the 6th power that you are referring to is the approximate power of the total scattering cross section for small particles (R << wavelength).

i.e.,

cross section (cm^2) ~ R^6 (approx.) for molecules and very small particles (assumed spherical, but that's just a detail).

Provocateur
2008-Mar-21, 10:36 PM
This color range looks extraordinary. It is rare to see an orange or red Moon except when it is on the horizon. Red is surprisingly rare, which applies also for the Sun. Is this range based on a given approximate altitude?

Yes, the red moon was on the horizon, on the most humid day I've encountered.

I know little of how humidity affects scattering. I think water vapor will attach itself to very small existing particles in the air. This should limit the effects of scattering.

Rayleigh Scattering is the effect that applies. Lord Rayleigh first worked a mechanical model for the scattering profile, but quickly changed it when Maxwell showed light was electromagnetic.

This is what I wanted. Was Rayleigh's original model that the atmosphere acts like a prism?

Provocateur
2008-Mar-21, 10:37 PM
Presumably these observations of color correspond to times when the Moon lies not far above the horizon.

This article (http://homepages.wmich.edu/%7Ekorista/atmospheric_optics.pdf) by acclaimed atmospheric physicist, Craig Bohren, gives an excellent accounting of a lot of atmospheric phenomena.

Thanks

George
2008-Mar-22, 03:08 AM
I think the 6th power that you are referring to is the approximate power of the total scattering cross section for small particles (R << wavelength).

i.e.,

cross section (cm^2) ~ R^6 (approx.) for molecules and very small particles (assumed spherical, but that's just a detail).
From the excellent link you gave to Bohren, one Grant gave me some time back. He first mentions that subwavelength droplets scatter 10^5 more than that of an equal number of separated molecules, which is interesting. Then he states (pg. 14) ...

Scattering increases as the sixth power of droplet diameter only when the molecules scatter coherently in phase. If a droplet is sufficiently small compared with the wavelength, each of its molecules is excited by essentially the same field and all the waves scattered by them interfere constructively.

This sounds like he is saying that for certain very small particle size, a 10^6 power of scattering is possible, depending on both particle size and wavelength. Is this your impression?

This is what I wanted. Was Rayleigh's original model that the atmosphere acts like a prism? I think not.

He studied Tyndall who showed that polarization was a required consequence of whatever scattering was taking place in the sky. They knew light was a transverse wave, but they assumed it traveled in the aether medium.

Rayleigh's original work, which was a landmark in giving an actual explanation to scattering, considered a primary light wave as causing a very small particle, much smaller than the wavelength, to oscillate in accord with the lightwave's influence. Motion of a particle in the medium expends energy, so he assumed, so that secondary waves would be formed. Think of cork bobbing up and down by a series of waves. It too will create secondary waves, though small in amplitude.

Since the particle would move back and forth only along one axis, due to the fact the lightwave is a transverse wave (think of the cork going only up and down), then it could not emit secondary waves along this axis. If it could, then they would be longitudnal waves, which light is not.

As a result, he showed the distribution pattern the secondary waves could take. He also showed polarization was a result, and his work became respected quickly.

Once he understood that light was electromagnetic, he reformulated his equation and changed, slightly, this distribution pattern which is today's explanation for scattering.

Gotz Hoeppe has recently written a wonderful book entitled Why the Sky is Blue that is surprisingly interesting and informative for rookies like me. Gotz is an editor for a German physics publication, IIRC.

Spaceman Spiff
2008-Mar-22, 03:35 PM
From the excellent link you gave to Bohren, one Grant gave me some time back. He first mentions that subwavelength droplets scatter 10^5 more than that of an equal number of separated molecules, which is interesting. Then he states (pg. 14) ...

Scattering increases as the sixth power of droplet diameter only when the molecules scatter coherently in phase. If a droplet is sufficiently small compared with the wavelength, each of its molecules is excited by essentially the same field and all the waves scattered by them interfere constructively.

This sounds like he is saying that for certain very small particle size, a 10^6 power of scattering is possible, depending on both particle size and wavelength. Is this your impression?

I think you might be confusing wavelength and size dependencies of scattering probability (aka "cross section").

In general the cross section of a particle (of radius r) to scatter photons goes like:

cross section (cm^2) = Q * pi*r^2

For the kinds of particles that Craig Bohren is discussing (x = 2*pi*r/lambda << 1, where lambda is the wavelength of light scattered),

Q = K * (r/lambda)^4

(assuming ideal spherical scatterers, and this particularly simple wavelength relation is true only for asymptotically small x), where K is some constant that depends on the geometry and optical parameters of the scatterer, which are usually weakly wavelength dependent. This latter bit adds weak, higher order wavelength-dependent terms to the above cross section.

Thus -

cross section (cm^2) = K * pi * r^6 / lambda^4,

See Figure 7 in that paper I linked to (http://homepages.wmich.edu/%7Ekorista/atmospheric_optics.pdf).

Does that help?

George
2008-Mar-22, 03:54 PM
Thanks. I am starting to get it, I think.

It appears a whole new world of scattering exists for molecules that is contrary to what little I knew based on single particle scattering. Things just got more complicated, though I should have guessed it would. :)

The result of Fig. 7 is surprising since the peak scattering results when the molecular structures of water are about 1000nm in diameter. That's larger than the wavelength of visible light. Also, it shows that the smaller the water particle below 1000nm, much less scattering takes place, whereas the scattering rate for particles larger than 1000nm do not drop off as quickly. [I assume this is all elastic scattering.]

Spaceman Spiff
2008-Mar-22, 05:09 PM
Thanks. I am starting to get it, I think.

It appears a whole new world of scattering exists for molecules that is contrary to what little I knew based on single particle scattering. Things just got more complicated, though I should have guessed it would. :)

Hi George -

I added a little bit to my post (see the italicized part) that might also be part of what you might be thinking of.

The result of Fig. 7 is surprising since the peak scattering results when the molecular structures of water are about 1000nm in diameter. That's larger than the wavelength of visible light. Also, it shows that the smaller the water particle below 1000nm, much less scattering takes place, whereas the scattering rate for particles larger than 1000nm do not drop off as quickly. [I assume this is all elastic scattering.]

Yes, this is all elastic scattering. Figure 7 is for a fixed wavelength of light (500 nm, I think). The peak scattering efficiency usually occurs near r = lambda (or x = 2 * pi). Note that the wavelength scale is logarithmic, and that the broadish peak does indeed occur near r = lambda.

The steep drop off at small particle size is that r^6 dependence I mentioned. Since what is plotted isn't cross section, but cross section per unit volume, which is within a scale factor of a cross section per unit particle, at large particle sizes this quantity falls off nearly linearly with particle size (whereas the cross section at large particle sizes, x >> 1, asymptotes to a constant: twice the geometric cross section).

It's the constructive and destructive interference (phase stuff) that adds all the joy to understanding this. :razz:

2008-Mar-22, 06:06 PM
I've noticed that as humidity h increases, the color of the moon progresses as follows:

h : c
Low: White
Medium: Yellow
High: Orange
V High: Red

Makes sense. Antares is noticeably redder in my humid home state versus the low-humidity region I now live. Sol is also paler yellow here.

[I've sometimes wondered if I'd been born/raised in this low-humidity region, if Antares would have been my favorite star; it was the redness which captured my attention and imagination in the humid Midwest.]

mugaliens
2008-Mar-22, 06:20 PM
I've noticed that as humidity h increases, the color of the moon progresses as follows:

h : c
Low: White
Medium: Yellow
High: Orange
V High: Red

I noticed there's no "blue moon" in there.

How do you explain that rather common comment in folklore?

Spaceman Spiff
2008-Mar-22, 06:25 PM
Makes sense. Antares is noticeably redder in my humid home state versus the low-humidity region I now live. Sol is also paler yellow here.

[I've sometimes wondered if I'd been born/raised in this low-humidity region, if Antares would have been my favorite star; it was the redness which captured my attention and imagination in the humid Midwest.]

Even if the air contained the same particulate "crud", differences in airmass due to differences in your latitude can also alter the appearance of color in a star. For a fixed observer latitude, a particular star reaches a maximum altitude (or minimum zenith angle) in the sky, and the optical depth at zenith angle theta is scaled from that straight overhead by approximately a factor of 1/cos(theta) = sec(theta). Greater optical depths mean that molecular and aerosol scattering can scatter out relatively more of the shorter wavelengths. The further south you live, the higher up in the sky that Antares reaches, and the less selective scattering occurs (also - the largest differences in color will occur for stars with significant minimum zenith angles, like Antares as observed from the northern hemisphere).

Likewise, your elevation plays an important role - the molecular and especially aerosol airmasses diminish with elevation.

So is your new environment (a) further south and/or (b) at greater elevation, in addition to being drier?

2008-Mar-22, 06:36 PM
I noticed there's no "blue moon" in there.

How do you explain that rather common comment in folklore?

Why ask such questions when such questions are 30 seconds away on Wikipedia?

It is folklore but I can't recall the story behind it.

2008-Mar-22, 06:38 PM
Makes sense. Antares is noticeably redder in my humid home state versus the low-humidity region I now live. Sol is also paler yellow here.

[I've sometimes wondered if I'd been born/raised in this low-humidity region, if Antares would have been my favorite star; it was the redness which captured my attention and imagination in the humid Midwest.]

....The further south you live, the higher up in the sky that Antares reaches, and the less selective scattering occurs (also - the largest differences in color will occur for stars with significant minimum zenith angles, like Antares as observed from the northern hemisphere).

Likewise, your elevation plays an important role - the molecular and especially aerosol airmasses diminish with elevation.

So is your new environment (a) further south and/or (b) at greater elevation, in addition to being drier?

George
2008-Mar-22, 07:14 PM
I noticed there's no "blue moon" in there.

How do you explain that rather common comment in folklore? This event does occur only rarely when large quantities of particles of sizes near the wavelength of red light are thrown into the atmosphere, such as from forest fires or volcanoes. Due to their size, blue light will hardly scatter, whereas the red ones will. Thus, more blue light will reach the eye of the observer than red, giving the Moon a slightly blue hue.

This is the explanation for the blue halo around the Sun the exists for an observer on Mars.

It is known as selective scattering, and it is presented in the paper of Bohren linked to earlier.

grant hutchison
2008-Mar-22, 07:14 PM
I noticed there's no "blue moon" in there.

How do you explain that rather common comment in folklore?A common phrase to describe a rare event ...
In the US, the phrase seems to have become attached to a second full moon in a calendar month, which isn't that rare at all.

For a visibly blue moon (or sun) you need an atmosphere in which the size of the dominant particulates is comparable to the wavelength of visible light. The mechanism is discussed in Section 4.2 of Bohren's article on atmospheric optics (http://homepages.wmich.edu/~korista/atmospheric_optics.pdf), which Spaceman Spiff linked to earlier.
Clouds of particulates of the required small size are passing rare, but they do occur after volcanic eruptions and forest fires, and do produce blue moons.

Grant Hutchison

Edit: I see George and I posted much the same information at the same time

George
2008-Mar-22, 07:30 PM
Figure 7 is for a fixed wavelength of light (500 nm, I think). The peak scattering efficiency usually occurs near r = lambda (or x = 2 * pi). Note that the wavelength scale is logarithmic, and that the broadish peak does indeed occur near r = lambda. The peak in Fig. 7 is much closer to r = 2 lambda. The peak seems very close to log 0, which is a wavelength of 1 micron, or 1000 nm. This is in contrast to the amount of scattering by single particles which have peak scattering when the particle size is a fair bit smaller than lambda.

I certainly don't doubt the results, and it does make some sense because light is entering more of a lattice and there must be resonance issues that will make photons dance a little differently. :)

It's the constructive and destructive interference (phase stuff) that adds all the joy to understanding this. :razz: I bought a senior level optics book and discovered my brain is 180 deg. out of phase with their term for phase. I hope to wrestle with it someday in hopes I can present it here for the real story. :)

George
2008-Mar-22, 07:34 PM
For a visibly blue moon (or sun) you need an atmosphere in which the size of the dominant particulates is comparable to the wavelength of visible light. The mechanism is discussed in Section 4.2 of Bohren's article on atmospheric optics (http://homepages.wmich.edu/~korista/atmospheric_optics.pdf), which Spaceman Spiff linked to earlier.
About time you got here! ;) [I see we even tied on the post time. :)]

Provocateur
2008-Mar-24, 04:02 AM
I think not.

He studied Tyndall who showed that polarization was a required consequence of whatever scattering was taking place in the sky. They knew light was a transverse wave, but they assumed it traveled in the aether medium.

Ok, this was the source of my question. From somewhere I've always had the impression that light scattering implied the light from the sun and moon were refracted, so I thought it was odd that the transition doesn't follow the ROYG pattern. :doh: Thanks.