## Wavelengths of sunlight, blackbody radiators, Planck's law, CCT

A blackbody radiator emits radiation across the entire radiation spectrum. The "temperature" of the blackbody radiator (measured in kelvin) can be directly calculated from the peak wavelength of its radiation using Wien's displacement law.
At shorter wavelengths, the temperature is higher.

Most objects, even stars, are not actually blackbody radiators as predicted in theory, for various reasons. A spectrum of radiation that is not a true blackbody radiator is not described by its actual temperture but by its correlated color temperature (CCT) essentially by the closest blackbody radiator's temperature.

My question is in regards to natural daylight which apparently can reach 25,000 kelvin. This is in contrast to the actual temperature of the surface of the sun which is closer to 5,800 kelvin. A high CCT implies the peak wavelength is shorter. I have read unconfirmed assertions that a cloudy day or morning might be closer to 5,800 while a clear bright day might reach a much higher CCT like 25,000.

I have read about Rayleigh scattering and other atmospheric effects, but I haven't been able to find resources specifically about the direct impact of these effects on the radiation spectrum of daylight. One person asserted to me that clouds filter out longer wavelengths, but this would imply the highest CCT of daylight is on cloudy days, not sunny days.

I tried searching in the astrophysics and earth forums, and I found some tangential threads but nothing directly addressing this. I am not a physicist and my interest in this question arises from photography. Can anyone here explain, or point me to a resource that explains, the mechanics of how the radiation spectrum of daylight can sometimes be at very short wavelengths (and hence have a very high correlated color temperature)?

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 Are you referring to something like this? http://www.ephotozine.com/article/gu...mperature-4804 The principle is the same although the numbers are somewhat different from yours. Note the author refers to the temperature of 'blue sky'. So this is equivalent to the question "why is the sky blue?" And the answer to that is already in your post. It is because the red light has been removed by the passage of the light through our atmosphere.

Thank you for your reply. That's a general photographer's website, I have basically described some of the underlying theory behind some of those ideas. However, the specific reason for why CCTs reach 25,000 in daylight is not really touched in that article. There are a lot of photography websites with articles making assertions like those in that article. None of them seem to really understand the underlying theory and mechanisms. Every photography article has a different assertion about what the peak CCT of daylight is and under what conditions such peak temperature occurs.

 Quote by Studiot Note the author refers to the temperature of 'blue sky'. So this is equivalent to the question "why is the sky blue?"
As far as I recall reading, the red (longer) wavelengths penetrate directly. It's the blue (shorter) wavelengths that are scattered by Rayleigh scattering. That's how wikipedia describes Rayleigh scattering. If the blues are scattered, that does not explain how the daylight that we perceive at ground level is primarily blue wavelengths of light. It should be the opposite, based on that explanation.

Note: I am NOT asking why the sky is blue. I am asking why the wavelengths which penetrate to ground level are primarily blue at certain times of the day (and what mechanism makes the distribution peak at the short wavelengths).

## Wavelengths of sunlight, blackbody radiators, Planck's law, CCT

If they penetrate to the ground they are not in the sky, n'est ce pas?

The scattered blue light 'bounces around' (that is what scattering is), whilst the longer wavelengths are absorbed by the ground.

Hopefully a geo-expert will come in here with asome facts and figures. My explanation was 'qualitative'.

 In Color and spectral analysis of daylight in southern europe, there is a histogram (see attached) that suggests CCT is uncorrelated with the existence or absence of cloud cover. Very curious if anyone knows of the atmospheric physics that explains this, or can point me in the right direction. What explains such wide variations in the peak wavelengths of the daylight spectrum? Attached Thumbnails

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 Quote by teddoman As far as I recall reading, the red (longer) wavelengths penetrate directly. It's the blue (shorter) wavelengths that are scattered by Rayleigh scattering. That's how wikipedia describes Rayleigh scattering. If the blues are scattered, that does not explain how the daylight that we perceive at ground level is primarily blue wavelengths of light. It should be the opposite, based on that explanation.
If you look at the Sun, the spectrum will have slightly less blue than it should because of scattering. This scattered light eventually comes down from the atmosphere. So if you have blue being scattered, and you measure the incoming light from the sky, (not from the Sun) then you get a very high temperature. That's what your first graph has. Not the Solar spectrum, but the spectrum of just the light scattered out of the beam.

 Note: I am NOT asking why the sky is blue. I am asking why the wavelengths which penetrate to ground level are primarily blue at certain times of the day (and what mechanism makes the distribution peak at the short wavelengths).
The wavelengths that PENETRATE to ground level are not primarily blue, ever. If they penetrated to the ground they wouldn't be scattered about in the atmosphere and you would be measuring the light directly from the Sun. Instead it is the light that fails to penetrate that eventually makes its way down to your eye from another path in the atmosphere after scattering.

On a cloudy day the clouds scatter ALL wavelengths of light equally, so the spectrum of the sky, which includes the clouds, is made up of all colors, lowering the temperature back towards 5,000-6,000 k.

I honestly don't think the conventional wisdom type explanations really explain things, but thanks for giving it a shot.

 Quote by Drakkith On a cloudy day the clouds scatter ALL wavelengths of light equally, so the spectrum of the sky, which includes the clouds, is made up of all colors, lowering the temperature back towards 5,000-6,000 k.
Well, I guess that's the common sense mechanism that we expect or that we have been told, but the data suggests otherwise. The histogram attachment shows there is little to no correlation between cloud cover and CCT. High and low CCTs occur on both cloudy and clear days. Which leaves me still searching for a mechanism that explains the data we see.

 Quote by Drakkith If you look at the Sun, the spectrum will have slightly less blue than it should because of scattering. This scattered light eventually comes down from the atmosphere. So if you have blue being scattered, and you measure the incoming light from the sky, (not from the Sun) then you get a very high temperature. That's what your first graph has. Not the Solar spectrum, but the spectrum of just the light scattered out of the beam. The wavelengths that PENETRATE to ground level are not primarily blue, ever. If they penetrated to the ground they wouldn't be scattered about in the atmosphere and you would be measuring the light directly from the Sun. Instead it is the light that fails to penetrate that eventually makes its way down to your eye from another path in the atmosphere after scattering.
Yes, this explanation occured to me as well. If the blue wavelengths have been scattered into the atmosphere to bounce around, then that suggests direct penetrating sunlight will have a low temperature (due to peaking in the long wavelengths). However, as the blue light in the atmosphere makes its way to the ground, this will supplement the blue wavelengths.

What doesn't make sense to me is that there is an absolute amount of irradiation received by the earth. Whether the wavelengths spend a little time bouncing around in the atmosphere before falling to the earth, there is still an absolute spectrum radiation coming in from the sun. What I would expect is for the net total radiation reaching the ground to roughly equal the spectrum originating from the sun. Unless wavelengths of light are actually transformed in the atmosphere somehow, and a red wavelength gains energy and becomes a blue wavelength, there is no reason why blue should massively exceed on the ground what is emanating from the sun. I am assuming for the moment that the sun's radiation roughly approximates a blackbody radiator (not 100% but close) and has a smooth warm spectrum around 5800 emanating from its surface. I don't know this for a fact.

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 Quote by teddoman Well, I guess that's the common sense mechanism that we expect or that we have been told, but the data suggests otherwise. The histogram attachment shows there is little to no correlation between cloud cover and CCT. High and low CCTs occur on both cloudy and clear days. Which leaves me still searching for a mechanism that explains the data we see.
What? The paper linked in the 2nd post, where the graph comes from, states otherwise.

Figure 5 shows the h0 dependence of CCT for clear and
overcast skies. The mean CCT for overcast skies is
greater than that for clear skies, as is its variability (for
h0 . 10°, the overcasts’ mean CCT exceeds that for clear
skies at the 5% significance level).

The mean CCT is greater, meaning the wavelengths measured from the sky are longer on average. Keep in mind this is coming from multiple days, not just one, and cloud cover varies significantly.

 Yes, this explanation occured to me as well. If the blue wavelengths have been scattered into the atmosphere to bounce around, then that suggests direct penetrating sunlight will have a low temperature (due to peaking in the long wavelengths). However, as the blue light in the atmosphere makes its way to the ground, this will supplement the blue wavelengths.
How are they measuring this radiation? Are they taking the spectrum of the background sky, or what? I doubt their spectroradiometer is looking at the Sun at all.

 What doesn't make sense to me is that there is an absolute amount of irradiation received by the earth. Whether the wavelengths spend a little time bouncing around in the atmosphere before falling to the earth, there is still an absolute spectrum radiation coming in from the sun. What I would expect is for the net total radiation reaching the ground to roughly equal the spectrum originating from the sun. Unless wavelengths of light are actually transformed in the atmosphere somehow, and a red wavelength gains energy and becomes a blue wavelength, there is no reason why blue should massively exceed on the ground what is emanating from the sun. I am assuming for the moment that the sun's radiation roughly approximates a blackbody radiator (not 100% but close) and has a smooth warm spectrum around 5800 emanating from its surface. I don't know this for a fact.
The most reasonable explanation I can think of is that they aren't taking the light penetrating through the atmosphere into account, only what is scattered. I haven't done the math, but it seems like it would match the 25,000 k temperature curve AND a cloudy day would scatter all the light bringing it back down like I said in my earlier post.

 Quote by Drakkith What? The paper linked in the 2nd post, where the graph comes from, states otherwise. Figure 5 shows the h0 dependence of CCT for clear and overcast skies. The mean CCT for overcast skies is greater than that for clear skies, as is its variability (for h0 . 10°, the overcasts’ mean CCT exceeds that for clear skies at the 5% significance level). The mean CCT is greater, meaning the wavelengths measured from the sky are longer on average. Keep in mind this is coming from multiple days, not just one, and cloud cover varies significantly.
But the paper also says:
As it indicates, clear skies occur ;3.5 times more frequently in Granada than do overcasts. Yet perhaps surprisingly, Fig. 4 shows only subtle differences in inverse-CCT frequency distributions for these two extreme sky states.

So fair enough, the mean CCT for overcast skies is greater, suggesting the cloud scattering mechanism probably plays some role in the process (this is what we are speculating explains it). But the paper also says on the grand scale of things, this is only a "subtle difference". Just analyzing the histogram itself, you can see many high CCT (low inverse-CCT) readings for clear days. Likewise, there are also many low CCT (high inverse-CCT) readings for cloudy days.

So this scattering mechanism we're speculating on is only a small part of the story here.

 Quote by Drakkith How are they measuring this radiation? Are they taking the spectrum of the background sky, or what? I doubt their spectroradiometer is looking at the Sun at all. The most reasonable explanation I can think of is that they aren't taking the light penetrating through the atmosphere into account, only what is scattered. I haven't done the math, but it seems like it would match the 25,000 k temperature curve AND a cloudy day would scatter all the light bringing it back down like I said in my earlier post.
They state at the top of section 2 that their readings are for direct sunlight hitting the spectrometer and for scattering daylight hitting the spectrometer. I imagine they just set up a spectrometer on the roof and it reads all direct and indirect sunlight that hits it.
Here our SPDs are of hemispheric daylight: global spectral irradiances E(l) on a horizontal surface from direct sunlight (when present) and the entire sky

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Hold on, if they are getting both the direct sunlight AND the scattered light from the sky, then it makes much more sense to me. There is very little variation in the CCT because overall almost the same amount of light from each wavelength hits the sensor during both the overcast and clear days. Like you said, the wavelength doesn't change. However the variation shown is probably the result of different kinds of absorption from moisture, atmospheric dust, and other related items that change with the weather.

As for the 25k spectrum recorded, consider the following:

 The curve with CCT 5 4250 K was measured during an overcast sunrise, and the 24,380-K spectrum was taken during a partly cloudy sunrise.
Since it was taken during a partly cloudy sunrise, if a thick cloud blocked most of the direct sunlight, then the spectrum could be full of background scattered light that is mostly blue. Does that sound like a reasonable explanation?

 Quote by Drakkith Hold on, if they are getting both the direct sunlight AND the scattered light from the sky, then it makes much more sense to me. There is very little variation in the CCT because overall almost the same amount of light from each wavelength hits the sensor during both the overcast and clear days. Like you said, the wavelength doesn't change. However the variation shown is probably the result of different kinds of absorption from moisture, atmospheric dust, and other related items that change with the weather.
If every reading was 5800, it would to me too. 5800 or so makes sense because that's the temperature of the sun's surface. But to have all those histogram readings at the 25000 temperature range does not make sense to me. We haven't explained where all the net extra blue light came from (i.e. there aren't enough 500 temperature readings to offset the ones towards 25000). To me, if wavelengths don't change, then don't they have to originate from somewhere?

 Quote by Drakkith As for the 25k spectrum recorded, consider the following: Since it was taken during a partly cloudy sunrise, if a thick cloud blocked most of the direct sunlight, then the spectrum could be full of background scattered light that is mostly blue. Does that sound like a reasonable explanation?
Except there were many 25000 type spectrums recorded, not just that one, including on clear blue days.

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 Quote by teddoman If every reading was 5800, it would to me too. 5800 or so makes sense because that's the temperature of the sun's surface. But to have all those histogram readings at the 25000 temperature range does not make sense to me. We haven't explained where all the net extra blue light came from (i.e. there aren't enough 500 temperature readings to offset the ones towards 25000). To me, if wavelengths don't change, then don't they have to originate from somewhere?
Offset the ones towards 25k? What do you mean? And there is no extra blue light. The reason the spectrum is at 25k is that you have a lack of longer wavelengths so the spectrum looks similar to one from a weak emitter at 25k.

 Except there were many 25000 type spectrums recorded, not just that one, including on clear blue days.
You've never seen a few clouds out on a clear sunny day? I have. I can easily believe that every once in a while the Sun is blocked out by a cloud on an otherwise clear day.

 Tags atmosphere, blackbody radiation, cct, rayleigh scattering, sunlight