Checkout the more comprehensive: The Sun and Max Planck Agree – Part Two
For regular readers of this blog, this post adds nothing new. Think of it as placeholder – a link to send people to when they ask about this basic subject.
A very handy aspect of climate science is that we can easily differentiate between solar (from the sun) radiation and terrestrial (from the earth) radiation. We can do this because emission of radiation changes with wavelength and depends on the temperature of the body radiating:
Picture the scene, if you will.
The climate science enthusiast explains that the sun heats the atmosphere and the surface of the earth – both land and sea. And everyone agrees. Of course some solar radiation is reflected and no one disputes it.
The climate science enthusiast explains that the earth, when heated up by the sun, emits thermal radiation which is upward radiation (of course). And everyone agrees.
The climate science enthusiast explains that the atmosphere absorbs some terrestrial radiation, heats up and emits thermal radiation in all directions – some of it downward. Many are not so sure.
You are mixing up solar radiation with this ‘back-radiation’ from the atmosphere. Please provide data from night-time only.
This has been a theme on many other blogs and in many comments on Science of Doom so it’s worth pulling together the basics.
Max Planck and Blackbody Radiation
Max Planck was awarded the Nobel Prize in 1918 for his contributions to science, including this gem about radiation:
This equation describes the spectral intensity of a “blackbody” as a function of temperature (absolute temperature) and wavelength.
The values of h, k and c0 are constants. T is absolute temperature and λ is wavelength.
If we plot the result of this equation for a temperature of 5780K – the sun – we get a graph which looks remarkably like the radiation we actually measure from the sun outside the atmosphere.
That’s a good thing, and Max won’t have to hand back his Nobel prize:
This is from Incropera and DeWitt – for those suspicious of everything produced by climate science, a work untouched by climate scientists – which goes by the enthralling name of Fundamentals of Heat and Mass Transfer and is now in its sixth edition.
From climate science itself, from Professor F.W. Taylor of Oxford University, from Elementary Climate Physics (2005):
Much the same. And it gives us confidence that Max Planck was right. In which case we can calculate some key parameters about the radiation from the sun and from the earth.
Solar vs Terrestrial Radiation
Solar radiation at 5780K has a few interesting properties which are easily calculated using the equation above. You can put the equation into excel and work it out for yourself.
Or you can use spectralcalc.com to do the heavy lifting. With spectralcalc just select a temperature and at the bottom select an “Upper limit” and “Lower limit” of wavelength. This will calculate the spectral intensity between these two wavelengths using Planck’s equation. Don’t forget to make sure you divide this Band Radiance by the Radiance, and not the Radiant emittance (check the units to make sure you are comparing like with like).
Some important results from Max and from the sun..
As a proportion of total solar irradiance:
- Total energy from 0 – 0.75μm 54% – all energy up to infra-red
- Total energy from 0.39μm – 0.75μm 43% – visible light only
- Total energy from 0 – 4μm 99% – all “shortwave”
- Total energy from 4-infinity 1% – all “longwave”
- Total energy from 13μm-infinity 0.03% – major 15μm CO2 band and above
- >0.75μm is infra-red (slightly different conventions exist about the maximum value for visible light, but nothing substantial)
- 0-4μm is “shortwave” – a climate science convention referring to solar radiation
- 4μm-infinity is “longwave“- a climate science convention referring to terrestrial radiation
For various temperatures of the earth’s surface, the proportion of its radiation which is in the “longwave” band (4μm and above):
- 15°C (288K) – 99.9%
- -50°C (223K) – 99.99%
- 50°C (323K) – 99.6%
The last important point to consider is that sometimes people get confused about the relative magnitude of solar and terrestrial radiation – for example, with the first graph in the post the solar radiation is much higher than the terrestrial radiation. But this is because the solar radiation in that example is the value close to the surface of the sun. But the earth only receives about one two-billionth of the solar radiation due to its distance from the sun.
Overall, and on average, the solar energy into the atmosphere is of a similar magnitude to the terrestrial radiation out of the atmosphere. (Otherwise the earth would heat up or cool down very quickly).
But in any one location on any given day it is possible for the solar radiation to vary from zero (night-time) to potentially over 1000 W/m2 (sun overhead on a cloudless sky). The absolute maximum is the total solar irradiance of 1367 W/m2 – this would be the case if the sun was directly overhead and the atmosphere reflected or absorbed nothing, which is never the case, but let’s consider this condition to get an idea of the maximum possible solar radiation in the longwave.
With the sun directly overhead and no atmospheric reflection or absorption we would have:
- 13.7 W/m2 > 4μm
- 4.1 W/m2 > 6μm
- 0.4 W/m2 > 13μm
- 0.25 W/m2 in the CO2 band of 13μm – 17μm
Well, hopefully everyone can see that even though the radiation spectrum by wavelength for any radiating body extends to infinity, the amount of solar radiation which is >4μm is 1% and the amount of terrestrial, or longwave, radiation which is <4μm is much less than 1%.
- This means, if we measure radiation with a wavelength of >4μm it is not from the sun, even if it is daytime (to a 96 – 99% accuracy).
- And if we measure radiation with a wavelength of >13μm it is not from the sun, even if it is daytime (to greater than 99.9% accuracy).
That is, unless Max Planck and the sun are wrong.
If you think this explanation or conclusions are wrong in any way then stay on this post and ask questions or explain what is wrong with it. Because if this basic element is confusing it will be difficult to make any progress in understanding climate science.
Update – followup article – The Sun and Max Planck Agree – Part Two