<p>There is simply no strong enough absorption of any of the greenhouse gases at this wavelength. However this does not mean that there is none.</p>
<p>Remember that what you are seeing here is the transmission function, and plotted on a linear scale, to add to it. The transmission function per wavelength at a certain atmospheric altitude z is defined as <span class="math-container">$T = I(z)/I_0 = e^{-\tau(z)}$</span>, where the optical depth <span class="math-container">$\tau$</span> is the line-of-sight integral over all species' opacities times densities along a path, i.e. <span class="math-container">$\tau(z)=\int_z^\infty dz\; \sum_{\rm species} \rho_s(z) \kappa_{s}(z)$</span>, where <span class="math-container">$\rho(z)$</span> is the density of a species <span class="math-container">$s$</span> at a given altitude, and <span class="math-container">$\kappa_{s}$</span>.<br />
A quick look at the opacity of water at 1 bar and 300K in logscale (taken from the <a href="https://dace.unige.ch/opacity/" rel="noreferrer">DACE opacity database</a>) shows that there is just a significant drop in the regular molecular wavebands at this wavelength, and nothing else. Same with the other species.</p>
<p><a href="https://i.sstatic.net/06vz0.png" rel="noreferrer"><img src="https://i.sstatic.net/06vz0.png" alt="Opacity function of water at 1 bar and 300K" /></a></p>
<p>So the fact that just at 4 micron there seems to be a suspicious drop is because our atmospheric column depth integral over <span class="math-container">$\rho(z)$</span> at this wavelength just gives a small, but nonzero value for <span class="math-container">$\tau(z)$</span>. If the transmission plot were logarithmic, you'd see this nonzero value.</p>
<p>Additionally, to try and make sense of</p>
<blockquote>
<p>Why is this? It seems like a rather odd coincidence for so many things to be transparent to 4 μm (a specific wavelength of mid-wavelength infrared) EM radiation.</p>
</blockquote>
<p>Just think of molecular opacities being periodic signals in wavelength space. If you stack enough periods, you will always find a minimum somewhere, by superposition. For the few ingredients you mentioned, this minimum just happens to be at 4<span class="math-container">$\mu$</span>m.</p>

CC BY-SA 4.0
2022-06-28T14:25:27.307Z
2022-06-28T14:25:27.307Z
AtmosphericPrisonEscape
<p>Looking at <a href="https://en.wikipedia.org/wiki/Absorption_band" rel="noreferrer">the Wikipedia page for absorption bands</a>, it seems to me that there's a sizable window - i.e. a <a href="https://en.wikipedia.org/wiki/Maxima_and_minima" rel="noreferrer">local minimum</a> - in the graph for <a href="https://en.wikipedia.org/wiki/Electromagnetic_radiation" rel="noreferrer">electromagnetic radiation</a> absorption, as per the edited image below.</p>
<p><a href="https://en.wikipedia.org/wiki/Water_vapor" rel="noreferrer">Water vapor</a>, <a href="https://en.wikipedia.org/wiki/Oxygen" rel="noreferrer">oxygen</a>, <a href="https://en.wikipedia.org/wiki/Ozone" rel="noreferrer">ozone</a>, and <a href="https://en.wikipedia.org/wiki/Methane" rel="noreferrer">methane</a> appear to be entirely transparent to radiation of 4 μm wavelength, <a href="https://en.wikipedia.org/wiki/Carbon_dioxide" rel="noreferrer">carbon dioxide</a> only appears to start absorbing it <em>after</em> that point, and even <a href="https://en.wikipedia.org/wiki/Nitrous_oxide" rel="noreferrer">nitrous oxide</a> has a window there. Moreover, <a href="https://en.wikipedia.org/wiki/Rayleigh_scattering" rel="noreferrer">Rayleigh scattering</a> is also minimal there.</p>
<p>On top of <em>that</em>, <a href="https://earthscience.stackexchange.com/a/13621/23134">this Earth Science Stack Exchange answer</a> by <a href="https://earthscience.stackexchange.com/users/11908/camilo-rada">Camilo Rada</a> and <a href="https://webbook.nist.gov/cgi/cbook.cgi?ID=C7446095&amp;Type=IR-SPEC&amp;Index=0" rel="noreferrer">its source</a> show minimal (sub-0.5%) absorbance of sulfur dioxide at that wavelength.</p>
<p>Why is this? It seems like a rather odd coincidence for so many things to be transparent to 4 μm (a specific wavelength of <a href="https://en.wikipedia.org/wiki/Infrared#Regions_within_the_infrared" rel="noreferrer">mid-wavelength infrared</a>) EM radiation.</p>
<p><a href="https://i.sstatic.net/jOhUm.png" rel="noreferrer"><img src="https://i.sstatic.net/jOhUm.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-06-27T04:09:58.527Z
Wonder if this may wind up being more of a general chemistry question, as I'd imagine if there is a focused reason, it's to do with specific molecular reasonings?  But perhaps someone has some insight here.
JeopardyTempest
CC BY-SA 4.0
2022-06-27T04:11:50.930Z
Looking at the layout of the different absorption graphs, though, it would seem it's just mainly that there's periodic gaps in H2O, and nothing else happens to be there.  But there are very similar sized depressions along the absorptions/scattering profile, wherever water vapor has gaps and there doesn't happen to be another major constituent in that window.
JeopardyTempest
CC BY-SA 4.0
2022-06-27T04:16:45.547Z
@JeopardyTempest Well, my point is that everything on the graph seems to have depressions there, which isn't the case in other places on it - if this is a coincidence, it's a rather impressive one. The next candidate for such a spot appears to be at the 6 μm mark, where everything except for water vapor appears to have a gap.
KEY_ABRADE
CC BY-SA 4.0
2022-06-27T04:25:06.380Z
in that single gap is the cause for and explanation of the greenhouse effect,and it show why CO2 concentration is important for our planets temperature.
trond hansen
CC BY-SA 4.0
2022-06-27T04:34:21.897Z
@trondhansen So, essentially: thermal radiation gets in through that gap, which is transparent to it, soaks into the Earth, and then is radiated away at a wavelength that the atmosphere does absorb?
KEY_ABRADE
CC BY-SA 4.0
2022-06-27T04:50:20.463Z
@KEY_ABRADE it works like this:short wave radiation from the sun heats the ground and air and this heat gets radiated  out at a longer wavelenght that is at or close to the wavelenght in the gap in your graph,as you can see CO2-methane and nox blocks radiation in different parts of the gap.
trond hansen
CC BY-SA 4.0
2022-06-27T07:38:22.360Z
Overall looking at the figure I'd suggest all the other factors (other than Rayleigh scattering) are predominantly low everywhere on the graph, so I wouldn't want to call them gaps. A bit like being surprised you can see the sun when there are no clouds (the dominant factor)... because planes, meteors, etc in rare circumstances block the sun? From your graphs, water vapor's cyclical blocking shape (which would seem an interesting Q itself) seems the dominant factor, and the other gases very localized impacts (of which CO2/CH4 happen to fall more in IR than visible and so are important to us)
JeopardyTempest
CC BY-SA 4.0
2022-06-27T07:40:04.440Z
(Rayleigh scattering seems a much less complex thing, [continually increasing as wavelength decreases because the relative size of particles increases vs the light ray](http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html#:~:text=Rayleigh%20scattering%20refers%20to%20the,gives%20us%20the%20blue%20sky.))
JeopardyTempest
CC BY-SA 4.0
2022-06-27T14:47:55.867Z
"Why is this?" -Because there are no GHG in the atmosphere whose band structure is suitable for absorbing. https://en.wikipedia.org/wiki/Electronic_band_structure                        
The two infrared windows in the wavelength ranges 3.4-4.1 μm and 8-13 μm are of particular importance.  A further increase in atmospheric carbon dioxide concentration can lead to a narrowing of the atmospheric window at 3.4-4.1 μm. Water(red) and ice(blue) absorb much better than water vapor(green) in this range. https://upload.wikimedia.org/wikipedia/commons/0/0f/Water_infrared_absorption_coefficient.gif
Rammstein
CC BY-SA 4.0
2023-04-25T12:53:14.717Z
For laughs,
http://cires1.colorado.edu/jimenez/AtmChem/CHEM-5151_S05_L22_Climate.pdf slide 5 "Transparent in visible and atmospheric window
Also e.g. @ 4 µm, but we don’t care!"
bsb
<atmosphere><atmospheric-chemistry><atmospheric-radiation><electromagnetism>
Why is there a window in the absorption spectrum of Earth's atmosphere at a wavelength of 4 μm?
KEY_ABRADE
# Why is there a window in the absorption spectrum of Earth's atmosphere at a wavelength of 4 μm?

(Asked by: username_0 on 2022-06-27)

Looking at [the Wikipedia page for absorption bands](https://en.wikipedia.org/wiki/Absorption_band), it seems to me that there's a sizable window - i.e. a [local minimum](https://en.wikipedia.org/wiki/Maxima_and_minima) - in the graph for [electromagnetic radiation](https://en.wikipedia.org/wiki/Electromagnetic_radiation) absorption, as per the edited image below.

[Water vapor](https://en.wikipedia.org/wiki/Water_vapor), [oxygen](https://en.wikipedia.org/wiki/Oxygen), [ozone](https://en.wikipedia.org/wiki/Ozone), and [methane](https://en.wikipedia.org/wiki/Methane) appear to be entirely transparent to radiation of 4 μm wavelength, [carbon dioxide](https://en.wikipedia.org/wiki/Carbon_dioxide) only appears to start absorbing it *after* that point, and even [nitrous oxide](https://en.wikipedia.org/wiki/Nitrous_oxide) has a window there. Moreover, [Rayleigh scattering](https://en.wikipedia.org/wiki/Rayleigh_scattering) is also minimal there.

On top of *that*, [this Earth Science Stack Exchange answer](https://earthscience.stackexchange.com/a/13621/23134) by [Camilo Rada](https://earthscience.stackexchange.com/users/11908/camilo-rada) and [its source](https://webbook.nist.gov/cgi/cbook.cgi?ID=C7446095&Type=IR-SPEC&Index=0) show minimal (sub-0.5%) absorbance of sulfur dioxide at that wavelength.

Why is this? It seems like a rather odd coincidence for so many things to be transparent to 4 μm (a specific wavelength of [mid-wavelength infrared](https://en.wikipedia.org/wiki/Infrared#Regions_within_the_infrared)) EM radiation.

[![enter image description here](https://i.sstatic.net/jOhUm.png)](https://i.sstatic.net/jOhUm.png)

**Tags:** atmosphere, atmospheric-chemistry, atmospheric-radiation, electromagnetism

> **Comments:**
> **username_1**: Wonder if this may wind up being more of a general chemistry question, as I'd imagine if there is a focused reason, it's to do with specific molecular reasonings?  But perhaps someone has some insight here.  
> **username_1**: Looking at the layout of the different absorption graphs, though, it would seem it's just mainly that there's periodic gaps in H2O, and nothing else happens to be there.  But there are very similar sized depressions along the absorptions/scattering profile, wherever water vapor has gaps and there doesn't happen to be another major constituent in that window.  
> **username_0**: @username_1 Well, my point is that everything on the graph seems to have depressions there, which isn't the case in other places on it - if this is a coincidence, it's a rather impressive one. The next candidate for such a spot appears to be at the 6 μm mark, where everything except for water vapor appears to have a gap.  
> **username_2**: in that single gap is the cause for and explanation of the greenhouse effect,and it show why CO2 concentration is important for our planets temperature.  
> **username_0**: @username_2 So, essentially: thermal radiation gets in through that gap, which is transparent to it, soaks into the Earth, and then is radiated away at a wavelength that the atmosphere does absorb?  
> **username_2**: @username_0 it works like this:short wave radiation from the sun heats the ground and air and this heat gets radiated  out at a longer wavelenght that is at or close to the wavelenght in the gap in your graph,as you can see CO2-methane and nox blocks radiation in different parts of the gap.  
> **username_1**: Overall looking at the figure I'd suggest all the other factors (other than Rayleigh scattering) are predominantly low everywhere on the graph, so I wouldn't want to call them gaps. A bit like being surprised you can see the sun when there are no clouds (the dominant factor)... because planes, meteors, etc in rare circumstances block the sun? From your graphs, water vapor's cyclical blocking shape (which would seem an interesting Q itself) seems the dominant factor, and the other gases very localized impacts (of which CO2/CH4 happen to fall more in IR than visible and so are important to us)  
> **username_1**: (Rayleigh scattering seems a much less complex thing, [continually increasing as wavelength decreases because the relative size of particles increases vs the light ray](http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html#:~:text=Rayleigh%20scattering%20refers%20to%20the,gives%20us%20the%20blue%20sky.))  
> **username_3**: "Why is this?" -Because there are no GHG in the atmosphere whose band structure is suitable for absorbing. https://en.wikipedia.org/wiki/Electronic_band_structure                         The two infrared windows in the wavelength ranges 3.4-4.1 μm and 8-13 μm are of particular importance.  A further increase in atmospheric carbon dioxide concentration can lead to a narrowing of the atmospheric window at 3.4-4.1 μm. Water(red) and ice(blue) absorb much better than water vapor(green) in this range. https://upload.wikimedia.org/wikipedia/commons/0/0f/Water_infrared_absorption_coefficient.gif  
> **username_4**: For laughs, http://cires1.colorado.edu/jimenez/AtmChem/CHEM-5151_S05_L22_Climate.pdf slide 5 "Transparent in visible and atmospheric window Also e.g. @ 4 µm, but we don’t care!"  

---

## 1 answers

### Answer by username_5 on 2022-06-28. Score: 5 | Accepted answer

There is simply no strong enough absorption of any of the greenhouse gases at this wavelength. However this does not mean that there is none.

Remember that what you are seeing here is the transmission function, and plotted on a linear scale, to add to it. The transmission function per wavelength at a certain atmospheric altitude z is defined as $T = I(z)/I\_0 = e^{-\tau(z)}$, where the optical depth $\tau$ is the line-of-sight integral over all species' opacities times densities along a path, i.e. $\tau(z)=\int\_z^\infty dz\; \sum\_{\rm species} \rho\_s(z) \kappa\_{s}(z)$, where $\rho(z)$ is the density of a species $s$ at a given altitude, and $\kappa\_{s}$.  
A quick look at the opacity of water at 1 bar and 300K in logscale (taken from the [DACE opacity database](https://dace.unige.ch/opacity/)) shows that there is just a significant drop in the regular molecular wavebands at this wavelength, and nothing else. Same with the other species.

[![Opacity function of water at 1 bar and 300K](https://i.sstatic.net/06vz0.png)](https://i.sstatic.net/06vz0.png)

So the fact that just at 4 micron there seems to be a suspicious drop is because our atmospheric column depth integral over $\rho(z)$ at this wavelength just gives a small, but nonzero value for $\tau(z)$. If the transmission plot were logarithmic, you'd see this nonzero value.

Additionally, to try and make sense of

> Why is this? It seems like a rather odd coincidence for so many things to be transparent to 4 μm (a specific wavelength of mid-wavelength infrared) EM radiation.

Just think of molecular opacities being periodic signals in wavelength space. If you stack enough periods, you will always find a minimum somewhere, by superposition. For the few ingredients you mentioned, this minimum just happens to be at 4$\mu$m.


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