3. Light transmission through the atmosphere

In part 2 I looked at transmission of infrared light through a gas containing a molecule which absorbs infrared light at one particular frequency.

We saw that at higher concentrations, the absorption at specific frequencies broadened until entire bands of frequencies were ‘blocked’.

We saw that the width of the ‘blocked bands’ continued to increase with increasing concentration.

Here we look at how that insight can be applied to transmission of infrared light through Earth’s atmosphere.

This is even more complicated.

• We are mainly interested in transmission of infrared light from the Earth’s surface out through the atmosphere and into space, but the atmosphere is not at a uniform temperature or pressure.
• When absorbing gases are present, the air is not just a ‘conduit’ through which infra-red light passes – the air becomes a source of infrared radiation.
• We are mainly interested in the effect of carbon dioxide – but there are several other infrared ‘active’ gases in the atmosphere.
• Gases are not the only thing in the atmosphere: there is liquid water and particulates.

So it’s complicated: Here are a few more details.

1. Density.

If the carbon dioxide is distributed in a fixed proportion to the amount of oxygen and nitrogen through the atmosphere, then it will have more effect where the atmosphere is most dense: i.e. lower down in the atmosphere.

And density is affected by both temperature and pressure.

Since carbon dioxide molecules absorb 100% of the infrared light with wavelengths around 15 micrometres, as we saw in the previous article, increasing the concentration of carbon dioxide increases the range of wavelengths that are ‘blocked’. This is illustrated in the figure at the head of the article.

Increasing the concentration of carbon dioxide also changes the height in the atmosphere at which absorption takes place.

2. Re-radiation.

Once absorbed by a carbon dioxide molecule, the infrared light does not just disappear.

It increases the amplitude of vibration of the molecule and when the molecule collides with neighbouring molecules it shares that energy with them, warming the gas around it.

A short while later the molecule can then re-radiate light with the same frequency. However the brightness with which the gas ‘glows’ relates to its local temperature.

Some of this re-radiation is downward – warming the Earth’s surface – and giving rise to a ‘greenhouse’ effect.

And some of this re-radiation is upward – eventually escaping into space and cooling the Earth.

3. Other things.

Carbon dioxide is not only the infrared active gas in the atmosphere. There is also methane, ozone and, very significantly, water vapour.

There is also condensed water – clouds.

And then there are particulates – dust and fine particles.

All of these affect transmission of light through the atmosphere to some extent.

For an accurate calculation – all these effects have to be considered.

MODTRAN

Fortunately, the calculation of transmission through the atmosphere has been honed extensively – most notably by the kind people at the  US Air Force.

However the code is available for anyone to calculate atmospheric transmission.

David Archer and the University of Chicago kindly host a particularly friendly front end for the code.

Aside from just clicking around, it is possible to download the results of the calculations and that is how I plotted the graphs at the head of the page.

To get that data I removed all the other greenhouse gases from the atmosphere (including water), and varied only the concentration of carbon dioxide.

Notice that the absorption lines grow into bands that continue to broaden as we add more and more  carbon dioxide. This is exactly what we saw in the simple model in the second article.

This shows that the transmission through the atmosphere is still being affected by additional carbon dioxide, and these bands have not ‘saturated’.

Asking a question

MODTRAN can answer some interesting questions.

Assuming that the Earth’s surface is at a temperature of 15 °C, we can ask MODTRAN to calculate how much infrared light leaves the top of the atmosphere (100 km altitude) as we add more carbon dioxide. The result of these calculations are shown below:

The first thing to notice is the qualitative similarity between this graph – the result of complex and realistic calculations – with the simple spreadsheet model I showed in the second article.

The second thing to notice is that the calculations indicate that increasing the concentration of carbon dioxide in the atmosphere reduces the amount of radiation which escapes at the top of the atmosphere. And that it will continue to do so even as the concentration of carbon dioxide increases well beyond its current 400 parts per million (ppm).

Where does that absorbed radiation go? The graph below shows the results of another calculation. It imagines being on the ground and asks how much infrared light is re-radiated back to the Earth’s surface as the concentration of carbon dioxide increases.

The graph shows that matching the decline in infrared radiation leaving the top of the atmosphere, there is a matching increase in radiation falling back down to Earth.

Importantly, both these effects still depend on the concentration of carbon dioxide in the atmosphere even as the concentration grows past 400 ppm.

Over the longer term, this increase in downward radiation will increase the temperature of the Earth’s surface above the assumed 15 °C. This process will continue until the outgoing radiation leaving the top of the atmosphere is balanced with the incoming solar radiation.

That’s all for this article:

In this article we saw that transmission of infrared light through the atmosphere is complicated.

Fortunately MODTRAN software can cope with many of these complexities.

The conclusions of our calculations with MODTRAN are similar to conclusions we came to in the previous article.

Increasing the concentration of a molecule such as carbon dioxide which absorbs at a single frequency will continue to reduce transmission through the atmosphere indefinitely: there is no limit to the amount of absorption.

The next article is about the conclusions we can draw from these calculations.

2: Light transmission through a gas

In the first article I showed experimental data on the spectrum of light travelling through the atmosphere.

We saw that some frequencies of light are ‘blocked’ from travelling through the atmosphere.

Sometimes this ‘blocking’ occurs at specific frequencies, and sometimes at ranges of frequencies – known as ‘blocked bands’.

In this article, we will consider how both single frequency absorption and blocked bands arise.

Air and Light

Air is composed mainly of nitrogen, oxygen, and argon molecules. The frequencies at which these molecules naturally vibrate are very high, typically greater than 400 terahertz. High frequencies like this correspond to light in the visible or ultraviolet part of the spectrum.

Larger molecules – ones composed of more than two atoms – can vibrate more easily.

They are – in a very rough sense – ‘floppier’ and have lower natural frequencies of vibration, typically a few tens’s of terahertz.

Frequencies in that range correspond to light in the infrared part of the spectrum.

The animation below shows qualitatively the relative frequencies of a vibrational mode of an N2 molecule and a bending mode of a CO2 molecule.

When light travels through a gas containing molecules that can vibrate at the same frequency as the light wave, the molecules begin to vibrate and absorb some of the energy of the light wave.

The molecules then collide with other atoms and molecules and share their energy – warming the gas around them. The light has been absorbed by the gas.

But this absorption only happens close to the specific frequencies at which the molecules vibrate naturally.

The effect of a single frequency of vibration

The figure below shows the effect of the presence of a low concentration  of a molecule that can absorb light at a specific frequency.

The figure describes how ‘white’ light – in which all frequencies are present with equal intensity – travels through a non-absorbing gas with a low concentration of molecules which absorb at one specific frequency.

Light with a frequency – represented by a colour: yellow, orange or red – which just matches the vibrational frequency of the molecule is absorbed strongly and doesn’t make it far through the gas.

But light with frequencies on either side of this vibrational frequency is absorbed less strongly. So the percentage of light transmitted has a dip in it at the frequency of molecular vibration.

If we increase the concentration of the absorbing molecule, something really interesting happens.

The light at the central vibrational frequency is absorbed even more rapidly. But since it is already 100% absorbed – it doesn’t affect the overall transmission at this frequency. However it does affect where the light is absorbed.

But the additional concentration of absorbing molecules now absorbs strongly on either side of the main absorption frequency.

Eventually, the absorption here becomes so strong that the absorption is 100% even for frequencies that differ significantly from the main vibrational frequency.

This leads eventually to bands of frequencies that are 100% absorbed.

Band Width

Importantly, as the concentration of the absorbing molecule increases – the width of the blocked band increases.

This increase in absorption band width isn’t a property of an individual molecule – each of which just absorbs at frequencies centred around a particular frequency.

The formation of the band – and its width – is a property of a column of gas containing many absorbing molecules

This can be modelled quite easily and the output of a spreadsheet model is animated below as a function of the concentration.

In each frame of the animation, the concentration increases by a factor 2.7 – so that the concentration range covered in the seven frames is 387 (~2.7 to the power 6).

The figure shown in percent on each frame of the animation is the fraction of light in the range from 212 to 228 terahertz which has been absorbed.

Please note that the line-widths and frequencies in the model are arbitrary and approximate. However the qualitative behaviour is universal and independent of the particular mathematics I have used.

• As the concentration of an absorbing gas increases, the transmission at the central absorbing frequency eventually reaches zero.
• As the concentration increases further, the absorption increase at frequencies on either side of the central frequency.
• This eventually forms a range of blocked frequencies – and the width of this blocked range continues to increase with increasing concentration.

The fraction of light transmitted is plotted below.

Once again I would like to emphasise that the graph qualitatively characterises the absorption from a single absorption frequency as a function of concentration.

Significantly, the amount of light transmitted continues to fall even after the transmission at the central frequency reaches zero.

And notice that this broadening of the absorption bands is a property of the transmission of light through a column of gas. It is not caused by line-broadening by individual molecules.

That’s all for this article:

The story so far is that when one looks up through the atmosphere, we see ‘blocked bands’ at a range of frequencies.

In the infrared region of the spectrum, these bands arise from particular modes of vibration of specific molecules which occur at specific frequencies.

In this article we saw that even when the transmission through a gas was saturated, increasing the concentration of the absorbing molecule still reduced transmission through the gas.

This is because the width of the ‘blocked band’ is not a property of the individual absorbing molecules: it arises from transmission of light through a column of gas.

The next article is about how this effect works in Earth’s atmosphere.