Posts Tagged ‘CO2’

3. Light transmission through the atmosphere

January 3, 2017

co2_band_formation

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.

modtran-web-interface

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:

toa-radiative-power

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.

downward-flux-graph

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

January 3, 2017

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.

co2-animation

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.

absorption1

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.

absorption2

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).

single-line-absorption

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.absorption-graph-from-single-line

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.

Carbon dioxide – the full picture

November 21, 2011

Week 4 of Protons for Breakfast is approaching in which we discuss Global Warming. I have just been updating the PowerPoint slides, and checking all the links and I came across the above video (from NOAA here) . It shows the whole story in 3 minutes and 15 seconds. I think it is wonderful, but I feel it needs some explanation to get the most out of it.

Update: I asked Andy Jacobsen from NOAA (who made the video) for his comments and I have included these in blue below. We disagreed over one point and I have included our exchange at the bottom of the page.

Start to 1 minute 42 seconds:

  • This covers the period from 1980 to 2011 shows carbon dioxide concentration from at first a few, and then a few dozen, stations in the northern and southern hemisphere.
  • Look at the map for the location of the stations
  • One can see that the concentration in the southern hemisphere shows an inexorable rise, but the concentration in the northern hemisphere shows quite large annual oscillations. These are summarised in the graph on the right which shows data from the south pole in blue and data from Mauna Loa in red.
  • Looking at the ‘clock’ in the middle of the picture one can see that the CO2 concentration in the northern hemisphere falls sharply in northern hemisphere summer – when growing things grab CO2 out of the air using photosynthesis. Its amazing to think of this subtle process changing CO2 concentrations globally!
  • Notice the spikes in some of the data – presumably from monitoring sites positioned close to industrial centres.
  •  The “spikes” can also be due to natural processes, such as respiration by plants, animals, and microbes.  This is why Keeling went to Mauna Loa and the South Pole–not only were previous measurement techniques unreliable, but the ambient variability of CO2 is generally quite strong.  As the measurement network has expanded, we have begun taking measurements at sites with more local signals…hence the outliers.

 1 minute 42 seconds to 2 minutes 2 seconds:

  • Now we end the modern era measurements, and go backwards in time from 1980 to 1960 with the original data taken by Keeling at Mauna Loa.

2 minutes 2 seconds to 2 minutes 22 seconds:

  • Now the data compresses and we go backwards in time quite quickly to show the first ice core measurements which are in fantastic detail – extending back two thousand years. At this point it becomes clear how amazingly rapid the rise in CO2 concentrations has been.

2 minutes 22 seconds to 2 minutes 2 seconds to 3 minutes 15 seconds:

  • Now we reach the deep ice core results showing data that extends back first 400,000 years, and then 800,000 years.
  • We see the CO2 concentrations rising and falling by around 100 ppm – correlating with the Earth descending into ice ages when the CO2 concentration is low (180 ppm) and experiencing interglacial warm periods when the CO2 concentration is high (280 ppm). Although the CO2 concentration is not thought to have directly driven these changes, it is thought to have reinforced the changes.
  • Now we really see the context of the modern measurements. Since the period that human beings have existed as a distinct species (roughly 1 million years) we have never lived on a planet with CO2 concentrations this high.
  • The rise of humanity has all occurred since the last glacial maximum, about 20,000 years ago.
  • Concentrations now are more than 100 ppm higher than a ‘normal’ interglacial melt and will certainly rise by at least another 200 ppm in the coming decades – truly a massive change of geological significance. And although we don’t know the consequences of this for certain, they almost certainly imply a warmer and less icy world.

It would be good to know what happens next, but we have to work that out for ourselves. Sadly the BBC report today that the rate at which CO2 concentration is rising is accelerating. NOAA have the actual data which can be seen in the figure below.

NOAA data showing the rate of rise of CO2 concentrations. It appears to be accelerating.

NOAA data showing the rate of rise of CO2 concentrations. It appears to be accelerating.

Andy also wrote

I’m puzzled by your comment about CO2 not having a primary role in glacial-interglacial climate changes.

Paleoclimate researchers would all agree, I believe, that ice ages cannot be explained without invoking the radiative forcing impacts of 100ppm CO2 shifts.  Perhaps the thinking has evolved since I last checked in on this issue, but my understanding is that CO2 is the most direct driver of glacial cycles.  Of course, part of this is how you define drivers and feedbacks; water vapor is a classic example of this paradox.  It has a big radiative impact, but is generally classified as part of a feedback loop due to its short atmospheric lifetime.

I responded:

My comment about the role of CO2 is that (as I understand it) the interglacial changes are driven by orbital factors – Milankovitch cycles – and similar effects. These factors cause some warming and then this warming causes a rise in CO2 which then reinforces the warming. Similarly with glaciation – I thought the slow loss of CO2 reinforced a cooling climate trend, but did not trigger it. Obviously the situation is different now and clearly CO2 is now the trigger.

Atmospheric CO2: Looking at the data

March 23, 2010
C13/C12 Isotope Ratio. The systematic decline in this ratio is due to the distinctive isotopic ratio of fossil fuel derived CO2

C13/C12 Isotope Ratio. The systematic decline in this ratio is due to the distinctive isotopic ratio of fossil fuel derived CO2

It might seem there was very little left to say about the rise in atmospheric CO2 due to anthropogenic emissions. But the other day my colleague Martin sent me a link to two presentations at the Scripps Institute ‘Home of the Keeling Curve‘, and I found out there was plenty left to say. Scientists there presented data which actually evaluated the things I have heard people chat about for years.

  • The first topic covered was changes in the isotopic composition of the carbon dioxide in the atmosphere. This change unambiguously links the rise in CO2 to anthropogenic emissions – in case anyone really doubted that.
  • The second topic covered was the corresponding decline in the oxygen concentration of the atmosphere caused by burning all that CO2.

Isotopic Composition

Carbon is made primarily from two stable isotopes: C12 with 6 protons and 6 neutrons, and C13 with 6 protons and 7 neutrons. The heavier C13 comprises only about 1% of natural carbon. As was first observed in 1961, plants preferentially build their cells from C12 based molecules. Thus fossil fuels, which are derived from plants, have a slightly reduced  ratio of C13 to C12. Thus if the increase in the atmospheric CO2 that we have observed is really due to the emissions from fossil fuels then we should observe a corresponding decline in the ratio of C13 to C12 in the atmosphere. The Figure at the head of this article shows the data, and more detailed graphs are available at the Scripps site which explains the different curves and dots on the graph.What I found pleasing was just to encounter this data that I have heard people chat about for years.

Oxygen Depletion

Graph showing the depletion of atmospheric oxygen due to fossil fuel burning

Graph showing the depletion of atmospheric oxygen due to fossil fuel burning

One natural consequence of the reaction C + O2 → CO2 is that the amount of oxygen in the atmosphere must be decreasing. Its a small effect but once again the people at Scripps have measured the effect and made calculations to determine that the effect observed is in line with the observed CO2 emissions. The relevant data shown above and can be found several slides into this pdf presentation.

And so…

And so it is 10:48 p.m. and time for bed. But I feel the need to comment, that what I really admire about the data in these presentations is that they are so basic. Somehow people have scrabbled together enough funding to keep the measurements going for long enough for someone to recognise their profound importance. This is IMHO really admirable science. Goodnight.


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