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.

Climate Contrarians and Miocene Warmth

This is the second of two articles focussing on stories highlighted by the Climate Contrarians over at the Register.

Over the last 0.8 million years, the mean temperature of the Earth’s Surface has been highly correlated with the atmospheric concentration of carbon dioxide. The figure below shows the data over the last 0.4 million years and there is an obvious correlation between global mean temperature (blue: inferred from the relative amounts of oxygen isotopes found in water in ice cores) and atmospheric CO2 concentration (green: deduced form the concentration of CO2 in bubbles in the ice). Very roughly 100 ppm CO2 corresponds to around 10 °C of warming – a truly terrifying statistic if it holds for warming as well as cooling. The role of carbon dioxide is perfectly clear.

Graph of atmospheric concentration of CO2 (Green graph) and Global Mean temperature (Blue graph), deduced from the Vostok, Antarctica ice core as reported by Petit et al., 1999.The data are plotted at ‘thousands of years before the present, so ‘now’ is on the left of the graphs and the past runs over to the right. The main oscillations arise from changes in Earth’s orbital eccentricity, tilt, and precession called Milankovitch cycles. The correlation between CO2 concentration and global mean temperature is very clear. Picture taken from wikipedia, but other versions are available.

Into this clear situation The Register highlight a paper in Nature called Late Miocene decoupling of oceanic warmth and atmospheric carbon dioxide forcing  with the natty headline:

10 million years ago there was less CO2 – but the Earth was WARMER.

The unspoken implication is that scientists don’t understand the Climate or the role of carbon dioxide, and so maybe carbon dioxide is not necessarily causing the current bout of global warming. This implication is mischievous. Just to put the time scale into context, there were of course, no human beings alive during this era. Our evolutionary path is unsure but modern humans probably evolved a little over 1 million years ago.

All those years ago, the continents were not in very different positions from the present day: for example the Atlantic was only around 100 km narrower. And so one might assume that oceanic and atmospheric circulation were probably similar. However, it is well known that this was not the case.

One of the key differences was that the Central American Seaway closed around 5 million years ago, creating a land bridge between North and South America. This closure process – partly volcanic and partly caused by plate movement – gradually split a single pan-global ocean into two, creating separate Pacific and Atlantic Oceans. Other sea passages have also changed significantly over this period, for example the Bering Straits, which affects communication with the Arctic Sea. But the closure of the Central American Seaway is probably the most significant.

This article by the Woods Hole Oceanographic Institute  explains how this process dramatically affected oceanic and atmospheric circulation and led to the creation a few million years later of the Arctic ice sheets. Incidentally, the article points out that the Antarctic was already frozen at this point, an event triggered by the opening of the another ocean-linking region. The opening of the gap between the tip of South America, and the northern end of the Antarctic Archipelago around 34 million years ago allowed circumpolar weather systems to stabilise over the Antarctic, de-coupling it from the transport of heat from the Equator.

The closure of the Central American Seaway around 5 million years ago is thought have gradually affected circulation between the Atlantic and Pacific Oceans. These figures are collated from The Woods Hole Oceanographic Institute web site Oceanus. Click for larger version.

So in the era under discussion, ocean and climate circulation is known to have been significantly different from the present day. Given this background, the paper presents evidence from isotopic analysis of fossils for both sea-surface temperature and carbon dioxide concentration in the atmosphere – amazingly difficult data to get!

The key experimental result of the paper is shown in the figure below. The upper part shows estimates of sea surface temperatures rising as we go back in time by roughly 1 °C for each 1 million years. The lower part shows estimates of carbon dioxide concentration. I have added the current level of atmospheric CO2 concentration for reference. The gist of the paper is that back to around 5 million years ago, the elevated sea surface temperature is correlated (roughly) with CO2 concentration. But further back CO2 concentrations are lower, while sea surface temperature remains high.

The link between atmospheric carbon dioxide and global mean temperature is very clear from ice core data (purple) back to 800,000 years ago. Going back further to about 3 million years ago the data on carbon dioxide concentration are very widely spread and beyond 4.5 million years ago, there is very little data. To the extent that the older data is trustworthy, it indicates that 10 million years ago atmospheric CO2 was about the same level as it was in the late twentieth century (roughly 350 ppm) but the estimated global mean temperature was around 10 °C  warmer.

The main author LaRiviere suggests some ways in which, with a radically different oceanographic and atmospheric circulation, this de-coupling of global temperature and carbon dioxide concentration might have occurred. In particular, he highlights fossil evidence for differences in the temperature profile of the surface layers of the oceans.

Despite reading the paper several times, I confess I could not follow all his arguments in detail. However I doubt The Register had studied the paper at all, because they make no mention of this radical change in oceanographic circulation. Instead they conclude with a quote from the author:

“It’s a surprising finding, given our understanding that climate and carbon dioxide are strongly coupled to each other,” LaRiviere says.
“In the late Miocene, there must have been some other way for the world to be warm.”

The Register‘s implication is that ‘this other way’ has not been understood by modern Climate Science. And indeed it hasn’t been fully understood: that’s why this is a paper in Nature! But LaRiviere is doing his best.

Does his paper yield any insight on our current situation? In my opinion, not directly. However:

• It does highlight how relatively small geographic changes can radically affect Earth’s Climate.
• It does highlight that ice free arctic regions were possible with a world around 10 °C warmer than the present day
• It does highlight that the estimated 0.75 °C warming in 100 years that humans have achieved is a little bit less than a MILLION times faster the rate of temperature change seen on the Figure.

However these are not insights to which the Climate Contraians over at the Register wish to draw to our attention. Instead they relish confusion. How I wish they would instead take the time to present scientific papers in context, and then instead of this turgid article, I could write short articles saying what great journalists they had, and we would all be the wiser. C’est la vie.

Climate Contrarians and Glacier Retreat

Have you ever met people who just love to disagree? These contrarians revel in discord, and over at the ‘technology news’ website  The Register, they have a pile of them.

I wouldn’t normally care about this, but in addition to its regular news and views about the computer industry, The Register frequently comments on issues related to Climate Change. They don’t have a well-defined editorial view that I can discern, they just disagree with things.

One pernicious technique they use for spreading confusion is to report current scientific papers as ‘news’ items. This is fair enough in itself,  but they select only papers reporting apparently ‘odd’ results. By missing out the broader context of the work, the articles imply that this particular paper changes views radically, something which is rarely true. In fact, the reporting is the journalistic equivalent of gleefully poking sticks into the spokes of a bicycle wheel.

Let me give you a couple of examples of this stick-pokery. The first concerns glacial retreat and the second (in a following article) concerns estimates of pre-historic global temperature in the era before the Arctic developed its current ice sheet. Researching these articles has taken hours and has felt like the tedious equivalent of mending a bicycle wheel into which someone has poked a stick.

Global Glacial Retreat. This chart shows records of the numbers of glaciers which advance (BLUE) or retreat (RED) in different parts of the world. Notice the different scales on each chart. The bottom chart is the sum of the all the previous charts. Note also that the data are not exhaustive and glaciers which are stable are not counted. Click for a much larger version of this graph.

As I mentioned in a previous article, and as the figure above makes clear, we are living in an era of near global retreat of glaciers. However, this retreat cannot be blamed directly on global warming, anthropogenic or otherwise – because it began in the nineteenth century, before global temperatures rose substantially. So why are the glaciers retreating?

The best efforts at understanding this consider that the retreat in each region is due to different factors, but that global warming and changes in global climate are probably a contributory factor in explaining why the same ‘regional factors’ are causing a near universal, simultaneous and accelerating retreat.

Into this situation The Register chooses to highlight a paper which has unearthed aerial photographs of glaciers in Greenland from the 1930s. Now I didn’t actually read the paper concerned: so taking The Register‘s reporting as correct, the pictures show glacial retreat at an even faster rate than today. As the figure above shows, this is not news.

Looking at the admittedly scant early Arctic data, we see that this datum is not anomalous in any way. The paper simply adds one more point to the 30,420 points we already have. However, by highlighting the paper The Register  implies that it somehow punctures arguments that carbon dioxide is associated with global warming.

“It now appears that the glaciers were retreating even faster eighty years ago: but nobody worried about it, and the ice subsequently came back again.

The implication is that global glacial retreat is just ‘a natural phenomenon’ and that anthropogenic influence is incidental.

So they have taken a perfectly innocent paper and spun its contents to make it look like the science behind our understanding of climate is in disarray. Which it isn’t.

Click here to find out The Register’s views on the effect of carbon dioxide in Miocene Era around 10 million years ago.

The data for the figure came from Chapter 5 (pdf) of a report to the United Nations Environmental Program, but you can also find data at the World Glacier Monitoring Service:

Previous articles on Climate Sceptics can be found here, here, here and here.