Arctic Sea Ice update: everything is proceeding exactly as we had foreseen

March 25, 2017

Graph 2017

If you read The Guardian’s news coverage of the extent of Arctic Sea Ice, you might be forgiven for thinking that something special had happened.

Arctic ice falls to record winter low after polar ‘heatwaves’

They state that2017 is the third year in a row the Arctic’s winter ice has set a new low.“. And they quote the director of the US National Snow and Ice Data Centre (NSIDC) as saying

“I have been looking at Arctic weather patterns for 35 years and have never seen anything close to what we’ve experienced these past two winters,”. 

But the truth is simpler and can be seen and understood by a child.

The extent of Arctic Sea Ice is declining year on year.
It has been happening for a couple of decades and we have no reason to think it will stop. 

The graph at the head of the page shows the extent of Arctic Sea Ice in millions of square kilometres. This has been assessed by satellites* every day since 20th October 1978 and the data can be downloaded from here.

As the graph shows, each year the sea ice grows in the northern hemisphere winter by an astonishing 10 million square kilometres. And shrinks by a corresponding amount in the summer.

The graph shows that on average:

  • The maximum extent of the sea ice in winter has been falling by about 44,000 square kilometres every year.
  • The minimum extent of the sea ice in summer has been falling about twice as fast – by about 84,000 square kilometres every year.

So since 1979,

  • the extent of the winter sea ice maximum has fallen by about 1.6 million square kilometres  and,
  • the extent of the summer sea ice minimum has fallen by about 3.2 million square kilometres .

To put that into context, the 3.2 million square kilometres is about 12 times the land area of the UK – or roughly the land area of India.

The two graphs below show the decline in winter maxima and summer minima in more detail.

And what is clear is that the decline in Arctic Sea Ice this year is pretty much exactly what we would have anticipated.

Graph 2017-3

Graph 2017-2

What happens next?

Well, we are now talking about ‘the future’ so the answer has to be ‘nobody knows’.

But the trends look to be well-established, and in our best understanding, the ultimate cause of the decline – the warming of our planet’s surface – will not abate for many decades.

So eventually we will see the Sea Ice Extent fall to zero in the summer. Drawing a straight line through the data, one obtains an estimate of about 2065.

However many ‘so-called experts’ think that an ice-free summer will come much sooner. They argue that sea ice extent is a 2-dimensional measure of a 3-dimensional quantity – the volume of sea ice.

They argue that accompanying the decline in sea ice area, there has been a thinning of the sea ice.

Satellite measurements of sea ice thickness are relative new, and don’t yet show any clear trend. But despite that, scientists have been combining the sparse data that do exist with the data on sea ice area to produce an estimate for Sea Ice Volume . Their estimates are shown below.

Sea Ice Volume March 2017

Now we can see the true drama of the situation. While the sea ice minimum area has declined by approximately 30%, the sea ice minimum volume has declined by approximately 70%.

For this data, a linear decline no longer captures the trend of the data. Fitting a quadratic trend and extrapolating, the estimate of the date at which summer sea ice volume reaches zero moves forward from 2065 to 2021.

As I mentioned, we are discussing ‘the future’ so no-one knows what is really going happen: 2021 is probably too early, but 2065 is probably too late

But as the trend continues, the likelihood is that the sea ice will become more fragile, and eventually it will become thin enough that even mild storms will break it up.

In our lifetimes** we will reach a condition where the sea ice in the northern hemisphere entirely melts every summer. The North Pole will have become the North Pool.

====================================================

*Reader: I had thought the measurement was made from analysing visual images, but in fact it is made using microwaves. The emission of microwaves from water and ice have different characteristic polarisations and the contrast allows the fraction of sea-ice to be estimated. Details here. Sorry for the initial mistake, and thank you to Victor Venema for spotting it.

**Reader: I hope your life is long and healthy.

How would you take a dinosaur’s temperature?

March 15, 2017
A tooth from a tyrannosaurus rex.

A tooth from a tyrannosaurus rex.

Were dinosaurs warm-blooded or cold-blooded?

That is an interesting question. And one might imagine that we could infer an answer by looking at fossil skeletons and drawing inferences from analogies with modern animals.

But with dinosaurs all being dead these last 66 million years or so, a direct temperature measurement is obviously impossible.

Or so I thought until earlier today when I visited the isotope facilities at the Scottish Universities Environmental Research Centre in East Kilbride.

There they have a plan to make direct physical measurements on dinosaur remains, and from these measurements work out the temperature of the dinosaur during its life.

Their cunning three-step plan goes like this:

  1. Find some dinosaur remains: They have chosen to study the teeth from tyrannosaurs because it transpires that there are plenty of these available and so museums will let them carry out experiments on samples.
  2. Analyse the isotopic composition of carbonate compounds in the teeth. It turns out that the detailed isotopic composition of carbonates changes systematically with the temperature at which the carbonate was formed. Studying the isotopic composition of the carbon dioxide gas given off when the teeth are dissolved reveals that subtle change in carbonate composition, and hence the temperature at which the carbonate was formed.
  3. Study the ‘formation temperature’ of the carbonate in dinosaur teeth discovered in a range of different climates. If dinosaurs were cold-blooded, (i.e. unable to control their own body temperature) then the temperature ought to vary systematically with climate. But if dinosaurs were warm-blooded, then the formation temperature should be the same no matter where they lived (in the same way that human body temperature doesn’t vary with latitude).
A 'paleo-thermometer'

A ‘paleo-thermometer’

I have written out the three step plan above, and I hope it sort of made sense.

So contrary to what I said at the start of this article, it is possible – at least in principle – to measure the temperature of a dinosaur that died at least 66 million years ago.

But in fact work like this is right on the edge of ‘the possible’. It ought to work. And the people doing the work think it will work.

But the complexities of the measurement in Step 2 appeared to me to be so many that it must be possible that it won’t work. Or not as well as hoped.

However I don’t say that as a criticism: I say it with admiration.

To be able to even imagine making such a measurement seems to me to be on a par with measuring the cosmic microwave background, or gravitational waves.

It involves stretching everything we can do to its limits and then studying the faint structures and patterns that we detect. Ghosts from the past, whispering to us through time.

I was inspired.

=============================

Thanks to Adrian Boyce and Darren Mark for their time today, and apologies to them both if I have mangled this story!

Light Sabre Research

March 5, 2017

img_5001

Sometimes one finds oneself by chance at the cutting edge of a new field of research.

This Saturday, I found myself in a secret laboratory in the heart of England, and I was fortunate enough to try out the latest in Light Sabre technology.

It’s risky: It’s scary: but if one is guided by ‘the force’ then great things may be possible.

May the force be with you.

Remarkably Unremarkable

February 24, 2017

img_4966

The ‘Now’

‘The future’ is a mysterious place.

And our first encounter with ‘the future’ is ‘the now’.

Today I felt like I encountered the future when I drove a car powered by a hydrogen fuel cell. And far from being mysterious it was remarkably unremarkable.

The raw driving experience was similar to using a conventional car with automatic transmission.

But instead of filling the car with liquid fuel derived from fossil plant matter,  I filled it with hydrogen gas at a pressure 700 times greater than atmospheric pressure.

img_4976

This was achieved using a pump similar in appearance to a conventional petrol pump.

img_4964

This was the interface to some industrial plant which generated 80 kg of hydrogen each day from nothing more than electricity and water. This is enough to fill roughly 20 cars.

This is small scale in comparison with a conventional petrol station, but these are early days. We are still at the interface with the future. Or one possible future.

The past

Some years ago, I remember making measurements of the temperature and humidity inside a fuel cell during operation.

The measurements were difficult, and the results surprising – to me at least.

And at the end of the project I remember thinking “Well, that was interesting, but it will never work in practice”.

Allow me please to eat my words: it works fine.

Today I was enormously impressed by the engineering prowess that made the fuel cell technology transparent to the driver.

The future

What I learned today was that the technology to make cars which emit no pollution at their point of use exists, now.

The range of this car is 300 miles and it takes only 5 minutes to re-fill. When there are more re-filling stations than the dozen or so currently around the UK, this will become a very attractive proposition.

I have no idea if fuel cell cars will become ubiquitous. Or whether they will become novelties like steam-powered cars from the end of the nineteenth century.

Perhaps this will represent the high-water mark of this technology. Or perhaps this will represent the first swallow in a summer of fuel cell cars.

None of us can know the future. But for the present, I was impressed.

It felt like the future was knocking on the door and asking us to hurry up.

Coping by counting

February 12, 2017

months-to-retirement

Just 6 weeks ago, I reflected that 2016 hadn’t been as bad as some previous years.

Sadly the start to 2017 has been a nightmare. But I am trying to stay positive.

As many people know, one way to cope with stress is to breathe deeply, and count slowly.

Following this reasoning, I created the chart above which allows me to count down the months  until I can claim my state pension.

In fact I could possibly retire a few months before that. The single red figure in April 2025 is the date that our mortgage will be paid off – and that is less than 100 months away!

It’s a long count but if I just keep calm and remember to breathe…. two…three…,  I think I can count down from 107.

Resources

If you would like to do something similar:

  • You can calculate the number of days between different events here:
  • You can find out your State Pension Age here

Keep calm!

Do you really want to know if global warming is real?

January 28, 2017

About a year ago, I thought that Climate Change Deniers had lost the argument.

I thought that we were all moving on to answering more interesting questions, such as what to do about it.

But it seems I was wrong. It seems that in this post-truth world, climate change deniers are uninterested in reality – preferring instead alternative facts.

I am left speechless in the face of this kind of intellectual dishonesty.

Actually I am only almost speechless. I intend to continue trying to empower people by fighting this kind deception.

Rather than trying to woo people over to my view, my aim is simply to offer people the chance to come to their own informed opinion.

See for yourself

As part of my FREE University of Chicago Course on Global Warming, I have been using some astonishing FREE software. And its FREE!

1

The ‘Time Series Browser’ allows one to browse a 7000 station subset of our historical temperature records from meteorological stations around the world.

  • The data are the local station temperatures averaged over 1 month, 1 year or 1 decade. Whichever you choose you can also download this data into a spreadsheet to have fun with on your own!
  • One can select sets of data based on a variety of criteria – such as country, latitude band, altitude, or type of geographical location – desert, maritime, tropical etc. Or you can simply pick a single station – maybe the one nearest you.

Already this is enormously empowering: this is the pretty much the same data set that leading climate scientists have used.

For this article I randomly chose a set of stations with latitudes between 20°N and 50°N.

7

The bold dots on the map show the station locations, and the grey dots (merging into a continuous fill in parts) are the available locations that I could have chosen.

The data from the selected stations is shown below.  Notice the scale on the left hand side runs from -10 °C to + 30 °C.

2

In this form it is not obvious if the data is warming or cooling: And notice that only a few data sets span the full time range.

So how do we discover if there are trends in the data?

The first step

Once you have selected a set of stations one can see that some stations are warm and others cool. In order to be able to compare these data fairly, we subtract off the average value of each data set between 1900 and 1950.

This is called normalisation and allows us to look in detail at changes from the 1900-1950 average independent of whether the station was in a warm place or a cold place.

3

Notice that the scale on the left-hand side is now just ± 3.5 °C.

The second step

One can then average all the data together. This is has the effect of reducing the fluctuations in the data.

One can then fit a trend-line to see if there is a recent warming or cooling trend.

5

For this particular set of stations its pretty clear that since 1970, there is a warming trend. The software tells me it is approximately 0.31 ± 0.09 °C per decade.

What I have found is that for any reasonably diverse set of stations a warming trend always emerges. I haven’t investigated this thoroughly, but the trend actually seems to emerge quite clearly above the fluctuations.

But you can check that for yourself if you want!

Is it a cheat? No!

You can check the maths of the software by downloading the data and checking it for yourself.

Maybe the data is fixed? You download the source data yourself – it comes from the US Global Historical Climatology Network-Monthly (GHCN-M) temperature data-set.

But accessing the raw data is quite hard work. If you are a newbie, it will probably take you days to figure out how to do it.

There is more!

This ability to browse, normalise, average and fit trends to data is cool. But – at the risk of sounding like a shopping channel advertorial – there is more!

It can also access the calculations of eleven different climate models.

For the particular set of stations that you have selected, the software will select the climate model predictions (a) including the effect of human climate change and (b) without including human-induced climate change.

For my data selection I chose to compare the data with the predictions of the CCSM4 Climate model. The results are shown below

6

You can judge for yourself whether you think the trend in the observed data is consistent with the idea of human-induced climate change.

For the particular set of stations I chose, it seems the CCSM4 climate model can only explain the data by including the effect of human-induced climate change.

But Michael: this is just too much like hard work!

Yes and no. This analysis is conceptually challenging. But it is not crazily difficult. For example:

  • Schoolchildren could do this with help from a teacher.
  • Friends could do it as a group and ask each other for help.
  • University students could do this.
  • Scout groups could do it collectively.

It isn’t easy, but ultimately, if you really want to know for yourself, it will take some work. But then you will know.

So why not have a go?  The software is described in more detail here, and you can view a video explaining how to use the software here.

[January 28th 2017: Weight this morning 71.2 kg: Anxiety: Sick to my stomach: never felt worse]

5.What was all that about?

January 3, 2017

duty_calls

Interviewer: So Michael, why did you write the last four articles (1,2,3,4) on the transmission of infrared radiation through the atmosphere: that stuff is already well known?

Me: I know, but I was irritated by a friend of a friend who wrote an “exposé” of why carbon dioxide can’t cause global warming.

Interviewer: Curious. Were they an expert in Climate Science? Or had they made a study of radiative transfer through the atmosphere?

Me: Neither. I think they were an electrical engineer.

Interviewer: An electrical engineer? Why did they think that their assessment outweighed the view of the large number of experts who had studied this intensively over the last century or so?

Me: I think it is an example of the Dunning-Kruger effect in which people who don’t know about a subject fail to appreciate how little they know. We are all affected by it at times.

Interviewer: OK, So you wrote all this just to set them straight?

Me: Yes, and hopefully to help others who are curious about radiative transfer. It is complicated.

Interviewer: And how do you feel about it now?

Me: Numb and Tired. But OK. I like one or two of the graphs I have created, and I enjoyed learning how to make animated GIFs. I have also learned quite a bit about MODTRAN.

Interviewer: But…

Me: But the articles took literally weeks to prepare and I still don’t feel satisfied with them. However now, if I see anyone else write stuff like this:

The bottom line is that once Carbon Dioxide reaches a concentration that makes the atmosphere completely opaque in the band where it resonates,  further increases in the concentration cannot result in any additional blocking

I will know exactly where to send them. And so will you.

 

4. Feedback and Climate Models

January 3, 2017

In the last two articles I have written at great length (sorry) about the way carbon dioxide affects the transmission of infrared light vertically through the atmosphere.

Changes in this transmission are – we think – causing Global Warming.

The physics of the effect on infrared transmission is beyond argument. However this is just one component in the energy flows that constitute Earth’s climate system.

What else do we need to consider before we can conclude that carbon dioxide is causing global warming?

What else do we need to consider?

atmosphericmodelschematic

There is so much! The calculations in the previous articles only considered the transmission of infrared radiation and light up and down a vertical column of air with a variable temperature and pressure.

However in reality:

  • Light transmission does not just take place in one dimension (up and down) but in three dimensions.
  • Illumination from the Sun strikes each part of the Earth at different angles.
  • The infrared radiation from the Earth also takes place at many angles, and from many different heights in the atmosphere.
  • There are clouds which dramatically change atmospheric transmission.
  • The air moves in complicated ways “up and down and round and round”.

Additionally, the energy balance is dynamic – all the above factors change from minute to minute – around the surface of the Earth. And the Earth is not a sphere, and is not uniform and does not move in a circle around the Sun. And the Sun’s output varies from year to year.

In order to calculate the long-term averages of temperature and rainfall that determine the climate, we need to take into account all – or as many as possible – of the above effects.

There will be a cascade effects caused by increased  atmospheric carbon dioxide – such as changes in the location or timing of cloud formation. Additionally changes in the Earth’s surface temperature will affect the temperature of the atmosphere.

These changes may either ameliorate or exacerbate the initial effects of increased carbon dioxide concentrations.

In the end one ends up with a complex General Circulation Model of the entire Climate of the Earth – such as that illustrated above. The MODTRAN code – or something similar – is incorporated as one element of all the extant general circulation models.

If it’s all so complicated…why are scientists so sure of themselves?

There are, I think, two or possibly three reasons.

The first concerns calculations of the future effect of increasing carbon dioxide concentrations.

Simple calculations made more than 100 years ago agree pretty well with the results of most recent complicated calculations.

This indicates that the simple calculation has captured the essence of the problem.

Secondly, there is broad agreement with experimental observations – the Earth’s surface really is warming (Data Analysis 1 and Data Analysis 2). You can download the raw data from land stations here.

The third reason – which is really just a different way of thinking about the previous two reasons – is that given its effect on infrared transmission, it would be truly astonishing if adding carbon dioxide to the atmosphere did not affect the climate at all!

Once one admits to this point it becomes a question of asking what the effect will be? And every calculation I have ever seen predicts warming. If anyone has found something different, I would love to hear about it.

What about the saturation of the carbon dioxide bands?

A friend of a friend wrote an analysis in which he argued that increased concentrations of carbon dioxide could not cause global warming because:

The bottom line is that once Carbon Dioxide reaches a concentration that makes the atmosphere completely opaque in the band where it resonates,  further increases in the concentration cannot result in any additional blocking.

He was imagining that the ‘band’ where carbon dioxide molecules resonate is fixed. He was wrong.

For the individual molecules, the frequencies at which they vibrate are fixed. And the width of their ‘natural’ absorption line is fixed by the local temperature and pressure.

But transmission through the atmosphere is complicated, and the width of the band that absorbs radiation just keeps growing in width as the concentration increases.

Additionally the height in the atmosphere at which the absorption takes place gets lower – and hence warmer – and re-radiates more radiation back down to Earth.

That’s all for this article:

Here we looked at how the MODTRAN calculations fit into more complex models of global climate.

The next (and final) article is about the conclusions we can draw from these calculations.

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.


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