Archive for the ‘Personal’ Category

Not everything is getting worse!

April 19, 2017

Carbon Intensity April 2017

Friends, I find it hard to believe, but I think I have found something happening in the world which is not bad. Who knew such things still happened?

The news comes from the fantastic web site MyGridGB which charts the development of electricity generation in the UK.

On the site I read that:

  • At lunchtime on Sunday 9th April 2017,  8 GW of solar power was generated.
  • On Friday all coal power stations in the UK were off.
  • On Saturday, strong winds and solar combined with low demand to briefly provide 73% of power.

All three of these facts fill me with hope. Just think:

  • 8 gigawatts of solar power. In the UK! IN APRIL!!!
  • And no coal generation at all!
  • And renewable energy providing 73% of our power!

Even a few years ago each of these facts would have been unthinkable!

And even more wonderfully: nobody noticed!

Of course, these were just transients, but they show we have the potential to generate electricity which has a significantly low carbon intensity.

Carbon Intensity is a measure of the amount of carbon dioxide emitted into the atmosphere for each unit (kWh) of electricity generated.

Wikipedia tells me that electricity generated from:

  • Coal has a carbon intensity of about 1.0 kg of CO2 per kWh
  • Gas has a carbon intensity of about 0.47 kg of CO2 per kWh
  • Biomass has a carbon intensity of about 0.23 kg of CO2 per kWh
  • Solar PV has a carbon intensity of about 0.05 kg of CO2 per kW
  • Nuclear has a carbon intensity of about 0.02 kg of CO2 per kWh
  • Wind has a carbon intensity of about 0.01 kg of CO2 per kWh

The graph at the head of the page shows that in April 2017 the generating mix in the UK has a carbon intensity of about 0.25 kg of CO2 per kWh.

MyGridGB’s mastermind is Andrew Crossland. On the site he has published a manifesto outlining a plan which would actually reduce our carbon intensity to less than 0.1 kg of CO2 per kWh.

What I like about the manifesto is that it is eminently doable.

And who knows? Perhaps we might actually do it?

Ahhhh. Thank you Andrew.

Even thinking that a good thing might still be possible makes me feel better.


25 years ago…

April 4, 2017

25 years ago, the atmospheric concentration of carbon dioxide was 350 ppm  – just 70 ppm higher than its pre-industrial concentration.

Oh yes. And I got married.

Objectively, I can describe this elapsed time as 9131 days. Or almost 789 million seconds.

And I can describe the way in which the atmospheric concentration of carbon dioxide has changed since then by more than 50 ppm.

And I can even describe the wonder of seeing two new human beings come into the world and evolve from being babies to being adults.

But subjectively, words fail me.

Version 2

But it is a fact that on this date, 25 years ago, friends and relatives gathered and supported Stephanie and myself as we got married.

And this post is just to say ‘Thank you’ to everyone who was there that day, and whose good wishes felt like a very tangible blessing. Our aim this year is to try to visit each of you. We have a list and you have been warned!

But whether you were there or not, I leave with you the Epithalamion written by my brother Sean and read by him at the wedding.

Epithalamion for Michael and Stephanie

Young people dance and drink a lot,
Draw close in metaphysical discussion,
Make light of commitments in making love
Celebrate the sadness of casual encounters,
Make art from them, and then repeat them.
Moments exhilarate; memory excruciates; the future’s a dream.
Years pass; what was painfully beautiful becomes untenable.
There comes time to move from testing the limits of resilience
To exploring the possibilities of permanence

Flitting is fine for adolescents and Peter Pan,
But now this woman is a woman, and this man a man.

Michael played guitar and sang a lot.
Went with women, but not a lot;
Sought the wrong thing in the wrong places,
And thus made the necessary errors;
Skirted sanity’s edge and touched insanity’s terrors.
I knew him as an orphaned six-year old; I have known
the need, and comfort of, his hand.
I have sought the warmth of his palm; welcomed his embrace;
Suffered the full force of his anger
— And see! Here I am unharmed.
And here is the baby I held in my arms
Become an adult who,
In looking for his mother, found a lover;
And in loving a lover, found a wife;
And, after a long search,
The needed even tenor of a stable life.

In seeking after women, he was never a Don Juan;
But now the child whose hand I held is become a man.

I don’t know Stephanie’s past;
However I strongly suspect
That happy women don’t jump from Aeroplanes;
And I know for a fact
That Ireland is the best
But least happy nation to stem from;
And that an uncertain constitution of your blood
Doesn’t do your humour any good.
This is not to carp, but just to establish
A youth that was below emotional perfection,
So that future adventures – this moment –
Might allow scope for improvement.
How sad, if all her relations, now full-stomached and dyspeptic,
Were also silently lamenting her deteriorating spirit,
Her vanished prospects,
The poor calibre of chap who’s landed in it!
To them I would say:
“The Chosen Path is the best!
And this is it!”

Today Stephanie puts on her Bridal Gown
To follow a dream that is her own.
Today good faith and trust may light hope’s flame;
She thus assumes perfection and a woman’s name.

Today is the ceremonial,
The tip of the huge and hidden thing to come;
The speckle and glass-glint of sun on the sea’s surface,
Eye-pleasing and transient, above depths that would terrify.
Today is about sex and the containment of sex;
About fear and the overcoming of fear;
About flesh and the fact flesh is fertile;
And the fact flesh decays;
And the fact flesh is human and lovely.
Today, too, is about family,
About what your Mother and Father do to you,
And for you;
It is about fertility and the bearing of children,
About the repetition of familiar things — and old errors;
The discovery of particular new joys,
New ways of two people meeting,
The miracle, perhaps, of new human beings.
Today is about what — what no ceremony could proclaim —
Informing the mundane with a proper focus,
With the laser intensity of life, and making it last;
About enlivening the drudge of living,
The dulling-ness of day to day.

It is about making do, and doing the best you can.
It is about Stephanie being a woman, and Michael a man.

If that’s all, then what’s the point?
Why are we here?
Why not reach for our revolver
And place it in our ear?
Because… because there’s more.
Today is about this…
We need each other;
We are nothing if connected to nothing.
Today we celebrate connectedness;
Cutting the crap we acknowledge love,
And the power of love to sustain.
And love is a light thing —
Not just the fleshly decaying ponderousness of sex,
But the shock of seeing, and then seeing afresh.
Today we dignify love,
Erecting a social carapace to protect it,
To allow it, in the private vision of two lovers.
We try to fix a hope — that love is not a flimsy.
Can such a light thing — love — though ever be strong enough?
All brides and all their grooms are optimists or fools.
But. Imagine egg-shell-skating carefulness; Consider how caution kills.
Let’s learn, and be thankful for the lessons of these optimistic fools;
Aristocrats of human risk, they let love open the future.
To feed hope’s flames, their noble folly’s fuel.

Come, then let us thank them; let us now applaud;
Today, this woman is a lady; and this man a lord.

Sean de Podesta , 1992

Climate Reflections

March 28, 2017

I am currently in Exeter attending the 22nd meeting of the WMO GCOS/WCRP AOPC. Let me translate:

In short, I am here to talk about monitoring the global climate with some of the best climate scientists from around the world.

The topics being discussed are diverse, and I am here to talk about one small part of the work. However, I feel honoured to take coffee with these people and to be able to legitimately call them ‘colleagues’.

My contribution is to speak on Thursday about creating a reference network of climate monitoring stations.

Historically, we have used records from normal weather stations to monitor the changing climate. But these stations have known biases that have to be detected and corrected.

It would have been really helpful if 100 years ago, scientists had thought to create a reference network where every time a new thermometer screen was installed, they recorded the fact. But they didn’t.

So the idea is to create that reference network now so that in 100 year’s time when climate scientists look back they will say:

“Thank heaven for AOPC-22: that’s when our job got easier! They created a Climate Reference Network that has allowed us to detect anomalies in the climate signal inferred from analysing regular weather stations.

But that’s not what I wanted to talk about.

The mood of the meeting

This meeting is busy. People are mindful of the ability of a roomful of scientists to chat endlessly about details. And to counter this there is a powerful focus on getting things done.

However President Trump casts a shadow over the meeting.

Trump collage

Headlines from news sites today.: BBC, Guardian and Ars Technica

And the news today is that he has signed executive orders that effectively scrap energy policies based on avoiding the worst effects of climate change.

Most people at the meeting find this depressing. And it would be an understatement to say that colleagues from the US are ‘concerned’.

Trump’s policies are ultimately based on a simple belief which is summed up in the graph below from the Gapminder foundation.

2013 data for the countries of the world showing GDP per person versus carbon dioxide emissions per person. Each bubble represents a country and the size of each bubble is proportional to its  population.

2013 data for the countries of the world showing GDP per person versus carbon dioxide emissions per person. Each bubble represents a country and the size of each bubble is proportional to its population.

The graph shows that countries that emit a lot of carbon per person are richer.

However the graph shows correlation not causation. Emitting carbon dioxide of itself does not make anyone richer.

Burning carbon produces energy, and it is access to energy that makes countries rich, and unequivocally improves the quality of people’s lives.

But emitting ~30 billion tonnes of carbon dioxide per year also has another effect which is not documented on the ‘bubble graph’. As the people at this meeting have helped make clear, it has warmed the surface of the planet and will continue to do so for centuries to come. But we no longer need to emit carbon to produce energy.

Currently renewable energy sources are (generally) more expensive than fossil fuels. But there is no reason why that will always be the case.

Indeed, if Trump’s aim is to make America independent of foreign energy sources, the best thing he could do would be to increase exploitation of renewable energy which would reduce its cost.

Personally, I think that it is already too late for coal and that Trump’s efforts to open coal mines and burn more coal will fail, just like efforts to create ‘clean coal’ have utterly failed.


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


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


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.


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


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


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.


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!

5.What was all that about?

January 3, 2017


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.


When will the North Pole become the North Pool?

December 16, 2016


It is a sad fact, but it is likely that within my lifetime it will become possible to sail to the North Pole. I am 56.

Tragically it is also true that there is absolutely nothing that you or I can do about it.

In fact, even in the unlikely event that humanity en masse decided it wanted to prevent this liquefaction, there would be literally nothing we could do to stop it.

The carbon dioxide we have already put in the atmosphere will warm the Earth’s surface for a few decades yet even if we stopped all emissions right now.


The particular line of causation between carbon dioxide emissions and warming of the arctic is long, and difficult to pin down.

Similarly it is difficult to determine if a bull in a china shop broke a particular vase, or whether it was a shop helper trying to escape.

Nonetheless, in both cases the ultimate cause is undeniable.

What does the figure show?

The animation at the head of the page, stolen from NASA’s Earth Observatory, is particularly striking and clear.

The animation shows data from 1979 to this past November 2016 showing the extent of sea ice versus the month of year.

Initially the data is stable: each year is the same. But since the year 2000, we have seen reductions in the amount of sea ice which remains frozen over the summer.

In 2012, an additional one million square kilometres – four times the area of England Scotland and Wales combined – melted.

The summer of 2016 showed the second largest melt ever.

The animation highlights the fact that the Arctic has been so warm this autumn, that Sea Ice is forming at an unprecedentedly slow rate.

The Arctic Sea Ice extent for November 2016 is about one million square kilometres less than what we might expect it to be at this time of year.

My Concern 

Downloading the data from the US National Snow and Ice Data Centre, I produced my own graph of exactly the same data used in the animation.

The graph below lacks the drama of the animated version at the head of the article. But it shows some things more clearly.


This static graph shows that the minimum ice extent used to be stable at around 7 ± 1 million square kilometres. The minimum value in 2012 was around half that.

The animated graph at the head of the article highlights the fact that the autumn freeze (dotted blue circle) is slower than usual – something which is not clear in the static graph.

My concern is that if this winter’s freeze is ‘weak’, then the ice formed will be thin, and then next summer’s melt is likely to be especially strong.

And that raises a big question at the very heart of our culture.

When the North Pole becomes the North Pool, where will Santa live?


Global Warming for Electrical Engineers

November 21, 2016
An electrical analogy to the flux of energy from the surface of the Sun energy as it reaches and then leaves the Earth's surface on its journey into deep space. If these fluxes are not equal then the Earth's surface temperature will change.

An electrical analogy to the flux of energy from the surface of the Sun as it reaches and then leaves the Earth’s surface on its journey into deep space.

I haven’t written much about global warming lately, but I have noticed that the resurgence of the ‘alt-right‘ seems to have emboldened people to express ‘sceptical’ views.

People expressing these views are in general no more or less stupid than anyone else. However, they do fail to understand that their own competence in one area, or the popularity of their views in polls, has no bearing on the correctness or otherwise of their understanding of anthropogenic global warming.

In a recent interaction with a Nameless American, it became clear that despite being able to assemble the facts, this individual was unable to understand the basic process by which the surface temperature of the Earth comes to be what it is. And hence they could not understand why it is rational to expect that increased amounts of carbon dioxide in the atmosphere are affecting the surface temperature of the Earth.

So here, for that Nameless American, is Global Warming for Electrical Engineers: Apologies to everyone else.

Basic Circuit

Figure 1: A simple electrical circuit. The key feature is that the same current flows through both resistors R1 and R2.

Figure 1: A simple electrical circuit. The key feature is that the same current flows through both resistors R1 and R2.

The basic circuit required to understand the way in which the surface temperature of the Earth is established is shown in Figure 1. Two key features of this resistor-divider circuit are that:

  1. The current flow through circuit elements R1 and R2 is the same.
  2. The DC steady state operating point of the circuit is determined just by the resistances and the voltage of the DC power supply

Now the analogy we will make is this:

  • Voltage is analogous to temperature: In the same way that voltage differences drive electrical currents, temperature differences drive energy flows.
  • V0 is like the surface temperature of the Sun
  • V1 is like the surface temperature of the Earth
  • V2 is like the temperature of the deep space – almost absolute zero.

Importantly, the only way to get thermal energy on or off the Earth is by electromagnetic radiation – mainly visible and infrared light.

Notice that the surface temperature of the Earth is determined (in the steady state) by the requirement that the average flux of energy onto the Earth’s surface is the same as the average flux off the Earth’s surface.

This is analogous to the way Kirchoff’s current law is used to establish the steady state DC voltage V1.

Figure 2: We are drawing an analogy between the flow of electrical current through resistors in series and the flow of energy from the Sun onto the Earth's surface and then secondly off the Earth's surface and out into space.

Figure 2: We are drawing an analogy between the flow of electrical current through resistors in series and the flow of energy from the Sun onto the Earth’s surface and then secondly off the Earth’s surface and out into space.

How the analogy works

The surface of the Sun is hotter than the Earth: Radiation travels from the surface of the Sun through space and arrives at the top of the atmosphere.

For the moment let’s forget about the radiation reflected from the cloud tops, and consider only radiation which travels through the atmosphere and reaches the Earth’s surface. We’ll discuss the effect of this assumption in Subtlety #2 below.

The radiation which travels through the atmosphere is mostly visible light – the sunlight which warms the Earth’s surface.

The resistance R1 then determines the amount of heat delivered to the Earth’s surface from the Sun’s Surface. The actual value of R1 is determined by factors such as the distance from the Sun to the Earth.

Now we consider the re-radiation of thermal energy from the Earth’s surface. This is in the form of infrared light. In the same way that warming happens mainly on the ‘day’ side of the Earth, cooling happens mainly on the ‘night’ side of the Earth.

Whereas the atmosphere is mainly transparent to incoming radiation, the atmosphere is mainly opaque to infrared radiation. If we humans could see at the relevant the wavelengths, and looked up at the night sky, we would not see the stars, but just a ‘fog’.

The atmosphere would appear to be totally opaque at these wavelengths: but it is not.

When we shine light into a fog, it is multiply scattered and only a tiny amount of light makes it out the other side of the fog. We can consider the fog as presenting an impedance R2 to the transmission of radiation out to the heat sink of deep space.

The surface temperature of the Earth is determined in the steady state by the requirement that it is hot enough to ‘drive’ infrared radiation through the impedance R2 and out into space.

  • If the Earth’s surface temperature is ‘too low’, more energy will arrive on the surface of the Earth than leaves and the surface temperature will rise.
  • Similarly, if the Earth’s surface temperature is ‘too high’, more energy will leave the surface of the Earth than arrives and the surface temperature will fall.

Eventually, a steady-state is reached: a dynamic equilibrium. The temperature of the Earth’s surface becomes hot enough, that it glows brightly enough to drive sufficient infrared radiation through the Earth’s atmosphere and out into space.

In our circuit, this is equivalent to the voltage V1 rising until it reaches a value sufficient to drive the operating current  through the resistor R2.

Anthropogenic global warming is caused by an increase in the impedance R2. For a fixed surface temperature, this reduces the amount of radiation which leaves the Earth’s surface and reaches space.

In order to re-establish the equilibrium and drive the requisite energy flux through the atmosphere and out into space, the temperature of Earth’s surface needs to rise

Subtlety #1

The electrical analogy in Figure 1 is ridiculously simple, so let’s make it more complicated and (very slightly) more realistic.

Figure 2: Ra, Rb etc represent transmission through the atmosphere in different wavelength bands.

Figure 2: Ra, Rb etc represent transmission through the atmosphere in different wavelength bands.

Figure 2 replaces a single resistance R2 with an array of parallel resistances each of which radiatively couples the surface of the Earth to the coolness of space. We could imagine that each parallel resistance represents (say) transmission in a different wavelength band.

The important observation is that increasing the impedance any of Ra, Rb etc always increases, the total impedance R2. Since the current through the circuit is fixed, this will cause an increase in the voltage V2.

Considering our Earth analogy, if we decrease the transparency of the atmosphere to infrared light in any waveband, this will increase the overall impedance. Since the flux of radiation onto the Earth is unaffected, this will cause an increase in the surface temperature of the Earth.

Of particular interest is the radiation which leaves the Earth’s surface in wavelength bands that are absorbed by carbon dioxide molecules.

Aside on Subtlety #1: ‘blocked bands’

The conclusion of the previous section is that if we make the atmosphere more opaque in any wavelength band, the surface temperature of the Earth will increase. This conclusion is inescapable. Unless…

…The only time that increasing a number makes no difference to the number’s value is if that number is already infinite.

So global warming sceptics frequently argue that ‘the carbon dioxide bands are blocked‘. They argue that carbon dioxide absorbs infrared light so effectively, that at certain specific wavelengths the atmosphere is (practically) 100% opaque.

Their argument is that increasing the amount of carbon dioxide cannot therefore increase the opacity of the Earth’s atmosphere any further. The problem with this argument is that it is ‘just wrong‘.

[We can see why in various ways, but firstly I feel compelled to note that water vapour is dramatically more effective than carbon dioxide at blocking infrared light, and yet sceptics don’t apply the same argument to water vapour!]

The actual mechanism of transmission of infrared light through the atmosphere is complex: it is illustrated schematically in Figure 3.

At infrared wavelengths the atmosphere looks ‘foggy’. Radiation travels through ‘fog’ in a process involving multiple scatterings – think of car headlights shining into fog: some of the light comes back in the direction towards your headlights and some goes forward and sideways.


Figure 3: Illustration of the energy flux onto and off the Earth's surface. On average, roughly 240 W/m^2 of solar energy reaches the Earth;s surface. This is re-radiated as infrared red light at wavelengths at which the atmosphere is opaque. The light is scattered, and some comes back to the Earth, and some makes its way further up the atmosphere. Eventually the light reaches a height - typically 6 km to 10 km - where it can radiate freely into space.

Figure 3: Illustration of the energy flux onto and off the Earth’s surface. On average, roughly 240 W/m^2 of solar energy reaches the Earth;s surface. This is re-radiated as infrared red light at wavelengths at which the atmosphere is opaque. The light is scattered, and some comes back to the Earth, and some makes its way further up the atmosphere. Eventually the light reaches a height – typically 6 km to 10 km – where it can radiate freely into space.

This process of multiple scattering goes on repeatedly until radiation makes it to an elevation of typically 6 km to 10 km above the Earth’s surface at which point the atmosphere is thin enough to allow radiation directly out into space.

Importantly, there are no ‘completely blocked bands’. If there were, our satellites would fly over the Earth at night and find no emission at all at some wavelengths: that is not what is seen.

What is seen is the ‘top of the fog’: the radiation from the highest part of the ‘fog’. Radiation at all wavelengths does eventually make its way through the atmosphere in a process of multiple random scatterings.

Increasing the concentration of carbon dioxide makes the atmosphere less transparent in some wavelength bands and, as we saw in the previous section, that inevitably drives an increase in the temperature of the Earth’s surface.

Calculating the sensitivity of the Earth’s surface temperature to an increase in carbon dioxide concentration is complex, but in fact our estimates have not changed much since Arrhenius’s first estimate in 1896.

Arrhenius calculated that doubling carbon dioxide concentration from the historical value of 280 ppm  to 560 ppm would cause an increase of 4 °C.

Now using supercomputers and complex climate models we estimate this sensitivity to be 3 °C ± 1.5 °C. The robustness of this estimate in the face of the overwhelming additional calculational complexity is testament to the fundamental simplicity of the physics involved.

Subtlety #2

This article is already long enough, but back when I was a few hours younger, I said I would comment on the effect of reflections at the top of the Earth’s atmosphere.

We can model this by splitting R1 into two series resistances describing transmission from the surface of the Sun to the top of atmosphere (R1a) and subsequent transmission through the atmosphere to the surface of the Earth (R1b). The equivalent circuit diagram is shown in Figure 4.

Figure 4. Modification of the equivalent circuit to describe reflection from the top of the atmosphere.

Figure 4. Modification of the equivalent circuit to describe reflection from the top of the atmosphere.

In this modification, R3 describes the reflection of light from the top of the atmosphere.

  • If there are lots of white cloud tops during the day, then R3 is small: it is small compared with the sum of R1b and R2, But notice that clouds at night don’t affect R3.
  • If very little light is reflected from white cloud tops during the day, then R3 is large compared with the sum of R1b and R2.

In practice, on average the flux of energy from the Sun is 340 watts per square metre at the top of the atmosphere, and about 100 watts per square metre are reflected into space. This indicates that R3 is approximately twice as large as the series sum of R1b and the components of R2.


The reason I mention this additional complexity is because of the role of clouds. It is important to look at clouds from both sides, from up and down and from night and day.

The inevitable warming caused by increasing carbon dioxide concentrations will inevitably cause changes in the amount of water vapour in the atmosphere. And these changes can affect the pattern of clouds formed on Earth and give rise to effects which alter R1b – the transmission of visible light between the top of the atmosphere and the surface of the Earth.

Roughly speaking, additional cloudiness during the day could cool the Earth, reducing the warming effect. But additional cloudiness at night will warm the Earth.

On balance the effect is difficult to calculate, but our best estimates result in warming consistent with that observed experimentally.


This article is written for one individual: the Nameless American  who thinks that his cleverness and popularity means that their’gut belief’ that global warming is a hoax is correct. They are, sadly, ‘just wrong’.

I too would love to believe that global warming is a hoax, but it isn’t.

The electrical models I have described could be improved by adding some capacitances to the circuit to allow the dynamics of the changes in temperature to be simulated.

These electrical capacitances, would be analogous to the heat capacity of the top layers of the land and ocean surfaces of the Earth.

But there is not much point: scientists have done this calculation and the results are in. We have already made the measurements, and the results are in also.

The real argument for the ‘alt-right’ is this: if you think the economic benefits of burning unlimited coal and emitting unlimited carbon dioxide outweigh the costs: please make this argument. I disagree with you, but it’s a fair argument.

But don’t attack the science. Our understanding of this process is a collective triumph for humanity.

[November 21st 2016: Weight this morning 73.5 kg: Anxiety: High: off the scale]



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