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]



We need to talk about bullshit

October 6, 2016

[If you are offended by my use of the word ‘bullshit’: I apologise.
Please leave this post now and do not read any further]

Friends and Colleagues: We are being showered with bullshit.

My consciousness of this has been raised by a paper in the journal Judgment and Decision Making: On the reception and detection of pseudo-profound bullshit by Gordon Pennycook and colleagues. Thanks to Stephen Giblin for the link.

Before discussing sub-genres of bullshit, the authors clarify precisely what they mean by bullshit in general. They write eloquently:

The Oxford English Dictionary defines bullshit as, simply, “rubbish” and “nonsense”, which unfortunately does not get to the core of bullshit. Consider the following statement (a):

“Hidden meaning transforms unparalleled abstract beauty.

Although this statement may seem to convey some sort of potentially profound meaning, it is merely a collection of buzzwords put together randomly in a sentence that retains syntactic structure. The bullshit statement is not merely nonsense,as would also be true of the following (b), which is not bullshit:

“Unparalleled transforms meaning beauty hidden abstract”.

The syntactic structure of a), unlike b), implies that it was constructed to communicate something. Thus, bullshit, in contrast to mere nonsense, is something that implies but does not contain adequate meaning or truth.

The authors focus on what they call pseudo-profound bullshit and try to identify the factors that lead people to be receptive to such statements.

We focus on pseudo-profound bullshit because it represents a rather extreme point on what could be considered a spectrum of bullshit. We can say quite confidently that the above example (a) is bullshit, but one might also label an exaggerated story told over drinks to be bullshit. In future studies on bullshit, it will be important to define the type of bullshit under investigation

Their analysis is interesting, and occasionally amusing as they generate meaningless statements using a website ‘bullshit generator

But my own interest is in the bullshit I encounter every day. It consists of syntactically correct structures about work, science or technical activities. These sentences slip through my first layer of ‘nonsense filters’. And it then requires active thinking to evaluate and reject the content – and that can be hard work.

Of course, I could use an agile methodology to incisively shortcut the usual appraisal process. And if I did that in a dynamic way, it might be more effective.

Did you see what I did there? The above paragraph is bullshit. It sounds like it might possibly mean something. But the words themselves do not convey that meaning.

They do fill up the space on the page making it appear that something has been said, but it hasn’t.

Once again the eloquence and insight of the authors helps us to see the essence of bullshit. I have edited their words below because I think their comments apply to all bullshit, and not just pseudo-profound bullshit:

Despite the lack of direct concern for truth … bullshit betrays a concern for verisimilitude or truthiness.

We argue that an important adjutant of bullshit is vagueness which, combined with a generally charitable attitude toward ambiguity, may be exacerbated by the nature of recent media. As a prime example, the necessary succinctness and rapidity of “Twitter” (140 characters per “Tweet”) may be particularly conducive to the promulgation of bullshit.

Importantly, vagueness and meaning are, by definition, at cross purposes, as the inclusion of vagueness obscures the meaning of the statement and therefore must undermine or mask “deep meaning” (i.e., profundity) that the statement purports to convey.

The concern for “profundity” reveals an important defining characteristic of bullshit (in general): that it attempts to impress rather than to inform; to be engaging rather than instructive.

Their conclusion that bullshit attempts to “impress rather than inform” seems to me to cut to the heart of it.

I have often thought that human beings are ‘meaning machines’: we seek out nuggets of meaning in the world around us, digesting information with a voracious appetite, and discarding vast amounts of irrelevant information.

But if we are exposed to too much bullshit, it clogs up our senses, and makes it harder to recognise and communicate meaning. It is a kind of intellectual pollution.

I am really grateful to these authors for taking the time to analyse the key characteristics of bullshit.

With my consciousness raised I hope to recognise bullshit more easily, and to avoid ingesting it. Or worse still – producing any.

Friends: I leave you with the words of the late great Jake Thackray singing ‘The Bull’


The Bull by Jake Thackray

On my farm, the bull is the king of the yard;
He’s big and bad and fast, he’s strong he’s . . . hard.
All my other animals would readily concur
That he is the one you salute, he’s the one you call “Sir”.
But my hens, a noisy, flighty flock –
Led, of course by my unsubmissive cock –
Whenever His Majesty the bull importantly goes by
They dance along behind him and they cry:
“Beware of the bull!”

The bull, the bull is the biggest of all.
He is the boss, he is, because he’s big and we are small.
But the bigger the bull, bigger the bull, bigger the balls.
The bigger the bull, the bigger and quicker and thicker the bullshite falls.

Beware of the bull! The dancing cock is right:
Beware of whoever looks down upon you from a height.
Beware of His Honour, His Excellence, His Grace, His Worshipful,
Beware of His Highness, because of the bull.
For if the boss, the chief, the chap at the top
Should let a single lump of claptrap drop,
The greater the weight and the height he is, the harder it will go
With a grander splat! on the bleeders below.
Beware of the bull!

The bull, the bull is the biggest of all.
He is the boss, he is, because he’s big and we are small.
But the bigger the bull, bigger the bull, bigger the balls.
The bigger the bull, the bigger and quicker and thicker the bullshite falls.

The hero arrives, we hoist him shoulder-high.
He’s good and wise and strong, he’s brave, he’s . . . shy.
And how we have to plead with him, how bashfully he climbs
Up the steps to the microphone – two at a time.
Then down it comes: slick, slithery pat!
If you must put people on pedestals, wear a big hat.
The tongue he’s got is pure gold, the breast is pure brass,
The feet are pure clay – and watch out for the arse.
Beware of the bull!

The bull, the bull is the biggest of all.
He is the boss, he is, because he’s big and we are small.
But the bigger the bull, bigger the bull, bigger the balls.
The bigger the bull, the bigger and quicker and thicker the bullshite falls.

At long last, the revolution comes
And in no time at all we’re erecting podiums.
Comrades with chests of medals by the balcony-full;
After the Red Flag, the galloping bull.
The Saviour came especially from on high
To face up to the punters eye-to-eye.
No sooner is he dead and gone, there’s blessed pulpits-full;
Bestride the holy lamb, behold the bull.
Beware of the bull!

The bull, the bull is the biggest of all.
He is the boss, he is, because he’s big and we are small.
But the bigger the bull, bigger the bull, bigger the balls.
The bigger the bull, the bigger and quicker and thicker the bullshite falls.

These well-known men, so over-glorified –
There’s one of them here his name’s on the poster outside –
And he’s up here like this, and you are all down there.
Remember his cock and his bull and mutter: “Beware!”
For when they’ve done, we clap, we cheer, we roar:
“For he is a jolly good fellow! Encore! More, more!”
How glorious it would be if before these buggers began
We all stood up together and solemnly sang:
“Beware of the bull!”

The bull, the bull is the biggest of all.
He is the boss, he is, because he’s big and we are small.
But the bigger the bull, bigger the bull, bigger the balls.
The bigger the bull, the bigger and quicker
And the bigger and quicker and thicker
And the bigger and quicker and thicker and slicker the bullshite falls.



°C and C are not the same!

October 5, 2016
Sometimes one has to write to the papers!

Sometimes one has to write to the papers!


Sometimes I am unable to stop myself writing to the papers.

Some issues – such as people not using measurement units correctly  – are just too important to let pass.

And people referring to temperature units incorrectly induces apoplexy!

For the record, the degree Celsius is an SI unit for temperature: the degrees C********e and F********t are not.

Their use in everyday language is understandable – many people use the F-word occasionally – and in the correct context, it gives no offence.

But for newspapers and media outlets to do so is outrageous!

And using the abbreviation C instead of °C is just wrong.

As I wrote to The Guardian recently:

Dear Guardian,

The measurement system that underpins all of our physical measurements of the world around us is called the International System of Units, widely referred to as ‘the SI’.

It is a staggering achievement, used daily by hundreds of thousands of scientists and engineers.

It provides a standard way of comparing measurements around the globe and of referring to those measurements. So why has The Guardian invented its own system of units?

To refer to a temperature of 25 degrees Celsius, the standard abbreviation is 25 °C. However The Guardian routinely refers to this as 25C, using the symbol ‘C’ which refers to the SI ‘coulomb’, an amount of electric charge. Why?

You might argue that your meaning is clear in context. And generally it is. But why be wrong when you can be right so easily?


Michael de Podesta

National Physical Laboratory.

P.S. In MS Windows™ systems, the degree symbol is [ALT] + 2 + 4 + 8 on the number keypad and in MacOS the degree symbol is [ALT] + [SHIFT] + 8. In iOS, on numeric keypad use a long press on the zero key to reveal the degree symbol.

P.P.S. There should also be a space between the number and its unit, but I didn’t want to mention that in case you thought I was being pedantic.

More seriously, reporting measurements in the correct units aids clarity of understanding and establishes the basic competence of the author.

Reporting, as The Guardian did this week, that:

“the 2016 temperature is likely to be 1.25C above pre-industrial times, following a warming trend where the world has heated up at a rate of 0.18C per decade.”

merely establishes that the writer knows nothing about measurements.

This is not a matter of style, it’s a matter of just being wrong.


[October 5th 2016: Weight this morning 73.5 kg: Anxiety: Low. I don’t know why, but I just felt OK today :-)]

Uncertain Uncertainty and Variable Variability

October 4, 2016
Graph prepared by John Kennedy illustrating the effect of some of the uncertainties. Any one of the blue of the blue lines - or an un-drawn similar line - could be what actually happened. We don't know - but all of them show significant warming.

Graph prepared by John Kennedy illustrating the effect of some (but not all) of the uncertainties in the data. Any one of the blue lines – or an un-drawn similar line – could be what actually happened. We don’t know – that’s the nature of uncertainty. The significant thing is that even considering the confounding factors, all of the estimates show significant warming.

Variable Variability

One of the real pleasures of attending WMO CIMO TECO last week was the chance to meet some of my heroes. And among them I finally met Victor Venema.

Victor is climate scientist whose primary interest is in identifying and removing biases from the instrumental temperature record. He is – in the very best sense of the word – a sceptic.

His blogVariable Variability – is one of my few ‘must reads’.

Uncertain Uncertainty

Victor’s last article drew together many representations of our instrumental temperature record to ask the question: what makes people pay attention to the fact that OUR PLANET’S SURFACE IS WARMING UP!

This shocking fact has gone from being widely denied or ignored to being widely accepted and ignored.

The aim of all the presentations Victor draws together is to fairly communicate the reality of the uncertainty of the conclusions drawn – but also that the warming trend is strong when compared with these uncertainties.

Alternative Reality

But Victor’s page does not (yet!*) contain the beautiful representation at the head of this page.

The animated graph was devised by John Kennedy from the UK’s Met Office and illustrates many of the possible curves – alternate realities – that are consistent with the data.

There are more curves that would be consistent with the data but John wasn’t quite sure how to represent them.

One of the most important ‘uncertain uncertainties’ that John didn’t include is called ‘coverage uncertainty’. It arises from the fact that the instrumental record derives from thermometers that are not optimally positioned around the globe.

When I wrote to him to ask permission to use the graph he said:

The coverage uncertainty has, I suspect, an important low-frequency component. We know HadCRUT4 has a tendency to slightly under-represent Arctic areas, which have been relatively warm these past 10 years. Over time, the balance of land and ocean changes too and we know these warm at different rates. The coverage uncertainty also has a high-frequency component too.

I will get round to writing a blog post about the wiggles at some point, but in the meantime I’m interested in what people think about it. Lots of the animated presentations that I see don’t obviously add anything beyond what the standard static time series graph would show, so one concern I have is, does it add anything to that? Is there any way we can improve the representation of uncertainty in our graphs and other visual aids, particularly where there are more complex error structures that can affect the interpretation?

I love John’s attitude. Critical of his own work and looking for feedback to improve it.


Certain Certainties

I think the animation does add something. Each line represents a possible ‘reality’ that is consistent with the data we have.

The animation shows which features persist from one ‘possible reality’ to another.

In general, a year which is hotter than it’s predecessor, stays hotter in all ‘realities’.

Critically, none of the realities consistent with the data reverse or cancel the overall warming trend.

And that makes it essentially certain that the warming trend is real. And that the world really is hotter than it has been for a long, long time.


*The image is there now!


October 3, 2016

The hall for WMO CIMO TECO early on the first day before anyone turned up. (Except for the VIPs in the middle of the picture!)

I spent last week in Madrid at the WMO CIMO TECO 2016.

The acronym stands for:

  • World Meteorological Organisation (WMO)
  • Commission on Instruments and Methods of Observation (CIMO)
  • Technical Conference (TECO)

For the last couple of years I have sat with two of the WMO ‘Expert Teams’ (A2 and C1) as a representative of the International Bureau of Weights and Measures, the BIPM.

My presence on these teams, and at the conference, is the result of an agreement between BIPM and WMO to formally recognise each other’s structures.

I see my personal role as to make sure that the voice of metrology – measurement science – is heard in the technical committees of WMO that make recommendations about the measurement procedures that underpin meteorological and climatological work.

There are still cultural differences between metrologists and meteorologists. But I felt my presence at this conference was a heartfelt attempt to break through these cultural barriers.

I was really honoured to be able to speak to the conference on its first day on the effects of the forthcoming redefinition of the kelvin, and of the impacts of the latest measurements of the errors in the temperature scale used by meteorologists (and everyone else).

These impacts are small or zero, but meteorologists should be aware of these changes because temperature is the most significant meteorological measurement.

  • The PowerPoint file for my presentation is here (.pptx file).
  • The paper (.pdf) accompanying the talk is here.

I spent a long time removing content from the presentation until  I had removed as much extraneous material from the talk as I could.

But I did leave in one slide that might at first sight seem superfluous but which I felt really earned its place.


The last slide

Having told people that they would be unaffected by the latest developments in thermometry, I felt I needed to explain why the work was still important.

I explained that if my work had been polishing a lens to make an image clearer, then nobody would even ask me why I was doing it: it would be obvious. You don’t know what details will be revealed until you have the sharpest image possible.

What my new measurements do is analogous. They allow us to ‘see’ small differences between quantities that previously appeared the same. And they allow us to see that a property of two materials is really the same – and to wonder why.

It is like removing a ‘blur’ from our perception of the physical world.

I have converted the last slide’s animation into a six-second movie below.


The downside of all this preparation was a certain level of anxiety. But my anxiety about that presentation has now evaporated – and I am already anxious about the next thing!

Only 82 days until Christmas, and then I can take a break.

[October 3rd 2016: Weight this morning 72.9 kg: Anxiety: High: back to work!]


Grammar Schools:Their formula for success revealed!

October 2, 2016


Thanks to everyone who responded to last week’s article on Grammar Schools. I feel I am slowly becoming able to articulate what I think about this.

An article in The Guardian today has clarified things further:

Latymer grammar school asks parents to make up financial shortfall

The gist of the story is that Latymer School, a Grammar School with 96% A*-C pass rate at A-level, has asked its parents for more money. The Guardian quotes the school as saying:

“We are now appealing to all parents and carers of current students to support the school either by making a new or increasing an existing voluntary regular donation. Typically the amount you would pledge would be £30-£50 per month (£360-600 per annum) over the period your child attends Latymer. This averages out at between £1.89 and £3.15 per school day and is considerably less than the average fees of an independent school.”

It seems like a perfectly reasonable request. I think Tiffin School asked – but did not require – something similar.

The contribution amounts to roughly £50,000 per school year (i.e. about £350,000 per year across all seven school years). But not all schools have parents who could afford such a contribution.

And isn’t the point of state schools that parents don’t have to pay directly?

Latymer has been able to keep going in the last couple of years despite cuts to their budget because of the Latymer Foundation, which clearly has substantial funds available.

In a  June 2015 letter to parents available on the school web site, the trustees write:

 To balance the budgets over the next two years, the Foundation will underwrite the school deficits for 2015/16 and 2016/17 for potentially in excess of £1million. The funding will help buffer the impact of the significant drop in funding and increased costs for the next 18 months.

Over half of this sum relates to one-off capital and non-recurring revenue expenditure. However, the school will need to use this window of time to plan for and adjust to the, as yet unknown, longer term forecast of revenue and capital funding streams being made available by central government.

The Latymer Foundation wishes to express its thanks to the large number of parents who have been donating to the Standards Fund over many years and whose continuing contributions make this funding support possible.

So it seems that there are two elements to the success of Latymer, and by inference, other successful Grammar Schools. We can summarise this simply:

Money + Selection = Success


I arrived at the money connection at the end of the previous article where I pointed out that private schools cost approximately twice as much as state schools.

But what about the role of selection?

Grammar schools select children who – at the relevant age – can display a particular kind of mental agility. Typically – as Latymer’s appeal suggests – this also selects parents with an ability to contribute financially to the school.

But did anyone else notice Ed’s radical suggestion in the discussion of last week’s article? He proposed selection by behaviour rather than ability.

He suggested that schools selected the 95% of children who – given the right culture – are capable of benefiting from an academic education.

An alternative statement would be that we identify the 5% of children who disrupt every class they are in, and do something – I have no idea what – to engage them in a way which doesn’t disrupt the education of the majority.


In the end, its about the money

The education of the majority of people is a critical cultural endeavour. Our culture is our collective treasure.

We need more than an elite capable of understanding the technology our our brave new world. We do need that elite – but we need a culture in which their enhanced skills make sense.

But this costs money.

And when we see how expensive it is in the private sector – supposedly the most efficient provider of services – is it any surprise that the state sector struggles on half that level of funding? Maybe the formula is even simpler:

Money + Selection = Success

[October 2nd 2016: Weight this morning 74.0 kg: Anxiety: Medium]

Grammar Schools

September 24, 2016


Sammy's Science House. My son was given tasks to complete at school aged 11 that he had completed aged 2 (two) using this software. I think that represents a lack of ambition and a problem with the culture at the School.

Sammy’s Science House. My son was given tasks to complete at school aged 11 that he had completed aged 2 (two) using this software. I think that represents a lack of ambition and a problem with the culture at the School.

I have been wondering what I think about Grammar Schools. However, I am trapped in a perspective vortex.

I attended a Grammar School myself in the 1970s, and benefited from the education I received. And this could explain why I am inclined to be sympathetic towards Grammar Schools in general. Also my children have benefited from attending a Grammar School, but more details about this below.

People who ‘failed’ to get in to a Grammar School can also be affected by this perspective vortex. Michael Morpugo speaks loudly of the sense of ‘shame and anxiety’ at failing the entrance exam for Grammar School. However this did not hold him back because his aunts paid for him to attend a private school.

Had there not been a possibility to attend Grammar School, that is presumably where he would have gone in any event! To me this illustrates the fact that what Grammar Schools are for is to give a ‘private school style education’ to people who can benefit from it – without regard for income. In isolation, this is definitely ‘a good thing’.

What questions should we ask?

The real questions which need to be asked and answered are not whether Grammar Schools benefit the children who attend them: they do.

Instead we should ask whether the presence of Grammar Schools in an educational system improves outcomes more generally over a comprehensive system.

Also, we need to ask whether the advantages enjoyed by children who attend Grammar Schools are gained at the expense of educational opportunities which are denied to others.

These questions are difficult to answer, but the answer appears to be that Grammar Schools do not improve the system as a whole.

But there is one final question: Even if Grammar Schools are ‘unfair’, do they embody a valuable culture which might be worth preserving?

What are schools for?

Broadly speaking, schools are the way we pass on our integrated cultural and technical understanding of the world.

We know more and understand more about the world and our experiences than at anytime in history.

And we need people with high levels of education in order to be able to thrive in an increasingly complex and technological world.

So it ought to be a good time to be a teacher, or a student. But somehow it isn’t.

Some problems with Schools

One way to think about schools is to look at the exams students take.

At the high achieving end of the scale, ‘A’ levels are hard. But they could be harder and offer some discrimination between students achieving A* grades.

However, it is at the GCSE level where things are a complete mess, with the exams (and the courses leading to them) being simultaneously, much too easy for a wide range of pupils, but much too hard – and widely irrelevant – for another wide range of pupils.

Grammar schools do potentially address the low standards and lack of ambition at some secondary schools. But this is linked to school culture as well as selection.

My experience as a student

I attended Xaverian College in Manchester in the 1970s, a Catholic Grammar School for Boys. The school culture was weird:

  • Our recommended revision strategy for GCSE ‘O’ level Maths was “to get down our knees and pray to the Blessed Virgin Mary
  • ‘Sex Education’ was taught by a celibate monk.
  • Assaults on students by teachers were just accepted.
  • More recollections here

However all that really mattered was academic performance. So despite the weirdness, I am still genuinely grateful, because the education I received enabled me to go to University and have a career in Physics.

My experience as a parent

Fast forwarding to 2007 and 2009, both my children took an ’11+ exam’ to attend Tiffin School for Boys. Neither were intensively tutored and the older one ‘passed’ and the younger one ‘failed’.

The culture at Tiffin was familiar to me from my own experience, although it was considerably more benign than Xaverian! It suited my older son, and he had a good time there. He achieved good GCSEs and A levels and is now at University. And that’s all I wanted from the school.

I spoke with my younger son last week and he remembered being disappointed after the 11+ results, but actually he had a great time at Teddington School. As a parent I perceived a lack of ambition at the school, but he fell in with a good crowd and achieved better GCSEs than his older brother!

And after achieving good GCSE’s, he then left Teddington and moved into the 6th form at Tiffin School for his A levels and achieved essentially the same A level results as his older brother. We both doubt that he would have achieved such good results had he stayed at Teddington School, or gone to Richmond College, the other state-funded alternative in the area.

Perhaps there is a lesson there: if a route is held open to a more academic education for those starting out on a less academic route, then maybe Grammar schools could end up making sense within a wider comprehensive ‘ecosystem’.

Culture and ambition

Teddington School and Tiffin School differed massively in their ambition. And that is a matter of culture and not directly related to selection.

For example, in his first year at Teddington my son was given ‘science’ tasks that he had completed at home when he was 2 years old. Yes. Two years old.

He was asked to place cartoon panels in order showing the stages of a volcanic eruption. We have a video of him completing the same task in ‘Sammy’s Science House‘ software at the age of two! (The task is 12 minutes and 10 seconds into the YouTube clip below)

It’s not that my son was a genius. Instead it was a measure of the facile and uninspiring teaching that was, literally, suitable for toddlers.

Similarly, at Tiffin School, the Music Department was, and is, outstanding, and the scale and ambition of their endeavours is breathtaking. I didn’t like everything they did, but my son was given a musical education that was truly precious.

Another aspect of the culture change struck my son immediately: at Tiffin School children did not (in general) talk in lessons, and at Teddington, they did.

So many aspects of school culture which make a difference are not related to selection. But for a variety of reasons these valuable cultural traits thrive in Grammar schools. I would hesitate to destroy anything so precious as a culture of respect for academic goals.

Final Thoughts.

I have ignored many complicating factors: Religion: Gender: Class and Discipline come to mind.

I have ignored them because they all seem to me to be secondary to the basic task asked of schools: to pass on to its future owners, the wonderful inheritance of our culture, in all its varied forms.

Ultimately, the current Grammar school proposals may help a few children. And divisive as the move is, I wish them good luck. But the proposals are really irrelevant to most children.

We need a way of developing the culture of schools so that they become inspiring and wonderful places to learn.

And I can only imagine that happening if they are inspiring and wonderful places to teach.

I think we need subject teachers with better subject knowledge and more time to teach creatively. And that almost certainly means spending more money on schools.

  • The amount of money we spend per state school pupil is difficult to estimate definitively, but it appears to be between about £4000 and £8000 per pupil per year.
  • The BBC report that average day school fees in the private sector are around twice this level. (~£13,000 per pupil per year).

So if education were a purchasable commodity, private school students would be getting about twice as much of it.

And more education is something I would definitely vote for, and be happy to pay taxes for.

[September 24th 2016: Weight this morning 72.3 kg: Anxiety: Medium]


William Smith

August 29, 2016
The geological map of the UK is now available as an app. The first version was created by William Smith and was considerably more difficult to obtain.

The geological map of the UK is now available as an app. The first version was created by William Smith and was considerably more difficult to obtain.

Apologies for the lack of blog articles, but it has been a busy and difficult summer and despite my best efforts, anxiety levels have been high.


News that the Earth has entered a new geological era – the Anthropocene – should cause us all to reflect a little.


Personally, the news adds to my general sense of anxiety.

But the news reminded me of my summer holiday this year, spent in rural isolation near the lonely village of Churchill, in Oxfordshire.

The village was the birthplace of the astonishing William Smith, the man who created the first geological map of England.

On our first day of adventuring  we came across a small museum dedicated to his memory. By chance they had the very readable biography (The Map that Changed the World) for sale.

One of the pleasures of the biography was to read about a topic so profound, and one of which I was so profoundly ignorant.



I had been dimly aware of the map previously. I had noticed it when I was honoured in November 2014 to address the London Petrophysical Society  at the Geological Society’s premises in Burlington Arcade.

The map hangs on the wall to the right of the main hallway beyond the reception desk. I was so impressed that I asked for a copy for Christmas that year, but I think my wife thought it might be a bit too big😦

Just seeing the map, I had enjoyed its grandeur. But reading about its creation was awe-inspiring.

Smith worked as a surveyor and was fortunate enough (!) to descend down shafts in mines separated by just a few miles.

He noticed that the very obvious strata which the miners used to locate the coal were similar in different mines, but that they occurred at different depths.

He was then employed to build a canal, and was amongst the first people to cut open a slot in the Earth many miles long. This time he noticed that surface rocks changed from one location to another.

Piecing these experiences together allowed him to realise the three-dimensional layer structure of the Earth beneath the surface of England.

He realised that the strata were originally laid down horizontally, but were now slightly tilted, and that this explained both the surface and sub-surface observations.

There was one more clue that helped him piece together the confusing strata encountered in different places: fossils. He realised that the type of fossil in each layer formed a unique identifier for that layer.

With these insights, and a prodigious amount of energy, he travelled the length and breadth of the country constructing his grand map, the first of its kind anywhere in the world.

The map is in someways akin to the periodic table.

The periodic table contains chemical information, but more importantly than the information it contains, it provides a structure and a context that gives meaning to all chemical information.

Similarly, William Smith’s map contains geological information, but more importantly it provided a framework for understanding all geological information.

Imagine discovering that the fossils collected at Whitby on the North Yorkshire coast were of the same type as those collected in Lyme Regis on the South coast!

Who would have connected the two places before Smith traced the layer of rock across the whole of England? But after he had made the connection, and after you have seen the map, the connections seem almost obvious.

As I read of William Smith’s travails, I reflected that despite the enclosed fields and the robotic harvesters, the countryside hereabouts would probably have been recognisable to Smith if he could re-visit now.

And I wondered how he would react to news that the Anthropocene layer had begun.


P.S. The Geological Map is now downloadable as an app called iGeology.


[August 29th 2016: Weight this morning 72.9 kg: Anxiety: Very High]


Hinkley C: An alternative response

August 1, 2016

My earlier article on Hinkley Point C received a well-conceived and written response that deserves to be somewhere better than a comment page: here it is:

Hi Michael,
I am no economist either but I will make a few comments on your article about the Hinkley C project. Your conclusion is that overall the project is neither the best thing nor the worst thing could do and therefore sort of Ok. This rather equivocal judgement is made on the basis that the ongoing cost (of £1.15 billion p.a. for 35 years) is probably worth the price because it frees the UK government is from any upfront investment or later costs due to failure or delays. I think this is a very naive view.

This project aims to provide at least 7% of the nation’s power. As far as I am aware the UK government has no Plan B to meet this energy gap. This makes the Hinkley Point C scheme simply “too big to fail”. And if it falters or fails it will be for the UK government to salvage it regardless of contracts agreed at the beginning. The deals will be renegotiated when problems arise and the government / nation needs this power so it cannot just walk away or buy an alternative power station off the shelf.

The situation strikes me as analogous to the Private Finance Initiative (PFI) used to build public sector infrastructure for the last few years. This was sold as a wonderful risk free way of financing new hospitals and schools by using the private sector. Certainly new infrastructure has been built (though often not what was wanted) but at enormous cost which will cripple the public sector for decades. The scheme was devised to avoid government borrowing (even though the costs of this are much lower that for the private sector) but still has to be paid for year in & year out. (It is estimated that the UK owes £222 billion to banks & businesses via the PFI. (The Independent 11 April 2015)

By seeking to avoid public borrowing to finance Hinkley C the government has made a political and ideological choice which reduces it’s control (through lack of ownership), inflates the cost (even if kicked a few decades into the future) and does nothing to reduce the risks (because the government / nation really needs this energy so has no choice but to stick with it).

Best Wishes

It is also the case that the UK government has explicitly underwritten £2 billion of costs through the Treasury’s (infrastructure) Guarantee Scheme. This was announced by George Osbourne on a visit to China in September 2015 as an incentive to get the Chinese to invest in the project. EDF itself, in its own press release on the deal refers to “further amounts [being] potentially available in the longer-term.” So there is real chance that the UK government will increase the amount of the project it will explicitly underwrite.

I basically agree with everything you are saying. And if I had had the time I might already have written some of it myself.

However the point of the article was that in narrowly financial terms, this deal isn’t as insane as it is being made to sound.

Concerning Plans A and B, here are some other thoughts.

  • If we want nuclear power, then the current EDF design is one of the very few options available. The real missed opportunity here is that the decision to build was delayed so long that the option for using UK technology was lost.
  • Like you, I find the government’s aversion towards state ownership bizarre. How can it be OK for foreign governments to own our infrastructure, but not the UK government? That is just bonkers. As you say, if this is critical infrastructure then the owners of the infrastructure – the Chinese and French governments – will be able to hold us to ransom in the future.
  • Assuming the project goes ahead, then – taking a positive view – the government will have freed up the capital resources to invest in what I think is the real challenge facing us: integrating energy storage into our generating mix. But that is a story for another evening.

Thanks for your thoughts.



[August 1st  2016: Weight this morning 73.4 kg: Anxiety: Very High]

Hinkley Point C: What should we think?

July 30, 2016
A schematic diagram of the European Pressurised Water Reactor to be built at Hinkley Point. What could possibly go wrong?

A schematic diagram of the European Pressurised Water Reactor to be built at Hinkley Point. What could possibly go wrong?

One of the pleasures of writing a blog is that one can re-visit one’s own thoughts on a subject.

Given the current turmoil around the contract for the Hinkley Point C nuclear power station, I was interested to read what I had thought about it 1014 days ago back in October 2013.

First some light relief: I opened with:

So the UK is finally ready to embark on building some new nuclear power stations. I – like most people – don’t know whether this is a good thing or a bad thing. But I do feel a sense of relief that we have finally made a decision.

Ha Ha Ha. Nearly three years on and we have still to make up our mind.

Back in 2013, newspapers and commentators seemed resigned to the inevitability of the contract.

Now, given the significant fall in energy prices worldwide, they portray the project with much greater contrast: some calling it a white elephant, and others an essential piece of national infrastructure, all the while prevaricating on whether it is a good idea or not.

What has not changed much are the numbers. Back then I wrote:

The power station, planned to begin operating in 10 years time in 2023, consists of two massive plants each generating 1.6 GW of electricity. The build cost is estimated to be £16 billion  which French and Chinese government-owned companies will invest. Yes, this really is an investment backed by foreign governments.

The start date is now shifted to 2025 and the estimated build cost has increased to £18 billion.

However what is not made clear in many news stories is that the UK (government, taxpayer or electricity consumer) still does not have to pay one penny of this.

The gist of the deal is that these foreign governments take all the risk in return for a premium on the price of the electricity they produce. And the risk is substantial.

  • Construction of the first reactor of this type at Olkiluotu in Finland began in 2005 and the reactor is still not operational. Currently it is ‘expected’ to begin generating in 2018.
  • Construction of the second reactor of this type at Flamanville in France began in 2007 and the reactor is still not operational. Currently it is ‘expected’ to begin generating in 2018.

Both projects are billions of euros over-budget, and the ‘expected’ start dates are questionable. The Hinkley Point C project is larger than either Olkiluoto or Flamanville.

Considering only the financial aspects of the deal, whether it makes sense or not depends on the size of premium we have promised to pay when account is taken of:

  • the investment required (£18 billion)
  • the length of time before the investors make any return (>10 years),
  • and the risk (substantial)

So how much have we promised to pay them?

If the plants operate for 90% of time generating 3.2 GW of electricity then the guaranteed minimum income for the plant is £2.3 billion per year. Subtracting the operational costs – typically relatively low for nuclear plant – then after 10 years of no income and substantial risk of construction problems and delays, the operators should generate around 13% per annum return on their investment every year for 35 years.

It has been argued that this electricity is as much as twice as expensive as  the current price. So we are effectively paying a premium of £1.15 billion per year for the privilege of (a) not investing a penny up front; (b) not paying a penny if the project is delayed or fails to deliver; (c) having 60% of the contracts awarded to UK companies.

Does that represent good value? Back in 2013 I wrote:

I am not an economist, but in this context [this may not be] the best possible thing we could do. But it is probably not the worst either.

And I still think the same.


[July 30th 2016: Weight this morning 74.1 kg: Anxiety: Very High]

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