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How is knowledge lost?

April 20, 2017

At some point in the 1950’s the physics of the Greenhouse Effect was so uncontroversial in the United States that it was the subject of a children’s song. A really great song.

WARNING: This song contains a BANJO accompanimentWARNING

The song is on the You Tube link above and the lyrics are at the end of this article.

Written by folk-singer Tom Glazer, the lyrics show an excellent appreciation of the physics of the greenhouse effect.

After first describing how a greenhouse works, the song describes how the Earth is warmed by solar radiation

The atmosphere is like a greenhouse too
It lets most of the solar rays through
The surface of the Earth absorbs these rays
And re-radiates them as long heat rays

And then, in very sophisticated terms it describes the role of water vapour in the atmosphere

There’s vapour in the air, What does it do?
It doesn’t let the long heat rays pass through
Trapped by the vapour they bounce back and forth,
Re-radiated and re-absorbed

Did you read that?

re-radiated and re-absorbed

Tom Glazer is describing the basic physics of the MODTRAN model of atmospheric transmission! (Link).

Can you imagine a world where it is OK to say “re-radiated and re-absorbed” to primary school children?

Children who learned this song would have a better operational understanding of the physics of the greenhouse effect and global warming than a fair fraction of the population of this country or the USA!

But the terrible truth is that 60 years after it was written, this song and the knowledge it embodies has been lost to popular culture and become – apparently – controversial.

How did we lose this collective knowledge?

Lyrics

What does the glass of a Greenhouse do?
It lets the short solar rays pass through
The objects in the house absorb these rays
And re-radiate them as long heat rays

What does the glass of a Greenhouse do?
It doesn’t let the long heat rays pass through
Trapped by the glass they bounce back and forth,
Re-radiated and re-absorbed

Stay Stay, you long heat rays, Warm up the house on cold cold days
Stay Stay, you long heat rays, Warm up the house on coooooold cold days

The atmosphere is like a greenhouse too
It lets most of the solar rays through
The surface of the Earth absorbs these rays
And re-radiates them as long heat rays

There’s vapour in the air, What does it do?
It doesn’t let the long heat rays pass through
Trapped by the vapour they bounce back and forth,
Re-radiated and re-absorbed

Stay Stay, you long heat rays, Warm up the house on cold cold days
Stay Stay, you long heat rays, Warm up the Earth on cooooooold cold days

Weather Songs

Global Warming: we were warned.

April 2, 2017

Human beings – including the one writing this – often find it hard to grasp the rates of processes involved in Global Warming.

When thinking about the physics, there are three important rates to consider.

  • The rate at which human emissions have taken place.
  • The rate at which the emissions affect Earth’s temperature.
  • The rate on which human emissions will dissipate.

But we also need to consider one other ‘rate’:

  • The rate at which humanity can respond to a warning after it has been given.

Let’s look at each of these ‘rates’ in turn:

Rate of Emissions

We are emitting carbon dioxide into the atmosphere at an astonishing rate: about 33 billions tonnes of carbon dioxide every year.

Humanity's Cumulative Emissions of Carbon Dioxide expressed in two ways. The left-hand axis shows the data as a fraction of the emissions. The right-hand axis shows the data as billions of tones (i.e. Gt) of carbon.

The graph above shows data from the Carbon Dioxide Information Analysis Centre. It shows humanity’s cumulative emissions of carbon dioxide expressed in two ways.

  • The left-hand axis shows the data as a fraction of the emission up to 2013 (100%)
  • The right-hand axis shows the data as billions of tonnes (i.e. Gt) of carbon. Multiply this number by 3.67 to convert it to billions of tonnes (i.e. Gt) of carbon dioxide.

From the graph we can see that:

  • 80% of the carbon dioxide we have put into the atmosphere has been put there in my lifetime. I am 57.
  • Although climate emissions have stabilised in the last three years, this only means that the slope of the graph has stopped increasing.
  • Continuing at the current rate, every 7 years we will emit carbon dioxide equivalent to the entirety of human emissions from the dawn of time to the date of my birth.

Climate Impact

Below is the estimate of the Earth’s average surface temperature made by the team at the NASA GISS laboratory. Alongside the data is a trend-line smoothed over a 10 year period.

The temperature rise is shown relative to the average temperature over the period 1951 to 1980.

Global Land Ocean 10 year smoothing

  • The graph shows that since 1980, the temperature trend has been rising roughly linearly at about 0.02 °C per year i.e. 0.2 °C per decade, or 2 °C per century.

Carbon absorption

The 33 billion tonnes of carbon dioxide we emit annually into the atmosphere corresponds to about 9 billion tonnes of carbon – these are the units used in the info-graphic below.

Carbon_cycle

This image is from Wikipedia and was adapted from U.S. DOE, Biological and Environmental Research Information System. – http://earthobservatory.nasa.gov/Features/CarbonCycle/, Public Domain, Link All the numbers are in billions of tonnes of carbon (Multiply by 3.7 to obtain the numbers in billions of tonnes of carbon dioxide). Figures in red are human emissions.

Natural processes remove about 2 billion tonnes of carbon from the atmosphere each year by dissolving it in sea water. And a further 3 billion tonnes of carbon a year is removed by increased plant growth.

If we stopped emitting carbon dioxide now, then these processes would the lower the carbon dioxide concentration in the atmosphere back to 1960’s levels in about 100 years.

As a consequence of these slow rates of removal, we are already committed to many decades of further warming at a rate similar to that which we are experiencing already.

Summary. 

  • The bulk of human emissions have occurred relatively recently.
  • We are now in an era when the Earth’s surface is definitely warming.
  • When we eventually take action we will still experience warming for many decades more.

But we have known all this for a long time: at least 36 years

The process which limits our rate of response. 

Arguably, the emergence of ‘popular’ appreciation of the effect of carbon dioxide emissions can be timed to 1981, when James Hansen and colleagues published a landmark paper in Science 

The paper is complex, but readable. But in case you are busy, here are some extracts.

A 2 °C global warming is exceeded in the 21st century in all the CO2 scenarios we considered, except no growth and coal phaseout.

This is happening now.

Floating polar sea ice responds rapidly to climate change. The 5 °C to 10 °C warming expected at high northern latitudes for doubled CO2 should open the North-west and North-east passages along the borders of the American and Eurasian continents. Preliminary experiments with sea ice models suggest that all the sea ice may melt in summer, but part of it would refreeze in winter. Even a partially ice-free Arctic will modify neighbouring continental climates.

This is happening now well before CO2 concentrations have doubled.

The global warming projected for the next century is of almost unprecedented magnitude. On the basis of our model calculations, we estimate it to be ~2.5°C for a scenario with slow energy growth and a mixture of nonfossil and fossil fuels. This would exceed the temperature during the altithermal (6000 years ago) and the previous (Eemian) interglacial period 125,000 years ago, and would approach the warmth of the Mesozoic, the age of dinosaurs.

This is happening now, but the warming is faster than the ‘worst case’ scenario they envisaged.

Political and economic forces affecting energy use and fuel choice make it unlikely that the CO2 issue will have a major impact on energy policies until convincing observations of the global warming are in hand.

How true! And even after the observations have become convincing, ‘political and economic forces‘ are still resisting a change in fuel use.

In light of historical evidence that it takes several decades to complete a major change in fuel use, this makes large climate change almost inevitable. However, the degree of warming will depend strongly on the energy growth rate and choice of fuels for the next century. Thus, CO2 effects on climate may make full exploitation of coal resources undesirable.

An appropriate strategy may be to encourage energy conservation and develop alternative energy sources, while using fossil fuels as necessary during the next few decades.

In retrospect, we could not have asked for a clearer or more accurate warning or better advice.

As I look at it now, the physical rates of processes make this problem really difficult

But it is our inability to respond to warnings which makes this potentially insoluble.

All the warnings above have come to pass: Let’s hope the paper’s warnings about sea level rise prove to be less accurate.

Danger of rapid sea level rise is posed by the West Antarctic ice sheet, which, unlike the land-based Greenland and East Antarctic ice sheets, is grounded below sea level, making it vulnerable to rapid disintegration and melting in case of general warming.

The summer temperature in its vicinity is about -5°C. If this temperature rises ~5°C, de-glaciation could be rapid, requiring a century or less and causing a sea level rise of 5 to 6 m (55). If the West Antarctic ice sheet melts on such a time scale, it will temporarily overwhelm any sea level change due to growth or decay of land-based ice-sheets. A sea level rise of 5 m would flood 25 percent of Louisiana and Florida, 10 percent of New Jersey, and many other lowlands throughout the world.

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

March 25, 2017

Graph 2017

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

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

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

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

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

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

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

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

The graph shows that on average:

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

So since 1979,

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

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

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

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

Graph 2017-3

Graph 2017-2

What happens next?

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

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

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

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

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

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

Sea Ice Volume March 2017

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

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

As I mentioned, we are discussing ‘the future’ so no-one knows what is really going happen: 2021 is probably too early, but 2065 is probably too late. This 2012 article discusses the complexities of this extrapolation in detail.

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

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

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

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

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

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

January 28, 2017

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

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

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

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

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

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

See for yourself

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

1

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

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

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

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

7

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

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

2

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

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

The first step

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

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

3

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

The second step

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

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

5

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

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

But you can check that for yourself if you want!

Is it a cheat? No!

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

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

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

There is more!

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

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

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

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

6

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

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

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

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

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

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

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

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

Still learning after all these years

December 31, 2016
David Archer teaching a course on Global Warming

David Archer teaching a course on Global Warming

I have had to teach myself the physics of global warming.

And as an autodidact, I have suffered from the misfortune of having been taught by an idiot.

So ‘attending’ an online course about Global Warming is a genuine pleasure: it is so much easier than teaching oneself!

All I have to do is to listen – and re-listen – and then answer the questions.

Someone else has selected the topics that they feel are most important and determined the order of presentation.

Taking the course on-line allows me to expose my ignorance to no-one but myself and the course-bot.

And in this low-stress environment it is possible to remember the sheer pleasure of just learning stuff.

On line courses

Using the FutureLearn platform, I have taken courses on Global WarmingSoil, and Programming in Python.

I have participated with dual aims. In part I have wanted to learn about the topic. But also I have been curious to experience ‘a course’ from a student’s perspective.

The current course uses the Coursera platform and is much more technical than any of the Futurelearn courses I have tried previously.

For me that’s fine, but my guess is that the mathematical level is somewhere between GCSE and ‘A’ level and many people would find that intimidating.

The course assessments are also genuinely challenging, requiring the use of quite complex online software, and implicitly, the use of a spreadsheet or calculator.

One pleasing aspect of the course – for me at least – is that the course lecturer (David Archer) basically stands in front of a blackboard and talks.

He dresses like a physicist, and sounds like a physicist, and makes mistakes on the blackboard – it’s just like being back at University!

And in the vacuum between Christmas and New Year it has been a pleasure to lose myself in this on-line world.

Continuous Professional Development

‘Attending’ this course has also had a curious personal resonance for me.

I recently applied to become a ‘Fellow’ of the Institute of Physics – I am currently ‘only’ a member.

I first filled out the application form in 2013 – three years ago – and I thought I was doing well until I came to the section marked ‘CPD- Continuous Professional Development’.

The section was marked with a stern warning that it was not optional. Unfortunately, I couldn’t think of a single word to put in the section. So I just forgot about the application.

Each year since I have re-visited the form and fallen at the same hurdle.

But this year I asked some colleagues for help. It turns out that attending courses like this is actually CPD!

Who knew!

 

 

Grandmother’s kilograms

December 28, 2016

weight-2016

One of the reasons that I feel better this Christmas than last is because I have managed to lose weight.

In the 11 months since the end of January 2016 my weight has fallen from about 88 kg to around 73 kg.

For US readers, that’s a weight loss of 33 pounds, and for older UK readers, that’s about two and a half stone. It is a transformative amount of weight to loose. I feel much better.

I mention it here, because I have showed similar graphs before. For example, in 2011 I wrote “The Mass of Sisyphus” which has a graph of my weight from 1995 to 2011 (Ages 35 to 51)

So I have achieved similar weight loss previously, but previously my weight crept back onto my body. However I don’t have any data about the times when my weight is increasing.

It is like the game of Grandmother’s Footsteps in which children have to sneak up on ‘Grandmother’ but they can only move when ‘Grandmother’ is not looking.

Similarly, my weight seems happy to stay still or indeed to go down, as long as I weigh myself every day. But when I stop weighing myself – it slowly creeps up on me in the most sinister way.

My conclusion is that in order to maintain my weight I need to weigh myself every day.

It is yet another example of the power of measurement: because it is not until one measures a thing that one can begin to understand it, and control it.

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

The graph also shows the busy year I have had with trips to Canada just before the graph began, India, the USA (twice), Poland, Italy and Spain.

Irritatingly, each trip has broken my weight loss trend.

However another good feature of the year has been running. Compared with 2015, I have increased the distance I have run from about 14 km per month, to around 100 km /month.

running-record-2016

Running has helped keep anxiety at bay and happily I can take my running shoes with me when I travel.

This seems to have settled down into a routine, and although it seems quite sporty for a man of my age (57) it takes only just over two hours a week.

And as I have run more, even though I haven’t been trying to run faster, I found I have naturally speeded up.

running-speed

Looking at the graph I can see that even since July 2016 when my weight has been more or less stable, my speed has been slowly increasing.

So my aim for the new year is to keep on running – and weighing myself every day. And hopefully I will keep Grandmother’s kilograms from creeping up on me!

 

 

 

Happy Christmas 2016

December 24, 2016

christmas-card-2016-explosion-3

First of all, thank you for having taken the trouble to stop by.

I had been going to write my reflections on the year – but I am too tired, and too likely to say negative things. So I will put that off for now.

And looking back at my blog, I realise that I do feel better than I felt in 2013.

All the things I wrote back then are still true, and some even more so.

But my campaign to manage my own anxiety has partially alleviated their personal impact. So there are positives from the year!

But horrifically I also realise that I am struggling to complete exactly the same ‘3 month’ project that I was desperate to complete by last Christmas! Aargh

Hey Ho! “plus ça change, plus c’est la même chose!” Anyway, please allow me to wish you a…

…Happy Christmas, and a splendid 2017.

 

 

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.

Clouds

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.

Conclusions

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]

 

 

Grammar Schools:Their formula for success revealed!

October 2, 2016

education

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]

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.

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

[Reflect]

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.

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

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

 


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