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BBC SCIENCE
CLIMATE CHANGE
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BBC SCIENCE
CLIMATE CHANGE
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PART 1 OF 4
10:00:07
Woman
This is the story of climate change.
10:00:12
Man
But told in a way you’ve never heard before.
10:00:19
Man
Because we’re not climate scientists, we’re three
mathematicians
Man
And we’re gonna use the clarity of numbers to cut through
the complexity and controversy that surrounds climate
change.
10:00:37
Woman
Understanding what’s happening to the Earth’s climate is
perhaps the biggest scientific endeavour this human race
has ever taken on.
Man
From the masses of data we’ve chosen just three numbers
that hold the key to understanding climate change.
Woman
0.85 degrees
10:00:59
Man
95%
10:01:02
Man
And one trillion tons.
10:01:06
Woman
Just by looking at these crucial numbers we’re gonna try
and get to the heart of the climate change controversy.
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10:00:24
Woman
They are three numbers that represent what we know about
the past, present and future of Earth’s climate.
10:01:18
Woman
And it’s not just the numbers themselves that are
important, the stories behind them, how they are
calculated, are equally intriguing and revealing.
10:00:28
Comm
We’ll see how the methods using everything from the
Moon landings
10:00:30
Woman
To early twentieth century cotton mills and motor racing
have fed into the numbers we’ve chosen.
10:00:32
Comm
These three numbers tell an extraordinary story about our
climate and take us to the limits of what it is possible for
science to know.
10:02:05
Opening titles
CLIMATE CHANGE
BY NUMBERS
10:02:14
10:02:16
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Man
Every minute of every day all over the planet scientists are
VO
collecting data on the climate. Around ten thousand
weather stations monitor conditions of the Earth’s surface.
Some twelve hundred buoys and four thousand ships
record the temperature of the oceans. And more than a
dozen satellites continuously observe the Earth’s oceans
and atmosphere.
10:02:50
Man
All science starts with collecting data and when it comes to
VO
our climate we’ve got masses of it, but what story about
our planet is all that data telling us?
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10:03:03
10:03:11
MUSIC IN
Woman
Thousands of scientists are trying to answer that question,
VO
their results are summarised in a series of huge reports by
the Intergovernmental Panel on Climate Change. The three
numbers we’ve chosen all come from the IPCC’s reports.
10:03:37
Woman
Molly.
10:03:39
Hannah
I’m Doctor Hannah Fry and I use numbers to reveal
patterns in data. I’m looking at one number that answers a
critical question, is climate change really happening?
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10:03:58
Hannah
Our first number is
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Dr Hannah Fry
University College London
0.85 degrees. Now this number represents what we know
about our climate in the recent past because it’s the number
of degrees Celsius that scientists say our Earth has warmed
since the 1880s.
Hannah
10:04:20
But how can they be so precise?
After all our climate is complex and extremely varied.
Temperatures change from season to season, place to place
and even minute by minute.
10:04:42
PTC
As if it wasn’t hard enough to try and find an average
temperature of the Earth for now we also need to go back
in time and compare it to the average temperature of the
Earth in the past when we didn’t have the luxury of modern
measurement techniques.
10:04:55
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10:04:59
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Working out how the planet’s temperature has changed
over more than a century is a huge challenge. It’s a bit like
trying to work out the route I’m taking across this park, if
you only had the route Molly is taking to go on. You have
to identify the trend, my path, from all those changing
temperatures, Molly’s path and it all starts with the quality
of the data. Now that’s not such a problem for the recent
past, but what about further back in time?
10:05:42
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10:05:45
MUSIC IN
10:05:53
VO
Up until the middle of the nineteenth century the
temperature record as measured by instruments is patchy
and unreliable and there is some controversy about how
you reconstruct temperatures before this time. But the
record improves from the 1880s due to the efforts of one
man.
10:06:27
PTC
Now the key man in this story, the man with a plan, is a
guy called Matthew Fontaine Maury. Now Maury was a
lieutenant in the US Navy and from even when he was a
small boy was obsessed with mathematics and data and
analysis. But in 1839 Maury had a coaching accident
where he broke his thigh bone and dislocated his kneecap
and while he was recovering he spent his time studying
captains’ log books. And the data that he found there set
the path for his next fourteen years’ worth of work, so
much so that on the 23rd of August in 1853 he called
together a meeting of twelve countries surrounding the
North Atlantic, all to talk about one thing.
10:07:08
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10:07:11
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He wanted to improve the way that data about the oceans
was collected.
10:07:19
PTC
Captains record all sorts of information in their log books,
things like wind speed and direction, or the speed and
temperature of the sea currents. Now this wasn’t just
interesting to Maury from a scientific perspective, but also
because it was something he could sell to commercial ship
owners.
10:07:38
VO
He found great commercial success from mapping the
position of major sea currents like the Gulf stream which
enabled ships to use the currents to travel faster. But there
was a problem; different sailors took the same
measurements in different ways. That was particularly true
for one of the measurements climate scientists are
interested in, sea surface temperature.
10:08:10
10:08:11
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PTC
Now the way to measure sea surface temperature is
actually surprisingly simple, all you do is chuck a bucket
over the side of the ship and get the temperature from it.
But the problem is that the result that you get actually
depends quite a lot on the type of bucket that you use, so
let me just take the temperature of this now and in the
meantime I’m gonna throw this guy over.
10:08:46
VO
In the early nineteenth century some sailors used wooden
buckets, others used buckets made of canvas. This meant
that the measurements were not consistent.
10:09:01
PTC
The wooden bucket’s coming out as a surprisingly warm,
er 15.1 and if we make a comparison the canvas bucket,
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unlike the wooden bucket, isn’t insulated so things like, um
the air temperature are gonna make a much bigger
difference so the temperature has dropped below 15.1
degrees.
10:09:20
VO
It may not sound like a lot but even tiny discrepancies
undermine the accuracy of the data.
10:09:27
PTC
Now Maury knew this and so at his conference in 1853 he
came up with a standardised way for everyone across the
world to measure sea surface temperature.
10:09:37
10:09:42
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VO
He wanted everyone to use wooden buckets and designed
special forms for them to fill in with all their data. Maury
also introduced standardisation to air temperature
measurements on land. That’s why our 0.85 degrees
Celsius figure is measured from 1880, it’s the date from
which the temperature data is generally well standardised.
But despite Maury’s efforts the data was still far from
perfect, not everyone stuck to the rules, for example over
time canvas buckets made a comeback because they were
lighter, so there were still errors, some of which were
pretty obvious.
10:10:24
10:10:29
PTC
So here is the sea surface temperature data between
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1880 and 1980. And the first thing that you really notice
about this graph is this huge spike that happens where it
looks like the sea surface temperature’s raised by 0.8
degrees Celsius. Or at least it looks that way until you
realise that this spike happened, er in 1941 when during the
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Second World War understandably sailors didn’t much
wanna go up on deck with a torch and a bucket to record
10:10:55
sea surface temperature levels. So instead during that time
they used, er the water that was coming in through the
engine room which is hence why the data is a lot higher.
Now after the Second World War people gradually started
returning to using uninsulated canvas buckets, but
unfortunately we don’t know who was using them or when.
And so in all of this big mess of data how do we get
accurate
10:11:19
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temperature readings for land and sea from the past?
10:11:27
VO
The answer is related to a mathematical technique that was
used to help solve one of history’s greatest challenges.
10:11:41
VO
In a mission fraught with difficulties one of the biggest was
how to navigate a quarter of a million miles through Space
to the surface of the Moon.
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10:11:53
10:11:57
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VO
It’s a feat of navigation all the more astonishing when you
consider how difficult finding our way around can be
even down here on the ground.
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10:12:07
PTC
Working out exactly where you are on the Earth at any
point in time is actually a surprisingly difficult problem,
especially if you want really, really precise information.
10:12:18
VO
It’s tricky because tracking opposition, just like measuring
temperatures over time, is prone to error.
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10:12:26
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Not the easiest thing ever.
10:12:28
VO
Take dead reckoning, timing how long you’ve travelled in
a particular direction from your last known position.
10:12:35
Man
About three miles an hour.
10:12:36
PTC
Lovely, three miles an hour, hang on one second.
10:12:43
VO
It’s easy to drift off course as inaccuracies build up.
10:12:48
PTC
Hang on.
10:12:50
VO
Even more high tech methods can get it wrong.
10:12:54
PTC
Actually the GPS is putting us over there at the moment
which is less than ideal.
10:12:59
VO
So when it comes to navigating the problem is which
measurement of your position do you trust?
10:13:06
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In the 1950s a young Hungarian born mathematician,
Rudolf Kálmán, devised an elegant algorithm to solve this
problem.
10:13:17
PTC
Kálmán’s method uses a matrix algebra, er and takes into
account all of the errors to give you the best possible
estimate of your position at any point in time.
10:13:30
VO
So how does Kálmán’s method work? In 1969 NASA
gave it its ultimate test in the mission to land men on the
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Moon. Navigating in Space poses particular challenges.
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The spacecraft was being tracked by four radar stations on
Earth. Onboard instruments were also estimating its
position, but each of these measurements could be wrong.
So how could NASA be sure of Apollo Eleven’s position?
This is where Kálmán’s algorithm came in. Moment by
moment it compared each position measurement with the
others, looking for differences that fell outside the expected
margin. If the algorithm had found significant
disagreement the mission would have been aborted, but it
didn’t and the rest is history.
10:14:59
PTC
So this process is now known as Kálmán filtering and has
been used in everything from, er cleaning up
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grainy video to looking for trends in economics. And a lot
of the underlying principles are exactly the same as you see
in the processes used for climate science. So, er knowing
when to trust your data and picking out when the errors are
big enough to flag up a deeper underlying issue, but the
process in climate science is
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instead known as homogenisation.
10:15:33
VO
Homogenisation has allowed climate scientists today to
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clean up data gathered in the past. Unreliable
measurements can be corrected or discarded.
10:15:47
PTC
So what homogenisation process is doing effectively is
taking all of the data from all of the weather stations and
comparing it on a day by day basis. Now in doing that if a
particular data set starts to look a bit unusual it will really
stand out.
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10:16:05
VO
You can see what happens when scientists homogenise a
data set by looking at how they corrected the unusual jump
in sea surface temperature in the early 1940s.
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10:16:17
PTC
So once you’ve applied this homogenisation process here is
what the sea surface temperature data will look like. So we
have the original data here, er in yellow and the cleaned up
version
10:16:29
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also available in blue.
Now the first thing that you notice is that the big jump that
we had in 1940 has dramatically reduced, er there is still a
bit of a jump because there was an El Niño that year which
meant that the sea surface did actually warm. But the jump
that was down to the difference in measurements, the, the
error in the way that people were measuring, has been
taken away completely from the graph.
10:17:00
VO
All the big scientific groups that work with climate data
use homogenisation methods like this to try and clean up
the records of past temperature.
10:17:12
PTC
And it’s absolutely vital that you account for some of these
errors in measurement that have occurred in historical data
otherwise you’ve got no hope of finding any kind of
underlying patterns in your data. But inevitably as soon as
you start applying these mathematical
10:17:27
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recipes to clean things up other people will start accusing
you of building in biases into your data.
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10:17:37
VO
Perhaps the best defence against bias is scientists’ own
scepticism. Many different groups work on climate data
using slightly different homogenisation methods and all are
subjected to searching scrutiny
10:17:52
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by their peers. But even after homogenising the historical
data climate scientists face a further problem, gaps in the
temperature record. Even today we do not have
temperature measurements for the whole planet.
10:18:14
PTC
If you look at where we have temperature data for, if you
split the Earth into a grid it becomes very obvious that
there are some areas where we have much more
information on than others.
10:18:25
VO
The black squares show when we had hardly any weather
data at all.
10:18:30
PTC
So if you take The Arctic for example it’s very obvious
there are almost no sample points in The Arctic.
10:18:36
VO
The gaps in places like Africa and the Poles can affect how
we calculate the average temperature of the whole planet.
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PTC
Now if you take an average across the whole of the Earth
and don’t take into account the fact that you have a lot less
data for The Arctic you’re gonna end up with a really
biased average and something that doesn’t really represent
the Earth properly. Now there is actually a mathematical
solution to this problem that climate scientists are
beginning to use, but it’s one that wasn’t even devised
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10:19:06
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by a mathematician.
10:19:11
VO
The attempt to fill in gaps in the temperature data begins in
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the gold fields of South Africa in the 1950s where a mining
engineer was grappling with a problem. Danie Krige was
in charge of the leases of the country’s very valuable gold
fields and was inundated by companies desperate to mine
them.
10:19:36
PTC
But until each plot of land had been mined he had no way
of knowing how valuable each area would be. What he
needed was a systematic way of working out how much
each lease was worth and so turned to spatial statistics.
10:19:54
VO
To understand the challenge Krige faced I’ve come to gold
mining country, to Dolaucothi in Wales. All Krige had to
go on were a few scattered core samples that had been
taken across the gold fields as miners tried to find more
gold. He had to find a way of working out much gold there
was in each plot of land with just these few measurements,
just like climate scientists have to work out the temperature
in places where they don’t have measurements.
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10:20:30
10:20:31
PTC
So what I’m gonna do here is show you how Danie Krige’s
method worked using these as my core samples.
10:20:39
VO
Imagine each of these poles represents a core sample and
the number of lights indicates the amount of gold found in
it.
10:20:51
PTC
So our first core sample is giving us a reading of sixteen
parts per million
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10:20:56
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all the way up there into the red. And this core sample is
giving us a reading of only six parts per million.
10:21:14
VO
Danie Krige’s samples were often around a kilometre
apart. Climate scientists have weather stations that might
be hundreds or even thousands of kilometres apart,
especially in regions like The Arctic. The problem in each
case is the same, how to fill in the gaps in the data.
10:21:35
PTC
So one more core sample to do and then I can show you the
map. So our last reading is only giving us two parts per
million, so we’re still on the gold field but we’re at a much
lower grade of gold than we were before. But the real
question that Danie Krige wanted to ask was how can you
tell what happens in between the core samples, how can
you tell how much gold is in the middle?
10:22:05
VO
His answer was to use maths to take into account both the
amount of gold in each sample and the distances between
them. So Krige’s method would take the first exciting
strike of gold and look at how far away the neighbouring
samples are, as well as how high the levels of gold found in
them are. This helps estimate how much the gold levels
drop off around each strike. The process is then repeated
over the whole field. It may not sound like it, but the
maths is relatively simple.
10:22:43
PTC
Now it’s so powerful that this method has been used all
across the world in everything from looking at gold mines
to forestry and even temperature data and it’s even been
named after the great man himself, now known as Krigeing
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10:22:48
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10:23:00
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10:23:02
VO
Krigeing is now being used to throw new light on the
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biggest recent climate change controversy, what’s
happened to the temperature of the planet since the turn of
the century? The issue is how you account for gaps in the
record of global temperature.
10:23:20
PTC
If you take the UK Met Office’s Hadley Centre for
example and their data on the changing global temperatures
in the recent past they leave blanks in regions where they
don’t have any information. But if you look at the
temperature set you can see that it demonstrates an effect
that’s become known as the Pause which is the temperature
of the Earth doesn’t appear to have risen since the year
10:23:42
2000.
10:23:47
VO
This Pause in the Earth’s rising temperature is
controversial. Some climate change sceptics say it shows
that global warming is not real, but most climate scientists
say they would expect pauses every now and again within a
warming trend. But whether there even is a pause depends
on how you account for the gaps in the temperature record.
10:24:13
PTC
When this data set was Kriged by an independent scientist
in 2014 so that they could take into account the little data
that you have in The Arctic he found that the graph
changed.
10:24:26
VO
Krigeing put more weight on the few temperature points
we have from The Arctic and there the temperatures are
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rising fast. The impact of Krigeing on the original
incomplete data is to turn the Pause into a small
temperature rise.
10:24:43
PTC
Now you might think that this doesn’t necessarily represent
reality either, but it does demonstrate an important point,
what you do with your data has an impact on how you
make your conclusions.
10:24:55
VO
It’s not to say that Krigeing The Arctic figures has really
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shown that there isn’t a Pause, it remains an area of debate,
but techniques like this offer scientists the only way they
have to overcome the inevitable limitations of incomplete
data. It doesn’t matter how much effort scientists go to,
temperature data will never be perfect and the trouble is
mathematical manipulation of the raw data can look like
10:25:30
fiddling the figures. But the techniques that climate
scientists have used are well understood, they’re open to
scrutiny and they all lead in the same direction. Three
major research groups have contributed to the IPCC’s
reconstruction of past temperature. They’ve each used
slightly different methods to clean up the historical data
and account for gaps in the temperature record.
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PTC
And here are their results. So in the top left hand side you
have the results from The Global Historical Climatology
Network, er top right you have the results from The
Goddard Institute of Space Studies, um and in the bottom
left you have the results from The Met Office’s Hadley
Centre. Now just these three graphs show pretty similar
results, they all seem to be showing a very similar shape,
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especially when you take into account the fact that all of
the groups were using different techniques.
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VO
From there how did the groups arrive at an average
temperature rise? This bit is surprisingly simple.
10:26:39
PTC
Now rather than all of the zigging and zagging the groups
put a line through each of their graphs and from there it’s
very easy to just read off how much the temperature has
risen.
10:26:50
VO
These three lines show the trend in the average temperature
since 1880 for each data set.
10:26:59
PTC
But the IPCC then took the average of each of these three
lines and come up with the value of 0.85 degrees Celsius,
the most accurate measure that we have for how much the
Earth’s temperature has risen by since 1880.
10:27:16
VO
But that doesn’t mean it’s perfect, the exact figure is
always going to be uncertain.
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Scientists have done their best to try and compensate for
imperfections in the historical temperature record. They’ve
applied mathematical record to patchy, unreliable and
erroneous data.
10:27:44
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PTC
Now 0.85 degrees is itself just a symbolic figure. I could
have averaged the data in several different ways and ended
up with a slightly different figure every single time, but
that’s not really the point. Looking at how this number is
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produced you can see that it doesn’t matter how you collect
your data, how you measure your data, or how you treat it,
one point still stands overall, the Earth’s temperature has
been
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rising in the last hundred and thirty years.
10:28:20
VO
Different groups using different techniques, each
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scrutinising the others, have all arrived at pretty much the
same conclusion. That’s why it’s now relatively
uncontroversial to say that the Earth’s temperature has
risen by just under a degree since the 1880s. There’s far
less agreement though on the answer to the big question all
this raises, why did the Earth’s temperature rise?
10:28:58
10:29:00
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PTC
We can only look at a very different number, a number that
answers one of the most difficult and controversial
questions in the whole climate change debate. Just to what
extent is the rise in temperature caused by human activity
and to what extent is it caused by just natural fluctuations?
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10:29:18
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10:29:30
VO
I’m Professor Norman Fenton,
Woman
Hi there, how are you?
Norman
Hi
a mathematician and life long Tottenham Hotspur fan.
From financial services to transport and even football I use
numbers to work out the most likely causes of different
events.
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10:29:47
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Prof Norman Fenton
Queen Mary University of London
The climate change number I’m looking at is all about
cause and effect.
10:29:52
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The scientists have made a big statement, they say they’re
95% sure of the main cause of the Earth’s recent warming.
10:29:59
10:30:01
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VO
And that cause they say is us. All science involves
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identifying not just what is happening, but also why it’s
happening. When it comes to the climate scientists say
they’re 95% sure that over half of the warming in the last
sixty years has been caused by humans. How can they be
so sure? Well by using statistics we can analyse the most
likely cause of something whether that’s success at football
or climate change.
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PTC
I’ve been coming to Spurs for over fifty years and I have to
say this isn’t one of their finest seasons, but like most fans
I’m pretty confident I know which factors are gonna be
most important for determining whether they’re gonna play
better or worse than expected
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10:30:50
in any given season.
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VO
Unsurprisingly, there’s no shortage of opinions here.
10:30:56
Man
Definitely the manager, you know, the manager, they need
to respect the manager, the manager needs to have sort of
like respect to the players as well.
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10:31:02
Man
If you’ve got the tactics right and you’ve got the players in
the right places where they should be.
10:31:07
Man
Well you need a very good executive board, your players
need to stay very fit, your manager needs to be focused,
have a very good philosophy.
10:31:15
10:31:17
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VO
Beyond opinion there is a way to use maths to work out
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which factors are the most crucial. It’s called an attribution
study and it’s what the IPCC did to arrive at their 95%
figure. All attribution studies start with identifying the
factors that might cause an outcome. Let’s take footballing
success.
10:31:43
10:31:44
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PTC
Here I’ve got lots of statistics on all the Premiership teams
going back many seasons. It’s interesting when you look
at the league tables to see how the performance of a team
will vary from season to season. I wanna understand
which of many possible factors are the most important
causes of this. Is it the length of time the manager’s been
with the club? Is it the injury rate? Is it how much they
spend on players? I’m gonna put all those factors together
with many others and plot my own attribution study.
10:32:12
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10:32:21
VO
To work out why some teams win and some lose we need
the second part of the attribution study. The different
factors we’ve identified that could affect the team’s
performance are put into a mathematical model. It’s the
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same process climate scientists use to try to work out what
is driving climate change. I can now check the accuracy of
my model against teams’ past performance.
10:32:48
10:32:50
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PTC
So what I’ve got here for example is I’ve taken one of the
teams, Manchester city and I’ve plotted the actual
performance in terms of points that they achieved in each
of the last few seasons. Now we look at what the model
would have predicted and you can see it’s actually a pretty
good prediction of what actually happened.
10:33:09
10:33:12
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VO
And this is true for all the teams in the Premier League.
Now I know I can trust my model I can move on to the
clever bit, isolating the factors that make the most
difference to the team’s success.
10:33:27
PTC
10:33:29
I found that there was one factor which had
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far greater impact on performance than any other, the wage
bill. If I take out the wage bill factor it’s no longer a good
estimate at all, it’s quite a long way off and in fact we can
repeat that for all of the other teams.
10:33:47
VO
Using the same methods as the IPCC I can even put an
actual figure on how big an effect the wage bill has.
10:33:59
PTC
I can say there’s a 95% chance that if you increase the
wage bill by 10% there’ll be at least one extra point at
Premiership season.
10:34:09
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10:34:10
VO
I can be so confident because the answer’s so clear from
my model. But how can climate scientists be equally sure
of their results? After all what drives changes in the
Earth’s climate is one of the most complex puzzles
scientists have ever tried to unlock. Before trying to work
out the impact humans have, scientists have to account for
natural variations in the Earth’s climate.
10:34:40
PTC
10:34:42
The key science involves a number of factors,
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all of which play a role in changing the climate. If this was
a court case
10:34:47
MUSIC IN
they’d be our suspects.
10:34:51
VO
Many natural factors are known to cause changes to the
Video clips
climate, they include the sun, the energy it emits varies and
this can change the temperature here on Earth. Volcanic
eruptions, the vast gas clouds they throw up can cause
sharp global cooling as they affect the chemistry of the
upper atmosphere and climate cycles like El Niño that can
cause global temperature fluctuations lasting many years.
But climate scientists say they’re 95% sure that recently all
these natural factors have been overshadowed by one other.
10:35:49
10:35:50
PTC
For most climate scientists
MUSIC OUT
there’s one prime suspect in this case, us, and that’s
because of a colourless, odourless gas called carbon
dioxide that we’re pouring into the atmosphere. One of the
first people to try and unravel the role of carbon dioxide on
changing the Earth’s temperature was a depressed Swedish
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physicist called Svante Arrhenius. Arrhenius wasn’t
interested in the Earth’s warming however, but cooling.
10:36:16
10:36:19
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VO
In 1894 Arrhenius’ marriage broke up. Searching for
Video clip
distraction he set his mind to one of the great mysteries of
his time, the origin of the Ice Ages. Scientists had long
wondered how the great mountain landscapes of Europe
had been formed. Once the rugged valleys were thought to
be the relics of a biblical flood, but in Arrhenius’ time it
was realised that the Earth had been beset by periodic Ice
Ages over the last two and a half million years.
10:07:02
PTC
On trips through Northern Europe he studied the vast
palatial landscapes that surrounded him and wanted to
know how the Earth could possibly have undergone such
monumental change. What had caused the planet to cool
down so dramatically?
10:37:21
VO
Scientific understanding advances by developing theories
and then testing them. It was already widely accepted that
so called greenhouse gases worked like a huge blanket
around the Earth keeping it warm. Arrhenius’ developed a
theory that changes in the concentrations of these gases, in
particular carbon dioxide, might also have caused the
planet to cool. The only way he could test his theory was
to use maths to work out the relationship between changing
levels of carbon dioxide in the air and the Earth’s
temperature.
10:38:06
10:38:07
MUSIC OUT
PTC
It was painstaking work; every calculation had to be
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written out by hand, Arrhenius himself described it as
tedious, but eventually he had his answer. He predicted
that a halving of carbon dioxide in the atmosphere could
lower the temperature by over four degrees and perhaps
trigger an Ice Age. Almost as an afterthought he also
calculated that a doubling of carbon dioxide could increase
the temperature by the same amount.
10:38:36
10:38:42
MUSIC IN
VO
Eventually it would turn out that changing carbon dioxide
levels weren’t the main cause of the Ice Ages, but using
maths Arrhenius had established the crucial underlying
relationship between carbon dioxide in the atmosphere and
the temperature of the planet.
10:39:00
PTC
Much of Arrhenius’ efforts and the related work that
follows can be summarised in one simple equation, this
enables you to calculate the heating effect that comes from
raising carbon dioxide above its base level. It’s one of the
fundamental building blocks of climate science.
10:39:22
VO
The equation shows that the heating effect represented by
Delta F rises in proportion to the amount of carbon dioxide
in the atmosphere. Put simply, you can’t raise carbon
dioxide levels without heating the atmosphere. But there
are many factors that influence the climate, each with their
own equations. The rate of energy coming from the sun,
the cooling effect of volcanic eruptions, human pollution
from things such as industry and agriculture, ocean
currents, cloud cover, wind speeds, all of which influence
each other in a web of complex interactions. Unlike my
10:40:17
football study, modelling the climate is unbelievably
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complicated, so how do climate scientists create a model
that accurately represents the complex interactions of all
these different factors? The answer comes from the very
earliest days of weather forecasting.
10:40:36
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10:40:37
Video clips
MUSIC IN
10:41:01
VO
One of the earliest pioneers of weather forecasting was a
man called Lewis Fry Richardson. At the start of the
twentieth century he set out to revolutionise weather
forecasting using maths.
10:41:21
PTC
Our climate is governed by the circulation of the
atmosphere and Richardson recognised just how complex
this
10:41:26
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system was, declaring that the atmosphere is like London,
there’s more going on than anyone can properly attend to,
yet despite this complexity he wanted to find a way to
unravel its secrets.
10:41:38
10:41:43
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VO
Richardson had an idea of how to do this that was
revolutionary. Using the rows of the theatre as his
template he thought of dividing the world into grid squares,
this would break the problem down into a series of discreet
and achievable tasks. He imagined positioning people
within each square would only have to solve the
calculations relevant to the weather in their area. A
director standing at the centre would take in the results of
all the calculations to form a forecast.
10:42:32
PTC
Richardson made just one attempt to put his ideas into
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practice,
10:42:3
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retrospectively trying to calculate the weather over Europe
for a particular day. But his calculations took him six
weeks to complete
10:42:44
MUSIC IN
and they were far from accurate.
10:42:48
VO
Despite this failure Richardson was ahead of his time. By
dividing the world into grid squares he had made the
crucial theoretical advance that would not only
revolutionise weather forecasting, but also allow scientists
to model the climate. All that was needed was enough
computing power to put it into action.
10:43:15
PTC
Fry Richardson had calculated that he’d need over sixty
thousand people using slide rules in order to predict the
next day’s weather before it arrived. I’m sure he wished
he’d had access to this, the world’s most powerful
meteorological super computer, part of the European
Weather Centre here in Reading. It may be noisy but it can
perform over one thousand trillion calculations every
second.
10:43:44
VO
The world’s biggest super computers are now used to
Video clips
model the climate. Just like Richardson they divide the
world into a grid and solve the complex equations
governing the climate for each square. As computers get
more powerful the squares get smaller and the models get
better at representing reality. No computer is ever
powerful enough to simulate it in as much detail as
scientists would like, but this method has allowed scientists
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to build a model for factors that affect the climate, the
crucial second step of an attribution study.
10:44:23
PTC
10:44:26
However impressive our super computers are,
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however much the climate models exploit the very limits of
our technology, climate modelling remains a simplification
which raises the question, how can scientists be confident
that their simplified models accurately capture reality?
10:44:44
VO
When I made a model for football success I was able to
check it against the past results of dozens of teams.
Video clips
But climate scientists have only one Earth and one set of
past data to check their models against, so they’re always
looking out for new opportunities to test their models.
10:45:04
MUSIC IN
In June 1991 they found a big one. On the Philippine
island of Luzon a volcano called Mount Pinatubo erupted.
It spewed twenty million tons of sulphur dioxide and ash
more than twelve miles up into the atmosphere. It was one
of the most devastating eruptions of the twentieth century.
But climate scientists at NASA realised it also offered a
chance to test their climate model. Could their model
predict the effects of the gases given off on the climate?
10:45:53
After adding the eruption into their model it predicted that
over the next nineteen months there would be an average
global cooling of around half a degree. As the real data
came in month by month it matched the model’s
predictions. It was good evidence that climate modelling
could be reliable.
10:46:18
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10:46:20
MUSIC IN
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10:46:23
VO
Unfortunately opportunities to test the models against data
are few and far between and as a mathematician I find that
frustrating. What’s reassuring is that the underlying
physics on which the models are based is robust, so despite
Video clip
their limitations the models offer a powerful tool to
identify the main causes of warming. It’s a process of
elimination.
10:46:52
10:46:52
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PTC
To show you what I mean let’s take the example of the sun.
If the cycles of the sun were a major cause of the rise in
temperature we’ve measured then what we should see
would be all the layers of the Earth’s atmosphere warming
together like this.
10:47:05
10:47:07
10:47:18
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VO
This is called a fingerprint, a characteristic pattern that
Video clip
would point to the sun’s influence as the cause.
PTC
What we actually have from the measurements of the past
sixty years is that only the lower levels of the atmosphere
have warmed while the upper levels have cooled.
10:47:28
VO
So what we’re actually seeing in the atmosphere is an
Video clip
entirely different fingerprint.
10:47:37
10:47:39
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PTC
What the models show is that’s a pattern which only fits
well with the main cause of the warming being human
activity.
10:47:46
MUSIC IN
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10:47:47
VO
That’s human activity primarily in the form of burning
Video clips
fossil fuels that release carbon dioxide into the atmosphere.
And since the 1970s the human fingerprint has become
more obvious. From the loss of sea ice in The Arctic,
increasing frequency of heat waves to the warming and
acidification of the oceans, the models predict all of these
patterns only as a result of increasing greenhouse gases like
carbon dioxide.
10:48:26
MUSIC OUT
10:48:27
MUSIC IN
The evidence that human activity is the major cause of
recent warming is compelling. But the models can go one
step further and help us put a figure on the level of
certainty behind this statement.
10:48:46
PTC
The yellow line on this graph is the real world data. This is
how much warming we’ve measured across the world since
1951, 0.6 degrees.
10:48:58
VO
Firstly in red let’s look at how the climate models expected
Video clips
the global temperatures to change when taking into account
all known factors. The shading shows the amount of
fluctuation around the average that they would expect to
happen. The most obvious features are a general rise, the
result of the increasing carbon dioxide levels with some
sharp dips caused by big volcanic eruptions.
10:49:33
PTC
But look what happens if we run our models without any
human influences like greenhouse gases, so now only
natural forces are included in our model data. The line
doesn’t match the real data well at all. This is what the
model suggests our climate would be like if there was no
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human impact on it at all.
10:49:56
VO
The models say that without any human influence global
Video clip
temperature would not have risen significantly over the
past sixty years. It’s as clear as taking the wage bill out of
my football prediction. The models also help scientists put
a figure on how certain they are of human impact on the
climate.
10:50:17
10:50:18
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PTC
From the models they found there was a greater than 99%
probability that more than half of the warming was due to
human activity.
10:50:26
Video clip
MUSIC IN
10:50:27
VO
Given that high level of certainty how did the IPCC arrive
at its slightly lower 95% certainty figure? All of us who
work with mathematical models know that they’re
simplifications, so we have to take into account their
limitations. That’s why the IPCC downgraded its final
conclusion from 99% to greater than 95% sure that humans
have caused more than half the recent warming.
10:51:00
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10:51:01
MUSIC IN
All science proceeds by producing theories and then testing
them, but when it comes to our climate it’s impossible to
test the influence of different factors on the planet. That’s
why scientists have turned to maths to help model the
climate. It’s not perfect, but it is the only way to put a
figure on how sure we are the Earth’s warming is down to
human activity.
10:51:30
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10:51:32
Video clip
10:51:34
PTC
Years of scientific research and statistical analysis have
brought us as far as 95% and that’s close enough for most
people to believe it. That just leaves the question, what’s
gonna happen with our climate in the future?
10:51:48
10:51:54
MUSIC IN
VO
I’m Professor David Spiegelhalter and I use numbers to try
to help organisations like the Health Service predict the
future. I’m looking at one number that aims to give us a
clear guide to how our actions now might affect the
climate.
10:52:15
PTC
The number I’m looking at
Prof. David Spiegelhalter
University of Cambridge
is one trillion, this rather unimaginably big number may be
crucial to the future of our planet. It’s the best estimate
that climate scientists have made of the number of tons of
carbon that we could
10:52:30
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burn before we
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run the risk of causing what’s been called dangerous
10:52:32
climate change.
10:52:37
VO
That’s defined as an average warming across the globe of
Video clips
more than two degrees Celsius. All fossil fuels contain
carbon, when we burn them it converts this carbon into the
carbon dioxide that warms the atmosphere, so the trillion
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tons figure puts a limit on the amount of fossil fuels we can
burn.
10:53:01
PTC
In effect this gives the world a budget, it says that if we
want to avoid a two degrees rise then we can’t afford to
spend, or burn, more than a trillion tons of carbon and
that’s a total going right back to the beginning of
industrialisation.
10:53:15
MUSIC OUT
10:53:16
Video clips
10:53:22
VO
A trillion tons sounds like a lot, but the trouble is we’ve
already burnt around half a trillion tons and that’s given us
almost a degree of warming and if we carry on the way
we’re going we’ll burn the other half a trillion tons in about
thirty years. The implications are profound.
10:53:41
MUSIC IN
10:53:45
We’ve already identified several trillion tons of fossil fuel
reserves buried inside the Earth, so to keep warming below
two degrees will probably mean leaving most of those
reserves in the ground. Before we take such drastic action
I’d like to know a bit more about the trillion tons figure.
Where does this number come from?
10:54:12
PTC
10:54:20
10:54:20
And how much confidence should we have in it?
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VO
The one trillion ton limit is based on being able to predict
the future. That may make it sound unscientific, but for
centuries people have been working on ways to make
predictions using statistics.
10:54:35
PTC
The history of statistics and prediction has been driven by
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incentives, in fact the first people who worked on
probability and statistics were either advising gamblers or
pricing up pensions. So I think if you really want to know
who’s making good predictions look at people who are
putting their money
10:54:52
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where their mouth is.
10:54:58
Video clip
10:55:04
PTC
And there’s a lot of money in motor racing.
10:55:10
VO
And a lot of effort to try to predict the future because
Video clips
winning isn’t just about driving fast, it’s also about making
the right decisions, what to do as the race unfolds, the
weather changes and the unexpected happens. And this is
where prediction and statistics comes in. There are far too
many variables for the decision to be left to the driver, or
sometimes even to the people at the race track, it needs a
dedicated race strategist.
10:55:50
PTC
In the 2005 Monaco Grand Prix Kimi Räikkönen was in
Video clip
the lead after twenty five laps when there was a six car pile
up. The safety car came out and the team had to decide
very quickly should Räikkönen come into the pits or
should they leave him out there until the race restarted and
this would decide whether he won or not. They didn’t
know what to do and then a two word email came in from
the chief strategist who was in England and the email said
stay out.
10:56:21
PTC
So Räikkönen stayed out and the people who came into the
pits got all jammed up so Räikkönen went on to win the
race and all because of the power of prediction.
10:56:33
Video clip
10:56:35
Video clip
So how did Räikkönen’s strategist predict the outcome of
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10:56:41
VO
different strategies?
PTC
They used to just use gut feelings, just their instincts, but
now with huge amount of data available they can do
something much more sophisticated.
10:56:50
Video clip
MUSIC IN
10:56:52
VO
Throughout the race each car streams performance data
back to the team, from tyre fatigue to fuel consumption.
The team then plugs this data into a mathematical model of
the race.
10:57:09
PTC
They can constantly make changing predictions as the race
proceeds,
Video clip
as the positions change, as the lap times change, they can
predict the
PTC
possible outcome if they do a particular action, you know,
for example just come in
Video clip
for a pit stop. And then they can choose the strategy that
maximises
PTC the chance of the best possible result.
10:67:31
Video clip
As Räikkönen’s victory shows the predictions made by the
VO
models can be extremely powerful and it’s only possible
thanks to a mathematical technique that we now use for all
sorts of future predictions.
10:57:47
PTC
This technique that motor racing teams use to decide what
strategy will maximise the chances of winning a race is
exactly the same as the technique I use for medical
predictions and climate scientists use to predict what might
happen to the planet.
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10:58:02
Video clip
MUSIC IN
10:58:05
VO
And it’s all due to a stroke of misfortune that befell one
particular mathematician just after the Second World War.
10:58:10
PTC
Coffee please. In 1946 brilliant mathematician and
Video clip
physicist Stanislaw Ulam was struck down by a severe
bout of ill health, he was hospitalised for weeks and only
had the card game Solitaire for entertainment.
10:58:42
VO
The aim of the game is to sort a randomly shuffled pack of
cards into four piles according to a set of rules, whether
Ulam could successfully finish the game depended on the
order of the cards he was dealt.
10:58:58
PTC
As he played his instinct was to begin to pick apart the
game
MUSIC OUT
10:59:02
and analyse it mathematically. He became obsessed with
trying to predict whether a game would be successful.
10:59:11
VO
Ulam hoped he could calculate the probabilities of different
outcomes from the very first deal, but he quickly realised
this approach would get him nowhere.
10:59:23
PTC
The problem was there were just too many possible
combinations leading to ever increasingly complex
calculations and equations that became impossible to solve,
no matter how brilliant a mathematician you were.
10:59:36
VO
But Ulam didn’t give up.
10:59:40
Video clip
MUSIC IN
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10:59:42
He came up with an entirely different kind of method to
solve the problem, in fact it was one that hardly involved
maths at all, let me demonstrate with an analogy.
10:59:55
PTC
Ahead of me, between me and the wall, I can just about
make out a sheet of Perspex.
11:00:00
MUSIC OUT
11:00:01
There’s a hole cut out of the centre in a certain shape,
11:00:04
MUSIC IN
but from here there’s no way I can tell what that shape is,
but I can find out with a little help.
11:00:14
VO
Imagine that working out the shape of the hole is
equivalent to Ulam trying to predict outcomes in Solitaire,
there’s no way I could work out the answer with maths, I
need to play the game. In this case the equivalent of a
round of Solitaire is a shot with a paintball gun.
11:00:35
PTC
MUSIC IN
After a couple of shots I’ve got a few through against the
wall, but although I know there is a hole in the Perspex
I’ve still no idea what the shape is. It’s like after I’ve just
played a couple of rounds of the game, I’m still none the
wiser about what outcomes to expect. But if I do this …..
Now with enough shots I’m beginning to get a picture of
11:01:12
what the shape might be. Looks like a rough sort of
diamond to me, it’s great fun. This is the same principle as
playing the game thousands of times, with enough sample
runs we can begin to build an idea of what outcomes to
expect.
11:01:34
VO
At first sight it sounds like no solution at all, who could sit
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around actually playing Solitaire millions of times to find
an answer? What turned Ulam’s ingenious idea into a
useful tool was his timing.
11:01:50
Video clips
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The computer had just been invented, that meant you didn’t
11:01:53
have to play the game for real, instead it could be played
hundreds of times inside a computer and the computer
could then say which starting hands were most likely to
lead to a successful game. He called his technique the
Monte Carlo Method after the casino where his uncle made
so many repeated and random attempts to predict the
future. And it turned out to have uses well beyond
predicting the outcome of card games.
11:02:29
PTC
The beauty of Monte Carlo is that even in complex systems
it tells us not only what is likely to happen,
11:02:36
MUSIC IN
but how likely it is to happen.
11:02:39
VO
In climate science the equivalent of shooting the paintballs
Video clips
is running climate models hundreds of times, each time a
model is run it comes up with a different prediction about
the future of the Earth’s climate. The results of many
different climate models can then be combined. As the
models are run over and over again we can see where the
results cluster.
11:03:10
PTC
This is the Monte Carlo process in action, the pattern of
lines shows us a range of possibilities, but not only that,
where the lines are densest this is what the models are
saying is the most likely thing to happen. Of course it
doesn’t tell us exactly what the future holds, that would be
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impossible, the future is inherently unpredictable, but the
Monte Carlo Method gives us an idea not only of what the
outcomes might be, but how likely they are. And this is
where our crucial number comes from.
11:03:43
VO
The graph shows the model’s predictions of how much the
Video clip
climate will warm as a result of us burning one trillion tons
of carbon; the most likely outcome is just below two
degrees Celsius of warming.
11:03:58
MUSIC OUT
11:03:59
MUSIC IN
11:04:01
VO
Now we understand where the one trillion tons figure
comes from we need to consider the second part of the
prediction. Why should we worry about a rise of two
degrees Celsius?
11:04:18
PTC
When we think about what a small average rise in global
temperature might mean to us humans perhaps the first
thing to think of is weather because we don’t experience
climate on a day to day basis, we experience weather and
sometimes it can hit us really hard.
11:04:33
11:04:38
MUSIC OUT
VO
Just a small average temperature rise can hide very
Video clips
noticeable changes in weather, especially dangerous
extremes. As the average rises the tropics will experience
more devastating rain storms, whilst areas including the
Mediterranean will have more droughts. Britain will suffer
more flooding, but it’s not simply the fact that these events
might be more frequent that is a concern.
11:05:13
PTC
It’s critical that we understand extreme weather events,
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how often and how hard they might hit us and this is the
worry with a climate that might warm by as much as two
degrees, that it would disrupt that ability because the
method we use to predict extreme weather uses a particular
type of statistics that’s very sensitive to this type of change,
a method in fact that was developed for something quite
different.
11:05:39
Video clip
MUSIC IN
11:05:43
VO
In the early 1920s the cotton mills of England were a vital
industry, but the looms often sat idle for as much as a third
of the time. The problem was that cotton threads kept
snapping.
11:06:02
PTC
Every snap could stop production for hours so they needed
to work out why the threads broke and what they could do
to stop it happening. Fortunately they had the good sense
to call in a statistician.
11:06:15
Video clip
MUSIC IN
11:06:18
VO
The newly formed British Cotton Industry Research
Association charged with improving all aspects of the
industry dispatched one Leonard Tippit to investigate.
Tippit admitted he was woefully
11:06:34
PTC
inexperienced, but in the best traditions of British statistics
he managed to combine careful collection of data with
elegant statistical analysis.
VO
He toured the mills of Lancashire carefully recording
breakage rates and studying the strength of individual
fibres. Common sense said that if the average strength of
the fibres in one thread was higher than another you’d
think there’d be fewer breakages. But Tippit discovered
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that it wasn’t the average strength that was important, it
was the weakest thread that really mattered.
11:07:17
PTC
It’s like the old saying, a chain is as strong as its weakest
link. It’s the extremes that make all the difference
11:07:25
11:07:28
MUSIC OUT
VO
Tippit’s breakthrough came when he realised he could use
the data he’d gathered about the strength of the most
common threads to predict how often the very weakest
threads would be found.
11:07:37
11:07:42
MUSIC IN
VO
In other words he’d invented a method of using numbers to
predict extreme events from the spread of less extreme
events.
11:07:53
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Tippit’s insights from the cotton industry led to what is
called extreme value theory and it turned out to be
amazingly powerful. What used to be considered just
unpredictable could be analysed mathematically.
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And his breakthrough turned out to be vital in the
understanding of extreme weather.
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In 1953 a huge storm surge was driven down the North Sea
towards London, devastating coastal areas. Over three
hundred people died in Britain alone. After the floods it
was decided something had to be done to protect London in
case it ever happened again. It was time to put extreme
value theory to the test.
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11:08:52
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This extraordinary piece of engineering was conceived in
the 1960s after catastrophic and fatal floods in 1953.
These really were extreme events, literally a perfect storm
when rare conditions combined to create a terrible night.
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In order to ensure the Barrier would do its job the planners
had to predict the most extreme storm surge that could be
expected in the future, more extreme and unusual than
anything that had been seen before. Extreme value theory
together with classic British record keeping was the
answer.
11:09:35
PTC
They had a century’s worth of data on extreme high tides
and using Tippit’s models this allowed them to gauge the
chance of events occurring that were so extreme they’d
never occurred before.
11:09:52
VO
The Thames Barrier was built to stop a once in a thousand
years event and so far we’ve not seen a storm come
anywhere near testing its limits. But Tippit’s method has
an Achilles’ heel, its predictions are based on the
assumption that the future will be similar to the past.
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Extreme value theory uses the frequency of fairly extreme
events to give us a good idea of the chances of really
extreme events, things we haven’t observed even. But the
problem with climate change is that the patterns alter.
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When the planners were designing the Barrier they had a
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hundred years of data about storms to base their prediction
of the thousand year’s storm, but if the climate changes the
pattern of storms may well change too and that will mean
the data on past storms will no longer be relevant. Without
it the predictions made by extreme value theory are
unreliable.
11:10:56
PTC
The average shift might not actually seem that impressive,
but it’s what happens in the extremes that is so important to
us and these become a lot less predictable. We can’t just
tweak the extreme value theory.
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So as our climate changes not only are we likely to suffer
more frequent extreme weather we’ll also lose the tool that
has allowed us to prepare for such eventualities.
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11:11:35
VO
Climate scientists have used maths and statistics to give us
their most likely prediction of the future, sticking to a
trillion tons of carbon should cause less than two degrees
of warming. But given the inherent unpredictability of the
future and the imperfections of our climate models how
sure can we be that that prediction is right? With the help
of techniques like the Monte Carlo Method the climate
scientists have put a number on their certainty, they are at
least 66% sure, that means there’s a sting in the tail of the
trillion tons figure.
11:12:17
PTC
Climate scientists tell us that if you burn a trillion tons of
carbon they can be 66% certain that warming should stay
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below two degrees, but there’s another way of looking at
this, we could say that they think there’s a one in three
chance that warming will be more than two degrees.
11:12:36
VO
So the rather sobering conclusion is that even if we burn
less than a trillion tons we’re not guaranteed to keep
warming below this level, yet we also know that it would
take huge changes to our lives to keep to the trillion tons
limit, so how should we react?
11:12:56
PTC
It’s always really difficult to know what to do when we’re
uncertain about the future. Usually we might try to work
out the chances of something bad happening and do what
we can to avoid it, or to protect ourselves against it. So
there’s a very good chance we’ll get old and so we buy a
pension. There’s a small chance we’ll have a road accident
but we wear a seatbelt.
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In each case we weigh up the risk and the reward, that
calculation relies on the quality of information available.
Scientists have collected and analysed data, come up with
plausible theories and used mathematical models to make
predictions. But with the climate we can’t do experiments
to test those predictions, only time will tell how accurate
they are. And if we want to influence our future we can’t
wait to find out, we have to choose on the basis of what we
know now.
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When it comes to the climate the scientists have done the
calculations for us, but now it’s up to us to decide what
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action to take.
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