0:00:07 > 0:00:10This is the story of climate change.
0:00:12 > 0:00:15But told in a way you've never heard before.
0:00:18 > 0:00:21Because we're not climate scientists.
0:00:21 > 0:00:24We're three mathematicians.
0:00:28 > 0:00:30And we're going to use the clarity of numbers
0:00:30 > 0:00:33to cut through the complexity and controversy
0:00:33 > 0:00:35that surrounds climate change.
0:00:37 > 0:00:39Understanding what's happening to the Earth's climate
0:00:39 > 0:00:42is perhaps the biggest scientific endeavour
0:00:42 > 0:00:44the human race has ever taken on.
0:00:46 > 0:00:50From the masses of data, we've chosen just three numbers
0:00:50 > 0:00:53that hold the key to understanding climate change.
0:00:55 > 0:00:580.85 degrees.
0:00:58 > 0:01:0195%.
0:01:01 > 0:01:04And one trillion tonnes.
0:01:04 > 0:01:07Just by looking at these crucial numbers,
0:01:07 > 0:01:09we're going to try and get to the heart
0:01:09 > 0:01:11of the climate change controversy.
0:01:11 > 0:01:14They are three numbers that represent what we know
0:01:14 > 0:01:18about the past, present and future of Earth's climate.
0:01:18 > 0:01:22And it's not just the numbers themselves that are important.
0:01:22 > 0:01:25The stories behind them, how they were calculated,
0:01:25 > 0:01:28are equally intriguing and revealing.
0:01:29 > 0:01:31Ignition sequence starts...
0:01:31 > 0:01:33We'll see how the methods,
0:01:33 > 0:01:35using everything from the Moon landings...
0:01:37 > 0:01:40..to early 20th century cotton mills...
0:01:42 > 0:01:46..and motor racing have fed into the numbers we've chosen.
0:01:49 > 0:01:51These three numbers
0:01:51 > 0:01:54tell an extraordinary story about our climate...
0:01:55 > 0:01:59..and take us to the limits of what it is possible for science to know.
0:02:16 > 0:02:20Every minute of every day, all over the planet,
0:02:20 > 0:02:23scientists are collecting data on the climate.
0:02:26 > 0:02:29Around 10,000 weather stations
0:02:29 > 0:02:32monitor conditions at the Earth's surface.
0:02:34 > 0:02:37Some 1,200 buoys and 4,000 ships
0:02:37 > 0:02:40record the temperature of the oceans.
0:02:41 > 0:02:44And more than a dozen satellites
0:02:44 > 0:02:47continuously observe the Earth's oceans and atmosphere.
0:02:50 > 0:02:53All science starts with collecting data.
0:02:53 > 0:02:56And when it comes to our climate, we've got masses of it.
0:02:57 > 0:03:01But what story about our planet is all that data telling us?
0:03:11 > 0:03:15Thousands of scientists are trying to answer that question.
0:03:15 > 0:03:19Their results are summarised in a series of huge reports
0:03:19 > 0:03:22by the Intergovernmental Panel on Climate Change.
0:03:30 > 0:03:34The three numbers we've chosen all come from the IPCC's reports.
0:03:37 > 0:03:39Molly!
0:03:39 > 0:03:44I'm Doctor Hannah Fry and I use numbers to reveal patterns in data.
0:03:47 > 0:03:52I'm looking at one number that answers a critical question...
0:03:52 > 0:03:54is climate change really happening?
0:03:57 > 0:04:01Our first number is 0.85 degrees.
0:04:01 > 0:04:04Now, this number represents what we know about our climate
0:04:04 > 0:04:08in the recent past, because it's the number of degrees Celsius
0:04:08 > 0:04:12that scientists say our Earth has warmed since the 1880s.
0:04:16 > 0:04:18But how can they be so precise?
0:04:20 > 0:04:24After all, our climate is complex and extremely varied.
0:04:30 > 0:04:33Temperatures change from season to season...
0:04:35 > 0:04:37..place to place...
0:04:37 > 0:04:39and, even, minute by minute.
0:04:42 > 0:04:43As if it wasn't hard enough
0:04:43 > 0:04:46to try and find an average temperature of the Earth for now,
0:04:46 > 0:04:49we also need to go back in time and compare it to
0:04:49 > 0:04:52the average temperature of the Earth in the past,
0:04:52 > 0:04:55when we didn't have the luxury of modern measurement techniques.
0:04:58 > 0:05:02Working out how the planet's temperature has changed
0:05:02 > 0:05:05over more than a century is a huge challenge.
0:05:07 > 0:05:09It's a bit like trying to work out
0:05:09 > 0:05:12the route I'm taking across this park,
0:05:12 > 0:05:14if you only had the route Molly is taking to go on.
0:05:16 > 0:05:19You have to identify the trend, my path,
0:05:19 > 0:05:23from all those changing temperatures, Molly's path.
0:05:23 > 0:05:27And it all starts with the quality of the data.
0:05:29 > 0:05:32Now, that's not such a problem for the recent past.
0:05:36 > 0:05:39But what about further back in time?
0:05:52 > 0:05:55Up until the middle of the 19th century,
0:05:55 > 0:05:58the temperature record, as measured by instruments,
0:05:58 > 0:06:02is patchy and unreliable and there is some controversy
0:06:02 > 0:06:07about how you reconstruct temperatures before this time.
0:06:10 > 0:06:13But the record improves from the 1880s...
0:06:14 > 0:06:17..due to the efforts of one man.
0:06:26 > 0:06:30Now, the key man in this story, the man with a plan,
0:06:30 > 0:06:33is a guy called Matthew Fontaine Maury.
0:06:33 > 0:06:35Now, Maury was a lieutenant in the US Navy
0:06:35 > 0:06:38and from even when he was a small boy,
0:06:38 > 0:06:41was obsessed with mathematics and data and analysis.
0:06:41 > 0:06:44But, in 1839, Maury had a coaching accident
0:06:44 > 0:06:48where he broke his thigh bone and dislocated his kneecap.
0:06:48 > 0:06:50And while he was recovering,
0:06:50 > 0:06:53he spent his time studying captains' log books.
0:06:53 > 0:06:54And the data that he found there
0:06:54 > 0:06:57set the path for his next 14 years-worth of work.
0:06:57 > 0:07:02So much so, that on 23rd August in 1853 he called together a meeting
0:07:02 > 0:07:05of 12 countries surrounding the North Atlantic,
0:07:05 > 0:07:07all to talk about one thing.
0:07:11 > 0:07:15He wanted to improve the way that data about the oceans was collected.
0:07:17 > 0:07:21Captains record all sorts of information in their log books,
0:07:21 > 0:07:23things like wind speed and direction,
0:07:23 > 0:07:26or the speed and temperature of the sea currents.
0:07:26 > 0:07:30Now, this wasn't just interesting to Maury from a scientific perspective,
0:07:30 > 0:07:33but also because it was something he could sell
0:07:33 > 0:07:35to commercial ship owners.
0:07:37 > 0:07:39He found great commercial success
0:07:39 > 0:07:42from mapping the position of major sea currents,
0:07:42 > 0:07:44like the Gulf stream,
0:07:44 > 0:07:48which enabled ships to use the currents to travel faster.
0:07:54 > 0:07:55But there was a problem.
0:07:55 > 0:07:59Different sailors took the same measurements in different ways.
0:08:02 > 0:08:04That was particularly true
0:08:04 > 0:08:07for one of the measurements climate scientists are interested in,
0:08:07 > 0:08:09sea surface temperature.
0:08:11 > 0:08:13Now, the way to measure sea surface temperature
0:08:13 > 0:08:15is actually surprisingly simple.
0:08:15 > 0:08:20All you do is chuck a bucket over the side of the ship
0:08:20 > 0:08:21and get the temperature from it.
0:08:23 > 0:08:27But, the problem is that the result that you get
0:08:27 > 0:08:31actually depends quite a lot on the type of bucket that you use.
0:08:35 > 0:08:38So, let me just take the temperature of this now.
0:08:39 > 0:08:43And, in the meantime, I'm going to throw this guy over.
0:08:46 > 0:08:50In the early 19th century, some sailors used wooden buckets.
0:08:50 > 0:08:53Others used buckets made of canvas.
0:08:54 > 0:08:58This meant that the measurements were not consistent.
0:09:01 > 0:09:06The wooden bucket is coming out as a surprisingly warm 15.1.
0:09:06 > 0:09:08And if we make a comparison,
0:09:08 > 0:09:12the canvas bucket, unlike the wooden bucket, isn't insulated,
0:09:12 > 0:09:14so things like the air temperature
0:09:14 > 0:09:16are going to make a much bigger difference.
0:09:16 > 0:09:19The temperature has dropped below 15.1 degrees.
0:09:19 > 0:09:21It may not sound like a lot,
0:09:21 > 0:09:26but even tiny discrepancies undermine the accuracy of the data.
0:09:27 > 0:09:31Now, Maury knew this and so, at his conference in 1853,
0:09:31 > 0:09:34he came up with a standardised way for everyone across the world
0:09:34 > 0:09:37to measure sea surface temperature.
0:09:42 > 0:09:44He wanted everyone to use wooden buckets
0:09:44 > 0:09:49and designed special forms for them to fill in with all their data.
0:09:49 > 0:09:51Maury also introduced standardisation
0:09:51 > 0:09:54to air temperature measurements on land.
0:09:54 > 0:09:59That's why our 0.85 degrees Celsius figure is measured from 1880.
0:09:59 > 0:10:02It's the date from which the temperature data
0:10:02 > 0:10:04is generally well-standardised.
0:10:07 > 0:10:11But, despite Maury's efforts, the data was still far from perfect.
0:10:11 > 0:10:13Not everyone stuck to the rules.
0:10:13 > 0:10:17For example, over time, canvas buckets made a comeback
0:10:17 > 0:10:19because they were lighter.
0:10:19 > 0:10:22So, there were still errors, some of which were pretty obvious.
0:10:24 > 0:10:27So, here is the sea surface temperature data
0:10:27 > 0:10:30between 1880 and 1980.
0:10:30 > 0:10:33And the first thing that you really notice about this graph
0:10:33 > 0:10:36is this huge spike that happens,
0:10:36 > 0:10:39where it looks like the sea surface temperature's raised
0:10:39 > 0:10:42by 0.8 degrees Celsius.
0:10:42 > 0:10:44Or, at least, it looks that way
0:10:44 > 0:10:47until you realise that this spike happened in 1941
0:10:47 > 0:10:49when, during the Second World War,
0:10:49 > 0:10:53understandably, sailors didn't much want to go up on deck
0:10:53 > 0:10:57with a torch and a bucket to record sea surface temperature levels.
0:10:57 > 0:10:59So, instead, during that time,
0:10:59 > 0:11:02they used the water that was coming in through the engine room,
0:11:02 > 0:11:05which is hence why the data is a lot higher.
0:11:05 > 0:11:07Now, after the Second World War,
0:11:07 > 0:11:11people gradually started returning to using uninsulated canvas buckets.
0:11:11 > 0:11:15But, unfortunately, we don't know who was using them or when.
0:11:15 > 0:11:18And so, in all of this big mess of data,
0:11:18 > 0:11:21how do we get accurate temperature readings
0:11:21 > 0:11:23for land and sea from the past?
0:11:27 > 0:11:30The answer is related to a mathematical technique
0:11:30 > 0:11:34that was used to help solve one of history's greatest challenges.
0:11:34 > 0:11:37At Cape Kennedy, it's a wonderful day for a wonderful event,
0:11:37 > 0:11:39the first manned flight to the Moon.
0:11:39 > 0:11:42In a mission fraught with difficulties,
0:11:42 > 0:11:45one of the biggest was how to navigate
0:11:45 > 0:11:50a quarter of a million miles through space to the surface of the Moon.
0:11:56 > 0:11:59It's a feat of navigation all the more astonishing
0:11:59 > 0:12:03when you consider how difficult finding our way around can be
0:12:03 > 0:12:05even down here on the ground.
0:12:06 > 0:12:11Working out exactly where you are on the Earth at any point in time
0:12:11 > 0:12:13is, actually, a surprisingly difficult problem,
0:12:13 > 0:12:17especially if you want really, really precise information.
0:12:17 > 0:12:20It's tricky because tracking your position,
0:12:20 > 0:12:22just like measuring temperatures over time,
0:12:22 > 0:12:24is prone to error.
0:12:25 > 0:12:27Not the easiest thing ever.
0:12:27 > 0:12:29Take dead reckoning,
0:12:29 > 0:12:32timing how long you've travelled in a particular direction
0:12:32 > 0:12:34from your last known position.
0:12:34 > 0:12:38Three miles an hour. Lovely. Three miles an hour. Hang on one second.
0:12:43 > 0:12:46It's easy to drift off course as inaccuracies build up.
0:12:46 > 0:12:48Hang on...
0:12:50 > 0:12:53Even more hi-tech methods can get it wrong.
0:12:53 > 0:12:56Actually, the GPS is putting us over there at the moment,
0:12:56 > 0:12:58which is less than ideal.
0:12:58 > 0:13:01So, when it comes to navigating,
0:13:01 > 0:13:05the problem is which measurement of your position do you trust?
0:13:06 > 0:13:10In the 1950s, a young Hungarian-born mathematician, Rudolf Kalman,
0:13:10 > 0:13:14devised an elegant algorithm to solve this problem.
0:13:17 > 0:13:20Kalman's method uses matrix algebra,
0:13:20 > 0:13:24and takes into account all of the errors to give you
0:13:24 > 0:13:28the best possible estimate of your position at any point in time.
0:13:30 > 0:13:32So, how does Kalman's method work?
0:13:33 > 0:13:37In 1969, NASA gave it its ultimate test
0:13:37 > 0:13:40in the mission to land men on the Moon.
0:13:40 > 0:13:42Ignition sequence start.
0:13:42 > 0:13:43Six, five...
0:13:45 > 0:13:48Navigating in space poses particular challenges.
0:13:52 > 0:13:54We have lift off. Lift off on Apollo 11.
0:13:54 > 0:13:58The spacecraft was being tracked by four radar stations on Earth.
0:14:03 > 0:14:06Onboard instruments were also estimating its position.
0:14:08 > 0:14:10But, each of these measurements could be wrong.
0:14:10 > 0:14:14So, how could NASA be sure of Apollo 11's position?
0:14:14 > 0:14:16Go. Contol, go.
0:14:17 > 0:14:20This is where Kalman's algorithm came in.
0:14:20 > 0:14:22Moment by moment,
0:14:22 > 0:14:25it compared each position measurement with the others...
0:14:26 > 0:14:31..looking for differences that fell outside the expected margin.
0:14:31 > 0:14:33We're go. Same time. We're go.
0:14:34 > 0:14:37If the algorithm had found significant disagreement,
0:14:37 > 0:14:39the mission would have been aborted.
0:14:41 > 0:14:43But, it didn't.
0:14:45 > 0:14:47And the rest is history.
0:14:50 > 0:14:51Tranquillity Base here.
0:14:51 > 0:14:53The Eagle has landed.
0:14:59 > 0:15:03So, this process is now known as Kalman filtering
0:15:03 > 0:15:07and has been used in everything from cleaning up grainy video
0:15:07 > 0:15:09to looking for trends in economics.
0:15:09 > 0:15:13And a lot of the underlying principles are exactly the same
0:15:13 > 0:15:17as you see in the processes used for climate science.
0:15:17 > 0:15:20So, knowing when to trust your data
0:15:20 > 0:15:22and picking out when the errors are big enough
0:15:22 > 0:15:25to flag up a deeper underlying issue.
0:15:25 > 0:15:27But, the process in climate science
0:15:27 > 0:15:30is, instead, known as homogenisation.
0:15:32 > 0:15:35Homogenisation has allowed climate scientists today
0:15:35 > 0:15:38to clean up data gathered in the past.
0:15:40 > 0:15:44Unreliable measurements can be corrected or discarded.
0:15:46 > 0:15:50So, what the homogenisation process is doing, effectively,
0:15:50 > 0:15:53is taking all of the data from all of the weather stations
0:15:53 > 0:15:57and comparing it on a day-by-day basis.
0:15:57 > 0:15:58Now, in doing that,
0:15:58 > 0:16:01if a particular data set starts to look a bit unusual,
0:16:01 > 0:16:03it will really stand out.
0:16:04 > 0:16:08You can see what happens when scientists homogenise a data set
0:16:08 > 0:16:10by looking at how they corrected
0:16:10 > 0:16:15the unusual jump in sea surface temperature in the early 1940s.
0:16:17 > 0:16:20So, once you've applied this homogenisation process,
0:16:20 > 0:16:24here is what the sea surface temperature data will look like.
0:16:24 > 0:16:28So, we have the original data here in yellow
0:16:28 > 0:16:31and the cleaned up version also available in blue.
0:16:35 > 0:16:37Now, the first thing that you notice
0:16:37 > 0:16:41is that the big jump that we had in 1940 has dramatically reduced.
0:16:41 > 0:16:43There is still a bit of a jump
0:16:43 > 0:16:45because there was an El Nino that year,
0:16:45 > 0:16:49which meant that the sea surface did actually warm.
0:16:49 > 0:16:52But the jump that was down to the difference in measurements,
0:16:52 > 0:16:55the error in the way that people were measuring,
0:16:55 > 0:16:58has been taken away completely from the graph.
0:16:59 > 0:17:02All the big scientific groups that work with climate data
0:17:02 > 0:17:05use homogenisation methods like this
0:17:05 > 0:17:08to try and clean up the records of past temperature.
0:17:11 > 0:17:13And it's absolutely vital
0:17:13 > 0:17:16that you account for some of these errors in measurement
0:17:16 > 0:17:19that have occurred in historical data, otherwise you've got no hope
0:17:19 > 0:17:22of finding any kind of underlying patterns in your data.
0:17:22 > 0:17:25But, inevitably, as soon as you start applying
0:17:25 > 0:17:29these mathematical recipes to clean things up,
0:17:29 > 0:17:31other people will start accusing you
0:17:31 > 0:17:34of building in biases into your data.
0:17:37 > 0:17:42Perhaps the best defence against bias is scientists' own scepticism.
0:17:44 > 0:17:46Many different groups work on climate data,
0:17:46 > 0:17:50using slightly different homogenisation methods.
0:17:50 > 0:17:53And all are subjected to searching scrutiny by their peers.
0:17:58 > 0:18:02But, even after homogenising the historical data,
0:18:02 > 0:18:05climate scientists face a further problem...
0:18:05 > 0:18:07gaps in the temperature record.
0:18:08 > 0:18:11Even today, we do not have temperature measurements
0:18:11 > 0:18:13for the whole planet.
0:18:13 > 0:18:16If you look at where we have temperature data for,
0:18:16 > 0:18:18if you split the Earth into a grid,
0:18:18 > 0:18:21it becomes very obvious that there are some areas
0:18:21 > 0:18:24where we have much more information on than others.
0:18:25 > 0:18:29The black squares show where we have hardly any weather data at all.
0:18:29 > 0:18:31So ,if you take the Arctic, for example,
0:18:31 > 0:18:35it's very obvious there are almost no sample points in the Arctic.
0:18:36 > 0:18:39The gaps in places like Africa and the poles can affect how we
0:18:39 > 0:18:42calculate the average temperature of the whole planet.
0:18:44 > 0:18:47Now, if you take an average across the whole of the Earth
0:18:47 > 0:18:49and don't take into account the fact that
0:18:49 > 0:18:52you have a lot less data for the Arctic, you're going to end up
0:18:52 > 0:18:56with a really biased average and something that doesn't really
0:18:56 > 0:18:58represent the Earth properly.
0:18:58 > 0:19:01There is actually a mathematical solution to this problem
0:19:01 > 0:19:04that climate scientists are beginning to use,
0:19:04 > 0:19:07but it's one that wasn't even devised by a mathematician.
0:19:11 > 0:19:14The attempt to fill in gaps in the temperature data
0:19:14 > 0:19:18begins in the gold fields of South Africa in the 1950s,
0:19:18 > 0:19:22where a mining engineer was grappling with a problem.
0:19:25 > 0:19:28Danie Krige was in charge of the leases
0:19:28 > 0:19:31of the country's very valuable gold fields
0:19:31 > 0:19:34and was inundated by companies desperate to mine them.
0:19:35 > 0:19:38But, until each plot of land had been mined,
0:19:38 > 0:19:42he had no way of knowing how valuable each area would be.
0:19:42 > 0:19:45What he needed was a systematic way of working out
0:19:45 > 0:19:49how much each lease was worth and so turned to spatial statistics.
0:19:53 > 0:19:56To understand the challenge Krige faced,
0:19:56 > 0:20:00I've come to gold mining country, to Dolaucothi in Wales.
0:20:02 > 0:20:06All Krige had to go on were a few scattered core samples
0:20:06 > 0:20:08that had been taken across the gold fields
0:20:08 > 0:20:11as miners tried to find more gold.
0:20:13 > 0:20:15He had to find a way of working out
0:20:15 > 0:20:18how much gold there was in each plot of land
0:20:18 > 0:20:20with just these few measurements,
0:20:20 > 0:20:22just like climate scientists
0:20:22 > 0:20:25have to work out the temperature in places
0:20:25 > 0:20:27where they don't have measurements.
0:20:31 > 0:20:33So, what I'm going to do here
0:20:33 > 0:20:35is show you how Danie Krige's method worked
0:20:35 > 0:20:38using these as my core samples.
0:20:39 > 0:20:42Imagine each of these poles represents a core sample
0:20:42 > 0:20:46and the number of lights indicates the amount of gold found in it.
0:20:51 > 0:20:55So, our first core sample is giving us a reading of 16 parts per million
0:20:55 > 0:20:57all the way up there into the red.
0:21:02 > 0:21:06And this core sample is giving us a reading...
0:21:07 > 0:21:09..of only six parts per million.
0:21:13 > 0:21:17Danie Krige's samples were often around a kilometre apart.
0:21:18 > 0:21:20Climate scientists have weather stations
0:21:20 > 0:21:25that might be hundreds or even thousands of kilometres apart,
0:21:25 > 0:21:27especially in regions like the Arctic.
0:21:28 > 0:21:31The problem in each case is the same,
0:21:31 > 0:21:34how to fill in the gaps in the data.
0:21:34 > 0:21:36So, one more core sample to do
0:21:36 > 0:21:38and then I can show you the map.
0:21:42 > 0:21:48So, our last reading is only giving us two parts per million.
0:21:48 > 0:21:50So, we're still on the gold field,
0:21:50 > 0:21:53but we're at a much lower grade of gold than we were before.
0:21:53 > 0:21:56But the real question that Danie Krige wanted to ask was
0:21:56 > 0:21:59how can you tell what happens in between the core samples?
0:21:59 > 0:22:02How can you tell how much gold is in the middle?
0:22:04 > 0:22:07His answer was to use maths
0:22:07 > 0:22:11to take into account both the amount of gold in each sample
0:22:11 > 0:22:14and the distances between them.
0:22:14 > 0:22:18So, Krige's method would take the first exciting strike of gold
0:22:18 > 0:22:21and look at how far away the neighbouring samples are,
0:22:21 > 0:22:25as well as how high the levels of gold found in them are.
0:22:26 > 0:22:29This helps estimate how much the gold levels drop off
0:22:29 > 0:22:31around each strike.
0:22:32 > 0:22:36The process is then repeated over the whole field.
0:22:37 > 0:22:40It may not sound like it, but the maths is relatively simple.
0:22:42 > 0:22:44Now, it's so powerful,
0:22:44 > 0:22:46that this method has been used all across the world
0:22:46 > 0:22:49in everything from looking at gold mines to forestry
0:22:49 > 0:22:51and even temperature data.
0:22:51 > 0:22:54And it's even been named after the great man himself,
0:22:54 > 0:22:56now known as Kriging.
0:23:01 > 0:23:04Kriging is now being used to throw new light
0:23:04 > 0:23:08on the biggest recent climate change controversy -
0:23:08 > 0:23:11what's happened to the temperature of the planet
0:23:11 > 0:23:13since the turn of the century.
0:23:14 > 0:23:17The issue is how you account for gaps
0:23:17 > 0:23:20in the record of global temperature.
0:23:20 > 0:23:23If you take the UK Met Office's Hadley Centre, for example,
0:23:23 > 0:23:26and their data on the changing global temperatures
0:23:26 > 0:23:27in the recent past,
0:23:27 > 0:23:31they leave blanks in regions where they don't have any information.
0:23:31 > 0:23:34But, if you look at the temperature set,
0:23:34 > 0:23:39you can see that it demonstrates an effect that's become known
0:23:39 > 0:23:41as the pause,
0:23:41 > 0:23:43which is that the temperature of the Earth
0:23:43 > 0:23:46doesn't appear to have risen since the year 2000.
0:23:47 > 0:23:52This pause in the Earth's rising temperature is controversial.
0:23:52 > 0:23:55Some climate change sceptics say it shows
0:23:55 > 0:23:58that global warming is not real.
0:23:58 > 0:24:00But most climate scientists
0:24:00 > 0:24:03say they would expect pauses every now and again
0:24:03 > 0:24:05within a warming trend.
0:24:05 > 0:24:07But whether there even is a pause
0:24:07 > 0:24:11depends on how you account for the gaps in the temperature record.
0:24:13 > 0:24:18When this data set was Kriged by an independent scientist in 2014,
0:24:18 > 0:24:20so that they could take into account
0:24:20 > 0:24:23the little data that you have in the Arctic,
0:24:23 > 0:24:25he found that the graph changed.
0:24:26 > 0:24:27Kriging put more weight
0:24:27 > 0:24:30on the few temperature points we have from the Arctic
0:24:30 > 0:24:34and there the temperatures are rising fast.
0:24:34 > 0:24:38The impact of Kriging on the original incomplete data
0:24:38 > 0:24:41is to turn the pause into a small temperature rise.
0:24:42 > 0:24:44Now, you might think
0:24:44 > 0:24:47that this doesn't necessarily represent reality, either.
0:24:47 > 0:24:49But it does demonstrate an important point.
0:24:49 > 0:24:51What you do with your data
0:24:51 > 0:24:54has an impact on how you make your conclusions.
0:24:54 > 0:24:57It's not to say that Kriging the Arctic figures
0:24:57 > 0:25:00has really shown that there isn't a pause.
0:25:00 > 0:25:02It remains an area of debate.
0:25:02 > 0:25:07But, techniques like this offer scientists the only way they have
0:25:07 > 0:25:11to overcome the inevitable limitations of incomplete data.
0:25:17 > 0:25:20It doesn't matter how much effort scientists go to,
0:25:20 > 0:25:23temperature data will never be perfect.
0:25:24 > 0:25:29And the trouble is, mathematical manipulation of the raw data
0:25:29 > 0:25:31can look like fiddling the figures.
0:25:32 > 0:25:35But the techniques that climate scientists have used
0:25:35 > 0:25:37are well-understood,
0:25:37 > 0:25:39they're open to scrutiny
0:25:39 > 0:25:42and they all lead in the same direction.
0:25:42 > 0:25:43Three major research groups
0:25:43 > 0:25:48have contributed to the IPCC's reconstruction of past temperature.
0:25:48 > 0:25:51They've each used slightly different methods
0:25:51 > 0:25:53to clean up the historical data
0:25:53 > 0:25:56and account for gaps in the temperature record.
0:25:56 > 0:25:58And here are their results.
0:26:00 > 0:26:04So, in the top left-hand side, you have the results from
0:26:04 > 0:26:07the Global Historical Climatology Network.
0:26:07 > 0:26:10Top right, you have the results from
0:26:10 > 0:26:12the Goddard Institute of Space Studies.
0:26:12 > 0:26:15And in the bottom left, you have the results from
0:26:15 > 0:26:18the Met Office's Hadley Centre.
0:26:18 > 0:26:21Now, just these three graphs show pretty similar results.
0:26:21 > 0:26:24They all seem to be showing a very similar shape,
0:26:24 > 0:26:27especially when you take into account the fact
0:26:27 > 0:26:30that all of the groups were using different techniques.
0:26:30 > 0:26:32From there, how did the groups arrive
0:26:32 > 0:26:34at an average temperature rise?
0:26:35 > 0:26:37This bit is surprisingly simple.
0:26:38 > 0:26:41Now, rather than all of the zigging and zagging,
0:26:41 > 0:26:44the groups put a line through each of their graphs
0:26:44 > 0:26:47and from there it's very easy to just read off
0:26:47 > 0:26:49how much the temperature has risen.
0:26:49 > 0:26:53These three lines show the trend in the average temperature
0:26:53 > 0:26:56since 1880 for each data set.
0:26:58 > 0:27:03But the IPCC then took the average of each of these three lines
0:27:03 > 0:27:07and came up with the value of 0.85 degrees Celsius,
0:27:07 > 0:27:09the most accurate measure that we have
0:27:09 > 0:27:13for how much the Earth's temperature has risen by since 1880.
0:27:15 > 0:27:18That doesn't mean it's perfect.
0:27:18 > 0:27:21The exact figure is always going to be uncertain.
0:27:26 > 0:27:29Scientists have done their best to try and compensate
0:27:29 > 0:27:33for imperfections in the historical temperature record.
0:27:35 > 0:27:38They've applied mathematical methods
0:27:38 > 0:27:41to patchy, unreliable and erroneous data.
0:27:44 > 0:27:50Now, 0.85 degrees is, itself, just a symbolic figure.
0:27:50 > 0:27:53I could have averaged the data in several different ways
0:27:53 > 0:27:57and ended up with a slightly different figure every single time.
0:27:57 > 0:27:59But that's not really the point.
0:27:59 > 0:28:01Looking at how this number is produced,
0:28:01 > 0:28:04you can see that it doesn't matter how you collect your data,
0:28:04 > 0:28:07how you measure your data, or how you treat it,
0:28:07 > 0:28:10one point still stands overall -
0:28:10 > 0:28:14the Earth's temperature has been rising in the last 130 years.
0:28:19 > 0:28:22Different groups using different techniques,
0:28:22 > 0:28:24each scrutinising the others,
0:28:24 > 0:28:27have all arrived at pretty much the same conclusion.
0:28:39 > 0:28:42That's why it's now relatively uncontroversial
0:28:42 > 0:28:45to say that the Earth's temperature has risen
0:28:45 > 0:28:48by just under a degree since the 1880s.
0:28:49 > 0:28:51There's far less agreement, though,
0:28:51 > 0:28:54on the answer to the big question all this raises -
0:28:54 > 0:28:57why did the Earth's temperature rise?
0:28:59 > 0:29:01We're going to look at a very different number,
0:29:01 > 0:29:04a number that answers one of the most difficult
0:29:04 > 0:29:06and controversial questions
0:29:06 > 0:29:08in the whole climate change debate.
0:29:08 > 0:29:11Just to what extent is the rise in temperature
0:29:11 > 0:29:13caused by human activity
0:29:13 > 0:29:16and to what extent is it caused by just natural fluctuations?
0:29:20 > 0:29:22Scarf! Souvenir! Hat, scarf or the badge!
0:29:22 > 0:29:24Get your colours, lads, here!
0:29:29 > 0:29:31I'm Professor Norman Fenton...
0:29:31 > 0:29:33- Hi, there. How are you?- Hi.
0:29:33 > 0:29:36..a mathematician and lifelong Tottenham Hotspur fan.
0:29:38 > 0:29:41From financial services to transport and even football,
0:29:41 > 0:29:45I use numbers to work out the most likely causes of different events.
0:29:47 > 0:29:49The climate change number I'm looking at
0:29:49 > 0:29:51is all about cause and effect.
0:29:51 > 0:29:53The scientists have made a big statement.
0:29:53 > 0:29:58They say they're 95% sure of the main cause of the Earth's recent warming.
0:30:00 > 0:30:02And that cause, they say, is us.
0:30:03 > 0:30:07All science involves identifying not just what is happening,
0:30:07 > 0:30:09but also why it's happening.
0:30:10 > 0:30:12When it comes to the climate,
0:30:12 > 0:30:15scientists say they're 95% sure
0:30:15 > 0:30:18that over half of the warming in the last 60 years
0:30:18 > 0:30:19has been caused by humans.
0:30:21 > 0:30:23How can they be so sure?
0:30:26 > 0:30:28Well, by using statistics,
0:30:28 > 0:30:30we can analyse the most likely cause of something,
0:30:30 > 0:30:33whether that's success at football or climate change.
0:30:36 > 0:30:39I've been coming to Spurs for over 50 years
0:30:39 > 0:30:42and, I have to say, this isn't one of their finest seasons.
0:30:42 > 0:30:44But, like most fans, I'm pretty confident
0:30:44 > 0:30:47I know which factors are going to be most important
0:30:47 > 0:30:50for determining whether they'll play better or worse than expected
0:30:50 > 0:30:52in any given season.
0:30:52 > 0:30:55Unsurprisingly, there's no shortage of opinions here.
0:30:55 > 0:30:57Definitely the manager, you know?
0:30:57 > 0:30:59They need to respect the manager.
0:30:59 > 0:31:02The manager needs to have, like, respect of the players as well.
0:31:02 > 0:31:04If you've got the tactics right
0:31:04 > 0:31:07and you've got the players in the right places where they should be.
0:31:07 > 0:31:09Well, you need a very good executive board.
0:31:09 > 0:31:11Your players need to stay very fit.
0:31:11 > 0:31:15Your manager needs to be focused, have a very good philosophy.
0:31:17 > 0:31:20Beyond opinion, there is a way to use maths
0:31:20 > 0:31:23to work out which factors are the most crucial.
0:31:23 > 0:31:27It's called an attribution study
0:31:27 > 0:31:31and it's what the IPCC did to arrive at their 95% figure.
0:31:32 > 0:31:36All attribution studies start with identifying the factors
0:31:36 > 0:31:38that might cause an outcome.
0:31:38 > 0:31:40Let's take footballing success.
0:31:43 > 0:31:47Here I've got lots of statistics on all the Premiership teams
0:31:47 > 0:31:48going back many seasons.
0:31:48 > 0:31:51It's interesting, looking at the league tables,
0:31:51 > 0:31:54to see how the performance of a team will vary from season to season.
0:31:54 > 0:31:57I want to understand which of many possible factors
0:31:57 > 0:31:59are the most important cause of this.
0:31:59 > 0:32:02Is it the length of time the manager's been with the club?
0:32:02 > 0:32:03Is it the injury rate?
0:32:03 > 0:32:06Is it how much they spend on players?
0:32:06 > 0:32:09I'm going to put all those factors together with many others
0:32:09 > 0:32:11and plot my own attribution study.
0:32:15 > 0:32:18'It's another bad day for Tottenham at White Hart Lane.
0:32:18 > 0:32:19'Full time, Tottenham 1, Stoke 2.'
0:32:21 > 0:32:24To work out why some teams win and some lose,
0:32:24 > 0:32:27we need the second part of the attribution study.
0:32:28 > 0:32:30The different factors we've identified
0:32:30 > 0:32:33that could affect the team's performance
0:32:33 > 0:32:35are put into a mathematical model.
0:32:36 > 0:32:38It's the same process climate scientists use
0:32:38 > 0:32:41to try to work out what is driving climate change.
0:32:43 > 0:32:45I can now check the accuracy of my model
0:32:45 > 0:32:47against teams' past performance.
0:32:49 > 0:32:52So, what I've got here, for example,
0:32:52 > 0:32:55is I've taken one of the teams, Manchester City,
0:32:55 > 0:32:57and I've plotted the actual performance
0:32:57 > 0:33:01in terms of points that they achieved in each of the last few seasons.
0:33:01 > 0:33:04Now, we look at what the model would have predicted
0:33:04 > 0:33:08and you can see it's actually a pretty good prediction
0:33:08 > 0:33:10of what actually happened.
0:33:11 > 0:33:15And this is true for all the teams in the Premier League.
0:33:16 > 0:33:18Now I know I can trust my model,
0:33:18 > 0:33:20I can move on to the clever bit -
0:33:20 > 0:33:23isolating the factors that make the most difference
0:33:23 > 0:33:24to the team's success.
0:33:26 > 0:33:28I found that there was one factor
0:33:28 > 0:33:32which had far greater impact on performance than any other,
0:33:32 > 0:33:33the wage bill.
0:33:34 > 0:33:37If I take out the wage bill factor,
0:33:37 > 0:33:40it's no longer a good estimate at all.
0:33:40 > 0:33:42It's quite a long way off.
0:33:42 > 0:33:45And, in fact, we can repeat that for all of the other teams.
0:33:47 > 0:33:51Using the same methods as the IPCC,
0:33:51 > 0:33:56I can even put an actual figure on how big an effect the wage bill has.
0:33:59 > 0:34:01I can say there's a 95% chance that,
0:34:01 > 0:34:04if you increase the wage bill by 10%,
0:34:04 > 0:34:08there'll be at least one extra point per Premiership season.
0:34:09 > 0:34:13I can be so confident because the answer's so clear from my model.
0:34:15 > 0:34:18But how can climate scientists be equally sure of their results?
0:34:19 > 0:34:23After all, what drives changes in the Earth's climate
0:34:23 > 0:34:28is one of the most complex puzzles scientists have ever tried to unlock.
0:34:30 > 0:34:33Before trying to work out the impact humans have,
0:34:33 > 0:34:36scientists have to account for natural variations
0:34:36 > 0:34:38in the Earth's climate.
0:34:40 > 0:34:42The key science involves a number of factors,
0:34:42 > 0:34:45all of which play a role in changing the climate.
0:34:45 > 0:34:48If this was a court case, they'd be our suspects.
0:34:50 > 0:34:54Many natural factors are known to cause changes to the climate.
0:34:57 > 0:34:59They include the sun.
0:35:00 > 0:35:02The energy it emits varies
0:35:02 > 0:35:05and this can change the temperature here on Earth.
0:35:10 > 0:35:12Volcanic eruptions.
0:35:13 > 0:35:16The vast gas clouds they throw up
0:35:16 > 0:35:18can cause sharp global cooling
0:35:18 > 0:35:21as they affect the chemistry of the upper atmosphere.
0:35:24 > 0:35:27And climate cycles, like El Nino,
0:35:27 > 0:35:31that can cause global temperature fluctuations lasting many years.
0:35:35 > 0:35:41But climate scientists say they're 95% sure that recently,
0:35:41 > 0:35:45all these natural factors have been overshadowed by one other.
0:35:49 > 0:35:54For most climate scientists, there's one prime suspect in this case - us.
0:35:54 > 0:35:58And that's because of a colourless, odourless gas called carbon dioxide
0:35:58 > 0:36:01that we're pouring into the atmosphere.
0:36:01 > 0:36:05One of the first people to try and unravel the role of carbon dioxide
0:36:05 > 0:36:07on changing the Earth's temperature
0:36:07 > 0:36:10was a depressed Swedish physicist called Svante Arrhenius.
0:36:12 > 0:36:15Arrhenius wasn't interested in the Earth's warming, however,
0:36:15 > 0:36:16but cooling.
0:36:19 > 0:36:22In 1894, Arrhenius' marriage broke up.
0:36:23 > 0:36:25Searching for distraction,
0:36:25 > 0:36:28he set his mind to one of the great mysteries of his time,
0:36:28 > 0:36:30the origin of the ice ages.
0:36:35 > 0:36:37Scientists had long wondered
0:36:37 > 0:36:40how the great mountain landscapes of Europe had been formed.
0:36:43 > 0:36:47Once, the rugged valleys were thought to be the relics of a biblical flood.
0:36:50 > 0:36:51But, in Arrhenius' time,
0:36:51 > 0:36:55it was realised that the Earth had been beset by periodic ice ages
0:36:55 > 0:36:57over the last 2.5 million years.
0:37:01 > 0:37:03On trips through northern Europe,
0:37:03 > 0:37:07he studied the vast glacial landscapes that surrounded him
0:37:07 > 0:37:10and wanted to know how the Earth could possibly have undergone
0:37:10 > 0:37:12such monumental change.
0:37:12 > 0:37:16What had caused the planet to cool down so dramatically?
0:37:21 > 0:37:25Scientific understanding advances by developing theories
0:37:25 > 0:37:27and then testing them.
0:37:28 > 0:37:33It was already widely accepted that so-called greenhouse gases
0:37:33 > 0:37:37worked like a huge blanket around the Earth, keeping it warm.
0:37:38 > 0:37:40Arrhenius developed a theory
0:37:40 > 0:37:43that changes in the concentrations of these gases,
0:37:43 > 0:37:46in particular carbon dioxide,
0:37:46 > 0:37:49might also have caused the planet to cool.
0:37:51 > 0:37:54The only way he could test his theory was to use maths
0:37:54 > 0:37:56to work out the relationship
0:37:56 > 0:37:59between changing levels of carbon dioxide in the air
0:37:59 > 0:38:01and the Earth's temperature.
0:38:07 > 0:38:09It was painstaking work.
0:38:09 > 0:38:12Every calculation had to be written out by hand.
0:38:12 > 0:38:16Arrhenius himself described it as tedious.
0:38:16 > 0:38:18But, eventually, he had his answer.
0:38:18 > 0:38:22He predicted that a halving of carbon dioxide in the atmosphere
0:38:22 > 0:38:25could lower the temperature by over four degrees
0:38:25 > 0:38:27and, perhaps, trigger an ice age.
0:38:27 > 0:38:31Almost as an afterthought, he also calculated
0:38:31 > 0:38:33that a doubling of carbon dioxide
0:38:33 > 0:38:36could increase the temperature by the same amount.
0:38:41 > 0:38:45Eventually, it would turn out that changing carbon dioxide levels
0:38:45 > 0:38:48weren't the main cause of the ice ages.
0:38:48 > 0:38:51But, using maths, Arrhenius had established
0:38:51 > 0:38:53the crucial underlying relationship
0:38:53 > 0:38:56between carbon dioxide in the atmosphere
0:38:56 > 0:38:58and the temperature of the planet.
0:39:00 > 0:39:03Much of Arrhenius' efforts and the related work that follows
0:39:03 > 0:39:06can be summarised in one simple equation.
0:39:06 > 0:39:08This enables you to calculate the heating effect
0:39:08 > 0:39:13that comes from raising carbon dioxide above its base level.
0:39:13 > 0:39:17It's one of the fundamental building blocks of climate science.
0:39:21 > 0:39:26The equation shows that the heating effect, represented by Delta F,
0:39:26 > 0:39:31rises in proportion to the amount of carbon dioxide in the atmosphere.
0:39:37 > 0:39:40Put simply, you can't raise carbon dioxide levels
0:39:40 > 0:39:42without heating the atmosphere.
0:39:49 > 0:39:52But there are many factors that influence the climate,
0:39:52 > 0:39:54each with their own equations.
0:39:55 > 0:39:58The rate of energy coming from the sun.
0:39:59 > 0:40:02The cooling effect of volcanic eruptions.
0:40:02 > 0:40:06Human pollution from things such as industry and agriculture.
0:40:06 > 0:40:10Ocean currents. Cloud cover. Wind speeds.
0:40:11 > 0:40:15All of which influence each other in a web of complex interactions.
0:40:17 > 0:40:19Unlike my football study,
0:40:19 > 0:40:22modelling the climate is unbelievably complicated.
0:40:22 > 0:40:25So, how do climate scientists create a model
0:40:25 > 0:40:28that accurately represents the complex interactions
0:40:28 > 0:40:31of all these different factors?
0:40:31 > 0:40:36The answer comes from the very earliest days of weather forecasting.
0:40:40 > 0:40:43It's going to be a dull and wet start to the day.
0:40:43 > 0:40:46Well, after a few quite exciting days of weather,
0:40:46 > 0:40:48today's been a bit nondescript.
0:40:48 > 0:40:50And, as the day goes on, I think you're going to find
0:40:50 > 0:40:53these showers will become heavier and more frequent
0:40:53 > 0:40:55and many of them could well turn out later on in the day
0:40:55 > 0:40:57to be fairly thundery with some...
0:40:57 > 0:40:58- Oh, these- BLEEP.- Let's do it again.
0:41:00 > 0:41:03One of the earliest pioneers of weather forecasting
0:41:03 > 0:41:06was a man called Lewis Fry Richardson.
0:41:10 > 0:41:12At the start of the 20th century,
0:41:12 > 0:41:17he set out to revolutionise weather forecasting using maths.
0:41:20 > 0:41:24Our climate is governed by the circulation of the atmosphere
0:41:24 > 0:41:27and Richardson recognised just how complex this system was,
0:41:27 > 0:41:30declaring that, "the atmosphere is like London.
0:41:30 > 0:41:34"There's more going on than anyone can properly attend to."
0:41:34 > 0:41:36Yet, despite this complexity,
0:41:36 > 0:41:38he wanted to find a way to unravel its secrets.
0:41:42 > 0:41:46Richardson had an idea of how to do this that was revolutionary.
0:41:49 > 0:41:52Using the rows of the theatre as his template,
0:41:52 > 0:41:55he thought of dividing the world into grid squares.
0:41:57 > 0:41:59This would break the problem down
0:41:59 > 0:42:02into a series of discreet and achievable tasks.
0:42:05 > 0:42:09He imagined positioning people within each square
0:42:09 > 0:42:11would only have to solve the calculations
0:42:11 > 0:42:14relevant to the weather in their area.
0:42:16 > 0:42:19A director, standing at the centre,
0:42:19 > 0:42:24would take in the results of all the calculations to form a forecast.
0:42:31 > 0:42:36Richardson made just one attempt to put his ideas into practice,
0:42:36 > 0:42:38retrospectively trying to calculate
0:42:38 > 0:42:41the weather over Europe for a particular day.
0:42:41 > 0:42:44But his calculations took him six weeks to complete
0:42:44 > 0:42:46and they were far from accurate.
0:42:47 > 0:42:51Despite this failure, Richardson was ahead of his time.
0:42:51 > 0:42:55By dividing the world into grid squares,
0:42:55 > 0:42:58he had made the crucial theoretical advance
0:42:58 > 0:43:02that would not only revolutionise weather forecasting,
0:43:02 > 0:43:05but also allow scientists to model the climate.
0:43:07 > 0:43:10All that was needed was enough computing power
0:43:10 > 0:43:12to put it into action.
0:43:14 > 0:43:16Fry Richardson had calculated
0:43:16 > 0:43:19that he'd need over 60,000 people using slide rules
0:43:19 > 0:43:23in order to predict the next day's weather before it arrived.
0:43:23 > 0:43:26I'm sure he wished he'd had access to this,
0:43:26 > 0:43:30the world's most powerful meteorological super computer,
0:43:30 > 0:43:33part of the European Weather Centre here in Reading.
0:43:33 > 0:43:35It may be noisy,
0:43:35 > 0:43:40but it can perform over one thousand trillion calculations every second.
0:43:43 > 0:43:48The world's biggest super computers are now used to model the climate.
0:43:49 > 0:43:53Just like Richardson, they divide the world into a grid
0:43:53 > 0:43:55and solve the complex equations
0:43:55 > 0:43:58governing the climate for each square.
0:43:58 > 0:44:01As computers get more powerful,
0:44:01 > 0:44:03the squares get smaller
0:44:03 > 0:44:07and the models get better at representing reality.
0:44:07 > 0:44:10No computer is ever powerful enough to simulate it
0:44:10 > 0:44:13in as much detail as scientists would like.
0:44:13 > 0:44:16But this method has allowed scientists
0:44:16 > 0:44:19to build a model for factors that affect the climate,
0:44:19 > 0:44:22the crucial second step of an attribution study.
0:44:23 > 0:44:26However impressive our super computers are,
0:44:26 > 0:44:28however much the climate models exploit
0:44:28 > 0:44:30the very limits of our technology,
0:44:30 > 0:44:33climate modelling remains a simplification.
0:44:33 > 0:44:35Which raises the question -
0:44:35 > 0:44:37how can scientists be confident
0:44:37 > 0:44:41that their simplified models accurately capture reality?
0:44:44 > 0:44:47When I made a model for football success,
0:44:47 > 0:44:50I was able to check it against the past results of dozens of teams.
0:44:53 > 0:44:56But climate scientists have only one Earth
0:44:56 > 0:45:00and one set of past data to check their models against,
0:45:00 > 0:45:05so they're always looking out for new opportunities to test their models.
0:45:06 > 0:45:10In June 1991, they found a big one.
0:45:11 > 0:45:14On the Philippine island of Luzon,
0:45:14 > 0:45:17a volcano called Mount Pinatubo erupted.
0:45:19 > 0:45:23It spewed 20 million tonnes of sulphur dioxide and ash
0:45:23 > 0:45:25more than 12 miles up into the atmosphere.
0:45:33 > 0:45:37It was one of the most devastating eruptions of the 20th century.
0:45:40 > 0:45:41But climate scientists at NASA
0:45:41 > 0:45:45realised it also offered a chance to test their climate model.
0:45:48 > 0:45:49Could their model predict
0:45:49 > 0:45:52the effects of the gases given off on the climate?
0:45:53 > 0:45:56After adding the eruption into their model,
0:45:56 > 0:45:59it predicted that, over the next 19 months,
0:45:59 > 0:46:03there would be an average global cooling of around half a degree.
0:46:07 > 0:46:10As the real data came in month by month,
0:46:10 > 0:46:13it matched the model's predictions.
0:46:14 > 0:46:18It was good evidence that climate modelling could be reliable.
0:46:23 > 0:46:27Unfortunately, opportunities to test the models against data
0:46:27 > 0:46:29are few and far between.
0:46:29 > 0:46:33And, as a mathematician, I find that frustrating.
0:46:34 > 0:46:37What's reassuring is that the underlying physics
0:46:37 > 0:46:39on which the models are based is robust.
0:46:41 > 0:46:43So, despite their limitations,
0:46:43 > 0:46:48the models offer a powerful tool to identify the main causes of warming.
0:46:49 > 0:46:51It's a process of elimination.
0:46:51 > 0:46:54To show you what I mean, let's take the example of the sun.
0:46:54 > 0:46:57If the cycles of the sun were a major cause
0:46:57 > 0:47:00of the rise in temperature we've measured, then what we should see
0:47:00 > 0:47:03would be all the layers of the Earth's atmosphere
0:47:03 > 0:47:05warming together like this.
0:47:06 > 0:47:08This is called a fingerprint,
0:47:08 > 0:47:10a characteristic pattern
0:47:10 > 0:47:13that would point to the sun's influence as the cause.
0:47:18 > 0:47:22What we actually have from the measurements of the past 60 years
0:47:22 > 0:47:25is that only the lower levels of the atmosphere have warmed,
0:47:25 > 0:47:27while the upper levels have cooled.
0:47:28 > 0:47:30So, what we're actually seeing in the atmosphere
0:47:30 > 0:47:33is an entirely different fingerprint.
0:47:38 > 0:47:42What the models show is that's a pattern which only fits well
0:47:42 > 0:47:46with the main cause of the warming being human activity.
0:47:47 > 0:47:49That's human activity primarily
0:47:49 > 0:47:51in the form of burning fossil fuels
0:47:51 > 0:47:54that release carbon dioxide into the atmosphere.
0:48:04 > 0:48:10And since the 1970s, the human fingerprint has become more obvious.
0:48:11 > 0:48:13From the loss of sea ice in the Arctic,
0:48:13 > 0:48:15increasing frequency of heat waves,
0:48:15 > 0:48:19to the warming and acidification of the oceans,
0:48:19 > 0:48:22the models predict all of these patterns
0:48:22 > 0:48:27only as a result of increasing greenhouse gases like carbon dioxide.
0:48:29 > 0:48:31The evidence that human activity
0:48:31 > 0:48:34is the major cause of recent warming is compelling.
0:48:36 > 0:48:38But the models can go one step further
0:48:38 > 0:48:43and help us put a figure on the level of certainty behind this statement.
0:48:46 > 0:48:49The yellow line on this graph is the real world data.
0:48:50 > 0:48:54This is how much warming we've measured across the world since 1951,
0:48:54 > 0:48:560.6 degrees.
0:48:57 > 0:48:59Firstly, in red,
0:48:59 > 0:49:01let's look at how the climate models
0:49:01 > 0:49:04expected the global temperatures to change
0:49:04 > 0:49:07when taking into account all known factors.
0:49:10 > 0:49:13The shading shows the amount of fluctuation around the average
0:49:13 > 0:49:15that they would expect to happen.
0:49:18 > 0:49:21The most obvious features are a general rise,
0:49:21 > 0:49:24the result of the increasing carbon dioxide levels,
0:49:24 > 0:49:28with some sharp dips caused by big volcanic eruptions.
0:49:32 > 0:49:34But look what happens if we run our models
0:49:34 > 0:49:37without any human influences like greenhouse gases.
0:49:37 > 0:49:41So now, only natural forces are included in our model data.
0:49:42 > 0:49:45The line doesn't match the real data well at all.
0:49:49 > 0:49:52This is what the model suggests our climate would be like
0:49:52 > 0:49:55if there was no human impact on it at all.
0:49:56 > 0:49:58The models say that, without any human influence,
0:49:58 > 0:50:02global temperature would not have risen significantly
0:50:02 > 0:50:04over the past 60 years.
0:50:05 > 0:50:09It's as clear as taking the wage bill out of my football prediction.
0:50:10 > 0:50:13The models also help scientists put a figure
0:50:13 > 0:50:17on how certain they are of human impact on the climate.
0:50:18 > 0:50:22From the models, they found there was a greater than 99% probability
0:50:22 > 0:50:25that more than half of the warming was due to human activity.
0:50:27 > 0:50:29Given that high level of certainty,
0:50:29 > 0:50:35how did the IPCC arrive at its slightly lower 95% certainty figure?
0:50:36 > 0:50:39All of us who work with mathematical models
0:50:39 > 0:50:41know that they're simplifications,
0:50:41 > 0:50:45so we have to take into account their limitations.
0:50:47 > 0:50:51That's why the IPCC downgraded its final conclusion
0:50:51 > 0:50:55from 99% to greater than 95% sure
0:50:55 > 0:50:59that humans have caused more than half the recent warming.
0:51:02 > 0:51:06All science proceeds by producing theories and then testing them.
0:51:07 > 0:51:10But, when it comes to our climate,
0:51:10 > 0:51:14it's impossible to test the influence of different factors on the planet.
0:51:14 > 0:51:19That's why scientists have turned to maths to help model the climate.
0:51:20 > 0:51:22It's not perfect,
0:51:22 > 0:51:24but it is the only way to put a figure
0:51:24 > 0:51:28on how sure we are the Earth's warming is down to human activity.
0:51:32 > 0:51:33Come on, you Spurs!
0:51:33 > 0:51:37Years of scientific research and statistical analysis
0:51:37 > 0:51:39have brought us as far as 95%
0:51:39 > 0:51:42and that's close enough for most people to believe it.
0:51:42 > 0:51:44That just leaves the question -
0:51:44 > 0:51:47what's going to happen with our climate in the future?
0:51:54 > 0:51:56I'm Professor David Spiegelhalter
0:51:56 > 0:51:59and I use numbers to try to help organisations
0:51:59 > 0:52:02like the Health Service predict the future.
0:52:05 > 0:52:07I'm looking at one number
0:52:07 > 0:52:09that aims to give us a clear guide
0:52:09 > 0:52:12to how our actions now might affect the climate.
0:52:14 > 0:52:18The number I'm looking at is one trillion.
0:52:18 > 0:52:20This rather unimaginably big number
0:52:20 > 0:52:23may be crucial to the future of our planet.
0:52:24 > 0:52:28It's the best estimate that climate scientists have made
0:52:28 > 0:52:31of the number of tonnes of carbon that we could burn
0:52:31 > 0:52:34before we run the risk of causing what's been called
0:52:34 > 0:52:36dangerous climate change.
0:52:37 > 0:52:40That's defined as an average warming across the globe
0:52:40 > 0:52:42of more than two degrees Celsius.
0:52:45 > 0:52:48All fossil fuels contain carbon.
0:52:48 > 0:52:50When we burn them, it converts this carbon
0:52:50 > 0:52:53into the carbon dioxide that warms the atmosphere.
0:52:54 > 0:52:56So, the trillion tonnes figure
0:52:56 > 0:52:59puts a limit on the amount of fossil fuels we can burn.
0:53:01 > 0:53:03In effect, this gives the world a budget.
0:53:03 > 0:53:06It says that, if we want to avoid a two-degrees rise,
0:53:06 > 0:53:09then we can't afford to spend, or burn,
0:53:09 > 0:53:11more than a trillion tonnes of carbon.
0:53:11 > 0:53:13And that's a total going right back
0:53:13 > 0:53:15to the beginning of industrialisation.
0:53:21 > 0:53:24A trillion tonnes sounds like a lot.
0:53:24 > 0:53:26But, the trouble is,
0:53:26 > 0:53:29we've already burnt around half a trillion tonnes
0:53:29 > 0:53:32and that's given us almost a degree of warming.
0:53:32 > 0:53:34And if we carry on the way we're going,
0:53:34 > 0:53:36we'll burn the other half a trillion tonnes
0:53:36 > 0:53:38in about 30 years.
0:53:39 > 0:53:41The implications are profound.
0:53:45 > 0:53:48We've already identified several trillion tonnes
0:53:48 > 0:53:51of fossil fuel reserves buried inside the Earth.
0:53:52 > 0:53:55So, to keep warming below two degrees
0:53:55 > 0:53:59will probably mean leaving most of those reserves in the ground.
0:54:01 > 0:54:03Before we take such drastic action,
0:54:03 > 0:54:06I'd like to know a bit more about the trillion tonnes figure.
0:54:10 > 0:54:12Where does this number come from?
0:54:12 > 0:54:15And how much confidence should we have in it?
0:54:20 > 0:54:22The one trillion tonne limit
0:54:22 > 0:54:25is based on being able to predict the future.
0:54:25 > 0:54:27That may make it sound unscientific
0:54:27 > 0:54:30but, for centuries, people have been working on ways
0:54:30 > 0:54:33to make predictions using statistics.
0:54:34 > 0:54:37The history of statistics and prediction
0:54:37 > 0:54:39has been driven by incentives.
0:54:39 > 0:54:42In fact, the first people who worked on probability and statistics
0:54:42 > 0:54:46were either advising gamblers or pricing up pensions.
0:54:46 > 0:54:50So, I think, if you really want to know who's making good predictions,
0:54:50 > 0:54:53look at people who are putting their money where their mouth is.
0:55:03 > 0:55:06And there's a lot of money in motor racing.
0:55:10 > 0:55:14And a lot of effort to try to predict the future,
0:55:14 > 0:55:17because winning isn't just about driving fast.
0:55:19 > 0:55:22It's also about making the right decisions,
0:55:22 > 0:55:24what to do as the race unfolds,
0:55:24 > 0:55:26the weather changes
0:55:26 > 0:55:27and the unexpected happens.
0:55:29 > 0:55:33And this is where prediction and statistics comes in.
0:55:35 > 0:55:37There are far too many variables
0:55:37 > 0:55:39for the decision to be left to the driver
0:55:39 > 0:55:42or, sometimes, even to the people at the race track.
0:55:42 > 0:55:45It needs a dedicated race strategist.
0:55:47 > 0:55:50In the 2005 Monaco Grand Prix,
0:55:50 > 0:55:53Kimi Raikkonen was in the lead after 25 laps,
0:55:53 > 0:55:55when there was a six-car pile up.
0:55:56 > 0:56:00The safety car came out and the team had to decide very quickly
0:56:00 > 0:56:04should Raikkonen come into the pits or should they leave him out there
0:56:04 > 0:56:06until the race restarted?
0:56:06 > 0:56:08And this would decide whether he won or not.
0:56:08 > 0:56:10They didn't know what to do
0:56:10 > 0:56:14and then a two-word e-mail came in from the chief strategist
0:56:14 > 0:56:16who was in England.
0:56:17 > 0:56:19And the e-mail said, "Stay out."
0:56:21 > 0:56:23So, Raikkonen stayed out
0:56:23 > 0:56:26and the people who came into the pits got all jammed up,
0:56:26 > 0:56:28so Raikkonen went on to win the race.
0:56:30 > 0:56:33And all because of the power of prediction.
0:56:34 > 0:56:37So, how did Raikkonen's strategist
0:56:37 > 0:56:40predict the outcome of different strategies?
0:56:40 > 0:56:43They used to just use gut feelings, just their instincts.
0:56:44 > 0:56:47But now, with the huge amount of data available,
0:56:47 > 0:56:50they can do something much more sophisticated.
0:56:51 > 0:56:52Throughout the race,
0:56:52 > 0:56:56each car streams performance data back to the team...
0:56:58 > 0:57:00..from tyre fatigue to fuel consumption.
0:57:03 > 0:57:07The team then plugs this data into a mathematical model of the race.
0:57:08 > 0:57:13They can constantly make changing predictions as the race proceeds,
0:57:13 > 0:57:14as the positions change,
0:57:14 > 0:57:16as the lap times change,
0:57:16 > 0:57:18they can predict the possible outcomes
0:57:18 > 0:57:21if they do a particular action.
0:57:21 > 0:57:23You know, for example, just come in for a pit stop.
0:57:23 > 0:57:25And then they can choose the strategy
0:57:25 > 0:57:28that maximises the chance of the best possible result.
0:57:30 > 0:57:32As Raikkonen's victory shows,
0:57:32 > 0:57:36the predictions made by the models can be extremely powerful.
0:57:37 > 0:57:41And it's only possible thanks to a mathematical technique
0:57:41 > 0:57:44that we now use for all sorts of future predictions.
0:57:47 > 0:57:49This technique that motor racing teams use
0:57:49 > 0:57:51to decide what strategy
0:57:51 > 0:57:54will maximise the chances of winning a race,
0:57:54 > 0:57:55it's exactly the same
0:57:55 > 0:57:58as the technique I use for medical predictions
0:57:58 > 0:57:59and climate scientists use
0:57:59 > 0:58:02to predict what might happen to the planet.
0:58:05 > 0:58:07And it's all due to a stroke of misfortune
0:58:07 > 0:58:10that befell one particular mathematician
0:58:10 > 0:58:12just after the Second World War.
0:58:18 > 0:58:20Coffee, please.
0:58:22 > 0:58:27In 1946, brilliant mathematician and physicist Stanislaw Ulam
0:58:27 > 0:58:30was struck down by a severe bout of ill health.
0:58:30 > 0:58:32He was hospitalised for weeks
0:58:32 > 0:58:36and only had the card game solitaire for entertainment.
0:58:41 > 0:58:43The aim of the game
0:58:43 > 0:58:47is to sort a randomly shuffled pack of cards into four piles,
0:58:47 > 0:58:50according to a set of rules.
0:58:50 > 0:58:53Whether Ulam could successfully finish the game
0:58:53 > 0:58:56depended on the order of the cards he was dealt.
0:58:57 > 0:59:01As he played, his instinct was to begin to pick apart the game
0:59:01 > 0:59:04and analyse it mathematically.
0:59:04 > 0:59:07He became obsessed with trying to predict
0:59:07 > 0:59:10whether a game would be successful.
0:59:10 > 0:59:12Ulam hoped he could calculate
0:59:12 > 0:59:16the probabilities of different outcomes from the very first deal.
0:59:17 > 0:59:21But he quickly realised this approach would get him nowhere.
0:59:22 > 0:59:26The problem was there were just too many possible combinations,
0:59:26 > 0:59:30leading to ever increasingly complex calculations and equations
0:59:30 > 0:59:32that became impossible to solve,
0:59:32 > 0:59:35no matter how brilliant a mathematician you were.
0:59:36 > 0:59:38But Ulam didn't give up.
0:59:42 > 0:59:45He came up with an entirely different kind of method
0:59:45 > 0:59:46to solve the problem.
0:59:47 > 0:59:50In fact, it was one that hardly involved maths at all.
0:59:50 > 0:59:53Let me demonstrate with an analogy.
0:59:55 > 0:59:57Ahead of me, between me and the wall,
0:59:57 > 1:00:00I can just about make out a sheet of Perspex.
1:00:01 > 1:00:04There's a hole cut out of the centre in a certain shape.
1:00:04 > 1:00:07But, from here, there's no way I can tell what that shape is.
1:00:07 > 1:00:10But I can find out with a little help.
1:00:14 > 1:00:16Imagine that working out the shape of the hole
1:00:16 > 1:00:20is equivalent to Ulam trying to predict outcomes in solitaire.
1:00:21 > 1:00:24There's no way I can work out the answer with maths.
1:00:24 > 1:00:26I need to play the game.
1:00:29 > 1:00:32In this case, the equivalent of a round of solitaire
1:00:32 > 1:00:35is a shot with a paintball gun.
1:00:36 > 1:00:39After a couple of shots, I've got a few through against the wall.
1:00:39 > 1:00:42But, although I know there is a hole in the Perspex,
1:00:42 > 1:00:45I've still no idea what the shape is.
1:00:45 > 1:00:48It's like after I've just played a couple of rounds of the game.
1:00:48 > 1:00:51I'm still none the wiser about what outcomes to expect.
1:00:52 > 1:00:53But if I do this...
1:01:11 > 1:01:13Now, with enough shots,
1:01:13 > 1:01:17I'm beginning to get a picture of what the shape might be.
1:01:18 > 1:01:21Looks like a rough sort of diamond to me.
1:01:21 > 1:01:22It's great fun!
1:01:22 > 1:01:26This is the same principle as playing the game thousands of times.
1:01:26 > 1:01:28With enough sample runs,
1:01:28 > 1:01:31we can begin to build an idea of what outcomes to expect.
1:01:33 > 1:01:36At first sight, it sounds like no solution at all.
1:01:36 > 1:01:40Who could sit around actually playing solitaire millions of times
1:01:40 > 1:01:42to find an answer?
1:01:42 > 1:01:47What turned Ulam's ingenious idea into a useful tool was his timing.
1:01:53 > 1:01:55The computer had just been invented.
1:01:56 > 1:02:00That meant you didn't have to play the game for real.
1:02:00 > 1:02:04Instead, it could be played hundreds of times inside a computer
1:02:04 > 1:02:06and the computer could then say
1:02:06 > 1:02:10which starting hands were most likely to lead to a successful game.
1:02:11 > 1:02:15He called his technique the Monte Carlo method,
1:02:15 > 1:02:17after the casino where his uncle made
1:02:17 > 1:02:21so many repeated and random attempts to predict the future.
1:02:22 > 1:02:24And it turned out to have uses
1:02:24 > 1:02:27well beyond predicting the outcome of card games.
1:02:28 > 1:02:32The beauty of Monte Carlo is that, even in complex systems,
1:02:32 > 1:02:35it tells us not only what is likely to happen,
1:02:35 > 1:02:37but how likely it is to happen.
1:02:38 > 1:02:40In climate science,
1:02:40 > 1:02:43the equivalent of shooting the paintballs
1:02:43 > 1:02:46is running climate models hundreds of times.
1:02:46 > 1:02:48Each time a model is run,
1:02:48 > 1:02:50it comes up with a different prediction
1:02:50 > 1:02:53about the future of the Earth's climate.
1:02:53 > 1:02:56The results of many different climate models can then be combined.
1:03:00 > 1:03:03As the models are run over and over again,
1:03:03 > 1:03:06we can see where the results cluster.
1:03:10 > 1:03:13This is the Monte Carlo process in action.
1:03:13 > 1:03:16The pattern of lines shows us a range of possibilities.
1:03:16 > 1:03:18But not only that.
1:03:18 > 1:03:20Where the lines are densest,
1:03:20 > 1:03:23this is what the models are saying is the most likely thing to happen.
1:03:23 > 1:03:27Of course, it doesn't tell us exactly what the future holds.
1:03:27 > 1:03:31That would be impossible. The future is inherently unpredictable.
1:03:31 > 1:03:34But, the Monte Carlo method gives us an idea,
1:03:34 > 1:03:37not only of what the outcomes might be,
1:03:37 > 1:03:38but how likely they are.
1:03:39 > 1:03:42And this is where our crucial number comes from.
1:03:42 > 1:03:45The graph shows the model's predictions
1:03:45 > 1:03:47of how much the climate will warm
1:03:47 > 1:03:50as a result of us burning one trillion tonnes of carbon.
1:03:52 > 1:03:53The most likely outcome
1:03:53 > 1:03:57is just below two degrees Celsius of warming.
1:04:01 > 1:04:04Now we understand where the one trillion tonnes figure comes from,
1:04:04 > 1:04:07we need to consider the second part of the prediction.
1:04:09 > 1:04:13Why should we worry about a rise of two degrees Celsius?
1:04:17 > 1:04:20When we think about what a small average rise
1:04:20 > 1:04:23in global temperature might mean to us humans,
1:04:23 > 1:04:25perhaps the first thing to think of is weather,
1:04:25 > 1:04:29because we don't experience climate on a day to day basis,
1:04:29 > 1:04:30we experience weather.
1:04:30 > 1:04:33And, sometimes, it can hit us really hard.
1:04:37 > 1:04:41Just a small average temperature rise
1:04:41 > 1:04:43can hide very noticeable changes in weather,
1:04:43 > 1:04:45especially dangerous extremes.
1:04:48 > 1:04:50As the average rises,
1:04:50 > 1:04:53the tropics will experience more devastating rain storms,
1:04:53 > 1:04:56whilst areas, including the Mediterranean,
1:04:56 > 1:04:57will have more droughts.
1:05:01 > 1:05:03Britain will suffer more flooding.
1:05:05 > 1:05:07But it's not simply the fact
1:05:07 > 1:05:10that these events might be more frequent that is a concern.
1:05:12 > 1:05:16It's critical that we understand extreme weather events.
1:05:16 > 1:05:18How often and how hard they might hit us.
1:05:18 > 1:05:21And this is the worry with a climate that might warm
1:05:21 > 1:05:25by as much as two degrees, that it would disrupt that ability,
1:05:25 > 1:05:28because the method we use to predict extreme weather
1:05:28 > 1:05:30uses a particular type of statistics
1:05:30 > 1:05:33that's very sensitive to this type of change.
1:05:34 > 1:05:35A method, in fact,
1:05:35 > 1:05:38that was developed for something quite different.
1:05:43 > 1:05:47In the early 1920s, the cotton mills of England were a vital industry.
1:05:50 > 1:05:54But the looms often sat idle for as much as a third of the time.
1:05:57 > 1:06:00The problem was that cotton threads kept snapping.
1:06:01 > 1:06:04Every snap could stop production for hours,
1:06:04 > 1:06:07so they needed to work out why the threads broke
1:06:07 > 1:06:10and what they could do to stop it happening.
1:06:10 > 1:06:14Fortunately, they had the good sense to call in a statistician.
1:06:17 > 1:06:22The newly-formed British Cotton Industry Research Association,
1:06:22 > 1:06:24charged with improving all aspects of the industry,
1:06:24 > 1:06:27dispatched one Leonard Tippett to investigate.
1:06:31 > 1:06:35Tippett admitted he was woefully inexperienced.
1:06:35 > 1:06:38But, in the best traditions of British statistics,
1:06:38 > 1:06:41he managed to combine careful collection of data
1:06:41 > 1:06:43with elegant statistical analysis.
1:06:47 > 1:06:49He toured the mills of Lancashire,
1:06:49 > 1:06:52carefully recording breakage rates
1:06:52 > 1:06:54and studying the strength of individual fibres.
1:06:59 > 1:07:00Common sense said that,
1:07:00 > 1:07:03if the average strength of the fibres in one thread
1:07:03 > 1:07:05was higher than another,
1:07:05 > 1:07:07you'd think there'd be fewer breakages.
1:07:09 > 1:07:10But Tippett discovered
1:07:10 > 1:07:13that it wasn't the average strength that was important,
1:07:13 > 1:07:16it was the weakest thread that really mattered.
1:07:16 > 1:07:20It's like the old saying, a chain is as strong as its weakest link.
1:07:20 > 1:07:24It's the extremes that make all the difference.
1:07:27 > 1:07:30Tippett's breakthrough came when he realised
1:07:30 > 1:07:32he could use the data he'd gathered
1:07:32 > 1:07:34about the strength of the most common threads
1:07:34 > 1:07:38to predict how often the very weakest threads would be found.
1:07:42 > 1:07:45In other words, he'd invented a method of using numbers
1:07:45 > 1:07:49to predict extreme events from the spread of less extreme events.
1:07:52 > 1:07:55Tippett's insights from the cotton industry
1:07:55 > 1:07:58led to what is called extreme value theory
1:07:58 > 1:08:01and it turned out to be amazingly powerful.
1:08:01 > 1:08:03What used to be considered just unpredictable
1:08:03 > 1:08:05could be analysed mathematically.
1:08:07 > 1:08:10And his breakthrough turned out to be vital
1:08:10 > 1:08:13in the understanding of extreme weather.
1:08:17 > 1:08:20In 1953, a huge storm surge
1:08:20 > 1:08:23was driven down the North Sea towards London,
1:08:23 > 1:08:25devastating coastal areas.
1:08:27 > 1:08:30Over 300 people died in Britain alone.
1:08:34 > 1:08:36After the floods,
1:08:36 > 1:08:39it was decided something had to be done to protect London,
1:08:39 > 1:08:41in case it ever happened again.
1:08:41 > 1:08:45It was time to put extreme value theory to the test.
1:08:51 > 1:08:54This extraordinary piece of engineering
1:08:54 > 1:08:56was conceived in the 1960s
1:08:56 > 1:08:59after catastrophic and fatal floods in 1953.
1:09:00 > 1:09:05These really were extreme events, literally, a perfect storm,
1:09:05 > 1:09:09when rare conditions combined to create a terrible night.
1:09:14 > 1:09:17In order to ensure the barrier would do its job,
1:09:17 > 1:09:20the planners had to predict the most extreme storm surge
1:09:20 > 1:09:22that could be expected in the future,
1:09:22 > 1:09:26more extreme and unusual than anything that had been seen before.
1:09:27 > 1:09:31Extreme value theory, together with classic British record keeping,
1:09:31 > 1:09:33was the answer.
1:09:34 > 1:09:38They had a century's-worth of data on extreme high tides.
1:09:38 > 1:09:40And using Tippett's models,
1:09:40 > 1:09:43this allowed them to gauge the chance of events occurring
1:09:43 > 1:09:46that were so extreme they'd never occurred before.
1:09:51 > 1:09:56The Thames Barrier was built to stop a once-in-a-thousand years event
1:09:56 > 1:09:58and, so far, we've not seen a storm
1:09:58 > 1:10:00come anywhere near testing its limits.
1:10:04 > 1:10:07But Tippett's method has an Achilles heel.
1:10:07 > 1:10:10Its predictions are based on the assumption
1:10:10 > 1:10:12that the future will be similar to the past.
1:10:16 > 1:10:21Extreme value theory uses the frequency of fairly extreme events
1:10:21 > 1:10:25to give us a good idea of the chances
1:10:25 > 1:10:26of really extreme events,
1:10:26 > 1:10:29things we haven't observed, even.
1:10:29 > 1:10:33But the problem with climate change is that the patterns alter.
1:10:35 > 1:10:37When the planners were designing the Barrier,
1:10:37 > 1:10:40they had 100 years of data about storms
1:10:40 > 1:10:43to base their prediction of the 1,000-year storm.
1:10:43 > 1:10:44But, if the climate changes,
1:10:44 > 1:10:47the pattern of storms may well change, too.
1:10:47 > 1:10:51And that will mean the data on past storms will no longer be relevant.
1:10:51 > 1:10:54Without it, the predictions made by extreme value theory
1:10:54 > 1:10:56will be unreliable.
1:10:56 > 1:10:59The average shift might not actually seem that impressive.
1:10:59 > 1:11:02But it's what happens in the extremes
1:11:02 > 1:11:04that is so important to us
1:11:04 > 1:11:07and these become a lot less predictable.
1:11:07 > 1:11:10We can't just tweak the extreme value theory.
1:11:13 > 1:11:14So, as our climate changes,
1:11:14 > 1:11:18not only are we likely to suffer more frequent extreme weather,
1:11:18 > 1:11:21we'll also lose the tool that has allowed us
1:11:21 > 1:11:23to prepare for such eventualities.
1:11:34 > 1:11:37Climate scientists have used maths and statistics
1:11:37 > 1:11:40to give us their most likely prediction of the future.
1:11:41 > 1:11:44Sticking to a trillion tonnes of carbon
1:11:44 > 1:11:46should cause less than two degrees of warming.
1:11:48 > 1:11:51But, given the inherent unpredictability of the future,
1:11:51 > 1:11:54and the imperfections of our climate models,
1:11:54 > 1:11:57how sure can we be that that prediction is right?
1:11:59 > 1:12:02With the help of techniques like the Monte Carlo method,
1:12:02 > 1:12:05the climate scientists have put a number on their certainty.
1:12:07 > 1:12:10They are at least 66% sure.
1:12:11 > 1:12:16That means there's a sting in the tail of the trillion tonnes figure.
1:12:17 > 1:12:19Climate scientists tell us
1:12:19 > 1:12:21that, if you burn a trillion tonnes of carbon,
1:12:21 > 1:12:26they can be 66% certain that warming should stay below two degrees.
1:12:26 > 1:12:28But there's another way of looking at this.
1:12:28 > 1:12:31We could say that they think there's a one-in-three chance
1:12:31 > 1:12:34that warming will be more than two degrees.
1:12:36 > 1:12:38So, the rather sobering conclusion is that,
1:12:38 > 1:12:41even if we burn less than a trillion tonnes,
1:12:41 > 1:12:44we're not guaranteed to keep warming below this level.
1:12:46 > 1:12:50Yet we also know that it would take huge changes to our lives
1:12:50 > 1:12:53to keep to the trillion tonnes limit.
1:12:53 > 1:12:55So, how should we react?
1:12:55 > 1:12:58It's always really difficult to know what to do
1:12:58 > 1:13:00when we're uncertain about the future.
1:13:00 > 1:13:03Usually, we might try to work out the chances
1:13:03 > 1:13:05of something bad happening
1:13:05 > 1:13:07and do what we can to avoid it
1:13:07 > 1:13:09or to protect ourselves against it.
1:13:09 > 1:13:13So, there's a very good chance we'll get old and so we buy a pension.
1:13:13 > 1:13:16There's a small chance we'll have a road accident,
1:13:16 > 1:13:18but we wear a seatbelt.
1:13:23 > 1:13:26In each case, we weigh up the risk and the reward.
1:13:27 > 1:13:31That calculation relies on the quality of information available.
1:13:31 > 1:13:34Scientists have collected and analysed data,
1:13:34 > 1:13:36come up with plausible theories
1:13:36 > 1:13:39and used mathematical models to make predictions.
1:13:41 > 1:13:43But, with the climate,
1:13:43 > 1:13:46we can't do experiments to test those predictions.
1:13:48 > 1:13:50Only time will tell how accurate they are.
1:13:50 > 1:13:53And, if we want to influence our future,
1:13:53 > 1:13:54we can't wait to find out.
1:13:57 > 1:14:02We have to choose on the basis of what we know now.
1:14:07 > 1:14:09When it comes to the climate,
1:14:09 > 1:14:12the scientists have done the calculations for us.
1:14:12 > 1:14:16But now, it's up to us to decide what action to take.