CO2 vs Temperature

The idea that CO2 levels force temperature changes are key to the claims of global warmers. This post looks at how CO2 changes match temperature changes in the records.

Correlation

There are lots of ways to find out how well two sets of values correlate, and a relatively simple way is to plot one against the other. If there’s a good positive correlation, we should get a graph something like this:

We can see that as X is higher, so is Y, and when X is lower, Y is lower. More than that, the larger that X is, so Y is larger.

Negative correlations simply swap direction, and might look like this:

The better the correlation, the closer the points are to a straight line.

This approach can help in noisy or chaotic systems, where a ‘by eye’ glance at data can get taken in by apparent but irrelevant patterns. It can also be useful when there are apparent overall similar trends over a long term.

Pre-Graphing Checks

According to the physics, CO2 slows the re-radiation of heat from the earth. So we expect – at the small changes in CO2 that we see from month to month or year to year – that the more CO2 that is added or removed, the more temperature will change. (The relationship is not linear on the larger scale, but we don’t need to worry about that).

We need to allow for time lags, at least between CO2 changing and the temperature of the instruments recording it changing. Mauna Lao is assumed to be ‘well mixed’ CO2, and the repeating patterns imply CO2 mixing on the order of a month is sufficient. CO2 effects tend to be on the whole troposphere, and there is likely to be some delay while the various temperature ‘pressures’ cause the ground to heat up. It’s hard to see, given daily variations, that this would take much longer than a day, but this assumption is definitely ‘iffy’.

Another potential lag is that of the semi-mythical ‘climate sensitivity’ effects. The more enthusiastic climatologists need these to multiply the ordinary not-very-dangerous temperature rises expected from CO2 change (less than 1C for doubled CO2 levels) in order to get to the scary dangerous temperature rises (3-6C). As these may be decoupled by much more than a month, we cannot assume that any correlation seen is accurate.

The system is very noisy, so we shouldn’t expect a good correlation anyway; there are many effects on temperature other than CO2.

We also need to be wary of seasonal effects. Each year the globe’s CO2 levels fluctuate (as you can see in Mauna Lao’s graph of CO2 levels, which has that ripple effect) and the temperatures similarly change over the year. So we might get a correlation that is a result of the earth’s orbit rather than the cause of one value on the other – the classic ‘correlation is not cause’. So we may have to check against annual values too, which may have their own systematic errors due to the rather arbitrary calendar year cutoff.

As an aside: many people have already plotted CO2 levels against temperature. This is not particularly useful; CO2 has risen nearly exponentially since the 1950s, so plotting CO2 levels is almost entirely equivalent to plotting time.

The Graph

But anyway, using Hadley CRU temperature records, Law Dome ice proxy CO2 records (1850-1978, low resolution thus the stripey effect) and Mauna Lao instrument CO2 records (1959-2008), this is a plot of the month to month (Mauna Lao) or year to year (Law Dome) change in average global temperature against the change in atmospheric CO2 for the same period.

And, rather interestingly, there’s almost no correlation at all. No matter how CO2 changes, the temperature changes in an almost completey independent manner.

With a month lag (ie, comparing the CO2 change with the temperature change of the following month), there’s still none. However if the ordinary CO2/temperature forcing has a lag longer than a week or so (ie, it reaches the same order as the granularity of the records), then this is probably the wrong approach.

Other articles

CO2 Science
Collapse of arguments for high climate sensitivity

Oh no, not the Hockey Stick again

The “Hockey Stick controversy” centers around a graph published by a Dr Michael Mann. It showed how temperatures had remained fairly steady, until mankind started burning lots of coal and oil after which the globe heated alarmingly:

Because the world is mostly American, it’s an ice hockey stick rather than a real field hockey stick. The long steady decline is the hockey stick handle, the sudden rise the blade:

The wiki article linked above outlines the main arguments about whether it’s valid, but there are a couple of other interesting things.

It became centre-piece to the IPCC 2001 report appearing in the summaries, and featuring (if I recall, I haven’t counted recently) eleven times throughout the complete reports.

That overt, specific and limited selection raised skeptic alarm bells. If there is overwhelming evidence for something, then you expect to see overwhelming evidence. Not a focus on one graph from one paper.

1998 as an end date

The first ‘interesting thing’ is that the graph stops in 1998, an unusually warm year, with an end temperature of around 0.7C above the 1961-90 baseline, which is indeed worrying.

Now that’s just a matter of timing rather than fraud (Mann et al’s paper was published in 1998). But by the time the 2001 IPCC report was released it was clear that 1998 had been unusual; 1999 and 2000 were only around 0.25C according to Hadley (0.35C according to GISS).

This rather makes a mockery of the complaints about ‘deniers’ using 1998 as a start point to show that the world is cooling. It’s not right to cherry pick such a year to show a trend now, and it wasn’t right for the IPCC to do so then.

It also indicates a bias in Evil Big Climate; observations that show unusual warming are accepted and published with warnings of runaway effects. Observations of unusual cooling – as in early 2008 – are bounded by warnings of temporary anomalies and ‘noise’

Consensus? What Consensus?

More interestingly it ran counter to the existing ‘consensus’ that there was a medieval warm period and a victorian ice age, supported by various accounts and proxy measurements dotted across the globe.

Which makes a mockery of the warmists cry that a ‘consensus’ should be accepted, even putting aside that a ‘consensus’ is not a measure of scientific fact.

The new Hockey Sticks

The arguments between McIntyre et al and Mann et al led to that particular Hockey Stick being abandoned, and the results of some new studies were collected into a new iconic graph:

As you can see these – and particularly the later ones, coloured red – are no longer Hockey Stick shaped; there is no long straight handle with a marked sudden change at industrialisation. Nevertheless these are called ‘hockey sticks’ by the faithful in memory of the original one.

All that is left is the blade, and even that is artificial. Despite including studies up to 2005 (click on the graph to see the references), the Big Black Line of recent temperature records stops at the steep slope we saw in the unusual year of 1998.

The Latest Hockey Stick

And still there’s some ‘interesting’ choices being made for graphs, these easily-understood, easily-published, easily-misleading summaries of evidence.

Recently Mann published a new one in September 2008:

We can see the medieval warm period and victorian ice ages are returning, more pronounced. The big red line at the end, forming the blade and shooting up past 0.8C by the year 2000, is based on Hadley’s CRUT land only dataset. The grey line hidden behind it is Hadley’s official global temperature estimate.

However CRUs global monthly and average (land) temperatures only break 0.8C in 1998; the average for the subsequent ten years between then and the study being published is 0.6C. Which would put the end of the red line on the graph, rather than have it shoot off into the infinite unknowns in 2000.

(The baselines look similar: CRU land only just passes its own 0C baseline in 1945 according to those records and similarly does so on Mann’s graph).

But the past proxies are not all land only; the black line is land+sea, Moberg 2005 combines ocean and lake data, and Mann and Jones 2003 is of mean surface temperature. So if we replace the red line with Hadley’s global temperature estimate, we get something like this instead:

which, while “unprecedentedly high”, is not quite so alarming.

(Not that we should read too much into the temperature records alone)

With thanks to Sophist et al at Bad Science. See also McIntyre’s more thorough castigation of the original

Apparent Trends and Random Variations

Take a look at these graphs:

You can see trends and features: The noisy but steady drop in the first, a similar but slower rise in the second. The fourth has a slow rise followed by a sharp and maybe accelerating rise. And so on.

The thing is, these are randomly generated, using what are known as ‘random walks’. There are no underlying trends, no feature-causing events. There are just a set of random numbers added together. And these charts have not been specially picked, they are just six consecutive runs of the same random walk spreadsheet. Try it yourself:

Make Your Own Random Walk

Random walks are created where a value is changed by, rather than set to, a random value at each step.

For example, get a willing volunteer to walk across a field tossing a coin; if it shows heads he takes a step to the left and one forward, and if it shows tails he takes a step to the right and one forwards. If he’s really helpful, carries a leaky paint pot, and walks across several fields you get something like those graphs above.

However as it’s raining out and I don’t want to waste any paint, they were created in a very simple OpenOffice spreadsheet: enter the formula A1+RAND()*1 -0.5 into cell B1. This gives B1 a number between -0.5 and +0.5. Then copy it into, say, 200 cells below. Each cell creates a random number between -0.5 and 0.5 and adds it to the previous number.

What is perhaps remarkable, if you think of random numbers as being, well, random, are these long trends of steadily decreasing or increasing apparent trends.

Smoothing and Trends

So those are examples of randomly generated graphs that at first sight look quite similar to many graphs that we get when measuring features of the environment.

For example, if we look at a buoy bobbing about on the sea, it appears to change height from the sea floor in an almost random, unpredictable way, as the overlapping waves, boat wakes, splashes and wind push it about. These small changes are not random, or noise; the measurements are measurements of height at a particular point, and so are signal; they tell us how high the buoy is. However they are chaotic, and so (for most practical purposes) not predictable.

The difficulty is in telling the difference between random systems and ones that do actually have underlying trends. Sometimes simply time well tell: long observations of those random walks above will give us fewer and fewer consistent patterns. Long observations of buoy heights give us predictable tides.

When we’re looking at ways in which complex systems work, we can sometimes find underlying causes by smoothing out the inconvenient small scale changes that confuse the larger patterns. We look to remove the ‘noise’ to reveal the underlying signal.

This requires long observations though, where the patterns can be consistently and reliably repeated, and it requires looking at the right scale in the data. If we smoothed our buoy height data over weeks, we may see seasonal patterns but would miss out the tidal ones.

Linear fits

The simplest trend analysis is to see whether the data is tending to go up or down overall. We can see in the first two graphs at the top above that there is a steady fall; what about the last one? We can find out by a method called ‘linear regression’. The way it works doesn’t really concern us, but using it gives us a line through the data that is as close as it can be to every single point in that data set. The angle of the line tells us how fast the values have been increasing or decreasing, overall.

Sometimes this doesn’t tell us anything very useful. We can see in that last graph a sudden drop at the end; is this merely a disturbance to the underlying trend, or is it part of the underlying trend’s events? Similarly the third graph, with it’s large trough in the middle, doesn’t lend itself well to a straight line.

In fact none of them do. The key thing to remember here is that there is no underlying trend in these graphs; they are merely random numbers added together.

Fooling the Eye

Being humans we tend to look for patterns and trends, and the way our mind is wired we’ll spot them too – even in random data. This is probably because of something excitingly dangerous such as being able to spot predators, prey or mates in the dappled jungles of Africa. Whatever it is, it can lead us astray too, to think we’ve found things we haven’t.

Take the second graph above, and we can see that if we look at low scale trends (trends for short timescales), the trend lines (yellow) are much steeper – up and down – than the overall one (the blue one):

If we look at longer scales, the trend lines (red here) gradually flatten out to be come closer to the blue one:

Until we get to scales of the same order of magnitude as the whole graph, and the trend lines are very nearly those of the overall blue one:

This can lead us to think that the longer trends are ‘better’. But if we have a look at where that graph fits into the much longer run that it was clipped from, we can see that even the overall blue line trend of the clip (above the red bar) has little to do with the bigger picture:

The apparent smoothed trends we see above are only features of the length of the graph. They tell us nothing about longer term trends (well, they can’t, there aren’t any…).

Scale and Granularity

The above are actually clips from runs of 10,000 points. If we look at these longer ones, we can see similar effects: at no point do we start getting an overall smoothing, as the more steps we have, the more likely we are to have long runs of apparently biased direction. Here’s the first and third longer runs (the second is above):

(bear in mind the Y axis scales are different)

So What?

There is no ‘natural’ scale where a noisy-looking system can be smoothed out to. It is tempting to look at the data you have in front of you and fit a trend-line, but without more knowledge behind that data, that trend says nothing about any underlying one without something more.

We need either long enough observations to establish a pattern, and/or enough knowledge about the mechanics of the thing being recorded that we can relate features and trends in the data set to known changes in those mechnics.

For example, if someone’s body temperature is unusually high and increasing, we should worry. We should probably do more than just worry, but it’s not something to ignore because it might be random; I don’t know how the body works in detail, but I do know what a body temperature behaves like; it’s been observed so many times and for so long that patterns have been established, even if working knowledge has not.

So… Global Temperature…

So, yes, the next examples come from my favourite subject, Global Warming, because some people seem to have forgotten that it’s not enough to draw a straight lines through data and imply things about the future from it:

(IPCC showing how trends were increasing in the run up to their 2007 report, Working Group 1, chapter 3)

The recent claims that temperatures ‘are’ decreasing are on similarly shaky ground:

We could even take the full dataset that we have, which for Hadley runs 1850-2009, and look at the apparent trend there (ignore the green patch and line):

But, again, that tells us nothing about future behaviour by itself.

Some of the more frothing deluders enthusiastic GW advocates* say that small changes are ‘noise’ over an underlying trend or signal. However there is very little noise in the records; the values in datasets like Hadley’s are pretty much all signal (ignoring for the moment systematic errors).

There’s a fundamental error in an approach that dismisses inconvenient short-term variations as ‘natural’ but does not understand the range of time scales that ‘natural’ is valid for; there is no reason to assume that longer-term variations are not also natural. The temptation is just to ’smooth’ the data until it looks right to the eye, but that tells us interesting things about how the eye and brain interpret shapes and nothing about the data.

Summary

We really can’t say anything useful about temperature trends by just examining the recent record.

We need knowledge of how the climate works, captured usually as models. A lot of people are working hard to understand the climate based on the various records of various measurables; but most work on some small aspect of it, few but the most enthusiastic deluders claim anyone has complete understanding. And the good quality data is fairly recent, there are huge systematic problems with it (such as surface station placements, urban heat island effects, tidal station changes) and for anything more than a few decades we tend to have to use proxies and add another layer of systematic problems.

When we check the models, they need to be checked against features of the dataset, not carefully selected subsets or the overall trend. So we’ve seen a steady rise of CO2; why did temperature rise 1910ish-1940ish at the same rate as recently when little man-made CO2 was present? ie what was that natural variation and has it been included in our knowledge base – and eliminated as a candidate for the recent rise; do the models that ‘predict’ the 1980-2000 rise also ‘predict’ the earlier periods?

These models and their validation are key; it’s not sufficient to establish underlying trends by drawing a straight line through some data.

(Audit, full disclosure, etc: Example spreadsheet to create random walks and zip file of the 6 runs made )

* I must remember not to use the same tone here as I would in forum arguments. Apologies to tamino who was not at all frothing below.

Cherry Slopes: Picking trends in temperature records

Drawing straight lines through datasets is a popular and easy way of showing a trend.

We can say that I am more tipsy now than when I came into the pub, and conclude that the trend is increased blethering, and that I’m likely to continue that way all else being equal. But we know we cannot really predict trends from it: the bar may close, I may run out of money, I may drink faster or slower depending on who is in and what music is on.

There’s a similar approach that says that, as it’s warmer now than a hundred years ago and we industrialised since then, we can conclude Stuff about trends in temperature. However with any complex system, it’s highly likely that it would be different to what it was a hundred years ago, so we can’t conclude anything directly from the fact that there is a difference.

So rather than looking at a straight line drawn through a dataset, we can look at features in that record and compare them with the proposed causes, and for that we need to have an idea about what we would expect to be features and what are natural variations.

For example, unless you’re familiar with, it might be worth reading this on Random Walks. [Updated: this was inline here but is really a separate subject]

Now climate is chaotic, which is not quite the same as random. All the same, if we take an extremist view that the temperature record is entirely natural, then we would expect it to look somewhat like a random walk. The climate/earth components do not reset to some fixed value every year; we would expect one year to be some kind of change on the previous year.

‘Cherry’ Picking Periods for Trends

‘Cherry picking’ is deliberately choosing a range of data to demonstrate your point, and deliberately discarding data that does not.

Recently, as temperature measurements have plateaued or dropped, arguments rage over what a valid period is for establishing trends from the record. There is the IPCC showing how trends were increasing in the run up to their 2007 report (Working Group 1, chapter 3):

And the ‘deniers’ showing how trends are flat or decreasing:

Now they are for different periods, but the argument used is the same: show recent trend and imply future values. And those trends are obviously very susceptible to the range of values picked to draw a line through.

“Open Mind” quite rightly and rudely castigates people who cherry pick the last decade to show a plateau in temperature trend, and then in a remarkable example of ‘cognitive dissonance’ picks the last forty years to show global warming. (In fact shorter periods – such as two decades – can apparently be used to show warming). Similarly the ‘modern global warming era (1975-present)’ is used on the site to establish modern global warming, because it’s the period that warmed, a kind of self-harvesting cherry.

The UK Met Office simply say quite correctly that there’s not enough data to say that it’s stopped, but don’t go down the sticky avenue to say what would be enough to do so.

Double Cherried

If we choose two endpoints rather than run to the present, we can do even more, especially because we have the big lump in 1998 with the troughs either side. Even using just one endpoint, we can go from a 0.2K/decade drop ‘trend’ (as above), to a plateau, to a 0.04K/decade rising ‘trend’ by including it or not:

These guys claim [with an unsupported optimistic "It's not ideal but it's not too bad"] that we can remove the effects of the Ninos by modelling them, to reveal the underlying ‘trend’. But then they also reckon that maybe it the 1998 El Nino was more than just ‘weather’, and that it has had longer lasting effects and overheated the system which is just cooling slowly back to the ‘trend’.

In fact they draw a nice graph to show this, using a trend based on 1979-1997 records, which I’ve redrawn here using the same Hadley dataset, and it shows the current temperature trends returning to the underlying trend:

And they assure us that they haven’t been cherry picking by using 1979-1997, and that anything other range would be similar as long as you don’t include post 1998, and presumably that you do include up to 1997 (Otherwise I could carefully pick 1944 to 1976 and show a flat ‘trend’).

So they are cherry picking. In fact their own choice of range looks really quite dark and red and shiny and tasty: 1979-1997 removes the cooler 1978 and warmer 1998 years that are usually included to show how dangerously drastic the temperature increase is. By finding the slower rise shown above, the temperature record looks like it is ‘approaching’ the long term trend. Whereas if we include 1978 and 1998 to calculate the trend, the record is ‘departing’ from the trend:

We could take the full dataset that we have, which for Hadley runs 1850-2009. Using that to get our trend we get even longer to allow current temperatures to ‘fall’ to return to the trend (straight blue line) before continuing it’s ‘inexorable’ rise:

But claiming that the recent plateau is just a return to a longer trend gets in the way of the claim that the longer trend is dangerous. The 1850-2009 linear trend is about 0.05K/decade; by 2100 we would expect half a degree rise. Even realclimate’s 1979-1998 trend above is roughly 0.1K/decade; by 2100 we would expect a single degree rise. Few people claim any more that temperatures are “running away”.

Summary

It’s not true to say that you can [i]prove anything[/i] with statistics; but you can imply very different things using different methods. When you’re given some numbers or a graph, have a good look at the surrounding data and see if it perhaps gives a different story.

Snide Political Postscript

If earlier predictions are failing then putting off the Signs is a good political move. By claiming that there might be more cooling for another 10 or 20 years, then much faster rising, you can maintain the threat of doom while giving you plenty of time to drift into another job, or make your fame as a political activitist.

If in the meantime temperatures rises, well then your earlier predictions are vindicated. You can’t lose.

Testing Hansen’s Climate Predictions

The case for harmful global warming largely rests, understandably, on the climate models required to emulate the world’s complex climate and how it is expected to behave as humans continue on our merry way.

Validating these models is tricky as we only have one real world to test them against. Sometimes they can be checked against new historical data, but since this data is usually another aspect or refinement of existing knowledge this isn’t a proper validation. Where the models are found to deviate from the data, they are adjusted to fit which is a Good Thing, but this is merely a retrospective refit and can be done with any arbitrary multivariable model; it’s not a validation. 

Which is why James “Death Trains” Hansen’s predictions from 1988 are seen as an important test for the Man-Made CO2-induced Global Warming case. 

Setting the Scene

Essentially Hansen ran three predictions, based on three scenarios (abstract here):

“Scenario A assumes continued exponential trace gas growth, scenario B assumes a reduced linear linear growth of trace gases, and scenario C assumes a rapid curtailment of trace gas emissions”

Now Hansen claims that, if we look at the observations:

then because the observed temperatures match Scenario B, his predictions have been validated.

Which is a novel approach.

Everyday prediction tests

There’s nothing scarily complicated about testing models. Let me suggest a model for you:

“The more you eat, the fatter you get”

It sounds plausible, let’s test it. Here are three scenarios:

A: I will eat steak and chips and cheese omelettes and Big Macs, three times a day. I predict I will put on 4″ to my waistline by a month next Friday.

B: I will eat cereal for breakfast, meat and two veg for lunch and a sandwich for supper. I predict no great change.

C: I will drink watery soup and have muesli for supper. I predict my ribs will be showing and I shall be in a really foul temper. But it’s OK, I won’t have the energy to do anything about it.

So, after a month, we measure my waistline and see that I have slimmed down quite a bit. Brilliant! Scenario C, my prediction was correct!

Which is a bit daft, as it ignores the premise for the scenario; the whole point of the model is to test that the scenario prediction matches the observation. In this particular case I ate a high calorie diet but trained every day for the marathon; that’s Scenario A. I ate a lot, but slimmed; my model was wrong (or at best, very incomplete).

Hansen Prediction Tests

So when we look at Hansen’s predictions, we should be comparing the observations with those predictions from the right scenario.

Naively, we could pick the scenario from his abstract, which would give us scenario A, as our CO2 emissions have exponentially increased (which is the major component).  Hansen gave this scenario as his ”business as usual” one, and indeed that is what happened; we didn’t start reducing emissions as he would have needed to make Scenario B the ’plausible’ one. 

(update) However we can look at it in more detail if we look at pages 9631-2 of his paper. There he has CO2 emission increase at 1.5%/year in Scenario A, and has it reducing in steps to 0% in 2010 for Scenario B.  CO2 emissions have been 2%/year until 2000ish, then increasing to nearly 3% until last year, as you may recall causing panic and predictions of even worse effects of global warming with no eye on actual observations at all.

CH4, the next biggest forcing, is not so clear as there was low/no growth in the 1990s, but otherwise is overall consistent 1985-2005 with a 1% growth year-on-year which is lower than Scenario A (1.5%) and higher than Scenario B ( 1% 1990-2000, then 0.5%)

Scenario A had no volcanos, Scenario B had two or three (though I’m not clear on this), and in the end there was one of the right scale.

So it looks like mostly Scenario A-ish; possibly ’somewhere between A and B’ but given the above, heavily weighted toward A:  

(via Paul Macrae here)

Although Hansen and his friends get very upset when people compare observations with that scenario. Apparently it’s ‘fraud’

And he’s not only way off Scenario A, but if we plot out the later years (and remove that convenient estimate for 2005 and replace with the observation), we see that the observations drop lower (for a short period) than even Scenario C; where CO2 emissions were to stop increasing altogether:

This image is a clip from Hansens report, overlaid with the observed temperatures, from Climate Skeptic. Feel free to check with Hadley’s temperature measurements.  Note that in the text Hansen gives Scenario A as ‘growth… typical of the last 30 years’ though these days he insists it was Scenario B that he gave as the ’most plausible’, which is not quite the same thing.

So really, there’s no positive validation for his 1988 models (although of course modern models are a good 20 years more up to date…)

“It doesn’t matter how elegant your theory is, it doesn’t matter how smart you are, if the experiment says it’s wrong, it’s wrong” – Feynman

Postscript…

It gets more complicated though. It may be that actually there’s little difference in the CO2 forcing paramaters between Hansen’s Scenario A and B; Steve McIntyre thinks it’s mostly down to CFC forcings. 

Similarly, it may be that the scenarios are actually based on forcings rather than emissions as Hansen gives in his abstract. This would make for a different story, as the forcing strength decreases as CO2 increases (ie, as you add more and more CO2 the effect it has becomes a bit less each time).

Hansens predictions remain broken, these would just explain where. 

This is hard to verify as, like a lot of academic research, climatologists have yet to embrace “full disclosure” or many of  the other practices that would be associated with the ‘open’ and ‘welcoming criticism’ working environment they claim to have.