Phil Plait, over at Bad Astronomy has a short note about a friend whose life was saved by science. (Ok, the technologies that scientific discovery enabled.)
My own story goes back quite a few years, to my childhood. I had a severe case of pneumonia. Two major contributors to the fact that I'm still around to blog at you were penicillin and the oxygen tent. Penicillin's story starts in 1928 with Alexander Fleming. He wasn't looking for it at the time. And it took another 12-15 years before years before other people, including Howard Florey and Earnest Chain (recipients, with Fleming, of the 1945 Nobel prize in Medicine for this work), were able to make enough penicillin for it to be used clinically in any significant amount.
Oxygen, on the other hand, owes its availability not to accidental discovery (plus over a decade of hard work), but to thermodynamics. James Dewar took an interest in liquifying gases, and in general, trying to reach absolute zero. Along the way, he invented the Dewar flask (which the Thermos company started selling, hence the name you probably know). I'm fairly confident he wasn't thinking about medicine. He was doing some interesting science, and learning more about how the universe worked. (Liquid oxygen is magnetic -- he was the first person to know this.) He also invented a way to produce industrial quantities of liquid oxygen. Once you've got that around, you have a chance to discover that, gee, it's a useful treatment to give high concentrations of oxygen to people whose lungs are seriously impaired -- like, say, me with my major pneumonia.
Two different technologies, one discovered by accident, and one not thought of for health. So it goes in science quite often. The ultimate uses can be unpredictable. But it's an awfully good bet that there will be a use down the road.
23 March 2009
19 March 2009
Does CO2 correlate with temperature?
Lately I've been seeing the assertion that carbon dioxide (CO2) levels have no correlation with temperature changes, particularly not over the last 100-150 years. I discussed a form of this, where the site was asking you to estimate the correlation by eye and doing a misleading job of it. It's a bizarre claim, however, given that even at the eyeball level the figures in that previous note of mine show a pretty good correlation.
[Update April 9, 2009: Some recent commentators don't believe, and didn't bother to check, that there are sources which claim no correlation. See 20 who deny co2 is correlated with temperature. It's actually 21.]
But let's be quantitative. Eyeball estimation only gets you so far, and eyeballs can be deceived fairly easily (such as by the co2sceptics presenting different periods of data, and drawing in a misleading curve for one set). Also, showing the variation through time, separately, of temperature and carbon dioxide, is not the best way to look at the correlation. Better is to plot the temperature against the CO2 level for that year. I use the temperatures and CO2 values from my prior note. For the period of the Siple ice core (before 1959) I filled in the missing values by straight line fill. Fortunately, in this period the CO2 concentration is changing only slowly.
Before going further, though, a couple of reminders. One is, doing this analysis is not how professional climate change predictions are done. The prediction of warming from human-released CO2 was made 60 years before the first measurements of atmospheric CO2 levels. The estimates today of warming from CO2 are done, as was done originally, by examining how the laws of conservation of energy play out in the atmosphere. Second is, this analysis is one that is demanded by the people making the claim that there is no such correlation. They are badly wrong, as we'll see. They're either lying, or failing to do their homework. Either way, not sources to keep using.
So, for eyeball inspection, annual mean global temperature (deviation from baseline) plotted against CO2 annual average:
It's awfully hard to look at this and say that there's no correlation between CO2 and temperature. Since eyeballs can be deceived, we'll be quantitative. While I think the term 'correlation' is more or less known in common language, there are a few technical points I want to be sure we all have in hand. Correlation is a measure of how much one variable (temperature, in our case) depends on another (CO2 for us). It can range from +1 (perfect correlation in a positive sense -- that is, every time you increase CO2 by 10 ppm, you would increase temperature by the same, say, 0.1 degree) to -1 (perfect correlation in a negative sense, every time CO2 increased by 10 ppm, temperature would drop by 0.1 degree). At 0 correlation, there's no connection. But ... all of this is for straight line relationships. If the real relationship is not straight line, you have more work to do. We are going to assume that the relationship is straight line.
One last bit before trotting out numbers. Correlation itself is not really our goal even if we compute that number along the way. We generally want to predict some variable given knowledge of some other variable; in our case, predict temperature given CO2 levels. Now temperature varies around year to year. If we have a good prediction method, we can explain most of that variance. If we multiply the correlation by itself (square it), that number tells us how much of the variance we can explain. If a variable explains more than 50% of the variance, we can say that it is the predominant factor. If it's over 10% of the variance, it's notable even if not predominant. Such conclusions also have to be checked for whether they're statistically significant. If I threw dice only twice, their value would 'explain' 100% of the variance in temperature for 2 years (hence the comments about 'you can always draw a straight line through 2 points'). If something isn't even statistically significant, then it is definitely not notable or predominant. It's also entirely possible for a relation to be statistically significant, but not notable -- physically.
I'm doing a little algebra and will represent the predictions as:
T = slope * (CO2 - reference)
T is the temperature anomaly in global mean surface air temperature, slope we'll compute, CO2 is the annual average CO2, and reference is a reference level of CO2. (Temperature anomalies are in centigrade, and CO2 is in ppmv)
If we simply look over the whole period of temperature data, we see 78% of the temperature variance is explained as a linear response to CO2 changes. Perhaps you don't trust ice core CO2, or older temperature values. The more recent period shows CO2 explaining 82% of all variation. For either the record as a whole, or for the more recent period, temperature shows a very strong correlation to CO2.
Research (see the citations in the IPCC working group 1, 4th report) is showing that it is in the last half century that human-derived CO2 (and others) have been the predominant drivers of climate change. Both the full 158 year record and the recent shorter 50 year record support that -- explaining 78-82% of variance definitely qualifies (at least if it passes statistical significance, which we'll get to in a minute). On the other hand, the same report says that before about 1950, CO2 is not the major driver. Here we see 28% of the temperature variance in that period being from CO2. Consistent with CO2 being a notable component of the system, but not the predominant one in that period.
Now for the tests of statistical significance, which I'm afraid is more gory in detail than I write up here. But, the result is that all three correlations are significant at better than the 0.0005 level. In more normal language, we'd take 1 and divide by that number. The result is the number of times we'd have to collect data that were just random numbers before we'd find even 1 example with this high a correlation. In this case, at least 2000. Less than a 1 in 2000 chance of just being noise. (My statistical table only goes out this far. If I had better tables, they'd show much, much, higher odds against these correlations being chance.)
The IPCC estimate for climate sensitivity to doubling CO2 levels (which they took as 550 ppm, see, for example, the technical summary at the above link) is that it is 'likely' (see their definition of the word, it probably isn't what you think) 2 to 4.5 C, with a best estimate of 3 C. Using the highly simple-minded regression above, we get estimates of 2.4 and 2.7 C. Not only does CO2 indeed correlate with temperature, proving false the unreliable sources that started us here, but the sensitivity suggested by that correlation is in the range of what the IPCC arrives at by much more meaningful models of the physics of the climate system.
One last piece. Cast your eyes back up to the graph, and maybe click on it to get the full size version. Towards the right hand end, you see a dot that's far above the straight line fit. You're not surprised that this is 1998 -- the year of the major El-Nino that was concurrent with a time of high solar activity. The bit farthest below the curve around 357 ppm CO2 is 1992-3 -- cooling effects of Mount Pinatubo. Even against a statistically strong trend, there are still other effects in the system that can give some tenths of a degree weather variations.
There are many reasons climatologists don't approach climate this way, and they're good ones. I only did it because I've been encountering sources that say that the correlation is zero (nonexistent). Those places are wrong.
[Update April 9, 2009: Some recent commentators don't believe, and didn't bother to check, that there are sources which claim no correlation. See 20 who deny co2 is correlated with temperature. It's actually 21.]
But let's be quantitative. Eyeball estimation only gets you so far, and eyeballs can be deceived fairly easily (such as by the co2sceptics presenting different periods of data, and drawing in a misleading curve for one set). Also, showing the variation through time, separately, of temperature and carbon dioxide, is not the best way to look at the correlation. Better is to plot the temperature against the CO2 level for that year. I use the temperatures and CO2 values from my prior note. For the period of the Siple ice core (before 1959) I filled in the missing values by straight line fill. Fortunately, in this period the CO2 concentration is changing only slowly.
Before going further, though, a couple of reminders. One is, doing this analysis is not how professional climate change predictions are done. The prediction of warming from human-released CO2 was made 60 years before the first measurements of atmospheric CO2 levels. The estimates today of warming from CO2 are done, as was done originally, by examining how the laws of conservation of energy play out in the atmosphere. Second is, this analysis is one that is demanded by the people making the claim that there is no such correlation. They are badly wrong, as we'll see. They're either lying, or failing to do their homework. Either way, not sources to keep using.
So, for eyeball inspection, annual mean global temperature (deviation from baseline) plotted against CO2 annual average:
It's awfully hard to look at this and say that there's no correlation between CO2 and temperature. Since eyeballs can be deceived, we'll be quantitative. While I think the term 'correlation' is more or less known in common language, there are a few technical points I want to be sure we all have in hand. Correlation is a measure of how much one variable (temperature, in our case) depends on another (CO2 for us). It can range from +1 (perfect correlation in a positive sense -- that is, every time you increase CO2 by 10 ppm, you would increase temperature by the same, say, 0.1 degree) to -1 (perfect correlation in a negative sense, every time CO2 increased by 10 ppm, temperature would drop by 0.1 degree). At 0 correlation, there's no connection. But ... all of this is for straight line relationships. If the real relationship is not straight line, you have more work to do. We are going to assume that the relationship is straight line.
One last bit before trotting out numbers. Correlation itself is not really our goal even if we compute that number along the way. We generally want to predict some variable given knowledge of some other variable; in our case, predict temperature given CO2 levels. Now temperature varies around year to year. If we have a good prediction method, we can explain most of that variance. If we multiply the correlation by itself (square it), that number tells us how much of the variance we can explain. If a variable explains more than 50% of the variance, we can say that it is the predominant factor. If it's over 10% of the variance, it's notable even if not predominant. Such conclusions also have to be checked for whether they're statistically significant. If I threw dice only twice, their value would 'explain' 100% of the variance in temperature for 2 years (hence the comments about 'you can always draw a straight line through 2 points'). If something isn't even statistically significant, then it is definitely not notable or predominant. It's also entirely possible for a relation to be statistically significant, but not notable -- physically.
I'm doing a little algebra and will represent the predictions as:
T = slope * (CO2 - reference)
T is the temperature anomaly in global mean surface air temperature, slope we'll compute, CO2 is the annual average CO2, and reference is a reference level of CO2. (Temperature anomalies are in centigrade, and CO2 is in ppmv)
| time span | % variance explained | slope (C per ppmv CO2) | slope (C per 100 ppmv CO2) | reference (ppmv) |
| 1850-2007 | 78 | 0.00868 | 0.868 | 333 |
| 1850-1958 | 28 | 0.00962 | 0.962 | 329 |
| 1959-2007 | 82 | 0.00962 | 0.962 | 335 |
If we simply look over the whole period of temperature data, we see 78% of the temperature variance is explained as a linear response to CO2 changes. Perhaps you don't trust ice core CO2, or older temperature values. The more recent period shows CO2 explaining 82% of all variation. For either the record as a whole, or for the more recent period, temperature shows a very strong correlation to CO2.
Research (see the citations in the IPCC working group 1, 4th report) is showing that it is in the last half century that human-derived CO2 (and others) have been the predominant drivers of climate change. Both the full 158 year record and the recent shorter 50 year record support that -- explaining 78-82% of variance definitely qualifies (at least if it passes statistical significance, which we'll get to in a minute). On the other hand, the same report says that before about 1950, CO2 is not the major driver. Here we see 28% of the temperature variance in that period being from CO2. Consistent with CO2 being a notable component of the system, but not the predominant one in that period.
Now for the tests of statistical significance, which I'm afraid is more gory in detail than I write up here. But, the result is that all three correlations are significant at better than the 0.0005 level. In more normal language, we'd take 1 and divide by that number. The result is the number of times we'd have to collect data that were just random numbers before we'd find even 1 example with this high a correlation. In this case, at least 2000. Less than a 1 in 2000 chance of just being noise. (My statistical table only goes out this far. If I had better tables, they'd show much, much, higher odds against these correlations being chance.)
The IPCC estimate for climate sensitivity to doubling CO2 levels (which they took as 550 ppm, see, for example, the technical summary at the above link) is that it is 'likely' (see their definition of the word, it probably isn't what you think) 2 to 4.5 C, with a best estimate of 3 C. Using the highly simple-minded regression above, we get estimates of 2.4 and 2.7 C. Not only does CO2 indeed correlate with temperature, proving false the unreliable sources that started us here, but the sensitivity suggested by that correlation is in the range of what the IPCC arrives at by much more meaningful models of the physics of the climate system.
One last piece. Cast your eyes back up to the graph, and maybe click on it to get the full size version. Towards the right hand end, you see a dot that's far above the straight line fit. You're not surprised that this is 1998 -- the year of the major El-Nino that was concurrent with a time of high solar activity. The bit farthest below the curve around 357 ppm CO2 is 1992-3 -- cooling effects of Mount Pinatubo. Even against a statistically strong trend, there are still other effects in the system that can give some tenths of a degree weather variations.
There are many reasons climatologists don't approach climate this way, and they're good ones. I only did it because I've been encountering sources that say that the correlation is zero (nonexistent). Those places are wrong.
Unreliability at co2sceptics/climaterealists
Last Tuesday I wrote up Misleading yourself with graphs, prompted by plots on the main page at co2sceptics. As I mentioned then, it could have been an honest mistake, so I sent a note to them on their site (message form).
They've neither responded nor changed their site. So I'm afraid they're simply an unreliable source. Maybe the mistake is honest, maybe not. But a reliable site would respond on being shown that they'd made a mistake and were misleading themselves and their readers.
This is less of a surprise to me now since I searched on their name and found one of the references to them is an earlier post of mine about a different unreliable source icecap.us. In that case, they were being extremely un-skeptical.
In Does CO2 Correlate with Temperature, to appear shortly, I'll be taking a more quantitative look at the correlation they want readers to believe does not exist.
They've neither responded nor changed their site. So I'm afraid they're simply an unreliable source. Maybe the mistake is honest, maybe not. But a reliable site would respond on being shown that they'd made a mistake and were misleading themselves and their readers.
This is less of a surprise to me now since I searched on their name and found one of the references to them is an earlier post of mine about a different unreliable source icecap.us. In that case, they were being extremely un-skeptical.
In Does CO2 Correlate with Temperature, to appear shortly, I'll be taking a more quantitative look at the correlation they want readers to believe does not exist.
18 March 2009
Read original sources
I've mention it here and there before, but was reminded recently of the importance of reading the original sources. The recent round was a document which said the IPCC had not discussed some points about sea surface temperature. I thought that was odd, so I looked up the IPCC section that talks about sea surface temperature (SST) and in truth, they do talk about those issues. If somebody is lying about what someone else says in such an easily identified way, time to pitch that original source and go looking for someone honest to learn from. So that's one reason to read the original sources -- to see who's lying and weed them out.
There are also more pleasant reasons to follow up to original sources. One is, often the source is being cited for something that's a minor part of what they were talking about -- and the major part is even more interesting. In oceanography, one of the things often mentioned in classes is the Ekman Layer. Don't worry about what it is exactly. Usually, a reference says that Ekman (1905) studied the formation of what we now call the Ekman layer for conditions of an infinitely deep ocean, infinitely steady winds, with absolutely constant friction through the depth of the ocean. Well, it turns out that, although he did examine that highly idealized case, this was a small part of the paper. In fact he also examined varying winds and varying friction. And the results of doing so were much more interesting than what he's normally cited for.
A second reason can be particularly important in science. In the original papers on an idea, the author is explaining something new to the audience. He can't assume nearly as much as later papers on the idea will. You'll also get to see the first matchups of the idea against observations. So I usually learn more by reading the original than by reading the textbook description. (For the geophysical fluid dynamicists out there -- Charney's paper on baroclinic instability is the one exception I've found. There also turn out to be reasons why it came out that way.)
Part three is that you'll get to see much more discussion of why the approximation can be made, and where it can be expected to fail. So, for example, a modern paper talking about the color of the sky -- perhaps for a planet orbiting some other star -- will merely mention 'We apply Rayleigh scattering law and arrive at ...'. It's only when you read Rayleigh's papers that you find out that the 'law' is an approximation, and it will fail under certain, predictable, conditions.
It can be difficult to get hold of the original sources when you start going after Reynolds 1895, Ekman 1905, etc. So the ideal can't always be met. Still, the whole IPCC working group 1 (physical science) 4th report is readily available online or you can order a print copy (also groups 2 and 3, but I'm a physical science guy, so look more to that one). So, when you encounter someone making claims about what the IPCC says, go take a look yourself. And if the point isn't clear, or it is interesting to you, start following up the citations they give. (Unfortunately, I think that after the first report, the writing declined in terms of readability by nonprofessionals. Any more, once you're past deciding if someone lied about the IPCC, I think you'll have an easier time reading by hitting the cited sources rather than the IPCC reports.)
There are also more pleasant reasons to follow up to original sources. One is, often the source is being cited for something that's a minor part of what they were talking about -- and the major part is even more interesting. In oceanography, one of the things often mentioned in classes is the Ekman Layer. Don't worry about what it is exactly. Usually, a reference says that Ekman (1905) studied the formation of what we now call the Ekman layer for conditions of an infinitely deep ocean, infinitely steady winds, with absolutely constant friction through the depth of the ocean. Well, it turns out that, although he did examine that highly idealized case, this was a small part of the paper. In fact he also examined varying winds and varying friction. And the results of doing so were much more interesting than what he's normally cited for.
A second reason can be particularly important in science. In the original papers on an idea, the author is explaining something new to the audience. He can't assume nearly as much as later papers on the idea will. You'll also get to see the first matchups of the idea against observations. So I usually learn more by reading the original than by reading the textbook description. (For the geophysical fluid dynamicists out there -- Charney's paper on baroclinic instability is the one exception I've found. There also turn out to be reasons why it came out that way.)
Part three is that you'll get to see much more discussion of why the approximation can be made, and where it can be expected to fail. So, for example, a modern paper talking about the color of the sky -- perhaps for a planet orbiting some other star -- will merely mention 'We apply Rayleigh scattering law and arrive at ...'. It's only when you read Rayleigh's papers that you find out that the 'law' is an approximation, and it will fail under certain, predictable, conditions.
It can be difficult to get hold of the original sources when you start going after Reynolds 1895, Ekman 1905, etc. So the ideal can't always be met. Still, the whole IPCC working group 1 (physical science) 4th report is readily available online or you can order a print copy (also groups 2 and 3, but I'm a physical science guy, so look more to that one). So, when you encounter someone making claims about what the IPCC says, go take a look yourself. And if the point isn't clear, or it is interesting to you, start following up the citations they give. (Unfortunately, I think that after the first report, the writing declined in terms of readability by nonprofessionals. Any more, once you're past deciding if someone lied about the IPCC, I think you'll have an easier time reading by hitting the cited sources rather than the IPCC reports.)
17 March 2009
What is a good question?
I've often heard the comment that much of science is asking good questions. That's true. I also heard often in school that there are no bad questions, which is reasonably correct also. But there can be quite a distance between not bad and good. I can't, however, remember anybody describing how to go about asking better questions. There are probably many different ways of improving, so, as usual, I invite comments.
An important part of a good question is, it will be clear that it has been answered. Start with the not-bad question "What's up with climate?" Maybe you answer talking about sea ice and polar bears. But I'm unsatisfied because what I wanted to hear about was global temperatures. So I ask the improved question "What's up with global temperatures?", and you answer talking about how the stratospheric temperatures have dropped and surface temperatures have risen lately. But I'm still unsatisfied, because I don't care about the stratosphere, and the surface temperatures I care about are the ocean's. So now I ask "What's up with ocean surface temperatures?", and you say 'not much', or, maybe, 'they've risen'. Again, I don't have an answer. You're doing your best, and being honest, but the questions just aren't strong enough.
A strong question is "How much has global mean sea surface temperature changed over the past 150 years, and what are the uncertainties in that number?" This, neither you, nor I, nor any random spectator will have any difficulty telling whether I've gotten an answer to my question. It'll be something like "risen by 0.5 C and 0.1 C standard error in that estimate". Whether 0.5 and 0.1 are correct, I don't know offhand. But, at this point, the question has an answer which is fill in the blank. We can then hit the literature (say IPCC Ch. 3 and the citations in that chapter) looking for it. If the question didn't have an answer waiting for us in the literature, we also know how to start doing our research -- look for data sources about ocean surface temperature, that are distributed over the globe, and which go back 150 years (or more, of course).
A different strong question is "Why is the sky blue?" No reason that young kids can't be asking strong questions. An answer to this question must adress why the sky is blue, as opposed to green. And a strong answer will tell you how blue it will be under different conditions. If, for instance, you have a high humidity and many aerosols, the sky tends towards white -- under the action of the same process which tells us that the sky (away from the sun) is very blue when the air is clean and dry. (Rayleigh scattering).
Questions that start "What about ...", "How about ...", "What's up with ..." are almost never strong questions. Strong questions usually start "How much ...", "How fast ...", "How big ...", or say "How well do we know ...".
If we really don't know much about an area, which is the case for us for most areas of human knowledge, it can be hard to ask strong questions. So we start with the not-bad questions aimed at learning more about the area, and keep asking them until we can ask strong questions. Hence my 'question place'.
An important part of a good question is, it will be clear that it has been answered. Start with the not-bad question "What's up with climate?" Maybe you answer talking about sea ice and polar bears. But I'm unsatisfied because what I wanted to hear about was global temperatures. So I ask the improved question "What's up with global temperatures?", and you answer talking about how the stratospheric temperatures have dropped and surface temperatures have risen lately. But I'm still unsatisfied, because I don't care about the stratosphere, and the surface temperatures I care about are the ocean's. So now I ask "What's up with ocean surface temperatures?", and you say 'not much', or, maybe, 'they've risen'. Again, I don't have an answer. You're doing your best, and being honest, but the questions just aren't strong enough.
A strong question is "How much has global mean sea surface temperature changed over the past 150 years, and what are the uncertainties in that number?" This, neither you, nor I, nor any random spectator will have any difficulty telling whether I've gotten an answer to my question. It'll be something like "risen by 0.5 C and 0.1 C standard error in that estimate". Whether 0.5 and 0.1 are correct, I don't know offhand. But, at this point, the question has an answer which is fill in the blank. We can then hit the literature (say IPCC Ch. 3 and the citations in that chapter) looking for it. If the question didn't have an answer waiting for us in the literature, we also know how to start doing our research -- look for data sources about ocean surface temperature, that are distributed over the globe, and which go back 150 years (or more, of course).
A different strong question is "Why is the sky blue?" No reason that young kids can't be asking strong questions. An answer to this question must adress why the sky is blue, as opposed to green. And a strong answer will tell you how blue it will be under different conditions. If, for instance, you have a high humidity and many aerosols, the sky tends towards white -- under the action of the same process which tells us that the sky (away from the sun) is very blue when the air is clean and dry. (Rayleigh scattering).
Questions that start "What about ...", "How about ...", "What's up with ..." are almost never strong questions. Strong questions usually start "How much ...", "How fast ...", "How big ...", or say "How well do we know ...".
If we really don't know much about an area, which is the case for us for most areas of human knowledge, it can be hard to ask strong questions. So we start with the not-bad questions aimed at learning more about the area, and keep asking them until we can ask strong questions. Hence my 'question place'.
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