Friday, June 20, 2008

Anthropogenic Global Warming is Absolutely Occurring

[Reposted at Residual Analysis.]

I need to ask for the reader's indulgence, as this post is not about autism, except insofar as determining the merit of correlations has become a perseveration of mine. You see, it is trivial to come up with naive correlations of autism trends vs. practically anything about the modern world. The administrative prevalence of autism has been increasing almost always since records have been kept. Concurrent upward trends of nearly anything, from vaccines to environmental pollution, from trans fats to electromagnetic radiation, and so on, are easy to come by.

In my latest post at LB/RB I suggested that instead of correlating trends in a naive manner, we could attempt to correlate the residuals of time regression models of each trend. A residual is a delta or difference between an observed value and a modeled value. (Here's a concise explanation).

When modeling real world phenomena, regression models will never (or almost never) be perfect fits. For all sorts of reasons, even if simply random fluctuation, there will be deviations from a modeled trend. If there's a causative relationship between two trends, the residuals of (or deviations from) corresponding close-fitting regression models should correlate with one another as well. By this I don't mean that the residuals should always be in the same direction; but they should be in the same direction more often than not, in average.

The nice thing about this technique is that it is completely accessible to anyone with Excel installed. It can also be illustrated graphically, as the reader will see.

So it occurred to me to test this idea in a different field of science where there's controversy over correlation vs. causation. I thought global warming would be a great candidate. After all, the spoof about a decrease in the number of pirates correlating with many other arbitrary trends appears to originate in the global warming debate (see this).

To summarize what I found, there is a strong and statistically significant correlation between cumulative human CO2 emissions and northern hemisphere temperature anomalies. Because of the methodology used, I'm quite confident this cannot be explained by coincidence, data collection errors, solar output as a confound, or causation in the opposite direction.

Now, I fully recognize that I'm only superficially familiar with the debate over anthropogenic global warming. I am also not versed in climatology. Therefore, I cannot be entirely sure that this type of analysis hasn't been done before. Google and Google Scholar searches didn't seem to turn up anything, and given the importance of the topic, I thought it was not only prudent but necessary to put this evidence out there. As always, scrutiny and discussion are welcome.

Northern hemisphere temperature data from 1850 to 2004 was obtained from the Climatic Research Unit of the University of East Anglia, UK.

Global CO2 emission data was obtained from CDIAC. I did not use CO2 atmospheric concentration data because temperature increases can theoretically cause this concentration to increase. Human emissions are what we're interested in. More specifically, I calculated cumulative CO2 emissions for every year since 1850. Greenhouse temperature anomalies are presumably caused by the total amount of CO2 in the atmosphere, not by the emissions in any given year. Since CO2 stays in the atmosphere for 50 to 200 years (source) modeling the cumulative human contribution of CO2 should be adequate enough.

Figure 1 (click to enlarge) is a graph of the general time trends of these two sets of data. It also shows the modeled trend lines we will use to calculate residuals. In this analysis we're using third-order polynomial models. They seem to give a considerably closer fit than second-order polynomial models.



I calculated the residuals and built a scatter graph matching cumulative CO2 (X axis) and temperature (Y axis) residuals for each year from 1850 to 2004. As expected, the slope of a linear regression of the scatter was positive (1.9x10-5) and statistically significant (95% confidence interval 1.13x10-5 to 2.66x10-5).

[Note: Instructions on how to calculate the slope confidence interval of a linear regression with Excel can be found here.]

I suspected, however, that there should be lag between cumulative CO2 fluctuations and temperature fluctuations. It presumably takes some time for heat to be trapped. I proceeded to create a moving average trend line of the temperature residuals. It did in fact have a similar shape to the cumulative CO2 residuals graph, but it appeared to lag it by about 10 years. The reader should be able to roughly see this lag in Figure 1.

So I re-ran the whole analysis by only considering the years 1850 to 1997 and correlating CO2 residuals with residuals of temperature 10 years later. The correlation between these two sets of data is remarkable. Let's start with a bar graph of both sets of residuals, Figure 2.



Figure 2 is a good graph to get a subjective sense of the correlation. Let's see if the math confirms this. Figure 3 is the scatter graph of the residuals.



The slope of a linear regression of the scatter is 2.6x10-5, and it is statistically significant (95% confidence interval 1.88x10-5 to 3.33x10-5). Even the 99.99999999% confidence interval is entirely positive. Unless anthropogenic global warming is a reality, there is no apparent reason why the residuals of cumulative human CO2 emissions should correlate so well with the residuals of temperature 10 years later throughout the last 150 years.

The slope of the scatter is actually more steep than expected, if you consider the naive correlation between cumulative CO2 emissions and temperature. There are probably several reasons for this. The one I believe to be the most likely is that over time CO2 does get removed from the atmosphere. Adding this consideration to the analysis should produce a more accurate slope. The other potential reasons don't bode so well for our species.

39 comments:

  1. I discovered your blog through your comment on Russ Wilcox's "Forthegrandchildren" blog.

    Your comment policy is refreshing in view of the fact that Wilcox routinely deletes comments from those who disagree with him.

    Incidentally, I am the grandfather of a severally autistic 6 year old boy, so i'll be returning to your blog with some frequency

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  2. Edward Townes6/21/2008 1:42 PM

    Couple of comments;

    1) Beware of the temperature data. They claim they have corrected it for distortions, but they really haven't. www.climateaudit.org talks about that.

    2) Correlation does not equal casuality, but it does raise an issue.

    3) You are looking for a correlation between CO2 and temperature in a time period that amounts to a near infinitesimal blip in Earth's history.

    4) There is good data for the last million or so years that shows CO2 has a dependence on temperature and trails it by roughly 500-800 years.

    5) There is a much better correlation between sun activity and temperature over this same period.

    Otherwise this is interesting, I haven't looked closely at the maths, but it looks solid.

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  3. Thanks for stopping by, Edward.

    Beware of the temperature data. They claim they have corrected it for distortions, but they really haven't. www.climateaudit.org talks about that.

    Note that in this analysis, data distortions cannot explain the results. It doesn't matter if thermometers have a bias that changes with time. What this analysis looks at are deviations from the trend. The final correlation found cannot in any way be explained by measurement errors or bias (unless the errors were intentionally introduced anticipating this type of analysis).

    You are looking for a correlation between CO2 and temperature in a time period that amounts to a near infinitesimal blip in Earth's history.

    What matters is that there's statistical significance in the findings.

    There is good data for the last million or so years that shows CO2 has a dependence on temperature and trails it by roughly 500-800 years.

    That temperature increases can cause CO2 increases (due to ocean emissions) is accepted, and has no bearing on this analysis. I'm looking at cumulative CO2 emissions estimated from fossil fuel production. I'm finding a lag in the opposite direction.

    There is a much better correlation between sun activity and temperature over this same period.

    That sun activity correlates with temperature is expected, and has no bearing on this analysis.

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  4. Bud, you might want to check out the Autism Hub.

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  5. Edward Townes6/21/2008 2:42 PM

    Ok, fair enough.

    This is an interesting way of looking at it, and logically there should be at least some dependence.

    Another angle of attack is to mathematically calculate the contribution CO2 molecules make in terms of electromagnetic absorption and re-emission, and scale it with a model for the whole planet. When they do that, they find that the contribution is both logarithmic and very small. The models include multiplier effects and feedback mechanisms to enhance the effect of a small increase in CO2.

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  6. Another angle of attack is to mathematically calculate the contribution CO2 molecules make in terms of electromagnetic absorption and re-emission, and scale it with a model for the whole planet. When they do that, they find that the contribution is both logarithmic and very small. The models include multiplier effects and feedback mechanisms to enhance the effect of a small increase in CO2.

    I guess that goes to plausibility of the greenhouse effect. That's clearly important. I assume the scientific consensus is that it is plausible. But I don't know enough to comment on it. All I know is what I found statistically in terms of observed data.

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  7. Now that's interesting, thanks for linking me.

    Can you remind me what the scatter of residuals and its slope tells us? My statistics are a bit rusty, and this might be useful to others as well.

    I wonder if any current research could explain the 10 year lag. You might also consider trying this with a program besides Excel, if you haven't already. I recall that some regression and other statistical functions in Excel vary slightly from methods typically employed in science. Probably not enough to alter your result fundamentally, but it might be worth checking.

    Re Townes:

    Solar forcing may have some contribution to warming, but the mechanism, if there is one, is still unknown, as is its significance.

    It seems unlikely based on all I've seen on the subject that it's a bigger deal than human activity, but I guess we'll learn more as further work is done.

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  8. Can you remind me what the scatter of residuals and its slope tells us? My statistics are a bit rusty, and this might be useful to others as well.

    Here's an explanation that might be helpful.

    A scatter is a graphical representation of the association between two variables. In Figure 3 of the post, the two variables are CO2 residual (X axis) and temperature residual (Y axis). A dot in the scatter represents a year. For example, the uppermost dot in the upper-right quadrant is 1853 (actually 1863 for temp because of the 10 year lag). That was a year with relatively high cumulative CO2, compared to the modeled trend. It was also a year of high temperature, relative to the modeled trend.

    Theoretically, there's only a 5% chance that two independent variables would have a statistically significant trend (linear regression slope) in a scatter. But in the analysis I did, I can go further and say the variables are not independent with 99.999...% confidence.

    The variables in this case are deviations from predicted trends. The deviations run in both positive and negative directions. That these associate cannot be easily explained as coincidence.

    I wonder if any current research could explain the 10 year lag.

    No idea. Maybe a climatologist could confirm if this is a known finding. BTW, 10 years is an approximation. It could be anywhere from 9 to 12 years or so. It also probably depends on the concentration of CO2. Higher concentrations might take longer to turn into higher temperatures (which would be bad). What I found is applicable to the relatively small fluctuations from the trend, and the effect is relatively steep.

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  9. Very nice work, Joseph. I came here from Jonestown, where you left a comment on my post about John Coleman. I actually used to run a climate change blog, but got too busy to keep it up.

    One of the confounding things about all of this is how complex it really is. There are multiple forcings, both positive and negative, and many feedbacks too. So, our climate and how it changes are things that we are still learning about, and the more we learn, the more we find that we are indeed affecting it.

    If I could, I'd like to address some of Edward's obfuscation:

    1. The one "distortion" that people at sites like climateaudit.org like to discuss is the urban heat island effect. NASA has indeed corrected their data for this effect by using surrounding rural stations as a guide for nearby urban stations. No data is perfect, but there is no government conspiracy to produce a positive trend in temperature data, as McIntyre would insinuate.

    2. True. Correlation definitely does not equal causality, which is why so much research has been done on the subject help discover causality beyond correlation. We now have radiative forcing values for many contributing forcings, extremely accurate models, etc. Critics will brush all of this aside as "pseudo-science", but I haven't seen any credible, peer-reviewed scientific research to back up these claims.

    3. That this time period is a "blip" in Earth's history has no bearing not only on this particular statistical analysis, but also as a whole. We know that it takes a certain amount of time for certain greenhouse gases to get into the atmosphere, how long they stay up there, and what effect they have while up there. Period.

    4. Again, irrelevant. Sure, CO2 was once more of a feedback in a time before humans could mass produce it. Now, we emit much more CO2 into the atmosphere than the planet's natural carbon sink can absorb, leaving excess amounts to absorb more infrared and radiate more heat. Also, we know that, although the oceans emitted CO2 in the past, this is not happening presently because we know the oceans are absorbing more and more CO2.

    5. Just as correlation doesn't equal causation, neither does "better correlation" equal causality. A simple examination of the Sun's energy output would show that it cannot have a significant effect on climate change. True, the Sun's total output is enormous (1366 watts per meter squared). However, the fluctuation - which is what is important when discussing climate change - in its output is only 1 W/m^2, or about 0.07%. Now, that is the total change. The theory is that changes in the length of the Sun's approximately 11-year cycles are what cause changes in temperature. So, assuming we're talking about fluctuations in the cycle of about a year or so, we will need to divide by another factor of ten. This does not equal a significant effect on our climate.

    Now, there is also the unproven theory of cosmic ray flux/cloud formation, but only small correlations have been found between the two, and many problems remain to be addressed.

    Nice work on the statistics, Joseph. I enjoyed this post.

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  10. Thanks Reasic.

    One of the confounding things about all of this is how complex it really is. There are multiple forcings, both positive and negative, and many feedbacks too.

    And that is precisely the sort of thing this type of analysis attempts to control for - arbitrary time-dependent variables.

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  11. You seem to know statistics. You might like Tamino's site:
    http://tamino.wordpress.com/

    He (ok, could be she for all I know) looks at various Global warming issues using statistics, and seems to know what he is doing. And he'd probably agree with your post.

    The other important thing to remember about global warming is that there are several things predicted by the "extra greenhouse gases causes more warming" theory. Such as a cooling stratosphere, which would not happen if the extra energy was coming from the sun. I think another successfully fulfilled prediction is that it would get warmer at the higher latitudes in the northern hemisphere. Anyone seeking to explain away the current observations will also have to explain why stratospheric cooling isn't really happening.

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  12. Thanks guthrie. I've left a comment over there.

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  13. "That sun activity correlates with temperature is expected, and has no bearing on this analysis."

    "It could be anywhere from 9 to 12 years or so. "

    A Solar cycle (for sun spots) is 11 years long. Active solar cycles increase temps. The new and current Solar cycle is weaker.

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  14. I did not see Reasic's post number 5.

    However the question still remains. How much (or little) change in solar activity and for how long would have a global impact on temperatures (positive or negative)? How would this effect CO levels? Lower CO levels will reduce agricultural output. What is the optimal CO level from a human perspective?

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  15. A Solar cycle (for sun spots) is 11 years long. Active solar cycles increase temps. The new and current Solar cycle is weaker.

    Right, but a lag and a cycle are very different things. As you can see in Figure 2, the cycle of the residuals is roughly 80 to 90 years, although it seems to change. This is just how the human-caused cumulative CO2 cycle changes relative to the third-order polynomial fit. This cycle is what is clearly driving temperature fluctuations roughly 10 years later. (I've done additional calculations and the lag is actually between 7 and 9 years, probably 8).

    If we were to plot SunSpot number residuals, for example, in Figure 2, you'd see that's a much tighter cycle. And BTW, it does not correlate with cumulative CO2 emissions. (I actually had confirmed this).

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  16. "And BTW, it does not correlate with cumulative CO2 emissions."

    What is the lag time between solar activity and global tempratures?

    I do know the difference between lag time and cycles.

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  17. What is the lag time between solar activity and global tempratures?

    I don't know the official answer to that, but I did do this comparison. One year after gives a slightly better slope than the same year. It deteriorates after that. So I'd say it's most likely 1, but could be 0, which would make sense.

    (I do not get statistical significance comparing SunSpot to temperature residuals, btw, just a trend, but that might be just because I don't have enough data points).

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  18. I've started a new blog called "Residual Analysis" that I will use for non-autism posts like this one. I don't think it will be an active blog.

    I've written a post on the association between storms and global warming.

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  19. I am replying to your post on my blog. I think this is good work overall, the statistics involved are still over my head although I may sit down and study them. Because of this I cannot comment on your math (I am impressed by the 99.999% correlation).

    It dosn't answer my question of whether or not CO2 causes temperature increases. I do not doubt the correlation just the causeation.

    One other problem I have is that it has not been demonstrated in a controlled lab environment that CO2 increases cause temperature increases. That really does not bode well.

    Other then that I like your work in Autism. I supposedly has aspbergers syndrome (I will deny it to the death!!!) and so this is interesting. Keep working at it.

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  20. Hi Nowhereman. I can appreciate that the method is not straightforward. What I attempt to do with this sort of post is go over the analysis in a way that can be followed (and replicated) by someone who is not necessarily versed in statistics. I personally see that the data is completely convincing. I'd like others to see it as well. This is not necessarily easy to do.

    Let me explain it in a different way. There's a general trend of cumulative CO2 emissions. But actual cumulative CO2 emissions have a wobble around the trend. The same is true of temperature. The thing is that the wobbles around CO2 and temperature trends match almost perfectly. Also, the temperature wobble lags the CO2 wobble by about 8 years.

    Correlation is not causation, but when you have this repeating and consistent pattern, I don't see what other than causation could explain it. If CO2 is not causing temperature anomalies, then it would have to be something else that associates with human CO2 emissions.

    As far as I'm concerned, AGW is proven. Anyone who feels otherwise is just unfamiliar with the data.

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  21. Oh no I understand you statistics and your reasoning. I am not fully aquainted with your methodology as I have taken only basic statistics courses and am only familiar with the pearson correlation. (I excelled in hypothesis testing though and received an A and an A-... still mad at myself for the A-)

    As I said I understand the basic theory behind your argument and am working on figureing out this new kind of analisis.

    My only suggestion is that you state your findings cautiously if your intent is mearly to demonstrate the effectiveness of your method. If your intent is to prove a point then I would say you have done a good job of advancing your point to legitamacy.

    One other thing I thought of while picking up garbage in the hot sun at work today. I thought over your analisis and am trying to figure out a hypothesis test for this and the best I came up with that does not require a controlled lab experiment is an ANOVA test. The two IVs would be CO2 and Solar irradiance and the DV would of course be temperature. My logic is that if you take the early portion of the industrial revolution and compare it to the mid section and our much later end section then it stands to reason that as the early portion had little anthropogenic damage then the temperatures would be lower then later on.

    I like this as you can also see if their is an interaction between CO2 and solar irradiance. I figure that CO2 though wont warm the atmosphere it may slow its cooling a little, and hense an interaction.

    I still don't like this much though as it is not controlled and so any data that comes out of it is colored by this one way or the other. I don't know though how to build a controlled experiment though that would be acceptable. So my problem will continue with AGW for awhile till I see something convincing (other than corelations no matter how astounding they are)

    One final note, GHG emmisions may not be the most accurate measure so try instead world consumption of hydrocarbons (natural gas, oil etc...). That may be a more accurate measure.

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  22. I thought over your analisis and am trying to figure out a hypothesis test for this and the best I came up with that does not require a controlled lab experiment is an ANOVA test. The two IVs would be CO2 and Solar irradiance and the DV would of course be temperature.

    Without knowing much about the AGW literature, I predict there are dozens of papers that do multivariate analysis of CO2 and Solar irradiance, and do find CO2 to have an independent effect. The problem is that multivariate analysis is too abstract and probably not convincing to most laypeople.

    Another problem with multivariate analysis is that there can always be a variable you did not control for. Plus the modeling in multivariate analysis might not be adequate. For example, you might include 'year' as a variable to control for unknown time-dependent variables. But the part of the equation that controls for year will not be nearly as good a fit as the third-order polynomial fit I'm using in this analysis (which essentially amounts to a tight control for 'year' applied to both variables).

    One final note, GHG emmisions may not be the most accurate measure so try instead world consumption of hydrocarbons (natural gas, oil etc...). That may be a more accurate measure.

    This page explains how CDIAC emission statistics are estimated. It's based on production. It's reasonable to suppose that most of what's produced is consumed; or what's consumed is uniformly reflected in what's produced, year after year. Either way, I made it a point to only consider anthropogenic emissions and not emissions from other sources.

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  23. Edward Townes makes AT LEAST two statements that are provably false.

    One is that temperature always leads C02. It's a chicken-egg cycle around the start and end of glaciations, and other times, such as supervolcanoes going off, after the particulates settle the GHGs clearly lead temperature, unambiguously.

    Another is that the temperature data is not corrected for distortions. Not only is that false - in fact, most of the historical temperature distortions happened to minimize and mask the actual warming - but when a small subset of the temperature record, namely a fraction of US surface temperature, through multipurposed weather stations were claimed by Anthony Watts, a non-scientist in thrall to Stephen McIntyre, a non-climate-scientist, his crew took photos of weather stations and claimed they were distorting the record. Unfortunately for Watts, when he was put on the spot and forced to quantify the distortions, he HAD TO ADMIT they were imperceptible. It was a huge, glaring defeat for the climate audit people. They simply think the word has not gotten out yet.

    This doesn't detract from the basic point that the analysis accounts for noise like allegedly distorted surface records. It just means that the countervailing "evidence" is nonexistent the instant it's scrutinized.

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  24. Just writing to invite you to join a new social support group for Autism @ http://www.weareautism.org. Would love to hear your feedback and thoughts.

    Regards.

    Stephen

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  25. This is wonderful page. Keep up the good work!

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  26. I have been thinking over your methodology once again at work and figured something out. (I think often and do so that I may one day be good enough to come up with theories of my own relating to Psychology (my chosen field).

    There is a flaw in this here. The flaw is simple really. By using CO2 emmisions instead of atmospheirc CO2 concentrations you have caused a problem. As has already been stated by minds greater than my own, we produce only 5% of the CO2 that is created. Granted 5% is huge, very Huge, but not on a scale like this. Simply put there is too much going on in nature to simply ignore it. Lets say we massively increase our CO2 production by 300% but nature dropps her production by 20% - 30% due to natural variation. This would cause a drop in CO2 concentrations and hense a cooling.

    I still do not buy that CO2 causes warming, infact I think it more likely that CH4 would cause these effects though I am not sure to what degree. But I was not critisizeing AGW just this particular methodology. I hope you understand my objection to this work.

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  27. I don't understand how you handle the fact that the earth has cooled in the last 10 years.

    How is that fact displayed.

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  28. I don't understand how you handle the fact that the earth has cooled in the last 10 years.

    It is handled primarily by its being untrue. I've seen the data myself. Here's Tamino's deconstruction.

    Secondly, it is handled by it being irrelevant. Long term I don't see any significance in the trend of the last 10 years. There's a lot of noise in the data, which is clear from Figure 1.

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  29. Good grief!

    There is too much wrong with this analysis to do a thorough critique, but here's a couple of points:

    1) When you're trying to validate a theory, you have to use measurements of what's ACTUALLY IN THE THEORY. For AGW, this means you have to model the CO2 concentrations in the atmosphere. You cannot choose related measurements like estimated human emissions of CO2 just because they make your case better. It wouldn't be much more ridiculous to regress global temperature against the residual emissions of Joseph's own car!

    2) If you wish to prove Anthropogenic Global Warming, you'll need to use temperatures from the whole globe. You cannot simply ignore the entire Southern Hemisphere. And you really should test other temperature data sets using your methodology, especially the UAH and RSS satellite measurments, which although not perfect, are at least a consistent measurement across the whole planet.

    Also, there's not a thinking person on the planet who disagrees that from 1850 to present both carbon dioxide and temperature have increased. That alone will cause a positively-sloped line. There is nothing at all impressive about your statistics.

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  30. Jim, your points are unconvincing.

    1) If I'm trying to show that human CO2 emissions cause global warming, I should model human CO2 contribution vs. temperature.

    Of course, I could also model CO2 atmospheric concentrations vs. temperature, but then you or someone else would say, "well, maybe temperature causes CO2 levels to go up." (Furthermore, there aren't as many data points available as far as observed CO2 concentrations - a technical point).

    If you must know, there's a clear correlation between cumulative CO2 emissions and measured atmospheric concentrations. I've looked at this data as well.

    2) If you think that the analysis won't hold if I look at global temperatures as opposed to NH temperatures, you're dreaming, frankly.

    Also, there's not a thinking person on the planet who disagrees that from 1850 to present both carbon dioxide and temperature have increased. That alone will cause a positively-sloped line. There is nothing at all impressive about your statistics.

    You don't have to be impressed by my statistics, but it would be nice if you'd at least read them. As I explained, coincidental trends are controlled for via detrending.

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  31. 1) If you would like to posit a new theory that human emissions of CO2 cause global temperatures to rise irrespective of all other CO2 in the atmosphere, you should publish it to the world.

    But that is NOT the theory of AGW, as you have implied in your title. By your conjecture, we should believe that even if nature sequesters CO2 faster than humans emit it, the temperature would still rise. I'd love to see that theory fleshed out.

    2) Since the Southern Hemisphere has shown virtually NO warming for at least thirty years, inclusion of this temperature data will further weaken your already-weak statistical conclusions.


    I would be happy to read and comment on your explanation of "coincidental trends are controlled for via detrending." But since your latest comment was the first time you've mentioned detrending in this post, I'll need a link to wherever you might have expounded such explanation.

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  32. Jim...

    1) Your nitpick of terminology is irrelevant. It's well known that atmospheric CO2 has gone from about 300 ppmv to 370 ppmv in the last 50 years, and this increase is anthropogenic. The atmospheric half-life of CO2 is high, probably 70 years.

    And as a matter of fact, I've repeated the analysis considering a half-life of CO2 and the results are the same.

    There is a correlation with high statistical significance, and it can't be explained away simply because you think it would've been better to do the analysis in some other way, or because you think I didn't use the proper terminology to describe things.

    2) The NH has warmed faster, and it's not difficult to imagine why that is. While the slope would not be as steep in a SH analysis, I can assure you it will still be there.

    Finally, while I didn't mention detrending in this post, that's for all practical purposes an equivalent way to look at what I did. I compared the residuals of the time series trends. That's effectively the same as comparing detrended time series.

    I think I did mention a few times that the whole purpose of doing this analysis is to show how coincidental trends can be controlled for. I wouldn't have bothered otherwise.

    If you can suggest a different method that can be used to control for possibly coincidental trends, do let us know.

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  33. The same goes for nowhereman, whose last comment I had missed previously. Cumulative CO2 emissions model atmospheric concentrations rather well.

    Clearly, there must be CO2 emissions from other sources, but those emissions are roughly in equilibrium with the environment, enough to keep the atmospheric concentration between 260 and 280 ppmv. The current level of 370 ppmv means our contribution is about 90 ppmv.

    If I model cumulative CO2 vs. atmospheric concentration, I get a nearly perfect fit. I can get slightly better fits if I assume a half-life. I've modeled different half-life assumptions, and the best seems to be 70 years.

    And as I said, using data corrected for a half-life of 50 years produces the same result. The general trend is roughly the same with high half-lifes like this.

    Again, there's a correlation, and it can't be explained away by imprecisions in the data.

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  34. Thank you very much. This was a great help.

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  35. My expertise in this topic is quickly being pushed to its limits so I probably will have to make this my last reply here.

    I understand your argument regarding my question referring natural causes but it is predicated on the assumption that both CO2 and temperature readings are evenly distributed. Not a bad assumption as most things are evenly distributed. Unfortuanately one look at the Petit et al. analysis of the Vostok cores reveils that this isn't true.

    The cores show that temperature is heavily left leaning for the vast majority of time until about ten thousand years ago at which point for a reason I cannot fathom it changes into a cyclical cycle of upward and downward trends +- 1 degree C above and below current temperatures.

    Although the Petit et al. mesurements stop about 2k years ago it it is obvious that we could very well be at a peak right now and just happen to have started our industrial revolution at the same time it was going up, ie nature is affecting temperatures and not us.

    I know of no fault on your part with regard to this, your math or what little I know of it seems sound. The problem lies with the many who seem to use science to push their agendas instead of figureing out how the world works. Keep up fighting the good fight and of course read both sides of the debate, even if a person or persons involved have no idea what they are talking about, it is always educational.

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  36. I would expect that cumulative fuel usage and Urban Heat Island effects would also correlate, perhaps with a time lag as well. There is a fair amount of evidence that UHI effects contaminate the temperature record -- see the "Watts up with that" blog. How do you know that you are not simply measuring this correlation? It is a Human-caused temperature rise, although limited to urban areas and not relevent to the entire globe.

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  37. Anon: I don't think global cumulative CO2 emissions would confound heat-island causes. You need to consider the detrending. A fluctuation of cumulative emissions would have to cause a fluctuation of the heat-island effect, with a pretty good lag. That's a bit convoluted.

    The cumulative CO2 model is a good model for the total amount of excess CO2 in the atmosphere that is anthropogenic. I'm not sure the same thing works when we're talking about cities. The urban heat-island effect is caused by buildings, mostly.

    It's not just emissions either. In this post I show that CO2 concentrations as ascertained from ice cores have basically the same 3rd-order detrending as cumulative CO2 emissions.

    As to temperatures, I'd suggest using sea surface temperatures instead. No urban confounding there. To get an idea of how SSTs would detrend, see this graph of the 15-year central moving averages of SSTs in the northern hemisphere.

    Of course, there are also standard responses to your proposed confound, e.g. this explanation by RealClimate.org.

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  38. quranreading12/28/2008 9:28 PM

    Global warming is the huge threat for all world.No one is thinking,How to over come it.But day by day new technologies are introducing which are basic reasons of global warming.

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  39. Great synthesis of the data. I agree. But I can never figure out why there is always so much controversy around this issue.

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