Gore’s Graph Done Right

Thanks in large part to Al Gore’s book we’ve all seen the graphs showing temperature and CO2 levels for the last 600,000+ years (reproduced below). For many people today the image below serves as the iconic image of global warming. Al Gore even climbed onto a scissor lift to help make it so. Climatologists know that CO2 is a greenhouse gas; no one disputes this, and the graph underscores this by showing that, for the past 650,000 years, the peaks and valleys in temperature match up nicely with peaks and valleys in CO2. Mr. Gore then climbs onto the scissor lift, raises it up well above the screen displaying the graph and points out where CO2 levels are today, where they may be in 50 years and asks you to envision what the temperature will be like in 50 years.

dualplusnow

The data in this graph comes from the study of ice cores in Antarctica and Greenland. Many books, when discussing ice core data, give a background of the science behind the data. We’re skipping that here. Instead we’ll accept the data as given and spend more time analyzing what the data means. But before we go on, can we accept the data as given? Despite the fact that the science behind ice core data is somewhat involved, none of the raw data is being questioned by anyone, skeptics and believers agree that the data in these charts are accurate. Many lay people wonder how it is possible to get temperature and CO2 readings for 600,000 years ago, but understanding how the data is collected is not necessary to understanding the lessons that the data is trying to teach, especially when there is no scientific dissent about this data. We can take it as given and move on.

dualsmall

Same Data, Different View

Now let’s return to Al Gore’s temperature and CO2 graph. This technique, of showing multiple pieces of data on the same graph is one of several that scientists use, especially if they have reason to believe that the data are correlated. It can highlight certain features and it is a very simple graph to understand as it is merely a combination of two even simpler graphs, a temperature vs year and a CO2 vs year graph.

temp_co2Fortunately there are other ways to display data where we expect a correlation. Here, we’re expecting a correlation between CO2 levels and temperature. The graph above shows CO2 vs year and Temperature vs year, and we can see the correlation; the peaks and valleys in both graphs line up fairly well. But do we really care about the year? We accept that CO2 is a greenhouse gas and that large quantities of it in the atmosphere will cause temperatures to rise. But now that we’ve accepted that, aren’t we more interested in how high the temperature will rise for a given CO2 level? How strongly the CO2 and temperature are correlated with each other? One way to answer these questions is to remove the year from the graph and plot CO2 and temperature directly.

correlateraw

purelineThe graph above shows the 400,000 year ice core data plotted as we’ve been discussing. The first thing that stands out is that all the points do not fall on a neat little line. If variations in CO2 levels were the only thing that caused variations in temperatures then all the points would line up. But in reality there are many other things that cause temperature variations. Four hundred thousand years is a long time and the earth has seen a lot of changes in that time. Other greenhouse gasses besides CO2, methane for example, undoubtedly rose and fell during this time frame. The earth’s orbit changes significantly every 100,000 years, time enough for four cycles for the data shown above. And there were some large volcanic eruptions during this period, which put up clouds of material that have a cooling effect on the planet. And there are many other non-CO2 related causes that contribute to planetary temperature change. The point is that this graph correlates only CO2 levels with temperature and consequently we shouldn’t expect a neat line.

Let’s dig into this variation just a little more. For a given CO2 level these other factors could affect temperature strongly or weakly. The graph below highlights three temperature levels for the same CO2 level. Why aren’t these temperature values closer together? One reason is that these other factors could be strongly in play and making it either hotter or colder than would otherwise be the case. When the temperature is well above average, the earth could be closer to the sun and the methane levels could be high. When the temperature is well below average, the 100,000 year cycle in the earth’s orbit could put it farther from the sun, methane levels could be low and there could have been a large volcanic eruption. It is the variability due to the other factors besides CO2 that contribute to the variability of the temperature levels.

correlateexplainfull

While the data doesn’t fall into a neat line, another thing that stands out is that this data does fall into a straight line. Recall, all we knew from the other graph was that low CO2 levels matched low temperatures and high CO2 levels matched high temperatures. We didn’t have good sense of how the values in the middle lined up. There are many ways the intermediate levels could have played out, but it turns out that a straight line is a fairly good approximation.

sample_fits

Where Are We Today?

This data covers the last 400,000 years, but it turns out the most recent data it contains is 2300 years ago. It begs the question “Where are we today?” To answer that we will need to re-draw the graph since the modern CO2 level is well outside the range of the graph above. The re-drawn version is shown below. The black bar at the bottom right shows the range of the modern CO2 level. The point above that bar is the approximate location for our climate today.

correlateplusnow

The data we’ve been discussing shows 3 things, the CO2 level is well outside the range of what’s been normal for the past 400,000 years. Somewhat more subtly, the temperature vs CO2 levels are also well outside the normal range. The CO2/Temperature point for today’s climate is no where near the imaginary line that passes through the middle of all the other data. At the current CO2 level our temperatures should be much higher. How much higher is more apparent on this graph than on Al Gore’s graph. Finally, only the temperature level is within the normal range. Our relatively low temperature today could be due to a natural lag in the response of temperature to CO2. It could be the case that the earth is already warming as fast as it can and more CO2 in the atmosphere won’t make it warm any faster. The current low temperatures could simple be because the temperatures haven’t caught up yet. It could also be that, as others claim, if it weren’t for the current CO2 levels we’d be in the early stages of an ice age. However, whatever the reason two implications are clear. 1) CO2 levels are crazy-high and we need to take steps to reduce them and 2) the current “low” temperatures aren’t a sign that global warming is false, but rather that we may have a bit of a grace period before temperatures start to rise. Let’s not blow it.

References

The ice core data for the past 650,000 years comes from 2 different sources.

From 420,000 years before present to now was published in:

Petit, J.R., J. Jouzel, D. Raynaud, et al 1999. Climate and atmospheric history of the past 420,000 years from theVostok ice core, Antarctica. Nature 399: 429-436.

and is available online here: http://cdiac.ornl.gov/trends/temp/vostok/jouz_tem.htm

From 650,000 years before present to 390,000 years before present was published in:

U. Siegenthaler, T. F. Stocker, E. Monnin, et al. Stable Carbon Cycle-Climate Relationship During the Late Pleistocene. Science, v. 310 , pp. 1313-1317, 25 November 2005.

and is available online here:

http://www.ncdc.noaa.gov/paleo/metadata/noaa-icecore-2486.html

Information about the time lag between temperature change and CO2 change comes from several articles.

The 800 year lag is first presented in:

Caillon, N., Severinghaus, J. P., et al, “Timing of Atomspheric CO2 and Antarctic Temperature Changes Across Termination III.” Science, 14 March 2003, v299, pp 1728-1731

Another paper that suggests the correlation is even stronger than the data used in this article is presented in:

Cuffey K. M.; Vimeux, F. “Covariation of carbon dioxide and temperature from the Vostok ice corea after deuterium-excess correction.” Nature, 2 August 2001 v412 pp523-527

14 comments for “Gore’s Graph Done Right

  1. davidha
    January 3, 2010 at 8:37 am

    Thanks for compiling the detail on the temp vs CO2 correlation as shown in An Inconvenient Truth (pg 66-67 in the book). Can mankind maintain focus long enough to try and address this? Maybe not. Massive CO2 emissions are now a way of life, and one that much of mankind is ironically now hoping to achieve. This issue deserves a little more serious attention from leaders, and not the ones involved in maintaining the status quo. It is possible to live a carbon-negative lifestyle. It is possible to survive comfortably and sequester carbon. I fault Al Gore for not making any effort to lead by example on a small scale, though I respect his work on the megalomaniac scale. “World leaders” are putting us all at risk, and I have little faith that they can address this. We must learn to live in a new carbon-negative way as informed individuals, not as pawns, consumers and canon fodder. We can be productive and carbon-negative. The Draconian carbon-tax may be inevitable, but it can be popular, too. Please use your website to advocate carbon-negative living. It is about a whole new infrastructure. I am ashamed of our national chamber of commerce for not seeing this potential. See the keyword: Biochar. Thanks again.

  2. numbersguy
    January 4, 2010 at 11:00 am

    Hi David:
    Glad you liked the article. I’m surprised how timely it remains. If Gore were more truthful/complete about the data in his book I doubt the current “ClimateGate” scandal would have as much traction as it does. The data says CO2 levels are crazy-high by geological standards but temperature is both moderate (in the absolute sense) and way way below were it should be based on the 600,000 year trend line of CO2 vs temp. Regardless of whether people think the earth is warming or not, fact is CO2 is a green house gas and levels are dangerously high. This bodes ill for the future even if the “consensus” for the present day is mixed.

    I’m a little more optimistic about our “World Leaders” than you are. While I agree that it seems their techniques for leading are the same as they were 100 or 200 years ago, I have a strong faith that news reporting via data visualization techniques will lead to a more enlightened approach toward world leadership and planetary management. But it requires a change in the populace too. Leaders are political creatures. Even if an enlightened leader did the right thing, if the right thing did not appeal to his constituents he’d be voted out of office the next term. So both the leaders and the people need to recognize what the right thing is.

  3. August 12, 2010 at 6:53 pm

    Hello, good post.

  4. Jack Radish
    January 21, 2011 at 1:08 pm

    Anyone who still believes in man made global warming after all the debunking, physical evidence(it’s getting colder), and photo shopped pictures in Al Gore phoney movie, there is no hope for you. Climate models only work in “models” no real world evidence. Hmmmmm, similar to a Marxist College professor/community agitator looked like he’d make a good president. I think I see a scientific correlation here. See ya morons.

  5. numbersguy
    January 21, 2011 at 2:28 pm

    Hi Jack:
    Thanks for the comment. My point, which you seemed to miss as well as climate advocates AND deniers seem to miss, is that we are currently enjoying an as yet unexplained respite. The models say for our current CO2 levels we should be A LOT WARMER than we are now (so in that regard I AGREE with you).

    It’s like you have your gas pedal to the floor of your car and yet it’s only going 30 mph. Climate deniers seem to be saying that’s normal for the car. Climate advocates seem to be saying we’re going 100 mph. I’m saying something’s holding us back, let’s fix the whole car before we crash.

  6. Ben
    September 15, 2011 at 11:02 pm

    Yet more data showing Al Gore for the dishonest, self interested, evil douchebag that he is.

    As for the gas pedal to the floor analogy, can we perhaps suggest that Co2 and temperature are not related in such a fashion? You seem to be suggesting that we have our pedal to the floor (Co2 emmissions) and yet temperature is not doing what it should.

    Fortunately in a billion years the erath will be healed and this retarded experiment called mankind will be a distant (forgotten) memory.

  7. numbersguy
    September 18, 2011 at 8:45 pm

    Ben, I seriously doubt scientists are confused about CO2 being a greenhouse gas, consequently I believe them that it is. I don’t think the scientists are lying so much as over simplifying the story for the rest of us.

    Gore, on the other hand, by not being a scientist, should really know or at least strive for better more straightforward communication with the public.

    When a scientist over simplifies in an effort to get us to change our behavior, someone will find out and start spreading Fear, Uncertainty and Doubt. Better for scientists to stop, collect their thoughts, and present their arguments in a clearer and more concise way than to take a short cut that will be discovered and exploited by the skeptical.

  8. November 27, 2011 at 4:50 pm

    hei, 800 year lag according to climate fund debate may come from the period it takes from greenhouse gas accumulation unto it falls down into ice!

    • numbersguy
      November 28, 2011 at 4:42 pm

      Could be. It’s been a while since I read the paper. One thing I do remember is green house gasses don’t get trapped till the snow has been packed into ice. Which occurs at something like 20 to 100 feet down (IIRC). It’s not so much that it’s taking time to fall from the sky as it is taking time to be frozen in place. In the mean time the “thing” they are trying to correlate with the CO2 trapped in the ice is the ice itself. The heavy-water/normal-water ratio in snow is temperature dependent.

  9. wayne
    January 6, 2013 at 2:25 pm

    how come it shows co2 reads 8000 or so years after the temp rises if co2 causes the warminng not before it warms

  10. Jim M
    November 23, 2016 at 7:20 am

    Thank you very much for presenting the data in other ways to provide useful analysis. While the analysis was very helpful, there are a few fundamental questions that beg to be evaluated based on the CO2 vs. Temp chart which were not. When I first looked at the CO2 vs. Temp I noted 2 characteristics of the data which deserve more discussion. The first was that both charts seem to have a periodicity of about 80,000 years (my “eyeball calculation” of the periodicity) that is the real driver of both CO2 and temperature. Whenever I have seen charts that have this appearance I always ask what is driving these variables. Said another way, I view the 2 variables not as input (CO2) and output(temperature) variables but as output data points of the same process being driven or caused by some unknown input variable. The other observation is that temperature appears to be leading CO2 for about half of the time period shown (note that temperature peaks before CO2 at years 120000, -230000, and -320000). I am not a scientist but an engineer in manufacturing who looks at data all the time. I tend to be skeptical of most people’s data analysis conclusions because I have found, based on 3 decades of having people present data, that most people look at data to support their beliefs rather than striving to evaluate the data objectively to determine what it “says”. Except for the final conclusion I found the authors analysis to be very objective. Based on CO2 vs. Temperature chart along with the authors data analysis, to include the many comments that there appears to be many other factors besides CO2 impacting temperature, I do not understand the conclusion that we need to act quickly to take actions before the “crazy high” levels of CO2 lead to rapid rises in temperature. A more logical conclusion would be that the absence of increasing temperatures given the extremely high CO2 levels would seem to support the analysis of the data provided by the author that there are many factors other than CO2 level influencing temperature. Further, to conclude that CO2 gas levels are driving temperature is, at a minimum, overly simplistic, and worse, not true. I would challenge the author to reevaluate his conclusion. Specifically, I would encourage him to identify the driver behind the 80-100,000 period of both CO2 & Temperature as well as digging in deeper to understand the other factors that could be impacting temperature.
    Again, thanks for the data analysis. As a person who just wants to know the truth, I found this analysis of the data to be very objective, therefore very helpful.

    • numbersguy
      November 23, 2016 at 12:16 pm

      Hi Jim:
      By “Author” in your post I assume you mean me (vs authors of other sources I drew from). You raise several points, let me address them in order.

      Regarding whether CO2 is a driver vs another output… in theory it can be both. By comparison you’ve probably seen the studies that suggest methane locked in permafrost may be unleashed if/when the permafrost thaws. So in this case methane being released would be an “output” but methane is also a much more powerful greenhouse gas and so it too would be a driver.

      Later you raise an issue regarding “reporters” in general only digging as far as their confirmation bias allows. It’s surprising to me to see that I indeed changed my views on many topics in this blog based on research. The only bias I had is if I couldn’t pivot to an interesting conclusion, I’d drop the story, but if I could, even if it was the opposite of what I set out to do I’d publish it. I’m mentioning this here because I had expected to find a “smoking gun” that didn’t materialize. Specifically a carbon 14 vs carbon 12 signature in atmospheric CO2 that could indicate an uptick in fossil fuel burning. It’s been years since I wrote this article, but I do remember getting nowhere on that investigation.

      Regarding the periodicity… there’s been some articles others have posted (I may share here) that address orbital changes and the like. As I recall we should be in a cooling period now, but we’re not. So that may be part of the reason why we’re cooler than CO2 levels would indicate. Additionally there’s upper atmosphere seeding (accidentally) by jets that may be helping keep temperatures cool. Finally, regarding the lag, there’s also a lag in the ice core data that the scientists try to adjust for but I have no idea how good their adjustments are. Given the time scales involved, I’m happy with several hundred years worth of “play” in these numbers, but of course, today, several hundred years is a lot.

      Ultimately I find Gore’s graph to be hyperbolic because the CO2 levels spike and he implicitly asks you to imagine the temperature spike. But with my graph you don’t have to imagine the spike, you can see what it would be and it’s still alarming. Additionally, CO2 is a greenhouse gas, that much ought to be believed as it can be tested in a lab. What’s more of a question is how CO2 levels play out in the real world. While the CO2 vs Temperature correlation isn’t as close as a statistician would like, I imagine it would be closer if the chart was multivariate to include other factors such as orbital changes. After several years I’m surprised more mainstream scientists aren’t addressing this issue using my form of the charts vs Gore’s form of the charts. My charts raise questions I’d LOVE to see actual climate scientists address, but overall, I remain on their side. CO2 levels ARE crazy high, it will take decades or centuries for natural processes to reduce them and in the mean time whatever is keeping our temperatures at bay will most likely fail and global temperatures will rise.

      • Jim M
        November 24, 2016 at 6:52 am

        I apologize as I realize that I was not clear about my concern with the use of the CO2 versus Temperature chart when drawing conclusions as to the causes of changes in global temperatures. I am not arguing whether or not CO2 impacts temperature, just that that this chart should does not support the conclusion that increasing levels of CO2 have and will lead to higher global temperatures. My argument is based on a very fundamental, “high level” analysis of the chart. If someone gave this chart to me without telling me the what the chart represented, my initial response would be that this chart shows 2 output variables of a process with an 80-100,000-year periodicity. If another person showed me this chart and asked for help determining which of these variables is the input variable (the cause) and which is the output variable (the effect) my response would be that the input variable would appear to be the dotted line (temperature) since it appears that for most of the time it is leading the solid line data. I really want to emphasize that I am not arguing climate science as this is not my area of expertise. I don’t know whether CO2 levels impact global temperatures nor do I know the impact human activities have on global temperatures. I am arguing that while this chart raises some questions that deserve further study, I do not understand how one can draw the conclusion from this chart that CO2 levels impact global temperatures. If you can clarify my 2 concerns with this charts that would be great. Since my concerns are with the chart and not climate science, I just ask that you focus your response on my analysis of the chart and not on the underlying science of climate change.

        • numbersguy
          November 24, 2016 at 10:18 am

          Hi Jim:

          The short answer to your question is that technically there’s no way to tell “driver” from “output” by statistical analysis alone. You’ve undoubtedly heard the phrase “correlation is not causation” and that’s true. Causation is usually determined via other methods. In my earlier example, CO2 and methane are scientifically proven to be greenhouse gasses, but as I mentioned rising temperatures may also cause more methane to be released from (previously) frozen reserves, so rising methane levels is also a side effect of higher temperatures.

          Mathematically you raise an interesting question regarding whether switching “X and Y axes” can result in a higher degree of correlation (and thus, in your example, “prove” temperature is driving CO2 and not vice versa). I suspect it can change the correlation coefficient (while still not proving) since the least squares method minimizes the data’s Y-distance to the ideal line and exchanging the X and Y values would effectively result in a least squares method where the X-distance is what’s being minimized… in general two different lines, 2 different correlation coefficients. Oddly, or perhaps tellingly, I’ve never seen a study where X and Y were exchanged in an effort to determine cause and effect… as I said above that is determined by a physical analysis of the system, not a purely mathematical one. Math can both suggest and rule out cause-effect relationships, but can’t really rule them in.

          As a point of clarification, you can only see the 80K to 100K year periodicity and the ~800 year lead/lag on CO2 vs temperature on “Gore’s graphs” and not mine as I’ve removed time from my data opting instead to show just the CO2 and temperature data. So I can only conclude that you’re talking about all 3 graphs (the 2 graphs of Gore’s and my one graph).

          Finally, if I had to identify the one thing I’m trying to do both here and in the blog in general, that would be to get people to change from asking ‘yes/no’ questions and instead ask ‘by how much’ questions. We (you and I) have (hopefully) established CO2 is a greenhouse gas, but you are skeptical if it’s only a driver of global temperatures vs being both a driver and a side-effect of rising temperatures. I assume you do not believe that CO2 is a “pure” output of a higher temperature driver. So the first question is, how far outside of a 600,000 year history of CO2 and temperature data is our climate now? And the second question is, what should we do about it? [Edit] Because if it’s not a driver now it eventually will be and when it does, these graphs indicate it will be a huge temperature increase.

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