Joe Daleo, the number one guy over at Icecap.us, recently sent me the CDIAC (ice core) CO2 data as criticized in Beck (2007) and asked me what I made of it. Now, this data has been pored over by the great and small, so should we expect any revelations along the lines of “Has CO2 actually decreased?” Well…see below. I don’t often see this data pictured in one particular way that I find instructive, so I wanted to show it to you.
You’re probably used to seeing CO2 through time in plots very much like this cartoon.
The black line is the actual CO2 data, the two background colors representing, before 1958, estimates of CO2 based on ice cores, and after that on measurements from Mauna Loa. The green line is a suitably normalized estimate of the human population. Both increase at what looks like roughly the same rate. Right?
Side note: these are estimates, and, ideally, both lines would have a “plus or minus” line plotted above and below so that we can see the graphical representation of the uncertainty in the numbers, which might, or might not be, substantial. I don’t know what the error is for either curve, but we’ll ignore this not inconsequential problem today.
Now let’s take the exact same data and plot it in a slightly different way.
Click the image for larger version: you may wish to right click and “Open Link In New Window” (or words like that) so that you can view the graph and read its description at the same time. Or download a printable pdf version here.
This graph is complicated, so let’s take our time to understand it. The horizontal, or bottom, axis is still time. But now the black line is the yearly change in CO2. For example, in 2007 the CO2 was measured to be 383.32 parts per million (ppm) and for 2006 it was 381.83 ppm. The change, which was an increase, was 1.49 ppm. We measure this change for each year and keep the results, so that we can see the rate of increase (or possible decrease or no change) for each year. We could plot this raw change through time, but a lot of detail is hidden because the increase is exponential (the same shape as the cartoon plot above).
Instead of a raw plot, we take the log of all values so that detail can emerge. This should not change conclusions based on the data in any way, and it does allow us to see it better (technical note: the value of 1.2 was added to all values because some changes were negative and, without using complex numbers, we cannot take logarithms of negative numbers).
The detail pops now, doesn’t it? The first thing to notice is the marked qualitative and quantitative differences in the Mauna Loa and Ice Core estimates. The two methods are obviously not directly compatible, a fact which was hidden in the raw (non-differenced) plots. This makes decisions about the rate of increase of CO2 across the two regimes trickier than is commonly thought.
First concentrate just on the Mauna Loa regime. The rate of change has been over-plotted by a simple regression line, which fits rather well (I’ll spare you the formal statistical tests: but trust me). That is, the model of exponential acceleration of CO2 into the atmosphere is well supported over this range. This is acceleration because, recall, that this plot of the rate of increase of CO2.
To explain that further: suppose, every year, the exact same amount of new CO2 is added to the atmosphere. The graph for that would then be a straight line on our plot, which is roughly the case for the dates 1750 to 1800. During that time, about 0.12 ppm of new CO2 was added each year. At least, according to the estimates from ice cores.
To emphasize: if our graph shows a (rough) increasing line, as it does in the Mauna Loa regime, then the rate at which CO2 is being added to the atmosphere (according the chemical measurement method used) is increasing. If the graph shows a straight line for certain periods, then those periods contributed the same amount of new CO2 each year. But if the graph shows a (rough) decreasing line, as it does in several place in the ice core regime, then the amount of new CO2 being added to the atmosphere is decelerating: new CO2 is still being added, but at a slower rate.
There are even times when CO2 has decreased, i.e. removed from the atmosphere, from year to year (according to the measurements used): these are the points below the dotted-dashed line at 0. These times were roughly 1820, 1831-1838, times before wide-scale industrialization, and 1942-1944. 1942 to 1944? This was certainly a time in which the entire world, if you recall, was intent on adding as much of everything to the atmosphere that it possibly could. So this result is strange. One possibility is measurement error: something might have gone wrong in the way the ice cores were processed.
It is usually thought that the measurement method used for ice cores is accurate and unbiased and so on. So suppose that is true. Then it cannot have been the war that accounts for this dip in the mid-1940s, because there is no similar dip around the years of The Great War. In fact, during that time, the rate of new CO2 was accelerating, as indicated by the regression fit over the years 1898 to 1941.
Just for fun, I have drawn the two regression lines, for the ice core and Mauna Loa regimes, extending forwards and backwards through time (these are the light dotted lines). What I learn from this, again, is that the two measurement methods are probably not compatible.
On to the human population, again pictured in green, but here, like CO2, we are looking at logged differences in year to year population, suitably normalized for ease of comparison. Data from 1950 to 2007 was available for each year from the U.S. Census Bureau; from before that, I used, Lord help me, Wikipedia. Estimates before 1950 were sparse, generally only available every 50 years or so. I fit a variety of splines (B-splines, polynomial, etc.) and even a strict linear interpolation to estimate the missing values: all methods gave substantially the same results. What we have to say about human population isn’t that crucial, anyway.
You first see two dips, one around 1915 or so and another from the late 1940s. These dips certainly are from the two World Wars. Population was still increasing then, but, obviously, at a slower rate. The deceleration from the late 1960s to present time is well known to demographers: while population is still increasing, the rate at which it is doing so is dramatically decreasing, particularly in Enlightened countries. The odd dip around 1960 is probably due to the utopian joys of communism: Mao’s great leap forward (into the grave, apparently).
Ok, that’s the data. But it only takes us so far: human population numbers are only a rough, very rough, proxy of our ability to add CO2 to the air. For example, during 1831-1838 the human population was accelerating but the CO2 was decelerating! Human population also dropped during World War II, the same time as a measured drop of atmospheric CO2, as mentioned above. But a similar deceleration in human population in World War I did not find a concomitant deceleration of CO2.
What to make of plots of people versus CO2? My guess: not much. Particularly since current rates of population are decelerating and will continue to do so, yet CO2 rates are accelerating. The correlation between human population and CO2 is just too noisy and inexact to be of much use.
I am not an expert in measuring atmospheric CO2, but I will make three conclusions which I believe are well supported statistically. (1) The two methods of measuring CO2: ice core reconstruction and air-chemical, are not compatible. One is over-estimating or one is under-estimating. I have no idea which is which; whether, that is, historical numbers should be adjusted higher or current numbers should be estimated lower. Beck (2007) and Jaworski (2007) argue that the historical numbers are low.
(2) We should increase our uncertainty in models, such as global climate models, that use this CO2 data as input, particularly if they use the data which spans the two measurement regimes.
(3) There are odd discrepancies, unexplainable through human population correlations, in the ice core data. At times CO2 has been measured to actually decrease. This might be true, but the times of the decreases are not consonant with human activities. Clearly, measurement error is a likely possibility and should be investigated.
Lastly, of course, there is Beck’s paper, which is essential reading on this subject. I do not have Beck’s data, just the ice core data: some of the same signals, though not the same in magnitude, in the CDIAC data are also in Beck. His contention, supported by data, is that CO2 has been higher in the recent past. Like a peak around 1940 or so, declining afterwards: the decrease we also see.
I might be wrong about all this, so I welcome comments and discussion.