A while back, we started looking at a poorly thought-out article from the website C3Headlines. C3 is starting to make a name for itself as a goldmine of climate comedy- their claims have recently been addressed at Tamino and SkepticalScience.

We’re going to keep digging into C3‘s claim that carbon dioxide concentrations have been increasing linearly over the 20th century. They seemed to draw this claim by eyeballing the graph of CO2 concentrations and qualitatively describing them as linear, apparently using the inset in their first figure to compare linear, quadratic, and exponential trends. This is a faulty method: it’s an elementary fact of calculus that ANY smooth curve, when viewed appropriately, will appear linear. The point has already been made but it’s worthwhile to keep looking because there are some interesting graphical follies at play; examining them further might help us understand how and why graphs are misunderstood.

Figure 1: From C3Headlines’ article on “The Left/Liberal Bizarro Anti-Science Hyperbole”, which claims that CO2 concentrations are increasing linearly. Click to read it, if you dare…

C3‘s second graph in this article measures the change in atmospheric CO2 by calculating a month-to-month percentage change. It’s not entirely clear why they are using a percent change, rather than the standard practice of expressing rate of change as concentration change per year (like the source of their data uses). Whereas ppm/year is an absolute measure, each datum generated by the percentage-change method depends strongly upon the value of the previous month. As a measure of long-term rate of change, it is a bit questionable.

My primary concern, though, is with their use of monthly data in the first place. In my last article, we noted that, without explanation, C3 confined their focus to January CO2 concentrations. Were they consistent, they’d also look at January rates of change – of course, doing so might lead to unacceptable conclusions.

Figure 2. Rates of CO2 accumulation have been calculated for the month of January, consistent with earlier investigation of January CO2 concentration. Over the period of observation, rates have increased at a significant (P~0.0005) acceleration of 0.11 ppm/year^2. Monthly rates throughout this article have been calculated by considering the change in CO2 between adjacent months, and assuming that a month is 1/12 of a year. Interpolated values of CO2 were used to avoid annoying data holes early in the record.

Instead, they look at the rate of change for every single month on record. Why do I find that problematic? Well, let’s look at the full record, with monthly resolution:

Figure 3. The Mauna Loa CO2 record, at monthly resolution. Imagine the green line was a roller coaster – would you notice the slow climb uphill indicated by the red line? Or would you be too busy holding onto your dentures due to the quick up and down?

As you can see, superimposed on the long-term trend, there’s an annual oscillation. This is the result of annual cycles of photosynthesis. During the summer, plants store carbon in solid carbohydrates, removing it from the air. During the winter, there is little photosynthesis, and CO2 released from decaying leaves builds up in the atmosphere. The seasons are out of phase in the northern and southern hemispheres, but there is more landmass in the north, so its contribution dominates.*

This annual cycle means that, when you calculate the rate of change on a monthly time scale, it will be positive during the winter and negative during the summer. Look back at the CO2 concentrations plotted in Figure 3. The rate of change at each point on the graph is the slope of the graph at that point. Imagine the graph was the track of a roller coaster – every summer the car slides downwards, and every winter it climbs upwards. This means that over the course of a year, the rate of change in CO2 will fluctuate dramatically, from strongly negative to strongly positive values. When I calculate the monthly rates of change, their magnitude comes out much, much larger than the annual average rate:

[FIG]

Figure 4. Rates of change in atmospheric CO2. The red line is the monthly rate as measured at MLO; the black line is a linear regression to these data. The blue dots, included for reference, are the annual rates of CO2 accumulation, which have a significant increase over time. If it’s not obvious that they are increasing at this level of magnification, why should we believe that the monthly MLO data *aren’t* increasing?

Along with the monthly rates, I’ve plotted the annual rates. Although we already have seen a significant increase in the annual rates, the wild variations at the monthly time scale act to hide the incline. A linear regression to the monthly data agrees relatively well with the annual trend (actually, the regression to the monthly data gives an acceleration in CO2 concentrations about 1.5 times as large as the annual data), but the enormous variability reduces its significance. It’s a little like driving a car up a rocky mountain road: the trip may well be too bumpy, moment to moment, for you to notice that the road is slowly sloping uphill.

A graph of monthly rates obscures more than it reveals. So what can the monthly data tell us?

Figure 5. Acceleration in atmospheric CO2, by month. Asterisks denote significant (p<0.05) trends.

Here, I’ve calculated the long-term trend in the CO2 rates for each month; this tells how the CO2 is accelerating in each month. Between May and August, the acceleration is negative – this corresponds to the time of the year when CO2 is removed. The biosphere is taking deeper and deeper inhalations as CO2 levels rise. During the rest of the year, the acceleration is positive. Not only that, looking at the September-April months, it’s clear that there is more positive acceleration than there is negative acceleration – exhalations (which include fossil fuel emissions) are growing faster than inhalations. This means that, taken over the whole year, there is a net acceleration in CO2 concentrations. A linear trend would, by definition, show no acceleration, so the data that C3 presents once again undermines their thesis.

Figure 5 also gives some insight into a popular talking point, that increased carbon dioxide will be better for plants, and that it will be balanced by greater plant growth. Although it is true that the inhalations are getting deeper during the summer months, perhaps from CO2 fertilization, longer growing seasons, or other effects, we can see that they don’t balance out fossil fuel emissions.

In fact, while increased carbon dioxide can help plants to a certain extent, that extent has been over-estimated in the past. For example, many early measurements of CO2 fertilization were done in greenhouses or carefully controlled chambers. Such an experimental setup might be fine as a first approximation, but as (Long et al, 2006) point out,

“no agrochemical or plant-breeding company would base its business plan for a new chemical or variety solely on greenhouse studies without
rigorous field trials.”

Long et al. compare the results of greenhouse studies to those done under the more realistic Free Air Concentration Enrichment (FACE) experiments, in which plants are grown like any other crop, with sprayers elevating local CO2. What did they find?

“In [FACE] trials, elevated CO2 enhanced yield by ~50% less than in enclosure studies. This casts serious doubt on projections that rising CO2 will fully offset losses due to climate change. ”

It doesn’t take much creativity to imagine what would have happened if the results had come out the other way around, if early estimates of CO2 fertilization had been a factor of 2 too low, rather than too high. The c3Headlines might read: “Important Climate Figures Incorrect; Earth Scientists Don’t Know That CO2 Is Plant Food.”

All the elements are there – new developments overturning older accepted ‘truths’, major flaws in IPCC models – and yet, I’ve never seen the skuptix mention (Long et al. 2006).

I wonder why?

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* There is an excellent description of the annual CO2 cycle in this video near minute 40. It includes some very cool visualizations of data and animations of atmospheric models. I’ve also made a graph of the annual cycle at MLO by detrending the monthly data with the quadratic model we built last time. You can see it here.

Monthly CO2 Data and Annual Growth Rate Data from MLO

Long, S., Elizabeth A. Ainsworth, Andrew D. B. Leakey, Josef Nosberger, & Donald R. Ort (2006). Food for Thought: Lower-Than-Expected Crop Yield Stimulation with Rising CO2 Concentrations Science, 312 (5782), 1918-1921 DOI: 10.1126/science.1114722