Annual Cycle of CO2

The question arose, whether the size of the annual cycle in atmospheric CO₂ concentration has been changing recently. We’ve previously shown that it increased several decades ago, but has it increased or decreased more recently than that?

To investigate, let’s study CO₂ data from three different locations: Barrow (in the Arctic), Mauna Loa (not too far from the equator), and the south pole. For Barrow and south pole stations we’ll use monthly average data from the World Data Center for Greenhouse Gases. For Mauna Loa, rather than monthly data we’ll use weekly averages from NOAA, to provide more detail about the shape of the annual cycle.

Let’s start with the south pole, then head north. The data begin in late 1975, but to give a better view of the annual cycle let’s plot the data since 2000:

There’s not much of an annual cycle compared to northern-hemisphere locations, because the yearly ups-and-downs of CO₂ are mostly caused by the growth and decay of land plants, and there’s just not much land in the southern hemisphere compared to the northern.

To see how the size of the annual cycle changes over time, we first need to remove the trend to define de-trended data in order to isolate the annual fluctuation. Then we need to analyze that to determine how big the annual fluctuation is. There are many ways to do so. One is with a wavelet analysis, which (for one fortuitous choice of wavelet) approximates the data by fitting sinusoids. We can take the size of the best-fit sinusoid at each moment of time as an estimate of the size of the yearly cycle at that time. It’s not a perfect estimate, since the annual cycle is not a sinusoid, but if the shape doesn’t change that much, then as the real annual cycle shrinks or expands, the best-fit sinusoid should do the same.

Here’s the amplitude of the annual cycle (actually the semi-amplitude, which is half the full amplitude) according to that method:

It varies, but there’s no clear trend. We can also scan each year, and simply note the highest and lowest reported values. This gives us an estimate of the full amplitude which is noisier, but each year’s value will be independent of the others. It looks like this:

Again there’s no clear trend, and looking for one with linear regression indicates no statistically significant trend.

Another interesting aspect is to note when the annual cycle occurs, i.e., what it’s timing, or “phase” is. Here’s the phase of the peak of the best-fit sinusoid over time:

This isn’t so much an estimate of the peak timing, as it is of the timing of the entire cycle overall. Note that it tends to peak late in the year, toward the end of southern-hemisphere winter (which coincides with northern-hemisphere summer). Again there’s no clear trend, so we see no real evidence from south pole data of a change in either the size, or the phase, of the yearly oscillation.

Finally, we can simply take the de-trended data and average it by time of year, to compute an average annual cycle. If we do so for each decade (from the 1980s to the 2000s) separately, we can look for changes in the pattern:

There are some noticeable differences during the time when CO2 decreases in southern hemisphere spring/summer, but no discernable pattern. All in all, there seems to be no clear substantive trend in the size, shape, or timing of the annual cycle of CO₂ at the south pole.

How about Mauna Loa? The weekly data begin in 1974, but again I’ll graph the data since 2000 in order to show a more close-up view of the annual cycle:

The cycle is bigger here than it was at the south pole. It also peaks earlier in the year, because the seasons are reversed in the two hemispheres. If we follow the same procedure, we can estimate the semi-amplitude of the annual cycle by wavelet analysis:

Again, no clear indication of trend. We can also do so by noting the highest and lowest values in a given year:

Still no sign of a trend, and linear regression finds nothing significant.

But when we look at the timing of the annual cycle, we notice a change:

It appears that around 1990, the timing of the annual cycle (of the best-fit sinusoid at least) shifted. It’s happening earlier in the year, by about 4 days. This is confirmed by studying the average annual cycle for each decade:

Note that the decrease in CO₂ due to plant growth in spring/summer happened earlier in the 1990s and 2000s, than in the 1980s.

Finally, let’s take a peek at Barrow in the Arctic:

The annual cycle here is much larger than either at Mauna Loa or the south pole. The shape of the cycle is also different, with a more brief decline due to a shorter growing season.

Looking for size changes with wavelet analysis gives this:

Now we do see indication of a change — the annual cycle seems to have grown bigger. Taking each year’s max/min difference shows the same thing, and linear regression finds the change is statistically significant:

The timing has also changed, in a manner similar to that at Mauna Loa — it shifted to earlier in the year around 1990, but by a larger amount, about 5 days.

Again this is confirmed by the average annual cycle for each decade, which also shows the change in size of the cycle:

What’s the bottom line about the annual cycle of CO₂? At the south pole, I don’t see significant change. But at Mauna Loa and Barrow, the timing of the cycle is earlier. This seems to be primarily due to earlier spring decrease, i.e., that spring — in the sense of plant growth — is coming earlier, by 4 or 5 days. Finally, at Barrow the annual cycle has gotten bigger. My guess is that this is a direct effect of warming in the Arctic, so there’s simply more plant growth (and decay) happening each year.