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.

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22 responses to “Annual Cycle of CO2

  1. The previous commenter on the last post that requested this analysis had written that Keeling wrote back to say that the annual amplitude had increased since measurements began in the 1950s, perhaps there’s data prior to the 1975 start point above that would make it so?

    Theoretically this might make sense from a vegetation standpoint, more photosynthesis means more vegetation, hence stronger variability in the annual cycle since plants draw down more CO2 when they grow, and release more when they die (in winter). This wouldn’t be readily observed in the far Antarctic I presume, as far away from vegetation as it is, and maybe not so much in Hawaii due to its isolation from mainland.

    Just speculating.

    [Response: There is data prior to 1975 (at Mauna Loa at least), and that's where the cycle increase is seen. But the question was about more recent changes, so that's the focus here.]

  2. About 3 years ago I had a look at this.

    I could not / still cannot understand what causes the dip. It is very quick –

    Plant growth is quick but then the leaves have to decay to release the CO2 and that is not quick.
    The dip is inverted if water absoption differences due to temperature is the cause.
    Plankton is a possibility as warmth= growth
    plus as sea ice disappears in the summer more plankton is exposed? which is quikly covered as the ice reforms. Also with shrinking ice perhaps you get an increased dip.

    looking at an inland site like Sary Taukum (about as far from sea as possible then the plankto effect would be minimised and you would have to get the gases equalising over 1000km. But no delay is seen between Barrow and Sary Taukum. In fact Sary Taukum has an early start to the drop but a shallow slope to a minimum at the same time and a faster recovery.

    Daily and hourly data is available (many false readings however)
    data here

  3. My thought on Barrow is that for part of the year the local atmosphere can interact with the ocean, whereas when the ocean is frozen over that interaction is prevented. When the sea water is exposed to the atmosphere in the spring if it’s deficient in CO2 (Henry’s Law) it will suck CO2 out of the atmosphere, in the fall once the ice reforms that interaction is stopped and CO2 can accumulate in the atmosphere. Since the dates of ice-out and refreeze has changed then I’d expect the CO2 curve to change as well.

  4. Well, that’s neat! Any idea how the difference in spring decline for CO2 in this data compares to other measurements of the timing for spring? I know it’s been claimed that the cold seasons are starting later and ending more quickly based on things like phenology.

    Complicated, complex ecosystems in different environments that change very fast

  6. ps, my recollection is CO2, like methane, in the winter can be trapped under ice (in lakes, at least, if there’s no water circulating) and released when it melts; I suppose the algae that live inside the seasonal ice use some of it. I doubt the water under the winter ice is deficient in CO2 given the currents in and out under the ice.

    • But the CO2 levels a Barrow drop when the ice breaks up so the open sea water is acting as a sink not a source.

    • Yes but the plankton is in the water so as the bloom starts the plankton depletes the CO2 in the water and if the surface of the water is exposed to the atmosphere CO2 will be absorbed from the atmosphere per Henry’s law. The plankton will start to bloom before breakup since the ice becomes thin and light penetrates and the plankton colonies on the bottom of the ice begin to grow.

  7. This will find numbers on partial pressure and solubility; I can’t interpret with any expertise, but what I read says it’s biology not chemistry at work changing the local measurements:

  8. Alastair McDonald

    IMHO, The annual cycle of atmospheric CO2 is driven by two agents: physical and biological which are each mainly situated in mainly in opposing hemispheres.

    The NH is mainly continental and the CO2 cycle is driven by the biological cycle due to the growth and decay of vegetation. Here CO2 is drawn down during the Boreal spring and summer say April to August.
    In the SH, which is mainly oceanic, the cycle is driven by ocean surface temperature with the draw down occurring during the Austal autumn and winter say March to September.

    Since the two cycles are roughly synchronised they have the appearance of being only one. What I would be interested in knowing is whether it is possible to separate out the effect of those two cycles as seen at Manua Loa. The Manua Loa signal is not a simple sinusoidal curve, and gives the appearanc of being the sum of two sine waves slightly out of sync.

    Cheers, Alastair.

  9. FYI, I recently performed a similar seasonal CO2 analysis to what you did, but just for Mauna Loa.

    This compares against the seasonal equatorial Sea Surface Temperature (SST) data.

    Alastair says above:
    “What I would be interested in knowing is whether it is possible to separate out the effect of those two cycles as seen at Manua Loa. The Manua Loa signal is not a simple sinusoidal curve, and gives the appearanc of being the sum of two sine waves slightly out of sync.”

    I did exactly that and identified the harmonic in the signal, which creates a crook in the sinusoidal shape. That same crook shows up in the SST signal at the same place once the phase is adjusted. In other words, the two curves align if the time lag is removed. See this figure:

    • Good job Web. It would be interesting to check measurements from other latitudes and compare it to the corresponding latitude band SST.

  10. Martin Heimann

    Keeling published an analysis of the changes of the seasonal cycle (amplitude and phase) and its possible causes in Nature, 1996 (v382, 146-149). There’s a big increase (almost 20% at Mauna Loa and almost 40% at Pt. Barrow) of the amplitude from the 1960′s to the 1980′s and 1990′s. The data in that publication go only until 1995. Extending their analysis until 2010 shows that the amplitude at Mauna Loa did not increase that much further.

    In any case, the method to compute the changes in the amplitude is quite important – the wavelet method employed here might gives quite different results as the ones published by Keeling…

    • The authors of this poster find an increase in amplitude (~10%) from early 70′s thru the early 90′s and subsequent decrease (thru 2004).

      They mention that Keeling attributed the increase to “greening” due to warming and suggest that the subsequent “decrease” (based on just a decade.) may be due to drought.

  11. We thought that this Yale University study on the polarization of attitudes towards climate change over the last decade might be of interest, given the thread topic of rising CO2 concentrations. Please feel free to contact Steve Gibb for more information or to interview the author(s) – , 202-422-5425.

    The news release can be found at:

    [Response: Correction: the thread topic is not rising CO2 concentrations. It's the annual cycle of CO2 variations.]

  12. Just a couple of questions. How did you detrend the series? I assume that since the accumulated co2 trend approximates a quadratic fit, that is how you detrended it.

    I can see using a sinusoidal fit for the phase, but wouldn’t it be better to simply take the variance of each 12 month timeseries to measure the trend in the signal? That is, for a simple sinusoidal wave the variance is a measure of the amplitude and for a combination of sinusoids the variance is a measure of the average power of the signals. Then again, as you stated, there a many alternatives.

    • And by “variance is a measure of the signal” I meant amp=sqrt(2*var)

      If I were to choose a way to measure the “amplitude” of the signal, I’d probably use the R function pwelch to measure the average power and then convert back to amplitude. Once you start to lose the R^2 on the sinusoid, you also lose the amplitude. That might be important in the case of Barrow. Then again, I’d probably just use the trend in average power and forget about amplitude.

      I’d also consider using a running 24-36 month filter. A somewhat cryptic R demonstration of what I’m trying to convey is here:

    • I took my own advice and detrended the Barrow data quadratically and then used the variance for each 12 month period to calculate the amplitude. The results are generally the same as Tamino’s, only the linear trend is more apparent. I get a 20% increase in amplitude for the 30yrs after 1975.

      This source code should be copy and paste-able into R, assuming that wordpress doesn’t change it:

      # Get Barrow co2 data and create a 1D vector
      co2 = t(as.matrix(
      len = length(co2)
      dim(co2) = len

      # use quadratic fit to detrend

      x = 1:len

      quadfit = lm(co2 ~ x^2 + x)
      dtco2 = co2 – predict(quadfit)

      # show that slope and intercept are ~zero
      summary(lm(dtco2 ~ x))

      # setup an array of all 12 month periods in sample
      n = 12
      x = 1:(len-n+1)

      arrco2 = NULL
      for (i in x){arrco2 = rbind(arrco2,dtco2[i:(i+n-1)])}

      # use variance to calculate *semi-amplitude*
      var = apply(arrco2,1,var)
      amp = sqrt(2*var)

      # calculate trend line
      x = 0:(length(amp)-1)
      linfit = lm(amp ~ x)
      trndline = predict(linfit)

      t = seq(1976-1/24,2008-1/24,1/12) # seq of end-dates

      # plot results

      #linear regression summary

      # trend per decade
      linfit$coeff[2] * 120

  13. You can see the plankton pulse around 6:04-6:15 in this movie:
    That’s from this page:
    which was in a search result here:

  14. record-breaking phytoplankton bloom hidden under Arctic ice. The finding is a big surprise — few scientists thought blooms of this size could grow in Arctic waters. The finding implies that the Arctic is much more productive than previously thought — researchers now think some 25% of the Arctic Ocean has conditions conducive to such blooms (abstract).