Latest Trends in CO2

New and improved! This is the first in a series of group posts (mob blogging) by a few bloggers who are interested in the science of climate change. As a first topic, we have chosen the carbon cycle. All of us encourage comments and discussion. We will happily cross-post and feature comments that we think add value to the mob. There will also be a links to other resources on the carbon cycle that the mob and the mice thinks are really, really good. In addition to this post:

Eli Rabett at Rabett Run has a fascinating post about the cycling of carbon between atmosphere, oceans, and land, and the actual dynamics of how carbon moves around among the various reservoirs. He discusses a simple and comprehensible model and offers the interested reader a spreadsheet for calculations.

Meanwhile, Maribo ponders the question, “Where does all the carbon go?”

I’d like to tackle the question, just how fast is CO₂ increasing in earth’s atmosphere, really? I’ve posted about CO₂ in the atmosphere before, about its history and present rate of increase. Very recent developments indicate that the rate of change of atmospheric CO₂ may accelerate; while emissions from human activity have increased, the ability of the oceans and biosphere to absorb CO₂ may be poised to decrease. In this post I’d like to discuss the most current information about CO₂ levels and trends. In particular, I’d like to give you a good estimate of the present rate of increase of atmospheric CO₂, and show you how I arrived at that estimate.

Since 1958, atmospheric CO₂ concentration has been monitored at the Mauna Loa atmospheric observatory in Hawaii. It has since been measured at a number of locations around the world, which enables us to determine that CO₂ is a well-mixed greenhouse gas, i.e., it tends to mix thoroughly throughout the atmosphere so its concentration worldwide is very nearly equal. There are some regional differences, because the “mixing time” is about six months. This means that man-made CO₂, which is mostly generated in the northern hemisphere, takes a little while to mix into the southern hemisphere atmosphere, so the concentration in the southern hemisphere is generally slightly lower than in the northern.

Also, there is an annual cycle in CO₂ concentration. Most of the land plants are in the northern hemisphere (since most of the land is in the northern hemisphere), and during summer they remove CO₂ from the air as they grow, during winter they decay and return it to the air. We can see this cycle plainly in a graph of CO₂ concentration (measured in ppmv, or “parts per million by volume”) measured at a northern hemisphere station, Mauna Loa (data are monthly averages from Feb. 1958 to Apr. 2007):

But because the mixing time is around six months, the annual pattern takes a while to diffuse into the southern hemisphere. Because of this, it is both “smoothed” (so the southern hemisphere shows less annual variation than the northern) and delayed (so the southern hemisphere annual cycle peaks when the northern hemisphere cycle troughs, and vice versa). Also, the southern hemisphere measurements reflect the respiration of land plants in the southern hemisphere, where the seasons are opposite those in the north. We can note all these differences by comparing the CO₂ concentration measured at Mauna Loa, to that measured at the south pole station (south pole data are monthly averages from Jul. 1975 to Dec. 2005):

For both the Mauna Loa and south pole data, there are two obvious patterns present. One is an annual cycle (larger at Mauna Loa, smaller at south pole). The other is a steady increase during this observation window. Let’s focus on the time interval from 1975 to the present (we have data from both locations for almost all of this interval). We can remove the known trends by finding the best fit of an annual cycle, together with a steady (linear) trend, using mathematical curve-fitting methods. This gives the following patterns for Mauna Loa and the south pole:

This graph shows what the CO₂ concentration would be, if it followed a regular annual cycle together with a steady increase. For Mauna Loa, the rate of steady increase over the time interval 1975 to the present is 1.60 ppmv/yr, while at the south pole it’s 1.55 ppmv/yr. Also, at Mauna Loa the amplitude of the annual cycle (difference between maximum and minimum) is nearly 6 ppmv, while at the south pole it’s barely over 1 ppmv.

But the CO₂ concentration does not follow such a simple pattern. We can examine the deviation from simplicity, by subtracting the simple pattern from the observed data, leaving residuals. These residuals show us how CO₂ concentration is changing, in addition to the simple pattern of a regular annual cycle and steady increase. We can call these residuals the CO₂ Anomaly. Here are the results for Mauna Loa and south pole station:

From this we can plainly see that actual CO₂ concentration has deviated meaningfully from the annual+linear pattern we fit earlier. There are many mathematical models we can apply to approximate these deviations. For example, it is often stated that the concentration of atmospheric CO₂ shows exponential growth. It is sometimes stated that the concentration follows a quadratic trend. The fact is that the available data cannot distinguish between these models in a statistically significant way. In fact they all model the observed data effectively, and the difference between the models is very small. When choosing a mathematical model, we should pick one which matches the observed data within the limits of statistical significance, and is simple!

I’ll choose a very simple model for Mauna Loa data since 1975: the rate of change is steady but lower-than-average during a first time interval, then it is steady but higher-than-average for the remainder of the time interval. Using this model, we can determine mathematically the best choices of rates for each of the time intervals, as well as the moment when the rate changes from one value to another. This is modelled in this graph:

Let me emphasize that this is not to say that atmospheric CO₂ concentration actually did switch from one constant rate to another about mid-1997. Rather, this model fits the data better than the annual+linear model we used earlier. Furthermore, the difference is statistically significant, so we can say with confidence that since mid-1997, CO₂ has been increasing faster than it was before mid-1997.

The rate of change from mid-1997 to the present in this analysis is 0.37 ppmv/yr. But that is in addition to the average rate of 1.60 ppmv/yr we already accounted for. So the average overall rate from mid-1997 to the present is 1.60 + 0.37 = 1.97 ppmv/yr.

Just as before, we can subtract this trend from the data since mid-1997, to produce a second set of residuals (or anomalies, whatever we choose to call them. This general procedure, of identifying a pattern in data, subtracting out that pattern, finding new patterns in the residuals, subtracting away those, etc., is a procedure known as pre-whitening. If we graph the “2nd residuals” since mid-1997, we get this:

We can see that these 2nd residuals also show some pattern. In particular, they seem to rise rapidly at the beginning, then quickly decline, then show a more steady increase. So I’ll apply the “multi-rate” model again, but this time with three rates of change. Again, I’ll let the numbers decide what the three rates are and when the data changes from one rate to another. For this model we get:

The latest rate of increase in this model is from May 2000 to the present. The actual rate for these residuals is 0.14 ppmv/yr. But that, of course, is in addition to the 1.97 ppmv/yr we already found as the average rate from mid-1997 to the present. We conclude that for the time interval from May 2000 to the present, the average rate of increase of atmospheric CO₂ is 1.97 + 0.14 = 2.11 ppmv/yr.

We can, in fact, subtract this trend from the data since May 2000 to generate “3rd residuals,” and look for even more patterns. When we do so, however, we find that there are no patterns related to the overall trend that are statistically significant. So, when it comes to estimating the overall trend in the rate of increase of CO₂, we’ve gone about as far as we can go. We can identify many time intervals during which the rate is different, but the most recent interval is May 2000 to the present, and the rate during that interval is the highest of all: 2.11 ppmv/yr.

If we start by analyzing the data from May 2000 to the present, taking the original Mauna Loa data and fitting an annual trend plus a steady increase, then the rate we get for the steady increase is 2.11 ppmv/yr — exactly the same! This is reassuring, that we’re on the right track. But we wouldn’t have known, without looking further back in time, that May 2000 was the latest “turning point” for the CO₂ increase rate.

I emphasize again that this does not establish that the actual pattern is a set of straight lines, each corresponding to a constant rate. However, this analysis does establish that the rate since May 2000 has been constant as far as we can tell with statistical significance from the available data. The rate of change of CO₂ is different from year to year, and there are indeed random fluctuations, but right now, my best estimate of the sustained rate is an increase of 2.11 ppmv per year. The present level of CO₂ (not counting the annual cycle) is 383.5 ppmv.

This much is beyond doubt: the growth rate of atmospheric CO₂ is larger now than at any other time covered by modern instrumental measurements. It is also larger now than at any time during at least the last 600,000 years, according to measurements made from ice cores. CO₂ is increasing, its rate of increase is very rapid, and the cause is (without doubt) the burning of fossil fuels by humans.

I will close with a few interesting observations. When we looked at the 2nd residuals, we noted a rise from mid-1997 to about mid-1998, then a drop to May 2000, then the present rate of increase. The sharp rise mid-1997 to mid-1998 is associated with the strong el Nino of that year. The CO₂ change is not directly due to the warmer ocean water of the el Nino; rather it appears to be due to the drought conditions over land associated with the el Nino. Drought reduces the amount of carbon locked in the biosphere, and therefore increases it in the atmosphere — temporarily. This appears to be the reason for the spike in CO₂ in 1998.

Finally, we noted from the beginning the annual cycle in the Mauna Loa data, and I mentioned earlier that the amplitude of the cycle was about 6 ppmv. However, this amplitude has also shown changes over time. We can track the amplitude using a wavelet transform. This graph shows not the amplitude over time, but the semi-amplitude (which is just half the amplitude):

At the very beginning of the observation window, the cycle was considerably smaller. But even in more recent times, the cycle shows signs of growing larger, and the most recent data show the largest cycle of all.

Not only has the atmospheric concentration of CO₂ been increasing, not only has the rate of increase been getting larger, the amplitude of the annual cycle has also been increasing. Presently, about half the CO₂ emitted by human activity is absorbed (chiefly by the oceans) while the other half is responsible for the increase in atmospheric concentration. But recent signs are that both the oceans and the biosphere may soon reduce their ability to absorb the CO₂ emitted by humans. This would cause the rate of change of atmospheric CO₂ to increase, dramatically and rapidly, unless we compensate by reducing the amount of CO₂ emitted by mankind. There is also the possibility that other greenhouse gases may increase rapidly. If the permafrost thaws completely (and it is thawing now, due to global warming), it will release the trapped greenhouse gases, and that is a very large reservoir of both CO₂ and methane. There’s quite a bit going on with atmospheric CO₂ concentration, and as this has a profound effect on earth’s climate, it bears watching.

UPDATE UPDATE UPDATE UPDATE UPDATE:

Andrew Dodds was kind enough to provide a link to CO₂ emissions data. I estimated the high-time-resolution CO₂ growth rate by taking the difference between each monthly atmospheric CO₂ value and the value one year previously. This enables me to compare the growth rate to the emissions; the result is plotted here:

Clearly the growth rate shows a lot of natural fluctuation, and although the sustained growth rate (on multi-year timescales) is directly related to the emissions rate, the short-term fluctuations are not; emissions have been much smoother than the CO₂ growth rate.

Much of the fluctuations in growth rate are probably due to the biosphere, as mentioned in this post. It is also pointed out in reader comments to both Rabett Run and Maribo that recent research indicates wildfires (accelerated by drought conditions, such as are prominent during a strong el Nino) may be a very important factor in the biosphere influence on atmospheric CO₂ growth:

From Rabett Run’s reader comments:

Anonymous said…

I don’t see “wild-fire” anywhere on your Rube Goldberg contraption (unless that is included in “deforestation”)

As NASA has found, it can be very significant. For example,NASA has some interesting findings related to CO2 increase during El Niño

“Many scientists thought the increases in greenhouse gases during El Niño years were likely due to a changing balance of plant growth and death. However, new research is providing a different diagnosis to the source of the Earth’s heartburn.

El Niño Gives Wildfires a License to Burn

Wildfires seem to ignite the geological version of the big belch. During El Niño, vast areas of the tropic regions dry out and become vulnerable to fire. During the 1997/1998 El Niño, wildfires ravaged huge areas in Latin America and Southeast Asia, belching large quantities of carbon dioxide (CO2) and methane into the air.

“We found that a large part of the [carbon dioxide] increases [were] the result of increased fire activity,” said Guido R. van der Werf, of NASA’s Goddard Space Flight Center.

Horatio Algeranon

From Maribo’s comment fields:

Alexander said…

Hi,

good post, only I would add up some more info on the ii) possible feedback effects – a recent study using NOAA AVHHR satellites found no global increase in burned area -from 1980 to 2000. However, it found significant increase in some parts of the world. Still, the recent years experienced redord braking or unusual wild fire activity in many parts of the world (USA, Canada, Russia, Australia…) – see the graphs in my post – http://ac.blog.sme.sk/c/98483/Analyza-lesnych-poziarov-existuje-globalny-trend.html – see the graphs and links inside.

Further, after a wildfire, the ecosystem is “source” of CO2 for several years, due to increased soil respiration…