Friday, August 8, 2008

Just in case there are any doubts about anthropogenic influence in atmospheric CO2

You would think this is the least controversial aspect of the global warming debate, but you'd be surprised. I realized this after reading some of the comments in a post by Anthony Watts about a recent correction in the way Mauna Loa data is calculated (see also reactions by Tamino and Lucia).

Tamino subsequently wrote an interesting post on differences in CO2 trends as observed in three different sites: Mauna Loa (Hawaii), Barrow (Alaska) and South Pole station. Most notably, there's a pronounced difference in the annual cycle between these stations, which according to Tamino, is explained by there being more land mass in the Northern Hemisphere. I would imagine higher CO2 emissions in the Northern Hemisphere might also play a role, but I'm speculating.

In this post I want to show that available data is quite clear about anthropogenic influence in atmospheric CO2. Additionally, I want to discuss how we can tell that excess CO2 stays in the atmosphere for a long time.

I will use about 170 years of data for this. There's a reconstruction of CO2 concentrations from 1832 to 1978 made available by CDIAC, and derived by Etheridge et al. (1998) from the Law Dome DE08, DE08-2, and DSS ice cores. You will note that there's an excellent match between these data and Mauna Loa data for the period 1958 to 1978. Mauna Loa data has an offset of 0.996 ppmv relative to Etheridge et al. (1998), so I applied this simple adjustment to it in order to end up with a dataset that goes from 1832 to 2004.

CDIAC also provides data on global CO2 emissions. What we need, however, is an estimate of excess anthropogenic CO2 that would be expected to remain in the atmosphere at any given point in time. We could simply calculate cumulative emissions since 1751 for any given year, but this is not necessarily accurate. Some excess CO2 is probably reclaimed by the planet every year. What I will do is make an assumption about the atmospheric half-life of CO2 in order to obtain a dataset of presumed excess CO2. I will use a half-life of 24.4 years (i.e. 0.972 of excess CO2 remains after 1 year). I should note that I have tried this same analysis with half-lifes of 50, 70 and 'infinite' years, and the general results are the same.

Figure 1 shows the time series of the two data sets.

co2 concentration and emissions

The trends are clear enough. CO2 emissions appear to accumulate in the atmosphere and are then observed in ice cores (and at various other sites like Mauna Loa). Every time we compare time series, though, there's a possibility that we're looking at coincidental trends. A technique that can be used to control for potentially coincidental trends is called detrended cross-correlation analysis (Podobnik & Stanley, 2007). In our case, the detrended cross-correlation is obvious enough graphically, and we'll leave it at that. See Figure 2. Basically, we take the time series and remove their trends, which are given by third-order polynomial fits. You can do the same thing with linear fits or second-order first. The third-order fit is a better fit and produces more fluctuations around the trend, which makes the correlation more obvious and less likely to be explained by coincidence.

detrended residuals co2 concentration emissions

With that out of the way, how do we know that excess CO2 stays in the atmosphere for a long time? First, let's check what the scientific literature says on the subject, specifically, Moore & Braswell (1994):

If one assumes a terrestrial biosphere with a fertilization flux, then our best estimate is that the single half-life for excess CO2 lies within the range of 19 to 49 years, with a reasonable average being 31 years. If we assume only regrowth, then the average value for the single half-life for excess CO2 increases to 72 years, and if we remove the terrestrial component completely, then it increases further to 92 years.

In general, it is widely accepted that the atmospheric half-life of CO2 is measured in decades, not years.

One type of analysis that I have attempted is to select the half-life hypothesis that maximizes the Pearson's correlation coefficient of the series from Figure 1. If I do this, I find that the best half-life is about 24.4 years. Nevertheless, I had attempted the same exercise with the Mauna Loa series (1958-2004) previously, and the best half-life then seems to be about 70 years. It varies depending on the time frame, and there's not necessarily a trend in the half life. This just comes to show that there's uncertainty in the calculation, and that the half-life model is a simplification of the real world.

Another approach we can take is to try to estimate the weight of excess CO2 currently in the atmosphere, and see how this compares to data on emissions. The current excess of atmospheric CO2 is agreed to be roughly 100 ppmv. If by 'atmosphere' we mean 20 Km above ground (this is fairly arbitrary) then the volume of the atmosphere is about 1.03x1010 Km3. This would mean that the total volume of excess CO2 is 1.03x106 Km3, or 1.03x1015 m3. The density of CO2 is 1.98 kg/m3, so the total weight of excess CO2 should be about 2.03x1015 Kg, or 2,030,000 millions of metric tons.

Something is not right, though. If we add all annual CO2 emissions from 1751 to 2004, we come up with 334,000 millions of metric tons total. This can't be. I'd suggest that CDIAC data does not count all sources of anthropogenic emissions of CO2. It obviously can't be considering feedbacks either. Furthermore, our assumptions in the calculations above might not be accurate (specifically that a 100 ppmv excess is maintained up to an altitude of 20Km). In any case, it's hard to see how these numbers would support the notion that the half-life of CO2 is low.


Joel said...

A couple comments:

(1) Indeed as you note, the characterization of CO2 as having a single halflife is a large simplification. There is a good post by David Archer at RealClimate on the subject:
His conclusion is "A better shorthand for public discussion might be that CO2 sticks around for hundreds of years, plus 25% that sticks around forever."

(2) There is indeed something not right about your estimates of the total amount of CO2 we have released into the atmosphere and the total amount by which CO2 in the atmosphere has increased. The "correct answer" is that roughly half of what we have released has remained in the atmosphere, with the other half going into the biosphere and oceans. One clear mistake in your calculation of the amount of excess CO2 in the atmosphere is assuming a density of 1.98 kg/m^3. This is the density at some specific temperature and pressure (presumably 1 atmosphere and roughly room temperature). By the time one gets up to 20 km, the density would be only a small fraction of that since the pressure would be a lot lower. This is probably not enough of an effect to explain the full discrepancy in your calculation but should at least get you closer to the right answer.

Joseph said...

Thanks Joel. You might be right about (2). The relative volume of CO2 could still be close to 380 ppmv, say, 10 Km high (Mauna Loa is 4 Km high), but the weight of CO2 will not be the same.

Anonymous said...

Actually you should instead of 20 km use the (base-e) scale height of the atmosphere, 8 km. Then you get 800,000 Mt of CO2.

An alternative computation is considering the weight of the atmosphere, 1 kg/cm^2. 100 ppmv is then (44/29)*10^-4 mass fraction. Multiply by Earth surface area 512 million km^2 gives 777,000 Mt.

Anonymous said...

> Something is not right, though.
> If we add all annual CO2
> emissions from 1751 to 2004, we
> come up with 334,000 millions
> of metric tons total. This
> can't be.

Don't mix up carbon with CO2 -- you have to multiply with (44/12), yielding 1,130,000 Mt. Still seems a bit low, but deforestation is missing.

Joseph said...

So CDIAC data is on Carbon emissions? They sometimes say CO2 and sometimes Carbon. I thought that was confusing.