2011-08-11 18:44:06ADVANCED 66: CO2 has a short residence time
Dikran Marsupial
Gavin Cawley
gcc@cmp.uea.ac...
139.222.14.107

Skeptic arguments based on the short residence time of carbon dioxide in the atmosphere are based on a fundamental misunderstanding of the difference between residence time and adjustment time of atmospheric CO2.  The difference between residence time and adjustment time will be discussed shortly, however, we will begin by demonstrating that while the premise is true (CO2 does have a short residence time of only about 4 years), the conclusion does not follow from the premise; the post-industrial rise in atmospheric CO2 is known with great certainty to be of anthropogenic origin.

The Mass Balance Argument

The most basic proof that the rise in atmospheric carbon dioxide cannot be a natural phenomenon is given by the mass balance argument.  I we assume that the carbon cycle is a closed system, where carbon is neither created, nor destroyed, but merely circulates between the atmospheric, oceanic and terrestrial reservoirs, then the annual change in atmospheric carbon dioxide is simply the difference between total emissions into the atmosphere from all sources and total uptake by all sinks.  Mathematically, we can write this as:

C' = Fa + Fi - Fe

were C' is the annual change in atmospheric carbon (C is the mass of the atmospheric reservoir and the prime ' is used to denote the difference), Fa represents anthropogenic emissions (from fossil fuel and land use change), Fi represents the influx of carbon into the atmosphere from all natural sources and Fe represents the efflux of carbon due to all natural sinks.  Hopefully this ought to be uncontraversial!

The next step is a simple algebraic rearrangement of the mass balance equation to give:

Fi - Fe = C' - Fa

This says that the annual difference between the influx of carbon into the atmosphere from all natural sources and the uptake of carbon from the atmosphere by all natural sinks is equal to the difference between the annual change in the mass of the atmospheric reservoir and annual anthropogenic emissions.  Clearly if anthropogenic emissions exceed the annual increase in atmospheric CO2 (i.e. Fa > C') then the right hand side of this equation will be negative and thus so must be the right hand side, which means that Fe > Fi, implying that the natural environment is a net carbon sink, removing more carbon dioxide from the atmosphere each year than it emits.

So what do the data tell us?  Accurate observations of background atmospheric CO2 taken at the Mauna Loa obsevatory are available going back to 1958 here (Keeling 2009) from which the growth rate, C', can be calculated.  Estimates of anthropogenic emissions from fossil fuel (Boden 2009) and land use changes (Houghton 2008) are available here and here respectively.  These data are shown in Figure 1, along with the implied natural net flux Fi - Fe.  All data have been converted to units of GtC, using the conversion factor C = 2.35 × ppmv (Essenhigh, 2009).  Clearly anthropogenic emissions have exceeded the growth rate consistently over the last fifty years, and so we know that the natural environment has been a net carbon sink over this period, actively opposing the rise in atmospheric carbon dioxide!

Mass balance

Figure 1 Annual anthropogenic emissions, Fa, annual growth rate C' and inferred environmental net flux Fi - Fe, in GtC per year (c.f. Raupach et al (2008), Figure 1d).

Note that we don't need to know the magnitudes of the natural fluxes Fe and Fi to know that Fi-Fe is negative and the natural environment is a net sink.  As an analogy, consider a married couple with a joint bank account.  If the husband deposited £10 a week and never withdrew anything, but the balance rose by only £5 per week, he would know that his wife was taking £5 a week more out of the account than she was putting in.  This is true even if the husband knows nothing about the individual transactions his wife is making, she could be depositing £10 a week and withdrawing £15 a week, or depositing £1,000,000 a week and withdrawing £1,000,005 a week, he would still know that she was taking more out of their account than she was putting in!  A common skeptic counter-argument is that our knowledge of the activity of natural sources and sinks is highly uncertain and so it is impossible to tell whether the natural environment were a net source or a net sink.  However, the mass balance argument provides an indirect means of estimating the net natural flux without needing to know the magnitudes of the fluxes Fi and Fe themselves.  The error bars on the net natural flux estimated by the mass balance argument depends solely on the error bars on the growth rate and on anthropogenic measurements, both of which are known with a high level of certainty.  Regardless of the large error bars on Fi and Fe, we can still be highly confident that Fe > Fi i.e. the natural environment is known to be a net sink.

Residence Time versus Adjustment Time

Residence time is the average length of time a molecule of carbon dioxide remains in the atmosphere before being taken up by the oceanic or terrestrial reservoirs.  The standard definition of the residence time is the ratio of the mass of a reservoir and the total rate of removal from that reservoir (e.g. Solomon et al (2007), page 948, n.b. the IPCC refer to the residence time as "turnover time", but the concept is the same.).  FIgure 2 shows estimates of the fluxes into and out of the atmosphere from the IPCC WG1 report (Solomon et al. 2007).  The mass of the atmospheric carbon reservoir is 597+165 = 762 GtC; the fluxes from the atmosphere into the oceanic reservoir is 70+22.2= 92.2 GtC/year and into the terrestrial reservoir 0.2 + 120 + 2.6 = 122.8 GtC/year.  Thus the residence time is given by

T = 762/(92.2 + 122.8) = 3.54 years

Thus the IPCC estimate of the residence time is in fact slightly shorter than the estimate of 5-15 years suggested by Essenhigh (2009).

Figure 2 Estimates of the mass of oceanic, terrestrial and atmospheric reservoirs (in GtC) and fluxes between reservoirs (in GtC/year); figures shown in black represent the pre-industrial estimates, figures shown in red represent the post industrial peturbations of those reservoirs and fluxes (from Solomon et al. 2007, page 151).

A Simple One-Box Model of the Carbon Cycle

blah blah blah

A Challenge to those who Question the Anthropogenic Cause of the Post-Industrial Increase 

That the observed rise in atmospheric carbon dioxide is of essentially purely anthropogenic origin is one of the few issues in climatology where the science is settled beyond reasonable doubt.  The first challenge that anyone who seeks to overturn this gernerally accepted position is to explain why the observed annual rise in atmospheric CO2 has historically been less than anthropogenic emissions if both the natural environment and mankind are net sources of carbon into the atmosphere, or alternatively to explain how the natural environment can be the cause of the observed increase while having been a net sink for at least the last fifty years. 

References

Boden, T. A.; Marland, G.; Andres, R. J. Global, Regional, and National Fossil-Fuel CO2
Emissions. Carbon Dioxide Information Analysis Center, Oak Ridge Laboratory U.S. Department
of Energy, Oak Ridge, Tennesee, U.S.A., 2009.

Essenhigh, R. H. Energy and Fuels 2009, 23, 2773–2784.

Houghton, R. A. Carbon flux into the atmosphere from land-use changes: 1850-2005. In
TRENDS: A Compendium of Data on Global Change, Carbon Dioxide Information Analysis Center, Oak Ridge Laboratory U.S. Department of Energy, Oak Ridge, Tennesee, U.S.A.,
2008.

Keeling, R. F.; Piper, S. C.; Bollenbacher, A. F.; Walker, J. S. Atmospheric CO2 records
from sites in the SIO air sampling network. In Trends: A Compendium of Data on Global
Change, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S.
Department of Energy, Oak Ridge, Tennesee, U.S.A., 2009.

Raupach, M. R., Canadell, J. G. and Le Quére, C., Biogeosciences, 2008, 5, 1603-1613

Solomon, S., Qin, D., Manning, M., Marquis, M., Averyt, K., Tignor, M. M. B.,
Miller Jr., H. L., Chen, Z., Eds. Climate Change 2007 : The Physical Science Basis - Working
Group 1 Contribution to the Fourth Assessment Report of the Intergovernmental Panel on
Climate Change; Cambridge University Press: Cambridge, U.K., 2007.

(work in progress)