Residence Time and Prof Essenhigh

Residence Time is something that crops up now and then in the denialist literature.  A classic example is a 2009 paper titled “Potential Dependence of Global Warming on the Residence Time (RT) in the Atmosphere of Anthropogenically Sourced Carbon Dioxide” (Energy & Fuels 2009, 23, 2773) by Essenhigh.  Thankfully Gavin Cawley has now managed to publish a response, which should settle the matter (http://pubs.acs.org/doi/abs/10.1021/ef200914u).  However, I thought it might be helpful to explain the science with a simple analogy that is easily accessible.

In the original Essenhigh [1] paper a Sankey diagram is presented (reproduced below [2]).  It includes the following data:

Flows into the atmosphere:

Flows out of the atmosphere:

Atmospheric content: 750Gt

Essenhigh's argument is that residence time (which is the content divided by the outflow) is 750Gt divided 153.3Gt/y, which equates to ~5 years.  Therefore human contributions are irrelevant because the molecules of carbon dioxide that we put into the atmosphere are removed within 5 years.

What he ignores (though it’s equally clear in his own diagram) is that there is a net flow into the atmosphere of 2.2Gt/year.  It is this flow that would be absent without fossil fuels (and other activities like deforestation) and therefore is rightly attributed to man’s behaviour.

Allow me to make a simple analogy with a queue (this idea comes from Prof David MacKay’s [3] highly readable Sustainable Energy: Without The Hot Air, which is available for free on-line):

Consider a queueing system which can handle 150 people per hour (cf 150Gt/y).  Suppose 150 people are arriving per hour, and there are 750 people in the queue (cf 750Gt carbon content in the atmosphere).  Then it is clear that a person will be in the queue for 5 hours (cf 5 year residence time).  

However, if the number of people arriving goes up to 155 people per hour, clearly the queue will grow (cf an increase in the atmospheric carbon content), even though the queueing system will initially continue to have a ‘residence time’ of 5 hours (though it slowly grows from there).

From this it is apparent that the residence time is not the pertinent factor.  In our analogy, the important factor is the number of people in the queue (cf the amount of carbon in the atmosphere).  It is this that changes over the order of hundreds of years, even though any given molecule is only in the atmosphere for 5 years.  The studies that calculate this time scale are not making the elementary error of forgetting about natural flows as is suggested in the Essenhigh paper.

For a more detailed discussion, including evidence from the shift in isotope concentration, see the more recent IPCC reports (also available for free). Section 2.3 (Chemically and Radiatively Important Gases), and Section 7.3 (The Carbon Cycle and the Climate System) are particularly relevant in this context.

The Essenhigh paper also makes the assumption that the exit flow is proportional to the atmospheric concentration (that is, that the exit from the atmosphere will increase as the CO₂ concentration in the atmosphere increases).  This quibble is not as central as the queue analogy discussed above, but nonetheless is an interesting demonstration of how simple assumptions can give wrong results.  The reality is that there are positive feedback loops in many cases, so that increased CO₂ causes heating which causes an increase in CO₂ (and other greenhouse gases) through the melting of permafrost, the heating of the oceans (which releases CO₂ as it heats), and the reduction of vegetation (for example the Amazon is projected to become drier as the climate changes).  This could cause abrupt and irreversible climate change.  Completely the opposite of Essenhigh's a priori assumption that higher concentrations cause higher uptake.

[1] Robert Essenhigh is an Emeritus Professor of Mechanical & Aerospace Engineering at Ohio State University.

[2] For the sake of readers who may not have access to Energy & Fuels, below is the diagram from Energy & Fuels 2009, 23, 2774

Essenhigh Energy & Fuels, 23, 2774, 2009, Figure 1

[3] David MacKey is the Regius Professor of Engineering at the University of Cambridge, and chief scientific advisor to the UK Department of Energy and Climate Change.

Posted by Glenton Jelbert on Thursday, 3 October, 2013


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