Guest Post by Willis Eschenbach

A 2015 paper by Xiaochun Zhang and Ken Caldeira has come to my attention. Inter alia, the abstract says:

For example, the global and time‐integrated radiative forcing from burning a fossil fuel exceeds the heat released upon combustion within 2 months. Over the long lifetime of CO2 in the atmosphere, the cumulative CO2‐radiative forcing exceeds the amount of energy released upon combustion by a factor >100,000. 

That made my bad number detector start flashing red. So I decided to do my own rough calculations. Here’s my work. I’ve used values for the amount of carbon which would be needed to be burned in order to raise the atmospheric CO2 by one part per million by volume (1 ppmv)

BURNING CALCULATIONS 

2.1E+12 — kilograms of airborne carbon (as CO2) per ppmv of CO2

43% — airborne fraction, the amount of the CO2 emissions that remain airborne

5.0E+12 — kilograms of emissions of carbon needed to raise atmospheric CO2 levels by 1 ppmv

70% — average carbon content of coal

7.1E+12 — kilograms of coal burned per ppmv of CO2 increase

2.4E+07 — joules per kilogram, energy content of coal

1.7E+20 — total joules per year from burning 7.1E+12 kg of coal

FORCING CALCULATIONS 

0.013 — additional forcing in watts per square meter (W/m2) when CO2 goes from 400 to 401 ppmv

420,608  — convert watts per square meter to joules per year per square meter

5.1E+14 — square meters, surface area of earth

2.1E+20 — total joules per year from 1 ppmv additional forcing

So in year one, CO2 radiativeforcing gives about 30% more energy than we got from burning coal. 

And in the following thousand years, depending on the carbon model chosen (IPCC Bern model, or Joos model as in their paper), we end up with between 250 to 400 times the energy from the CO2 radiative forcing as from the burning of the coal.

Now, recall that the claim was that the “cumulative CO2‐radiative forcing exceeds the amount of energy released upon combustion by a factor >100,000”.

And I got a factor of 250-400. So my question is … have I made an error, and if so, where? Wouldn’t be the first time …

Notes:

Global coal consumption is about 8E+12 kilograms per year. Coincidentally, this is also about the amount of coal shown above as being needed to increase airborne CO2 by 1 ppmv.

I do not think that an increase in CO2 forcing perforce means a temperature increase. I think it is counterbalanced by changes in emergent phenomena that counteract the slight change in radiative forcing. 

I call it a “slight” change in radiative forcing because I divide the phenomena that affect some given system into 1st, 2nd, and 3rd order variables.

What I call “first order variables” represent and can change more than ten percent of a signal. You generally need to include these in even an initial analysis. They are large enough to be significant.

Second order variables make up from one to ten percent of a signal. You need to include these variables in any more detailed analysis of a situation. 

Third order variables represent less than one percent of the signal. They are lost in the noise, and can be neglected in any but the most exhaustive and detailed analysis.

And how does this question of variable types apply to the annual global coal burning issue?

Global average downwelling radiation (solar plus longwave) is about five hundred watts. A year of global coal burning gives a hundredth of a watt per square metre change in this half-kilowatt system. 

That’s about two thousandths of one percent of the signal. Third order.

How about a longer-term effect? Well, it’s possible that by the year 2100 we’ll see CO2 levels double from the present. Or not. Here are some representative supply-driven scenarios:

Note that none make it But heck, for the sake of discussion let’s assume that technology doesn’t progress and nuclear is ignored and at some point in the next eighty years the CO2 level doubles. That would increase downwelling radiative forcing by 3.7 W/m2 … which is still only three-quarters of one percent of the total signal. Third order.

Here’s the difference. Clouds are a first order variable regarding the global energy balance. They can move the downwelling energy up and down by hundreds of watts in minutes. That’s on the order of fifty percent of the total five hundred watt average signal. Over ten percent, first order.

CO2 changes, at the other end of the spectrum, are a third order variable. Even an improbable doubling represents a change of less than one percent of the five hundred watt system. Lost in the noise. Counteracted by a small change in cloud emergence time and prevalence.

But I digress … so let me ask again:

Where is the error in my calculation of thermal versus radiative forcing of coal? I get a very different answer from that of Zhang and Caldeira.

Best to all. I’m still doing building construction in Alaska, near the Kenai River. A moose wandered by the window the other day. Yesterday afternoon it was a bald eagle parting a gaggle of seagulls. What a place! 

And of course, it being solstice, it’s never too dark to read headlines in the newspaper.

Warmest midsummer (or midwinter) wishes to everyone, podal and antipodal,

w.

As Usual: When commenting or pointing out my error, please quote the exact words that you think are wrong. Only in that way can we be clear about your meaning.