Monday
Aug122013
by 
Bishop Hill
Bishop Hill A new look at the carbon dioxide budget - Part 4
Aug 12, 2013 In this final part of his paper on carbon dioxide control mechanisms, David Coe draws together all the different strands of the paper.
Reader Comments (60)
David,
I thought that it was already clear from the graph I sent:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1960_cur.jpg
That shows that the increase in the atmosphere simply follows the increase in total CO2 in the atmosphere.
But here is a more complete picture, be it prepared to show the effect of the 14CO2 spike as result of the atomic bomb tests in the 1950's. Here the fluxes for the year 2000:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/14co2_distri_2000.jpg
As you may suspect, I did follow the main lines of the IPCC, as composed by NASA:
http://earthobservatory.nasa.gov/Features/CarbonCycle/
The main difference with your approach is that all reactions are bidirectional, but that the net flow is from the atmosphere into all other reservoirs, not the reverse as your solution shows.
About the calculations, here the overall formula which works for a year by year to 800 kyr variability:
dCO2/dt(emiss) = 0.026*(C-Ce)/dt + 4.5*dT/dt
where Ce = equilibrium CO2 level at current T with Ce = Co + 8*(T - To)
and To is the average temperature over the period 1960-1990 (HadCRU global).
That fits for the past 50 years:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_T_dT_em_1960_2011.jpg
where Bart's alternative is plotted too as dCO2/dt(temp)
That fits for the trend since 1900:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_T_dT_em_1900_2011.jpg
and it fits for the past 800 kyr, as the CO2 levels simply follow the temperature controlled equilibrium of ~8 ppmv/K:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/Vostok_trends.gif
The 13C levels are followed in the atmosphere and in the ocean surface with the IPCC (and my) approach, the 14CO2 bomb spike is explained, the oxygen balance fits, the mass balance fits.
So, what do you want more?
I have not included the seasonal changes in the above, but these are hardly relevant, as only the difference after a full seasonal cycle is of interest for the increase of CO2 and the other balances over time.
Why the increase in the atmosphere follows the human emissions at such an incredible fixed rate is probably just coincidence. With constant emissions, one would expect an assymptotic slowdown to a new equilibrium level. But as the human emissions increased faster over time, the levels in the atmosphere also increased faster over time and thus so did the sink rates:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_co2_acc_1900_2011.jpg
I still need to read and comment the rest of your part 2...
Ferdinand
Aug 17, 2013 at 9:52 PM Ferdinand Engelbeen
Ferdinand - thank you. I'll spend time digesting what you have said.
Ferdinand
On reflection my previous response was terse and ungracious, for which I apologise. I am actually most grateful that you are taking the time to read and comment fully on my paper. I still cannot accept your explanations but it is now for me to explain why in more detail. That I will do shortly.
Ferdinand
My day job involves the use of infrared spectrographic analysis of atmospheric pollutants. My familiarity with infrared spectra including that of CO2 made me suspicious of the claims about the effects that increasing CO2 will have on global temperatures. I thus began to read more, starting of course with the IPCC assessment reports, particularly TAR. I was intrigued by the description of the carbon budget and by the fact that it appears to be predicated on a zero net biome production.
Global net primary production from photosynthesis, I believe, is estimated at some 300GtC/yr. That this huge flux can be accurately balanced by heterotrophic respiration and decomposition takes a huge leap of faith, particularly when there is direct evidence in the shape of fossil fuel deposits that shows that for periods in the past net biome production was far from zero. If it was not zero in the past, why should it be zero now? The figure of NBP of 1GtC/yr that you quote I suspect has more to do with the belief of an almost zero NBP rather than actual measurement.
I was attracted to the 2000 paper by Keeling that showed the extent of seasonal variation of atmospheric CO2, particularly the measurements made at Alert and Point Barrow in the Arctic Circle. The seasonal variation at those two stations shows a relatively short but rapid reduction in CO2 levels as the biosphere bursts into life in the short summer season. During the long winter months those CO2 levels increase back to their original values. I have great difficulty in accepting that that restoration is due to respiration and decomposition during an arctic winter, when the landscape is frozen solid. I also cannot accept the argument that the CO2 is somehow “blown in “ from the south. What is the source of the seasonal restorative CO2 flux in the Arctic Circle?
If you mix water and CO2 in a sealed vessel, equilibrium will be reached whereby the partial pressure of the solvated CO2 will be equal to the partial pressure of the gaseous CO2 above that water. One would reasonably assume that a similar effect would occur between the oceans and atmosphere. On that basis, using a standard two box model of the ocean, where the deep ocean is separated from the mixed layer by the thermocline, it is possible to produce a set of equations linking both sea surface and atmospheric CO2 partial pressure with the net CO2 biological fluxes of both sea surface and atmosphere.
Those equations are
Atmospheric CO2 Ca = Cs − 1/g2.Fa.(1 – e−t/τ2)
and sea surface CO2 Cs = C0 – 1/g1(Fa + Fs)(1 − e−t/τ1)
Fa and Fs are the respective net atmospheric and sea surface biological fluxes, while g1 and g2 are the effective transfer factors affecting CO2 diffusion across the thermocline and sea surface.
At this point I make no assumptions about the magnitude or even sign of any of these parameters. We have in these equations a list of unknowns, namely
Co (CO2 partial pressure of the deep ocean), the fluxes Fa and Fs and the response times t1 and t2 of the thermocline and sea surface/atmosphere interface, related to the factors g1 and g2.
The only reliable data that we have to work with is the CO2 record at Mauna Loa from 1960 onwards and the assessment of anthropogenic emissions from that same period. Here come the first assumptions
1 Before the advent of anthropogenic emissions the system was in equilibrium with stable atmospheric and sea surface CO2 partial pressures.
2 All the increase in atmospheric CO2 levels since 1960 can be attributed to anthropogenic emissions.
3 The deep ocean CO2 partial pressure Co is constant over the period 1960 onwards.
Introducing the anthropogenic flux A into the equations above results in the representation for atmospheric CO2 partial pressure
Ca = C0 – 1/g1(Fa – A + Fs)(1 − e−t/τ1) − 1/g2.(Fa – A)(1 – e−t/τ2)
or Ca = C1960 + 1/g1.A(1 − e−t/τ1) + 1/g2.A(1 – e−t/τ2)
where C1960 represents the atmospheric partial pressure at Mauna Loa in the year 1960.
This has now reduced the number of unknowns to two, namely t1 and t2 (these are mathematically related to g1 and g2). We can make an intelligent guess at a value of the sea surface/atmosphere response t2 from the many estimates of residence time, which should be of the order of three exponential response times. I have guessed 3 years, equivalent to a residence time of 9years.
I now simply use the published data for CO2 partial pressure and anthropogenic emissions from 1960 onwards to calibrate the linear relationship between anthropogenic flux and CO2 partial pressure predicted by the equation to obtain a value for t1, the response time of the thermocline. The result is an extremely close agreement between calculation and observation.
Seasonal CO2 variations are accounted for by assuming a sinusoidal photosynthetic flux
Fa = D – Ecos(wt)
Interannual variations are created by adding the variability of sea surface temperatures and hence Henry constant and its effect on sea surface partial pressure.
I find that with these equations I can account with some considerable degree of accuracy for every observed effect of CO2 and O2.
The significance of the assumption of a 20ppm/yr NBP is just to normalise the quations to the CO2 value at 1960
C1960 = C0 – 1/g1(Fa + Fs)(1 − e−t/τ1) − 1/g2.Fa (1 – e−t/τ2)
An incorrect estimation of this value does not invalidate the maths. It merely suggests that I have made an incorrect estimation of deep ocean CO2 partial pressure as well. Note also that I make no assumption about the chemistry of the ocean. Everything is related to partial pressure and therefore solvated CO2.
I hope that this clarifies some of the confusion that I may have created.
David,
I have been a chemical engineer myself, worked in the chemical industry as process engineer, but in later decades shifted the interests and job into process automation. Now already near a decade retired...
I have had a lot of practical experiences, but too little theoretical practice, so much of control theory etc. is lost in memory...
I think that we agree on the basic point that the increase of CO2 - whatever the cause - will have little impact on climate. Where we disagree is the cause of the increase...
My impression of your work is that it is very well thought out, but you did start with a few assumptions of what others (the IPCC in particular) wrote, which aren't completely right.
Take e.g.:
it appears to be predicated on a zero net biome production.
Until begin 1990's the total biosphere was a small, but net source of CO2 in the atmosphere. That was calculated from the change in 13C/12C ratio, taking into account the human emissions. Oxygen measurements with sufficient accuracy weren't possible then. That is what was reflected in the TAR.
SInce 1990 the accuracy of oxygen measurements increased enough to start the measurements (including several older samples), which showed that the biosphere is a net, but increasing sink for CO2. That is based on real oxygen measurements (at the edge of their accuracy) and the calculated oxygen use by human burning of fossil fuels with still as alternative the 13C/12C changes as check for the accuracy.
there is direct evidence in the shape of fossil fuel deposits that shows that for periods in the past net biome production was far from zero.
Think of the time scale:
Fossil carbon deposits are estimated at some 10,000 GtC. That needed many million years to form. 1 GtC/year uptake today would do that in only 10,000 years. Seems that the past wasn't that productive...
I have great difficulty in accepting that that restoration is due to respiration and decomposition during an arctic winter, when the landscape is frozen solid.
It seems that the tundra indeed is solid frozen, but that the snow layer in the Arctic forests effectively protect against deep frost, so that the (measured) decay in winter balances the summer uptake. Besides that, the Ferell atmospheric convection cells bring air from the mid-latitude forests to Barrow and Alert, so much of the seasonal variability there comes from elsewhere, where a lot less frost days are. The summer/winter differences at Schauninsland (Black Forest, SW Germany, 1000 m height), now abondaned, was larger than at Barrow.
Further, both the oxygen and 13C/12C measurements show that the up and downs of CO2 over the seasons are caused by vegetation, not by the oceans (which of course also play their role, but opposite).
Next comments for tomorrow (probably late)...
Ferdinand
Thanks for your patience. I have learned a lot from this exercise. One lesson is not to get too cocky! The key issue is understanding the mechanisms which govern the control of atmospheric and sea surface CO2 levels. I have realised that there should be a very simple control mechanism based upon partial pressure variations. What's more the equations which develop from that principle predict a linear relationship between CO2 levels and CO2 fluxes, a feature which I believe is borne out by observation. If this is true, it makes a huge difference to future predicted CO2 levels and to what should be the appropriate political response towards anthropogenic emissions. While I still believe there are many inconsistencies in the IPCC version, I think the mistake that I have made in these papers is in getting embroiled in peripheral issues which deflect from the key argument.
OK, I posted links to the four parts on BH Discussion.
David Coe:
Rest assured that the key argument has come across loud and clear in this small corner and I'm sure elsewhere. And the peripheral issues remain very interesting. As far as I'm concerned an outstanding start.
Future presentation could of course be improved. One thing I've been thinking about is how versioning might work for this new style of scientific paper. It's clearly vital that the URLs Andrew has created so far for your PDFs always point to the originals. On from there, I don't know the state of the art for this kind of thing - I'm a GitHub man but they're only getting onto richer text - but I'd be very eager to learn. It's partly a social question of course, not just a technical one. JJ or others?
David,
Sorry for the delay in response, there still were many comments going on at WUWT about the origin of the increase of CO2 in the atmosphere...
About part 2...
The main start is with Fig. 2.3, the three water tanks analogy...
Your idea is that the main flow is from deep oceans to ocean surface to atmosphere where in the latter two the biosphere is the main sink which deposits the CO2 removal either in/on soils or back into the deep coeans.
There are several problems with this:
- the removal of CO2 by the whole biosphere (land + seaplants) is only 1 GtC/year (2 ppmv/year), while human emissions are ~9 GtC/year nowadays, Thus instead of a continuous sink, the atmosphere is a continuous source of CO2. The 20 ppmv of CO2 uptake by land vegetation + a similar uptake by sea vegetation is thus way above reality.
- the partial pressure of CO2 in the atmosphere is (~ 7 micratm) higher than of the ocean surface. That leads to a flow from the atmosphere into the ocean surface, not reverse. That can be seen in an increase of DIC (dissolved inorganic carbon) in the ocean surface layer:
http://www.seafriends.org.nz/issues/global/acid2.htm halfway the page.
A release of CO2 from the oceans into the atmosphere would reduce DIC and thus reduce pCO2, but we see the reverse.
- rests the difference in pCO2 between the deep oceans and the ocean surface. As far as I have read, any diffusion between deep oceans and the ocean surface is extremely slow. That is the case for CO2, temperature, density and nutritients (Fe, S, N, P,...). Only at the upwelling places, like near the Chilean coast, the cold, rich deep ocean waters give way to abundant sealife...
As the ocean surface - atmospheric exchanges are opposite of what you expect, I am afraid that your model is not representing the real carbon cycle in nature...
Best regards,
Ferdinand
Dear David,
"Climate science is a science bereft of maths. Nature is too complicated I always hear. Rubbish! Science, like knitting, is only complicated when you don't understand it. The "complications" of climate science simply provide a smoke screen for wacky science."
Well said. You showed remarkable restraint in this debate.
I have looked through several of your papers, and find them refreshing. One thing I have not seen in your work is a study of the rate of production of carbon-14 by cosmic rays. Perhaps I missed it. Cosmic rays make roughly 8 kg/yr of carbon-14 (+-20%). I think you will find that, together with the carbon-14 concentration measurements in the ocean layers, the fate of carbon-14 is severely constraining of the carbon cycle. Here is the analytical solution to the unique two-part model that satisfies the equilibrium carbon-14 flow.
http://homeclimateanalysis.blogspot.com/2015/10/carbon-14-analytic-solution-to.html
The result is a model that predicts the current rise in CO2 concentration in the atmosphere in response to our emissions, predicts the changes is CO2 concentration with temperature for the past 400k years, and predicts the carbon-14 concentration in the atmosphere after the nuclear bomb test ban.
The carbon-14 equilibrium makes it impossible to contest the ready exchange of carbon between the shallow ocean and the deep ocean. With such communication, it will take thousands of years for us to double the concentration of CO2 in the atmosphere. Here is a summary with a portentous title.
http://homeclimateanalysis.blogspot.com/2016/10/falsification-of-anthropogenic-global_39.html
Yours, Kevan