## Residual airborne fraction

Hope everyone had a good, and safe, festive season. Towards the end of last year I wrote a couple of posts about the ocean carbonare cycle. I then ended up in a debate about what it would take to stabilise concentrations (hint: stabilising emissions will not stabilise concentrations).

One issue that people still seem unsure about is why we expect some fraction of our emissions to remain in the atmosphere for thousands of years. I thought I would try to illustrate this using the basic ocean carbonate chemistry that I described here.

Basically, in equilibrium, the amount of dissolved inorganic carbon (DIC) in the ocean determines the partial pressure of CO2 and, hence, the atmospheric CO2 concentration via Henry’s Law. The top panel of the figure on the right shows this. A DIC of $2002 \mu$mol/kg produces an atmospheric CO2 concentration of 280ppm (pre-industrial). As the DIC increases, so does the equilibrium atmospheric CO2 concentration.

We also know that the ocean holds about 38000 GtC (giga-tonnes of inorganic carbon). Therefore, we can associate a change in DIC with a change in the total amount of carbon in the ocean (i.e., the increase in inorganic carbon in the ocean is approximately ${\rm DIC} \times 38000/2002 - 38000$). Similarly, you can get the increase in atmospheric CO2 using $(p{\rm CO2} - 280) \times 2.12$. The sum of the increase in inorganic carbon in the ocean and the increase in atmospheric CO2 would be our total emission; the fraction of that in the atmosphere would be the residual airborne fraction. This is shown in the bottom panel of the figure on the right. The residual airborne fraction increases from about 15% for emissions of 100s of GtC (we’ve already emitted 600 GtC) to almost 30% if we were to emit as much as 5000 GtC.

The above is all approximate, but I think the basic idea is about right (happy to be corrected if it’s not). It also looks similar to what is obtained in Archer (2005), from which I’ve taken the table below. The “yes” refers to the analysis including temperature feedbacks (as does mine), while the “no” refers to it not including CaCO3 and silicate weathering (mine doesn’t either). The 4th column is total emissions (in GtC) and the 3 final columns are after times of 1kyr, 10kyr, and 100kyr and the reason the values are constant is because weathering isn’t included.

Credit: Archer (2005)

Essentially, in the absence of weathering (which occurs on kyr timescales) the oceans cannot dissolve all our emissions, and the residual amount in the atmosphere increases from about 15% (for total emissions of around 1000GtC) to around 30% (for total emissions of around 5000 GtC).

If anyone would like to download the code I used to produce these figures, it is here. You may need to uncomment some of the lines to get both figures.

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### 40 Responses to Residual airborne fraction

1. I cant follow your logic unless you plug in units, define terms such as the residual airborne fraction, etc. it would also help if you show how your equations match what has been happening from 280 to 400 ppm CO2 concentration.

On a different note, I used my own model to estimate a peak CO2 concentration of 630 ppm. But the peak isn’t the point. The question becomes, once West Antarctica raises sea level and the Russians are growing wheat in Vorkuta, most nations won’t be rooting for temperature to go down. And that point they may even want to consider coal a precious resource they need to burn carefully to avoid the return of the “20th Century Cold Period”

2. fernando,

I cant follow your logic unless you plug in units, define terms such as the residual airborne fraction, etc.

Okay, the residual airborne fraction is the fraction of our emissions that will remain in the atmosphere once dissolution of the excess CO2 in ocean has reached an equilibrium. You might need to tell me what other terms you need definitions for, but a great deal is explained in these two posts.

it would also help if you show how your equations match what has been happening from 280 to 400 ppm CO2 concentration.

The calculation I’m presenting here is really an equilibrium calculation. What it can do is illustrate how some amount of CO2 emissions is partitioned between the ocean and the atmosphere, but without considering CaCO3 or silicate weathering. For example, we’ve emitted about 600 GtC. This calculation would suggest that once an equilibrium is reach with the oceans, about 15% will remain in the atmosphere; so, about 90 GtC. To convert from GtC to ppm, divide by 2.12, so that gives 42ppm. So, if we were to halt all emissions now, the atmospheric concentration would asymptotically tend (over hundreds of years) to a concentration of just over 320 ppm, after which CaCO3 and silicate weathering would draw it back down towards 280ppm over thousands of years.

3. Nick Stokes says:

ATTP,
I think it should be emphasised that the equilibrium levels you describe are rather theoretical. Current AF is not 15% but about 44%. That reflects the slow dynamics of distributing carbon in the ocean. I think that will dominate on a century timescale.

4. Nick,

Current AF is not 15% but about 44%. That reflects the slow dynamics of distributing carbon in the ocean. I think that will dominate on a century timescale.

Yes, I agree (I covered some of that in this post). I was mainly just trying to illustrate why we expect there to be an amount that will remain in the atmosphere for a long time (the residual term in the Bern model, for example). If we halted all emissions, it would probably – as you say – take hundreds of years to reach the “theoretical” levels presented here. In some sense, they’ll never truly be attained, since CaCO3 (and silicate) weathering will continue to draw down atmospheric CO2 on even longer timescales. I guess one should probably say that something between 15% and 30% of our emissions (depending on how much we emit) will remain in the atmosphere for thousands of years.

5. izen says:

@-fernandoleanme
“…and Russians are growing wheat in Vorkuta…”

Do you have some insight into how weather patterns in this region will change under warming?
While summer temperatures MAY become warm enough for long enough to grow wheat in Vorkuta, rainfall is around 50mm (2inches). In the present US corn belt it averages 50 INCHES. ‘Drought’ conditions in the US, when rainfall is just ten times bigger than around Vortkuta, cause serve problems for wheat agriculture, how would this region avoid a ‘dust bowl’ scenario?

6. BBD says:

Tundra isn’t prime alluvial agricultural soil. Deniers never get this.

7. JCH says:

My wife is a Russian German.

They were very good farmers… especially wheat. Tens of thousands of them ended up in SIberia. No wheat. Tens of thousands of them ended up in North and South Dakota, and Canada. Presto: wheat belt.

Soil.

8. just a little context re atmospheric v. ocean carbon loading: both systems are overloaded with carbon, it becomes acidic in ocean context and it warms everything – air, sea, land – in the atmospheric accumulation, so stabilizing does not get it done, we have to figure out how to make the needle go in the other direction. And sooner is better than later.
noisy daily CO2 readings per co2.earth

Daily CO2

January 2, 2017: 407.05 ppm
January 2, 2016: 401.83 ppm

Last Week

December 25 – 31, 2016 404.78 ppm
December 25 – 31, 2015 402.09 ppm

Mike

9. verytallguy says:

I am surprised the first figure is non-linear, and would have expected it to curve the other way if anything (as pH falls, a greater proportion of dissolved carbon will be present as free CO2).

I can’t quite follow your previous post-are you imposing a “total alkalinity is constant” constraint here?

10. vtg,

I am surprised the first figure is non-linear, and would have expected it to curve the other way if anything (as pH falls, a greater proportion of dissolved carbon will be present as free CO2).

A greater proportion of our emissions are present as free CO2, but I don’t think its a greater proportion of total DIC.

I can’t quite follow your previous post-are you imposing a “total alkalinity is constant” constraint here?

Yes, the titrate alkalinity is assumed to be constant which – I think – is okay on timescales over which the impact of the CaCO3 weathering is minimal. I think this is explained in Zeebe (2012) but I can’t seem to access that at the moment.

11. vtg,
Managed to access Zeebe (2012). Figure 1 shows how total alkinity is influenced by the various processes. For CO2 invasion it can be assumed to remain constant, but changes when you also include CaCO3 dissolution, or formation.

12. Magma says:

Zeebe’s comprehensive review struck me as very good. The detailed aspects of carbonate chemistry in the oceans (gaseous, aqueous and solid phases) are surprisingly subtle and complex and would take far more time than I have to master.

I had previously assumed I understood the basics, but reading Zeebe and a few others taught me how much I didn’t know. A very useful — and humbling — exercise.

13. BBD says:

Magma

My first +1 of 2017. And so soon…

14. I had previously assumed I understood the basics, but reading Zeebe and a few others taught me how much I didn’t know. A very useful — and humbling — exercise.

You’re not alone; I keep realising that my understanding of the basics is not quite as good as I thought it was. My impression is that many (if not all) of those who claim to be rewriting our understanding of the carbon cycle have not yet grasped what you’re pointing out.

15. vtg,
Okay, I’ve redone the plot as the airborne fraction relative to total dissolved inorganic carbon, plotted against total dissolved inorganic carbon, and it does go the way I think you expected it to.

16. Andrew Dodds says:

fernandoleanme –

More generally, it is not the exact state of the climate that matters; you could build a civilization during an ice age maxima or a Cretaceous super-greenhouse. What matters is change and rate of change. If climate zones are continually moving, agriculture becomes a lottery. If sea level is consistently changing (as it will for a very long time with ice sheet melt) then you are constantly having to relocate coastal infrastructure and write off developments. If rivers dry up or dramatically increase their flooding, your river-based cities and industry have big problems.

17. angech says:

.”Basically, in equilibrium, the amount of dissolved inorganic carbon (DIC) in the ocean determines the partial pressure of CO2 and, hence, the atmospheric CO2 concentration via Henry’s Law”
This law works both ways. In other words the partial CO2 pressure determines the DIC as well.
Which is important for this discussion..

The amount of extra CO2 added to the atmosphere by human activity, while significant, and lets say cumulative to some degree, is still a small fraction of the total atmospheric CO2 720 GT and the 137 times greater DIC [136,800 GT of CO2.]

Atmospheric CO2 720 GT at 400 PPM, which is 1/182 of that in the ocean.
If you increased to 560 ppm 1008 GT, a 40% increase the amount of CO2 in the ocean would have to increase by 4% OR 5472 GT.
At 30 GT a year human contribution that would take 182 years.You did say elsewhere ” we’re dealing with a coupled system, so if you add new material to one of the reservoirs, it will rise in all reservoirs”
An important caveat or quibble is that the increased DIC stays in solution and does not precipitate out.

“The residual airborne fraction increases from about 15% for emissions of 100s of GtC (we’ve already emitted 600 GtC) to almost 30% if we were to emit as much as 5000 GtC.
Given what we’ve already emitted, we would expect about 20% of our emissions to remain in the atmosphere, but it’s currently more like 45%. This is because the timescale for ocean invasion is > 100 years, and so the system hasn’t yet had time to return to equilibrium.”
[From 1959 to the present, the airborne fraction has averaged 0.55. the terrestrial biosphere and the oceans together have consistently removed 45% of fossil CO2 for the last 45 years].
If 30 out of 720 GT is human origin then I feel any increase should be divided % wise ie only 4% contributes to the airborne fraction increase which would be 0.022.

18. verytallguy says:

Thanks AT.

I was thinking about it the wrong way around. The first graph is how it should be intuitively – as DIC rises, so the partial pressure of CO2 (at equilibrium) rises more rapidly, which is as it should be, given that pH is falling.

The plot of airborne fraction vs ocean carbon is striking.

Belated New Year’s resolution: to read axes more carefully.

19. angech,

This law works both ways. In other words the partial CO2 pressure determines the DIC as well.
Which is important for this discussion..

Well, yes, but that’s essentially the calculation I’m doing here. I start with the pre-industrial values for DIC (dissolved inorganic carbon) and total alkalinity and then solve for the equilibrium atmospheric CO2 concentration. I then change the DIC (with fixed total alkalinity) and solve again for the equilibrium atmospheric CO2 concentration. This allows one to estimate how equilibrium atmospheric CO2 concentration will change as we increase our emissions. As Nick Stokes points out, though, it’s important to realise that this is an equilibrium calculation. We’re not in equilibrium (that would probably take hundreds of years) and so the airborne fraction is higher than is indicated here.

while significant, and lets say cumulative to some degree, is still a small fraction of the total atmospheric CO2 720 GT and the 137 times greater DIC [136,800 GT of CO2.]

You’ve change units. The atmosphere contains about 850 giga-tonnes of carbon. The oceans contain about 38000 giga-tonnes of carbon. It’s about 50 times greater, not 137 times greater (you’ve used carbon for the atmosphere and CO2 for the oceans).

An important caveat or quibble is that the increased DIC stays in solution and does not precipitate out.

Well, yes, but that’s because the timescale for the carbon to precipitate out is thousands of years (CaCO3 and then silicate weathering).

If 30 out of 720 GT is human origin then I feel any increase should be divided % wise ie only 4% contributes to the airborne fraction increase which would be 0.022.

What are you on about here? The increase is essentially all anthropogenic, even if not every molecule is from an anthropegenic emission.

20. BBD says:

Angech

See my only other comment on this thread 🙂

21. BBD says:

Edit:

“See my only other previous comment on this thread”

22. ATTP, interesting calculations, indeed. The chemical equilibrium between the surface ocean and the air can be calculated, as you have done, using the assumption that surface ocean and surface air are in thermal equilibrium at a given location. The capacity of the surface ocean to absorb carbon dioxide is severely limited by the Revelle factor according to those chemical equilibrium calculations.

The large capacity for absorbing carbon dioxide is not in the surface ocean, though, but in the deep ocean. However, the ocean temperature is decreasing with depth:

Considering that the deep ocean is much colder than the air above it, there is no self evident chemical equilibrium between the carbon dioxide in the air and the carbonate species in the deep ocean. Instead there is probably a stationary state depending on the never ceasing dynamics of the ocean (that is also the reason that the deep ocean is that cold even if the surface air is 25 C, so you cannot calculate the deep ocean temperature using a thermal equilibrium assumption). How did you account for that in your calculations?

23. Pehr,

How did you account for that in your calculations?

I didn’t. As I said, this is all approximate. However, for it to make a big difference, I think it would need to change the vertical gradient of the DIC. So, what I was assuming here was that the % increase in DIC would be the same throughout the vertical column.

24. wehappyfew says:

Pehr’s comment ignores many basic facts about the actual ocean.

1. Organisms absorb CO2 at the surface, die, and fall to the ocean floor, releasing CO2 through decomposition along the way. This bypasses the thermocline barrier. Carbonate shells dissolve as well – see Carbonate Compensation Depth.

2. Salt fingering in the tropics exchanges warm salty surface water with cool, fresher water at depth.

3. At the poles, the water at the surface is colder, so it sinks – forming the Antarctic and Arctic Bottom Water masses.

These are basic oceanographic facts that contribute to the complexity of the real world carbon cycle… that Pehr seems unaware of. Over the long term, atmospheric carbon will equilibrate with the entire depth of the ocean due to these exchanges.

25. angech says:

“You’ve change units. The atmosphere contains about 850 giga-tonnes of carbon. The oceans contain about 38000 giga-tonnes of carbon. It’s about 50 times greater, not 137 times greater (you’ve used carbon for the atmosphere and CO2 for the oceans).”
Sorry about that. There is some confusion about whether the atmosphere is 720 GT of Carbon or 720 GT of CO2 [ One ton of carbon equals 44/12 = 11/3 = 3.67 tons of carbon dioxide.Joe Romm “The biggest source of confusion and errors in climate discussions probably concerns “carbon” versus “carbon dioxide.”]. Thinking the latter I converted the DIC to those units as well.

” The increase is essentially all anthropogenic, even if not every molecule is from an anthropegenic emission”
The increase is due to the anthropogenic component but the amount extra staying in the atmosphere remains natural. There is a difference between the fraction of our emissions remaining on the atmosphere and the effect of the emissions on the amount of extra [general] CO2 staying in the atmosphere.
” The increase is essentially due to anthropogenic, even if very few molecules are from an anthropegenic emission” would be more correct.

26. ATTP,

However, for it to make a big difference, I think it would need to change the vertical gradient of the DIC. So, what I was assuming here was that the % increase in DIC would be the same throughout the vertical column.

Am I right that you assumed that the chemical potential of dissolved carbon dioxide molecules was initially constant in the water column, giving a DIC gradient because of the changing temperature? I guess that such an assumption would correspond to a preindustrial ocean saturated with carbon dioxide.

27. wehappyfew January 5, 2017 at 12:30 am

The carbon cycle is complex, indeed. I was not questioning that in my comment to ATTP, but I simply wanted to know something more about the ideas behind his chemical equilibrium calculations.

Over the long term, atmospheric carbon will equilibrate with the entire depth of the ocean due to these exchanges.

If this is what carbon cycle science says, there is certainly solid arguments for this statement. However, this statement isn’t self evident, because the temperature of the ocean has not equilibrated, the ocean is not isothermal or even in thermal equilibrium with the air at the same location. So which are the arguments supporting that the chemical potential of carbon dioxide molecules in the ocean will equilibrate to a uniform value?

28. Pehr,
My calculation is for one temperature, one DIC value, and one Total Alkalinity value. I think it’s possible to do something more complex by splitting it into layers, but I haven’t done that.

So which are the arguments supporting that the chemical potential of carbon dioxide molecules in the ocean will equilibrate to a uniform value?

That comment wasn’t me, but I don’t think it was implying a uniform value (it certainly wouldn’t be a uniform value) but that it will reach some kind of equilibrium once it has invaded (dissolved in) the entire depth of the ocean. There will clearly be gradients, as there are now.

29. angech,

The increase is due to the anthropogenic component but the amount extra staying in the atmosphere remains natural. There is a difference between the fraction of our emissions remaining on the atmosphere and the effect of the emissions on the amount of extra [general] CO2 staying in the atmosphere.

No, there isn’t really a difference. The reason for the increase is our emissions, even if the exact molecules that make up the enhanced atmospheric CO2 concentration were not from an anthropogenic emission.

30. wehappyfew,
To be fair, I wasn’t including any of those things in what I was doing here.

31. Frank says:

ATTP: Only the mixed layer of the ocean is in equilibrium with atmospheric CO2. It takes up to a millennium for the ocean to overturn and reach equilibrium with the atmosphere. CFC11 (which was produced in volume beginning in the 1950s) is used as a marker for transport into the deep ocean (apparently even in AOGCMs). It seems reasonable to assume that CO2 has been following a similar path. (Note, the solubility of both is temperature dependent.)

About half of the CO2 that is “missing” from the atmosphere (airborne free fraction less than 1) is believed to be on land.

32. Frank,

Only the mixed layer of the ocean is in equilibrium with atmospheric CO2.

At the moment, yes.

It takes up to a millennium for the ocean to overturn and reach equilibrium with the atmosphere.

Indeed, but at this stage (after a millenium) there will still be something like 15 – 30% of our emissions (or, more correctly, an amount equivalent to) in the atmosphere. That’s mostly what I was trying to illustrate here; on the timescale of centuries the ocean cannot take up all of our emissions.

About half of the CO2 that is “missing” from the atmosphere (airborne free fraction less than 1) is believed to be on land.

Yes, but my understanding is that on long timescales the dominant sink will be the oceans; the total carbon mass of the biosphere is quite small by comparison.

33. ATTP,

I think that the following paper is interesting in the context of our discussion:
“Physical and biogeochemical modulation of ocean acidification in the central North Pacific”
http://www.pnas.org/content/106/30/12235.full

This figure shows how pCO2 and pH have developed in the water column:

This figure shows how temperature, oxygen concentration, salinity, TA, DIC, pH and pH rate of change vary with depth in the water column:

The capacity for the ocean water to absorb carbon dioxide is reflected in the value of the Revelle factor. The value of the Revelle factor is also a measure of how much pH sinks for a given amount carbon dioxide absorbed, that is a higher Revelle factor gives a faster sinking pH, that is a faster acidification of the ocean water due to the uptake of carbon dioxide. A Revelle factor equal to one, no Revelle effect, is equivalent to no pH decrease when carbon dioxide is absorbed.

Remarkably, the authors pointed out that the surface pH at the studied location did not sink, it even rose a little, during the period 1999-2003. This, the authors write, shows the necessity to look at pH trends for longer periods and in the full water column.

However, I think that it is also interesting that during this period there was no Revelle effect in the surface layer, because pH did not sink. I don’t know what that means, but perhaps this is a sign that it is not that easy to really understand what happens with the carbon cycle and the fate of the absorbed carbon dioxide.

Besides, I think that the physiological risks with increasing carbon dioxide levels in the atmosphere with respect to the whole world population is remarkably little discussed. Though healthy people according to occupational risk assessments are rather tolerant to high levels of carbon dioxide, there are many humans with diminished lung function. I have never seen any discussion of the problems that may cause, perhaps affecting hundred millions of people.

34. Sorry, I posted wrong second figure. Here it is:

35. Pehr,
Thanks, I hadn’t seen the first lot of figures, but had seen the last one. I’ll look at the paper.

36. angech says:

Pehr Björnbom says:
” I think that the physiological risks with increasing carbon dioxide levels in the atmosphere with respect to the whole world population is remarkably little discussed. Though healthy people according to occupational risk assessments are rather tolerant to high levels of carbon dioxide, there are many humans with diminished lung function. I have never seen any discussion of the problems that may cause, perhaps affecting hundred millions of people.-

This is the sort of comment that deserves further analysis.

The suggestion is that increasing CO2 levels may pose another health risk to humanity other than those already being considered.
The science, alluded to, says there is no problem with current or higher likely levels.
Humans with diminished lung function have problems with getting enough oxygen in, CO2 is not the issue and cannot be the issue as it has no deleterious effect on human respiration at these or higher likely levels.
That is why there is no discussion.

Scientifically I appreciate your diagrams and discussion with ATTP and the assessment of real and present dangers being discussed.

37. angech,

Thanks, and I can accept that there is no discussion, if according to science there is no problem with increased atmospheric levels of carbon dioxide in case of diminished lung function. However, even if increased atmospheric levels are insignificant in this context, people with chronic lung disorders, according to this Wikipedia article, may have serious problems with increased carbon dioxide levels in the blood causing chronic respiratory acidosis:
https://en.wikipedia.org/wiki/Respiratory_acidosis

38. angech says:

That is true, if you cannot get CO2 out of your body , due to diminished lung function with chronic lung disorders trapping the CO2 one produces metabolically you can develop respiratory acidosis, regardless of the level of CO2 in the atmosphere.

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