Bishop Hill is hosting a four part series “A new look at the carbon dioxide budget” where David Coe presents four PDF explaining what is going on.
Andrew Montford writes
A new look at the carbon dioxide budget
Jul 30, 2013
Climate: carbon budgetAs readers are probably aware, I don’t spend a lot of time on new hypotheses about global warming. Apart from intermittent looks at Svensmark’s cosmoclimatology work, I’ve tended to concentrate on mainstream science and its relationship with policy, as well as a lot of “meta” stuff like peer review.
However, I was recently sent a paper by reader David Coe that piqued my interest. It seemed to me to be put together pretty well, and was about an area of the science that I knew nothing about.
Tim writes, this deserves wide coverage.
In a nutshell Henry’s law does apply without the invented special pleading cited by the climatic community to explain why human CO2 is different.
Links below all in one place, left link to Bishop Hill article, right link to local copy of PDF, linked from BH pages. [updated: PDF links were unreliable, changed to local copies –Tim]
Part 1 and PDF
Part 2 and PDF
Part 3 and PDF
Part 4 and PDF
Posted by Tim Channon
Tallbloke's Talkshop 
In Part 3 of his analysis, Coe states:
“In order to quantify the effect of atmospheric mixing we need to develop a mathematical model to represent the various atmospheric CO2 and mixing fluxes. This model is detailed in appendix (i) where the globe is seperated into 18 equiangular lateral bands, each presenting 100 of latitude, extending from the North to the South Pole. Each band exchanges CO2 molecules with its neighbour, governed by the partial pressure gradiants between them. The model requires estimates to be made of sea surface temperatures and the extent of net biosperic fluxes for each latitudinal band. Results of such an analysis are shown in Figure 3.3.”
Here’s Figure 3.3:
According to Coe: “The resulting agreement with observed atmospheric CO2 levels … is good considering the crudeness of the mathematical model and the simplicity of the assumptions.”
Well, it would be if Figure 3.3 showed actual observed atmospheric CO2 levels, but it doesn’t. Here’s a plot of CO2 by latitude taken from actual records. The highest CO2 levels occur in the Arctic, not at the Equator:
Coe’s conclusion that “the Equatorial peak is explained by the high sea surface CO2 partial pressure in the tropical regions due to the high prevailing sea temperatures” is therefore invalid because there is no Equatorial CO2 peak.
A model that related the decrease in CO2 between 60N and 60S to the increase in the area of ocean relative to the area of land would have been more compatible with observations:
Hi Roger: Your graph of atmospheric levels is around 10ppm below Coe’s. That suggests his data is more up to date than yours. Both sets of figures vary around 3ppm across the latitudes but whereas Coe’ show a low-mid latitude NH hump, yours don’t. Unfortunately, I cant find a reference to the data he used in part 3.
Part 1 says this below fig 1.3
There is, however, absolutely no correlation between this
stratified CO2 emission and global CO2 levels which show not only a northern hemisphere
bias of around 2ppm but a distinct peak at the equator. (Data derived from Keeling et al,
reference 2).
It looks like his sample data might come from the modern end of the Keeling data plotted in fig 1.2
C D Keeling, S C Piper, R B Bacastow, M Wahlen, T P Whorf, M Heimann, A Meijer:
Exchanges of Atmospheric CO2 and 13CO2 with the Terrestrial Biosphere and Oceans
from 1978 to 2000; Scripps Insitiution of Oceanography Reference No. 01‐06, June
2001.
I’ve emailed Andrew Montford to see if he can put me in contact with David Coe.
Hi TB:
Here’s a plot of station means for 2007 (note the stations are not exactly the same as before). It shows the same thing as the earlier plot.
(tried in-lining images, WordPress refused, might be related to other changes)
I’m inclined to agree about distribution yet the official view is misleading, levels are not so simple, nor I suggest easy or reliably measured. I’m quite familiar with the bad state of the data.
Pull up a disk file (from world gas database), Tsukuba, Japan, 1992 or so, in the time window, mean looks around 367ppmv
Try another Schauinsland, Germany, about 357ppmv
(these two were already extracted from pub. format, is daily data, some of the files are here
http://ds.data.jma.go.jp/gmd/wdcgg/pub/data/current/co2/daily/ and other directories, CDIAC is another archive source)
Coe’s work needs a workout, bashing to see what falls out. Wouldn’t surprise me if he hasn’t gone to excess in places.
Andrew has passed on request to David, but it might be a few days due to travel.
Tim, I tried to inline images too. Tinypic doesn’t like it. We’d need to save/upload here.
The bish’s site baulks at the spaces in the doc titles sometimes too.
Anyway, stuff how many ppm’s of Co2 fit on the head of a pin for now, the Perseids will be peaking in around the next hour. Time for a bit of stargazing.
Updated PDF links.
AAO index fell below -3.
http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/aao/aao_index.html
http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/aao/month_aao_index.shtml
Records reaches a temperature of the stratosphere.
The Reveille factor: vital for Climate Science, unknown elsewhere and in violation of Henry’s Law. (Atmospheric CO2 swings 12.5X more than in the sea surface layer!)
“There is, here, undoubtedly a tragedy, a tragedy for science. The tragedy however is not that
the science is not settled, as was earlier proclaimed by certain UK government ministers. The
tragedy is not even that the science is wrong. The tragedy is that the science of climate
science is not actually science!”
In some respects, I’m with Ferdinand Engelbeen regarding Coe’s treatment of the chemistry. The Reveille factor does appear to be based on sound chemical equilibrium thermodynamics.
My biggest objections usually stem from the obsession with equilibrium in non-equilibrium situations. A sun warmed ocean might, hypothetically, pass through equilibrium with a hypothetically well mixed atmosphere of carbon dioxide twice a day (like the proverbial stopped clock).
And then there’s the agency of living organisms which consume and produce carbon dioxide by chemical processes that do not, in the short term, have to be constrained by chemical stoichiometry with respect to oxygen. There are processes that can change photosynthetic oxygen/carbon ratios significantly. [Some of these organisms also fix nitrogen. I recently read a 2012 paper where they quite calmly calculated that the oceanic nitrogen fixation might be double what previously thought. Didn’t surprise me in the slightest.]
Gross oceanic photosynthesis as measured by fluorescence is actually far higher than the net estimates. I have seen factors of 5 quoted, with one speaker saying the turnover (churn) was equal to 10% of the carbon in the biosphere EVERY 24 HOURS, (though he didn’t define the biosphere at the time).
Oceanic carbon-isotope fractionation of photosynthetic organisms has also been demonstrated to vary depending on CO2 levels. Coccoliths get bigger at higher CO2 concentrations.
Returning to kinetics vs thermodynamics, the chemical reaction of free CO2 is subject not only to Henry’s Law, but also the coupled equilibrium of the aqueous carbonate/bicarbonate system, which is of course also sensitive to temperature and pressure. This is actually quite a slow reaction, much slower than a reaction limited by the rate of diffusion.
Humans such as myself need carbonic anhydrase to expedite the extrusion of CO2 from the blood via the lungs: it speeds up the reaction rate by a catalytic factor of about 7 (seven) orders of magnitude. Every respiring organism uses the enzyme and, by golly, so does every photosynthesizing organism. Many of them excrete it extra-cellularly into the surrounding water, so there is a non-photosynthetic aspect to the biosphere’s effect on the carbon cycle.
I find it difficult to believe that these many factors have been well described in aggregate when recent papers are still explaining new ways to try and get a handle on all the individual components.
Fair play to David Coe for having a go, but it’s a big job.
michael hart, if you add up all the biotic carbon, mineralized biotic carbon, and carbon in the sky, ocean and on land you get 75,167,656 giggton. Now the oldest is about 360,000,000 years old, so we get an average of 75,167,656/360000000 or 0.21 gigaton a year disappearing or in turnover, which roughly what is emitted by volcano’s annually.
it is rather like there being exactly enough news everyday to just fill each newspaper.
When one seasonal SST cycle is over, it doesn’t necessarily follow that the background atmospheric CO2 returns to its starting point even when the temperature does. The seasonal temperature cycle may act as a ‘reciprocating pump’, pumpining CO2 into/outta oceans depending on the (annually averaged) temperature level.
Roger: Please could you add the data sources for your plots? Dave Coe has been in touch.
he extracted his data from the Keeling graphs.
He’ll be joining us in a few days, can’t access the Talkshop as it’s blocked in China!
Dave Coe writes from China:
When I interpolated my average CO2 data from Keeling’s graphs, the two stations that were the most difficult to assess were Alert and Barrow because of the high seasonal variability of around 20ppm. I therefore cannot dispute the data that you have just provided me with. It makes a bit of a bugger of my nice graphs however. It also provides a new puzzle. Since those two arctic stations have the highest CO2 levels it follows that there must be a CO2 flux, developed from the CO2 partial pressure differentials from north to south. What is the source of the necessary balancing flux into the arctic region necessary to maintain those concentration and pressure differentials. I have assumed not unreasonably at the poles that there are no biological fluxes. The only possible source therefore is the ocean.
If you look at my calculations used to developed my graphs you will see that I have assumed a constant global sea surface CO2 concentration with a corresponding partial pressure varying with sea surface temperature according to the known temperature coefficient of Henry’s constant. This produces an equatorial peak in sea surface CO2 partial pressure. I have made no allowances, because I didn’t think of it, for the fact that in the polar regions, there is no thermocline and thus no mixed layer. The deep ocean effectively is in direct contact with the atmosphere.
This whole ocean control theory is based upon the assumption of a high deep ocean CO2 content. It follows therefore that at those arctic stations the sea CO2 content and hence partial pressure would be significantly higher than I have allowed for thus providing a CO2 flux from ocean to atmosphere and a higher atmospheric CO2 content. To quantify this would require an estimate of sea CO2 content distribution.
I hope this adds something useful to the discussion.
A wildcard.
Some time ago I suggested the abnormal northern CO2 is caused by ice, sea water on freezing ejects most dissolved gas and on ice melt it is a sponge for gas. I showed some plots. Tried to talk to people in private.
Got a cold shower, no-one bought the idea.
I also pointed out the annual phasing, walk from Alaska to MLO and you will arrive with the CO2.
Lot of details and snippets, some I have never mentioned anywhere.
TB:
The CO2 data I used came from http://cdiac.ornl.gov/trends/co2/contents.htm
TB:
Some more data of potential interest to David Coe.
First is a plot of monthly CO2 values against latitude for ten stations (Alert, Barrow, La Jolla, Mauna Loa, Christmas Is., Samoa, Kermadec, Baring Head, Jubany and South Pole) for the year 2006. Other years give essentially the same results:
We do in fact see equatorial peaks in CO2 values, but only in July, August and September. These peaks are generated by the large decreases in Northern Hemisphere CO2 during these months.
As to what causes these decreases, one possibility is the seasonal decrease in Arctic sea ice extent, which converts most of the Arctic ocean from non-absorbent ice in winter to an open-ocean carbon sink in summer. A plot of monthly Arctic Sea Ice extent against monthly CO2 at Alert (82 degrees North) during 2006 shows this relationship:
Here are a couple of papers on the subject:
Click to access semiletov2003GL017996.pdf
Click to access 60%20Hansell.pdf
High CO2 levels in Arctic ‘because gases dissolve more easily in cold water’.
http://www.nature.com/news/2010/100722/full/news.2010.372.html
OB: Antarctic is cold too. Why lower levels?
Dave Coe writes again from China:
Just out of curiosity I have recalculated the stratified CO2 levels just with the sea surface values at 80 and 90 degN increased to 420microatmos from the 347microatmos previously used, just to see what changes would be necessary to achieve agreement with the data kindly sourced by Roger Andrews. I have absolutely no idea if these values represent reality but they certainly provide good agreement as shown in the attached graph.
With an 18 x 18 matrix there are enough variables to match any curve that is presented and as such this part of my paper is open to the usual von Neumann criticism. All I can do is to ensure that the values selected are within reasonable bounds of expectation. Is the value of 420 microatmos reasonable for the CO2 partial pressure of the arctic seas? I honestly don’t know, but I suspect that it is.
During a research cruise aboard the Chinese icebreaker Xuelong (Snow Dragon) in summer 2008, Cai and his colleagues took continuous measurements of CO2 concentrations in the upper layers of the Canada Basin (the Arctic Ocean sector bordering the northern Alaskan coast and northern Canada), where sea ice had melted dramatically and retreated to a near-record low. At the ocean margins, where deep water meets the continental shelf, the partial pressure of CO2 (a measure of its concentration) ranged from 120 to 250 microatmospheres, well below its atmospheric concentration of 375 microatmospheres. But in the ice-free areas further offshore, CO2 concentration was 320-365 microatmospheres, nearly matching atmospheric concentrations. In 1994 and 1999, scientists had observed surface water CO2 concentrations of below 260 and 260-300 microatmospheres, respectively, in these areas.
http://www.nature.com/news/2010/100722/full/news.2010.372.html
Phytoplankton blooms also occur underneath the Arctic Sea Ice.
http://www.vims.edu/newsandevents/topstories/archives/2012/icescape_nasa_smith.php
tallbloke says:
August 15, 2013 at 8:38 pm
OB: Antarctic is cold too. Why lower levels?
Open water is scarce in Antarctica.
But surrounded by colder open water than arctic
Perhaps there is a lower concentration of CO2 in the atmosphere in Antarctica waiting to be absorbed, compared to the Arctic.
‘Patterns of carbon dioxide distribution were also found to differ significantly between the northern hemisphere, with its many land masses, and the southern hemisphere, which is largely covered by ocean.’
http://phys.org/news142861794.html
Need to discuss this over a beer.
At 9.Jan.2009 – 19:09 hrs perdido showed a result
At 10.Jan.2009 – 14:29 hrs perdio wrote “Say again mate?”
Proof enough there of what happens on freezing.
Whole discussion between chaps is here if the above links don’t work
http://www.toytowngermany.com/lofi/index.php/t119524-15.html
There we learn streetwise German kids know beer is put outside on balconys to cool, nick it.
We also learn beer on a rope from a top floor flat into the river upsets the town fathers.
Back from my travels to find that Rog has thrown another spanner into the works with the paper from Nature showing arctic waters CO2 partial pressures lower than those of the atmosphere when I had been predicting the opposite. I must admit to being singularly unimpressed with the tripe in the Nature paper. This is not about defending my pet theories. I am open to anyone who can prove me wrong. By doing so they will improve my knowledge.
The problem is a simple one of physics. We have two conflicting pieces of information. One from CDIAC which suggest the the polar regions have the world’s highest concentration and hence partial pressure of CO2. This necessarily means that there will be a net flow of atmospheric CO2 from north to south as a result of the partial pressure gradient.
The second set of data shows that CO2 partial pressures in the arctic seas are lower than those in the atmosphere. We can thus expect there to be a net flow of CO2 from atmosphere to sea, unless the laws of physics have been changed when no-one was looking. Where the hell is all the CO2 coming from to feed this outward flow of CO2? There are no biological fluxes that we can blame in those regions. There has to be a large inward CO2 flow to feed these outward fluxes, unless one or both sets of CO2 partial pressure data is wrong.
The only reasonable response to two such contradictory pieces of evidence is to question the reliability of the data. When publishing the results of a scientific measurement I was taught to describe in complete detail my method of measurement with a full list of potential errors with estimates of total measurement uncertainty. Such information is sadly lacking in the Nature paper. As usual in a climate science paper detail is there none. How does one actually measure sea CO2 partial pressures? Since Henry’s law has been subsumed by the Revelle factor for climate science what relationship has been used to link CO2 concentration to partial pressure?
If both sets of data are correct it would be interesting to see what third flux exists in order to maintain the atmospheric levels.
Co-mod writes: Comment above is from David Coe who is the author of the subject material of this article.
Welcome to the Talkshop.
David, sorry if that came as a surprise. I emailed it to you at the same time I posted it here. I’m guessing there will be more biota just off the Canadian coast than in deeper and more northerly arctic water. But then, I’m not a marine biologist. Also, time of year must be a factor here. I haven’t read the Nature paper, just skimmed the article. I only pitched it in because it seemed relevant.
David:
Here are some additional data that may be of interest to you:
First a plot of the range of seasonal CO2 variation at 27 stations between Alert, NWT and the South Pole, plotted against latitude.
Seasonal CO2 variations are about 15 ppm in the Arctic, decrease to around 2 ppm at the Equator and remain in the +/-1 ppm range over the entire Southern Hemisphere. The area-weighted global average is 5.4 ppm. This represents a seasonal movement of about 3 gigatons of carbon into and out of the atmosphere, 90% of which takes place in the Northern Hemisphere.
The graph I showed in an earlier comment shows the same pattern using individual station CO2 data. Here it is again for reference:
Seasonal CO2 variations are larger in the Northern Hemisphere most likely because more vegetation grows and decays each year in the Northern Hemisphere than in the Southern. The match between CO2 and vegetation is illustrated in the plot below, which compares the Normalized Difference Vegetation Index estimated from the AVHRR and MODIS satellites at 45.9N, 12.8E against seasonal CO2 fluctuations measured at the nearby Monte Cimone station:
It’s difficult to relate the seasonal CO2 changes to changes in SST. First, there’s no clear relationship when we superimpose the seasonal changes in SST on the seasonal changes in CO2 shown in the first figure:
And second, while cold sea water absorbs more CO2 than warm sea water, meaning that we would expect to see a decrease in atmospheric CO2 in cold months and an increase in warm months, we actually see the opposite.
The question now becomes, do the mechanisms that govern seasonal CO2 variations also govern long-term CO2 variations? Over to you.
Roger Andrews
It was this seasonal variation in atmospheric CO2 that originally seized my attention, particularly that high level of variation at Alert and Point Barrow in the far north. It is reasonable to assume that during the summer the short but intense period of plant activity can produce the reduction in CO2 levels. In fact if you look closely at the variation you will see that at these latitudes the summer CO2 reduction is quite sharp, followed by a slower winter recovery. According to the consensus theories, the biosphere is in CO2 equilibrium with respiration and decomposition balancing photosynthetic CO2 absorption. At these northern stations the balancing winter CO2 flux required is of the order of 60ppm/year. I cannot sea how it is remotely possible for such a flux to be provided in the northern winters when everything is frozen solid (part 1 of the paper).
I argued (with myself unfortunately) that there had to be another “controlling flux” which provided this mechanism. I made the one assumption that the deep ocean can be considered to be an infinite source of CO2. There are then two interfaces between that ocean and the atmosphere. One is the thermocline, the other the sea surface. I postulated that the flow of CO2 across these interfaces will be directly proportional to the partial pressure differential across them, ocean and sea surface partial pressures being related to solvated CO2 levels (Henrys Law). Solving the resulting differential equations results in the simple exponential response equations relating CO2 partial pressures to net CO2 fluxes (part 2 of the paper).
With these equations it is possible to calculate the seasonal variation in atmospheric not only of CO2 but also O2 assuming a sinusoidal seasonal photosynthetic response (part 3). It is not necessary to argue for complex mechanisms. The simple one provides the answers.
These same mechanisms apply to every atmospheric time scale. The only assumption is that the deep ocean has a constant CO2 content. Over the current industrial age that seams to be the case. I offered an explanation for such a constant CO2 source based upon maintenance of deep ocean CO2 levels by the dissociation of CaCO3 into Ca(OH)2 and CO2, noting that the energy required to fuel this endothermic reaction was almost identical to the geothermal heat input into the oceans and might offer an alternative explanation for the low temperatures of that ocean (part 2). That caused some debate at BH.
Rog and Tim
Thank you for the opportunity to discuss these issues. I have absolutely no problems with being challenged by new (at least to me) data. My only interest here is to understand the science.
David C: “the energy required to fuel this endothermic reaction was almost identical to the geothermal heat input into the oceans and might offer an alternative explanation for the low temperatures of that ocean”
Some time ago we had a discussion about a piece written about pterosaur flight. In it the author argued for a much higher atmospheric concentration of co2, creating a much denser atmosphere which could enable pterosaurs to fly easily. hey showed that the subsequent drawdown of co2 by shelled marine biota would have reduced the atmospheric content considerably. Which of course implies a greater concentration into the deep ocean as David notes. I’d never considered the endothermic reaction of the transition of CaCO3 into Ca(OH)2 and CO2 before, but I have heard that the deeper ocean used to be a lot warmer than it is now.
This is getting very interesting.
David:
I don’t think seasonal CO2 variations in the Arctic are a problem. They seem to be caused mostly by CO2 being blown in from the south during the northern summer:
We had a lot of enthusiastic interchanges on the cause of the CO2 increase on the Talkshop last year. Here’s the thread if you want to read it.
And here’s my CO2 model. It makes just two assumptions – a residence time of 23 years for anthropogenic CO2 in the atmosphere and a 17 ppm increase for each degree C increase in surface air temperature. Is it realistic? Probably not. But it does give an almost exact fit to observations:
Roger A: we know residence time is a lot shorter than that. The question is what is the e-folding time.
TB:
There are a number of estimates that place residence time in the 5-15 year range, but I don’t think we “know” they’re correct. (If they are, however, then much of the atmospheric CO2 increase probably has a natural origin. This is something David Coe might look into.)
According to my mathematics the residence time equals the e-folding time (or time constant) times 0.69315. See:
Roger Andrews
The temperature coefficient of Henry’s constant for CO2 is just under 4%/degC. For a sea surface CO2 partial pressure of say 400 micro atmos this would give an atmosphere increase of around 15ppm/degC. Close to your 17ppm. However I don’t like the idea of CO2 getting blown in from the south. We need to focus on the basic physics, something that is alien to climate science. CO2 is moved round by pressure gradients, as is the wind.
A question for you. What is an e-folding time? Its an expression I have never heard before.
David,
See Richard Courtney’s explanation here:
Here’s Roger A’s final compromise on the previous thread:
” Using my 0.7 residence time/time constant conversion factor – which Richard at least agrees is reasonable – I find that anthropogenic CO2 explains about 25% of the CO2 increase since 1959 assuming a 5 year residence time, about 60% assuming 15 year residence time and about 40% if we use the average of all the estimates (8 year residence time).
I also find that time constants much greater than 50 years aren’t plausible because they leave too much CO2 in the atmosphere. If the IPCC’s 240 year estimate was correct atmospheric CO2 concentrations would now be much higher than they are.”
TB:
I think these conclusions highlight the importance of CO2 residence time as the key variable in determining how much of the recent CO2 increase is natural and how much anthropogenic.
Another reason to concentrate on residence time is that we have the data we need (carbon emissions and CO2 concentrations) to model its impacts, which isn’t the case for carbon cycle models.
I am in fact beginning to have doubts as to how good some of our carbon cycle flux estimates are. According to the IPCC, for example, about 120 Gt of carbon gets exchanged between the atmosphere and the terrestrial biosphere and about 90 Gt gets exchanged between the atmosphere and the oceans each year, but where did these numbers come from? As far as I can tell they’re based on models; no one has actually measured them. They also strike me as potentially gross overestimates. 120 Gt of carbon moving from the biosphere to the atmosphere and then moving back into the biosphere once a year would generate a global seasonal CO2 range of about 200 ppm, but observations show a range of only 5ppm. 90GT of carbon flux to and from the oceans each year would generate a seasonal range of about 150ppm, but I don’t see any compelling evidence to suggest there even is an ocean-related seasonal carbon cycle. The 5ppm range we do see can be explained mostly if not entirely by vegetation growth and decay.
And if these comments merely display my ignorance of how the carbon cycle works feel free to tell me.
Roger A: these comments merely display your ignorance of how the carbon cycle works.
Put an open goal in front of the tallbloke, and… He shoots! He scores! 🙂
It’s a game of two halves. When it’s colder in the north, it’s warmer in the south. And biggest flux in in-out of the tropics, which aren’t so seasonal anyway. greater summer absorption by the summer growth offsets greater sea to air flux from summer warmed ocean. It’s a co2 starved biosphere, it gets gobbled quickly…
TB: Take a look at:
You may have put the ball in your own net. 😉
No chance, you already moved the goalposts. 😉
You want to talk seasonal fluxes, or 10 year averages?
What’s your preference?
Extrapolation 26 years.
R2 rises to 0.995
Includes annual cycle
This was derived 2008 and a twist sorted out by 2010 when I stopped work apart from outputting an interactive version using a later software version 2012
Updated result to new published data, model untouched.
There are hundreds of hours of work behind this, a work I have been sitting on.
I know what is behind the plot.
Coe requires one curve, IPCC requires a different curve.
There is more. I’m undecided on what to do, good reason behind this.
Carry on, see where things go.
I have just read the link to Roger Courtney’s explanation of CO2 residence times and half life. It’s total cobblers.
The oceans do not breath CO2 into the atmosphere then later sequester it. The mechanism is actually extremely simple. There is a continuous two way exchange in CO2 molecules between atmosphere and ocean. This is simple two way diffusion. Typically it is thought that 10 to 20% of atmospheric CO2 is exchanged annually with the ocean. There is no net flux. In the absence of any other disturbing fluxes the partial pressures of CO2 in the ocean and atmosphere would be exactly the same.
Add now a large absorptive flux such as a photosynthetic flux to the atmosphere, the partial pressure of CO2 in the atmosphere will reduce as CO2 is absorbed. This reduced pressure will generate a net flux from ocean to atmosphere. A new equilibrium will now be established where the ocean/atmosphere CO2 flux is equal to the photosynthetic flux and the atmospheric CO2 partial pressure will now be at the lower level just necessary to sustain the net oceanic flux.
Seasonal variation of the photosynthetic flux then adds a variational element to the atmospheric partial pressure. See part 3 of my paper.
There is absolutely no need for concepts such as residence time and half life. The ocean/atmosphere interface has a response time dependent upon CO2 dissociation and wind and wave action. This response time typically appears to be about 3 years. It would thus take around 10 years (3 time constants for 99% effect) for the effects of a slug of CO2 injected into the atmosphere to dissipate. This value could if necessary be described as a residence time.
Tim
I am intrigued by the data on Mona Loa CO2 levels, but have so far failed to grasp the significance. Can you explain further?
Thanks David.
” In the absence of any other disturbing fluxes the partial pressures of CO2 in the ocean and atmosphere would be exactly the same.”
Surely this can’t be true at all latitudes due to the different solubility of co2 in water at different temperatures. Do you count insolation as a seasonally ‘disturbing flux’ here?
TB
At any point on the earths surface there will be an equilibrium established between CO2 partial pressure due to solvated CO2 in the ocean and the partial pressure in the atmosphere. As you point out this equilibrium will be at a different level of CO2 dependent upon the local CO2 concentration in the ocean and the ocean surface temperature at that point, since Henry’s constant is temperature dependent. This results in not just one equilibrium condition but an infinite number each dependent on local conditions. The resulting atmospheric CO2 levels are an average of all these single equilibrium points. Take a look at part 3 to see how atmospheric stratified levels may be calculated.
Thanks David.
Just a note to say don’t worry if Tim C doesn’t respond quickly. He is mighty cautious about discussing Mauna Loa data.
David Coe says:
August 19, 2013 at 2:23 pm
“I have just read the link to Roger Courtney’s explanation of CO2 residence times and half life. It’s total cobblers.”
Well, it might have been better if Richard Courtney had just stated that the e-folding time is the time it takes for CO2 emitted to the atmosphere to decline to 1/e of its initial value without going into the mechanics of how it happens, but the residence time concept remains valid.
“Typically it is thought that 10 to 20% of atmospheric CO2 is exchanged annually with the ocean. There is no net flux.”
Just as a matter of interest, where do these 10-20% numbers come from? And how do we know there’s no net flux?
“The ocean/atmosphere interface has a response time dependent upon CO2 dissociation and wind and wave action. This response time typically appears to be about 3 years. It would thus take around 10 years (3 time constants for 99% effect) for the effects of a slug of CO2 injected into the atmosphere to dissipate. This value could if necessary be described as a residence time.”
Okay, let’s assume that the residence time of slugs of CO2 injected into the atmosphere is 3 years. Here’s what we get when we calculate atmospheric CO2 concentrations by applying this number to historic anthropogenic carbon emissions, which I think will qualify as “slugs”:
If the 3 year residence time is correct then anthropogenic emissions only explain about 10ppm of the 90ppm increase in atmospheric CO2 between 1900 and 2010. So where did the other 80ppm come from?
Roger A: I read it as 3x that 3 years. So how does 9-10 years look in terms of human contribution according to your model?
TB: Three years is the time it takes for the slug of CO2 to decrease to 1/e of its initial value and nine years is the time it takes for it to dissipate altogether. So three years is the right number to use in the e^(-t/T) exponential decay rate formula.
However, there is a some confusion as to what exactly is meant by “residence time”. To reiterate, I assume that residence time is the time when the 50th molecule in a chain of 100 molecules gets absorbed, which gives me the 0.69315 factor for conversion to the time constant or e-folding time, which terms I used interchangeably.
Regarding what we get when we use 9-10 years instead of three, I think you answered this question in your comment of August 18, 2013 at 9:40 pm 🙂
Oops you’re right. My bad.
Rog is correct. I’ll contact you off blog. (already done)
I have a precise model of MLO CO2 data derived from old archive very high resolution data. There is a twist to this.
Nothing has has changed post 1986 from the law then, nothing in there for weather, humans, unless that follows the model. I don’t think that is plausible yet there it is.
If I tell all this puts things out of control. Is this the right time and place?
[…] a short while ago I highlighted a triplet of papers by David Coe [5] who has a slightly different specialism in atmospheric […]