CO2 and ocean uptake – maybe slowing

Hmmm…. do they account for the disappearance of large swaths of rain forest in the green line? Seems those are large hungry plants…

The ocean holds 50 times the CO2 that the atmosphere does as described by henry’s law. To double the Atmospheric CO2 you have to double the total CO2 in both the atmosphere and the oceans. At the present rate of emission that should take about 5000 years. This is why they lie about the lifetime in the atmosphere, because 49 out of 50 parts of CO2 emitted into the atmosphere will be happily be dissolved into the ocean at equilibrium.(assuming constant temp) Of course chemistry is foreign to these folk or they would have realised there is an unlimited supply of carbonate rock exposed to the ocean that will buffer against pH changes.

The first graph, which I presume is not part of the study, says either,
Atmospheric CO2 levels determine SSTs
or,
SSTs determine atmospheric CO2 levels.
Both of which are hard to accept. A puzzle.

I do not understand the first pink graph. What sense has to use “moving average” for X and Y axis values for constructing such graph? For me the graphs shows that rising atmospheric CO2 is a result of degassing of warmer water.

Oh dear use of the green function suggest correct boundary problems solutions which transfers the boundary Value problem(bvp) to an initial value problem (ivp)
eg Ghandouri,
http://www.jstor.org/pss/2100174
This requires a significant set of temporal measurements at the quantum and molecular interface, such as the geometry and size of the taxa say for phytoplakton eg
Changes in the Global Carbon Cycle: Evidence from the Measurements of O2/N2 in the Atmosphere and CO2 Partial Pressure at the Ocean–Atmosphere Boundary
V. G. Gorshkov and A. M. Makar’eva
Abstract
—The global carbon budget includes inorganic and organic constituents. The rates of fossil fuel combustion and inorganic carbon accumulation in the atmosphere and the ocean are known. The organic constituents include changes in the abundance of organic matter in ocean and land areas. Proceeding from changes in CO2 content and O2/N2 concentration ratio in the atmosphere and the known stoichiometric proportions of oxygen binding at organic matter decomposition, changes in the masses of organic substances were quantified in terrestrial and marine environments. The resulting values of organic constituents of the carbon budget are consistent with independent estimates based on the data on anthropogenic land cultivation and the concentration ratio 14C/12C in the dissolved organic carbon of the ocean. We took into account an increase with time in the rate of concentration changes of dissolved inorganic carbon in the ocean inferred from 13C/12C
measurements.Profiles were constructed for changes in CO2 partial pressure and
d13C through the atmosphere–ocean boundary, which correspond to the obtained values of the total carbon uptake by the ocean in inorganic and organic forms.
Concludes
: The traditional estimates of carbon flux on the basis of measurements of the difference of CO2 partial pressures and d13C in the atmosphere and the surface mixed oceanic layer do not account for the biotic changes in the profiles of CO2 and d13C in the microscopic nearsurface layer. This results in contradictions between the changes in the concentration of dissolved organic and inorganic carbon in the ocean calculated from measured 13C/12C and 14C/12C values. Accounting for carbon absorption by marine biota reveals small extrema of pCO2 and d13C at microscopic distances from the interface boundary comparable with the size of phytoplankton cells. The existence of these extrema, which are difficult to detect, eliminates the contradictions between the results obtained by various techniques for
the determination of atmospheric carbon uptake by the ocean. The necessary magnitudes of the extrema are attained if 5% of oceanic gross primary production is
produced by phytoplankton cells in direct contact with the interface boundary. This is consistent with the observed distribution of the phytoplankton biomass
with depth in the euphotic layer of the ocean
http://www.bioticregulation.ru/index.php
The absence of said measurements is a second law violation eg Morowitz
: Abstract Cartesian mind body dualism and modern versions of this viewpoint posit a mind thermodynamically unrelated to the body but informationally interactive. The relation between information and entropy developed by Leon Brillouin demonstrates that any information about the state of a system has entropic consequences. It is therefore impossible to dissociate the mind’s information from the body’s entropy. Knowledge of that state of the system without an energetically significant measurement would lead to a violation of the second law of thermodynamics.
:

Deforestation and other land-use changes continue at a rapid pace today—but now, each year the land appears to be absorbing 1.1 billion tons more carbon than it is giving off

There are two parts of this and they are sort of connected.
The “Deforestation …. continue at a rapid pace” isn’t quite as true as it was once thought to be. While there certainly has been deforestation in some areas, reforestation in the Northern Hemisphere has recently been discovered to be much more than expected making overall net deforestation close to zero. For example, look at a major Midwestern city. Count all the trees in all the yards and parks in an area that prior to settlement had no trees at all. There are trees growing now in areas that had no trees at all 50 or 100 or 200 years ago. How many trees grew in Las Vegas or Phoenix in 1909? How many in Wichita in 1809?
Now other land use changes is a big item not to be ignored, but it is only now being realized that we have more trees growing in the temperate zone of the Northern Hemisphere today than we have had since we started recording history.

Being an old country farmer who after close to three quarters of a century on this rock has developed a very skeptical bent and also being very mathematically challenged amongst the very erudite denizens of this blog, for my simplistic old farmer’s mind there are quite a few problems with the claims in this above paper.
The world’s ocean volumes are given at somewhere over 1.3 billion cubic kilometres of water.
The water in each one of those cubic kilometres weighs in at, for simplicity sake, more than a thousand million tonnes; ie; a billion tonnes of ocean water in each of those cubic kilometres.
Now this is simplistic in the extreme!
The Columbia University researchers claim that the oceans absorbed some 2.3 billion tonnes of CO2 annually or a mass of CO2 that equals the mass of just 2.3 cubic kilometres of ocean water out of all that 1.3 billion cubic kilometres of ocean water.
And that is a very serious situation??
I must try that one on my bank manager sometime when comparing my lack of financial assets to the financial assets of one of the “big four” banks here in Australia!
Now I know that the distribution of the CO2 absorption areas of the oceans is highly variable and only occurs at the ocean surface.
But there is another factor that those who never deal with anything biological will more often than not overlook.
Plants love CO2 and wheat, one of the wold’s major food grain crops gives it’s highest yields at around 700 ppm of CO2 so we still have a long way to go to improve wheat yields by possibly another 15% or 20% just by raising atmospheric CO2 levels to 700 ppm.
CO2 Science has a whole set of data tables on this; http://www.co2science.org/data/plant_growth/photo/photo_subject.php
The plant world of the oceans include truly enormous tonnages of Algae and other plant type animals who like all plants use CO2 as a part and parcel of the photosynthetic process.
I have yet to find estimates of algae and other ocean plant tonnages, their CO2 absorption rates, their growth rates and mass tonnage changes with increased or decreased ocean CO2, or the path of the CO2 as the plants are eaten or die and slowly disperse down into the deep oceans even while acting as an enormous food source for the myriad small creatures of the ocean food chain.
I have read some articles on this algal food chain and some on the possible path that absorbed CO2 follows in small shelled sea creatures but information on algal and other ocean plant growth due to increased ocean absorbed CO2 just does not seem to exist.
Nobody seems to take account of this universal ocean biological CO2 absorption / plant growth process or seems to have tried to assess the effects of increasing CO2 levels on the ocean biology.
And that regular annual variation if the CO2 levels could very easily be just the changes in the ocean’s algal and plant life as the seasons wax and wane and the ocean surface temperatures rise and fall with the seasons and the ocean plant life, booms, busts and dies.
Who would know as the relatively unexplored oceans cover close to 80% of the globe’s surface and the great Southern Ocean and the southern most parts of the Pacific and Indian Oceans have barely been touched let alone researched down to the levels of assessing the long term cycles and levels of ocean plant life activity.
And that annual CO2 variation at all the main global CO2 measuring stations may even have a simple way of checking the source of the CO2 variations.
Way back in 1963 experiments were held to see if Algae could be used as an O2 generator in submarines when supplied with CO2 and sufficient light and etc.
“Gas Exchange with Mass Cultures of Algae”
http://aem.asm.org/cgi/reprint/11/5/450.pdf
Simply measuring any changes in the O2 levels captured in the same CO2 measuring flasks at stations such as Mauna Loa might just show that there is a close correlation between the atmospheric levels of the two gases and if that is the case then the seasonal swings of the oceans are more than likely to be the reason for the annual swing in measured CO2 levels.

OK. As far as the ‘A look at human CO2 emissions -vs- ocean absorption’ post is concerned, I have some qualms, which were expressed by others, notably (and a bit caustically) JamesG (05:18:37).
According to the writer’s self-admittedly simple model, the steady state flux of CO2 from the planet is essentially 0.0215 * 285 = 6 ppm, whereas his annual emissions are 1.5-4.5 ppm, or roughly 50%. I have always read that anthropogenic emissions are more on the order of 1-4% of the total.
This is the biggest problem I have accepting the assertion that manmade CO2 is responsible for the atmospheric increase of the past 50-odd years – the increase due to anthropogenic forcing in a closed loop system like this really ought to be less percentage-wise than the greatest percentage of yearly forcing, or at least, not much more for a reasonably behaved climated system. Until someone can show me with rigorous mathematics a reason that the marginal sensitivity for the anthropogenic forcing should be so much greater than the average sensitivity for the natural forcing, I will continue to have doubts.
I also read with interest some of the other commenters who offered a variety of reasons that the CO2 record may not be entirely trustworthy. My wariness regarding proxy measurements of more than a half centrury ago, which may or may not be well founded, is this: resolution. All sensing devices are band-limited. Some still have very wide bandwidths, but nevertheless, they all have some limit. Time and entropy also tend to degrade materials, soften edges, and remove high frequency content. The warming we have seen recently is really just a blip in geologic time. Do such blips really have time to become fixated in the geologic record, and remain so throughout the ages of storage? Might what is seen in certain repositories, such as ice cores, essentially be low pass filtered versions of reality, in which such blips would essentially be flattened out?
Into this contemplation stepped Dave Middleton (07:34:58), who noted that studies of Plant Stomatal Index indicate far greater variation in historic CO2 concentrations. Does anyone out there have any recent news of where such studies stand?
As for the current post… eh? Looks like they found what they were looking for.

I put to thee these questions three:
Question One: How is CO2 measured?
Question Two: Where is CO2 measured?
Question Three: By whom is CO2 measured?
I just want know.

Personally, I find the use of the proportion of annual CO2 emissions taken up by the environment a pretty useless and probably misleading statistic.
I suggest that everyone refers back to the “A look at human CO2 emissions -vs- ocean absorption” link provided.
The rate of up take is closely related to the time integral of the of the (emission rate – up take rate), giving the degree of imbalance. If we held emissions constant (zero annual increase) the up take rate would take years to go down (half live ~50 years (ocean proportion only)) so the up take proportion ratio would become infinite.
For the up take proportion to be meaningful one would have to look at timescales greater than about 50 years. Also of note is the short (geologically) time scale of the CO2 excess, in truth there is a much longer time constant required to finally purge the CO2 from the atmosphere/ocean/biosphere by geological processes and that does indeed have a geological time scale.
Alex
The reco very rate

But we know the uptake rate is a lot quicker. When SE Asia caught fire in the early ’90s the smoke could be seen from space. That year there was a blip at Mauna Loa’s CO2 station, but gone within less than 5 years.

Looks like the same old….perhaps we have an interesting subject, but I must say at the end AGW is god or I wont get paid.
This is not science…it carrot on a stick.

Alexander Harvey (03:31:43) :
“Personally, I find the use of the proportion of annual CO2 emissions taken up by the environment a pretty useless and probably misleading statistic.”
I agree with this. There is some very wooly thinking in this study.
First, the statement “slowdown in the oceans’ ability to soak up excess carbon from the atmosphere” sounds almost anthropomorphic – the oceans have ability to do things like people. For people doing this study who are primarily politicians, not scientists, this is understandable.
The language is dumbed-down for greater political effect, at the expense of loss of clarity, confusion and ambiguity.
The word “slowdown” suggests that some properties of the ocean are changing due to CO2. The solubility? Capacity? This is confused thinking. Seawater has a certain CO2 solubility and capacity at all temperatures from 0-100C: this can be measured as a curve and is a property of seawater. This property does not change. The laws of physics and chemistry do not change with changing atmospheric CO2 concentration.
Furthermore, as is so often the case in AGW alarmist activist “science”, what is presented as experimental data turns out to be a hybrid of read data and mathematical modelling:
“Khatiwala and his colleagues came up with another method. Using some of the same data as their predecessors— seawater temperatures, salinity, manmade chlorofluorocarbons and other measures—they developed a mathematical technique to work backward from the measurements to infer the concentration of industrial carbon in surface waters, …”
This trick of presenting as data what is in the end a model prediction is a common one in AGW literature.
Of course the conclusions of the paper and the language and tone of the paper are intended to convey a sense of crisis, that even though the poor old oceans are doing the best they can, they are in a beleagured state and approaching CO2 fatigue, and cant prevent CO2 in the air or water reaching crisis levels, which will wipe out calcified marine life such as corals and calcified plankton, not to mention causing run-away atmospheric heating. All very gloomy stuff.
The “ability” (so to speak) of living organisms to calcify their tissue evolved in the sea during the Cambrian explosion (if you exclude the previous “small shelly fauna”). Tissue calcification is done by many groups of marine organisms from fish to molluscs, crustaceans and also single celled plankton, as well as sessile organisms notably corals. This whole ensemble of calcified organisms has flourished continuously (punctuated by mass extinctions followed by rapid recovery) over the half billion years from then to now. During this period the CO2 concentration in the atmosphere has fluctuated and has sometimes been up to 10 times higher than today for tens of millions of years.
What happened during those periods such as (if I remember rightly) in the Triassic with many times more CO2 in the atmosphere than now. Was seawater like lemonade? Could you see bubbles rising from it all the time – was the pH 2-3? Did all biological calcium in the sea dissolve? And did the earths surface become for tens of millions of years like Venus (then later somehow recover)?
None of these historic implications are explored nor indeed have they likely even crossed the minds of these somewhat uncurious authors.
How will the oceans “respond” to the current increasing levels of atmospheric CO2? Answer – in the same way that they always have in the past. We may not know exactly what that response was. But the response clearly did not include anything especially harmful for life in the seas or on land.

Is there some sort of carbon crisis/climate conference in the offing?
DaveE.

RobJM (23:36:57) : The ocean holds 50 times the CO2 that the atmosphere does as described by henry’s law. To double the Atmospheric CO2 you have to double the total CO2 in both the atmosphere and the oceans. At the present rate of emission that should take about 5000 years. This is why they lie about the lifetime in the atmosphere, because 49 out of 50 parts of CO2 emitted into the atmosphere will be happily be dissolved into the ocean at equilibrium.
Clearly we’re not ‘at equilibrium’. Isn’t that the whole point? We’re pumping CO2 into the atmosphere *much* faster than it can be absorbed by natural sinks. We’ve increased atmospheric CO2 by nearly 40% in (say) the last 200 years, and it’s been accelerating. What mechanism is suddenly going to kick in to make the other 60% take 5,000 years?

Good grief. The oceans regulate climate by “absorbing more than a quarter of the carbon dioxide that humans put into the air.” Funny, I thought they did it via absorbing energy from the sun and re-radiating it in varying intensities manifested by the PDO, AMO, and the thermohaline current. Silly me. The oceans apparently have struggled mightily all these years to take in our evil “Carbon”, but now are exhausted. The plants have stepped up valiantly to do their dirty work, but can’t be counted upon forever. Presumably, they will become exhausted too at some point.
It’s a shame this sort of codswallop is what passes for science nowadays.

Rom (01:22:10)
nice one, most don’t realise how much water there really is on this planet, but, if you have a globe (world map) and take it out of its mount and turn it so as the Antarctic is facing you, now tell me that we have land on earth. Its all water.

This comment is somewhat on topic, but more related to yesterday’s post:
CO2 still going up, but temperature not following the same trend
http://wattsupwiththat.com/2009/11/17/co2-still-going-up-but-temperature-not-following-the-same-trend/#more-12902
I just wanted to share an “Aha” moment I had yesterday. For a while I’ve been wondering why my best regression against total CO2 PPM was using a 3rd order polynomial. Then yesterday I saw the above post discussing a “paper – by scientists from the internationally respected climate research group, the Global Carbon Project (GCP)”.
The links led me to the following:
Powerpoint:
http://www.aussmc.org/documents/Raupach.CarbonCycle.V01.pdf
Carbon Budget Data:
http://lgmacweb.env.uea.ac.uk/lequere/co2/carbon_budget.htm
On page 13 of the Powerpoint they show the graph “Fraction of CO2 emissions remaining in the atmosphere”. This graph showed the fraction going from 40% to 45% between 1959 and 2008. It also stated that it is likely to increase another 5% over the next 50 years. This meant that they were using a linear regression to model the change in percentage.
As seen in the data file, the growth in CO2 emissions is also of a linear nature. My “Aha” moment was that the growth in CO2 concentration is the product of two linear equations which is a second order polynomial. If we take the integral of this we get a third order polynomial, which is the area under the curve, which is the total CO2 in the atmosphere.
Next I regressed the Mauna Loa annual CO2 PPM growth rates and Carbon Budget Data’s (CBD) atmospheric CO2 GTon growth rates. As suspected, these are highly correlated with 1 PPM ~ 2 GTon and the intercept near zero. Not surprising as the GCP’s data is probably derived from the Mauna Loa data. I just wanted to confirm the relationship.
I then regressed the annual mean PPM’s for 1959-2008 against x^3, x^2, and x, with x=0 at 1959. The hindcasting skill of the model was great with r2 = 0.999. One surprise was that the x^3 coefficient was negative, even after allowing for stdev. This could only be true if the CO2 fraction remaining in the atmosphere was trending negative, which was contrary to the GCP’s powerpoint. Looking back at the GCB’s data, however, the stdev was greater than the trend coefficient itself so it is entirely possible.
Do I personally believe that the fraction trend is negative. Maybe. In the universe of all plausibilities, I believe this to be as plausible as the atmospheric trend being positive. You would have to believe, however, that the growth in the growth of atmospheric CO2 will at some point turn negative, which seems counter-intuitive. It could be true if the land sink’s portion is increasing greater than the ocean sink’s decrease. My guess is that at some point the fraction will be constant, but what that fraction might be is anybody’s guess.
Aren’t regressions fun? One can look at the same set of data and reach the opposite conclusion of someone else. Even an “internationally respected climate research group”. More fruit for the bakery, I guess.

Luboš Motl (01:47:16) :
I think this very parameterization and methodology of the “airborne fraction” and the fraction that is being absorbed is incorrect.
The increase in plant growth in response to increasing [CO2] is enhanced by increasing global precipitation in response to increasing temps. Who says warmer is bad?
Icarus (05:45:27) :
Clearly we’re not ‘at equilibrium’. Isn’t that the whole point? We’re pumping CO2 into the atmosphere *much* faster than it can be absorbed by natural sinks. We’ve increased atmospheric CO2 by nearly 40% in (say) the last 200 years, and it’s been accelerating. What mechanism is suddenly going to kick in to make the other 60% take 5,000 years?
Since CO2 is beneficial to plant growth and warming temperatures increase precipitation, then I hope there is no mechanism. And I’m unconcerned about sea level, polar bears, and glaciation.

I see a bright, green crap table in the middle of this enormous casino; around its thick, rich polished sides stand rows of spectators, all eyes on the passionate thrower at the player’s end of the field.
To his left is the steely-eyed keeper-of-the-game, handing out a seemingly endless stack of chips to the sweaty-browed player casting his dice as fast as his free hand can sling, while the other claw doubles down on every bet — taking time only to scribble another IOU to add to the growing pile.
He is the passionate ‘warmist’ come to play his final game, and the stakes are the house.
The fascinated spectators grow in number, knowing the very floor where they stand depends on the luck of the throw:
Will they walk away or will they tear down the house?

Lubos Motl,
I have difficulty in believing that the upper portion of the ocean is somehow ‘saturated’ as you claim, when Henry’s law postulates that it is the partial pressure that drives the absorbtion. So, if the partial pressure of CO2 is seen to have increased by 3ppmv, then the equivalent of 50X this amount will have been absorbed.
Can you explain why Henry’s law somehow gets suspended in the conditions we are talking about?
And just to forestall claims that “things are not in equilibrium because it takes a long time for Henry’s Law absorbtion/outgassing to happen” … it seems to work pretty quickly enough for the fizzy-drink bottling industry. So if possible I’d like to know if there are any experimental values for the absorbtion rates of CO2 in water.

The article says:

Khatiwala and his colleagues came up with another method. Using some of the same data as their predecessors— seawater temperatures, salinity, manmade chlorofluorocarbons and other measures—they developed a mathematical technique to work backward from the measurements to infer the concentration of industrial carbon in surface waters, and its transport to deep water through ocean circulation. This allowed them to reconstruct the uptake and distribution of industrial carbon in the oceans over time.

We only have somewhat accurate seawater temperature measurements for the last half century or so. We have very little information about global salinity. Chlorofluorocarbons have only been made for half a century. Our understanding of the totality of ocean currents is low.
Could someone explain to me how they can use these to say how much carbon was absorbed by the ocean in say 1850 or 1920? Sounds like guesswork to me, not science.

Gosh what a lot of mays and might bes, and what delightfully circular way of going about it.
For a rather different opinion try this excellent article at CO2 Science.
http://www.co2science.org/articles/V12/N31/EDIT.php
It has further links worth exploring.
Kindest Regards

supercritical (10:25:29) :
4. What will happen if the vessel is 4 km deep?

Here’s a carbon sink for you, http://spacefellowship.com/2009/09/11/plentiful-plankton-from-space/
Raw numbers on something that size? Better than the estimates for this one? http://www.earthweek.com/2009/ew091016/ew091016c.html
And catch the snow on the ground in the first shot, not exactly prime living conditions, but hey as long as the plankton like it!
Putting more food into the bottom of the food chain leads to a larger food chain, hard to see how that could be a bad thing.

supercritical (09:43:37) :
Lubos Motl,
I have difficulty in believing that the upper portion of the ocean is somehow ’saturated’ as you claim, when Henry’s law postulates that it is the partial pressure that drives the absorbtion.

It’s not that the upper ocean is saturated with CO2 that is the issue, it’s that only the upper ocean is in direct contact with the atmosphere. It’s over the ocean-atmosphere boundary that diffusional CO2 exchange occurs and hence the boundary layers (both atmospheric and oceanic) where CO2 exchange is occuring is where Henry’s Law directly applies.

So, if the partial pressure of CO2 is seen to have increased by 3ppmv, then the equivalent of 50X this amount will have been absorbed.

Not quite. The roughly 50:1 partitioning of inorganic C (as CO2 in the atmosphere and DIC in the ocean) is simply the ratio you get for the prevailing chemical conditions. The partitioning of CO2 between the air and seawater fractions is not constant though–it varies non-linearly as you change DIC concentration and/or total alkalinity (i.e., acid neutralizing capacity). See Stumm and Morgan (Aquatic Chemistry), Zeebe and Wolf-Gladrow (CO2 in Seawater), etc. for extensive discussions of carbonate chemistry.
The change in buffer intensity for a given change in DIC is often expressed with the short-had Revelle factor (good for back of the notebook estimations). For more precise answers you’ve gotta do the calculations.

Can you explain why Henry’s law somehow gets suspended in the conditions we are talking about?

As above, it doesn’t, but Henry’s Law only directly operates at the ocean-atmosphere interface, where CO2 exchange actually occurs.

And just to forestall claims that “things are not in equilibrium because it takes a long time for Henry’s Law absorbtion/outgassing to happen” … it seems to work pretty quickly enough for the fizzy-drink bottling industry.

Yes, definitely. A soda or bottle of soda in contact with pure CO2 is something like the boundary layer in the ocean and atmosphere. CO2 exchange is relatively fast there. However, it takes thousands of years for an equivalent parcel of water to be transported though the ocean via thermohaline circulation.

So if possible I’d like to know if there are any experimental values for the absorbtion rates of CO2 in water.

Yep, there is a fair bit of data. I’d suggest Millero, 2006 Chemical Oceanography as a starting point.

Chris,
Thanks for your post. I am trying to keep things simple, so given the rough 1:50 ratio of atmospheric CO2 to dissolved CO2, that Henry’s law predicts at any level of partial pressure of CO2, I do understand that this ratio varies a bit for different conditions of salinity, etc .. (as well as temperature which I haven’t go to yet )
But, surely it does not vary all the way down to 1:2 as Lubos Motls’ post implies?
And \as I note that you do agree that the soda-bottle analogy does support Henry’s law; perhaps you could have a go at my experiment-quiz, which you can find upthread a little.

Re: Phillip Bratby (23:18:04)
What do suggest we re-name it, NOAA ?

Vincent (04:35:09) :
“Wasn’t there a recent paper from Bristol universtity that came to the opposite conclusion, that the absorbtion of CO2 has been increasing steadily? ”
I was wondering if anybody would notice these two papers were on similar topics. That paper (Knorr, 2009) was much, much more simple than this one. Knorr basically divided the red curve (air) by the black curve (emissions)* in the figure above, and found that there was no significant trend in the resulting fraction (airborne fraction). Though by his method, if there was a subtle change in the airborne fraction in the last decade, I don’t think he’d have found it. If these guys (Khatiwala et al) discuss the airborne fraction, I didn’t see it on skimming the paper. So it isn’t obvious there is an opposite conclusion.
[*Also, I think Knorr’s version of the black curve included some things that are in these guys’ green curve (land); something to check. Note that the curves look smoothed in this new paper.].
Knorr did not even attempt to find the blue curve (ocean) above, as it requires a good deal more work. So the major contribution of this paper is that they found that blue curve, assuming they did a good job of it. The green curve is then simply found by subtraction, they they claim it roughly matches what others have found going forwards.
The attention comes from the ocean sink (blue curve) not quite keeping up the pace recently. On the other hand, the land and biosphere (green curve) picks up some of the slack.
Given how complicated this one is, I’d remember this work, but wait to see what else gets published in this area.

bob,
Do your results point to Henry’s law needing to include a term for the ratio of gas and liquid volumes?

Bart, let me maybe make it more clear.
You have a term (Co – C)/tau. You don’t know what Co is, which is itself troubling, but let’s go with it. If the concentration in the air exceeds Co, then this term will get rid of it by removing it to some unspecified sink, by unspecified physical processes. Very well.
But Co-C is just your driving force. If you really want to equate the term with some physically observed value, then it has to be the global NET carbon flow into the atmosphere. For the moment, let’s use the numbers in here, as they’re handy:
http://en.wikipedia.org/wiki/File:Carbon_cycle-cute_diagram.svg
At the time of the diagram, your term (Co-C)/tau is equivalent to -2.2 GtonCarbon/year (I’m not going to bother fussing with the conversion to ppm).
Meanwhile, at the given time, your term ‘a’ is equivalent to +5.5 GtonCarbon/year (again, not bothering with converting to ppm)
Assuming I added correctly, about 60% is staying in the air.
So far, so rough, but OK for limited purposes. We should stop there, as it’s as far as this line of inquiry is going to take us.
Here’s your problem: you try to go further, and try to assign physical values to things which you cannot. “Co/tau actually represents the rate of CO2 coming back into the system to keep it steady at C = Co without the anthropogenic forcing.”
No, it doesn’t represent that, at all. You seem really wanting to separate (Co-C)/tau into two separate elements, Co/tau and C/tau, and setting them equal to things you see on the diagram: the sum of the inflows, and the sum of the outflows. You simply can’t. Co-C is just your global driving force; written as you have, you can’t break it up and give the two parts some physical meaning. Over the globe, the term adds up to -2.2 gton carbon/year at the time of the diagram. You really want to equate Co/tau with 211.6 gton/year and C/tau with 213.8 gton/year, but that isn’t valid. In order to actually find the INDIVIDUAL flows in and out of the atmosphere, you absolutely need a global model that describes all those individual flows, as in my last comment – a global model that has oceans, ocean chemistry, ocean biology, ocean circulation, and the works. All your model can do is give some really rough idea of the overall NET flow, based on the assumption that the net flow will have a single time scale and a simple driving force, as expressed by (Co-C)/tau.

Has anybody out there looked at Henry’s Law lately? That “experience curve” looks a LOT like a plot of experimental data for a chemistry lab on Henry’s Law.

carrot eater (07:01:51) :
None of this matters, really. What I said is true no matter what your model is. If it is globally linear, then the sensitivity to forcing is linear.
“The main disconnect is that I don’t understand exactly what Bart is trying to learn from his little model. What, exactly, are you trying to show?”
What I am showing is that things are not so simple as “we have put in X gT of carbon and atmospheric CO2 has risen by 1/2 that amount, therefore the rise is due to us”. That statement is naive to the point of imbecility, and I have ground the enamel off my teeth from hearing it so often.
The other thing I am showing is that, in order to accept the AGW hypothesis, you have to accept an nonlinear climate response with dramatically increasing sensitivity, for which there appears to be little evidence, at least in what has filtered down to my level. In situations like that, my experience has been that a narrative has been constructed, and the caution and uncertainties expressed behind closed doors have not made it out to the final report for public consumption. On a topic as critical as this one for the health and well-being of the citizens of this nation, I am not content merely to take the word of “experts”. I want proof.
I looked up your David Archer on the web. He does not appear to have published anything openly available which delves into the nuts and bolts of the actual climate models. Do you have a link to such a reference?

bob
From my thought-quiz, with a sealed container with N litres of water and a 1 litre headspace initially filled with CO2 at 1 bar. My first approximation at a result would be a for an absolute pressure reading stabilising at a steady 0.02 bar, within seconds.
Then if I increased the CO2 into the headspace so that I got a steady 2 bar reading, I reckon I’d need to inject 100 litres of C02. Again, this should be pretty quick.
So if I started the quiz again to simulate the atmosphere, and filled the 1litre headspace with CO2 to get a steady reading of 300 ppmv ( or 0.3 millibars, or 0.3 cc) I’d reckon on injecting about 15 cc of CO2.
And then, if I wanted to simulate the increase of atmospheric CO2 by 2 ppm/year, ( i.e. ~ 0.003 millibars, or 0.003cc) I would have to inject another initial 0.15 cc of CO2.
So what? It means that, to increase the 300 ppm of CO2 in the atmosphere by 2ppm, I would need to initially add 50x this amount, or 100 ppm. And then it would not take very long at all for the new reading to stabilise at the new 302 ppmv.
But there are estimates that claim that man puts out about 4 ppm/y of CO2 directly into the atmosphere ..so if after a short while 49/50 of it will be absorbed then we can only be accountable for around 0.04 ppm/y of the residual CO2 in the atmosphere. Where is that other 2 – 0.04 = 1.96/y ppm coming from?
My first idea is that we are looking for a CO2 source which is entirely coincidentally emitting some 50x more than man.
And, I would start by looking at CO2 from those recently discovered huge numbers of ocean hydrothermal vents (a form of volcano, after all ) and maybe separately, their warming effect down in the deep oceans, which could cause considerable outgassing from the local waters as well.
But next, I need a quick rule-of-thumb for the temperature effects on the Henry’s law ratio of 1:50 for CO2 and water, in the form of a modifier for the ratio, per degree C. Does anybody have such a number to hand?

The CO2/H2O equilibrium is complicated:
http://www.chem.usu.edu/~sbialkow/Classes/3600/Overheads/Carbonate/CO2.html
The simplest explanation is the information in the above link is that, for a given pH, the warmer the temperature of the water – the higher the pressure of CO2 in the air that will be in equilibrium with it. The alkali content of the water (“hardness” if you prefer) will ‘pull’ the carbonic acid / bicarbonate / carbonate distribution towards the carbonate, making room for more CO2 to dissolve in the water while lowering the pH *very* slightly.
The heat capacity of the ocean overwhelms the trace concentration of CO2 in the air and makes the temperature the driver of this system.
Bottom line, the ocean becomes a HUGE sink for CO2, and the correlation between CO2 levels and temperature shown in the “experience curve” demonstrates that this system is in equilibrium, so minor fluctuations in the CO2 levels from other sources will be dealt with quantitatively.
The real source of CO2 in the atmosphere (and the driver for ‘global warming’ models) is therefore whatever is supplying heat to the oceans: solar energy or geothermal energy (recall the Mid-Atlantic ridge, ‘black smokers,’ and the multi-year Gakkel Ridge eruption, to name just a few).

Supercrit,
I don’t know how you figured out how fast the gas would dissolve in solution, but here is the equation I came up with to figure out the pressure.
P= (Henry’s K)(moles of CO2 gas)(Volume of CO2 gas)(R)(T)
——————————————-
((Volume Tank)(R)(T)+(Henry’s K)(Volume of CO2 gas))(Volume CO2 gas)
where Henry’s K is the Henry’s law constant (variable)
R is the Ideal gas law constant
T is temperature
So, I’m wondering where you got the 50 to 1 ratio.
I think it comes from the natural sources (and sinks) of CO2 being 50 times what man produces.
We don’t need to look for a source we already know that.
The reason CO2 doesn’t go up as fast as 4ppm per year is that about half is absorbed by the sinks one of which is the oceans.
And then there really is no simple rule of thumb for Henry’s law with temperature but there is an equation.
Henry’s Constant for temp T = H time e to the exponent -2400(1/T-1/298)
and I apologize for being in a hurry and not doing sub and superscripts for the above equation.
thanks

Sorry, correction:
Sea temperature increase of ~ 0.08 degrees needed to increase atmospheric CO2 by 2ppm.
Stil a ‘Wow!’ result?

There is an annual dip in CO2 caused by something water temp/flora/algae/etc.
http://img175.imageshack.us/img175/9698/manyco219992001.jpg
If absorbed by flora/algae (living stuff) then presumably the rise from the dip would be less than the fall into the dip – some CO2 would be retained by the growth. This is not apparent.
If it is sea water then its the wrong way up – summer would be higher CO2 (warm water). Also sea water is not saturated by CO2 so would it breathe with temperature?
Since 1974 the depth of the annual dip in CO2 (Start April end August) has increase from 14.5 to 20ppm approx:
http://img183.imageshack.us/img183/1212/depthofptbarrowdip.jpg
If warming is happening then sea water and air temp will be warmed to the same value where absorption occurs earlier each year:
days from Jan 1st = -1.945E-04x + 2.377E+02
plot here:
http://img89.imageshack.us/img89/1610/barrowdateofminiman.jpg
Note that in Barrow there is little/no change in the date of minimum (.0002 days/year) but temperature has significantly increased.

carrot eater (12:07:39) :
“Oh, please. It is no such thing.”
This shows you do not understand the tenets of formal logic or the minimum requirements for proof. This is the kind of thinking which led humankind for centuries to believe that bleeding patients with leeches would cure illness, or that “night gases” were responsible for sickness, or that regular bathing was bad for your health. Not knowing of microbial life, they had exhausted all other possibilities, therefore, the logic of their conclusions appeared inescapable.
We like to imagine that we are intellectually superior to our forebears, merely because we know more. But, the processes of logic never change, and though the fallacies to which we cling may become more sophisticated, to them we remain magnificently vulnerable via our innate hubris.
“I still don’t follow what you mean. You add carbon to the system; it builds up in different places. What’s the big mystery?”
It doesn’t just build up, it also dissipates. The rate at which it builds up and dissipates is key to the entire puzzle. By placing a limit on the rate at which we are forcing the buildup (my 3%), we gain insight into the possible trajectories of its concentration as a result of our actions, and can falsify various hypotheses as to how it will all unfold.
“And what is the natural flow back out of the atmosphere, Bart?”
That is my whole point. And, that outward flow rate is lower bounded by the rate at which we are putting emissions into the air, the rate at which we have observed concentrations rise, and the plausibility of the given flow rate models.
carrot eater (10:45:25)
“The paper I had in mind was “Fate of fossil fuel CO2 in geologic time”, Journal of Geophysical Research, vol 110 (2005).”
I found the paper here. Color me unimpressed. A paper this sketchy would never have passed the peer review of the journals in my field in which I have been published. It is difficult to grasp his entire methodology given the level of detail. But, at the very least, I notice two things:
1) He states that “the maximum amount that could ultimately be released would seem to be about 5000 Gton C, on a timescale of several centuries.” He then projects his two significantly alarming accumulation projections based on “…2000, and 5000 Gton C are released following a Gaussian trajectory of 150 years half-width centered on the year 2100.” That is, he releases 40% and 100% of the entire reservoir in a mere 150 years.
2) The responses have a large transient, which indicates only the degree to which his forcing exceeds the bandwidth of his assumed system response, and when you are pumping out so much in such a short time, and assuming a 1000 year fundamental time constant, it is hardly surprising that you get a huge blip before the system eventually settles out in the very long term steady state to just barely above the level he started with.
In short, the worst case results in this analysis are almost completely conjectural, and depend critically on assumptions which are not based on real world behavior.
“The Global Carbon Project or somebody else must have stuff available to look at.”
Meaning, you have taken it on faith that “somebody else” has looked at this, and that is good enough for you. It is not good enough for me.

carrot eater (16:23:34) :
“Spare me the lecture on unrelated matters. “
Spare me the pose. If you are uninterested in formal logic, there is no point in further discussion. You can go back to reading chicken entrails or beseeching burning bushes for enlightenment if that is what you choose, it does not really matter to me.
“He did it for 300, 1000, 2000 and 5000. The amount we’ve already emitted is in the 300 range, isn’t it? Why did you neglect to point that out?”
The increases for the first two cases do not appear to be particularly worrisome, so I focused on the latter two. That is why I stated “…his two significantly alarming accumulation projections…”.
For the rest, I have to admit, I was not familiar with the currently claimed levels of output. I jumped to the conclusion that, after he had stated that “the maximum amount that could ultimately be released would seem to be about 5000 Gton C, on a timescale of several centuries,” and he then appeared to proceed to release it all over a 1.5 century interval, then by his own description, he appeared to have speeded up the process considerably. That, however, may not be the case, depending on what he meant by “Gaussian trajectory”, which suggests different types of functions in different disciplines. It could mean that his effective forcing interval is at least 300 years, which can fit the definition of “several”. The details of how that trajectory is formed are, lamentably, missing.
Regardless, it still falls flat, because in the time that anthropogenic emissions would be 2000 to 5000 Gtons, natural processes would add over 100 Tera-tons. So, we have a net 5% or so additional input at most. To get the type of amplification he is projecting, his model has to be extraordinarily sensitive to high frequency behavior (the model has to be dependent on derivatives of the forcing rate) or his marginal sensitivity has to be extraordinarily high (the system is very nonlinear), and his dominant time constants have to be extraordinarily and unrealistically long (the very fact that the rise in CO2 concentrations of the last 50 years is only half of the recognized anthropogenic forcing is not compatible with the asserted 1000 year dominant time constant).
I have argued each and every one of these points over this series of exchanges with you. If you can point me to sources which have detailed mathematical descriptions of the model or models, then I can deconstruct them for you and tell you precisely what is going on, and which parts of the models are, by my lights, reasonable and which are not. Otherwise, I believe we are at an impasse, and we no doubt both have more productive uses for our time than to continue reiterating points we have already made to one another.

supercritical —
The Mauna Loa figures are quite consistent with trends from other monitoring stations. There is also now a satellite which makes global measurements. The Mauna Loa readings do not seem to be a local effect.
http://cdiac.ornl.gov/trends/co2/sio-keel.html

Supercritical,
It is plausible (based mainly on Henry’s Law) but there are complicating factors, e.g., buffering. Seems the sort of question that could be answered experimentally, i.e., de-gassing a volume of seawater, introducing an atmosphere above it with a known concentration of CO2, and measuring the equilibrium points at different temps. Don’t know if anyone has done this.
Of course, if atmospheric CO2 is the effect, not the cause, of rising SSTs, then you need another energy source for the temp increase.

Just a few comments from a physical chemist regarding Henry’s Law. This law says that the CO2 in the atmosphere will seek an equilibrium with the dissolved CO2 in the water (as carbonic acid – H2CO3). The exact proportions will depend on the temperature of the water, with warmer water less able to hold CO2 in solution. The mathematical statement is that at equilibrium the ratio of the partial pressure of CO2 to the concentration of H2CO3 is a temperature-dependent constant:
K(T) = P[CO2]/[H2CO3]
(see Wiki’s section on Henry’s_law#Temperature_dependence_of_the_Henry_constant)
This simple truth is complicated by the fact that there are two other equilibria involved, both of which depend on the pH of the water, rather than the temperature.
H2CO3 ionizes in water to produce a bicarbonate ion (HCO3-) and a proton (H+, acidity).
Bicarbonate ion ionizes further in water to procude a carbonate ion (CO3=) and a proton (acidity, again).
The pH of sea water ranges froma high of about 8.4 to a low of about 7.5.
At a pH of 8.4, 98% of the dissolved carbon dioxide is present as bicarbonate ion, and only 1 percent of the dissolved CO2 is present as carbonic acid, and another 1% as carbonate. That mean that 99% of the CO2 that the ocean absorbs becomes ions that cannot be released back into the air. Only carbonic acid can release CO2 back into the air.
The airborne CO2 is in equilibrium with only 1% of the CO2 in the sea. The sea is a terrific sink for CO2.
Even at a pH of 7.5, 90% of the CO2 in sea water is present as bicarbonate, and only about 10% as carbonic acid. [Carbonate holds only about 0.1% of the dissolved CO2 at this pH.] This relatively high concentration of carbonic acid means that the atmospheric CO2 reaches equilibrium with the dissolved CO2 faster in the more acidic portions of the sea.
Carbonic acid only predominates as the dissolved form of CO2 when the pH is less than 6.37 – a situation we have not yet seen. Above this pH the sea absorbs more CO2 that it releases.
CO2 can be driven out of solution by raising the temperature or by lowering the pH. Since the pH is not low enough to make an isothermal sea a net source of CO2, the way to take CO2 out of the sea is by raising the temperature.
Can anybody tell us if any of the IPCC models account for submarine heat sources? These heat sources are not trivial. I am talking about “black smokers”, mid-ocean rifting, and ocean floor vulcanism (e.g. Gakkel Ridge, Arcitc Ocean; Lo`ihi volcano, Hawaii:). I don’t believe that they do.

Bart (19:02:57) :
The data say that for every unit of CO2 emitted by humans, about half accumulates in the atmosphere, and half accumulates in the oceans/biosphere/land. This distribution seems rather surprising to you, though I don’t follow why. You also seem to think that there are other ways of explaining the accumulation in the atmosphere. So, out with it. Put forth any sort of hypothesis. Where is the other source? Is it the ocean? Is it the soil? Volcanoes? Then, give a rough idea of what the net flow from that source would need to be, in order to account for the atmospheric accumulation, as well as drown out the effect of the human-related emissions. Describe the other flows around the system, as well. Then explain why this source would have become active just at the same time as human-emissions, and followed the same ramp. Also explain how this other source has the isotope signature of fossil fuel use.
You invoking an unknown unknown, and stopping there, seems hugely unproductive, as well as strangely incurious.
“2000 to 5000 Gtons, natural processes would add over 100 Tera-tons. ”
You continually make statements like this, without noting the simultaneous natural outflow. Those natural processes were active before human emissions, too. Are you somehow amazed then, that the atmospheric CO2 level was fairly stable during the thousands of years of the current interglacial, before human emission? That’s thousands of years of natural processes, adding gigantic amounts of carbon. And yet the atmospheric level remained within a band 20 ppm wide or so.
We are taking carbon that has been out of the cycle, and putting it back in. It has to accumulate somewhere. I don’t know why it is surprising to you that it accumulates in both air and sea. Where did you think it was going to go?
“That, however, may not be the case, depending on what he meant by “Gaussian trajectory”,”
A Gaussian distribution with a half-width of 150 years. That’s unambiguously defined; I don’t see how there is confusion.

carrot eater (15:40:43)
“You continually make statements like this, without noting the simultaneous natural outflow.”
Are you kidding?!!! It’s all I talk about. The natural outflow does not discriminate between the natural inflow and what we put in. It takes it all back out, and it does so elastically. It opposes the deviation from the mean. This is negative feedback in action. This is what negative feedback does. It is what makes feedback so marvelously useful, and feedback regulated systems so marvelously robust.
The whole point is that the system is removing all that naturally produced CO2 just fine, but then it supposedly chokes up on a measly few percent-at-most additional input. That would make it, most decidedly, a non-robust feedback loop.
“A Gaussian distribution…”
How do you read “trajectory” and get “distribution”? I could think of a dozen ways to generate a trajectory off the top of my head which would fit such a description. There are all kinds of possibilities, which is why I said this paper would never have gotten past peer review in my field. We take pains to outline each and every step, and rigidly define each and every quantity, in our papers so that they will be useful to others who wish to replicate our results. That does not appear to be the goal at all here, and that in itself is a travesty.
The system response can be extremely sensitive to the type of function used. As I stated before, frequency components beyond the bandwidth of the system can excite transients, and the plots in the paper do appear to show large transient spikes, though it is difficult to tell from the resolution of the time axis. If it is not a transient spike, then it makes no sense at all, for reasons I have outlined previously.
There is no reason at all to arbitrarily choose the profile of a Gaussian distribution. And, it would leave plenty of questions if that is what he did, such as, how far down the tail did he go for the start date? If, e.g., he used a distribution centered at 2100 with a “standard deviation” of 150 years, and he started the model in the year 2000, then he was already way up the curve when he started, and that would introduce horrendous high frequency content to feed a transient. Even starting 200 or 300 years previous would require a huge initial step. Where did he start?

Bart (16:43:05) :
I think I’ve finally figured out what’s driving your thinking.
Basically, you are surprised that CO2 is able to accumulate to any appreciable extent in the atmosphere, because you imagine the carbon cycle as a feedback control loop that keeps the atmospheric level in check. You are drawing analogies to whatever systems you study in your work, and you are thinking that the carbon cycle will work the same way, without stopping to consider the actual physical processes and time scales involved. I think this is a rather poor approach. You should put some time into studying the ocean-atmosphere exchange and the time scales involved, as well as the other processes involved, such as the weathering of rocks (which, as one might imagine, is quite slow). Only then would you have an idea of where the carbon should go, and how quickly it should go there.
On the level that you are thinking, you could flip the picture upside-down and reach the opposite conclusion. If man were pumping CO2 directly into the ocean, shouldn’t your feedback mechanism oppose the deviation from the alleged setpoint and promptly put all the CO2 into the atmosphere? How do you know that your feedback mechanism will work to keep stasis in the air, instead of the ocean?
These are the dangers that arise when you don’t actually look at how carbon is cycled throughout the system (and ultimately removed from the system), and just imagine it as some black box feedback control loop.

Bart, one more – Archer and Caldeira (freshly of Superfreakonomics fame), among others, recently published a intermodel comparison of how different models handle a pulse of CO2 emissions. I haven’t had time to read it carefully, but it has a better discussion, and being more recent, it gives more recent references as well. Mainly, I think it’d be useful to actually consider the different processes at hand, so you don’t imagine the thing as some sort of black-box PID loop.
The paper actually discusses the sorts of confusion seen among the public regarding issues such as CO2 lifetime; apt as this exact confusion was seen in the thread here about the Bristol work (Knorr).
http://dge.stanford.edu/labs/caldeiralab/Ongoing_changes.html , the 2009 publication with Archer, et al

Note: I am interpreting “half-width” as the width at which the function reaches half its peak, in reference to how power engineers measure the half power bandwidth of a network. But, maybe this refers to a width such that the tail of the distribution is “negligible”. If that is the case, then he is dumping up to 100% of the carbon reservoir of the Earth into the atmosphere in a very short time interval, which is not realistic.

Bart —
“I am not qualified to comment on the “stripping” action, but there is a hell of a lot of surface area there. Do you have any reliable references in which this is studied?”
Given a nominal pH of 5.7 for rainfall (the usual figure), and assuming all the acidity is due to carbonic acid, then each liter of rainwater should be removing 0.0000878 g of CO2.

Contrarian (03:24:04) :
According to this site, there is globally 914 trillion liters of rainfall on the planet each day, or 334 tera-liters per year. That, given your figure (I am assuming “g” is for grams), could remove 30,000 metric tons of CO2 per year. As our emissions appear to be estimated at about 30 Gtons per year, this does not appear to be very significant.

Contrarian (03:24:04) :
According to a site which the spam filter appears not to like (Wiki-answers) there is globally 914 trillion liters of rainfall on the planet each day, or 334 tera-liters per year. That, given your figure (I am assuming “g” is for grams), could remove 30,000 metric tons of CO2 per year. As our emissions appear to be estimated at about 30 Gtons per year, this does not appear to be very significant.
Maybe the spam filter distrusts the site for good reason. Maybe this is just rainfall over land, or is totally wrong altogether. Does anyone have a different estimate? I can’t seem to find one in a cursory search.

Contrarian (23:06:23) :
But with that much smoothing on the SST side, you shouldn’t be surprised the correlation looks so good. All the pink plot says is that both CO2 and SST are going up. But we knew that.

Carrot eater —
“But with that much smoothing on the SST side, you shouldn’t be surprised the correlation looks so good.”
Why not? The smoothing does not effect the slopes of those curves, and thus the correlation.

Carrot eater —
“Does the value of the slope have any particular significance? Does 143.6 mean anything to you?”
I assume the 143.6x is the conversion from monthly data to annual; the 334.1 the CO2 baseline. The slope agreement is significant because it is so close. It may have a bearing on the direction of causation. Ocean outgassing of CO2 with temperature occurs instantly, while ocean warming from increased atmospheric CO2 would be slower, and would lag. The tight correlation suggests (to me) the former causal arrow.
Maybe Anthony can give a link to the source of the graphic.

I think that the top chart on this page is the most convincing evidence that I have yet seen that the current carbon dioxide level in the atmosphere may be an ‘effect’ rather than a ’cause’ of ocean warming.
I believe the slope of the curve would depend on the total effective volume of ocean being heated and the average reduction of CO2 solubility of per degree C in that volume plus the net anthropogenic CO2 that happened to be released per degree C of ocean temperature increase.

Bart: Ah, let’s just put an end to the thing. I hate the little linear model, as I would not expect it to reflect reality much at all, but if you really want to use such a form, let’s see what happens. I solved it for the case where human emissions decrease to zero, instantaneously. Let’s see what it looks like if human emissions continue over time. Pick a functional form for the human emissions term – the front end of a gaussian curve, maybe? or linear, from some point in time? From the look of it, I might be able to eke out an analytical solution if we use linearly increasing emissions; anything else would require numerical solution (which would probably be faster and easier to do, anyway).

Again, Spector – your lock-step disappears if you add data before 1980 to the plot, or if you don’t use a 21 year average. This should be obvious if you look at data plotted against time. So I wouldn’t draw any conclusions like that, at all.
If the ocean is a net source, then it cannot be a net sink.

Here is a clickable link to the Endersbee paper:
http://icecap.us/images/uploads/OceansandCO2EngrsAustapr08.pdf
(Thanks Spector)
Carrot eater —
Endersbee used SSTs after 1980 because that is the extent of the more accurate satellite record. The 21-year average was used to embrace 2 solar cycles, and even out ENSO/PDO variations. The oceans can be a net source, and still a sink for anthro emissions.
He may not be right WRT to a “decline in levels of CO2 in the atmosphere” with SST cooling. The oceans could not re-absorb CO2 when cooling as quickly as they would release it when warmed, because the excess CO2 is dispersed throughout the atmosphere.

Carrot Eater —
“If you’re actually going to think about the physics, you’ll just see that the ocean is increasing in carbon content. It cannot both increase in carbon content, and cause the increase in carbon content in the atmosphere.”
Your second statement there is certainly true, and would settle the question. But there is no evidence that the carbon content of the oceans has increased. The IPCC claims that “The uptake of anthropogenic carbon since 1750 has led to the ocean becoming more acidic with an average decrease in pH of 0.1 units.”
http://www.ipcc.ch/pdf/assessment-report/ar4/syr/ar4_syr_spm.pdf
But that claim is based on model calculations which assume that the oceans are a net carbon sink, not on empirical evidence (and it would be virtually impossible to reconstruct a global ocean pH trend accurate within 0.1 unit).
Here are a couple of sources. If you know of others, please post links.
http://pangea.stanford.edu/research/Oceans/GES205/Caldeira_Science_Anthropogenic%20Carbon%20and%20ocean%20pH.pdf
http://www.ipsl.jussieu.fr/~jomce/acidification/paper/Orr_OnlineNature04095.pdf