Steve Fitzpatrick writes in with a short essay:
On May 11 you reposted a blog from Dr. Roy Spencer, where he suggests that much of the increase in atmospheric CO2 could be due to warming of the oceans, and where he presents a few graphs that he claims are consistent with ocean surface temperature change contributing more than 80% of the measure increase in CO2 since 1958. Dr. Spencer’s suggestion is contradicted by many published studies of absorption of CO2 by the ocean, with some studies dating from the early 1960’s, long before “global warming” was a political issue. In this post I offer a simple model that shows why net absorption of CO2 by the ocean is most likely the main ocean effect.
If the rise in CO2 is being driven by human emissions, then the year-on-year increase in atmospheric CO2 ought to be a function of the rate of release of CO2, less any increase in the rate of removal of CO2 by increased plant growth and by absorption and chemical neutralization of CO2 by the ocean. Both ocean absorption and plant growth rates should increase with increased CO2 concentration in the atmosphere. To simplify things, I focus here only on ocean absorption.
On the other hand, surface temperature changes ought to have a relatively rapid effect, because the surface of the ocean is in contact with the atmosphere and so can quickly absorb or desorb CO2 as the water temperature changes. In fact, the ocean surface continuously absorbs CO2 where the temperature is falling, mostly at high latitudes, and emits CO2 where the water is warming, mostly at lower latitudes. Cold upwelling water from the deep ocean warms at the surface and desorbs CO2, while very cold water at high latitudes absorbs CO2 before it falls to the deep ocean. An increase in average ocean surface temperature will cause more CO2 to be emitted from surface water, but this effect is limited to a very small volume fraction of the ocean. Effects due to rapid temperature changes (annual time scale and less) are limited to a relatively thin layer, while the gradual absorption/neutralization process takes place at a rate controlled by ocean circulation and replacement of the surface water with upwelling (and “very old”) deep ocean water.
Any change in sea surface temperature should add to or subtract from the atmosphere’s CO2.
Annual change = (Annual emissions) – K1 * (CO2 – 285) + K2 * (delta SST)
Where “CO2” is the atmospheric concentration, K1 is a unitless “ocean uptake constant”, and K2 is a sea surface absorption/temperature constant, with units of PPM per decree C. Delta SST is the year-on-year change in average sea surface temperature. K1 is related to how quickly surface water is replaced by deeper water, and it should be a relatively small number, since ocean circulation and mixing are slow. K2 should be a relatively large number, since surface water temperature changes are relatively fast and we know that there is a strong short-term correlation between the rate of change of CO2 concentration and SST changes.
The model performs an iterative calculation (a step-wise approximation of integration) of the evolution of CO2 in the atmosphere. Each year a change in CO2 is calculated using the above equation, that change is added to the atmospheric CO2 concentration from the previous year, and the process is then repeated. The calculation starts with 1959, using a starting CO2 concentration of 315 (the value from Mauna Loa in 1958).
Measured CO2 values and measured year-on-year changes are from Mauna Loa. Average SST’s are from GISS. CO2 emissions, expressed as PPM potential increase in CO2 in the atmosphere, are based on worldwide carbon emissions (according to CDIAC at Oak Ridge) converted to an equivalent weight of CO2, divided by an assumed atmosphere weight of 5.3 X 10^9 million tons. This result was scaled by a constant factor of 0.7232, which is 28.96/44 = 0.6582 (to convert weight fraction CO2 to volume fraction), multiplied by 1.099 to match up with the range of CO2 emissions that Dr. Spencer used in his May 11 blog post. Note that nobody really knows the total carbon emissions, so different sources offer different estimates of total emissions. The final two years of CO2 emissions I had to estimate beacause the CDIAC data ended in 2006. I assumed an equilibrium ocean CO2 level of 285 PPM. I optimized K1 and K2 by hand so that the model had a reasonable fit with the data; the values were 0.0215 for K1 and 5.0 for K2. So the model equation is:
Annual change = (Annual emissions) – 0.0215 * (CO2 – 285) + 5.0 * (delta SST)
The graph titled “Annual Increase in CO2” compares the measured and calculated year-on-year changes along with the potential increase from fossil fuels.
The graph titled “Correlation: Model Increase vs. Mauna Loa Increase” shows that the model does a decent job of capturing the year-on-year temperature driven change in atmospheric CO2.
I suspect that if the model used monthly data and the 6-month lag between SST changes and CO2 changes that Dr. Spencer used, then the model fit would be better.
The graph titled “Measured CO2 versus Ocean Uptake Model” shows the final result of the calculation.
The evolution of CO2 in the atmosphere calculated by the model between 1958 and 2008 is reasonably close to the Mauna Loa record. The model suggests that about 2.15 PPM equivalent of emitted CO2 is currently being absorbed, or about half the total emissions.
My only objective is to show that the CO2 released by human activities, combined with slow ocean absorption/neutralization and sea surface temperature variation, is broadly consistent with the measured historical trend in atmospheric CO2, including the effect of changing average SST on short term variation in the rate of CO2 increase. Temperature changes in ocean surface waters cause shifts of a few PPM up and down in the rate of increase, but surface temperature changes do not explain 80% to 90% of the increase in atmospheric CO2 since 1958, as suggested in Dr. Spencer’s May 11 post. Because of its relatively high pH, high buffering capacity, enormous mass, and slow circulation, the ocean is, and will be for a very long time, a significant net sink for atmospheric CO2.
With a bit of luck, continuing flat-to-falling average surface temperatures and ocean heat content will discredit the model predictions before too much economic damage is done.
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As I suggested after the Dr. Spencer post, I think there is real potential to understand the solubility pump a lot better if we disaggregate the net absorption term into a term for absorption in the cold oceans and outgassing in the tropical oceans. Averaging global SST adds a lot of noise, because solubility of gases in water are exponential, following the vapor pressure. Warming the the surface of the tropics from 28 to 29C will release only a third as much CO2 as raising the northern ocean temps from 0 to 1C.
How would I determine the SST anomalies for specific latitude bands? I would start with a roughly equal area split, neglecting the polar caps, so about 35S to 35N.
JamesG (05:18:37) :
You are just sniping about all we don’t know about ocean circulation. There is nothing unphyscial about the tropics outgassing more CO2 due to temperature (but slightly less due to higher atmospheric CO2) while the cold ocean waters absorb about the same as before due to the offsetting effect of slightly higher temps with slightly higher CO2. In fact, simple vapor pressure effects from the recent .5C anomally would increase outgassing from 90GT to 94GT and depress absorption from 92GT to 88GT. In the short term, the 40% increase in atmospheric CO2 would increase absorption by 40% and decrease outgassing by 30%. Clearly, the scale of the ocean “breathing” overwhelms the anthropogenic additions and it is only because the upper ocean is saturated that half the CO2 is still waiting to be pumped down the sink.
The sharp changes in CO2 at northern latitudes looks like a change in the wind pattern, which would change the source and “history” of that air cell. Can anyone comment on the typical seasonal wind patterns of those locations?
The simplification that the ocean circulation is a conveyor and water going down the conveyor all over the high latitudes moves in lockstep and pops up exactly 800 years later is very misleading. The flow is wildly turbulent and there are certainly flows that take longer and shorter. But I think this is a useful number to keep in mind as an average residence time. It would indicate that we have about 800 years before we would see a significant step up in the outgassing from our current anthropogenic emissions.
If I may interject a completely unscientific observation:
The CO2 graphs produced at Mauna Loa Et Al. have always looked a little too “sweet” for me. I work with data every day, and you just don’t see anything that smooth and regular unless something has been done to the data to average or smooth it and remove outliers.
I’m not claiming malfeasance. I just don’t see any indication of volcanic eruptions, Mid 70’s US gas crisis, introduction of catalytic converters, $4 gas, etc. Nothing.
That says to me that all of the things listed above are completely swamped out by whatever is really causing the increase.
Someone please enlighten this little pea sized brain.
Joseph (08:08:07) :
Steve wrote:
[An increase in average ocean surface temperature will cause more CO2 to be emitted from surface water…]
‘Steve, this basis for your argument is flawed because the relationship describing the solubility of CO2 in water versus temperature is exponential, not linear.’
There’s a bit more going on than just dissolution of CO2 in water. The ocean is heavily buffered by dissolved carbonate and bicarbonate ions, which is evident in a typical pH of ~8.1 for the ocean. A solution of CO2 in water at the concentration which is in equilibrium with the atmosphere (like rain water) has a pH of ~5.6. When more CO2 dissolves in ocean water, some of it combines with water to form hydrogen ions and bicarbonate ions. The hydrogen ions react with carbonate ions to form more bicarbonate. By this ‘neutralization’ reaction, CO2 gas is chemically absorbed, and is not longer just ‘in solution’. The overall concentration of inorganic carbon in seawater (some dissolved CO2, but mostly as bicarbonate and carbonate ions) is many times higher than the equilibrium concentration of dissolved CO2 that would be present in un-buffered water. Of course the equilibrium between dissolved CO2, bicarbonate ion, and carbonate ion is in fact temperature sensitive (which is why the ocean carbon cycle includes temperature driven absorption and desorption), but not as nearly as temperature sensitive as the straight dissolution of CO2 in water.
Joseph (08:08:07) :
‘A better way to approach this would be to use gridded SST data to calculate the solubility change for those specific temperatures in each grid cell over time, and then averaged globally, and compare that to atmospheric CO2. That would be interesting.’
A lot of this sort of thing has already been done, starting with Keeling in the late 1950’s (yes, the Keeling who started collecting Manua Loa CO2 data, and discovered the annual oscillation on atmospheric CO2). Keeling (and others) cruised around the world collecting and measuring the equilibrium CO2 level in ocean water. They measured the concentration of CO2 in air that would be in equilibrium with the water the ship was passing through, as well as the concentration of CO2 in the air surrounding the ship at the same time, or in other words, they measured if the ocean was absorbing or desorbing CO2. They found that the air and the ocean are often far from equilibrium; at low latitudes the ocean is more likely to be adding CO2 to the atmosphere, while at high latitudes the ocean was mostly absorbing CO2.
Dave Middleton (07:34:58) :
The pre-industrial CO2 concentration could certainly have been be a bit higher than 285PPM, I used 285 because it seems to be the most commonly accepted value.
I am no expert in the response of plant stomata to changing CO2, but my guess is that there may be some uncertainty in stomata generated CO2 concentrations. However, since the ‘age’ of the deep ocean water that is currently upwelling is likely in the range of ~1000 years, I do not see that inferred CO2 concentrations from >2000 years ago are important. Do the stomata data suggest CO2 concentration much above 285 PPM during the last 1000 or 2000 years?
Bill et al.
If you are going to explore the phase difference from temperature to CO2, recommend exploring the impact of earth’s short term (4 month) vs long term (~ 8-12 year) effective heat capacities.
See:
Nicola Scafetta, “Comment on “Heat capacity, time constant, and sensitivity of Earth’s climate system’ by Schwartz.” In press on J. Geophys. Res. (2008).
Correction – that’s about 5 months for the short term heat capacity.
superDBA (08:49:21) :
‘Someone please enlighten this little pea sized brain.’
Unlikely that people who read this blog have a pea size brain..
The overall flux in CO2 between ocean and atmosphere is very large compared to human emissions, so it is not so easy to see the (rather smaller) changes in human emissions. You can see variations in the Mauna Loa trend more clearly by looking at the trend with the seasonal signal removed (as best they can). There you can see some obvious effects, like an early 1990’s volcanic eruption and the strong 1998 El Nino. I have never heard anyone suggest that the Mauna Loa record has been fudged; after all, Keeling started in 1958, long before “global warming”, and during a period of slowly falling temperatures.
Considering a change of temperature equal in the three systems, air, oceans and clay soil, the heat capacity of air is insignificant when it’s compared against heat capacity of oceans and dry clay ground:
Air ρC = 1,200 J/m^3 K
Oceans ρC = 4,190,000 J/m^3 K
Dry Clay Ground ρC = 1,420,000 J/m^3 K
Specific Heat Capacity is not the same as Heat Capacity.
layne Blanchard (06:02:17) :
‘Steve,
Some things about this model seem counter intuitive to me. If I understand you correctly, (emissions) are anthropogenic emissions only? If yes,
1. Why would annual emissions be limited to anthropogenic emissions?
Then,
2. How could K1 not vary by temperature?
3. What data supports the assumption of 285 ppm as a point of equilibrium in this absorption?
4. If no one really knows the actual total emissions (and here I mean anthropogenic as well as natural), how can we determine anything?’
1. I assumed that at equilibrium (in the absence of human emissions) there would be equal (and very large) emissions and absorption from natural sources. The much smaller human emissions are assumed to be adding to the concentration of CO2 in excess of the natural background.
2. By separating the temperature effect (K2) from the concentration driven effect (K1) I am implicitly saying that the changes in absorption/desorption due to temperature changes can be treated as a linear temperature effect that is superimposed on the background of “normal” ocean absorption and desorption. This would be far from correct if there were big differences in average SST, but we are only talking about a small (0.36C) change over 50 years in average SST, so the approximation should not be too bad.
3. The 285 number is a widely accepted value for pre-industrial CO2, and is supported by ice core data from Greenland and Antartica. Could it have been a little higher or lower in 1850? Sure, but I don’t know of any other good values.
4. I should have said that nobody knows the *exact* emissions. People make reasonable estimates based on coal production records, oil production records, natural gas production records, forest clearing, and production estimates for Portland cement. Different estimates vary a bit, but all agree approximately.
Steve Fitzpatrick (08:20:21) :
“The test of any model (my very simple model or complex climate models) is how well they predict the future, not how well they predict the past, since hind-casts can always be optimized by ‘curve-fitting’. My great frustration with climate modelers is how they ALWAYS argue that we can never have a legitimate test of the model, saying something like: “It would take 100 years, and by then it will be too late, since the ocean will have flooded New York and Washington!”. This kind of non-sense from the modelers ought to bring loud laughter all around, not new laws limiting carbon releases.”
That is sort of the point that I am trying to make – since the models can’t be falsified (in any meaningful way short of wait and see), they should be developed independantly of the data or they are simply a case of curve-fitting.
As I mentioned, you simply wouldn’t get this published in an economics journal. My wife tried by randomly selecting half of her data to build the model and using the other half to test it (quite clever I thought, but I am biased) and it was still turned down.
Not sure quite what the answer is, but what depresses me the most is the way that I feel we are losing the whole scientific process of theory and refutation. I’m not too worried about AGW alarmism anymore (although that is thanks to the recession not enlightenment), but the use of “science” for political ends and the concommittent use of legal approaches (selection of evidence and manipulation of significance) is a trend I can’t see being reversed.
Wow, that sounds really depressing – time for a beer!
For example, if ∆T = 0.8°C in each system, the heat stored (Qsto) is:
Air = 956.16 J
Oceans = 3.352 x 10^6 J
Dry Clay Ground = 1.136 x 10^6 J
I don’t know how is it that some people thinks that air transfers energy to the surface if the surface always is in a higher energy density state than the air.
I find this stuff fascinating. I have often pondered that ocean’s absorption rate coupled with the potential absorption in the huge expanses of Canadian and Soviet forests, would completely dominate any output by man. Has anyone ever calculated the enormous capability of a large forest for Co2 uptake? Not just current intake, but potential intake. A large thank you to Steve Fitzpatrick. It is obvious that he enjoys his work. What could be better than that?
Steve Fitzpatrick (08:20:21) :
But please note that I was not trying to make a perfect prediction, I was only trying to point out that a temperature-only driven increase in atmospheric CO2 (as proposed by Dr. Spencer on May 11) is not at all consistent with the 1958 to 2008 record, while a rather simple model (where CO2 emissions and concentration dependent uptake are primarily responsible) is more consistent with the record, and also explains just as well the temperature driven variation in CO2 increase that Dr. Spencer noted.
Spencer’s model is hampered by his initial assumption that the ocean was outgassing for the duration of the record, that necessarily meant a low coefficient for the retention of anthropological CO2. The more reasonable model that Steve used which allows variable absorption to modulate the retention of anthropological CO2 gives a better fit.
On this annual-average CO2-temp graph, it looks like there is a close relationship between temperature and, after a delay, CO2.
http://www.woodfortrees.org/plot/esrl-co2/isolate:60/mean:12/scale:0.2/plot/hadcrut3vgl/isolate:60/mean:12/from:1958
The mean of the CO2 causes the seasonal variation to not be visible, but if you remove the mean it’s harder to see the pattern, although it is visible in the peaks.
http://www.woodfortrees.org/plot/esrl-co2/isolate:60/scale:0.2/plot/hadcrut3vgl/isolate:60/mean:12/from:1958
Not surprisingly, using the prime number 11 for the mean pulls the calculation out of sync with the annual cycle and the variations become more apparent, although the two curves still resemble each other.
http://www.woodfortrees.org/plot/esrl-co2/isolate:55/scale:0.2/mean:11/plot/hadcrut3vgl/isolate:55/from:1958/mean:11
On this annual-average CO2-temp graph, it looks like there is a close relationship between temperature and, after a delay, CO2.
http://www.woodfortrees.org/plot/esrl-co2/isolate:60/mean:12/scale:0.2/plot/hadcrut3vgl/isolate:60/mean:12/from:1958
The mean of the CO2 causes the seasonal variation to not be visible, but if you remove the mean it’s harder to see the pattern, although it is visible in the peaks.
http://www.woodfortrees.org/plot/esrl-co2/isolate:60/scale:0.2/plot/hadcrut3vgl/isolate:60/mean:12/from:1958
Not surprisingly, using the prime number 11 for the mean pulls the calculation out of sync with the annual cycle and the variations become more apparent, although the two curves still resemble each other.
Well the last graph of measured CO2 versus the here constructed model, is a whole lot better fit than the curves that Dr Spencer had in his recent essay of another simple model.
But then Steve forced that fit, with the choice of his K1 and K2 parameters; so is it really a model or is it just a curve fitting exercise ?
If it is a real model, the values of K1 and K2 would need to be justified by some physical or chemical rationale based on the processes going on.
Scientists have sadly discovered to their great embarrasment; that you can fit a model to actual physical data measurement to any level of accuracy you want; simply by ****ing around with numbers.
Most Physicists (maybe I should say many) are familiar with the great “Fine Structure Constant debacle” involving Sir Arthur Eddington; who “proved” in a paper, that the value of alpha, the fine structure constant was indeed exactly 1/136; the best experimental measurments being close to that number. Sadly, the experimentalists slowly moved alpha closer to 1/137; whereupon Eddington wrote another paper in which he “proved” that indeed alpha was exactly 1/137 (I am sure Anna V is familiar with this story).
Well that got the community riled up at the good professor who was then dubbed Professor “Adding one”. Well that was just the first fine structure constant caper.
In the 1960s somebody wrote a paper in which he proved that the inverse of the fine structure constant was in fact the fourth root of a product of pi to some small integer power times several other small integers to small integer powers; something like :-
1/alpha = (pi^a *b^c*d^e*f^g*h^i)^0.25
Now alpha^-1 currently has the value 137.0359895 with an error of 0.045 ppm.
The expression above, where (a) through (i) are all small integers (<20) agreed with this value to better than 2/3 of the standard deviation of the best then available experimental result.
So clearly the model had to be correct; because you couldn't get that close by just ****ing around with numbers; so everybody embraced this wonderful paper; even though nowhere in the paper was there any informational input from the physical universe. No measured or observed quantity went into the derivation of this formula; it was purely mathematical; yet it purported to to compute one of the most fundamntal constants of Atomic Physics. Man what a pickle to be in. About a month later a computer geek had programmed his computer to seek all such values for a-i, and find any that gave an answer within the standard deviation of the experimental value of alpha^-1. He came up with a list of about eight such numbers, one of which was within about 20-25% of the standard deviation; proving that indeed you can hit a number to better than one part in 10^8 by simply ****ing around with numbers. Subsequently a geometer offered a theory of a multidimensional spherical shell in a lattice of points defined by the above expression, and grid points in the lattice that fell within the shell, were solutions to the fitting problem; the radii of the multidimensional shell being alph+/- one standard deviation. Thus he located all of the possible values of the function that fit the criterion.
Well if you bought into this farce, even though no-one could find a link to the universe; you ended up with an egg on the face problem. This whole mess took place in Applied Optics or some similar publication as I recall.
So fitting data to a "model" is a snap. Fitting the model to the reality of the universe is another matter.
So be careful what you buy into.
George
RobP (06:48:14) :
“Devloping a model which shows great correlation to poorly understood data just shows your skill in model tuning and reveals no underlying scientific causation.” and later
“Come back in, say, 10 years and see if your predicted values still match observations.”
We don’t need to wait for 10 years, because we can use different time periods for calibrating the model and using it for predictions. Let’s take for example years 1959-1979 to calibrate K1 and K2 and then observe its behavior in 1980-2009. Using several time periods to avoid cherry picking the data, gives more confidence on the findings.
This controversial issue was never a scientifical issue but a political one, so it does not matter if CO2 increases or decreases, THEY will tell the mobs that IT IS THE CAUSE OF CLIMATE CHANGE (it is not longer of “global warming” because of evident reasons), so it does not matter how profound are the arguments against it, they have the money, they have the power, they are the ones in control…and, for sure,…one day they will knock at our doors…
“Do the stomata data suggest CO2 concentration much above 285 PPM during the last 1000 or 2000 years?”
Yes they do…
Warm periods in A.D. 1000, 1300 and 1700 had CO2 levels between 300-320ppm. So the “equilibrium” value for the post-Little Ice Age should be 300-320 ppm…If the SI data are more accurate than the ice core data.
David Ball
Don’t tell anyone else or my sceptic credentials will be ruined, but some years ago I ‘bought’ some amazon rain forest in order to prevent it being logged, with all that entails (there are arguements both ways).
A little later I was able to confound someone with impeccable green credentials (i.e highly sanctimonious)who was highly impressed (briefly) with me, because he thought my reason for this action was do my bit for reducing co2.
Positively aglow with new found fervour I checled out my contribution to this great AGW cause and found, as in so many things in this settled science, that things weren’t as clear cut as they first seemed however.
See this article;
http://planetearth.nerc.ac.uk/news/story.aspx?id=351
If you can, try to get hold of the original document from US Science. It seems that the Amazon (and presumably other great forests) may be a source after all. Or perhaps it is a sink. Or…Well you decide.
Tonyb
Ok so it looks like we’ve all made up our minds about climate change.
I can’t seem to find any mention of ocean acidification though, surely thats what we should also be concerned with if we keep pumping co2 out at the current rate?
Steve Fitzpatrick (10:41:45):
layne Blanchard (06:02:17) :
‘Steve,
Some things about this model seem counter intuitive to me. If I understand you correctly, (emissions) are anthropogenic emissions only? If yes,
1. Why would annual emissions be limited to anthropogenic emissions?
Then,
2. How could K1 not vary by temperature?
3. What data supports the assumption of 285 ppm as a point of equilibrium in this absorption?
None data supports 285 ppmV as the point of equilibrium between emission and absorption of CO2. Biochemists say the point of equilibrium is up to 600 ppmV when photosynthesis increases linearly with temperature increases independently of O2 concentration. On the other hand, actually, sand (whether saturated or not) absorbs six times more CO2 than the biosphere.
Oops! I forgot to include references:
http://www.ecostudies.org/press/Schlesinger_Science_13_June_2008.pdf