Carbon Dioxide And The Ocean: Temperature Is Driving CO2, And Not Vice Versa

Carbon Dioxide and the Ocean
By Ed Caryl

In my last post, Figure 1 illustrated how much the annual carbon dioxide flux, the red trace, varied from year to year. Studies (here, here, and here, among others) have been done on the annual carbon flux, but they ignore this variation by using running averages, or by simply ignoring the data during El Niño periods. This seems like an effort to avoid actually learning something.

Figure 1 is a plot of the annual carbon flux into and out of the biosphere.

The shape of the annual carbon increase resembles the shape of the global sea surface temperature (HADSST3), especially after reliable CO2 measurements began by Keeling after March 1958. Several known events are visible. Counting backwards: the 1998 El Niño, the 1994-5 El Niño, Mt Pinatubo in 1991, the 1986-7 El Niño, Mt Ruiz in 1985, El Chichon eruption in 1982, the 1972-3 El Niño, etc. Every positive peak is an El Niño and  every negative peak is associated with a major volcanic eruption.

As can be seen in Figure 1, there is no relationship between the fossil carbon emissions curve and the annual carbon increase curve. That is because all the fossil emissions carbon is taken up by the biosphere or by the oceans according to Henry’s Law, and then sequestered there. The carbon in the atmosphere is controlled by temperature. This has been described by Dr. Murry Salby in this presentations at Sydney and Hamburg. He compares the CO2 curve to the integral of temperature. Here, I am going the other way mathematically, taking the differential of the CO2 curve as temperature and comparing it to known temperature data, the HADSST3 data.

Figure 2 is a plot of the annual carbon increase in the atmosphere (the differential of the Mauna Loa data) and the HADSST3 sea surface temperature anomaly.

The spikes in the SST correspond to the spikes in CO2 increase, and they go in the same direction. As the ocean surface warms, it emits more CO2 (or takes in less). The balance changes with temperature. Why should this be?

Figure 3 is CO2 solubility in water: 0.08g/kg/degree C below 20C. Above 20C the solubility drops by half to about 0.04g/kg/°C.

The ocean surface area is 360 million sq. kilometers, or 360 trillion sq. meters. The top meter is 360 trillion tons of water. A change of temperature of one degree for cold water changes the solubility by:

360 X 1012 tons = 360 X 1015 kg X 0.08 g/kg = 28.8 X 1015 g CO2 or 28.8 Petagrams CO2. A tenth of a degree temperature change changes solubility by 2.88 Petagrams CO2. This is about 780 Gigatons carbon equivalent. (3.7 grams CO2 = 1 gram carbon.)

The tropical oceans are well above 20°C so the solubility there will be roughly half the above figure. The plots in figure 3 indicate about 1 Gigaton carbon change from a tenth of a degree temperature change. A scatter plot trend line will give us a more exact figure.

Figure 4a is a scatter plot of SST versus annual CO2 change. Figure 4b uses the linear trend formula from 4a to convert SST to the carbon equivalent.

Studies of the CO2 emission and absorption have shown that the tropical seas emit CO2 and the cold, sinking, north Pacific and Atlantic absorb CO2. This has even been mapped. This is all due to the variation in CO2 solubility with temperature.

Figure 5: Source link for the above figure and caption.

The sea surface CO2 partial pressure is always very close to the CO2 partial pressure in the atmosphere above it. The sea surface is always in equilibrium with the atmosphere. This means that as we add CO2 in burning fossil fuels, some is taken up by the land biosphere. The remainder CO2 is dissolved and added to the CO2 reservoir in the surface waters. The mixed layer in the ocean is the top 20 to 200 meters, depending on the amount of wave and current mixing. That mixed layer is about 1/50th of the ocean volume. It contains roughly the same amount of CO2 as the atmosphere, as dissolved inorganic carbon (DIC). The difference, whether the ocean is emitting CO2 or absorbing it, is driven by temperature. As can be seen in the above figures, an El Niño can drive 2 or 3 Gigatons of carbon into the atmosphere and a La Niña can take it right out again. The rise in CO2 is due to rising SST, not fossil fuel burning.

Figure 6 is a plot of figure 4b and the biosphere increase from the previous biosphere article here, subtracted from the annual carbon increase.

The above is a residual. But the curve looks familiar.

Figure 7 is Figure 6 with the average annual AMO index inverted.

Note on the map, figure 5, that the warm tropical seas emit CO2, and the cool northern seas absorb CO2. The AMO index is a temperature index for the North Atlantic. It is derived by subtracting the global SST from 60°N to 60°S from the total SST, or alternatively, the Atlantic temperate and tropical SST from the whole north Atlantic. This means that as the tropical ocean warms more than the average global ocean, this drives the AMO index negative. This shifts the CO2 solubility (figure 2) downward and to the right. That peak in the 1970’s occurs because the tropical oceans were warmer than the average during that period, emitting more CO2. Since that time, the difference has gone the other way, the biosphere is taking up increasing amounts of CO2, lowering the amount of CO2 left in the atmosphere. You can also see a one year lag between AMO and the carbon flux. This is because the AMO lags the tropical Pacific by about a year.

The point of all this is that temperature is driving CO2, not the other way around.

We have good measurements of atmospheric CO2 only since 1958. Before that time our measurements were at the mercy of whatever ice does to captured CO2. We have good global measurements of temperature only from 1979, the beginning of the satellite era. This means that all of our measurement periods are shorter than the natural cycles. We have hints only from surface and ship measurements that go back 120 years, that some of the natural cycles are ~60 years long. We are presently at a convergence and peak of several of those natural cycles. There are suggestions that we are past the peak of some longer solar cycles. I use the words “hints” and “suggestions” because of the large errors, lack of global coverage, and wishful thinking adjustments to these measurements. There are two possibilities. If CO2 drives temperature, then temperatures should continue to climb. If it doesn’t, then temperatures will fall, then, shortly, CO2 will fall also. Nature is in the process of demonstrating which is which. We can just watch.

32 responses to “Carbon Dioxide And The Ocean: Temperature Is Driving CO2, And Not Vice Versa”

1. When you’re looking back into past, you may see a time lag of 800 years between the temperature rise and CO2 concentration rise. This refers to the following diagram:
http://www.egbeck.de/treibhaus/CO2-Dateien/petit.gif
Is is possible that we’re currently seeing a change of CO2 concentration which is a result of previous medieval warming phase?

1. I don’t think so. The overturning cycles all seem to be in the range of 20 to 200 years.

2. Ed Caryl, Dr. Salby makes it quite clear in his presentation that man-made CO2 emissions (he never called them carbon flux) comprise only four percent of the total annual global CO2 emissions. Moreover, his discussion of the impact of trends of atmospheric CO2 includes all of atmospheric CO2, not just the small, man-made portion of it.

Interestingly, and quite different from your approach to addressing atmospheric CO2, Dr. Salby specifically illustrates the correlation of global temperatures and atmospheric CO2, while especially focusing on the *signature* of the tiny portion of atmospheric CO2 that is man-made.

On the other hand, your treatment of CO2 emissions persists in mislabling them “carbon flux” and in ignoring the 96 percent of global CO2 emissions that are not man-made but come from natural sources.

1. On the contrary, all the CO2 flux described above is natural. It is CO2 emitted from the ocean due to rising SST.

2. If you have a problem with the scales in GTons carbon, multiply by 3.7 to include the Oxygen.

3. May I respectfully disagree with the reasoning used here (and by Dr. Salby)?

There are several points which make it clear that the oceans are not the cause of the current increase, but that humans are.

That is because all the fossil emissions carbon is taken up by the biosphere or by the oceans according to Henry’s Law

According to Henry’s law, an increase of 1 K in temperature gives some 16 microatm increase of pCO2 in seawater. That increases the emissions of CO2 from the upwelling zones around the (Pacific) equator and decreases the uptake of CO2 at the cold polar waters. The net effect is an increase of CO2 in the atmosphere, which counters the disturbance (Le Châteliers Principle): with an increase of ~16 ppmv in the atmosphere, the in- and outgoing fluxes are restored to what they were before the temperature increase:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/upwelling_temp.jpg
Thus temperature can’t be the source of the 100+ ppmv (70+ since 1960) increase in the atmosphere.

The whole biosphere is a net sink for CO2 at a rate of ~1 GtC/yr.
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
Humans add 9 GtC/yr and the increase is ~4 GtC/yr in the atmosphere. That means that ~4 GtC/yr must be absorbed somewhere in nature, probably the (deep) oceans. Thus the oceans are a net sink for CO2, not a source. See the complete chart:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em2.jpg
Thus the variability you see in the atmospheric increase, is the (mainly temperature caused) change in sink capacity, not source capacity…
That is confirmed by a lot of pCO2 measurements over the oceans:
http://www.pmel.noaa.gov/pubs/outstand/feel2331/exchange.shtml
currently not available due to the government shutdown in the US…
But the average pressure difference air-oceans is 7 microatm, thus from atmosphere to oceans, not reverse.

Further, have a look at between dT and Tanom in WoodForTrees.
Both dT and Tanomaly give a perfect match with dCO2, but the dT gives zero contribution to the slope (even slightly negative), while the human emissions give about twice the slope seen in dCO2 (human emissions are not in the WFT database). Tanomaly seemingly gives the same slope, but that is completely spurious, as one need an arbitrary offset and slope to match both. Further, there is no know natural process that emits non-linear increasing amounts of CO2/year, based on a sustained temperature difference…

4. Nice work Ed. I did a similar analysis looking specifically at the 1998 El Nino. The dCO2dt chart matched up very well with the peak in 1998, and the slope was 0.69ppmCO2/mo/°C or 8.31ppmCO2/yr/°C (huge indeed).

The other interesting feature was that the response is instantaneous. dCO2 reacted immediately to the temperature increase.

http://naturalclimate.home.comcast.net/~naturalclimate/CO2_growth_vs_Temp.pdf

http://naturalclimate.home.comcast.net/~naturalclimate/dCO2Slope.pdf

This used MSUGlobe. I think I also have one for HADSST3

Deseasonalizing monthly CO2 to take the derivative is an interesting exercise isn’t it?

5. I don’t think that anybody denies that short term temperature swings are the cause of the dCO2 swings as seen in the atmosphere. Pieter Tans of NOAA showed that temperature and precipitation are the main drivers:
http://esrl.noaa.gov/gmd/co2conference/pdfs/tans.pdf from halve the sheets on.

Where several skeptics go wrong is that they attribute the longer term increase to temperature. But that is impossible: any increase of temperature gives not more than 16 ppmv/K increase in the atmosphere, according to Henry’s Law. But we are at 100+ ppmv above equilibrium, thus the flux is from the atmosphere into the oceans, not reverse. That is also the case for dCO2: the variability is a variability in sink rate, not in source rate, mainly for the (deep) oceans:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em2.jpg

CO2 levels follow T, dCO2 follows dT both with some lag. That makes that dCO2 and Tanomaly are exact in timing, but that has not the slightest physical meaning. Thus integrating Tanomaly, as Salby (and Bart) does, based on an arbitrary offset and slope has no equivalent in any physical process.
To the contrary: dCO2(emissions) has twice the slope of dCO2(atm), while dT has zero slope, simply because T is quite linearly increasing, while CO2 levels are slightly quadratic increasing:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_co2_acc_1960_cur.jpg

Conclusion: the year by year variability in CO2 increase rate is entirely caused by natural variability (temperature and precipitation), while most of the increase is from human emissions…

6. 10.000 year old leaves show stomata indicating over 400 ppm CO2 in Sweden:
http://www.sciencedirect.com/science/article/pii/S0277379113000553

7. Ice core data from both Antarctica and Greenland have clearly shown that over the long term temperature and carbon dioxide levels are related. The temperature variations are clearly caused by the Milankovitch Cycle, and there is a significant delay in the response of carbon dioxide.

The major ocean currents take years to run their course with colder water sinking and warmer water rising, thereby explaining the delay in response of the carbon dioxide levels.

In view of the fact that, notwithstanding all of the fear mongering about carbon dioxide, the earth is now colder than it was 1,000 years ago, and 1,000 years ago it was colder than some 6,000 years ago, I see no reason to be concerned about either current or projected carbon dioxide levels. The multi-thousand year long term downward trend in temperature, confirmed by numerous studies, speaks to the real problem.

8. The mixed layer is at equilibrium with the atmosphere. The time from a change in partial pressure in the atmosphere to a equilibrium in the ocean is 5 to 10 years.
This means that the partial pressure difference can never be more than 10 or so ppmv. There can’t be any rate change in dT/dCO2. That would be visible in the scatter plot. There is no indication in the d(atmospheric CO2) of d(emissions CO2).
https://notrickszone.com/2013/03/02/most-of-the-rise-in-co2-likely-comes-from-natural-sources/

9. I have thought for many years that the reason cold produces less CO2 and heat produces more is simply because that is what the biosphere wants. When it gets cold, plant life contracts and the CO2 is not needed. When it gets warm, just the opposite.

10. Ed, sorry for the duplicating message, did take a few days before the first message was published…

The mixed layer indeed is in rapid equilibrium with the atmosphere, but that is for the average. In reality there are huge differences between the equatorial upwelling places (~700 microatm), atmosphere (~400 microatm) and polar downwelling places (~250 microatm). That gives a continuous flow of CO2 from the equator to the poles via the atmosphere, which returns via THC and the deep ocean waters from the NE Atlantic to the Pacific Equator after ~1000 years.

That pCO2 differences could be seen in the Feely e.a. link at NOAA, but they still are off-line. But have a look at your figure 5: the in- or outflux is directly proportional to the pCO2 difference between ocean waters and air…

There can’t be any rate change in dT/dCO2

Sorry, but that isn’t true: if CO2 levels follow T, then dCO2 follows dT, the only difference is that the trend is removed: because T is increasing rather linear, dT is flat, but the fast changes are all retained.
CO2 emissions increased somewhat quadratic over time (~3-fold since 1960), which gives a linear increasing slope in dCO2. Here the direct increase:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/base_co2_temp_1960-cur.jpg
and here the derivatives + what T anomaly gives:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/base_dco2_Tanom_1960-cur.jpg

As you can see, the slope in dCO2 can be explained entirely from human emissions, while the variability around the slope can be entirely explained by the variability in temperature.

The problem you have is that the short term variability of dCO2 doesn’t say anything about the cause of the longer term slope of dCO2, because two independent processes are at work…

11. Ben:

10.000 year old leaves show stomata indicating over 400 ppm CO2 in Sweden

While stomata index data have a much better resolution than ice cores, they have their problems too. The number of stomata is reversaly proportional to the CO2 levels in the previous growing season, but that are local/regional CO2 levels. Ice cores have a reasonable good (less than a decade for Law Dome) to a very long resolution (560 years for Dome C), depending of snow accumulation speed. But they represent global CO2 levels (assymetric) averaged over the resolution period.

Over land, where the stomata index is measured, one always has a local/regional bias above the CO2 levels measured in the bulk of the atmosphere. Therefore the stomata data must be calibrated against current CO2 levels, firn and/or ice cores over the past.
The main problem is that nobody knows how much the local/regional bias changed over previous centuries because of land use changes in the main wind direction and even the main wind direction may have changed over different periods like between an ice age and melting ice sheets and the Younger Dryas…

Thus while the stomata data certainly have a much better resolution, one should take the absolute CO2 values with a grain of salt…

12. Peter Wells

“Ice core data from both Antarctica and Greenland have clearly shown that over the long term temperature and carbon dioxide levels are related.”

Indeed and the ratio is rather constant at ~8 ppmv/K over the full 420 kyear of Vostok, recently confirmed by the 800 kyear record from the Dome C ice core…
The same ~8 ppmv/K drop in CO2 can be seen in the Law Dome ice core with a lag of ~50 years after the temperature drop (~0.8 K) between the MWP and LIA:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_1000yr.jpg

The global CO2 variability over the seasons is ~5 ppmv/K (mainly from NH vegetation) and the interannual variability is also 4-5 ppmv/K.

Thus if somebody now wants to prove that the current 70+ increase since 1960 is all natural, I am interested to know where the over 100 ppmv/K CO2 is coming from.

Henry probably will return from his grave to shout out that his law doesn’t give that kind of ocean releases…

13. […] NO TRICKS ZONE Carbon Dioxide And The Ocean: Temperature Is Driving CO2, And Not Vice Versa By P Gosselin on 8. Oktober 2013 Carbon Dioxide and the Ocean By Ed Caryl https://notrickszone.com/2013/10/08/carbon-dioxide-and-the-ocean-temperature-is-driving-co2-and-not-v&#8230; […]

14. Ferdinand Engelbeen @ Oktober 2013 at 21:01
“Thus if somebody now wants to prove that the current 70+ increase since 1960 is all natural, I am interested to know where the over 100 ppmv/K CO2 is coming from. “

You have the wrong units. The sensitivity is in ppmv per unit of time per deg of temperature. Integrated over many years, a small sensitivity results in a large change. For more discussion, see here.

15. Bart,

We have discussed that already several times, but for the readers here not familiar with the discussion the main points of disagreement:

– the historical record over hundreds to hundred thousands of years and the current variability (seasonal to a few years) show a direct relationship between temperature changes and lagged CO2 level changes. That is transient for short term at about 4-5 ppmv/K up to 8 ppmv/K for time frames of ten thousand years of a sustained temperature increase during an interglacial.

– the most recent record over the past 50 years shows an increase of 70 ppmv (Mauna Loa, South Pole,…) with a temperature increase of ~0.5 K.

– the temperature record and the CO2 variability around this 70 ppmv increase are tightly linked in the rate of change records. But that can be interpretated as either a lagged reaction of dCO2 after dT (CO2 levels lag T at all times) with a slope which is caused by human emissions or as a synchronized reaction of dCO2 on T anomaly. See the graph of both at WFT.

T anomaly is what Ed Caryl, Bart en Salby use as argument. In that case, a sustained difference in temperature above a baseline will give a sustained increase of CO2. In the past 50 years that would be average near 3 ppmv/year/K if Bart is right.

But that means that you need a different offset and slope (and thus a different reaction of CO2 changes on temperature changes) for different time frames. During the melting of ice sheets from a glacial to an interglacial period, the increase is ~80 ppmv and ~10 K over a period of 5000 years, or 0.0016 ppmv/year/K. During the long glacial and interglacial periods, it is virtually zero, etc… And you have to change the offset too, or one would have very low CO2 levels during the Little Ice Age (and zero CO2 during glacials) with the 1960-2010 baseline…

Moreover, such a sustained increase of CO2 can’t be caused by the current temperature record: dCO2 increased a 1.5-fold over the past 50 years (human emissions increased a 3-fold), while dT is completely flat. Thus there is no direct contribution of dT to the slope of dCO2 (and maximum 8 ppmv extra CO2 from the rise in T according to Henry’s law).
The only possibility is an enormous upwelling from the deep oceans which also increased a 3-fold over exactly the same time frame as human emissions.

But that violates so many observations that it easily can be discarded as non-existent.

16. “- the historical record over hundreds to hundred thousands of years and the current variability (seasonal to a few years) show a direct relationship between temperature changes and lagged CO2 level changes.

They don’t match at all. They are 90 degrees out of phase. It is not mathematically possible to have that relationship and not have an integral involved.

“That is transient for short term at about 4-5 ppmv/K up to 8 ppmv/K for time frames of ten thousand years of a sustained temperature increase during an interglacial.”

This is mere assertion. There is no possibility that a natural system exists which high pass filters the temperature effect on CO2, and low pass filters the anthropogenic input, and blends the two together with no phase distortion at the crossover frequency. Salby has explained the historical record based on the spatial distribution of CO2 migration through the ice cores.

“But that can be interpretated as either a lagged reaction of dCO2 after dT (CO2 levels lag T at all times) with a slope which is caused by human emissions or as a synchronized reaction of dCO2 on T anomaly.

Not possible. The “lag” is precisely 90 deg of phase. See above.

“But that means that you need a different offset and slope (and thus a different reaction of CO2 changes on temperature changes) for different time frames.”

A) Even if you did, so what? Why should there be any presumption that the response is uniform over time?

B) Salby showed that this is not necessary, and that the ice core data can be explained as above.

“Moreover, such a sustained increase of CO2 can’t be caused by the current temperature record: dCO2 increased a 1.5-fold over the past 50 years (human emissions increased a 3-fold), while dT is completely flat.”

dCO2/dt = k*(Teq – T)

that’s the equation. It holds perfectly, or as near perfectly as you can expect with noisy observational data. Even today, it tracks the lull in temperatures of the last decade+ perfectly, while anthropogenic emissions and atmospheric concentration have been diverging.

“But that violates so many observations that it easily can be discarded as non-existent.”

It violates no observations at all. It violates your interpretation of observations only.

17. Should have said

dCO2/dt = k*(T – Teq)

Either one works, with a sign flip in k. But, this equation holds for k positive.

18. Bart,

Of course there is a lag between temperature changes and CO2 changes. That is measured on all time scales (except the last 160 years). For a glacial-interglacial transition about 800 +/- 600 years. For the opposite transition several thousand years. For the MWP-LIA transition ~50 years. For the seasons +/- 3 months, for the interannual temperature changes ~6 months.
Thus if CO2 lags T, then dCO2 lags dT. That is how the natural processes work.

Your “perfect” match of T anomaly and dCO2 changes is simply because of the shift of dCO2 vs. CO2, thus because you compare variables of a different order.

Moreover the match is not that perfect if you look at the trends of dCO2 and Tanom: Tanom is a lot steeper with your factor.
To bring the trends to a match, you need a smaller factor and a different offset.
But that gives a problem: the amplitudes are much smaller than reality, while dT simply matches the variability of dCO2, whatever the cause of the slope, which is caused by a different process.

“There is no possibility that a natural system exists which high pass filters the temperature effect on CO2, and low pass filters the anthropogenic input”

Again, you see the CO2 sources/sinks as one process, but there are a lot of processes at work at the same time: fast processes with limited capacity (ocean surface) and medium fast processes with a lot of capacity (deep oceans, vegetation) and very slow processes with near unlimited capacity (carbonate deposits, rock weathering). The fast processes are which show the short term variability, but they can’t cope with human emissions (only ~10%), the medium fast processes are which remove ~50% of human emissions with a decay rate of ~53 years. On longer time scales that is more than sufficient to keep CO2 levels in relative tight bonds around temperature changes.

“Salby has explained the historical record based on the spatial distribution of CO2 migration through the ice cores.”

Sorry, but that is proving one’s theory by assuming that the observations are wrong. There is no measurable migration of CO2 in the coldest (and oldest history) ice cores and hardly any in the less cold coastal ice cores.

To the contrary, if Salby was right, then with each 100 kyr step back in time, the CO2/temperature ratio of ~8 ppmv/K over glacial-interglacial transitions should get lower and lower, flattening the CO2 record to near zero. Moreover, as ice core migration does flatten the differences, it doesn’t change the average, which means that the theoretically much higher CO2 levels during interglacials – according to Salby – must be averaged with below zero CO2 levels during the glacial periods…

“anthropogenic emissions and atmospheric concentration have been diverging”

As I said already a few times before: the sink rate of CO2 is directly correlated to the pressure difference between CO2 in the atmosphere and the equilibrium pressure at the current temperature (around 290 ppmv). Not to the emissions. But WFT has no possibility to combine two variables.

It violates no observations at all. It violates your interpretation of observations only.

Some people with a beautiful theory ignore any observation that doesn’t fit their theory (or are sure that the observations must be wrong)…

19. The link to the real match between T anomaly and dCO2 is here with a smaller factor and a different offset. If it works… A pre-submit test would be wonderful…

20. The plot I showed was qualitative – I only eye-balled the parameters. It isn’t hard to adjust them to produce a better fit of the long term trend. You can argue that the peaks do not match as well, but that is primarily due to processing which goes into the temperature series, as this better agreement with the RSS data set shows.

Here’s is your fundamental problem with such games: a dogmatic insistence on matching the peaks as well as possible always points to an even higher long term sensitivity of CO2 to temperature. Humankind would have to be removing CO2 from the system.

When dealing with uncertain data, you simply have to make allowances for the fact that the measurement data are not perfect. And, you then use Occam’s Razor to determine what is more probable: that an exotic (and by that, I mean, extremely improbable, essentially impossible in Nature as we know it) system response exists whereby the temperature dependence and the human inputs blend just perfectly in such a way as to create our observations? Or, that CO2 is simply mostly due to temperature alone, and human inputs have little effect? The feedback prescription which would render human inputs a minor player is, in fact, not at all exotic or uncommon. The choice is pretty obvious, when you really understand feedback systems.

“Some people with a beautiful theory ignore any observation that doesn’t fit their theory (or are sure that the observations must be wrong)…”

Indeed. That is what you are doing. But, you are ignoring the direct observation of the excellent fit between dCO2/dt and temperature, and relying instead on significantly less reliable proxy measurements which have no means of verification. Moreover, you are relying on a particular interpretation of those proxy measurements which Salby has shown to be unfounded.

21. Bart,

I didn’t have a theory about the increase of CO2 in the atmosphere. I saw that human emissions were about twice the observed increase in the atmosphere and that nature was a net sink for the difference. Further, all known observations did and do agree with humans as cause of the increase.

Now somebody comes with an alternative theory (you are not the first…). No problem with that, but because the prevailing theory is rock solid, one need to show rock solid proof that the alternative theory is better than the prevailing one. And there it completely fails.

From the past in ice cores (ice cores are direct measurements, not proxy’s, be it smoothed) we know that CO2 follows T with a lag and thus that dCO2 lags dT over time frames from 50 years to multi millennia. That is also visible on short term variations: seasons to several years. The ratio is quite modest: from 4-5 ppmv/K to 8 ppmv/K for the shortest to the longest time frames. The related increase/decrease rate of CO2 after T is very low, down to 0.0 ppmv/year/K over very long time frames.

Now you come with the theory that it is not T that influences CO2 levels, but T that influences dCO2. That all is based on the quite nice fit of dCO2 with T anomaly against a baseline and a factor. But that is just curve fitting, without any base in reality.
As said before, one can fit every combination of human and natural causes with such an approach:
95% human, 5% natural (the prevailing theory) where CO2 changes lag T changes (based on realistic data, with a simple sine function over a linear increase of T):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_co2_temp_95.jpg
with its derivatives:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_dco2_dT_Tanom_95.jpg

As you can see, there is a perfect fit of T anomaly with the sine function and the slope of dCO2. From which you deduce that T is the only variable which influences CO2 levels, while 95% was from human emissions and dT has zero contribution to the slope of dCO2.
dT is completely flat and the full slope of dCO2 is from the slightly quadratic curvature of the CO2 increase in the atmosphere (as good as the accumulated human emissions are slightly quadratic and the slope of dCO2(emissions) is twice the slope of dCO2 in the atmosphere).

Thus your “perfect” match with Tanomaly has zero value for predicting what caused the increase in the atmosphere.

BTW, both your WFT plots give a too high CO2 increase when integrated, you need to match the averages too, which means a reduction of the offset, but also a reduction in the factor, which gives you troubles to have the same amplitude in variability…

“what is more probable: that an exotic system response exists whereby the temperature dependence and the human inputs blend just perfectly”

Nothing exotic at work, simply a blend of different natural sources/sinks at work. Some heavily temperature dependent: ocean surface, seasonal vegetation swings, others heavily CO2 pressure (difference) dependent: deep oceans upwelling and downwelling and vegetation growth. The first are fast but limited in capacity which gives you the CO2 rate of change variability, the second are slower but (near) unlimited in capacity. These give you, together with human emissions, the slope in dCO2.

“The choice is pretty obvious, when you really understand feedback systems.”

The choice is pretty obvious if you have a deeper look at the different processes in nature that release and absorb CO2. And I don’t think that you have looked at how the feedback of an increase of CO2 in the atmosphere influences the release and uptake of CO2 out/into the oceans…

Moreover, you are relying on a particular interpretation of those proxy measurements which Salby has shown to be unfounded.

I was specifically thinking of Salby who theorized a huge migration in ice cores which doesn’t exist, only to fit his (and yours) hypothesis. But you aren’t any better in that way:
– any huge increase in circulation from the oceans (a threefold needed) which might give the observed increase in CO2 would reduce the residence time of CO2 in the atmosphere with a threefold. But we observe a slight increase in residence time in the more recent estimates, compared to the older estimates. That means little increase in circulation in an increased mass of CO2 in the atmosphere.
– any huge increase in circulation from the oceans would increase the d13C level of the atmosphere (that are real measurements, not proxy’s), but we see a firm decrease in ratio with human emissions:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_increase_290.jpg
If the deep oceans were the cause of the increase in the atmosphere, these should increase from 40 GtC/yr to 290 GtC/yr to increase the total CO2 circulation a threefold since 1960.
– nothing special to see in the 14CO2 atomic bomb spike decay, no acceleration of the decrease since 1960.
– a few million of measurements over the oceans give a weighted average 7 microatm difference between atmosphere and ocean surface. Thus the average flux of CO2 is into the oceans, not from the oceans.

Is there any observation in the world that fits your theory?

22. “As said before, one can fit every combination of human and natural causes with such an approach:”

You are wrong. There is a precise 90 deg phase shift, which cannot be fit any other way.

“Nothing exotic at work, simply a blend of different natural sources/sinks at work.”

Sorry, no. Your prescription is physically impossible. Anyone who truly understands magnitude and phase relationships in natural systems can see this.

“Thus the average flux of CO2 is into the oceans, not from the oceans.”

Nope.

“Is there any observation in the world that fits your theory?”

23. Bart:

“You are wrong. There is a precise 90 deg phase shift, which cannot be fit any other way.”

Bart, there is a 90 deg phase shift between T changes and CO2 changes in the atmosphere which makes that there is a 90 deg phase shift between dT and dCO2. And which makes that there is zero phase shift between T(anomaly) and dCO2, here simulated with a nice sine function:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_co2_temp_95.jpg
and here the derivatives:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_dco2_dT_Tanom_95.jpg

There is nothing special about the 90 deg phase shift between dT and dCO2 and nothing magical about the zero phase shift between T(anomaly) and dCO2. That is simply the result of comparing variables of a different order.

“Nope.”

“Note, the modelled fluxes in this illustration are from the pre-industrial period”

That was some 0.5 GtC/yr (1.9 in, 2.4 out) net flux from the oceans into the atmosphere in the pre-industrial period. Humans currently emit 9 GtC/yr…

The pre-industrial period was followed by a maximum 16 µatm more CO2 pressure in the ocean surface due to maximum 1 K of temperature increase since the LIA, according to Henry’s law. Meanwhile the CO2 pressure in the atmosphere increased with over 100 µatm, 70 µatm (and 0.5 K temperature increase) since 1960. What do you think has happened to the CO2 fluxes in and out of the oceans?

“The most direct, most modern, most reliable measurements available.”

Curve fitting by comparing variables of a different order, not based on any real world process and wrongly attributing the slope of dCO2 to temperature alone, while dT gives zero slope and dCO2(emissions) gives twice the slope of dCO2…

24. “There is nothing special about the 90 deg phase shift between dT and dCO2 and nothing magical about the zero phase shift between T(anomaly) and dCO2.”

Yes, there is. It means that CO2 is related to the integral of temperature anomaly. And, that means that the temperature relationship accounts for virtually all of the CO2. There is no room for human inputs to make a significant contribution.

‘“Note, the modelled fluxes in this illustration are from the pre-industrial period”’

It shows that the knowledge of the carbon cycle is incomplete, and assumptions about what is going on are merely that: assumptions.

“The pre-industrial period was followed by a maximum 16 µatm more CO2 pressure in the ocean surface due to maximum 1 K of temperature increase since the LIA, according to Henry’s law. “

I have demonstrated that your static analysis is inappropriate. The differential between current temperatures and equilibrium temperatures produces a pumping action into the atmosphere from CO2 rich upwelling waters.

25. Bart,

“Yes, there is. It means that CO2 is related to the integral of temperature anomaly. And, that means that the temperature relationship accounts for virtually all of the CO2. There is no room for human inputs to make a significant contribution.”

Bart, all what the exact match of the phase between dCO2 and T anomaly around the trend shows is that there is a 90 deg. phase shift between T and CO2 variability around the increase in the atmosphere. It has zero predictive value for the origin of the increase itself.

While some (too long) time ago for me, here some math:

– One has two variables influencing the increase of CO2 in the atmosphere: human emissions and temperature, according to the formula:

C(atm) = (a*C^2 + b*C + c) + (m*T + n*sin(T))
where C and T are the anomalies from a zero start point and there is a 90 deg lag between n*sin(T) and the result in C(atm). CO2 emissions show a slighlty quadratic increase over time, while temperature is near linear and the chaotic nature of the variability of T here is reduced to a nice sine function.

Now the derivative of the above:
dC(atm) = a*C + b + T + m*cos(T).
where there is again a 90 deg shift between the variability in dC(atm) and cos(T), but zero shift between sin(T) in the anomaly and dC(atm) in the derivative.
Further, there is zero slope in T and cos(T) only varies around a completely flat T, while the full slope is caused by aC.

For all values of C and T, it is possible to match the slope of the derivative aC with T anomaly:
a*C + b = T + n*cos(T)
which gives:
C = ((T + n*cos(T) – b)/a
Thus it is perfectly possible to attribute the full slope of the derivative and thus the full increase of C in the atmosphere to the T anomaly by multiplying T anomaly with a factor f (= a) and adding an offset g (= b).
No matter if the real contribution is 95% human / 5% temperature or the reverse ratio.

But there is a problem:
If most of the increase in dCO2 is caused by C, then there is little influence on the amplitude of the variability factor cos(T), providing one uses the right factor and offset. But if somebody wrongly attribute the full slope of dCO2 to temperature, then the factor f needed to compensate for the factor a gets smaller dan a, thus reducing the amplitude of the variability. And that is exactly what we see if we match both slopes of T anomaly and dCO2.

Reality is a lot simpler: the slope in dCO2 is (near) fully attributable to the slightly quadratic increase of human emissions and the variability is (near) fully attributable to temperature variability, (near) independent of each other.

“It shows that the knowledge of the carbon cycle is incomplete, and assumptions about what is going on are merely that: assumptions.”

There is a lot of a difference between incomplete knowledge and assuming that nature follows a new theory which violates all known observations…

“I have demonstrated that your static analysis is inappropriate. The differential between current temperatures and equilibrium temperatures produces a pumping action into the atmosphere from CO2 rich upwelling waters.”

Only that you didn’t see that your “dynamic” analysis completely forgot that an equilibrium like CO2 between the oceans and the atmosphere also has sinks and that both sink and source fluxes react on CO2 increases in the atmosphere, no matter if that is caused by temperature, more upwelling or humans…

The dynamic response of the atmosphere of the atmospheric CO2 level to a sudden temperature increase of 1 K:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/upwelling_temp.jpg
The flux rates are between the deep oceans and the atmosphere, estimated on the basis of the observed d13C changes in the atmosphere. Absolute values of the flux rates are of no interest, as these don’t influence the ultimate increase in CO2 level, only the response time.

Here the dynamic response of the atmospheric CO2 level to a sudden 10% increase in concentration of CO2 in the upwelling waters:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/upwelling_incr.jpg

And finally here a combination of the two:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/upwelling_incr_temp.jpg
which shows that increases in upwelling and temperature are simply additional. Thus an increase in upwelling (for which there is no proof, to the contrary) would increase CO2 in the atmosphere, whatever temperature does and even if upwelling was the cause of the increase, then temperature still is not the cause of the slope in dCO2 in current times, thus T anomaly has little to do with the increase of CO2 in the atmosphere.

26. Sorry, but m, not T is in the derivative:

dC(atm) = a*C + b + m + q*cos(T).
Need to update the graphs accordingly with the offset caused by the linear increase in T…

Further:
For all values of C and T, it is possible to match the slope and offset of dCO2 with T anomaly:
a*C + b + m = T + q*cos(T)
(where cos(T) replaces sin(T), for its shift in timing)

which gives:
C = ((T + q*cos(T) – b – m)/a

or C = T/a + q/a*cos(T) – (b + m)/a

Thus one can replace any contribution of the human emissions to dCO2(atm) with T anomaly, no matter if that was 95% or 5% of the contribution… More later…

27. “Bart, all what the exact match of the phase between dCO2 and T anomaly around the trend shows is that there is a 90 deg. phase shift between T and CO2 variability around the increase in the atmosphere.”

Wrong. There is a unique, minimum phase system with 90 deg phase shift across all frequencies. And, that system is an integrator.

“One has two variables influencing…”

This is nothing like the system we are looking at. You don’t even have the derivative of your function right:

C(atm) = (a*C^2 + b*C + c) + (m*T + n*sin(T))

dC(atm)/dt = 2*a*C*dC/dt + b*dC/dt + m*dT/dt + m*(dT/dt)*cos(T)

We’re not looking at a sine of temperature, but of a sine of the product of frequency and time. You are desperate to rationalize all this but, and I want to say this as gently as possible because you are such a nice fellow, but you just don’t have the maths.

“Reality is a lot simpler: the slope in dCO2 is (near) fully attributable to the slightly quadratic increase of human emissions and the variability is (near) fully attributable to temperature variability, (near) independent of each other.”

Not physically possible.

“Only that you didn’t see…both sink and source fluxes react on CO2 increases in the atmosphere, no matter if that is caused by temperature, more upwelling or humans…”

No. I showed it mathematically at the HockeySchtick. Temperature modulates the release from the oceans. They are completely intertwined.

I weary of this exchange. If I fail to answer further, it is because we have gone over everything, and there is nothing more to be said. The emissions and measured atmospheric concentration are diverging from their superficial affine similarity over a few decades of the 20th century. It will soon become undeniable.

“Wrong. There is a unique, minimum phase system with 90 deg phase shift across all frequencies. And, that system is an integrator.”

That is only for the fast frequencies. The trend of CO2 itself has a period of at least 600 years, if the current reduction in rate of change holds. Thus you can’t deduce anything about any phase shift of the CO2 trend based on a period of 50 years…

With such a long period even the worst resolution ice cores (Dome C: 560 years, Vostok: 600 years) would show a similar increase as the one which occurs today…