CO2: Ice Cores vs. Plant Stomata

Guest post by David Middleton

INTRODUCTION

Anyone who has spent any amount of time reviewing climate science literature has probably seen variations of the following chart…

A record of atmospheric CO2 over the last 1,000 years constructed from Antarctic ice cores and the modern instrumental data from the Mauna Loa Observatory suggest that the pre-industrial atmospheric CO2 concentration was a relatively stable ~275ppmv up until the mid 19th Century. Since then, CO2 levels have been climbing rapidly to levels that are often described as unprecedented in the last several hundred thousand to several million years.

Ice core CO2 data are great. Ice cores can yield continuous CO2 records from as far back as 800,000 years ago right on up to the 1970’s. The ice cores also form one of the pillars of Warmista Junk Science: A stable pre-industrial atmospheric CO2 level of ~275 ppmv. The Antarctic ice core-derived CO2 estimates are inconsistent with just about every other method of measuring pre-industrial CO2 levels.

Three common ways to estimate pre-industrial atmospheric CO2 concentrations (before instrumental records began in 1959) are:

1) Measuring CO2 content in air bubbles trapped in ice cores.

2) Measuring the density of stomata in plants.

3) GEOCARB (Berner et al., 1991, 1999, 2004): A geological model for the evolution of atmospheric CO2 over the Phanerozoic Eon. This model is derived from “geological, geochemical, biological, and climatological data.” The main drivers being tectonic activity, organic matter burial and continental rock weathering.

ICE CORES

The advantage of Antarctic ice cores is that they can provide a continuous record of relative CO2 changes going back in time 800,000 years, with a resolution ranging from annual in the shallow section to multi-decadal in the deeper section. Pleistocene-age ice core records seem to indicate a strong correlation between CO2 and temperature; although the delta-CO2 lags behind the delta-T by an average of 800 years…

Ice cores from Greenland are rarely used in CO2 reconstructions.  The maximum usable Greenland record only dates as far back as ~130,000 years ago (Eemian/Sangamonian); the deeper ice has been deformed.  The Greenland ice cores do tend to have a higher resolution than the Antarctic cores because there is a higher snow accumulation rate in Greenland.  Funny thing about the Greenland cores: They show much higher CO2 levels (330-350 ppmv) during Holocene warm periods and Pleistocene interstadials.  The Dye 3 ice core shows an average CO2 level of 331 ppmv (+/-17) during the Preboreal Oscillation (~11,500 years ago).  These higher CO2 levels have been explained away as being the result of in situ chemical reactions (Anklin et al., 1997).

PLANT STOMATA

Stomata are microscopic pores found in leaves and the stem epidermis of plants. They are used for gas exchange. The stomatal density in some C3 plants will vary inversely with the concentration of atmospheric CO2. Stomatal density can be empirically tested and calibrated to CO2 changes over the last 60 years in living plants. The advantage to the stomatal data is that the relationship of the Stomatal Index and atmospheric CO2 can be empirically demonstrated…

Wagner et al., 2004. Reproducibility of Holocene atmospheric CO2 records based on stomatal frequency. Quaternary Science Reviews 23 (2004) 1947–1954.

When stomata-derived CO2 (red) is compared to ice core-derived CO2 (blue), the stomata generally show much more variability in the atmospheric CO2 level and often show levels much higher than the ice cores…

Plant stomata suggest that the pre-industrial CO2 levels were commonly in the 360 to 390ppmv range.

GEOCARB

GEOCARB provides a continuous long-term record of atmospheric CO2 changes; but it is a very low-frequency record…

The lack of a long-term correlation between CO2 and temperature is very apparent when GEOCARB is compared to Veizer’s d18O-derived Phanerozoic temperature reconstruction. As can be seen in the figure above, plant stomata indicate a much greater range of CO2 variability; but are in general agreement with the lower frequency GEOCARB model.

DISCUSSION

Ice cores and GEOCARB provide continuous long-term records; while plant stomata records are discontinuous and limited to fossil stomata that can be accurately aged and calibrated to extant plant taxa. GEOCARB yields a very low frequency record, ice cores have better resolution and stomata can yield very high frequency data. Modern CO2 levels are unspectacular according to GEOCARB, unprecedented according to the ice cores and not anomalous according to plant stomata. So which method provides the most accurate reconstruction of past atmospheric CO2?

The problems with the ice core data are 1) the air-age vs. ice-age delta and 2) the effects of burial depth on gas concentrations.

The age of the layers of ice can be fairly easily and accurately determined. The age of the air trapped in the ice is not so easily or accurately determined. Currently the most common method for aging the air is through the use of “firn densification models” (FDM). Firn is more dense than snow; but less dense than ice. As the layers of snow and ice are buried, they are compressed into firn and then ice. The depth at which the pore space in the firn closes off and traps gas can vary greatly… So the delta between the age of the ice and the ago of the air can vary from as little as 30 years to more than 2,000 years.

The EPICA C core has a delta of over 2,000 years. The pores don’t close off until a depth of 99 m, where the ice is 2,424 years old. According to the firn densification model, last year’s air is trapped at that depth in ice that was deposited over 2,000 years ago.

I have a lot of doubts about the accuracy of the FDM method. I somehow doubt that the air at a depth of 99 meters is last year’s air. Gas doesn’t tend to migrate downward through sediment… Being less dense than rock and water, it migrates upward. That’s why oil and gas are almost always a lot older than the rock formations in which they are trapped. I do realize that the contemporaneous atmosphere will permeate down into the ice… But it seems to me that at depth, there would be a mixture of air permeating downward, in situ air, and older air that had migrated upward before the ice fully “lithified”.

A recent study (Van Hoof et al., 2005) demonstrated that the ice core CO2 data essentially represent a low-frequency, century to multi-century moving average of past atmospheric CO2 levels.

Van Hoof et al., 2005. Atmospheric CO2 during the 13th century AD: reconciliation of data from ice core measurements and stomatal frequency analysis. Tellus (2005), 57B, 351–355.

It appears that the ice core data represent a long-term, low-frequency moving average of the atmospheric CO2 concentration; while the stomata yield a high frequency component.

The stomata data routinely show that atmospheric CO2 levels were higher than the ice cores do. Plant stomata data from the previous interglacial (Eemian/Sangamonian) were higher than the ice cores indicate…

Rundgren et al., 2005. Last interglacial atmospheric CO2 changes from stomatal index data and their relation to climate variations. Global and Planetary Change 49 (2005) 47–62.

The GEOCARB data also suggest that ice core CO2 data are too low…

The average CO2 level of the Pleistocene ice cores is 36ppmv less than GEOCARB…

Recent satellite data (NASA AIRS) show that atmospheric CO2 levels in the polar regions are significantly less than in lower latitudes…

"AIRS can observe the concentration of carbon dioxide in the mid-troposphere, with 15,000 daily observations, pole to pole, all over the globe, with an accuracy of 1 to 2 parts per million and a horizontal surface resolution of 1 by 1 degree. The monthly map at right allows researchers to better observe variations of carbon dioxide at different latitudes and during different seasons. Image credit: NASA" http://www.nasa.gov/topics/earth/agu/airs-images20091214.html
"AIRS data show that carbon dioxide is not well mixed in Earth's atmosphere, results that have been validated by direct measurements. The belt of carbon dioxide concentration in the southern hemisphere, depicted in red, reaches maximum strength in July-August and minimum strength in December-January. There is a net transfer of carbon dioxide from the northern hemisphere to the southern hemisphere. The northern hemisphere produces three to four times more human produced carbon dioxide than the southern hemisphere. Image credit: NASA" http://www.nasa.gov/topics/earth/agu/airs-images20091214.html

So… The ice core data should be yielding lower CO2 levels than the Mauna Loa Observatory and the plant stomata.

Kouwenberg et al., 2005 found that a “stomatal frequency record based on buried Tsuga heterophylla needles reveals significant centennial-scale atmospheric CO2 fluctuations during the last millennium.”

Plant stomata data show much greater variability of atmospheric CO2 over the last 1,000 years than the ice cores and that CO2 levels have often been between 300 and 340ppmv over the last millennium, including a 120ppmv rise from the late 12th Century through the mid 14th Century. The stomata data also indicate higher CO2 levels than the Mauna Loa instrumental record; but a 5-point moving average ties into the instrumental record quite nicely…

A survey of historical chemical analyses (Beck, 2007) shows even more variability in atmospheric CO2 levels than the plant stomata data since 1800…

WHAT DOES IT ALL MEAN?

The current “paradigm” says that atmospheric CO2 has risen from ~275ppmv to 388ppmv since the mid-1800’s as the result of fossil fuel combustion by humans. Increasing CO2 levels are supposedly warming the planet…

However, if we use Moberg’s (2005) non-Hockey Stick reconstruction, the correlation between CO2 and temperature changes a bit…

Moberg did a far better job in honoring the low frequency components of the climate signal. Reconstructions like these indicate a far more variable climate over the last 2,000 years than the “Hockey Sticks” do. Moberg also shows that the warm up from the Little Ice Age began in 1600, 260 years before CO2 levels started to rise.

As can be seen below, geologically consistent reconstructions like Moberg and Esper are in far better agreement with “direct” paleotemperature measurements, like Alley’s ice core reconstruction for Central Greenland…

In fairness to Dr. Mann, his 2008 reconstruction did restore the Medieval Warm Period and Little Ice Age to their proper places; but he still used Mike’s Nature Trick to slap a hockey stick blade onto the 20th century.

What happens if we use the plant stomata-derived CO2 instead of the ice core data?

We find that the ~250-year lag time is consistent. CO2 levels peaked 250 years after the Medieval Warm Period peaked and the Little Ice Age cooling began and CO2 bottomed out 240 years after the trough of the Little Ice Age. In a fashion similar to the glacial/interglacial lags in the ice cores, the plant stomata data indicate that CO2 has lagged behind temperature changes by about 250 years over the last millennium. The rise in CO2 that began in 1860 is most likely the result of warming oceans degassing.

While we don’t have a continuous stomata record over the Holocene, it does appear that a lag time was also present in the early Holocene…

Once dissolved in the deep-ocean, the residence time for carbon atoms can be more than 500 years. So, a 150- to 200-year lag time between the ~1,500-year climate cycle and oceanic CO2 degassing should come as little surprise.

CONCLUSIONS

  • Ice core data provide a low-frequency estimate of atmospheric CO2 variations of the glacial/interglacial cycles of the Pleistocene. However, the ice cores seriously underestimate the variability of interglacial CO2 levels.
  • GEOCARB shows that ice cores underestimate the long-term average Pleistocene CO2 level by 36ppmv.
  • Modern satellite data show that atmospheric CO2 levels in Antarctica are 20 to 30ppmv less than lower latitudes.
  • Plant stomata data show that ice cores do not resolve past decadal and century scale CO2 variations that were of comparable amplitude and frequency to the rise since 1860.

Thus it is concluded that:

  • CO2 levels from the Early Holocene through pre-industrial times were highly variable and not stable as the Antarctic ice cores suggest.
  • The carbon and climate cycles are coupled in a consistent manner from the Early Holocene to the present day.
  • The carbon cycle lags behind the climate cycle and thus does not drive the climate cycle.
  • The lag time is consistent with the hypothesis of a temperature-driven carbon cycle.
  • The anthropogenic contribution to the carbon cycle since 1860 is minimal and inconsequential.

 

Note: Unless otherwise indicated, all of the climate reconstructions used in this article are for the Northern Hemisphere.

References

Anklin, M., J. Schwander, B. Stauffer, J. Tschumi, A. Fuchs, J.M. Barnola, and D. Raynaud, CO2 record between 40 and 8 kyr BP from the GRIP ice core, Journal of Geophysical Research, 102 (C12), 26539-26545, 1997.

Wagner et al., 1999. Century-Scale Shifts in Early Holocene Atmospheric CO2 Concentration. Science 18 June 1999: Vol. 284. no. 5422, pp. 1971 – 1973.

Berner et al., 2001. GEOCARB III: A REVISED MODEL OF ATMOSPHERIC CO2 OVER PHANEROZOIC TIME. American Journal of Science, Vol. 301, February, 2001, P. 182–204.

Kouwenberg, 2004. APPLICATION OF CONIFER NEEDLES IN THE RECONSTRUCTION OF HOLOCENE CO2 LEVELS. PhD Thesis. Laboratory of Palaeobotany and Palynology, University of Utrecht.

Wagner et al., 2004. Reproducibility of Holocene atmospheric CO2 records based on stomatal frequency. Quaternary Science Reviews 23 (2004) 1947–1954.

Esper et al., 2005. Climate: past ranges and future changes. Quaternary Science Reviews 24 (2005) 2164–2166.

Kouwenberg et al., 2005. Atmospheric CO2 fluctuations during the last millennium reconstructed by stomatal frequency analysis of Tsuga heterophylla needles. GEOLOGY, January 2005.

Van Hoof et al., 2005. Atmospheric CO2 during the 13th century AD: reconciliation of data from ice core measurements and stomatal frequency analysis. Tellus (2005), 57B, 351–355.

Rundgren et al., 2005. Last interglacial atmospheric CO2 changes from stomatal index data and their relation to climate variations. Global and Planetary Change 49 (2005) 47–62.

Jessen et al., 2005. Abrupt climatic changes and an unstable transition into a late Holocene Thermal Decline: a multiproxy lacustrine record from southern Sweden. J. Quaternary Sci., Vol. 20(4) 349–362 (2005).

Beck, 2007. 180 Years of Atmospheric CO2 Gas Analysis by Chemical Methods. ENERGY & ENVIRONMENT. VOLUME 18 No. 2 2007.

Loulergue et al., 2007. New constraints on the gas age-ice age difference along the EPICA ice cores, 0–50 kyr. Clim. Past, 3, 527–540, 2007.

DATA SOURCES

CO2

Etheridge et al., 1998. Historical CO2 record derived from a spline fit (75 year cutoff) of the Law Dome DSS, DE08, and DE08-2 ice cores.

NOAA-ESRL / Keeling.

Berner, R.A. and Z. Kothavala, 2001. GEOCARB III: A Revised Model of Atmospheric CO2 over Phanerozoic Time, IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2002-051. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.

Kouwenberg et al., 2005. Atmospheric CO2 fluctuations during the last millennium reconstructed by stomatal frequency analysis of Tsuga heterophylla needles. GEOLOGY, January 2005.

Lüthi, D., M. Le Floch, B. Bereiter, T. Blunier, J.-M. Barnola, U. Siegenthaler, D. Raynaud, J. Jouzel, H. Fischer, K. Kawamura, and T.F. Stocker. 2008. High-resolution carbon dioxide concentration record 650,000-800,000 years before present. Nature, Vol. 453, pp. 379-382, 15 May 2008. doi:10.1038/nature06949.

Royer, D.L. 2006. CO2-forced climate thresholds during the Phanerozoic. Geochimica et Cosmochimica Acta, Vol. 70, pp. 5665-5675. doi:10.1016/j.gca.2005.11.031.

TEMPERATURE RECONSTRUCTIONS

Moberg, A., et al. 2005. 2,000-Year Northern Hemisphere Temperature Reconstruction. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2005-019. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.

Esper, J., et al., 2003, Northern Hemisphere Extratropical Temperature Reconstruction, IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2003-036. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.

Mann, M.E. and P.D. Jones, 2003, 2,000 Year Hemispheric Multi-proxy Temperature Reconstructions, IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series #2003-051. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.

Alley, R.B.. 2004. GISP2 Ice Core Temperature and Accumulation Data. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series #2004-013. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.

VEIZER d18O% ISOTOPE DATA. 2004 Update.

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Joel Shore
January 9, 2011 5:27 pm

Bart:
Independent, rational thought is an admirable trait. However, if it comes with a sort of lack of humility that prevents you from realizing that others are also capable of it and accepting the idea that people who have studied something for a long time may have collectively reached their conclusions for good reason then it can do more harm than good.
I think when the definitive sociology of this site is written, it will be found that it is populated by a lot of very intelligent people who were nonetheless led astray by a gap between how smart they are and how smart they think they are, particularly in relation to others (namely, the scientists in the field).

Ferdinand Engelbeen
January 10, 2011 2:31 am

Bart says:
January 9, 2011 at 11:29 am
But, that variability of the emissions has a definite proportion to the “dc” component, which purportedly integrates into the secular increase.
The main point is that the variability of the emissions is small (some 5% of the emissions trend – 2 sigma), compared to the emissions trend itself and integrated doesn’t add to the emissions trend (which is 200% of the trend in the atmosphere), while temperature variability causes +/-300% variability in CO2 increase rate over a temperature trend which integrated gives less than 10% of the atmospheric trend (if we may use the historical trends). That makes that finding back the variability of the emissions in the total noise of the endresult is not that simple…

Bart
January 10, 2011 10:53 am

Joel – If you can address the arguments, do so. If you cannot, stop wasting my time.
Ferdinand – But, the variability of the emissions IS NOT small. Look at the coefficients.
C = A*( -1 + 2.9937*t + 0.059546*t^2 + 2.0847*cos(0.20944*t + 0.59063) + 0.97556*cos(0.2992*t + 1.4507) + 0.37059*cos(0.4161*t + 3.0854) + 0.080103*cos(0.55116*t + 1.7641) + 0.19865*cos(0.69046*t + 2.85) + 0.043587*cos(0.87266*t – 1.4495) + 0.059123*cos(1.0217*t – 3.1232) + 0.029266*cos(1.232*t – 2.6294) + 0.014691*cos(1.5708*t + 1.7792) + 0.019549*cos(1.848*t + 2.6659) + 0.017115*cos(2.0601*t – 0.30909) )
The coefficient of the trend is 2.9937. The coefficient of the 15 year cycle is 0.37059. That’s 12% of the trend, more than enough to be picked out in a PSD where we can see down several orders of magnitude.
“…and integrated doesn’t add to the emissions trend…”
Why stop there? Why not integrate again, and really make it negligible? Or, put in a 12th order low pass filter and really beat the hell out of it, then claim it isn’t observable?
You are grasping at straws. If the cycles in the emissions data are real, they should appear in the measured data. Period. Your only out is to claim the cycles are spurious in the emissions data. But, I have to ask, do you really think there are no ups and downs in anthropogenic emissions? Why would you imagine that to be the case?

Bart
January 10, 2011 11:00 am

And, look at the measurement data:
C = B*( 1 + 0.0032006*t + 2.9249e-005*t^2 + 0.0018552*cos(0.2992*t – 2.1391) + 0.0011578*cos(0.7392*t + 2.4275) + 0.00083587*cos(1.7453*t – 0.93748) + 0.0090819*cos(6.2832*t – 1.6924) + 0.0025457*cos(12.5664*t + 1.0631) + 0.00036225*cos(18.8496*t + 1.9666) + 0.0002946*cos(25.1327*t – 1.3672) )
12% of 0.0032006 is 3.962e-4, a little greater than the 1/3 year cycle (18.8496 rad/year) which I can clearly see.

Joel Shore
January 10, 2011 11:59 am

The coefficient of the trend is 2.9937. The coefficient of the 15 year cycle is 0.37059. That’s 12% of the trend, more than enough to be picked out in a PSD where we can see down several orders of magnitude.

Ah, Bart…The two numbers that you are comparing don’t have the same units. To make a meaningful comparison, you have to compare the coefficient of the linear trend to the coefficient of the cycle multiplied by its omega, which knocks it down to 5%. (And, the reason that you can see the 1/3 year cycle in the CO2 concentration data is because, for the same reason, it is a much larger fraction of the linear trend than what you have calculated.)

Your only out is to claim the cycles are spurious in the emissions data. But, I have to ask, do you really think there are no ups and downs in anthropogenic emissions? Why would you imagine that to be the case?

If one believes that the cycles seen in the emissions data, it does not follow that there are no ups and downs in the anthropogenic emissions (although my guess is that such ups and downs are in fact quite small on a global scale). It just means that whatever ups and downs there are may bear little relation to the spurious ups and downs seen in the data.

Bart
January 10, 2011 2:23 pm

Actually, Joel, it isn’t meaningful even that way. I was trying to keep things simple but (sigh)… I wonder if this is worth the effort of explaining.
What matters is the level of noise, not so much the relative sizes of the coefficients. With no noise, defined as that broadband, incoherent part of the measurement signal, then the relative sizes would not matter at all – I could see all components with infinite precision. Of course, you never have zero noise, hence never infinite precision.
The point was that, if you make the assumption that the relative sizes of the terms should be roughly the same in the emissions input and the measurement output, then if I can see a comparably sized component in the measurement to the expected component from the input, then I ought to be able to see that input’s influence as well.

Ferdinand Engelbeen
January 11, 2011 12:56 am

Bart says:
January 10, 2011 at 10:53 am
The coefficient of the trend is 2.9937. The coefficient of the 15 year cycle is 0.37059. That’s 12% of the trend, more than enough to be picked out in a PSD where we can see down several orders of magnitude.
If we may assume that the slightly quadratic trend is the real emissions trend, the variability around that trend is the sum of all the other, cyclic terms. Not of one of the cyclic terms alone. The 15 years cycle may (or may not) represent a real cycle in the emissions, but its amplitude doesn’t show the real amplitude of real variation around the trend. That is what the total sum of all cycles does. And that shows less than 5% variation around the trend.
Why stop there? Why not integrate again, and really make it negligible?
As far as I remember, the integral of the variability around a least squares trend is zero by definition…
And why would there be any real variability in the emissions data at all? The basic emissions scheme is number of people x their wealth. The number of people ever increased, the average wealth ever increased. There are only two items which may have influenced the emissions on global scale: a global war (1940-1945 was before the better data) and a global economic crisis. The latter may give some (unsure) frequency in the data.
Need some more time for some more experiments with the data…

Ferdinand Engelbeen
January 11, 2011 1:21 am

Bart says:
January 10, 2011 at 2:23 pm
The point was that, if you make the assumption that the relative sizes of the terms should be roughly the same in the emissions input and the measurement output, then if I can see a comparably sized component in the measurement to the expected component from the input, then I ought to be able to see that input’s influence as well.
As said before, while the increase in output is roughly half the increase in input, the variability is leveled off at different stages:
– locally, because of capturing in the next nearby tree. That doesn’t change the average increase in the atmosphere, as a molecule CO2 captured from human emissions would replace a CO2 molecule from another source that would have been captured instead. But it reduces the variability, as higher/lower local CO2 levels increase/decrease the CO2 capturing by photosynthesis.
– hemispheric, because of the huge countercurrent natural CO2 flows between atmosphere and vegetation/oceans, especialy in the NH (as measured at Mauna Loa). While the variability around the emissions is around 5%, that represents not more than 0.25% of the seasonal variability and less than 0.05% of the total amount of CO2 in the atmosphere. The expected variability of the emissions input is within the measurement accuracy of CO2 in the atmosphere, thus in fact undetectable by the current measurement procedures.
– globally, because of the relative small mixing of the NH and SH atmospheres, the hemispheric variability is further filtered out in the SH, with even the seasonal variability hardly visible.

January 11, 2011 7:26 am

I haven’t been following the comments in this thread, but I thought readers might be interested in this reply to Middleton:
http://rhinohide.wordpress.com/2011/01/11/a-response-to-middleton-ice-cores-vs-plant-stomata/

Tom van Hoof
January 11, 2011 8:24 am

To come back on questions about the validity of Stomatal index (read, NOT stomatal density) as a CO2 proxy…
We use an index value between the number of leaf stomata and the number of epidermis cells called the stomatal index instead of just the number of stomata per leafarea as some people tned to do, the reason for thsi is that indeed drought can have an influence on stomatal density, but only through the mechanism on epidermal cell expansion… By using the stomatal index the response of leaf anatomy to changes in water availability are covered, temperature itself has almost no influence on leaf anatomy, only if you would change the annual average temperature 10 of degrees celcius as is done in soem experiments… but this is not comparable with a natural situation… So basically using this index proxy we are pretty sure we are looking at CO2 levels… how big they are is something different… calibration is difficult as it relies on historical CO2 data…
The amount of noise, we choose not to put all sorts of high tech statistical tricks over our data so we are very open about our data, in my opinion noise reduction is possible when more leaves are counted….

Bart
January 11, 2011 9:53 am

“The 15 years cycle may (or may not) represent a real cycle in the emissions, but its amplitude doesn’t show the real amplitude of real variation around the trend.”
Of course it does. That is what “amplitude” means. The area under the PSD is the amplitude squared over 2. If I were attempting to compare rates of change, then you and Joel would have a valid complaint. But, that is not what I was doing, as I did my best to explain above.
“As far as I remember, the integral of the variability around a least squares trend is zero by definition…”
It would then be called a “zero squares” trend. We generally measure “variability” in a mean square sense.
An integral attenuates signals inversely proportional to their frequencies.
“And why would there be any real variability in the emissions data at all?”
Are there variations in economic activity? Numbers of cars sold? Tons of steel and cement poured? New efficiencies attained? Come on, Ferdinand. This is not a static world.

Joel Shore
January 12, 2011 2:10 pm

Bart says:

“And why would there be any real variability in the emissions data at all?”
Are there variations in economic activity? Numbers of cars sold? Tons of steel and cement poured? New efficiencies attained? Come on, Ferdinand. This is not a static world.

Well, Bart, 2009 featured what was presumably the largest recession since the Great Depression (or at least it was for the U.S.) and global CO2 emissions were down by only 1.3% http://www.reuters.com/article/idUSTRE67C1IU20100813 . Since CO2 levels are rising roughly 2 ppm per year, that means one would have to be able to detect CO2 levels to ~0.02 ppm in order to see the effect of this.

Bart
January 12, 2011 7:07 pm

Joel… Let me get this straight. You are arguing that the lack of a significant single year variation in the official CO2 emissions record establishes that previous variations in that same record are spurious?
Did you even realize that was what you were arguing?

Ferdinand Engelbeen
January 13, 2011 1:41 pm

Bart says:
January 12, 2011 at 7:07 pm
Joel… Let me get this straight. You are arguing that the lack of a significant single year variation in the official CO2 emissions record establishes that previous variations in that same record are spurious?
Did you even realize that was what you were arguing?

Still lack time to go deeper into the frequency analyses…
2008 did show a rise of 2% in CO2 emissions (see http://planetark.org/enviro-news/item/54185 ), despite a reduction of output in the USA and Europe. 2009 did show a reduction of 1.3%. The general trend in emissions 1959-2006 was an increase by average 2.6% per year. Thus the two consequtive years may show a real decline in output due to the global economic crisis.
But the emissions estimates are only accurate to -6 to +12%, thus all variability around the trend is less that the accuracy of the emissions estimates.
That makes that the variability in the emissions may be largely spurious, except for major disturbances like a world war or a global economic crisis. That also makes that a frequency analysis of the emissions doesn’t say much about the real variability.
Even worse, the variability of the emissions is thus small that the resulting amplitude of the variability after mixing in the atmosphere in the atmosphere (even if there was no filtering and no other – far more variable – natural variables at work), is less than the measurement accuracy of CO2 levels in the atmosphere. Thus no wonder that you can’t see the variability of the emissions in the atmospheric measurements.
All you can see is the (relative) huge variability caused by seasonal changes (150 GtC in and out, largely countercurrent), the result of temperature variations on the CO2 sink rate (-4 +/- 3 GtC) and average some 50% of the emissions (currently +4 GtC as mass, not as original anthro CO2 molecules) which aren’t absorbed by the sinks.
Thus anyway, the lack of fingerprint of the emissions in the atmospheric trend is inconclusive for the cause and effect relationship involved.

Bart
January 13, 2011 2:54 pm

“Even worse…”
Everything you said up to there is worth considering. After that, you would have to show that the variability of the measurements was such as to cancel out the specific cycles of the input, something very unlikely indeed. Otherwise, it would just be additional noise which would add to the floor, but not affect the shape of the peaks.
I agree that the possibility of spurious cycles in the emissions data is the key weakness in the argument, and have stated so previously. But, I believe it is likely that there should be significant variability in the emissions from year to year, and Joel’s objection on that score is specious, as I explained above.
So, the question becomes, how much of the emissions data do we believe is real? And, if we open ourselves up to that possibility, then given that the variability in the emissions data is greater than the trend which produces positive curvature in the integrated data, how do we even know that the real integrated emissions actually has positive curvature, this being the key reason you guys see a match between the measurements and integrated emissions? If you posit that there is too little information to draw conclusions about the cyclic nature of the emissions data, then you are also positing that the apparent agreement between the measurements and the scaled and translated integrated emissions may, itself, be a phantom.

Ferdinand Engelbeen
January 16, 2011 1:02 pm

Bart says:
January 13, 2011 at 2:54 pm
So, the question becomes, how much of the emissions data do we believe is real? And, if we open ourselves up to that possibility, then given that the variability in the emissions data is greater than the trend which produces positive curvature in the integrated data, how do we even know that the real integrated emissions actually has positive curvature, this being the key reason you guys see a match between the measurements and integrated emissions? If you posit that there is too little information to draw conclusions about the cyclic nature of the emissions data, then you are also positing that the apparent agreement between the measurements and the scaled and translated integrated emissions may, itself, be a phantom.
Sorry for the late reaction, was changing some electricity circuits at home (a recurrent problem in older houses…), but underestimated the amount of work involved…
As said before, the error margins of the emissions estimates are around -6 to +12% of the emissions data. Any variability within these limits may be (but isn’t necessary) spurious. In my opinion more important is the fact that the net result of the variability of the emissions (not of the emissions themselves) in the atmosphere is smaller than the accuracy of the atmospheric measurements and is largely overruled by other (natural) variables which show a much larger variability (mainly temperature changes).
That doesn’t mean that the emissions themselves are spurious! Only that the variability of the emissions around the trend is too small to be detected in the measurements, thus a frequency analyses says next to nothing about the cause and effect relation.
Worst case of the integrated emissions is that the real total is 6% less to 12% more than the trend shows, but still the trend of integrated emissions is real and positive, as good as the trend in atmospheric data is real and positive, with in this case a very probable cause and effect relationship (as all other observations show…).

Bart
January 24, 2011 6:41 pm

But, Ferdinand, the slope of that emissions line is what gives you the positive curvature which you believe convincingly matches the measurements. And, the slope is within the range of the cyclic variations. Therefore, if the cyclic variations are suspect, so is the slope. So, then, you cannot even be sure of what I claim is a superficial resemblance between the measurements and the accumulated emissions, but which you find so convincing.

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