Orders of Integration

I(0), I(1) or I(2)? What does it all mean? Below is a visual presentation of CO2 concentration from Mauna Loa and global temperature from GISS, demonstrating the difference in their order of integration.

differences

The blue series is the increasing level of CO2 in annual steps. Differencing means to successively subtract the previous value at each step, giving the change at each step (the delta or dCO2 shown in magenta). Differencing again gives ddCO2 shown in yellow. After these two differences the values are clearly oriented around the zero line (or stationary).

The red series is the global temperature in annual steps. The purple series is the first difference. The first difference is clearly oriented on the zero line.

Series that are oriented on zero are called I(0) — no differencing is required for them to be stationary. Series like temperature that require one differencing to become stationary are called I(1). Series like CO2 that require two differences to become stationary are called I(2).

One of the central ideas around cointegration is that series that require differencing to become stationary are very prone to ‘spurious regression’. That is they look like they are correlated because they have the same trend, but will tend to wander further away from each other over time. Special methods have been developed to distinguish when series are really related, when simple correlation will be fooled.

Another idea is that series with different orders of integration can always wander arbitrarily far away from each other. In order for two series to be related, they must be of the same order. This is the basis for the claim that the first difference of CO2, or change in CO2, is related to temperature and not absolute level of CO2.

  • http://www.ecoengineers.com/ Steve Short

    Again very interesting David. Please be aware that Mauna Loa is not the global average CO2 and has itself exhibited a slowly increasing positive anomaly against the ‘official’ NOAA global mean CO2.

    The monthly and annual average CO2 levels for Mauna Loa (MLO), Easter Island (EIC) and all the Southern Hemisphere stations from 40 S to the South Pole may be found in here:

    http://jump.fm/PJHXF

    • Anonymous

      I think its not clear yet that a trend in absolute values should not
      make any difference to the order of integration. The trend gets
      removed first difference. Integration order is more ‘intrinsic’ to
      the AR behaviour. Mauna Loa is a longer record than the global one
      too. Whether something is global, regional or local doesn’t seem to
      matter much to integration order either.

      • Jan Pompe

        “Whether something is global, regional or local doesn’t seem to matter much to integration order either.”

        I’m fairly sure it doesn’t. If there is zero trend it will be I(0) if non zero linear it will be I(1) if nonlinear non zero it will be I(p | p>1). At least that is how I understood it.

  • http://www.ecoengineers.com/ Steve Short

    Again very interesting David. Please be aware that Mauna Loa is not the global average CO2 and has itself exhibited a slowly increasing positive anomaly against the 'official' NOAA global mean CO2. The monthly and annual average CO2 levels for Mauna Loa (MLO), Easter Island (EIC) and all the Southern Hemisphere stations from 40 S to the South Pole may be found in here:http://jump.fm/PJHXF

  • davids99us

    I think its not clear yet that a trend in absolute values should notmake any difference to the order of integration. The trend getsremoved first difference. Integration order is more 'intrinsic' tothe AR behaviour. Mauna Loa is a longer record than the global onetoo. Whether something is global, regional or local doesn't seem tomatter much to integration order either.

  • Jan Pompe

    “Whether something is global, regional or local doesn't seem to matter much to integration order either.”I'm fairly sure it doesn't. If there is zero trend it will be I(0) if non zero linear it will be I(1) if nonlinear non zero it will be I(p | p>1). At least that is how I understood it.

  • Anonymous

    David S.
    Would Bejan’s constructal law models of earth’s convection heat flow relative to simple radiative cooling be significant in your cointegration/order analysis? Note the difference in order of 3/2 vs simple heat flow model order 1 in Equations 23, 27.

    See:
    Thermodynamic optimization of global circulation and climate Adrian Bejan and A. Heitor Reis, INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Int. J. Energy Res. 2005; 29:303–316

    • http://www.ecoengineers.com/ Steve Short

      That’s a very interesting paper by Bejanb and Reis David. I’ve saved a copy for careful reading. Thanks.

      I notice that the paper carefully avoided using the words ‘entropy’ and ‘maximization’ 100%! Yet, they quote Lorenz, (R.D. not E.N.) et al. 2001, by noting that the value of D (the convective conductance in the horizontal direction, expressed per unit of horizontal (earth) area) is 0.6 W/m^2/K. Of course this is straight out of the mainstream MEP (Maximization of Entropy Production) literature!

      Given that this paper essentially lifts almost all its math from the body of MEP literature while avoiding acknowledging that 99%+ and yet ascribes it all to something mysterious called ‘Bejan’s constructal laws of heat flow’ I’m beginning to suspect yet another idiosyncratic attempt at academic demagoguery!

      • Anonymous

        Yes Bejan is a bit extravagant in his claims as he is fishing for a Nobel prize (though I hear they go cheap these days.)

        See Bejan’s book Shape and Structure, From Engineering to Nature ISBN0-521-79388-2 which has a lot of interesting insights and correlations.
        (PS be warned his arguments supporting evolution are invalid.)

      • Anonymous

        Steve Short
        Thanks for the reminder on MEP and RD Lorenz. That led to:

        Energetics of IPCC4AR Climate Models: Energy Balance and Meridional Enthalpy Transports Valerio Lucarin, Francesco Ragone, arXiv:0911.5689v1 [physics.ao-ph] 30 Nov 2009
        Note especially:

        We consider the climate simulations performed using pre-industrial and SRESA1B scenarios and analyse the outputs – provided by the PCMDI/CMIP3 project – of the state-of-the-art models included in the 4th Assessment Report of the IPCC. We show that are energy biases are present for several models both when global climate budgets and when energy budgets of the atmospheric, oceanic, and land subdomains are considered.. . .
        Surprisingly, the interannual variability of the energy budgets is model-wise very different, with values spanning almost an order of magnitude, both in the global case and when subdomains are considered. The energy biases do not result from transient effects tied to a still unattained steady state, but rather depend on more basic flaws related to the imperfect closure of the energy cycle in the fluid components of the climate system and to issues in the treatment of phase transitions and heat fluxes over land. . .
        It is apparent that climate dependent energy biases may contribute to increasing the uncertainty in climate sensitivity, and we may conjecture that this may play a role in the ubiquitous relatively large discrepancies among state-of-the-art models on the definition of this crucial quantity . . .

        David S. This should provide for further productive exploration of foundational IPCC errors.

        I also found the following:
        Thermodynamics of Climate Change: Generalized Sensitivities
        Valerio Lucarini, Klaus Fraedrich & Frank Lunkeit

        A. Kleidon, K. Fraedrich, E. Kirk, F. Lunkeit (2006)
        Maximum entropy production and the strength of boundary layer exchange in an atmospheric general circulation model. Geophysical Research Letters, 33, L06706,
        doi:10.1029/2005GL025373.

        THE SECOND LAW OF THERMODYNAMICS AND THE GLOBAL CLIMATE SYSTEM: A REVIEW OF THE MAXIMUM ENTROPY PRODUCTION PRINCIPLE
        Hisashi Ozawa, Atsumu Ohmura, Ralph D. Lorenz, and Toni Pujol, American Geophysical Union. Reviews of Geophysics, 41, 4 / 1018 2003
        8755-1209/03/2002RG000113; Doi:10.1029/2002RG000113

        Planets, life and the production of entropy
        Ralph D. Lorenz, International Journal of Astrobiology 1 (1) : 3±13 (2002) DOI: 10.1017}S1473550402001027 # 2002 Cambridge University Press

        Non-equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond Axel Kleidon (Editor), Ralph D. Lorenz (2004)

  • DavidLHagen

    David S.Would Bejan's constructal law models of earth's convection heat flow relative to simple radiative cooling be significant in your cointegration/order analysis? Note the difference in order of 3/2 vs simple heat flow model order 1 in Equations 23, 27.See: Thermodynamic optimization of global circulation and climate Adrian Bejan and A. Heitor Reis, INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Int. J. Energy Res. 2005; 29:303–316

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  • Anonymous

    Typo: CO22

  • DavidLHagen

    Typo: CO22

  • http://www.ecoengineers.com/ Steve Short

    That's a very interesting paper by Bejanb and Reis David. I've saved a copy for careful reading. Thanks.I notice that the paper carefully avoided using the words 'entropy' and 'maximization' 100%! Yet, they quote Lorenz, (R.D. not E.N.) et al. 2001, by noting that the value of D (the convective conductance in the horizontal direction, expressed per unit of horizontal (earth) area) is 0.6 W/m^2/K. Of course this is straight out of the mainstream MEP (Maximization of Entropy Production) literature!Given that this paper essentially lifts almost all its math from the body of MEP literature while avoiding acknowledging that 99%+ and yet ascribes it all to something mysterious called 'Bejan's constructal laws of heat flow' I'm beginning to suspect yet another idiosyncratic attempt at academic demagoguery!

  • DavidLHagen

    Yes Bejan is a bit extravagant in his claims as he is fishing for a Nobel prize (though I hear they go cheap these days.)See Bejan's book Shape and Structure, From Engineering to Nature ISBN0-521-79388-2 which has a lot of interesting insights and correlations. (PS be warned his arguments supporting evolution are invalid.)

  • http://www.moyhu.blogspot.com Nick Stokes

    What these plots illustrate is the vacuousness of the I(n) approach. When B&R describe CO2 is I(2), they are saying it has a double unit root, and is prone to drifting away stochastically with no stable mean. But anyone who isn’t an econometrician knows that the upward movement of CO2 is not stochastic. It’s a response to the fact that we’re burning 10 Gt of carbon a year. And this has nothing to do with unit roots.

    • Jan Pompe

      “It’s a response to the fact that we’re burning 10 Gt of carbon a year. ”

      and that varies in response to what?

      There are actually times in recent history where fossil fuel burning has reduced for a while and CO2 just kept right on rising so we can at least guess that it’s not just fossil fuel use that accounts for the rise. I see no reason to assume CO2 rise is not stochastic except maybe that it’s chaotic.

  • http://www.moyhu.blogspot.com Nick Stokes

    What these plots illustrate is the vacuousness of the I(n) approach. When B&R describe CO2 is I(2), they are saying it has a double unit root, and is prone to drifting away stochastically with no stable mean. But anyone who isn't an econometrician knows that the upward movement of CO2 is not stochastic. It's a response to the fact that we're burning 10 Gt of carbon a year. And this has nothing to do with unit roots.

  • Jan Pompe

    “It's a response to the fact that we're burning 10 Gt of carbon a year. “and that varies in response to what?There are actually times in recent history where fossil fuel burning has reduced for a while and CO2 just kept right on rising so we can at least guess that it's not just fossil fuel use that accounts for the rise. I see no reason to assume CO2 rise is not stochastic except maybe that it's chaotic.

  • Anonymous

    You can difference by looking at adjacent pairs, but also pairs that are two apart in the series, pairs that are 3 apart, … pairs that are n apart in the series. As you leave one apart and approach some initially unpredictable n apart, the values lose connectivity and one can’t really be used in the prediction of another. The longer the series, the better.

    So I suspect that this is not the final chapter in the book on cointegration.

    It’s fascinating to me because I had to learn about graphical integration using a pencil and graph paper and eraser. Even way back then, it was easy to understand physical systems like distance, velocity, acceleration, but less easy too see the relevance to more esoteric and less studied systems. Question. Is therea concept of rate of increase of acceleration, and then a rate if increase in that rate, etc. So do we have (my nomenclature wrong here) I(0), I(1), I(2), I(3), I(4) … concepts?This is real fun. Than you David.

    Nick, why do you distinguish between CO2 sources? There is an equally valid argument that one should distinguish between temperature series because they have a natural plus a man-made component. But, it is not required that the source is known to be man made. (Or, as a guy on talk back said the other morning “Man made? No, mate, blame the sheilas”).

    • http://www.moyhu.blogspot.com Nick Stokes

      Nick, why do you distinguish between CO2 sources? There is an equally valid argument that one should distinguish between temperature series because they have a natural plus a man-made component.
      The distinction is between deterministic and stochastic. There’s a big issue with the use of purely stochastic models, which is what B&R are using. They deduce from a unit root that there is no restoring tendency. The rising tendency of CO2 is interpreted as a random walk, which can go on without limits. But it’s not random – we know what causes it and what limits it.

      • Anonymous

        Nick
        Please expound on: “what causes it and what limits it” – which is the cause and which the response on ocean temperature, absorption/desorption and biomass productivity vs atmospheric CO2.

        • http://www.moyhu.blogspot.com Nick Stokes

          What causes it is human activity in digging up about 10 Gt fossil C a year and burning it. What limits it is basically the total amount of C in circulation (and the finite rate of mining).

          I’m reminded in reading some of this stuff of the economist who didn’t carry an umbrella, because supply would always meet demand. There are physical constraints on how carbon can move around, which do not comply with a random walk model.

          • Anonymous

            Nick,

            that answer is so poor I wouldn’t even use it (besides the fact it is on the wrong side of the issue). Aren’t your arms getting tired from waving??

            What percentage of the total CO2 flux is that 10Gt Fossil C again??

            How large is the unaccounted for C??

            Get serious boy.

          • Anonymous

            The CO2 Flux Estimated from Air-Sea Difference in CO2 Partial Pressure is reported as -1.38 PG/year (-1.38*10^15 g) between air and sea. Citing Takahashi, et al. (2009), DSR II, 56, 554-577.

          • Anonymous

            How much up and how much down??

            How much not accounted for??

            The net flux is virtually meaningless in this. (I’ve seen 1.68 PG/yr also)

  • geoffsherrington

    You can difference by looking at adjacent pairs, but also pairs that are two apart in the series, pairs that are 3 apart, … pairs that are n apart in the series. As you leave one apart and approach some initially unpredictable n apart, the values lose connectivity and one can't really be used in the prediction of another. The longer the series, the better. So I suspect that this is not the final chapter in the book on cointegration.It's fascinating to me because I had to learn about graphical integration using a pencil and graph paper and eraser. Even way back then, it was easy to understand physical systems like distance, velocity, acceleration, but less easy too see the relevance to more esoteric and less studied systems. Question. Is therea concept of rate of increase of acceleration, and then a rate if increase in that rate, etc. So do we have (my nomenclature wrong here) I(0), I(1), I(2), I(3), I(4) … concepts?This is real fun. Than you David.Nick, why do you distinguish between CO2 sources? There is an equally valid argument that one should distinguish between temperature series because they have a natural plus a man-made component. But, it is not required that the source is known to be man made. (Or, as a guy on talk back said the other morning “Man made? No, mate, blame the sheilas”).

  • http://www.moyhu.blogspot.com Nick Stokes

    Nick, why do you distinguish between CO2 sources? There is an equally valid argument that one should distinguish between temperature series because they have a natural plus a man-made component.The distinction is between deterministic and stochastic. There's a big issue with the use of purely stochastic models, which is what B&R are using. They deduce from a unit root that there is no restoring tendency. The rising tendency of CO2 is interpreted as a random walk, which can go on without limits. But it's not random – we know what causes it and what limits it.

  • DavidLHagen

    NickPlease expound on: “what causes it and what limits it” – which is the cause and which the response on ocean temperature, absorption/desorption and biomass productivity vs atmospheric CO2.

  • http://www.moyhu.blogspot.com Nick Stokes

    What causes it is human activity in digging up about 10 Gt fossil C a year and burning it. What limits it is basically the total amount of C in circulation (and the finite rate of mining). I'm reminded in reading some of this stuff of the economist who didn't carry an umbrella, because supply would always meet demand. There are physical constraints on how carbon can move around, which do not comply with a random walk model.

  • cohenite

    Nick, you say the CO2 levels are not random or stochastic because we know what causes and limits them; but that at best only addresses one side of the issue; the anthropogenic output; Knorr’s paper;

    http://wattsupwiththat.files.wordpress.com/2009/11/knorr2009_co2_sequestration.pdf

    Shows that the natural side is not so predictable as does the Frank et al paper on CO2 sensitivity; what is interesting about the Frank paper on defining a limit to CO2 climate sensitivity is that major variations in CO2 have occurred without anthropogenic input as the Lithui paper shows;

    http://www.nature.com/nature/journal/v453/n7193/full/nature06949.html

    This would suggest that there are natural elements, probably dominant and stochastic ones, which determine CO2 levels.

    • http://www.moyhu.blogspot.com Nick Stokes

      Well, the Knorr paper is not at herald of unpredictability “no trend in the airborne fraction can be found.” And I don’t think Frank helps much here. The point is that there’s all sorts of physics known, but not in the time series models.

      There’s nothing special about anthropogenic – that’s just the biggest thing happening to total CO2 at the moment.

      • Anonymous

        You are stating definitively that anthro CO2 is the largest source in the system??

      • Anonymous

        Here is a good example of why your statement of ACO2 being so important is not necessarily valid:

        http://climaterealists.com/index.php?id=5436

        • http://www.moyhu.blogspot.com Nick Stokes

          No, it;s a convincing refutation by the authors of the Nature paper. Key quote:
          “Even if it did, the projected CO2 increase from the soils (0.1 Pg/yr) is around 1% of fossil fuel emissions (8 Pg/yr).”

          • Anonymous

            Nick,

            the soil is estimated to emit 98Pg/yr and humans you said earlier 10. you only quote the estimated INCREASE of soil emissions. Again, the human contribution to the system is still TINY!!!

            The unknowns and error bars swallow the human contribution.

            You and others are silly touting it as a huge deal.

          • http://www.moyhu.blogspot.com Nick Stokes

            I think it’s 98 Pg CO2, or about 30 Pg C. Humans 10 Pg C. But it’s the old story, constantly muddied. The soil emission is C that was recently taken from the air by photosynthesis. It’s just part of the cycling of C between atmosphere and biosphere. The human 10 Pg is new C added to the system.

    • http://www.ecoengineers.com/ Steve Short

      Recent studies have indicated that the oceanic remineralization depth – the mean depth at which organic carbon from sinking particles of (largely) dead cyanobacteria from the surface euphotic layer is converted back to (dissolved) CO2 can have a profound effect on atmospheric CO2.

      For example, when the (e-folding) depth at which 63% of sinking organic carbon is respired increases by only 24 m globally, atmospheric CO2 concentrations would decrease by 10 – 27 ppmv. This reduction in atmospheric CO2 concentration results from the redistribution of remineralized carbon from intermediate to bottom waters.

      As a consequence of the reduced concentration of respired concentration in upper oceans waters, atmospheric CO2 is preferentially stored in storages such as newly formed North Atlantic Deep Water and other deep oceanic zones

      Climate change-induced changes in remineralization depth might also influence the oceanic uptake of anthropogenic CO2 in the future. Transient simulations show that considerable fractions (>30%) of the full response occur on decadal timescales.

      Possible changes in remineralization depth could well feed back on 21st century climate change.

      Kwon et al. Nature Geoscience. September 2009. Vol. 9. No. 2, 630 -635.

      It is useful to note that in 1982 the estimated global average CO2 level was 340.54 ppmv and below 40 S it was lower by 1.14 ppmv. World CO2 levels then surged at their fastest rate to about 1991 but below 40 S it was still lower by 1.94 ppmv. By 2008 CO2 levels below 40 S were 2.10 ppmv below the global average and that anomaly was still slowly increasing.

      • Anonymous

        Steve Short
        That N/S difference appears related to fossil fuel emissions. See: Tracking Carbon Dioxide Emissions from Fossil Fuel BurningMarch 1997

        Latitudinal distribution of emissions have also been calculated. The data show continual growth with time over most of the world, with increased growth rates in major urban areas. A slow southerly shift in the bulk of the emissions is apparent as Asian countries increase their energy consumption to support their growing economies and populations. The digital data sets are available by anonymous ftp.

        Andres, R.J., G. Marland, I. Fung, and E. Matthews, 1996: A 1° × 1° distribution of carbon dioxide emissions from fossil fuel consumption and cement manufacture, 1950-1990. Global Biogeochem. Cycles, 10, 419-429, doi:10.1029/96GB01523.

        Steve & David S.
        With Steve’s observation on CO2 remineralization, it would be interesting to see what the order analysis shows for global fossil fuel CO2 emissions.

        Note the LOG of oil consumption by Patzek Slide 20

        See especially Figure 7: Exponential rate of growth of world crude oil production was 6.6% per year between1880 and 1970. Exponential growth, energetic Hubbert cycles, and the advancement of technology, Tad W. Patzek 2008

        Sources: , US EIA.

        • http://www.ecoengineers.com/ Steve Short

          “That N/S difference appears related to fossil fuel emissions.”

          I don’t think so. If that were so we should have been observing, at least by 2008, a convergence of the mean CO2 level over all 13 CO2-measuring stations in operation below (say) 40 S towards the global mean value.

          However, in 2008 that mean level still lagged -0.53±0.08% below the global average – further down not up) from -0.33±0.06% in 1983 (errors at ± one standard deviation level). Even the Mauna Loa station differed from the global mean in 2008 by +0.21% and that had nothing to do with fossil fuel emissions. Northeast of Mauna Loa lies a well known oceanic upwelling zone and the prevailing winds at NE->SW.

          What I think this data tells us is that:

          (1) sure there is a lag in mixing of CO2 between the NH and SH but that;

          (2) some other process is in operation, probably related to the greater proportion of ocean in the SH (and it’s cyanobacterial primary productivity),

          which is keeping the SH mean CO2 level consistently below the global mean level (despite the latter’s seemingly inexorable rate of rise) and resisting convergence with the global mean – even allowing for the mixing time. BTW – we know that the inter-hemispheric mixing time is only of the the order of 2 years. For example, the SH Chernobyl 137/134Cs signature appearance showed that quite elegantly (my own work too ;-).

          The bulk of the world’s oceanic cyanobacteria are the nano-cyanobacterium Prochlorococcus (~100,00 cells/mL) and the larger species Synechococcus (~10,000 cells/mL). These organisms make up only about 47% of the planet’s living biomass.

          What if the world’s oceanic cyanobacteria were evolving and adapting to higher atmospheric levels of CO2 (and other anthropogenic influences) even as we speak? How would that differ from (say) the evolution of Aids, or swine flu, or SARs?

  • cohenite

    Nick, you say the CO2 levels are not random or stochastic because we know what causes and limits them; but that at best only addresses one side of the issue; the anthropogenic output; Knorr's paper;http://wattsupwiththat.files.wordpress.com/2009…Shows that the natural side is not so predictable as does the Frank et al paper on CO2 sensitivity; what is interesting about the Frank paper on defining a limit to CO2 climate sensitivity is that major variations in CO2 have occurred without anthropogenic input as the Lithui paper shows;http://www.nature.com/nature/journal/v453/n7193…This would suggest that there are natural elements, probably dominant and stochastic ones, which determine CO2 levels.

  • http://www.moyhu.blogspot.com Nick Stokes

    Well, the Knorr paper is not at herald of unpredictability “no trend in the airborne fraction can be found.” And I don't think Frank helps much here. The point is that there's all sorts of physics known, but not in the time series models.There's nothing special about anthropogenic – that's just the biggest thing happening to total CO2 at the moment.

  • Anonymous

    Shouldn’t the calculation be on log[CO2]? This is what should be proportional to temperature.

    • Anonymous

      And natural log of [H2O]

      • Anonymous

        Same thing as far as a correlation goes. The important thing is that it is likely to change the order. Its dln[CO2] not dCO2.

        • Anonymous

          Would not the the sign being the same or inverted make some difference?
          Ie is feedback positive or negative?
          Or does it appear positive because the climate is shifting equilibrium due to changing external forcing?

  • rehuie

    Shouldn't the calculation be on log[CO2]? This is what should be proportional to temperature.

  • kuhnkat

    Nick,that answer is so poor I wouldn't even use it (besides the fact it is on the wrong side of the issue). Aren't your arms getting tired from waving??What percentage of the total CO2 flux is that 10Gt Fossil C again??How large is the unaccounted for C??Get serious boy.

  • http://www.ecoengineers.com/ Steve Short

    Recent studies have indicated that the oceanic remineralization depth – the mean depth at which organic carbon from sinking particles of (largely) dead cyanobacteria from the surface euphotic layer is converted back to (dissolved) CO2 can have a profound effect on atmospheric CO2.For example, when the (e-folding) depth at which 63% of sinking organic carbon is respired increases by only 24 m globally, atmospheric CO2 concentrations would decrease by 10 – 27 ppmv. This reduction in atmospheric CO2 concentration results from the redistribution of remineralized carbon from intermediate to bottom waters.As a consequence of the reduced concentration of respired concentration in upper oceans waters, atmospheric CO2 is preferentially stored in storages such as newly formed North Atlantic Deep Water and other deep oceanic zonesClimate change-induced changes in remineralization depth might also influence the oceanic uptake of anthropogenic CO2 in the future. Transient simulations show that considerable fractions (>30%) of the full response occur on decadal timescales.Possible changes in remineralization depth could well feed back on 21st century climate change.Kwon et al. Nature Geoscience. September 2009. Vol. 9. No. 2, 630 -635.It is useful to note that in 1982 the estimated global average CO2 level was 340.54 ppmv and below 40 S it was lower by 1.14 ppmv. World CO2 levels then surged at their fastest rate to about 1991 but below 40 S it was still lower by 1.94 ppmv. By 2008 CO2 levels below 40 S were 2.10 ppmv below the global average and that anomaly was still slowly increasing.

  • DavidLHagen

    And natural log of [H2O]

  • rehuie

    Same thing as far as a correlation goes. The important thing is that it is likely to change the order. Its dln[CO2] not dCO2.

  • DavidLHagen

    Would not the the sign being the same or inverted make some difference? Ie is feedback positive or negative?Or does it appear positive because the climate is shifting equilibrium due to changing external forcing?

  • DavidLHagen

    Steve ShortThat N/S difference appears related to fossil fuel emissions. See: Tracking Carbon Dioxide Emissions from Fossil Fuel BurningMarch 1997

    Latitudinal distribution of emissions have also been calculated. The data show continual growth with time over most of the world, with increased growth rates in major urban areas. A slow southerly shift in the bulk of the emissions is apparent as Asian countries increase their energy consumption to support their growing economies and populations. The digital data sets are available by anonymous ftp.

    Andres, R.J., G. Marland, I. Fung, and E. Matthews, 1996: A 1° × 1° distribution of carbon dioxide emissions from fossil fuel consumption and cement manufacture, 1950-1990. Global Biogeochem. Cycles, 10, 419-429, doi:10.1029/96GB01523.Steve & David S. With Steve's observation on CO2 remineralization, it would be interesting to see what the order analysis shows for global fossil fuel CO2 emissions. Note the LOG of oil consumption by Patzek Slide 20See especially Figure 7: Exponential rate of growth of world crude oil production was 6.6% per year between1880 and 1970. Exponential growth, energetic Hubbert cycles, and the advancement of technology, Tad W. Patzek 2008Sources: , US EIA.

  • DavidLHagen

    The CO2 Flux Estimated from Air-Sea Difference in CO2 Partial Pressure is reported as -1.38 PG/year (-1.38*10^15 g) between air and sea. Citing Takahashi, et al. (2009), DSR II, 56, 554-577.

  • Anonymous

    The sign is whatever you want – it depends upon the standard state for the units. (Can’t take a log of units.)

    The forcing for CO2 is positive, it absorbs ir radiation. A feedback can be either positive (more water vapor) or negative (more clouds). That’s the shift in equilibrium. Which, of course, can be very complex.

  • rehuie

    The sign is whatever you want – it depends upon the standard state for the units. (Can't take a log of units.)The forcing for CO2 is positive, it absorbs ir radiation. A feedback can be either positive (more water vapor) or negative (more clouds). That's the shift in equilibrium. Which, of course, can be very complex.

  • cohenite

    Speaking of cynaobacteria Steve this investment opportunity seems to have been mishandled;

    http://blogs.discovermagazine.com/80beats/2009/03/24/iron-dumping-experiment-is-a-bust-it-feeds-crustaceans-doesnt-trap-carbon/

    • http://www.ecoengineers.com/ Steve Short

      “Within two weeks of the iron sulfide dump, the algae were being eaten by tiny creatures called copepods, which were then in turn eaten by amphipods, a larger type of crustacean [BBC News]. ”

      It was iron sulfate not iron sulfide. That will give you some small idea of the nature of the wiseacre hayseed that wrote this load of twaddle.

      Think on this:

      Like the 1.5 kg of bacteria in your own guts, like the soil beneath your feet, like the air, and the sea itself, it is a bloody jungle absolutely everywhere on this planet. Amazing isn’t it that many of the 7 billion primates on this planet deluded enough to consider themselves a sentient life form still don’t get that simple fact (despite ripping each other off and slaughtering and oppressing each other by the millions on a constant basis).

      Surprise!

      Like cyanobacteria, all copepods die (either through age or predation) and intact dead copepods sink, amphipods also die (either through age or predation) and intact dead amphipods sink, fish die and the intact dead fish sink, whales die and intact dead whales sink (after abit of flaoting (;-), sharks who feed on their carcasses also die and some also sink ad infinitum (or ad nauseum if you are weak of stomach or brain pan)……

      The important point is simply that the cyanobacteria were induced to bloom by adding the iron sulfate. After that, it just doesn’t really matter where in the great and gory food chain the organic carbon which the cyanobacteria had fixed (from dissolved CO2 and bicarbonate) ends up!

      CO2 was removed from the atmosphere and fixed as organic carbon and that is all we need to know!

      Eventually, nearly all of that organic carbon sinks through the water column and either settles onto the sea bed or gets mineralized (in yet another ‘jungle’ by, you’ve guessed it – bacteria) and hence gets transferred in into the deep ocean to be deposited as calcium carbonate and/or stored in the dissolved form for millenia.

      Beware of every passing bit of AGW sophistry, my friend.

  • cohenite

    Speaking of cynaobacteria Steve this investment opportunity seems to have been mishandled;http://blogs.discovermagazine.com/80beats/2009/

  • http://www.ecoengineers.com/ Steve Short

    “Within two weeks of the iron sulfide dump, the algae were being eaten by tiny creatures called copepods, which were then in turn eaten by amphipods, a larger type of crustacean [BBC News]. “It was iron sulfate not iron sulfide. That will give you some small idea of the nature of the wiseacre hayseed that wrote this load of twaddle. Think on this:Like the 1.5 kg of bacteria in your own guts, like the soil beneath your feet, like the air, and the sea itself, it is a bloody jungle absolutely everywhere on this planet. Amazing isn't it that many of the 7 billion primates on this planet deluded enough to consider themselves a sentient life form still don't get that simple fact (despite ripping each other off and slaughtering and oppressing each other by the millions on a constant basis).Surprise!Like cyanobacteria, all copepods die (either through age or predation) and intact dead copepods sink, amphipods also die (either through age or predation) and intact dead amphipods sink, fish die and the intact dead fish sink, whales die and intact dead whales sink (after abit of flaoting (;-), sharks who feed on their carcasses also die and some also sink ad infinitum (or ad nauseum if you are weak of stomach or brain pan)……The important point is simply that the cyanobacteria were induced to bloom by adding the iron sulfate. After that, it just doesn't really matter where in the great and gory food chain the organic carbon which the cyanobacteria had fixed (from dissolved CO2 and bicarbonate) ends up!CO2 was removed from the atmosphere and fixed as organic carbon and that is all we need to know!Eventually, nearly all of that organic carbon sinks through the water column and either settles onto the sea bed or gets mineralized (in yet another 'jungle' by, you've guessed it – bacteria) and hence gets transferred in into the deep ocean to be deposited as calcium carbonate and/or stored in the dissolved form for millenia.Beware of every passing bit of AGW sophistry, my friend.

  • http://www.ecoengineers.com/ Steve Short

    “That N/S difference appears related to fossil fuel emissions.”I don't think so. If that were so we should have been observing, at least by 2008, a convergence of the mean CO2 level over all 13 CO2-measuring stations in operation below (say) 40 S towards the global mean value. However, in 2008 that mean level still lagged -0.53±0.08% below the global average – further down not up) from -0.33±0.06% in 1983 (errors at ± one standard deviation level). Even the Mauna Loa station differed from the global mean in 2008 by +0.21% and that had nothing to do with fossil fuel emissions. Northeast of Mauna Loa lies a well known oceanic upwelling zone and the prevailing winds at NE->SW.What I think this data tells us is that:(1) sure there is a lag in mixing of CO2 between the NH and SH but that;(2) some other process is in operation, probably related to the greater proportion of ocean in the SH (and it's cyanobacterial primary productivity),which is keeping the SH mean CO2 level consistently below the global mean level (despite the latter's seemingly inexorable rate of rise) and resisting convergence with the global mean – even allowing for the mixing time. BTW – we know that the inter-hemispheric mixing time is only of the the order of 2 years. For example, the SH Chernobyl 137/134Cs signature appearance showed that quite elegantly (my own work too ;-). The bulk of the world's oceanic cyanobacteria are the nano-cyanobacterium Prochlorococcus (~100,00 cells/mL) and the larger species Synechococcus (~10,000 cells/mL). These organisms make up only about 47% of the planet's living biomass.What if the world's oceanic cyanobacteria were evolving and adapting to higher atmospheric levels of CO2 (and other anthropogenic influences) even as we speak? How would that differ from (say) the evolution of Aids, or swine flu, or SARs?

  • Anonymous

    From Tim: You illustrated I(0) etc rather neatly at your current thread “Orders of Integration”, and I love that graph, yet in my view you reached a wrong conclusion, when you said “this is the basis for the claim that the first difference of CO2, or change in CO2, is related to temperature and not absolute temperature”. As typed it makes no sense to contrast “temperature” with “absolute temperature”, by me they are the same. Moreover the whole of climate science is based on the idea that it is the level of the atmospheric concentration of [CO2] that determines warming – net emissions of CO2 are relevant only in so far as they add to total [CO2] but as annual pulses are never enough to make the slightest difference (too small at only 1.5 ppm). Likewise “the” science of AGW is always cast in terms of increases in temperature, so that implies dT =x(RF or[CO2]).Granted that absolute temperatures are perfectly valid as the dependent variable, but not apparently in climate “science”.

    • Anonymous

      Fixed. I meant absolute level of CO2

      • http://www.ecoengineers.com/ Steve Short

        David

        I must admit that I also have great difficulty understanding the applicability of the conclusion you reached, along similar lines to Tim’s.

        Over time I have begun to suspect that there is something dubious about the tendency of modern climate science to shy away from absolute temperature as the dependent variable – or indeed other absolute parameters such as rainfall, sea level etc., and to treat most dependent variables, other than the assumed pCO2 ‘independent variable’ in terms of arbitrarily defined ‘anomalies’.

        The acme of what particularly annoys me about this approach is IPCCs insistence on the effect of carbon dioxide being roughly logarithmic. IPCC assumes that every time time CO2 (or some other greenhouse gas) is doubled, the increase in temperature is the same as the previous increase.

        If I may paraphrase Jeffrey Glassmann’s excellent summation their (IPCC’s) description is simply wrong.

        Jeffrey rightly points out that the relationship between pCO2 and any dependent variable is a decaying exponential, not a logarithmic curve. So, for example, if y is the % of Radiation Remaining and C is the CO2 Concentration, then the curve is y = e^-kC, where k is a positive constant.

        All empirical scientists know very well that this equation is a physical necessity to make any sort of filter work logically and correctly. I know this from my catchment model fits to flow recessions (and yes I do measure the Nash-Sutcliffe). I am positive Jan too knows this from his process control circuits.

        For example, Radiative Forcing (RF) is the amount of radiation absorbed, not remaining, that is, not the amount transmitted forward. So the normalized RF = 1 – y = 1 – e^-kC. The fact that the equation can be turned around to C = -ln(y)/k is immaterial.

        IPCC makes the reasonable approximation that the temperature and radiative forcing are proportional, ΔTs = λRF, where λ, is the climate sensitivity parameter refer AR4, Para 2.2, p. 133. So ΔTs = λ(1 – e^-kC), and Ts = To + λ(1 – e^-kC).

        Doubling the pCO2 concentration squares the proportion of radiation absorbed, y. However, temperature change does not follow a logarithmic curve, but instead is the complement of a decaying exponential.

        Since the logarithmic curve and this complement function are convex in the same sense (“convex down”), sure the logarithmic curve can make a pretty good fit to most any (discrete) region but in extremis it extrapolates to impossible results (far too hot).

        For an increasing independent variable, the complement of the exponential has a horizontal asymptote, while the logarithm has none. On the contrary, the flawed IPCC model goes to infinity.

        This in effect means that worse than no saturation, CO2 (and H2O) are each ‘capable’ (according to IPCC) of exceeding their own share of the LW IR band! The Beer-Lambert Law by definition correctly expresses saturation in each and every IR band.

        IPCC really needed to determine whether, and under what conditions the Beer-Lambert Law was valid, and then to find where the atmosphere was on the saturation curve described by the complement of a decaying exponential. Instead IPCC simply brushed that problem under the carpet and thus making the climate e.g. surface temperature, too sensitive to CO2 overall.

        They have repeated this type of flawed approach again and again.

        • Jan Pompe

          Steve I can go along with all of that.

        • Anonymous

          Thank you Steve!

  • davids99us

    From Tim: You illustrated I(0) etc rather neatly at your current thread “Orders of Integration”, and I love that graph, yet in my view you reached a wrong conclusion, when you said “this is the basis for the claim that the first difference of CO2, or change in CO2, is related to temperature and not absolute temperature”. As typed it makes no sense to contrast “temperature” with “absolute temperature”, by me they are the same. Moreover the whole of climate science is based on the idea that it is the level of the atmospheric concentration of [CO2] that determines warming – net emissions of CO2 are relevant only in so far as they add to total [CO2] but as annual pulses are never enough to make the slightest difference (too small at only 1.5 ppm). Likewise “the” science of AGW is always cast in terms of increases in temperature, so that implies dT =x(RF or[CO2]).Granted that absolute temperatures are perfectly valid as the dependent variable, but not apparently in climate “science”.

  • davids99us

    Fixed. I meant absolute level of CO2

  • http://www.ecoengineers.com/ Steve Short

    DavidI must admit that I also have great difficulty understanding the applicability of the conclusion you reached, along similar lines to Tim's. Over time I have begun to suspect that there is something dubious about the tendency of modern climate science to shy away from absolute temperature as the dependent variable – or indeed other absolute parameters such as rainfall, sea level etc., and to treat most dependent variables, other than the assumed pCO2 'independent variable' in terms of arbitrarily defined 'anomalies'.The acme of what particularly annoys me about this approach is IPCCs insistence on the effect of carbon dioxide being roughly logarithmic. IPCC assumes that every time time CO2 (or some other greenhouse gas) is doubled, the increase in temperature is the same as the previous increase.If I may paraphrase Jeffrey Glassmann's excellent summation their (IPCC's) description is simply wrong. Jeffrey rightly points out that the relationship between pCO2 and any dependent variable is a decaying exponential, not a logarithmic curve. So, for example, if y is the % of Radiation Remaining and C is the CO2 Concentration, then the curve is y = e^-kC, where k is a positive constant. All empirical scientists know very well that this equation is a physical necessity to make any sort of filter work logically and correctly. I know this from my catchment model fits to flow recessions (and yes I do measure the Nash-Sutcliffe). I am positive Jan too knows this from his process control circuits.For example, Radiative Forcing (RF) is the amount of radiation absorbed, not remaining, that is, not the amount transmitted forward. So the normalized RF = 1 – y = 1 – e^-kC. The fact that the equation can be turned around to C = -ln(y)/k is immaterial. IPCC makes the reasonable approximation that the temperature and radiative forcing are proportional, ΔTs = λRF, where λ, is the climate sensitivity parameter refer AR4, Para 2.2, p. 133. So ΔTs = λ(1 – e^-kC), and Ts = To + λ(1 – e^-kC).Doubling the pCO2 concentration squares the proportion of radiation absorbed, y. However, temperature change does not follow a logarithmic curve, but instead is the complement of a decaying exponential. Since the logarithmic curve and this complement function are convex in the same sense (“convex down”), sure the logarithmic curve can make a pretty good fit to most any (discrete) region but in extremis it extrapolates to impossible results (far too hot). For an increasing independent variable, the complement of the exponential has a horizontal asymptote, while the logarithm has none. On the contrary, the flawed IPCC model goes to infinity. This in effect means that worse than no saturation, CO2 (and H2O) are each 'capable' (according to IPCC) of exceeding their own share of the LW IR band! The Beer-Lambert Law by definition correctly expresses saturation in each and every IR band. IPCC really needed to determine whether, and under what conditions the Beer-Lambert Law was valid, and then to find where the atmosphere was on the saturation curve described by the complement of a decaying exponential. Instead IPCC simply brushed that problem under the carpet and thus making the climate e.g. surface temperature, too sensitive to CO2 overall. They have repeated this type of flawed approach again and again.

  • Jan Pompe

    Steve I can go along with all of that.

  • kuhnkat

    How much up and how much down??How much not accounted for??The net flux is virtually meaningless in this. (I've seen 1.68 PG/yr also)

  • kuhnkat

    Thank you Steve!

  • kuhnkat

    You are stating definitively that anthro CO2 is the largest source in the system??

  • cohenite

    Thanks Steve; the exponential decay of the pCO2 and temp relationship is the primary reason, along with, imo, OD, and the, hopefully, revised Lindzen and Choi piece on TOA LW flux, for disputing the AGW mechanism. Simply put, CO2 change has already had its temp response at levels well below current CO2 ones; extra CO2 is surperflous because of Beer-Lambert. It would also seem that the inbuilt saturation factor is further enhanced by biomass such as the cynaobacteria and convective processes. So, while the forcing for CO2 is theoretically +ve the feedbacks make it increasingly problematic. The remaining issue of incremental CO2 vs bulk CO2 [as determined by cointegration] would seem only to be an issue if the extra CO2 caused an increase in atmospheric weight and pressure as eli relies on;

    http://rabett.blogspot.com/2007/07/temperature-anonymice-gave-eli-new.html

    • http://www.ecoengineers.com/ Steve Short

      Yes, I’ve looked at Eli Rabett’s more recent stuff on this matter. I also followed as a lurker very closely all the detailed ‘explanation’/discussion (over 600 posts) on this subject in Real Climate back in 2007. I recall another ‘Tim’ played a fairly big role in that discussion as well.

      I remain unconvinced by the earlier and latter sets of arguments.

      Both Eli and the earlier stuff on Real Climate, following the post by Weart and Pierrehumbert (re the histric Koch experiment etc., etc.) conspicuously concentrated on the effects on and by CO2 alone and carefully dodged the issue of a real atmosphere with finite LW IR bandwith naturally filling up with absorption lines by CO2, water vapor, methane, nitrous oxide etc.

      Sure, it is easy to show that in a dry atmosphere it would take a fair bit of CO2 to approach bandwidth saturation. But this planet has a rather wet lower atmosphere with lots of water vapor available, amplified by the effect of rising CO2. The LW IR bandwidth is also largely progressively filled by water vapor in the lower atmosphere, surely?

      Given that over the last decade where the reduced rate of rise in global surface temperatures has been actually or almost stalled it is therefore very difficult for the AGW gurus to explain that radiometrically in the context that not only has CO2 continued to rise inexorably but also Specific Humidity below 700 mb has continued to rise almost as strongly (7.74 g/kg in 2000 to 7.92 g/kg in 2009 or 2.3%/decade). Over the same 10 year period CO2 rose from 368.77 ppmv to 386.28 ppmv or 4.6%/decade.

      Can someone show me how Weart, Rabett etc., can all have their cake and eat it too?

  • cohenite

    Thanks Steve; the exponential decay of the pCO2 and temp relationship is the primary reason, along with, imo, OD, and the, hopefully, revised Lindzen and Choi piece on TOA LW flux, for disputing the AGW mechanism. Simply put, CO2 change has already had its temp response at levels well below current CO2 ones; extra CO2 is surperflous because of Beer-Lambert. It would also seem that the inbuilt saturation factor is further enhanced by biomass such as the cynaobacteria and convective processes. So, while the forcing for CO2 is theoretically +ve the feedbacks make it increasingly problematic. The remaining issue of incremental CO2 vs bulk CO2 [as determined by cointegration] would seem only to be an issue if the extra CO2 caused an increase in atmospheric weight and pressure as eli relies on;http://rabett.blogspot.com/2007/07/temperature-

  • http://www.ecoengineers.com/ Steve Short

    Yes, I've looked at Eli Rabett's more recent stuff on this matter. I also followed as a lurker very closely all the detailed 'explanation'/discussion (over 600 posts) on this subject in Real Climate back in 2007. I recall another 'Tim' played a fairly big role in that discussion as well.I remain unconvinced by the earlier and latter sets of arguments.Both Eli and the earlier stuff on Real Climate, following the post by Weart and Pierrehumbert (re the histric Koch experiment etc., etc.) conspicuously concentrated on the effects on and by CO2 alone and carefully dodged the issue of a real atmosphere with finite LW IR bandwith naturally filling up with absorption lines by CO2, water vapor, methane, nitrous oxide etc.Sure, it is easy to show that in a dry atmosphere it would take a fair bit of CO2 to approach bandwidth saturation. But this planet has a rather wet lower atmosphere with lots of water vapor available, amplified by the effect of rising CO2. The LW IR bandwidth is also largely progressively filled by water vapor in the lower atmosphere, surely? Given that over the last decade where the reduced rate of rise in global surface temperatures has been actually or almost stalled it is therefore very difficult for the AGW gurus to explain that radiometrically in the context that not only has CO2 continued to rise inexorably but also Specific Humidity below 700 mb has continued to rise almost as strongly (7.74 g/kg in 2000 to 7.92 g/kg in 2009 or 2.3%/decade). Over the same 10 year period CO2 rose from 368.77 ppmv to 386.28 ppmv or 4.6%/decade.Can someone show me how Weart, Rabett etc., can all have their cake and eat it too?

  • Anonymous

    Steve Short, This might be of no relevence, but you mention “Jeffrey rightly points out that the relationship between pCO2 and any dependent variable is a decaying exponential, not a logarithmic curve. So, for example, if y is the % of Radiation Remaining and C is the CO2 Concentration, then the curve is y = e^-kC, where k is a positive constant. ”

    The classic case is natural radioactive decay. We had the problem of Radon-222 gas in the open pit at Ranger Uranium. The excavators were fitted with a compressed air system to keep the Radon out of the cabin, because it harms the lungs.

    The partial chain runs …. Radium-226 (half life 1600 years) to Radon-222 (3.8 days) to Polonium-218 (3.1 min)…….

    If you pump the cabin free of Rn-222, then leave it, the subsequent build-up of radioacticity depends on the half life of any Radium-226 that might be there as contamination. The 3.8 day half life of Radon-222 does not set the rate of recharge of radon.

    Over now to natural global systems, where CO2 is degassing from the sea. If it follows the same rules, then the main figure of relevance in calculations is the release rate from the sea, not the residence time in the atmosphere. Any shock to current atmospheric CO2 levels has to take the (slow) rate of release from the sea into account when modelling. Of course, it is more complicated here because absorption has the be calcuated also.

    Steve, do you have separate confirmation that decaying exponentials are the correct equations to apply to CO2 in your scenario?

    • http://www.ecoengineers.com/ Steve Short

      Geoff, as you in effect point out the complement of a decay is an ingrowth.

      A simple decay is a exp(-k1t) term and an ingrowth is a [k2/(k2-k1)][(1 - exp(-(k2-k1)t] term where the k1 and k2 terms are the decay rates of daughter (product) and parent (source) concentrations. Of course, in the case of 226Ra and 222Rn, because k = ln2/half-life = 0.693/half-life so k2>>k1.

      The facile physical uptake of CO2 by the oceans is driven by the difference in gas pressure in the atmosphere and in the oceans and by the air–sea transfer velocity. Because pCO2 is increasing in the atmosphere, CO2 moves into the ocean in an attempt to balance the oceanic and atmospheric gas pressures.

      The mechanisms that control the speed with which the CO2 gas can move from the atmosphere to the oceans (air–sea transfer velocity) are not well understood. The physical transfer velocity is particularly related to the surface roughness of the ocean and the wind speed (for any constant water temperature) and there are numerous parameterizations covering this.

      However it is possible to bypass this ‘choke’ because, most importantly, the total reversible uptake of CO2 into the ocean is actually controlled not by the gas exchange pump referred-to above but by a combination of (a) the soft tissue pump (phytoplankton uptake), the (b) carbonate pump (formation of carbonate secreting phytoplankton) and the gas exchange pump.

      It is known that it is the (a) and (b) biological uptakes which dominate the long term reversible uptake and that these are controlled by the global mean preformed phosphate (Ppre) and surface total phosphate (P) levels in the sea. Biological uptake is parameterized as a linear damping of phosphate at the surface layer of a model where biological uptake depletes surface nutrients over a prescribed timescale tau(bio).

      The theory predicts a simple response of atmospheric pCO2 to perturbations in the inventory of regenerated phosphate, expressed in terms of a parameter P*. Atmospheric pCO2 decreases by ~30 ppmv for every 0.1 increase in globally averaged P*. Atmospheric CO2 can vary by approximately 300 ppmv between the minimum and the maximum efficiency of the soft tissue pump (0 < P* < 1)

      Climatological distributions of phosphate and oxygen indicate P* = 0.36 for the modern ocean. If P* were to increase up to 0.7, the simple theory suggest that atmospheric CO2 would be expected to decrease by 100 ppmv, which is similar to the difference in atmospheric pCO2 between the Last Glacial Maximum (LGM) and the Holocene.

      P* has some notable properties:
      ● P* cannot be greater than 1.
      ● P* is conserved in the interior ocean.
      ● Water masses tend to exhibit distinct P* concentrations.

      For any given atmospheric CO2 and typical constant P* the relationship between the atmospheric partial pressure of CO2 (pCO2) and the timescale tau(bio) for development of that partial pressure is described by a typical ingrowth curve for pCO2 with a half life of the order of 10 – 15 years.

      In the modern ocean, the value of the globally averaged P* is approximately 0.36, indicating that 36% of phosphate returns
      to the interior ocean through biological export and remineralization.

      Significantly for AGW, the soft tissue carbon pump of the modern global ocean is operating WELL BELOW the theoretical maximum efficiency. Sound familiar?

      Here is a typical reference (but consider yourself warned):

      http://ocean.mit.edu/~mick/Papers/ItoFollows-preformed-JMR2005.pdf

      • Anonymous

        Steve noted:
        “Doubling the pCO2 concentration squares the proportion of radiation absorbed, y. However, temperature change does not follow a logarithmic curve, but instead is the complement of a decaying exponential.”
        and
        “the timescale tau(bio) for development of that partial pressure is described by a typical ingrowth curve for pCO2 with a half life of the order of 10 – 15 years.”
        (Thanks for that reference.)

        Is this CO2 absorption (into the ocean by biomass formation and carbonate precipitation) effectively an exponential decay? Or is it dominated in the near term by ocean oscillations and temperature variations?

        • http://www.ecoengineers.com/ Steve Short

          Yes, for any FIXED atmospheric pCO2 it would be an exponential decay, the decay constant of which is dictated largely by the P* value of the ocean over which it was occurring (present global average P* ~ 0.36 but could conceivably go as high as ~0.7).

          The decay constant should be only very weakly affected (if at all) by the gas exchange pump (itself dependent on surface roughness, wind speed, temperature etc). My understanding is that ocean oscillations and temperature variations would have little effects as they work much faster than the soft tissue and carbonate pumps.

          The oceanic phosphorus P* limitation arises from the fact that cyanobacteria (phytoplankton) have a fairly fixed composition – the so-called Redfield stoichiometry C106 H263 O110 N16 P1

        • http://www.ecoengineers.com/ Steve Short

          Forgot to mention that numerous empirical estimates for the atmospheric CO2 residence time provide values less than 12 years, and average 7 years (refer Segalstad).

          • Anonymous

            Steve,

            you mention the roughness of the water surface being a variable for CO2 uptake. I have read that winds have been less strong over the last decade. Would this DECREASE CO2 uptake, all else being equal, if true?

          • http://www.ecoengineers.com/ Steve Short

            It is my understanding from the series of 3 papers by Farquhar et al on the downward trend in land pan evaporation over the last 50 years that wind speeds have trended downwards over land but upwards over the oceans (don’t ask me why).

            This should mean that oceanic CO2 uptake rate increases hence the soft tissue and carbonate pumps should speed up.

            However it should also mean that the flux rate of oxygen into the surface layer should speed up perhaps reducing the remineralization depth (which transfers more CO2 back to the atmosphere). Clearly this is a field which is ripe for lots more work.

            Amazing isn’t that we know so little about the oceanic CO2 conveyor.

          • Anonymous

            OK, I won’t ask you why. Thank you for the answer.

            Anyone else have any ideas about why we would have wind over ocean increasing and over land decreasing??

  • geoffsherrington

    Steve Short, This might be of no relevence, but you mention “Jeffrey rightly points out that the relationship between pCO2 and any dependent variable is a decaying exponential, not a logarithmic curve. So, for example, if y is the % of Radiation Remaining and C is the CO2 Concentration, then the curve is y = e^-kC, where k is a positive constant. “The classic case is natural radioactive decay. We had the problem of Radon-222 gas in the open pit at Ranger Uranium. The excavators were fitted with a compressed air system to keep the Radon out of the cabin, because it harms the lungs.The partial chain runs …. Radium-226 (half life 1600 years) to Radon-222 (3.8 days) to Polonium-218 (3.1 min)…….If you pump the cabin free of Rn-222, then leave it, the subsequent build-up of radioacticity depends on the half life of any Radium-226 that might be there as contamination. The 3.8 day half life of Radon-222 does not set the rate of recharge of radon.Over now to natural global systems, where CO2 is degassing from the sea. If it follows the same rules, then the main figure of relevance in calculations is the release rate from the sea, not the residence time in the atmosphere. Any shock to current atmospheric CO2 levels has to take the (slow) rate of release from the sea into account when modelling. Of course, it is more complicated here because absorption has the be calcuated also.Steve, do you have separate confirmation that decaying exponentials are the correct equations to apply to CO2 in your scenario?

  • http://www.ecoengineers.com/ Steve Short

    Geoff, as you in effect point out the complement of a decay is an ingrowth. A simple decay is a exp(-k1t) term and an ingrowth is a [k2/(k2-k1)][(1 - exp(-(k2-k1)t] term where the k1 and k2 terms are the decay rates of daughter (product) and parent (source) concentrations. Of course, in the case of 226Ra and 222Rn, because k = ln2/half-life = 0.693/half-life so k2>>k1.The facile physical uptake of CO2 by the oceans is driven by the difference in gas pressure in the atmosphere and in the oceans and by the air–sea transfer velocity. Because pCO2 is increasing in the atmosphere, CO2 moves into the ocean in an attempt to balance the oceanic and atmospheric gas pressures.The mechanisms that control the speed with which the CO2 gas can move from the atmosphere to the oceans (air–sea transfer velocity) are not well understood. The physical transfer velocity is particularly related to the surface roughness of the ocean and the wind speed (for any constant water temperature) and there are numerous parameterizations covering this.However it is possible to bypass this 'choke' because, most importantly, the total reversible uptake of CO2 into the ocean is actually controlled not by the gas exchange pump referred-to above but by a combination of (a) the soft tissue pump (phytoplankton uptake), the (b) carbonate pump (formation of carbonate secreting phytoplankton) and the gas exchange pump. It is known that it is the (a) and (b) biological uptakes which dominate the long term reversible uptake and that these are controlled by the global mean preformed phosphate (Ppre) and surface total phosphate (P) levels in the sea. Biological uptake is parameterized as a linear damping of phosphate at the surface layer of a model where biological uptake depletes surface nutrients over a prescribed timescale tau(bio).The theory predicts a simple response of atmospheric pCO2 to perturbations in the inventory of regenerated phosphate, expressed in terms of a parameter P*. Atmospheric pCO2 decreases by ~30 ppmv for every 0.1 increase in globally averaged P*. Atmospheric CO2 can vary by approximately 300 ppmv between the minimum and the maximum efficiency of the soft tissue pump (0 < P* < 1)Climatological distributions of phosphate and oxygen indicate P* = 0.36 for the modern ocean. If P* were to increase up to 0.7, the simple theory suggest that atmospheric CO2 would be expected to decrease by 100 ppmv, which is similar to the difference in atmospheric pCO2 between the Last Glacial Maximum (LGM) and the Holocene. P* has some notable properties:● P* cannot be greater than 1.● P* is conserved in the interior ocean.● Water masses tend to exhibit distinct P* concentrations.For any given atmospheric CO2 and typical constant P* the relationship between the atmospheric partial pressure of CO2 (pCO2) and the timescale tau(bio) for development of that partial pressure is described by a typical ingrowth curve for pCO2 with a half life of the order of 10 – 15 years.In the modern ocean, the value of the globally averaged P* is approximately 0.36, indicating that 36% of phosphate returnsto the interior ocean through biological export and remineralization. Significantly for AGW, the soft tissue carbon pump of the modern global ocean is operating WELL BELOW the theoretical maximum efficiency. Sound familiar?Here is a typical reference (but consider yourself warned):http://ocean.mit.edu/~mick/Papers/ItoFollows-pr

  • DavidLHagen

    Steve noted:”Doubling the pCO2 concentration squares the proportion of radiation absorbed, y. However, temperature change does not follow a logarithmic curve, but instead is the complement of a decaying exponential.”and “the timescale tau(bio) for development of that partial pressure is described by a typical ingrowth curve for pCO2 with a half life of the order of 10 – 15 years.”(Thanks for that reference.)Is this CO2 absorption (into the ocean by biomass formation and carbonate precipitation) effectively an exponential decay? Or is it dominated in the near term by ocean oscillations and temperature variations?

  • http://www.ecoengineers.com/ Steve Short

    Yes, for any FIXED atmospheric pCO2 it would be an exponential decay, the decay constant of which is dictated largely by the P* value of the ocean over which it was occurring (present global average P* ~ 0.36 but could conceivably go as high as ~0.7). The decay constant should be only very weakly affected (if at all) by the gas exchange pump (itself dependent on surface roughness, wind speed, temperature etc). My understanding is that ocean oscillations and temperature variations would have little effects as they work much faster than the soft tissue and carbonate pumps.The oceanic phosphorus P* limitation arises from the fact that cyanobacteria (phytoplankton) have a fairly fixed composition – the so-called Redfield stoichiometry C106 H263 O110 N16 P1

  • http://www.ecoengineers.com/ Steve Short

    Forgot to mention that numerous empirical estimates for the atmospheric CO2 residence time provide values less than 12 years, and average 7 years (refer Segalstad).

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  • kuhnkat

    Steve,you mention the roughness of the water surface being a variable for CO2 uptake. I have read that winds have been less strong over the last decade. Would this DECREASE CO2 uptake, all else being equal, if true?

  • http://www.ecoengineers.com/ Steve Short

    It is my understanding from the series of 3 papers by Farquhar et al on the downward trend in land pan evaporation over the last 50 years that wind speeds have trended downwards over land but upwards over the oceans (don't ask me why).This should mean that oceanic CO2 uptake rate increases hence the soft tissue and carbonate pumps should speed up. However it should also mean that the flux rate of oxygen into the surface layer should speed up perhaps reducing the remineralization depth (which transfers more CO2 back to the atmosphere). Clearly this is a field which is ripe for lots more work.Amazing isn't that we know so little about the oceanic CO2 conveyor.

  • kuhnkat

    OK, I won't ask you why. Thank you for the answer.Anyone else have any ideas about why we would have wind over ocean increasing and over land decreasing??

  • cohenite

    Windspeed is decreasing over the land areas;

    http://www.agu.org/pubs/crossref/2007/2007GL031166.shtml

    Including Australia

    http://www.agu.org/pubs/crossref/2008/2008GL035627.shtml

    but I couldn’t find a piece on increasing wind speed over the oceans.

    • http://www.ecoengineers.com/ Steve Short

      Wentz et al. 2007, has data on oceanic wind speeds and is the paper which the Roderick et al team referenced. Here it is:

      http://www.remss.com/papers/wentz_science_2007.pdf

      “Climate models and satellite observations both indicate that the total amount of water in the
      atmosphere will increase at a rate of 7% per kelvin of surface warming. However, the climate
      models predict that global precipitation will increase at a much slower rate of 1 to 3% per kelvin. A
      recent analysis of satellite observations does not support this prediction of a muted response of
      precipitation to global warming. Rather, the observations suggest that precipitation and total
      atmospheric water have increased at about the same rate over the past two decades.”

      Very interesting paper too!

      Note that if rainfall is rising at the same rate as specific humidity this must only means that both cloud formation AND latent heat release rates are rising at the same rate.

      As latent heat release re-radiates about 63% downwards and about 37% upwards (to OLR) this suggests the latent heat ‘pump’ is keeping pace with any tropospheric warming.

      Tends to also support my contention that oceanic biogenic production of CCN must rise in concert with rising CO2.

      May be worthwhile checking out some of Frank Wentz’s other papers:

      http://www.remss.com/people/frank_wentz.html

  • cohenite

    Windspeed is decreasing over the land areas;http://www.agu.org/pubs/crossref/2007/2007GL031…Including Australia http://www.agu.org/pubs/crossref/2008/2008GL035…but I couldn't find a piece on increasing wind speed over the oceans.

  • http://www.ecoengineers.com/ Steve Short

    Wentz et al. 2007, has data on oceanic wind speeds and is the paper which the Roderick et al team referenced. Here it is:http://www.remss.com/papers/wentz_science_2007.pdf“Climate models and satellite observations both indicate that the total amount of water in theatmosphere will increase at a rate of 7% per kelvin of surface warming. However, the climatemodels predict that global precipitation will increase at a much slower rate of 1 to 3% per kelvin. Arecent analysis of satellite observations does not support this prediction of a muted response ofprecipitation to global warming. Rather, the observations suggest that precipitation and totalatmospheric water have increased at about the same rate over the past two decades.”Very interesting paper too! Note that if rainfall is rising at the same rate as specific humidity this must only means that both cloud formation AND latent heat release rates are rising at the same rate. As latent heat release re-radiates about 63% downwards and about 37% upwards (to OLR) this suggests the latent heat 'pump' is keeping pace with any tropospheric warming.Tends to also support my contention that oceanic biogenic production of CCN must rise in concert with rising CO2. May be worthwhile checking out some of Frank Wentz's other papers:http://www.remss.com/people/frank_wentz.html

  • cohenite

    Interesting Steve, especially this almost throwaway at the end:

    “Lastly, there is the possibility that the climate
    models have in common a compensating
    error in characterizing the radiative balance for
    the troposphere and Earth’s surface. For example,
    variations in modeling cloud radiative forcing at
    the surface can have a relatively large effect on
    the precipitation response (4), whereas the temperature
    response is more driven by how clouds
    affect the radiation at the top of the troposphere”

    Both of these cloud effects would seem to be moderating feedbacks to temperature increases.

    • http://www.ecoengineers.com/ Steve Short

      Whoever coined the phrase: ” Which came first, the chicken or the egg?” was of course the supremo of all eggheads….

      Frank Wentz would seem to be a very quiet achiever in a very noble tradition indeed.

  • cohenite

    Interesting Steve, especially this almost throwaway at the end:”Lastly, there is the possibility that the climatemodels have in common a compensatingerror in characterizing the radiative balance forthe troposphere and Earth’s surface. For example,variations in modeling cloud radiative forcing atthe surface can have a relatively large effect onthe precipitation response (4), whereas the temperatureresponse is more driven by how cloudsaffect the radiation at the top of the troposphere”Both of these cloud effects would seem to be moderating feedbacks to temperature increases.

  • http://www.ecoengineers.com/ Steve Short

    Whoever coined the phrase: ” Which came first, the chicken or the egg?” was of course the supremo of all eggheads….Frank Wentz would seem to be a very quiet achiever in a very noble tradition indeed.

  • kuhnkat

    Here is a good example of why your statement of ACO2 being so important is not necessarily valid:http://climaterealists.com/index.php?id=5436

  • http://www.moyhu.blogspot.com Nick Stokes

    No, it;s a convincing refutation by the authors of the Nature paper. Key quote:“Even if it did, the projected CO2 increase from the soils (0.1 Pg/yr) is around 1% of fossil fuel emissions (8 Pg/yr).”

  • cohenite

    Nick, the Bond-Lamberty paper on increased soil CO2 is a bit ambivalent about how much CO2 comes from this natural source; they do mention your figure of 100 mt pa since 1989 but they also mention that the total of this source of CO2 is 98 bt bigger than previously thought; apart from anything else this extra CO2 throws into question the measurement of total atmospheric CO2 concentrations and explains Gary Gulrud’s comment that the statutes of Callender and Keeling now have a few more dints in them.

    • http://www.moyhu.blogspot.com Nick Stokes

      I agree the reporting is confusing. But I’m just quoting one of the authors, in KK’s link.

      I think the confusion is this. They say total flux of CO2 from the soil is 98 Gt/yr. If that’s CO2 and not 98 Gt C, it sounds about right. They say their estimate is 15% higher than previously measured. Again, it’s a hard number to pin down, so a 15% discrepancy is not surprising.

      Separately, they say that the flux has been increasing by 100 Mt/yr. That’s separate from the total measure issue – I assume they have a different way of estimating the flux increase. They point out that this is small relative to fossil fuel use.

      None of this has anything at all to do with the measurement of atmospheric CO2.

  • cohenite

    Nick, the Bond-Lamberty paper on increased soil CO2 is a bit ambivalent about how much CO2 comes from this natural source; they do mention your figure of 100 mt pa since 1989 but they also mention that the total of this source of CO2 is 98 bt bigger than previously thought; apart from anything else this extra CO2 throws into question the measurement of total atmospheric CO2 concentrations and explains Gary Gulrud's comment that the statutes of Callender and Keeling now have a few more dints in them.

  • http://www.moyhu.blogspot.com Nick Stokes

    I agree the reporting is confusing. But I'm just quoting one of the authors, in KK's link. I think the confusion is this. They say total flux of CO2 from the soil is 98 Gt/yr. If that's CO2 and not 98 Gt C, it sounds about right. They say their estimate is 15% higher than previously measured. Again, it's a hard number to pin down, so a 15% discrepancy is not surprising.Separately, they say that the flux has been increasing by 100 Mt/yr. That's separate from the total measure issue – I assume they have a different way of estimating the flux increase. They point out that this is small relative to fossil fuel use.None of this has anything at all to do with the measurement of atmospheric CO2.

  • cohenite

    If the total CO2 flux is 15% bigger surely that must impact on both the size of the sinks and the total CO2 concentration.

    • http://www.moyhu.blogspot.com Nick Stokes

      No. Air CO2 is as measured. Accounting for its sources is harder.

      If you want to know your weight, you check the scales, rather than estimate your calorie intake.

  • cohenite

    If the total CO2 flux is 15% bigger surely that must impact on both the size of the sinks and the total CO2 concentration.

  • kuhnkat

    Nick,the soil is estimated to emit 98Pg/yr and humans you said earlier 10. you only quote the estimated INCREASE of soil emissions. Again, the human contribution to the system is still TINY!!!The unknowns and error bars swallow the human contribution.You and others are silly touting it as a huge deal.

  • http://www.moyhu.blogspot.com Nick Stokes

    I think it's 98 Pg CO2, or about 30 Pg C. Humans 10 Pg C. But it's the old story, constantly muddied. The soil emission is C that was recently taken from the air by photosynthesis. It's just part of the cycling of C between atmosphere and biosphere. The human 10 Pg is new C added to the system.

  • http://www.moyhu.blogspot.com Nick Stokes

    No. Air CO2 is as measured. Accounting for its sources is harder.If you want to know your weight, you check the scales, rather than estimate your calorie intake.

  • http://www.moyhu.blogspot.com Nick Stokes

    I think it's 98 Pg CO2, or about 30 Pg C. Humans 10 Pg C. But it's the old story, constantly muddied. The soil emission is C that was recently taken from the air by photosynthesis. It's just part of the cycling of C between atmosphere and biosphere. The human 10 Pg is new C added to the system.

  • http://www.moyhu.blogspot.com Nick Stokes

    No. Air CO2 is as measured. Accounting for its sources is harder.If you want to know your weight, you check the scales, rather than estimate your calorie intake.

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