CO2 Emissions And Ocean Flux: Long-Term CO2 Increase Due To Emissions, Not Ocean Temperature

If you take the annual CO2 atmospheric content, and differentiate it, that is calculate the year-to-year change, then you get a plot that looks a lot like the ocean temperature. This has led many people to think that the ocean is the source of the additional CO2. This is not the case.

The additional CO2 is from about one-half of our emissions. The year-to-year “noise” is from the year-to-year change in ocean temperature riding on the change from our emissions. Changes in our emissions are somewhat filtered by the time constant of CO2 biosphere absorption. Here is what happens.

Many of you will be familiar with the concept of “half-life” from radioactive decay. For a radioactive element, half of the radioactivity will decay in a certain period of time, then half again in the next period, and so on until the radioactivity can no longer be detected. The same principle applies to absorption. Half of a compound will be absorbed in a certain period, then another half in the next period, then another half, and so on. Here is the curve for a pulse of CO2 absorbed into the biosphere.

CO2 Fraction Absorbed

Figure 1 is the absorption curve for a single pulse of CO2 emitted into the atmosphere. The half-life of that pulse is a bit over 8 months. It is undetectable after about six years.

Imagine that you have just taken a deep breath, held it until the maximum CO2 has been exchanged, then exhaled. Half of the CO2 in that puff will be gone from the atmosphere in 8 months, 33% will remain in a year, only 11% will be around in 2 years, and so on. The series is actually 1/3, 1/9, 1/27, 1/81… Now add up all breathing for many years, or all the fossil fuel emissions.

Summation Half-Lives

In Figure 2 above the top gold trace is the summation of all the individual annual half-life traces. For instance, year one is the sum of the remainders from year -4 to year zero. It is the sum of 1/243 + 1/81 + 1/27 + 1/9 + 1/3 = very close to 1/2. The CO2 fraction that we observe is close to 0.5. If emissions completely ceased in year six, the extra CO2 added to the atmosphere would be nearly zero in year 10.

Annual Emissions and Remainder

Figure 3 is a plot of annual fossil fuel emissions and the amount of those emissions that annually remain in the atmosphere. The remainder plot has been corrected for half-life.

Remaining Fraction Compared

Figure 4 is a plot of the fraction of emissions that remain in the atmosphere, the ocean temperature anomaly (from UHA satellite data), and the change (delta) in emissions with the data corrected for half-life using the fraction change data. (The half-life has been decreasing over time by 2.8% per decade). The left scale is for both the remaining fraction and temperature anomaly. The right scale applies to the delta emissions (the annual change in added emissions). This is scaled to match the fraction change. On a year-to-year basis the ocean temperature changes overwhelm the emission changes, but not the emissions themselves.

SST Change CO2 Change

Figure 5 is a plot of  change: SST, CO2, and annual emissions added since 1980. This is the annual delta (differential) of all three. The Mt. Pinatubo cooling and the 1998 and 2010 El Niño warming is clearly visible in the CO2 data. It looks like the CO2 increase is due to ocean temperature, but this is an illusion. The annually added emissions are much larger than the ocean temperature CO2 flux change.


Figure 6 is a scatter plot of CO2 and SST anomaly with a linear trend applied. The trend is 17,239 million metric tonnes of CO2 emitted per degree C of SST change. Now look back at Figure 6. The long term change in temperature is about 0.3°C. This would be equivalent to about 5 billion tonnes of CO2. But the increase in CO2 over that time period was 483 billion tonnes, about 100 times that amount. The long-term CO2 increase is due to emissions, not ocean temperature. Temperature drives only the short-term changes.

About half of fossil carbon emissions appear to be responsible for the atmospheric CO2 rise, and that fraction is decreasing. The year-to-year changes in the CO2 rise are mostly due to ocean temperature changes, but those changes should be considered weather.


45 responses to “CO2 Emissions And Ocean Flux: Long-Term CO2 Increase Due To Emissions, Not Ocean Temperature”

  1. sod

    I actually agrre with the majority of this post!

  2. A C Osborn

    Changed your mind then

    So does the trend in the Increase in Atmospheric CO2 equal the Trend in increases in CO2 Emissions?
    As I thought the Atmospheric increase was fairly constant whereas Human out put has increased dramatically in the last 25 years.

  3. Stephen Richards

    So what you are saying is that the oceans are co² saturated.
    They have to be under your hypothesis because if they were not they would absorb at a constant rate with wind stirring noise in the level. Wouldn’t they?

  4. Frederick Colbourne

    Can this model be validated by the isotope composition of the atmosphere?

  5. MJSnyder

    Thanks Ed.
    How does this jibe with the IPCC assertion that CO2 remains in the atmosphere for 100 years or more?

    1. DirkH

      Well that’s a completely ludicrous statement by the IPCC.
      Seasonal fluctuations of ocean outgassing/absorption.
      natural 770000 (Mill t of Gas)
      human 23000
      absorption 781000
      Annual increase 11700
      Total amount 3.16×1015 kg = 3.16×1012 t= 3.16×10^6 Mt= 3.16×10^3 Gt

      1. DirkH

        So, at 3160,000 Mill t total, yearly turnover is about 1/4.5 it seems. So, a 100 years? Whatever they mean with that, they only know themselves.

  6. AndyG55

    “The long-term CO2 increase is due to emissions, not ocean temperature.”

    If true, this is good news, because China et al will be continuing to push life giving CO2 into the atmosphere for a long, long time.

    Towards 700+ ppm !

    Let the world’s plant life breathe and flourish.

    1. David Appell

      Plants are doing fine, and were at 280 ppm. Increasing atmospheric CO2 for their sake is beyond reckless (and many plants wouldn’t do well in the higher temperatures and changed precipitation patterns.

      1. AndyG55

        NO, plants do mediocre at 280ppm. It is borderline CO2 level. It like a human living on stale bread and water.

        Plants luv much higher levels and thrive when allowed a reasonable level of plant food and nutrients. And as all greenhouse horticulturalists know, the level is 1000+ ppm

        And what higher temperatures?? They haven’t changed by more than a degree for a long, long time.

      2. AndyG55

        And yes, plants are starting to do fine, because of the increased atmospheric CO2 levels.

        You really need to brush on basic plant biology such as stomata density, transpiration etc etc..

        There are literally thousands of papers showing that plant start to grow more strongly as CO2 increases, and are not at all happy below or near 280ppm.

  7. Bart

    “Here is the curve for a pulse of CO2 absorbed into the biosphere.”

    That is a model curve, not an actual observation. But, let’s go with it…

    “The series is actually 1/3, 1/9, 1/27, 1/81… Now add up all breathing for many years, or all the fossil fuel emissions.”

    I’m sorry, but this is not a legitimate analysis. You cannot extrapolate the fractional remainder of a step response to the fractional remainder of a ramping input (and, CO2 emissions have been ramping up – they didn’t just jump up to their present level and halt). You miss an entire polynomial degree doing that.

    We can approximate your decay series based on exponential decay with half life of 8 months. Then, exp(-8/tau) = 0.5, so the time constant tau = 11.5. Each month, we will retain exp(-1/tau) = 0.917 of the previous inventory.

    So, we have a series

    C(k) = 0.9170*C(k-1) + in(k)

    where each step k represents a monthly interval. If you inject a one-time unit pulse, and watch the decay, this gives 8 months, 1 year, 2 years, etc… to be 0.917^[8 12 24] = [0.5000 0.3535 0.1250], so pretty close to your values.

    Let’s make in(k) a unit ramping input.

    C(k) = 0.9170*C(k-1) + k

    The asymptotic response (for k large) is approximately

    C(k) = := k/(1-0.917) -133

    The cumulative sum, however, is

    S(k) = S(k-1) + k = k*(k+1)/2

    The virtual accumulated sum S(k) is quadratic in k, while the C(k) series is only linear, just like the input (that’s what a negative feedback does, it makes the output track the form of the input). They diverge substantially over time.

    The amount C(k) relative to the virtual accumulation S(k) is not 1/2, it is asymptotically (k/(1-0.917) – 133)/(k*(k+1)/2) or more asymptotically 24/k, which is 1/n for n in years. Within two years, it less than 1/2. In 50 years, it is 0.02. (See actual curve for fraction remaining versus months here).

    This is why your mdoel does not work. It does not allow long term tracking of the virtual accumulation at some constant, or even nearly constant, factor. It takes down the resultant curve by a full polynomial degree, resulting in progressive divergence.

    “Figure 3 is a plot of annual fossil fuel emissions and the amount of those emissions that annually remain in the atmosphere.”

    Again, this is just a model. It is not based on anything but desired outcome.

    “Figure 4 is a plot of …”

    Another model.

    “Figure 6 is a scatter plot of CO2 and SST anomaly with a linear trend applied.”

    Again, an inappropriate method of analysis. The sensitivity of CO2 to temperature is not in units of ppmv/degC. It is in units of ppmv/degC/unit-of-time. There is an integral relationship with time.

    This plot does indeed show, unequivocally, that human inputs have very little impact on atmospheric CO2. Atmospheric CO2 evolves according to a differential equation

    dCO2/dt = k*(T – T0)

    i.e., the change in CO2 from one epoch to the next is the integral of an affine function of temperature anomaly. Human inputs are essentially superfluous. If I want to know the atmospheric CO2 at any given time in the last 57 years, all I need is the starting value, and the temperature data to integrate this equation, and I will get a very close result.

    It is the nature of negative feedback systems to track the level dictated by boundary conditions, and sharply attenuate disturbances. That is all we are, a small disturbance. There is nothing unusual or exotic about this. The Earth’s CO2 regulatory system shrugs off our puny inputs with barely an acknowledgement, and goes where it wants to go.

    1. Bart

      BTW, you can fix this to have atmospheric CO2 track emissions, somewhat, with a 1/2 fraction if you extend your decay rate out (a very long way) and basically put half the emissions into the oceans with rapid dynamics. This is what the standard modeling does.

      It doesn’t mesh with the observations, though, because CO2 absolutely depends on temperatures to the tune of

      dCO2/dt = k*(T – T0)

      There is a ramp observable in T, and that ramp must be responsible for the ramp in dCO2/dt. But, emissions also have been ramping up. There is no room for this additional ramp input, because the ramp in dCO2/dt is already accounted for by the temperature relationship.

      Ergo, CO2 in the atmosphere is regulated by a feedback system which tracks the above equation, and severely attenuates the emissions input.

      1. Ed Caryl

        The point is that the ramp in Temperature is 100 times too small to account for the ramp in CO2. Only the ramp in emissions is large enough.

        1. Bart

          That simply isn’t the case. There is a seamless correlation between the temperatures and the rate of change of CO2, from low frequency (the ramp) to high frequency (the variations).

          That means a temperature modulated process is driving atmospheric CO2. Human emissions are not temperature modulated, hence they cannot be the dominant driving force.

    2. Ed Caryl

      First, I said a pulse, not a ramping input. That whole bit is intended as an approximation. My point is that only some (about a third) of emissions this year are absorbed this year.
      Figures 3 and 4 are calculated from measurements, they are not models. They are based on emissions and CO2. The CO2 is converted to tonnes of CO2. There is no “desired outcome”.
      In figure 6 the unit of time is one year.

      1. Bart

        It’s a bad approximation. If yearly emissions have a ramp in them, then the virtual accumulation of those emissions will be quadratic, yet the output of the process you have described would still be linear. They diverge. Rapidly. Within a few years, they are nowhere near having a 2:1 ratio.

        “Figures 3 and 4 are calculated from measurements, they are not models.”

        The figure descriptions claim a fraction remaining in the atmosphere. That is supposition. That is imposing a model. There is no reason anything remaining has to have any relationship to emissions at all. If sinks are active, and they are, they can absorb every bit of the emissions, and whatever is left has to be from natural tracking of level imposed by boundary conditions.

        This is getting worryingly close to the horrible “mass balance” argument, in which it is argued that, because the rise is less than what we have put in, it has to be due to what we have put in. It does not, and the “mass balance” argument is utterly fatuous.

      2. Bart

        It’s a bad approximation. Further discussion held up in moderation.

  8. Brian

    Ed, what about the time-lag, between temperature and CO2 concentration (as shown in the differential). Does this tell us anything?