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Murry Salby's Correlation Conundrum

Posted on 5 July 2012 by Dikran Marsupial

Prof. Murry Salby of the Department of Environment and Geography at Macquarie Universiry in Sydney gave a talk last year (August 3, 2011) to the Sydney Institute (described at Wikipedia), in which he claimed that the rise in atmospheric CO2 is not driven by anthropogenic emissions. The abstract of the talk is as follows:

Atmospheric Science, Climate Change and Carbon – Some Facts

Carbon dioxide is emitted by human activities as well as a host of natural processes. The satellite record, in concert with instrumental observations, is now long enough to have collected a population of climate perturbations, wherein the Earth-atmosphere system was disturbed from equilibrium. Introduced naturally, those perturbations reveal that net global emission of CO2 (combined from all sources, human and natural) is controlled by properties of the general circulation – properties internal to the climate system that regulate emission from natural sources. The strong dependence on internal properties indicates that emission of CO2 from natural sources, which accounts for 96 per cent of its overall emission, plays a major role in observed changes of CO2Independent of human emission, this contribution to atmospheric carbon dioxide is only marginally predictable and not controllable.

Naturally the talk stirred considerable interest in the blogsphere (e.g. at Climate Etc.).  More recently, a video of this talk was made available, so we can now investigate Prof. Salby's argument in more detail.


Why we can be Confident that Prof. Salby's Conclusions are Incorrect

Ironically, the first 11 minutes of the talk provide all the components required to show beyond reasonable doubt that anthropogenic emissions are responsible for 100% of the observed increase in atmospheric CO2 and that natural sources do not play a major role. At 08:39, Prof. Salby correctly states that

"What is relevant is net emissions, net collected from all sources and sinks, human and natual, that is what ultimately controls atmospheric CO2"

This is then supported by a slide (at 8:58) containing an equation that will be familiar to those that have followed the discussion of earlier claims that the rise in atmospheric CO2 is a natural phenomenon at SkS, for example my rebuttal of Prof. Essenhigh's residence time argument.

This is known as the mass balance equation, and it simply states that as the carbon cycle obeys the principle of conservation of mass, the annual increase in atmospheric CO2 is equal to the difference between total emissions from all sources (both natural and anthropogenic) and the total uptake from all sinks (natural and anthropogenic, although the anthropogenic sink is essentially zero as we are not yet performing significant amounts of carbon sequestration).

For convenience, we can re-write Prof. Salby's mass balance equation in the form

C' = Ea + En - Un,

where Ea represents annual carbon emissions from anthropogenic sources (fossil fuel use and land use change), En represents the carbon emissions from all natural sources (the oceans, soil respiration, volcanos etc.) and Un represent the uptake of carbon by all natural carbon sinks (oceans, photosynthesis, etc.).  C' represents the net emissions rate, which as Prof. Salby says is approximately equal to growth rate of global mean atmospheric CO2.

The problem is then that we don't know the values of En and Un with any real certainty as our knowledge of the natural carbon cycle is limited.  However, we do have good knowledge of anthropogenic emissions, Ea, as Prof. Salby says (at 7:53)

"In truth only one component of the CO2 budget is known with any certainty, human emissions, implicitly through records of extraction - how much coal and oil are dug up"

There are also good records of emissions due to land use changes as well.  We also have reliable observations of the growth rate of CO2 in the atmosphere, as Prof. Salby says (10:35)

"That [CO2 being well mixed in the atmosphere] is a good thing because it means that local values are good approximations of the global average, which in turn provides a record of net global emissions.  In fact we have a long record of CO2 from only one site in the free atmosphere, Mauna Loa Hawaii.  The local record from Mauna Loa therefore approximates the global mean, which through its growth rate chronicles the history of net global emissions, collectively from all sources, human and natural."

In other words we can reliably work out the net emission rate from the Mauna Loa CO2 record by computing the annual growth in atmospheric CO2, i.e. C'.

This allows us to find out something interesting about the natural carbon cycle:  The mass balance equation can be rearranged to give an estimate of the difference between annual emissions from all natural sources and annual natural uptake by all natural sinks.

En - Un = C' - Ea

While we don't know the values of En or Un, the difference between them is constrained by conservation of mass to be the same as the difference between C' and Ea, which we do know!  More importantly if we knew the right hand side of this equation was negative, then we would know that the left hand side must also be negative, so whatever their actual values, Un > En.

O.K., so if we look at the data (for details, see Cawley, 2011), we find that the annual rise in atmospheric CO2 has been less than anthropogenic emisssions every year for at least the last fifty.  We therefore can also be sure that the natural environment has been a net carbon sink, taking in more carbon than it has emitted, every year for the last fifty.  As the natural environment is known to be a net carbon sink, far from being the cause of the observed rise in atmospheric CO2, it has been actively opposing it!

illustration of CO2 mass balance

Figure 1: Results of the mass balance analysis.

This analysis is based on three assumptions:

  1. The carbon cycle obeys the principle of conservation of mass (i.e. the annual growth in atmospheric CO2 is approximately equal to the net emission rate, which is the difference between emissions from all sources and uptake by all sinks).
  2. We know anthropogenic emissions, Ea, with reasonable certainty.
  3. We can reliably estimate the net emissions rate, C', from the Mauna Loa atmospheric CO2 record.

The rest is just trivial algebra.  Prof. Salby has explicitly accepted all three of these assumptions in the quotes presented above taken from his Sydney Institute talk, but unfortunately did not see the natural conclusion arising from those (very reasonable) assumptions.  We know with high certainty that the rise in atmospheric CO2 is not a natural phenomenon and is 100% anthropogenic (at least since 1959).

Prof. Salby's Argument

Prof. Salby's argument appears to be based on an observed correlation between net global emissions (estimated from the Mauna Loa CO2 observations) and "surface conditions", a combination of MSU temperature and soil moisture, as shown in the figure below, from the slide at 17:52 in the Sydney institute talk.

 

Figure 2: Correlation between net global CO2 emissions and the component due to "surface conditions" (temperature and soil moisture).

 The correlation is indeed impressive, clearly there is a relationship between net global emissions and the component due to "surface conditions".  Prof. Salby then determines the contribution to atmospheric CO2 by calculating the cumulative sum of the component due to "surface conditions, which appears to explain essentially all but the annual cycle in the Mauna Loa observations, as shown in this figure from 20:53 in the video.

 

Figure 3: The component of the increase in atmospheric CO2 attributed by Prof. Salby to "circulation dependent component"

 The flaw in this argument is quite subtle, and lies in the fact that the bulk of the long term increase in atmospheric CO2 is due to the mean value of net global emissions, and correlations do not depend on the mean value.  Essentially the correlation only explains the variability of CO2 measurements around the long term trend, but not the trend itself.  Sadly, Prof. Salby's presentation did not include nearly enough information to reproduce the graphs shown above, so I will explain the flaw in his reasoning first via a simple thought experiment, and then illustrate the mainstream understanding of this issue, that is based on the correlation between the annual growth rate and the El Nino Southern Oscillation (ENSO), which was first mentioned in the peer reviewed literature way back in 1979.

 A Simple Gedankenexperiment

Let us assume for the moment that the CO2 observations are composed of a linear component due to anthropogenic emissions, rising at a constant 1.5 ppmV per year, plus a sinusoidal component that was due to the effects of "surface conditions", with a period of five years, such that

C(t) = 1.5*t + 0.5*cos(2*pi*t/3)*sin(2*pi*t/5) - 2630

The numbers are chosen such that the resulting CO2 observations superficially resemble those of the real world (except for the seasonal variation which is not relevant to the thought experiment).

Figure 4: Synthetic atmospheric CO2 observations for thought experiment

Following Prof. Salby's method, we then take the annual differences to estimate the net global emissions:

 

Figure 5: Net global emission derived from synthetic CO2 observations shown in Figure 4.

So far, so good, our synthetic net global emissions are similar to Prof. Salby's in that there is an average value of about 1.5 ppm per year, but superimposed on top of that there is an oscillatory behaviour that sometimes reduces net global emissions almost (but not quite) to zero, and sometimes means that net global emissions are much higher than average.

Happily, as this is a synthetic thought-experiment, we can work out the natural contribution to net global emissions analytically, and we get this:

 

Figure 6: Natural contribution to net global emissions.

Which looks very much like net global emission, and if we compute the correlation between the two then we get a value of 1, i.e. a perfect correlation!  This means we can conclude that the natural component "explains" 100% of the variability in net global emission - obviously we are onto something here!

So, again following Prof. Salby's methodology, we compute the cumulative sum of the natural contribution to net global emission, which gives us the natural contribution to the increase in observed CO2, which gives us this:

Figure 7: Natural contribution to the long term increase in atmospheric CO2.

Oh...., that doesn't look very much like the result obtained by Prof. Salby; the natural component doesn't seem to explain the long term increase at all, even though it is perfectly correlated with the net global emission!

So what is going on?  Well if we compare net global emission (Fig. 5) with the natural contribution to net global emission (Fig. 6), they are identical, except for their mean values.  The mean value of net global emission is about 1.5 ppmv per year, and for the natural contribution it is zero.  When we compute the cumulative sum of the natural contribution, the positive values cancel with the negative values, so the cumulative sum stays near zero.  Thus we can see that the long term rise is principally because of the mean value of net global emission, not because of the wiggles.  Why doesn't the correlation reveal this?  Here is the formula for the sample correlation (courtesy of Wikipedia):

where xand y represent samples from net global emissions and the natural component respectively.  They important thing to notice is that the mean (x or y with a bar over the top) is subtracted from x and y wherever they appear in the equation.  This means that the value of the correlation is the same no matter what the mean values of x and y are.  Thus the correlation doesn't tell you very much about the cause of the long term rise, because that is mainly due to the mean value, not the variablity around the mean.

Next, let's perform the same exercise for the anthropogenic component of the net global emission, which is just 1.5 ppmV per year.

Figure 8: Anthropogenic contribution to net global emission.

If we compute the cumulative sum of the anthropogenic contribution to net global emission, we get the component of the observed increase in CO2 that is due to anthropogenic emissions, which is a steady linear trend rising at 1.5 ppmv per year.

Figure 9: Anthropogenic contribution to the long term increase in atmospheric CO2.

Which clearly does a much better job of explaining the long term trend in atmsopheric CO2, even though the correlation between the anthropogenic component and net global emission is precisely zero!

Key Point: It isn't the variability (the general up and down wiggliness) in net emissions that gives rise to the long term trend, it is the mean value of the net emissions, and the value of the correlation does not depend in any way on the mean value.  Therefore the correlation with net global emission tells you very little about the cause of the long term trend.

What does Mainstream Science say about all this?

It is well known that the annual growth rate of CO2 appears to be influenced by the El Nino Southern Oscillation (ENSO); this correlation was first noticed by Bacastow more than thirty years ago (Bacastow, 1979), and has been widely discussed since then.  The effect of ENSO however is not principally due to changes in sea surface temperatures, but the effect of ENSO on the terrestrial biosphere: According to Jones et al (2001).

"Climatic changes over land during El Nino events lead to decreased gross primary productivity and increased plant and soil respiration, and hence the terrestrial biosphere becomes a source of CO2 to the atmosphere. Conversely, during El Nino events, the ocean becomes a sink of CO2 because of reduction of equatorial Pacific outgassing as a result of decreased upwelling of carbon-rich deep water. During La Nina events the opposite occurs; the land becomes a sink and the ocean a source of CO2."

It seems possible that the effects of temperature and soil moisture investigated by Prof. Salby are essentially a proxy for ENSO as ENSO affects both temperature and precipitation in the Americas and Australasia.

Prof Salby suggests that the IPCC were not aware of the variability in growth rate discussed in his presentation (29:30):

"The climate modelling framework just described [i.e. one based on the assumption that CO2 levels are predictable] is the cornerstone of the IPCC, ..., I used to be a reviewer.  Much of the public debate stems from the IPCC's last report; the behaviour you have seen was not known at the time of that report".

However, these interannual changes in the carbon cycle are discussed in section 7.3.2.4 of the IPCC AR4 WG1 report.  This states that the variability of fossil fuel emissions and estimated variability in net ocean uptake are too small to account for this signal and is therefore thought to be due to year-to-year fluctuations in the land-atmosphere fluxes.  Furthermore. it states that high CO2 growth rates correspond to El Nino conditions and conversely low growth rates with La Nina conditions.  An additional period (1992-3) of low growth rate followed the eruption of Mount Pinatubo in 1991.  References are also provided to support various lines of evidence confirming that the variability of CO2 fluxes is mostly due to land fluxes.

Notes

I have sent several emails to Prof. Salby asking for clarification on the methods he used in the work described in his Sydney Institute talk, but so far I have had no reply.

References

Bacastow, R.B.  1976.  Modulation of atmospheric carbon dioxide by the Southern Oscillation.  Nature 261: 116-118. (www)

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Comments 1 to 50 out of 61:

  1. DM,

    In your link to Climate etc above Judith Curry predicted that Salby's paper with his potentially "AGW science revolutionising analysis" would be published in a journal within 6 months...about 6 months ago. Has it seen the light of day?
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  2. Oneiota In fact it is now 11 months since Prof Curry claimed that it was "in print" and was expected in 6 months. Salby has since indicated that he is having trouble getting it accepted (how does that figure with "in print"). To quote


    The technical paper underpinning my presentation to the Sydney Institute
    has certainly not been withdrawn. The cycle of scientific publication is slow,
    typically about a year. For a subject as political as this one, it can
    be very slow.
    The fiasco surrounding Spencer and Braswell (2011), a thinly-veiled exercise
    in coercion, didn’t help. But, with patience, we will eventually get there.




    In due course I expect that we will see either an "Energy and Environment" paper or a WUWT post claiming yet another conspiracy to block the publication of an inconvenient paper or possibly both.
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  3. It is beyond my comprehension, why the simple arithmetic equasion:
    1) En - Un = C' - Ea
    2) the principle of conservation of mass
    altogether understood by primary school kids;

    are being denied by contrarians like Salby, who confuses the issue by taking about correlations, instead.

    The only explanation is: Salby hopes that people are less likely to know about correlations, or specifically about their irrelevance to the subject question. In other words: his hopes are to confuse the simple issue rather than to explain it.

    The same observation applies to larger teachings on the subject of AGW. E.g.: why am I confused/find hard to understand what I'm reading on WUWT or in contrarian books like Heaven+Earth? As opposed to the clarity and simplicity of information here on SkS or in books by people like James Hansen? Precisely, because contrarians are interested in spreading disinformation and confusion only. The case of prof Salby here is a classic one.
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  4. This is the typical denier tricks: remove the trend and then claim there is no trend!
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  5. @oneiota and @skepticalwombat I have tried contacting Prof. Salby, pointing out the lines of reasoning that show his conclusion to be false, and asking for clarification on exactly how the analysis was performed, but have recieved no reply (I also sent him an early draft of this blog post for comment). I would hope that the paper has now been withdrawn.
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  6. Scpetical Wombat at #2:

    Salby has since indicated that he is having trouble getting it accepted (how does that figure with "in print").

    [snip]

    In due course I expect that we will see either an "Energy and Environment" paper or a WUWT post claiming yet another conspiracy to block the publication of an inconvenient paper or possibly both.


    Another option is The Science World Journal, which would publish it without critical assessment... as a recent issue has shown with respect to another mathematically-challenged paper.
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  7. Sorry, Spectacled Wombat!
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  8. I just tried to watch the video but the embedding has been disabled.
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  9. HH @8 - yes, the YouTube host has disabled embedding of this video, but you can watch it by clicking on the link provided when you try to play it.
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  10. May I suggest that Dr. Salby submit his paper to the Journal of Scientific Exploration (JSE)?

    JSE publishes cutting-edge research like this. (I forget who found this gem -- otherwise, I'd give due credit.)
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  11. Here's an alternative (simpler, though less mathematical) way to explain it.

    During El Niño events, atmospheric CO2 grows faster, and during La Niña events, atmospheric CO2 grows slower. That does not mean that the oceans and soils emit more CO2 during El Niño, and emit less during La Niña (as Salby would have us believe).

    Rather, it means that the oceans and soils absorb less CO2 during El Niño, and absorb more CO2 during La Nina.

    The correlation is real, but Salby's interpretation of its meaning is exactly reversed from what's really happening.
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  12. As a Chemical Engineer, I deal every day with mass, energy, and momentum balances. I just want to pull every hair from my head every time I see such cranks!!! I mean, ancient sophists would have declare him their supreme leader.
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  13. My vote is Principia Scientific International.
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  14. Caerbannog - John Mashey, surely?
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  15. ...net collected from all sources and sinks... that is what ultimately controls atmospheric CO2.
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  16. I guess it would be a study in behavioral economics where we might say that this convoluted conjecture in science is far easier to wrangle than ramifications of human caused climate change. This is because fore-shortened survival scenarios, and violent weather/wild fire events appear increasingly more often in a changing climate that stupidly, we have refused to mitigate.

    So any convoluted, twisted and wrong theories of climate is going to be easier to ponder and invent than considering our painful demise, reviewing shameful blunders, noting the deliberate deceits, and standing up to blatant marketing PR manipulations in support of rapacious carbon capitalism.

    It is not very wise, but it may just be easier for some people to contort, ignore and deny.

    Thank you so much for not allowing it to fester.
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  17. Seems to me that the problem is that anthropogenic emissions are (roughly) constant during the analysis period. If we look at the broader picture and compute a correlation coefficient with a dataset that spans a period of time with and without human emissions, then we would get a nicer fit, right?

    As an analogy, what Salby is doing seems to me like taking the temperature of a sick child during a week and computing the rate of increase and decrease. Then try to correlate it with , let's say, influenza virus counts in his blood and with time of day. Let's assume that there's a day-night cycle in our body temperature and that the rate of increase in temperature produced by the virus is constant. Then the variations in rate of increase in temperature would be only explained by the night-day cycle and the influenza virus would have nothing to do with it.
    This way we can conclude that cause of his fever is not influenza, but the night-day cycle. There's no need to give this child any treatment.

    Also, any treatment would cripple his family's economy... and the rise in temperature is plant food... I mean, it's good for him.
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  18. So if your business has revenue of $10 a week and costs of $9, but I steal $2 a week the reason you go broke is those costs and not my theft.

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    Moderator Response: [Dikran Marsupial] Accusation of dishonesty deleted. Please lets keep to the science and avoid discussion of motives.
  19. Tony O, I do not think the channel is Salby's. More likely to be that of The Sydney Institute
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  20. Dikran,
    in the Judith Curry thread link above there was a disagreement between Bart and Ferdinand Engelbeen on the mass balance argument that i
    think should be mentioned.

    the disagreement hinges around the issue that the mass balance argument alone is insufficient to conclude that C' is due to Ea. that is another
    possibility is that all Ea is taken up by the environment which also emits excess carbon equal to C'.

    of course no physical mechanisms are described to explain this possibility.

    as far a i can make out, the argument is that since |En|,|Un| >> |Ea| or |C'| i.e. the absolute magnitude of natural emissions or uptake is so much more massive
    than the anthropogenic emission or the net emission rate all the following can be simultaneously satisfied

    |En - Un| can be bounded and decreasing
    En > E(n-1) and Un > U(n-1) there is a increasing trend in both emission and uptake over the last 50 yrs
    trend in Un rises faster than the trend in En

    this will allow a more complicated model of rise in net emissions where all Ea is absorbed by the natural environment Un but En is responsible
    for all of C'.
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  21. oarobin - so in essence that claim is that some mysterious mechanism absorbs all of human carbon emissions, and that natural emissions increase to compensate for this. I am curious as to how this mystery mechanism is able to identify and target only human carbon emissions, and more importantly, why?
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  22. Rob and oarobin - in principle it is possible that one natural source has increased its emissions, whereas another has increased its uptake. For example, it is possible that the oceans are a net emitter with this net emission being larger than the anthropogenic emissions. However, that requires an ENORMOUS net uptake from another source, such as the biosphere.

    We know, however, that this is not plausible: the biosphere would have had to take up hundreds of gigatons of CO2 in the last decade alone. Moreover, we should not have seen a decrease in ocean pH in that case.

    But how about the reverse situation? That is, the biosphere being the net emitter, larger than that of the anthropogenic emissions? It is possible that the oceans take up this much CO2. However, the biosphere would have had to decrease with several hundreds of gigatons of CO2 in the last decade alone. This should have been directly visible. Now, imagine that this net loss must have been sustained over several decades (at the very, very least since 1959): we must have observed such an enormous decrease in the biosphere (hundreds of gigatons of C, thousands of gigatons of CO2).
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  23. Oarobin & Marco, it really does not matter whether natural emissions and/or uptake are changing over time. That has no impact on the mass balance argument.

    We know that the rate at which humans are releasing fossil fuel carbon into the atmosphere is GREATER than the rate that carbon is accumulating in the atmosphere. Pick a year for the past few decades... there is sufficient data to calculate both of those values and show that human emissions have consistently exceeded atmospheric accumulations. Ergo, we also know that for that time period natural carbon sequestration has exceeded natural carbon emission and the atmospheric increase has been due to human emissions.

    Could the accumulation of human emissions in the atmosphere be causing the natural absorption and emission values to change? Absolutely. In fact, they definitely are changing. That just doesn't impact the mass balance argument at all. If the mass of human emissions is greater than the mass of atmospheric accumulation then human emissions ARE responsible for the atmospheric accumulation.

    The only options for 'defeating' the mass balance argument are;
    1 - Disprove (or deny) the data showing that humans have been emitting CO2 at a greater rate than the atmosphere has been accumulating it for decades.
    2 - Invalidate the law of conservation of mass.
    3 - Introduce a new variable... e.g. carbon emissions from aliens.
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  24. oarabin @20:

    Let Un(t+1)= En(t)+3.5*Ea;
    Let En(t+1)=En(t)+3*Ea

    This satisfies the conditions of the argument that you describe. However, even in this case atmospheric CO2 concentrations would decrease if it where not for anthropogenic emissions. Ergo, this argument as framed does not rebut mass balance argument.

    However, if we introduce the factor that the increase in Un is caused by Ea, then absent the increase in En, anthropogenic emissions would indirectly cause a reduction of atmospheric CO2. Alternatively, and more probably, increase in C' causes an increase in Un which drives C' towards an equilibrium value. A sufficiently large and rapid response in Un could have restricted C' to an increase one years anthropogenic emissions.

    In this case (only), a concurrent and coincidental rapid increase in En could be the cause of the increase in atmospheric CO2. However, an increase in concentration from natural sources would drive an increase Un as well. Therefore the increase in En must be orders of magnitude larger than the increase in En to overwhelm the tendency to return to equilibrium. As antrhopogenic emissions are 100 times larger than natural emissions (excluding equilibrium exchanges), that means the rate of increase of natural emissions must be many orders of magnitude larger than their initial (and measured) rates.

    In other words, the mass balance argument is an inductive argument (its conclusion could be false with true premises); but the probability of its leading to a false conclusion is very remote. What is more, if it where invalid the consequences would be immediately obvious as noted by Marco.

    Quite apart from that, as has been pointed out other measurements have also confirmed the mass balance argument.
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  25. Oarabin

    Strictly speaking, I'm sure one could construct a mathematical budget that could reconcile a natural source with a CO2 increase less than human emissions. But to be relevant such a budget should be realistic from a biophysical and chemical point of view, and it must be consistent with data in hand on reservoir sizes, stable isotopes etc. To summarize then, for a natural source to be responsible for the recent CO2 increase

    1) The anthropogenic CO2 to be taken up almost exclusively by natural sinks, while the natural CO2 remains in the atmosphere. I can think of no mechanism that could cause that to be true.

    2) The source must be terrestrial (because surface acidification of the ocean indicates net uptake of atmsopheric CO2 while C isotopes and atmspheric oxygen trends are inconsistent with oceanic outgassing)

    3) The net loss from this terrestrial source must amount to >40% of living terrestrial biomass (!!!) or >15% of soil organic carbon. It would have to be much larger as there should be some compensatory uptake by other reservoirs, and release from the mystery reservoir does not seem to be reaching some limit.

    4) That source must look like very old plant carbon interms of isotopic composition.

    5) Atmospheric oxygen must be consumed in rough proportion to release.

    That's a pretty hard list of requirements to satisfy, and I don't think you even can get past #1, which is why the budget approach has power. Then again, why look for an alternative explanation when we already have an explanation in hand that is consistent with everything we know about the carbon cycle?
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  26. @oarobin The mass balance argument is sufficient as it proves that natural emissions must be smaller than natural uptake, and hence the net action of the natural environment is opposing the rise in atmospheric CO2.

    "that is another possibility is that all Ea is taken up by the environment which also emits excess carbon equal to C'."

    There is no physical mechanism by which the natural environment could preferentially take up all of anthropogenic emissions. However, even if it could, in order to have conservation of mass natural emissions would still have to be less than natural uptake, in order for the observed rise to be less than anthropogenic emissions.

    Bart has frequently tried to dismiss the mass balance argument as being static rather than dynamic, however this simply isn't true. Figure 1 is the results of the mass balance argument, not that the net environmental sink has inter-annual variability and is gradually strengthening over time. One wonders how this is possible in a static analysis.

    Essentially introducing a time index variable is an attempt at obfuscation. The key result is that conservation of mass tells us that:

    En - Un = C' - Ea

    This is true for any time, i.e.

    En(t) - Un(t) = C'(t) - Ea(t)

    so if at any time the right hand side is negative, we know the left hand side is as well.

    You don't need a more complicated model, the only reason Bart intrduces it is to avoid discussion of the mass balance argument.
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  27. @Marco, even if some part of the natural environment had become a stronger emitter of CO2, and some other part a greater CO2 sink, the mass balance analysis still tells us that the natural environment is a net carbon sink, in which case how can it be causing the rise while taking more CO2 out of the atmosphere than it puts in?

    I think part of the problem is that the mass balance argument is so simple some find it hard to accept that it proves unequivocally that the rise is anthropogenic, but it does.
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  28. Stephen Baines wrote "Strictly speaking, I'm sure one could construct a mathematical budget that could reconcile a natural source with a CO2 increase less than human emissions."

    No, this is not possible, without contravening conservation of mass. The increase cannot be less than human emissions without the natural environment as a whole taking in more CO2 than it emits.

    It is important not to confuse the cause of the rise with the source of the molecules actually in the atmosphere (yes, I know that sounds odd). There are vast exchange fluxes that swap CO2 from the oceans/terrestrial biosphere and atmosphere each year, so anthropogenic CO2 only lasts on average about 4-5years in the atmosphere. However the exchange is a straight swap, so it doesn't have any effect on the amount of CO2 in the atmosphere. In my paper I have a simulation of a very basic model of the carbon cycle that shows that even though the rise is 100% anthropogenic, only a small percentage of the excess in the atmosphere consists of CO2 of directly anthropogenic origin; this is a result of the exchange fluxes.
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  29. Dikran, I fully agree that the natural environment is still resulting in a net uptake. I was merely pointing out that some may still claim, even after they accept the "net" versus "absolute", that there is a net natural emitter that is larger than the anthropogenic contribution. Better have arguments for that available, or they have another few hours to spread that new confusion!
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  30. DM. We're on the same page. The only rather academic difference is that I think conservation of mass is not a sufficient condition to argue that humans are the sole cause of the current increase in CO2. You also have to assume that removal processes do not distinguish between anthro and natural CO2 in the atmosphere. That assumption is implicit in the equations as you have presented them.

    Alternatively, one could characterize variations in atmospheric CO2 as a system of two distinct budget equations that track the anthropogenic CO2 and the natural CO2 in the atmosphere separately. One could then set the loss term for the anthro CO2 into one natural reservoir equal to anthropogenic emissions. In the other equation another natural reservoir could contribute CO2 to atmsophere while not interacting with the reservoir that serves as a sink for anthro CO2.

    Of course, in doing all that, one would be contradicting physical reality. Removal processes cannot distinguish between anthro and natural CO2 any more than my bank can discriminate between the dollars deposited as salary and those deposited from tax refunds once they are in my checking account. None of the evidence we have in hand suggests that atmospheric CO2 acts as anything other than single reservoir of well mixed gas with respect to loss processes.

    Still, I can't tell you how many people I meet are prone to think human derived CO2 must behave differently -- it's ingrained in their psyche.
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  31. Marco:

    OK. Let's assume that there is a natural source we don't know about. What characteristics would it have to have, to be the main cause of the increasing atmospheric CO2?

    To begin, we know that at least 50% of the anthropogenic emissions are removed, because the rate of increase is only 50% of those emissions. With that 50% amount, all the rise is anthropogenic. So, if only part of the rise is anthropogenic, then we need a natural sink that removes more than 50% of our anthropogenic source.

    Let's make a WAG that only 10% of the rise is anthropogenic, which requires that 95% of the emissions be removed (i.e., the 5% that is not removed is 1/10 of the rise that equals 50% of the emissions). The natural source then has to make up the other 90%. What are the implications of this?

    1) if natural sinks are just as efficient at removing this natural source as they are at removing the anthropogenic source, then this natural source has to be 9X larger than the anthropogenic one. (9+1=10, x5% not removed, leaves 0.5 as the atmospheric rise). This would be extremely unlikely to have gone unnoticed.

    2) in addition, the natural source has to have the same isotopic signature as the anthropogenic source. It has to smell, taste, look like CO2 from fossil fuels.

    3) to get away from 1), you need to find some plausible physical mechanism whereby CO2 from a natural source - CO2 that is indistinguishable from fossil fuel-derived CO2 - is somehow not soaked up by a sink that efficiently removes the anthropogenic source. This is akin to magic.

    Bluntly, the whole argument of an "unknown" natural source that is causing the increase, while the anthropogenic one is easily counteracted by natural sinks, is a dog that just won't hunt.
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  32. Bob Loblaw @31, as an addendum to your (2), the natural source must not be pure source of Carbon or a hydrocarbon that has been combusted. Otherwise the O2 concentration would be falling 10 times faster than it currently is.

    So, it must come from ancient plants (to account for the changes in C13 ratio and C14 ratio) but it must not be combusted. Therefore it can only be leakage from pure subterrainian reservoir of fossil CO2. The immediate problem is that no such reservoirs have been noticed; and buried organic materials do not form CO2 in large amounts because they are cut of from a ready supply of oxygen.
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  33. Bob, I fully agree with you. I have, in fact, made a very similar argument on several occasions. It's generally evaded by the pseudoskeptics that trot out the "only 5% of emissions are anthropogenic!"

    Just making sure others can make the same argument!
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  34. Stephen Baines Conservation of mass is all that is required to demonstrate that the natural environment (i.e. the oceans and terresrtial biosphere) are a net carbon sink. As such it is hard to argue that the observed rise in atmospheric CO2 can be a natural phenomenon when the natural environment is taking more CO2 out of the atmosphere that it puts in. Now if you can see an error in the line of reasoning, then please do point it out.

    The mass balance argument makes no assumptions about where CO2 from natural or anthropogenic emissions ends up. It would make no difference to the argument whether all anthropogenic CO2 were taken immediately by the natural environment, or whether it all stayed in the atmosphere permanently. The thing that causes the rise is an imbalance between total emissions and total uptake; mankind emits more CO2 than it takes up, and hence is a cause of the increase, the natural environment takes up more than it emits, and hence is opposing the increase.

    As I said, it is misleading to consider the fate of individual molcules in determining the cause of the rise, as their fate is largely determined by the exchange fluxes, which have no effect on atmospheric CO2 concentrations whatsoever.

    This in not merely academic. The mass balance argument on its own is sufficient, so it is important that any challenge to that position is resolved one way or the other.
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  35. Marco The mass balance argument makes no assumptions about natural sources and sinks, other than that they exist. The mass balance equation tells you the difference between total natural emissions and total natural uptake, whatever the natural sources and sinks are. Thus if there are unknown sources and sinks, their net activity is still represented by the green line in figure 1.

    The question to ask anyone making the "unknown source" argument is "if the natural environment is a net source, why isn't the observed increase greater than anthropogenic emissions?". Then then either need to show that the rise is greater than anthropogenic emissions (i.e. the observations are incorrect), or that nature can be the cause of the increase while being a net carbon sink! However, what they will probably do is dodge the question.
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  36. First: I agree that the observed CO2 increase is anthropogenic.

    However, I disagree that conservation of mass is a sufficient argument in and of itself (even though it makes nice intuitive sense).

    Dikran states: "Conservation of mass is all that is required to demonstrate that the natural environment (i.e. the oceans and terresrtial biosphere) are a net carbon sink. As such it is hard to argue that the observed rise in atmospheric CO2 can be a natural phenomenon when the natural environment is taking more CO2 out of the atmosphere that it puts in."

    My thought counterexample: I am in a room with a pool. A thermostat controls the pool temperature. I also have a humidifier. I insert X tons of water vapor into the air with the humidifier every year. Every year I raise the temperature of the pool a bit. I measure the water vapor of the atmosphere, and see that it has risen by X/2 every year. Therefore, I know that the atmospheric increase is less than what I have contributed with my humidifier, and that the pool is gaining X/2 tons of water every year. However, that atmospheric increase is NOT due to the humidifier at all! This is because the lifetime of water vapor in the room is short, so any addition of "anthropogenic" water vapor has no impact on long term water vapor abundance, whereas pool temperature does.

    THIS is the world that contrarians live in: a world where CO2 lifetime is measured in a few years or less. In such a world, CO2 concentration is controlled mainly by temperature, not by anthropogenic additions. Adding in isotope data isn't a magic bullet either because while the perturbation lifetime of CO2 is long, the atmospheric lifetime is indeed on the order of a few years. (contrarians can also try the smokescreen that oceanic carbon is old and 14C depleted, but then they have problems with 13C - but the 13C signal is more subtle).

    In my opinion, the key point that makes the whole story fit together is the Revelle factor, and how when you incorporate the Revelle factor, carbon cycle models can do a good job of reproducing observations of multiple isotopes. But that's harder to explain in 3 sentences, especially because there are still some open questions on some facets of the carbon cycle, and contrarians don't understand "we understand the system well enough to say X, even though we can't pin down Y yet".

    -MMM
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  37. (actually, the other killer argument is the CO2 concentrations are higher than they've been in at least 800,000 years - probably 5+ million years - but that's a hockeystick argument, and contrarians hate those. So then they attack the ice core records...)
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  38. (er: to clarify 36: the world that "sophisticated" contrarians live in - eg, the ones that can get published in E&E - is this short residence time world - many contrarians are in the less sophisticated territory of "natural big, anthropogenic small")
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  39. MMM,

    Your analogy thoroughly confuses me. What are your sources of water?

    In the case of CO2, it's pretty straightforward. The only viable sources and sinks are fossil fuels, biomatter, the oceans and the atmosphere. There's nothing else (there is carbon stored in the deep ocean and such, but it is in stable storage -- just like fossil fuels). There just aren't a lot of places to get the carbon from, or to hide it once it's been sucked from the ground.

    To violate the mass balance argument, one must show (a) where the 346 Gt of human, fossil-fuel-generated carbon went, (b) where the extra carbon in the atmosphere came from, and (c) why the mass balance, without that extra source of natural carbon, would have been zero otherwise (i.e. why the magical natural carbon increased atmospheric levels while non-magical anthro-carbon would have been sucked into whatever magical carbon sink is holding it).

    A whole lot has to happen, with a whole lot of carbon, to make any sort of argument that confounds the mass-balance argument.

    The core of the magical natural carbon source argument comes from the idea that there is so much carbon floating around in the ether that we can't possibly account for it... that volcanoes, oceans, coal fairies, carbon kobolds, petrol pixies and the like can all spread their magical carbon dust wherever they please without us silly, ignorant humans ever noticing.
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  40. MMM @36 the atmosphere and ocean maintain an equilibrium with regard to the vapour pressure of CO2. Therefore, if you increase the concentration, and hence vapour pressure', of CO2 is the atmosphere, the ocean will absorb more CO2. But if you increase the temperature of the ocean the equilibrium ratio will shift, raising the CO2 concentration in the atmosphere In the former case, the acidity of the ocean will increase, in the later the acidity of the ocean will decrease. So, unlike the case in your analogy, we have a simple means to check whether the increase in CO2 is due to increasing emissions or from warming of the ocean. It is the former.

    Further, we have a simple check of the theory that the rise in CO2 is due to increased temperature. The following is the CO2 record from Law Dome:


    (Source: Wikipedia)

    Multiple reconstructions of past temperatures have shown MWP warmth to be comparable to that in the 1950s, with an error range which does not exclude it being as cool as the 1910s or the 2000s. Fake Skeptics are convinced that those reconstructions underestimate MWP temperatures. If follows that if ocean warming is driving CO2 rise, the CO2 levels in the MWP should match current CO2 levels.

    So while I agree that unique scenarios can be constructed that void the mass balance argument, they do not show that the mass balance argument is faulty. The merely show that it is an inductive rather than a deductive argument, which has arrive at the correct conclusion (as sound inductive arguments typically do).
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  41. Hi Tom:
    What I'm trying to do is put myself in the mindset of the closest-to-sane of the contrarians. It is possibly useful to understand their mindset if we have any chance of convincing them, and possibly also to convince the fence-setters.

    I agree that the Law Dome is a strong argument - I think it has a better chance of standing alone than does the mass balance - you'll see I brought it up in #37. Of course, in combination, the law dome plus mass balance becomes nigh-indisputable.

    Hmm. The acidity argument might actually work too. At first, I was going to dismiss it based on the "pool" analogy - the pool having more water doesn't change the vapor pressure of the water - but yes, an ocean with higher total-dissolved-carbon does change the "vapor" pressure for CO2 in the atmosphere.

    -MMM

    ps. Sphaerica; The analogy is meant to be: pool water = CO2 in the ocean. Humidifier water = fossil fuels. Not a perfect analogy, but pretty close to what I think the Roy's & Salby's and other "sophisticated" contrarians must be thinking...
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  42. MMM,

    I don't think the analogy works, though, because water vapor is so sensitive to temperature, and will easily condense into the oceans as the temperature drops. CO2 is far more "long lived." Yes, for any individual molecule, it will drop out, but another will take its place. There are only three real places for CO2 to go in the short term, the air, the ocean, and biomatter. Biomatter can only grow so much, and is limited by other factors. The oceans can absorb a lot (and that's a huge problem, too), but not all of it.

    A better analogy would be two pools, one representing the atmosphere, the other the ocean, and a lot of people lounging around the pool, periodically scooping water out of each in tall glasses to drink it.

    Then some moron drives up with a huge tanker truck full of water, dumps it all at once and drowns everyone.

    Now there's an analogy for you.
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  43. Another pool analogy. I was going to post this in response to marco, but it may also address MMM's points.

    Suppose you have a large swimming pool. It has a pump/filter system that sucks 100 gallons per minute out of the pool, runs it through a filter, and dumps it back in the pool. It has run for months, and the level of the pool is essentially unchanged. There might have been a bit of evaporative loss, but let's ignore that for now.

    You then get a garden hose and start adding water to the pool (from the city water supply) at 1 gallon per minute. You say to yourself "it's only a fraction of the amount the filter system is cycling". You walk away, and come back two days later to find that the pool has overflowed.

    Do you think it is a serious argument that the garden hose can't possibly affect the level of the pool, because it is so much smaller a flow that the filter system? If so, what caused the pool to overflow? That's the argument put forth by the "skeptic" side, when they say the fossil fuel input is insignificant compared to the natural fluxes.
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  44. Hmmm. Looks like Sphaerica and I are pooling responses... (pun intended).
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  45. @MMM I can see what you are getting at, but the problem is that the analogy is not appropriate because CO2 is not a condensing gas, so there is no limit to the concentration of CO2 that the atmosphere can support (it isn't the temperature of the pool that matters, but the temperature of the air above it).

    The mass balance argument does not apply to water vapour because there is a limiting factor to the size of the atmospheric reservoir, which is independent of emissions, and much of the atmosphere is pretty near that limit most of the time.

    It is true that the fluxes between the oceans and atmosphere depend on temperature, so all things being equal, one would expect atmospheric CO2 to rise in a warming world. However, the thing the skeptics normally ignore is that CO2 solubility increases with increasing difference in the partial pressures of CO2 between atmosphere and surface waters. In the real world, all things are not equal, our emissions have caused a difference in partial pressures, which is increasing the oceanic uptake, which more than compensates for the temperature driven change in fluxes.

    Essentally the mass balance argument establishes that the rise is anthropogenic, but physics is needed to explain why it isn't a temperature driven natural phenomenon.
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  46. Tom Curtis I don't follow your argument here, please could you explain it in a bit more detail.

    I can't see how the conclusion of the mass balance argument (that the natural environment is a net carbon sink) can possibly be false if the assumptions (conservation of mass and the relatively low uncertainty in the observations) are true.

    Can you provide equations for Ea, En, Un and C', such that conservation of mass is observed and where Un < En while at the same time C' < Ea. As far as I can see, this is a mathematical imposibility.
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  47. Dikran Marsupial @46, the Mass Balance argument establishes beyond a shadow of a doubt that net natural carbon sinks are larger than net natural carbon sources. That, however, is insufficient to establish that natural emissions are not the cause of increasing CO2 concentration in the atmosphere.

    Consider a situation in which an increase CO2 concentration in the atmosphere causes an increase in the rate at which natural sinks draw down CO2 such that, up to a limit, any increase in CO2 is completely drawn down within a year or two. Suppose also that the increase in rate of draw down is capped, so that a sufficiently large increase in emissions will result in an increasing atmospheric concentration. Let the maximum rate of draw down by natural sinks be equal to k. Thus if En+Ea k, Un = k.

    Suppose then we have the situation that Ea = 0 before 1850, and k/2 after 1850. Suppose also that by coincidence, En increased from k/4 before 1850 to 2k after 1850.

    In this situation, emissions would have been k/4 before 1850, so atmospheric CO2 would have been constant. After 1850, if there had been no increase in En, En+Ea = 3k/4 so there would have been no increase in atmospheric concentration. In contrast, if the increase in En had occurred but the increase in Ea had not, net emissions would be 2k, so k CO2 would accumulate in the atmosphere every year, increasing the CO2 concentration.

    Therefore, in this scenario, the increase in natural emissions is both a necessary and a sufficient condition for the increase in atmospheric concentration. That makes it the cause of the increase in this scenario (although anthropogenic emissions would be a contributing factor to the rate of increase).

    Although you can set up bizarre scenarios like this that are (counterfactual) counterexamples to the mass balance argument as an argument that anthropogenic emissions are the cause of the rise in atmospheric CO2, such scenarios are a small portion of all possible scenarios, and are complex (and hence relatively improbable). Therefore they have a low intuitive probability. Consequently the mass balance argument is a strong inductive argument to the conclusion that anthropogenic emissions are causing the rise in CO2, but it is not a deductive argument. (It is, of course, a deductive argument to the conclusion that net natural sinks are larger than net natural sources.)
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  48. Tom, as far as I can see your countexample is incorrect.

    Prior to 1850, Ea = 0; En = k/4; Un = k/4; C' = 0

    In this case, mass balance tells us that the natural environment is neither a net source nor a net sink, which is the correct answer.

    After 1850 (first scenario) Ea = k/2; En = 2k; Un = k; C' = 3k/2

    In this case, the mass balance tells us that the natural envrionment is a net source and is contributing to the rise in C (in fact we can see that it is responsible for 2/3 of it as net natural emissions are twice Ea).

    After 1850 (second scenario) Ea = 0; En = 2k; Un = k; C' = k

    In this case, the mass balance analysis again gives the correct result that the natural environment is a net source and is responsible for 100% of the observed increase.

    After 1850 (third scenario) Ea = k/2; En = k/4; Un = 3k/4; C' = 0

    In this case the mass balance tells us that the netural environment is a net sink and has exactly opposed the rise that would have been caused by anthropogenic emissions. Which is correct.

    Now, as you say, it is possible to make a bizarre non-physical scenario where nature is set up in a way in which an increase in natural emissions were necessary for a rise in CO2, but in both of the examples you gave, when atmospheric CO2 is increasing, the natural environment was a net source. This is not what we observe, we observe that the natural environment is a net carbon sink.

    Can you give a counter example where the natural environment is a net carbon sink, but where the cause of the rise is natural?
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  49. Dikran Marsupial @48, you are correct, I forgot to retain the condition that En-Un < 0.

    Try this:

    En = 0.5 k prior to 1850, and increases by 0.1k per annum after 1850.

    Ea = 0 prior to 1800, and increases 0.25 k at 1800

    If En + Ea < 1k, Un = En + Ea

    If En + Ea > k, Un = (En + Ea - 0.2k)

    In this scenario, atmospheric concentration begins growing in 1851, and continues to grow thereafter; but at all times Un > En, and during the period of growth is always greater by 0.5 k. Never-the-less, the growth in CO2 concentration is, intuitively, caused by the growth in natural emissions rather than by the anthropogenic emissions, which are not growing.

    This, of course, is rather irrelevant. We both agree that bizarre non-physical scenarios can falsify the mass balance argument, and that therefore it is an inductive argument rather than a deductive argument. We also both agree that no scenario that has actually been presented seriously does falsify the mass balance argument; and that alternative explanations to anthropogenic emissions are falsified by other evidence in any event.
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  50. Thanks Tom. I can see what you are getting at, but in this case, I would still say that the mass balance argument is correct.

    I would not agree that in this case the rise was due to natural emissions. I find it useful to recast the problem into a financial setting, which is more intuitive. If I proposed a business proposal wher you put in Ea = 0.25K per month and I put in En = 0.5k + t*k/10 per month, but took out Un = Ea + En if En + Ea < k and otherwise took out Un = (En + Ea - 0.2k), would you say that I was responsible for the increase in our assets?

    If I suggested that we let the scheme run for 10 years, and you could keep all of the assets at the end, would you take the deal? Surely you ought to if I were respondible for the increase in the balance?

    I don't know why, but many people seem to apply different meanings to the idea of "causing the increase" in the two scenarios. To me they seem equivalent. You can only be the cause of an increase by putting in more than you take out, otherwise you are using a rather subtle and counter-intuitive definition of "causing the increase".

    [incorrect statement snipped for clarity]

    I would agree with something like "natural emissions were allowing anthropogenic emissions to cause atmospheric CO2 to increase", but I can't see how the rise is caused by natural emissions in this scenario.

    I don't really understand how mass balance is an inductive argument, since we start with premises (conservation of mass and that observed increase is less than anthropogenic emissions) and deduce from that that natural uptake must be greater than natural emissions. Unless the pemises are false, or there is an error in the deduction, then mass balance is sufficient as far as I can see.
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