Predicting future CO2 levels

Guest essay by Roger Graves

Anyone taking any notice of the mainstream media and more technical climate-related journals will no doubt be aware of the predictions of doom and gloom due to rising CO2 levels in the atmosphere, and the resultant catastrophic anthropogenic global warming. The desire to control CO2 levels is the ostensible reason for the vast amount of money being poured into renewable energy, mainly wind and solar.

Of course, an alternative point of view is that in the last 30 years, while CO2 levels have increased by about 14%, the Earth has greened significantly, i.e. there is more vegetation cover now than there was 30 years ago. Crop yields, moreover, are much improved, for which the increased level of CO2 must take some credit. Rather than predicting doom and gloom, perhaps we should be predicting that the world will become a better place in which to live.

One topic that is rarely mentioned by those advocating the control of CO2 is just what effect measures such as switching to renewable energy are likely to have. Will this have any noticeable effect on CO2 levels? Is there anything we can do to stop CO2 levels rising, assuming this is something we would want to do anyway? What levels of CO2 are we likely to see in the future? This article attempts to answer some of these questions.

CO2 and Population

Figure 1 plots atmospheric CO2 level as a function of world population, encompassing the period 1960 to 2015. CO2 levels are from those published by NOAA, population figures are from those published by the UN Population Division. Note that although each data point represents an individual year in sequential order, time is not explicitly represented on this graph, which merely shows how CO2 levels are related to overall world population.


It will be seen from figure 1 that population and CO2 appear to move in lockstep. (This correlation was first noticed by Newell and Marcus in 1987.) No evidence is shown of any significant decrease in the rate of rise of CO2 from beginning to end of this curve. We can conclude from this that none of the measures taken by industrialized countries to reduce CO2 output seem to have had any noticeable effect, at least up to 2015.

Whether population causes CO2 or CO2 causes population is another matter, but if we assume that this lockstep will continue for the foreseeable future, then if population goes up, so will CO2. Since the world population is quite certain to increase, at least in the short term, then CO2 levels will presumably also increase.

Since CO2 and population seem to be linked, the question that now arises is whether population is driving the CO2 level, or CO2 is driving population.

There are five possibilities to be considered:

1. There is no connection between the two, population and CO2 are completely unrelated phenomena and the apparent lockstep is just a fluke. Possible, but unlikely. While it is certainly true that correlation does not necessarily imply causation, it is also true that the better the correlation the more likely it is that some form of causation is involved. As shown below, the correlation in this case is sufficiently good that the possibility that there is no causal link can reasonably be ignored.

2. Population drives CO2. This is the ‘obvious’ explanation that most people would give. The more people there are on our planet, the more CO2-generating activities there will be, such as electric power generation, industrial activity, transport, domestic heating, and so on.

3. CO2 drives population. Much of the population growth in the foreseeable future will come from sub-Saharan Africa. Population growth in these regions is dependent to a large extent on the food supply, and as we know, more CO2 makes the world a greener place with greater crop yields. The greater the food supply, the more children will survive to maturity.

4. The connection between CO2 and population arises from both 2 and 3 acting together. The more people there are, the more CO2 they produce, and the more CO2 there is, the more food can be produced and hence the more children will survive to maturity.

5. Both CO2 and population are driven by a third, as yet unknown, quantity. While this cannot be dismissed out of hand, it must be considered as merely a theoretical possibility until this unknown quantity is identified.

My personal view, and this is only an unsupported guess, is that possibility 4 is the most likely. Larger populations produce more CO2, and more CO2 in turn results in larger populations.

But what of the future? Can we reasonably predict what CO2 levels will be like in ten, twenty or thirty years?

We can do this by superimposing a trend line on figure 1, which is simply a mathematical function which fits the data. The trend line can then be extended to make predictions of future CO2 levels based on predicted future population levels, assuming the relationship between CO2 and population remains constant.

Choice of Trend Line

It may easily be demonstrated that a polynomial function provides the best fit to the data. The question that remains is which order of polynomial to use (ax3+ bx2 + cx + d, for example, is a third order polynomial). Figure 2 shows the population/CO2 data of figure 1 (with extended axes) and trend lines ranging from 2nd-order to 6th-order polynomials. All five trend lines shown have an R2 value of not less than 0.999, i.e. the trend line correlates with the data to an accuracy of at least 99.9%. The data supporting this is on an MS Excel spreadsheet which is available on request.


Population Predictions

The United Nations Department of Economic and Social Affairs, Population Division, publishes a series of world population predictions up to the year 2100. Three different estimates are provided, high, medium and low, as shown in figure 3. (To access the source data, go to, then download the spreadsheet called Total Population – Both Sexes.)


CO2 Predictions

Future CO2 levels can be predicted using the CO2/population trend lines shown in figure 2 together with the population predictions shown in figure 3.

The 5th– and 6th-order trend lines of figure 2 have been rejected since there is no reasonable physical mechanism whereby the CO2 level would drop precipitously at a population of about 8 or 9 billion.

Predicted future CO2 levels based on the remaining three trend lines, i.e. the 2nd-, 3rd– and 4th-order polynomials, are shown in figures 4, 5 and 6 respectively. Each figure shows three separate CO2 predictions based on the high, medium and low population estimates of figure 3. While the UN population predictions extend to the year 2100, it is considered that CO2 trend lines are unlikely to be a reliable guide this far in the future, so CO2 predictions have been arbitrarily limited to 2050.


The results of these predictions for CO2 levels in the year 2050 are shown in table 1.

2nd-order trend 3rd-order trend 4th-order trend
Low population estimate 439 445 460
Medium population estimate 471 487 534
High Population estimate 508 540 659
Table 1: Predicted CO2 levels (ppm) in the year 2050

The results shown span a broad range, from 439 ppm to 659 ppm. However, this can be narrowed down somewhat. The 4th-order polynomial trend line shown in figure 2 is considered somewhat suspect because, unlike the 2nd– and 3rd-order trends, the rate of increase of CO2 beyond the historical data is significantly greater than that of the historical data itself. While this may be not be impossible, it appears to introduce a change in the CO2/population mechanism for which there does not appear at this time to be any justification. Consequently, the 4th-order trend line data will provisionally be ignored. If one then assumes that the medium population estimate given by the UN is the most likely, the most probable range of CO2 levels for 2050 becomes 471-487 ppm, within a total probable range of 439-540 ppm.

These results depend on two fundamental assumptions:

1. There is a causal relationship between CO2 and world population, which is represented by one of the trend lines discussed above, and this relationship will continue until at least mid-century.

2. Efforts to reduce CO2 will have little or no effect until that year, or indeed beyond it.

The second assumption is worth considering further. Certainly, significant efforts have been undertaken to reduce CO2 emissions in the Western world, but how effective these have been or will be is debatable. Much of the apparent reduction in Europe, for example, has resulted from shutting down carbon-intensive operations such as steel-making, but this has only resulted in those operations being transferred to other parts of the world such as China and India, so the total steel-making capacity of the world has not changed. Furthermore, while the introduction of renewable energy in the Western world has to some extent reduced carbon emissions (although to a lesser extent than was generally expected), in other parts of the world the use of fossil fuels is not decreasing and is often increasing.


The world’s population is growing. While the actual amount of population growth in the next few decades is a matter of debate, the fact that there will be at least some growth is not. Assuming that the CO2/population relationship still holds good, then based on the UN population estimates we can predict a most likely CO2 level in the range 471-487 ppm by the middle of this century, within a total probable range of 439-540 ppm, regardless of anything we do now. Whether the human race then disappears in a deluge of climate change catastrophes, or the world enters a golden age of unsurpassed crop yields, remains to be seen.

An earlier version of this article was published in WUWT in 2016. However, it was felt that the first version was not rigorous enough, so it is hoped that this version will be more satisfactory.


142 thoughts on “Predicting future CO2 levels

  1. The it must follow that prior to any statistically significant number of humans on this planet, CO2 levels were static.

  2. The CO2 levels in this article seem to be based on the assumption that the demand for fossil fuels can be met, without taking into consideration resources and reserves.

    The following paper argue that limited resources and reserves will also limit the CO2 levels in the atmosphere to a maximum of 610 ppm in the year 2100: The implications of fossil fuel supply constraints on climate change projections: A supply-driven analysis

    From the abstract: «The emission scenarios used by the IPCC and by mainstream climate scientists are largely derived from the predicted demand for fossil fuels, and in our view take insufficient consideration of the constrained emissions that are likely due to the depletion of these fuels. This paper, by contrast, takes a supply-side view of CO2 emission, and generates two supply-driven emission scenarios based on a comprehensive investigation of likely long-term pathways of fossil fuel production drawn from peer-reviewed literature published since 2000. The potential rapid increases in the supply of the non-conventional fossil fuels are also investigated. Climate projections calculated in this paper indicate that the future atmospheric CO2 concentration will not exceed 610 ppm in this century; and that the increase in global surface temperature will be lower than 2.6 DegC compared to pre-industrial level even if there is a significant increase in the production of non-conventional fossil fuels. Our results indicate therefore that the IPCC’s climate projections overestimate the upper-bound of climate change.»

    By that paper, both RCP 8.5 and RCP 6.0 seem to be wildly exaggerated:
    Figure 2 and figure 4 in the linked paper indicates that both RCP8.5 and RCP6.0 may be totally unrealistic ( SD-PC = supply-driven peak conventional fossil fuels’scenario / SD-PCU = supply-driven peak conventional & non-conventional fossil fuels’scenario )

      • The thing to worry about is what happens to crop yields when thorium and/or Mr. Fusion or whatever take over as mankind’s primary energy source(s), and CO2 levels begin to collapse. We’ve become quite spoiled by ever-increasing crop yields. That trend will slow, and might even reverse, when CO2 levels are falling.

      • daveburton,
        Yes, when the author said he saw no reason for a sharp decline in CO2 production my eyebrows raised as well.

    • I have wondered about this for some time – the amount of carbon based fuel on earth is finite, and my expectation is there is a maximum concentration of carbon dioxide that will ever exist in the air based on that finite resource.

      So we seem to be discussing a probably maximum range of 439 ppm (population) to 610 ppm (remaining burnable carbon). Our migration from around 280 ppm to 400 ppm has resulted in 0.7 degree of warming. So 120 ppm = 0.7 degrees, assuming all of this was caused by carbon dioxide, and the relationship is linear. So increasing to 439 ppm means we will experience, at most, an additional 0.23 degrees of warming. Increasing to 160 means 1.23 degrees of additional warming. 2 degree total is the MAX we will ever experience.

      But wait, there’s more. The temperature response to carbon dioxide is not linear, it is logarithmic. Meaning we would need to get to 800 ppm to get an additional 1.3 degrees. So our high end estimate is way off. Even at 610 ppm, we should see much less than 1 degree of additional warming, max.

      So, overall, our warming due to carbon dioxide is definitely going to be < 2 degrees, probably less than 1, meaning we are most of the way to whatever the final warming number will be.

      This means – look around – this is global warming. This is as warm as it is ever likely to be. We may warm a little bit more, but that's it. This is the dire, terrible future they warned us about. Famines, floods, weather events, rising sea levels. Sure we get occasional disasters, but if this is the world of the future, I'm okay with it.

    • Vukcevic,

      According to Henry’s law, the CO2 concentration in the atmosphere at full dynamic equilibrium with the current average seawater temperature should be ~290 ppmv, as seen over the past 800,000 years in ice cores. We are at 400+ ppmv, that is 33% higher…

      • Mr. Engelbeen thank you for your comment.
        You might recall that Henry’s law is not applicable if there is a chemical reaction between gas and liquid, but more importantly the principle of the dynamic equilibrium (state reached by a reversible reaction) applies only to a closed system, which ocean/land – atmosphere is not.
        Rate of a reaction in one direction is not the same as when the direction is reversed (absorption and emission rates) due to presence of biomass in the oceans, but more importantly due to a much larger land biomass which varies greatly between glacials and inter-glacials.
        Henry’s law is fine in an ideal chemical lab set-up, but fortunately for all of us the planet Earth is not a giant Florence flask.

      • Vukcevic,

        While indeed Henry’s law is only applicable to free CO2 in seawater (around 1%), not the other carbon species (90% bicarbonate, 9% carbonate), the ultimate ratio between the sea surface and the atmosphere is quite fixed by the Revelle factor at an around 10% change in the surface layer for a 100% change in the atmosphere.

        One can discuss if the ocean-atmosphere is a closed system or not.
        The ocean surface is a closed system with the atmosphere with an exchange speed of less than a year, where the amounts are rather alike: ~1000 GtC inorganics in the ocean surface against 800 GtC in the atmosphere.
        The exchanges with the deep oceans are much slower.
        Ultimately, almost all our emissions will end in the deep oceans and a small part in vegetation and in the atmosphere. The main point is the speed at which that happens. The past 60 years show a remarkable linear ratio between overall uptake and the CO2 increase in the atmosphere above the long-term dynamic equilibrium as seen over the past 800,000 years in ice cores.

        Land biomass is (according to the IPCC) some 550 GtC vs. 37,000 GtC inorganic carbon for the deep oceans, I don’t think that biomass (oceans+land) has much influence on the equilibrium…

  3. Nice analysis. Shows the futility of Paris Accord per se. UN’s population projections are suspect, covered in Chapter 1 of ebook Gaia’s Limits. But there are multiple other grounds for thinking the ‘medium’ UN projection is likely in the ballpark. Only thing the long, complicated food chapter of Gaia’s Limits missed was CO2 fertilization of C3 plants, which introduces an (experimentally derived, see essay Carbon Pollution in Blowing Smoke) ~5% error into the calculated food carrying capacity estimates given this posts most likely CO2 range.

    • Aw, Christ, people; get a grip. In the climate realm, nothing bad has happened, nothing bad is happening nor will anything bad happen based on current trends.

      Modelturbation and other numerical speculation is warping your minds. There is no factual information that would lead one to fundamentally alter our society, economy and energy systems.

      Bite me, Trolls and profiteers.

  4. Looks to me that you can build an immensely long list of apparent correlations:
    Industry growth.
    Increased whale populations,
    return and increase of temperate forests,
    Increased wildlife populations; deer, turkey, bear, etc.,
    increased seaweed consumption,
    increased consumption of chicken,
    increased consumption of Chinese takeout,
    increased water treatment worldwide,
    Improved medical treatment,
    etc. etc.

    The list is endless. Without absolute replicable proof linking one or multiple sources to CO2, all you have are some interesting charts.

    Correlation in not causation.

    • Increases in worldwide consumption of beer + wine since 1960 is just about in lockstep with CO2 rises.

      Calling Al Gore —
      —- We got to stop people drinking beer and wine!

    • Here is another beautiful graph a la ferdinand showing CO2 concentrations as calculated from changes in temperature and human emissions (which is essentially the same thing that the author of this post is doing). There is at least one mistake in this graph and maybe more. Ferdinand used bart’s data in his calculations, however, bart has never made his graphs with pin point accuracy. (he would essentially eyeball the relationship between temperature and the carbon growthrate in his graphs) This doesn’t matter so much when just calculating recent decades, but the further back in time that one goes (ice cores), the more the scaling of recent decades matters. Correct data would show only a max 10ppm difference between ice cores and calculated co2 levels in the early part of the 20th century, when changes in the carbon growth rate were most volatile and thus one would expect to see the most smoothing. Note that where one would expect to see the least smoothing, around 1900, the calculations are accurate. (this actually holds true going all the way back to 1850) Also note that the calculation from temps looks more like the keeling curve than the other two…
      In the MLO era, beginning in 1958, the temperature calculations look just as good as those that ferdinand calculated from emissions. It’s only when we hit those ice cores that the relationship begins to fail, but, as i’ve pointed out, not by much. So it looks as though the author of this post may have made an unfounded assumption that carbon levels are related to population growth (emissions). If we’re fortunate enough to see a little cooling in the future, it will be crystal clear whether the growth rate is driven by temperature or emissions. (at that juncture in time, this could be a whole new ball game)…

      • “In the MLO era, beginning in 1958, the temperature calculations look just as good as those that ferdinand calculated from emissions.”

        Ferdinand’s model violates continuity requirements, and treats anthropogenic and natural emissions on an uneven playing field. It is not physically valid.

        “It’s only when we hit those ice cores that the relationship begins to fail, but, as i’ve pointed out, not by much.”

        The ice cores cannot be validated in end-to-end tests. I do not consider them reliable.

        “So it looks as though the author of this post may have made an unfounded assumption that carbon levels are related to population growth (emissions).”

        The correlation exhibited here is spurious. It is merely a low polynomial order, and therefore low information, coincidence of two series going vaguely in the same general direction for a time. It wouldn’t match at all in the rate of change domain.

      • Bart:

        Ferdinand’s model violates continuity requirements, and treats anthropogenic and natural emissions on an uneven playing field. It is not physically valid.

        Bart, my “model” is based on only 2 assumptions: that the dynamic equilibrium between ocean surface and atmosphere for CO2 follows Henry’s law for the solubility of CO2 in seawater with temperature (about 16 ppmv/K) and that any deviation from that equilibrium gives a linear response by the dynamics of the oceans with about 51 years e-fold decay rate (~35 years half life time) as observed over the past near 60 years of Mauna Loa. It doesn’t matter in any way if the deviations are caused by volcanoes, humans or meteorites…

        What you always forget is that many different processes are at work, where the huge seasonal changes are opposite to the small longer term changes: higher temperatures mean lower CO2 seasonal, while higher temperatures show higher CO2 long term. The largest natural changes are seasonal, thus you can’t treat these changes the same as human emissions, the more that they nearly zro out over a full seasonal cycle…

        The ice cores cannot be validated in end-to-end tests. I do not consider them reliable.

        There is an overlap 1960-1980 between the high-resolution Law Dome ice cores and direct measurements at the South Pole. Deviations less than 1.2 ppmv (1 sigma). No reason to doubt these ice core data over at least the past 150 years.

        The correlation exhibited here is spurious.

        I agree, although there is a cause and effect, what the author missed is the increase in per capita fossil fuel use with increasing individual wealth. The correlation is between total human CO2 emissions and CO2 rise in the atmosphere.

      • Bart:

        Ferdinand’s model violates continuity requirements, and treats anthropogenic and natural emissions on an uneven playing field. It is not physically valid.

        Bart, my “model” is only the combination of two assumptions: that the dynamic CO2 equilibrium between ocean surface temperature and atmosphere follows Henry’s law for the solubility of CO2 in seawater (at ~16 ppmv/K) and that any deviation from that equilibrium leads to a reaction of the oceans with an observed linear response of ~51 years e-fold decay rate. That is all.

        What you forget is that multiple processes are at work: the bulk of the natural changes are seasonal, where higher temperatures give much lower CO2, while a long-term temperature increase gives slightly more CO2 in the atmosphere. There are opposite reactions even within natural emissions (oceans and vegetation) on temperature changes. The main point is that at the end of the seasonal cycle, the balance shows a deficit: more CO2 sinks in oceans and vegetation than was naturally emitted.
        Human emissions are near independent of temperature, they only increase the CO2 pressure (pCO2) beyond the temperature driven equilibrium. That gives the same reaction from the oceans for human as for natural emissions (volcanoes,…). As the emissions are higher than the sink capacity of the oceans (and vegetation), CO2 in the atmosphere goes up.

        The ice cores cannot be validated in end-to-end tests. I do not consider them reliable.

        There is a 20 year overlap 1960-1980 between the high resolution ice cores of Law Dome and direct measurements at the South Pole. Direct measurements are within the accuracy of the ice core values (1.2 ppmv, 1 sigma). Thus at least over the past 150 years, there is no reason to doubt the ice core measurements (with a resolution of less than a decade).

        The correlation exhibited here is spurious.

        In part yes, as the author didn’t take into account the increase in per capita CO2 emissions. The correlation and causation is between total CO2 emissions and CO2 increase…

      • “Bart, my “model” is only the combination of two assumptions: that the dynamic CO2 equilibrium between ocean surface temperature and atmosphere follows Henry’s law for the solubility of CO2 in seawater (at ~16 ppmv/K) and that any deviation from that equilibrium leads to a reaction of the oceans with an observed linear response of ~51 years e-fold decay rate. That is all.”

        And, those assumptions are invalid, because it requires treating natural and anthropogenic emissions unequally, though the sinks have no means of distinguishing between the two.

        I showed you last time that, to treat them equally, your time constant would be required to be on the order of a couple of years, and your result then does not match even superficially.

        There is no doubt about it. You will see.

      • (mods, how many indulgences does it take to get ferdinand’s comments out of “wp purgatory”? ☺)

        Bart, as is always, nice to “see” you… i thought i’d show you the above wft graph with the scale and offset matching exactly on your data going back to ’58. (then extrapolating backwards to 1850 where it shows an interesting thing or two) Looking at the late 19th century data alone, where we would expect the very least smoothing, we see a very good fit with the ice cores growthrate of about .2ppm per year. If recent warming had been just .1C less than what it has been, a larger scale would be needed to fit the two data sets. That scale would have produced a growthrate centered around 0ppm/year in the late 1800s which would be too low. Similarly, if recent warming were .1C higher than it has been, we would need a reduced scale which would result in a late 1800s growthrate of about .5ppm/year which, of course, would be too high. i would think this would constitute some validation of ice cores assuming the temperature relationship is true. (as well, ice cores provide some validation for the temp/co2 growthrate relationship, too) The late 19th century and ferdinands overlap from ’60 to ’80 are all we really have to validate ice cores. AND, guess what, they do a pretty good job at that. So at least it passes the smell test. Even in the early 20th century they ain’t that far off, basic logic telling us that the data in cores should be somewhat inflated (and it is). So, everywhere in the instrumental record that we have to confirm ice cores we do find confirmation. This may be useful going forward if and when the atmospheric carbon data departs from emissions enough to satisfy even the ferdinands of the world…

      • Bart, comment hung up in moderation pertaining to the WFTs graph (located above your comment)

        The problem i have with ferdinand’s explanation of henry’s law is that it takes way too long to get going. In the early 1990s, when atmospheric concentrations were about 65ppm above ferdinand’s steady state of 290ppm, his own calculated sink rate was just 1ppm. That means any increase in natural addition above 1ppm (and even much, much less than that going backwards in time) should have readily shown up in the atmosphere until the 1990s. That would be a far cry from the 16ppm/degree C figure…

      • Bart:

        those assumptions are invalid, because it requires treating natural and anthropogenic emissions unequally

        Again, the sinks treat natural and anthropogenic emissions completely equal (with a very small differentiation for different isotopes). The different sinks don’t treat temperature and pressure changes equally. That is the point.

        There are a lot of natural CO2 emissions over a full seasonal cycle: in summer ~50 GtC out of the oceans, in winter ~60 GtC out of vegetation. That is 110 GtC natural emissions in total. Thus the ~9 GtC from humans is peanuts compared to the 110 GtC natural emissions… With an equal treatment of all CO2 of whatever origin, human emissions are responsible for about 8% of the increase in the atmosphere, the rest is natural. That is your theory.

        Completely wrong reasoning: the emissions from the oceans are when the uptake by vegetation is maximal, thus instead of increasing the CO2 levels in the atmosphere, the levels drop with increasing temperatures.
        What is observed is the difference: ~10 GtC (5 ppmv) up and down over the seasons. Human emissions with 9 GtC/year one-way are of the same order.

        For the seasonal uptake, it doesn’t matter much how much and what the origin of the CO2 is in the atmosphere: increased CO2 pressure has little influence (~1% more growth) on the amplitude of the seasonal cycle:

        It makes more difference for the oceans, where the deep oceans take the bulk of the extra CO2. That is where the pressure change of the total amount of CO2 in the atmosphere has the main influence. Again it doesn’t matter what the origin of the extra CO2 is: the ocean sinks take any CO2, of whatever origin out of the atmosphere in ratio to the extra CO2 pressure in the atmosphere, no matter the cause. Again, the extra CO2 emitted by the oceans due to the increase in temperature in summer has zero influence on the uptake, as the opposite change from vegetation dominates.

        Again you see all CO2 changes as reaction on temperature, which simply is wrong: the largest natural in/out cycle is seasonal with a response rate to temperature of only a few months for both oceans and vegetation. The response of the oceans and vegetation to the increased CO2 pressure in the atmosphere on the contrary is a matter of decades…

      • Fonzie – Ferdinand’s conception of Henry’s law is only the short term partitioning between the surface oceans and the atmosphere. There is a long term partitioning with the deeper oceans as well.

        Short term consistency of the ice cores with the modern record cannot establish anything beyond that short interval.

        Ferdinand – I’m sorry, no. Your model is nonphysical. I see no point in rehashing our previous arguments, and I have no time for it today.

      • Fonzie,

        There is zero difference between my “model” based on temperature for the variability and CO2 emissions for the trend and your/Bart’s model that is based on “temperature explains it all”:

        Expecting that dCO2/dt variability and slope both are caused by temperature is shown in blue (RSS_CO2)
        Expecting that dCO2/dt variability is caused by temperature variability and the slope by the emissions is shown in red (emiss-nat-CO2-deriv)
        The observed rate of change is in green (dCO2/dt).

        All three trend lines haev the same slope. In the case of temperature as sole cause with a best fit factor and offset. In the case of temperature/emissions, with a factor only for the amplitude and near zero offset.

        Both graphs of expectations show exactly the same variability (in timing) and slope and the same deviations from the observations.
        The length of the period of interest was choosen small to show the details of the variability.

      • Ferdinand relies upon and fully believes gross “estimates” that have been cobbled together.

        Estimates are not and have never been actual data. Especially when those doing the estimating ignore Earth’s sheer size and geochemical processing.

        I stopped paying Ferdinand any attention when he claimed that Hawaii’s volcanoes, because it is a hot spot, are not major CO2 emission sources.
        This was in response to my posting estimates made from CO2 measurements at Yellowstone. Which just happens to be another hot spot volcano.

        Totally ignored are the magma chambers that form below volcanoes and serve as magma reservoirs. Magma chambers that consume or cook nearby carbonate deposits, releasing massive amounts of carbon dioxide in the process

        Untested unverified estimates are worthless. It’s far better to work without than to trust narrow view desk jockey estimates

      • ATheoK,

        Volcanoes are small contributors to CO2 in the atmosphere. One had huge emissions from the Pinatubo in the past century, its result on CO2 increase was negative: the lower temperatures and light scattering (more photosynthesis) had more effect than its CO2 emissions. That for eruptions.

        Then for continuous emissions of volcanoes and volcanic fields after an eruption:
        The highest volcanic CO2 emissions are from subduction volcanoes where one plate moves under another. The seabottom contains a lof of carbonates and organic stuff that is melted and decomposed. One of the largest and most active subduction volcanoes is mount Etna, Sicily, Italy. Here the report:

        Subduction volcanoes emit an order of magnitude more CO2 than deep magma volcanoes like Hawaii (and probable Yellowstone). Based on the measurements up and around mount Etna and a few other volcanoes, volcanic CO2 emissions on land are about 1% of human emissions… Undersea volcanoes play little role as the deep oceans are undersaturated in CO2 and thus most CO2 emissions don’t reach the atmosphere.

        As long as there is no reason to assume that extrapolation of measurements around a few volcanoes to all volcanoes is not warranted, I do assume that the extrapolation is not far off. Moreover, that doesn’t influence the debate about the origin of the CO2 increase in the atmosphere, neither its future, as it would be very remarkable that a lot of volcanoes increased their output in lockstep with human emissions and the increase in the atmosphere… Last but not least, CO2 from volcanoes in general has a (much) higher δ13C level than human emissions and higher than in the current atmosphere. Thus can’t be the origin of the enormous drop in δ13C level over the past 160 years…

      • Bart:

        Ferdinand’s conception of Henry’s law is only the short term partitioning between the surface oceans and the atmosphere. There is a long term partitioning with the deeper oceans as well.

        Yes and both have different time constants. The first is rapid with a time constants of a few months (for temperature) and less than a year (for CO2 pressure), the second is a lot slower with a time constant of ~51 years (for CO2 pressure) and hardly for temperature changes. Separated reservoirs and separated processes, where for the first reservoir the exxchanges are very sensitive to temperature variations, the second almost only to CO2 pressure changes.
        In both cases, the processes react exactly the same on natural as on human CO2.

        Your model is nonphysical

        Bart, my model simply reflects the effects of temperature and pressure changes on the uptake of all CO2, including human CO2, or any other extra CO2 injected in the atmosphere. It fits all CO2 levels from 800,000 years ago to today. It fits all other observations like δ13C decline, 14C decline, oxygen balance, etc…
        Your model has no bearing at all in reality, besides a nice fit of one graph, as it violates about every observation…

      • Ferdinand,

        I note your claim that your model “…fits all other observations like δ13C decline, 14C decline, oxygen balance, etc …”. You must have a superior model to Keeling then, because he has just admitted (2017 paper) that unless he introduces a new variable (non-constant isotopic discrimination for land photosynthesis), he cannot match the δ13C decline:

        “…no plausible combination of sources and sinks of CO2 from fossil fuel, land, and oceans can explain the observed 13C-Suess effect …”

        Wow, no plausible combination!

        Paper is pay-walled, but above quote is from the abstract. The abstract, reference and some discussion can be found here:

      • I hope your model for oxygen balance also takes the following conclusion from this 2017 paper into account (Keeling is a co-author):

        “These findings suggest a substantial and complex response of the oceanic O2 cycle to climate variability that is significantly (>50%) underestimated in magnitude by ocean models.”


        What I don’t get is all this stuff about complexity … yes, the atmosphere behaviour is surely complex, but its characteristics, in terms of δ13C and O2/N2 behaviour, are remarkably simple.

      • Jim Ross,

        It seems to me that Ralph Keeling is overly perfectionistic…

        The drop in δ13C is about 1/3 of what you can expect if all human emissions would remain in the atmosphere. In reality some is exchanged with the biosphere and some is exchanged with the oceans, rapid for surface and limited for the deep oceans.
        The exchanges with the ocean surface and the biosphere are largely seasonal: much of what was absorbed returns in the other seasons. That has not much influence on isotopic ratio’s.

        What has influence is the net balance in the biosphere: some 1 GtC/year doesn’t return and is captured in more permanent storage. As that is preferentially 12CO2, relative more 13CO2 remains in the atmosphere and increases the δ13C level, compared to the drop due to fossil fuel use, thus less decrease.
        If the 13C/12C discrimination during photosynthesis increased over time (per extra CO2), then the δ13C levels would show again a smaller decrease.
        The main influence on the human induced however are the deep oceans: what goes into the deep is the current atmospheric isotopic composition (minus the change at the air-water border), what comes out of the deep oceans is the composition of the deep oceans influenced by drop outs from the surface and the isotopic composition in the atmosphere of ~1,000 years ago (minus the change at the water-air border).

        The difference in isotopic composition can be used to estimate the CO2 exchanges between the deep oceans and the atmosphere:

        That is without taking into account the influence from the biosphere: some 40 GtC circulating between deep oceans and atmosphere, independently confirmed by the “thinning” of 14C from the atomic bomb tests.
        The influence of the biosphere probably can be seen in the deviation of the observations until about 1970, when the biosphere was thought to be a small source of CO2 in the early years, while an increasing sink after the 1990’s…

        Thus anyway, the drop in δ13C can’t be from the (deep) oceans, as these have higher δ13C levels than the atmosphere. That refutes Bart’s theory of an oceanic source.
        It can’t be from the biosphere either, as that is currently more sink than source.

        That Ralph Keeling does find more 13C/12C discrimination than expected may result in a (small) shift in CO2 sink distribution between oceans and vegetation and a (small) change in deep ocean – atmosphere CO2 circulation, but that doesn’t change the basics of the δ13C drop as caused by fossil fuel use.

        About the oxygen balance, that article looks at the influence of ENSO, which is a regional phenomenon with global consequences on temperature, CO2 uptake and thus O2 balance. That is the main problem with detailed research: the overall balances are (relative) simple to measure while the detailed fluxes are a hell of a job to obtain…

        The overall oxygen balance is here:
        Unfortunately no more recent updates found…

        BTW, I missed the discussion about the increased isotopic discrimination in plants as my wife and I had a nice camper trip in Quebec and New England…

      • “It seems to me that Ralph Keeling is overly perfectionistic…”

        Really? You must be kidding, or perhaps a bit too relaxed after your camper trip. Keeling updated his model with the latest Scripps data and found that (a) his model showed a δ13C decline rate that was over 20% too high and (b) making plausible adjustments to the model failed to fix the obvious bust. This is how science works. Unfortunately he then chose to make his model even more complicated by adding a new variable instead of taking a step back and looking at the fundamental assumptions underpinning the model. The δ13C decline rate is easily matched by simply assuming that the incremental atmospheric CO2 has a long-term average δ13C content of close to -13 per mil (which we know already because of the “Keeling plot” shown below). The issue then becomes more focussed: why is it constant (on average, given that the ENSO/temperature variations clearly lead to short term fluctuations) when it is recognised that the δ13C content of the fossil fuel mix will be changing over time (e.g. shift from coal to natural gas, leading to a decrease in δ13C from around -25 per mil in 1950 to around -28.5 per mil in 1991 – can anyone point me to more recent published estimates?).

        In addition, here is an up-to-date plot of atmospheric O2/N2 versus CO2 at the South Pole. If that is not a clear linear relationship then I do not know what is. Does “your” oxygen balance model forecast a constant value for the O2:CO2 exchange ratio? And does it include an adjustment for the changing ratio from fossil fuel burning over time due to the change in fossil fuel mix?

        These two plots are simply representations of the actual data (measurements) available from Scripps. I use the “seasonally adjusted” values since we are most interested in the longer term trends here and I prefer the South Pole data because this adjustment is minimal. This is the closest we get to having “facts” about the longer term characteristics of CO2 trends in the atmosphere in recent times. Any hypothesising about the source of the incremental atmospheric CO2 needs to start here.

      • Mods … I have a comment that’s been awaiting moderation for a few hours now. Could you take a look please. Thanks.

      • Nice, Jim. Yes, it is all a compact, tidy narrative. Until you start pulling at the threads, and realize it is basically just what a couple of guys thought might be the case, and a few others agreed, and it snowballed into a “Just So” story without any real underpinning.

      • Jim Ross,

        Indeed more relaxed back from Quebec and New England, where temperatures were high: 31ºC in Toronto for the return flight (must be global warming!), so we only had a little “Indian summer” high in the mountains, but lobster still is marvellous in Maine…

        To be clear: I haven’t build an overall, detailed model for all parameters involved. That isn’t even necessary, as long as the theory roughly fits the observations.

        Take the mass balance:
        All what is important is that for every year in the past near 60 years, nature was more sink than source, which is the case. No matter if that for each individual year is between 10% and 90% of human emissions.
        That is already a very strong indication that humans are the cause of the increase.

        Take the δ13C decline:
        That definitely excludes the oceans as source of the increase of CO2 in the atmosphere.
        If the ocean-atmosphere exchanges not only were “thinning” the δ13C “fingerprint” of fossil fuel use but also the main cause of the CO2 increase itself, the fourfold increase in human emissions since 1960 must be met with a fourfold increase in natural carbon cycle, for which is not the slightest indication, to the contrary… With such an increase, the δ13C levels in the atmosphere would go up again…
        So, for the attribution it doesn’t matter if the δ13C decline is 1/2 or 1/3 or 1/4 of what can be expected from fossil fuel use.
        For the attribution it does matter if there are no other sources of low-13C. The only other fast source of low-13C is the biosphere, but as that currently is a net sink for CO2 (based on the O2 balance), that is not a source of low-13C, just the opposite.


        As far as I remember, Battle e.a. used yearly fossil fuel sales x combustion efficiency for their oxygen balance, thus should have included the shift in fuel types over the years.

        Anyway interesting figures, will look further into it tomorrow…


        Your approach is looking into all the details, my approach is looking at the impossibilities to eliminate the wrong theories and what is left is the right one.

        Learned that as practical engineer in chemistry: eliminating the impossibilities works much faster in solving process problems than looking for possible causes…

        That is the main problem with Bart’s “solution”: that violates about all observations, while human emissions as cause doesn’t violate one, even if the “fit” isn’t perfect…

      • Thanks, Bart. I am not a climate scientist and am therefore not qualified to discuss Henry’s Law etc., but I can see a linear relationship with an R squared of .9985 and consequently feel very uncomfortable (understatement) with a model that has multiple variable parameters as an “explanation” of this linear relationship. I am now, more than ever, of the view that the O2:CO2 data are telling us (screeming at us) that we are looking at a very simple (one or two parameter) cause of the observations. My non-expert view is that this could be the oceans, bearing in mind that we have a coupled two outcome situation reflecting ENSO (temperature). I am absolutely not prepared to accept any proposed explanation (model) that does not show graphically its historical and predicted δ13C and O2/N2 trends.

      • Ferdinand,

        “Take the δ13C decline:
        That definitely excludes the oceans as source of the increase of CO2 in the atmosphere.”

        I disagree. The literature is not very helpful on this, and seems incapable of addressing the biological pump, but we know (or think we know) that phytoplankton discriminate against 13C in the same way (and proportion) that land-based plants do. It seems reasonable to assume, therefore, that when then are killed off by an El Niño they will release 12C preferentially (to the extent it is not carried to the ocean floor) in the same way.

    • Yup. The real correlation is between population and energy. It takes a lot of energy to support the current population levels. The fact fossil fuels provide 85-90% of that energy is the entire reason for the CO2 correlation. If another energy source shows up that is just as good as fossil fuels then the CO2 correlation will go away.

      If that happens and folks figure out that CO2 really was a good thing there are plenty of methane hydrates to keep the levels from dropping. Might have to subsidize the mining though. Wouldn’t that be ironic.

  5. I’m going with option 5. Population and CO2 are both driven by something else; the desire to engage in mating activities.

  6. The genesis of RGHE theory is the incorrect notion that the atmosphere warms the surface (and that is NOT the ground). Explaining the mechanism behind this erroneous notion demands some truly contorted physics, thermo and heat transfer, i.e. energy out of nowhere, cold to hot w/o work, perpetual motion.

    Is space cold or hot? There are no molecules in space so our common definitions of hot/cold/heat/energy don’t apply.

    The temperatures of objects in space, e.g. the Earth, Moon, space station, Mars, Venus, etc. are determined by the radiation flowing past them. In the case of the Earth, the solar irradiance of 1,368 W/m^2 has a Stefan Boltzmann black body equilibrium temperature of 394 K, 121 C, 250 F. That’s hot. Sort of.

    But an object’s albedo reflects away some of that energy and reduces that temperature.

    The Earth’s albedo reflects away about 30% of the Sun’s 1,368 W/m^2 energy leaving 70% or 958 W/m^2 to “warm” the surface (1.5 m above ground) and at an S-B BB equilibrium temperature of 361 K, 33 C cooler (394-361) than the earth with no atmosphere or albedo.

    The Earth’s albedo/atmosphere doesn’t keep the Earth warm, it keeps the Earth cool.

    Bring science, I did.—We-don-t-need-no-stinkin-greenhouse-Warning-science-ahead-

    “The first design consideration for thermal control is insulation — to keep
    heat in for warmth and to keep it out for cooling.”
    “Here on Earth, environmental heat is transferred in the air primarily by
    conduction (collisions between individual air molecules) and convection
    (the circulation or bulk motion of air).”

    Oops! WHAT?! Did they forget to mention RGHE “theory?” Global warming? Climate change? Bad scientists! Oh, wait. These must be engineers who actually USE science.

    “This is why you can insulate your house basically using the air trapped
    inside your insulation,” said Andrew Hong, an engineer (SEE!!) and thermal
    control specialist at NASA’s Johnson Space Center. “Air is a poor
    conductor of heat, and the fibers of home insulation that hold the air still
    minimize convection.”
    “”In space there is no air for conduction or convection,” he added. Space
    is a radiation-dominated environment. Objects heat up by absorbing
    sunlight and they cool off by emitting infrared energy, a form of
    radiation which is invisible to the human eye.”

    Uhh, that’s in SPACE where radiation rules NOT on EARTH.

    “Without thermal controls, the temperature of the orbiting Space
    Station’s Sun-facing side would soar to 250 degrees F (121 C), while
    thermometers on the dark side would plunge to minus 250 degrees F
    (-157 C). There might be a comfortable spot somewhere in the middle of
    the Station, but searching for it wouldn’t be much fun!”

    121 C plus 273 C = 394 K Ta-dahhh!!!!!

    Shiny insulation keeps the ISS COOL!!!! Just like the earth’s albedo/atmosphere keeps the earth COOL!!! NOT hot like RGHE’s BOGUS “Theory.”

    • Anthony actively discourages (Some of that free spirited dialogue.) engaging/commenting on my slayer type posts, but I thought I’d add my own parting shot.

      My WB papers have collected over 4,700 views and the ONLY qualified technical rebuttal has been a lecture on water vapor. Kind of misses the point. The alt-left climatards in goth garb aren’t protesting and demanding Exxon pay for Harvey because of fossil fueled water vapor.

      The ONLY^3 reason RGHE theory even exists is to explain how the average surface (1.5 m above ground) temperature of 288 K/15 C (K-T balance 289 K/16 C) minus 255 K/-18C , the average surface (now ground) temperature w/o an atmosphere (Which is just completely BOGUS!) equals 33 C warmer w/ than w/o atmosphere.

      That Δ33 C notion is absolute rubbish and when it goes in the dumpster it hauls RGHE “theory” in right behind it.

      The sooner that is realized and accepted the sooner all of us will have go find something else to do. Maybe that’s what keeps RGHE staggering down the road.

      • So when I look up Martian atmosphere at NASA website – interestingly 95% is CO2 – with all that ‘insulation’ one would think it would be have a higher average temperature than MINUS 63 C…considering the warmists say 0.04% is causing run-away temp increases on earth – how the? what the?

      • Mark Twain observed, “The trouble with most of us is that we know too much that ain’t so.”
        Adding to the “Δ33C without an atmosphere” (see other article) that completely ain’t so is the example of Venus.
        Venus, we are told, has an atmosphere that is almost pure carbon dioxide and an extremely high surface temperature, 750 K, and this is allegedly due to the radiative greenhouse effect, RGHE. But the only apparent defense is, “Well, WHAT else could it BE?!”
        Well, what follows is the else it could be. (Q = U * A * ΔT)
        Venus is 70% of the distance to the sun so its average solar constant/irradiance is twice as intense as that of earth, 2,615 W/m^2 as opposed to 1,368 W/m^2.
        But the albedo of Venus is 0.77 compared to 0.31 for the Earth – or – Venus 601.5 W/m^2 net ASR (absorbed solar radiation) compared to Earth 943.9 W/m^2 net ASR.
        The Venusian atmosphere is 250 km thick as opposed to Earth’s at 100 km. Picture how hot you would get stacking 1.5 more blankets on your bed. RGHE’s got jack to do with it, it’s all Q = U * A * ΔT.
        The thermal conductivity of carbon dioxide is about half that of air, 0.0146 W/m-K as opposed to 0.0240 W/m-K so it takes twice the ΔT/m to move the same kJ from surface to ToA.
        Put the higher irradiance & albedo (lower Q = lower ΔT), thickness (greater thickness increases ΔT) and conductivity (lower conductivity raises ΔT) all together: 601.5/943.9 * 250/100 * 0.0240/0.0146 = 2.61.
        So, Q = U * A * ΔT suggests that the Venusian ΔT would be 2.61 times greater than that of Earth. If the surface of the Earth is 15C/288K and ToA is effectively 0K then Earth ΔT = 288K. Venus ΔT would be 2.61 * 288 K = 748.8 K surface temperature. All explained, no need for any S-B BB RGHE hocus pocus.
        Simplest explanation for the observation.

  7. The limited time scale of the data concerns me. It is from such a short period of human habitation wherein our current technologies and CO2 production are assumed to have been and always will be the same per capita. This is demonstrably not so. True over the decadal scale of this analyses these “givens” hold true, but why should we assume them to be not time dependent as well (as they most certainly are). Why not take an even shorter period and attempt to fit a linear function to it?
    IMHO humans’ CO2 is but a cough in the deep breaths of the Earth.
    polynomials, hah….look for a wiggle on a long sine curve.

  8. here is a hint for the writer
    Understand the literature on this very problem.
    if you do, you’ll avoid being such a clown.

    Prior to AR5, which uses RCPs, the IPPC used SRES.

    Let me draw an analogy. When I used to do war gaming we had a whole department that did

    basically everyone understands that predicting human behavior ( especially copulating humans) is very hard.
    So, you develop scenarios. These are like “What ifs”
    What if everyone gets internet
    What if everyone gets a cell phone
    What if Russia invades X
    What if North Korea gets a nuke.

    Physics gets involved but only as a tangent.

    What is SRES?

    here is a clue. your post doesnt come close. dont quit your day job.

    • So, Mosh, why did the IPCC abandon SRES? Because they were merely fanciful guesses and detracted from the image that they were ‘doing science’.

      Now, the IPCC accepts that they have no idea what might happen in future, except they have confidence in their projections regarding the extent of forcing that will be caused by increasing CO2 concentrations. So they picked four alternative “pathways” (none of them scenario-based, and all internally incompatible), within the bounds provived by the literature. They leave it to others to debate the likelihood of each pathway.

      Just as the CO2/forcing correlation can be plausibly extended, so can the population/CO2 correlation.

  9. “…many assumptions used for fossil fuel availability and future production have been optimistic at best and implausible at worst. The SRES and RCP scenarios have been criticized for being biased towards “exaggerated resource availability” and making “unrealistic expectations on future production outputs from fossil fuels. Energy cannot be seen as a limitless input to economic/climate models and remain disconnected from the physical and logistical realities of supply.”

    That is from your own reference. It is, in fact, correct. Carbon fuels are not infinite, and neither is population growth, or energy use per capita. Putting realistic caps on any of these three factors blows a very large hole in most of the climate doomsday scenarios. Extending existing trend lines out indefinitely is a fool’s game.

    Since the beginning of the Industrial Revolution there has been a sustained growth in the scale of energy consumption by human civilization. Plotting data on energy usage, including wood, biomass, fossil fuels, hydro, nuclear, etc.) which shows an annual growth rate of 2.9%. If we start the clock today, in 275 years we will go from 16 TW we use today to 7,000 TW. Why, in just 1,300 years we will need to control the entire energy spectrum of the sun! Is that realistic? Or perhaps there are some hard limits built in there?

    Stephen – perhaps you should consider taking your own learned advice.

  10. I’ll take option #1 for $200 please Alex :)

    Seriously if option 1 is correct and I think it is then all that nice work goes out the window. My picking option 1 is just my SWAG.

  11. The largest mobile source of CO2 on the planet is the deep oceans. Now if sea level starts dropping and decreases the pressure enough, some of that CO2 near the top of the saturated zone could start bubbling up. That would be fun. Not that it will ever vent to the atmosphere, but there is enough CO2 in the deep ocean to asphixiate the lot of us if it did.

    • Steve,

      CO2 at the temperature of the deep oceans is undersaturated. If it comes at the surface in cold zones, as is the case when mixed by wind near the poles, it removes CO2 out of the atmosphere. If it is upwelling in warm zones near the equator, it releases CO2. A pressure releave of the oceans will not have any effect. Temperature at the surface of up- and downwelling zones does have an effect at about 16 ppmv/K in dynamic equilibrium with the atmosphere…

      • I didn’t know that the Oregon coast is located close to the equator – thank you for the update.

      • The Doctor,

        Sorry for the people of Oregon, their upwelling is not warm enough to give much CO2 releases, but still can give problems for their oyster culture…

        There are many coastal upwelling zones, in general where the winds blow off land. The most important one is the Humboldt Current System, where huge quantities of deep ocean water are upwelling to the joy of fishermen in Chili and Peru… Part of the extra CO2 and nutrients is used by plankton and feeds the food chain, part is emitted into the atmosphere as the waters warm up near the equator. The global estimates (based on the “thinning” of human δ13C and 14C from the atomic bomb tests) is around 40 GtC/year circulating between all upwelling and all downwelling (near the poles, main sink in the N.E. Atlantic)…

      • Ferd,
        Not just “warm zones near the equator,” but all along the west coast of North America.

      • Clyde,

        I didn’t say or imply that all upwelling is near the equator, even near the poles there is upwelling, indeed in most cases where there is much off-land wind.

        What happens with CO2 at the upwelling places depends of the temperature at the surface: near the equator, lots of CO2 are emitted, near the poles, lots of CO2 are absorbed. In balance, about 40 GtC/year is emitted by all upwelling deep ocean waters and some 40+ GtC/year is absorbed by sinking waters, mainly near the poles…

  12. CO2 levels are also related to the number of pirates at large, so correlation with population is an equally dubious statistic. What is certain is that rising temperatures release more CO2 from the Oceans. What the CO2 then does is quite another matter and one for a lot more study. Certainly it helps the plants.

  13. That population and CO2 increase with time says nothing about the causes of either (as has already been noted in comments). Of more interest to me is that global CO2 continues its steady rise despite all efforts to reduce the anthropogenic component.
    This suggests a much more dominant source of CO2 over which there is no control.

  14. At least we now have a good use for Co2 , apparently recycling lithium has been problematic but I’ve just seen a blurb where they put lithium batteries into a chamber ,charge it with Co2 and introduce heat and pressure and voila recycled lithium .

  15. The answer is obviously #5. The third factor is temperature itself. The warmer it is the more CO2 and the greater the population. As noted in the Little ice age …. population contracted. …. I’d venture to say CO2 probably decreased as well.

  16. When I saw you that you were using polynomials to do extrapolation, I stopped reading.

    Extrapolating using polynomials is a very bad idea and the higher the order of the polynomial the worse it gets. Straight line extrapolation is dubious; quadratic extrapolation is extremely doubtful; cubic extrapolation is totally indefensible; and anything beyond that is a meaningless joke.

  17. The AGW theory is that co2 in fossil fuel emissions increases atmos co2 levels and that in turn causes warming which in turn causes extreme weather and sea level rise, and has other catastrophic consequences.

    At the root of it all is the assumed relationship between emissions and changes in atmos co2 for which there is empirical evidence.

    Climate science did present a nearly perfect correlation in the data to support this relationship but that correlation is spurious.

    If this relationship can’t be established nothing remains of climate science because it exists only as a rationale to support a movement against fossil fuels.

    • Jamal,

      Your first reference starts with a false remark:

      The IPCC carbon budget concludes that changes in atmospheric CO2 are driven by fossil fuel emissions on a year by year basis.

      The IPCC never, ever, said or implied that yearly changes in atmospheric CO2 are driven by fossil fuel emissions over one year. That would only be possible if human emissions were the sole influence. As temperature shows a huge variability on year by year basis, that variability is the main driver of the year by year variability in CO2 rate of change, but that averages out to near zero within a few years. Human emissions are the main driver over periods longer than 3 years.

      • The rate of change matches temperature anomaly in both the short and the long term. Your explanation is epicyclic.

      • Bart,

        We do agree that (near) all year by year variability in CO2 rate of change is caused by temperature variability. Everybody agrees on that, including NOAA. Where we don’t agree is the origin of the long term slope.

        Where Jamal is wrong is assuming that because there is no correlation between year by year variability in CO2 rate of change and yearly emissions, the long-term slope is not from the emissions. Which doesn’t prove that at all.

  18. “There is no connection between the two, population and CO2 are completely unrelated phenomena and the apparent lockstep is just a fluke. Possible, but unlikely. While it is certainly true that correlation does not necessarily imply causation, it is also true that the better the correlation the more likely it is that some form of causation is involved.”

    Bzzt, wrong. Serial datasets with high autocorrelation tend to have spuriously strong correlations with each other. Compare CO2 with the population 75 years previous and you very likely still get a strong correlation even though the causation interpretations are clear nonsense.

    “Both CO2 and population are driven by a third, as yet unknown, quantity. While this cannot be dismissed out of hand, it must be considered as merely a theoretical possibility until this unknown quantity is identified.”

    How about time? Population is increasing over time for the whole time window and CO2 is increasing over time for the whole time window.

    Your statistics aren’t nearly strong enough to support your conclusions.

  19. Some time back I presented in one of observations in this site stating that: People take oxygen from the atmosphere and release carbon dioxide in to the atmosphere. As the population grows, the carbon dioxide release by humans increase proportionately. This may be the reason for the trend shown in Figure 1 of the article. So to reduce carbon dioxide in the atmosphere there appears to be a need to bring down the population. This is a phenomenon on the entire world land areas but other types of carbon dioxide releases in to the atmosphere are highly location specific only.

    Dr. S. Jeevananda Reddy

    • Dr. S.,

      Problem for that theory is that what humans (and bacteria, molds, insects, animals) release as CO2 is from plants that removed the same CO2 out of the atmosphere some months to decades before. In fact that is a zero-effect operation, as long as uptake and release are equal.

      With the increase of CO2 in the atmosphere, there is currently more CO2 uptake by the total biosphere than release…

      • Dear FE,

        the key word is “before”. That includes fossil fuels too – just a different time scale. As long burning bio mass puts additional CO2 into the atmosphere instead of causing(!) a drop of CO2 concentration AFTER burning there is no zero-effect!

      • TheDoctor,

        Depends of the definition of “fossil”… The IPCC implies “recent” carbon as part of the natural cycle: thus if you burn wood from a 50 years old tree, that is not fossil and indeed levels off if you count that over a few decades. Most food and feed is maximum a few months to a few years old and its digestion hardly influences current CO2 levels. Since about 1990, plant life in average takes more CO2 out of the atmosphere than alle users (bacteria, molds, insects, animals) bring back into the atmosphere… Thus despite our exhalation of CO2, the levels in the atmosphere would go down, if we didn’t burn fossil fuels.

        Most fossil fuels are millions of years old and they bring back CO2 in the atmosphere that was captured at that time with much higher levels in the atmosphere than today. That increases the CO2 level of the current atmosphere (which is a good thing, as plants like higher levels).

        Of course there are always edge cases. According to the IPCC, burning wood from a 600 years old oak still is non-fossil, while burning 600 year old peat is fossil, but as the first case is minimal in quantity, that hardly changes the balance…

      • “In fact that is a zero-effect operation, as long as uptake and release are equal.”

        It is an equilibrium process. The uptake is dynamic, and responds to the release with some lag. Equilibrium is achieved when uptake rises to balance input.

        One cannot alter such a balance by a greater proportion than one’s proportionate addition to the input which establishes the balance, and our inputs are a tiny fraction of natural inputs. Hence, our inputs have only a fractional influence on the balance.

      • Bart,

        As explained above, human emissions are about 9 GtC one-way additional, while the natural balance levels at any moment of time are between +/- 10 GtC, in average about zero. At no moment in time over the seasons there is 110 GtC extra in the atmosphere from the natural inputs.

        Your reasoning doesn’t fit what is observed in the atmosphere…

      • As explained above, that is quite impossible. You are assuming away issues that invalidate your narrative.

      • Bart,

        The natural carbon cycle, based on isotopic changes, oxygen and solubility is composed of approximately:
        seasonal oceans: + and – 50 GtC/season
        seasonal vegetation: – and + 60 GtC/season
        continuous oceans (between equator and poles): 40 GtC/year
        total: 150 GtC/year in and out.

        According to your reasoning, human emissions at 9 GtC/year have little influence compared to the 150 GtC/year natural emissions, as the sinks must equally remove that CO2, regardless of origin.

        The point is that there is never at any moment of time 150 GtC natural CO2 in the atmosphere: natural CO2 over the seasons is globally +/- 10 GtC and continuous CO2 is only a flux with zero effect on levels (*).
        Moreover, seasonal changes are negative with temperature: higher temperatures give lower CO2.
        In contrast, human emissions are one-way additional.

        Thus human emissions are of the same order of magnitude as the residual of the natural carbon cycle, which is far from trivial.

        (*) Basically as long as equatorial upwelling and polar sinks are in equilibrium. Currently more sink than source.

      • “Basically as long as equatorial upwelling and polar sinks are in equilibrium.”

        That is a major assumption, and it is wrong. That equilibrium does not simply exist. It is enforced by a balance between input and output. You cannot tip that balance proportionately by a greater amount than the proportion of your addition to the input which establishes the balance.

      • Bart,

        The observed change in equilibrium over time is about 16 ppmv/K over multi-millennia. A remarkably constant ratio. At this moment we are 110 ppmv above that equilibrium. That pushes more CO2 into the deep oceans than is released, as observed by lots of sea surface samples.

        Moreover, the total sink rate again is remarkably linear in ratio with the extra CO2 pressure above the theoretical equilibrium, even for a fourfold increase over the past 60 years.

        Your theory is only plausible when the sink rate for any extra added CO2 is very high and almost all of the human emissions of one year are removed by the sinks in the same year as emitted. That is not the case, as the observed decay rate of any extra CO2 above the long term equilibrium is about 51 years.

        The only fast exchange rates are seasonal between ocean surface and atmosphere and between seasonal growth and wane of vegetation and the atmosphere. That are temperature sensitive processes, hardly pressure sensitive. The removal of any extra CO2 in the atmosphere is in the deep oceans and more permanent vegetation. That are pressure sensitive processes, hardly temperature sensitive.

  20. Roger – can you let us have your ppm figures for the year 2100?

    Whilst you are no doubt correct in assuming that “CO2 trend lines are unlikely to be a reliable guide this far in the future”, all IPCC predictions are based on such endless projections.

    As the UN’s lower estimate for population bends down quite sharply in the second half of the century, I suspect the 2100 ppm outcome could be very similar to the ppm outcome of RCP2.6. If so, then there is a sound basis for treating this as the BAU base case.

    It would also be interesting to see the result of a fifth order polynomial, which has a shape somewhat akin to the 2.6 case. This would reflect the total disconnect between population and CO2 which will occur once the developed world adopts its next-generation energy source.

  21. A curve fitting polynomial has no predictive value and should not be portrayed as it has one.

    Roy Spencer used to add a high order polynomial to his monthly temperature presentations, but he correctly labeled them as “for entertainment purposes only”. That is all it is. All polynomials in figure 2 are rather meaningless and to link them to population predictions are equally meaningless.

  22. Whether population causes CO2 or CO2 causes population is another matter, but if we assume that this lockstep will continue for the foreseeable future, then if population goes up, so will CO2.

    There is no justification to assume that the lockstep will continue unless population causes CO2. If CO2 increase is not dominated by human activities (fossil fuels, land use …), falling back to Neanderthal level (both population and technology wise) won’t change a bit.

  23. Thank you Roger Graves. So far the misanthropogenic scare faith (yet to name itself sustainably), has been operating under elusive and relative terms of outside air temperature fraction anomalies and dollars per CO2 emission tons. Good to see it illustrated and quantified in more absolute terms.

    Whether there is any causality or not, it would be informative to calculate with UN logic, if e.g. “the Great Leap Forward” already cooled the planet enough to meet the UN targets.

  24. My opinion…

    Point 2 is the main driver: more people means more CO2 emissions as every individual in most countries uses fossile fuels directly or indirectly for heating, cooling, transport, comfort,…
    Point 2A should not be forgotten: As people get richer the per capita use of fossil fuels gets up and total CO2 release of a country goes up.
    Point 3 is reverse: more easely obtained food means wealthier people leading to less population growth, not more.
    Again, due to 2A, richer people have less children, but increased CO2 emissions…

    There is a direct link between CO2 emissions and CO2 increase in the atmosphere:

    All the variability in the rate of change is due to short-term temperature variability, while the overall trend is caused by human emissions, which are about twice the increase in the atmosphere. The red line in that graph is the theoretical response of the oceans to any extra CO2 pressure in the atmosphere based on a 16 ppmv/K response to temperature in dynamic equilibrium per Henry’s law and an observed about 51 years e-fold decay rate for CO2 pressure above that equilibrium.

    Further, a lot of other indications show that human emissions are the main cause of the increase in the atmosphere:

    That being said, what will bring the future?
    Human population probably will follow the peak 9.5-10.5 billion people scenario, as in most countries the human reproduction rate is already the minimum 2.1 or below. Exceptions are India and most of black Africa. The latter is the main unknown.

    Even if the population growth will get a peak, the increase of wealth in all countries will not stop and as long as there is no cheap, abundant alternative, fossil fuels will remain the main source of energy. There is enough coal to provide 10 billion people for hundreds of years with all energy needed and the shale revolution moved the “end of oil” and gas also forward with many decades.

    Thus my guess: CO2 will go up beyond population growth, as more people get richer and per capita energy use increases. At least up to 2050, as cheaper non-fossil fuel alternatives may come in (fusion, thorium reactors,…).

    • Gas pressure, volume, mass and temperature are part of the equation pV=nRT, not the composition. This is reproducible in a laboratory, upscaled in industry and can be observed on the planets of the solar system. Presuming run-away greenhouse overrides it at planetary scale, why has solid CO2 been reported to snow down from the CO2 atmosphere of Mars?

      All the variability in the rate of change is due to short-term temperature variability, while the overall trend is caused by human emissions, which are about twice the increase in the atmosphere.

      Planetary scale figures at ppm/year level defy metrology. Thank you for providing the source.

      The red line in that graph is the theoretical response of the oceans to any extra CO2 pressure in the atmosphere based on a 16 ppmv/K response to temperature in dynamic equilibrium per Henry’s law and an observed about 51 years e-fold decay rate for CO2 pressure above that equilibrium.

      Henry’s law presumes all the other parameters remain constant, which may be doable in a laboratory. Why do you think decay rate e-folding is sufficient to upscale it at planet-scale?

      • Jaakko,

        Mars atmosphere is 95% CO2, earth has 0.004% CO2. In the first case it is possible to reach low enough temperatures at the Mars poles to freeze CO2 out of the atmosphere, despite the much lower atmospheric pressure. On earth that is impossible…

        Henry’s law is applicable for every point of the ocean’s surface. There were over 3 million samples taken where the pCO2 of the ocean surface was measured and compared with the atmosphere. The partial pressure difference between ocean surface and atmosphere gives the direction and the CO2 flux is directly in ratio to that difference. As the diffusion of CO2 within the water mass is extremely slow, mixing speed with the atmosphere by wind is also very important. Using both factors, Feely e.a. have calculated the in/out fluxes between oceans and atmosphere:

        That shows that the oceans are a net CO2 sink at the current CO2 levels in the atmosphere. The same for the biosphere (based on δ13C and δO2).

        What if some other parameters change?
        – Higher temperatures at the surface: especially at the upwelling and downwelling zones with the deep oceans, will give more emissions at the equator and less uptake near the poles. That increases the CO2 levels in the atmosphere. The increase in the atmosphere gives the opposite reaction (Le Châtelier’s Principle) and ultimately the same dynamic (dis)equilibrium is reached at a CO2 pressure increase of ~16 ppmv/K. Not by coincidence the same change per Henry’s law as for a single sample in a laboratory.
        – Wind speed increase/decrease: only gives a change in exchange speed. That doesn’t influence the ultimate equilibrium, only the speed with which that is reached.
        – More upwelling from the deep oceans and/or higher CO2 concentration of the deep: temporary increase in natural emissions at the upwelling, leading to increase in the atmosphere, leading to increase in sink rate and decrease in source rate. New equilibrium gets up in ratio to increase in CO2 emissions from the upwelling. An improbable 10% increase in upwelling will give some 30 ppmv increase in the atmosphere.
        – More emissions in the atmosphere (humans, volcanoes,…): increase in pCO2 reduces natural emissions at the upwelling zones and increases the sink rate at the poles. Increase in the atmosphere depends of the difference between emissions and extra sink rate. At the current emissions of ~9 GtC/year (~4.3 ppmv/year) of CO2 the sink rate for 110 ppmv extra pressure in the atmosphere above steady state is ~4.5 GtC/year (2.15 ppmv/year). Not enough to remove all human CO2 emissions in the same year as emitted, thus the remainder accumulates in the atmosphere.

        The above decay rate of ~51 years was remarkably constant over the past near 60 years of accurate measurements. That means that the IPCC Bern model with increasing saturation of the deep oceans is not (yet) proven and there still is plenty of room in the deep oceans. The bottleneck is the exchange speed between the deep oceans and the atmosphere, as these are largely isolated from each other.

      • Your answers are appreciated Ferdinand. You are the first taking the effort to answer me these questions professionally. Had you been the first to encounter, I’d perhaps be elsewhere now. Thank you again. Some questions rather for information/consideration only, not necessarily expecting an answer in this chain.

        “Mars atmosphere is 95% CO2, earth has 0.004% CO2. In the first case it is possible to reach low enough temperatures…”

        In my view this favours pV=nRT over GHG model. If even carbon dioxide atmosphere temperature can lower, why couldn’t the nitrogen/oxygen mixture atmosphere temperature lower too?

        “Henry’s law is applicable for every point of the ocean’s surface”

        Based on the numbers declared in the related article, each measurement seems to represent about 15,000 square kilometres of ocean/year. How can “every point” be defined or measured accurately, let alone representatively for an entire year of the ocean? After all Henry’s law states: At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.” Biological processes are excluded from Henry’s equation by its own definition. How has this been taken into account in the ocean measurements?

        “The bottleneck is the exchange speed between the deep oceans and the atmosphere, as these are largely isolated from each other.”

        How can lithosphere-ocean-atmosphere interfaces be isolated e.g. fast eroding chalk-cliffs (CaCO3, presumably one of the most common stones) and volcanic activity, including the ring of fire. How can they be measured separately or excluded from s.c. fossil fuel signal?

      • Jaakko,,

        My pleasure to give you all information I know (but still don’t know everything I like to know…)

        The main points in this case is radiation balance and pCO2 in the Mars atmosphere vs, vapor pressure of solid CO2 at ambient temperature.

        At the Mars poles, little sunlight comes in and a lot of heat is radiated out of the surface as a 4th power function of the surface temperature. On earth that can give temperatures down of -80ºC, which is the condensation temperature of CO2 at 1 bar pressure. As the CO2 pressure on earth is only 0.0004 bar, you need extreme low temperatures to condense CO2. As Mars is farther from the sun, less sunlight is reaching the poles and temperatures can drop much lower. On the other side, the CO2 pressure is much less than 1 bar, so it depends of temperature and pressure if the solidification temperature will be reached.
        I doubt that the CO2 “greenhouse” effect will have much influence on the Mars poles (and little on earth too), it only delays the cooling in Mars polar winters, so ultimately it will make little difference for reaching the solid state of CO2…

        I agree that 3 million samples over time is not much over the wide oceans, but all of them did show the same basic chemistry: if you measure two variables, one can calculate all others. And everywhere temperature and pCO2 are closely coupled.
        While Henry’s law is about a fixed ratio of a gas between atmosphere and liquid at a fixed temperature, in the CO2 case it is the change in Henry’s rate constant with temperature which is important. That translates in an equilibrium pressure between ocean sample and atmosphere at the surface temperature and thus direction and CO2 flux between surface and atrmosphere.
        In overall exchange speed between ocean surface and atmosphere is less than a year, where the “surface” is the “mixed layer” of 50-200 m depth influenced by wind and waves.
        Biological processes seems to be excluded, but as they influence the amount of bicarbonates, they influence the whole chain of reactions and thus are included in the pCO2 measurements.

        In general the ocean’s inorganic content doesn’t change that rapid and even for long term sampling 4 samples per year are sufficient to show all (seasonal) variation as needed, including the influence of temperature and bio-life.
        There are a few stations which have longer, continuous data. That shows seasonal and longer term parameters, here for Bermuda:

        The main difference between fossil and recent organic CO2 at one side and inorganic CO2 is in the δ13C levels: practically all fossil and recent organics are low (C4-plants) to extremely low (natural gas) in 13C/12C ratio, while near all inorganic CO2 from oceans, carbonate rocks, volcanoes,… is higher in 13C/12C ratio.

        To differentiate between fossil and recent organics, one can use the oxygen balance: fossil fuel use needs oxygen, while vegetation growth/decay produces/needs oxygen. By subtracting the oxygen use from burning fossil fuels from the change in oxygen level, that shows a small deficit: less oxygen is used than calculated. Thus recent organics are a source of oxygen and thus a sink for CO2 and preferential of 12CO2 and thus not the cause of the decline in δ13C…

    • Your argument is somewhat faulty — fossil fuel use is not that high up to around 1990’s over several developing countries — in 80’s I travelled Ethiopia with a truck filled with diesel as there was internal war with poor road connectivity; in Mozambique there was no way to travel except through Air as roads are full of mines. Also, the figure indicates higher growth in CO2 during the same period. Also, WMO fact sheet showed the CO2 measurements were very sparse in 1960s.

      Dr. S. Jeevananda Reddy

  25. Between 134,000 and 128,000 years ago in at the start of the Eemian interglacial CO2 concentrations increased by 80 ppm and then declined by the same amount between 112,000 and 85,000 years ago. During these periods it is inconceivable that the driving force could have been changes in human population which was minuscule at all those times.
    Between 450MY ago and 300MY ago CO2 concentrations fell from +/- 4500 ppm to +/- 500ppm and then rose again to 3500ppm by 175MY ago. There was no human population at all during these periods.
    To draw conclusions on the rise in CO2 over the last handful of decades is hopelessly absurd.
    The probable cause of the two rising together is that the recovery of temperatures since the last Glacial Maximum has caused the rise in CO2 concentration and the benign climate and increased fertility from rising CO2 allowed the great increase in human population.

  26. catbirdgoblin,

    You can’t compare the earth of many million years ago with the earth today. CO2 of 60 miilion years ago was taken out of the atmosphere by calcifying plankton (Ehux) and now sits in thick layers of chalk in South England and many places on earth.

    Over the past few million years, there was a rather fixed ratio between CO2 levels and temperature: about 8 ppmv/K for the poles (as seen in ice cores), that translates to ~16 ppmv/K for the whole earth taking into account the polar magnification effect of temperature changes.
    The about 16 ppmv/K is not by coincidence what Henry’s law gives for the solubility of CO2 in seawater at different temperatures. That is what is seen in ice cores over the past 800,000 years. Since ~1850, the CO2 levels are increasingly higher than that fixed ratio, where human emissions are average twice as much in quantity as what is seen as increase in the atmosphere. Seems rather obvious that temperature is not the cause and humans are at the base…

    • Ice phases are dynamic – there may be 18 from ice under normal atmospheric pressure to possible crystal structures when progressively crushed under high pressure. It would be reasonable to expect the type of lattice influencing the amount of gas it can contain.

      How has this been taken into consideration when analysing, calculating and reporting carbon dioxide concentrations at ppm level in the Arctic ice cores presumably spanning over 800,000 years?

      • Jaakko,

        CO2 in ice cores is not in the ice matrix. When snow falls on the surface, it contains more air than ice with the air at ambient composition. When it compacts, the density of the loose ice (firn) increases and air is squeezed out, with decreasing pores between the ice crystals. Meanwhile there still is diffusion of air in both directions, which gets slower with decreasing pore diameter. At a certain depth the pores are too small and exchange ceases and at last only fully enclosed small bubbles of air remain in the ice. That is not air from one year, but a mix of several years: 10 to 600 years, depending of the accumulation speed of snow and thus the speed with which the air bubbles are fully isolated.

        The form of the ice thus is not important. What is important is that at a certain depth clathrates between CO2 and ice and deeper between O2 and N2 and ice are formed. Thus no visible air bubbles left. For that reason the ice cores recovered from the deep are put near te surface during at least a year at -20ºC for relaxation. During that time the ice cores expand a lot and the air bubbles come back.
        See for a nice overview:

  27. Thanks for your essay, Roger.

    But there’s one mistake in it. You presume a CO2/population relationship, disregarding there is a vast more quantity of CO2 in oceans and land mass controlled by temperature.
    Manmade CO2 is absolutely negligible versus the whole CO2 content of the planet.
    What you’ve made up, is a stork/babies fallacy.
    But at least, I agree your #1.

    • Petermue,

      How much CO2 is in other reservoirs is not of the slightest interest for any increase of CO2 in the atmosphere, as long as that stays there.
      How much CO2 is exchanged with other reservoirs is not of the slightest interest for any increase of CO2 in the atmosphere, as long as the inputs equal the outputs.
      Currently humans emit ~9 GtC/year. Currently the difference between natural inputs and outputs is ~4.5 GtC/year more output than input.
      Thus the other reservoirs are increasing and not the cause of the increase in the atmosphere…

      • Currently humans emit ~9 GtC/year. Currently the difference between natural inputs and outputs is ~4.5 GtC/year more output than input.

        How much CO2/year do Seven Sisters chalk cliffs in East Sussex emit?

      • Jaakko,

        Not much… Estimates of global rock weathering by CO2 (making soluble bicarbonates from the chalk rocks) are around 1% of human emissions. Look at how many millions of years it needs to carve the beatiful caves in carbonate rock everywhere…

      • paqyfelyc – it’s just awful. Very naive. An elementary mistake in dealing with dynamic systems. I explain why here.

      • paqyfelyc,

        Bart’s response in his reference contains several basic errors (*), but that was discussed here on WUWT many times in the past. The only way that his theory may be right is that the natural carbon cycle is very huge and increased over time, dwarfing human inputs to not important.

        Since 1960, when accurate measurements at Mauna Loa (and the South Pole) started, human emissions per year increased a fourfold. So did the increase in the atmosphere and so did the net sink rate. The latter is the difference between human input and observed increase in the atmosphere per mass balance.

        The simplest conclusion is: based on the mass balance, human emissions are the cause of the increase and the difference sinks somewhere in nature, wherever that may be. That fits all observations.
        Bart’s conclusion is that the natural cycle (due to temperature increase) is the main cause of the increase.

        The only way that can be true, is if the natural cycle also increased a fourfold since 1960, or you violate the equality of CO2 for the sinks, whatever the origin. Sinks don’t differentiate between CO2, no matter if that is of human or natural origin. Thus if human CO2 quadrupled, natural CO2 input (and output) must have quadrupled too (or not at all), to give a fourfold increase in net sink rate.

        That is not observed at all: to the contrary, all indications show a rather stable natural cycle (+/- 2%) with an increasing average residence time (while one may expect a fourfold decrease for Bart’s theory), decreasing δ13C (while one may expect an increase),…

        (*) Bart’s reasoning starts already with a false assumption:

        0.5*Ea := Ea + En + U

        There is no reason at all that the increase in the atmosphere is half of human emissions for any given year or not even in average over decades. The sinks don’t depend on the emissions (natural and/or human), they only depend on the momentary CO2 level (pressure) above equilibrium, the latter influenced by the momentary surface temperature.

      • @ Ferdinand Engelbeen
        I agree that “The sinks don’t depend on the emissions (natural and/or human), they only depend on the momentary CO2 level (pressure)”. Period.
        I mean, you cannot (and don’t need to!) assume any equilibrium. Indeed, we have hints that the whole system is out of equilibrium, just as living beings are. That is just what the Gaia hypothesis is all about (not some sort of goddess).

    • “There is no reason at all that the increase in the atmosphere is half of human emissions for any given year or not even in average over decades.”

      Of course there is. That is the observation. It’s not saying it has to be. It is just what is observed.

      This is really dumb. The pseudo-mass balance argument is really dumb.

      • @ Mark S Johnson
        your question is very dangerous, and irrelevant
        Dangerous because it is open door to some idea that human emitted CO2 behave in nature somehow differently from other CO2 (not saying you fell to that, but other may and did)
        Irrelevant, because it could very well be 264 or 2640 Gt (if it was absorbed and re-emitted 10 or 100 time during the year), this is not important; what is important is how much the total is increased (if it is; sometimes, increasing input actually reduce the output)

      • Bart,

        The sinks react on the total pressure of CO2 (pCO2) in the atmosphere, not (only) on the extra pressure from one year’s emissions.
        In your formulation you take the 0.5*Ea as fixed, while the sinks don’t react on Ea, they react on
        pCO2(actual) – pCO2(equilibrium) where the latter depends of the ocean surface temperature.

        The net sink rate is:
        U = k(pCO2(act) – pCO2(eq)) where k ~0.02, surprisingly linear in the past 60 years.
        pCO2(eq) does change with temperature at ~16 ppmv/K on a year by year basis.

        The increase in the atmosphere then is:
        dCO2/dt = Ea – U or
        dCO2/dt = Ea – k(pCO2(act) – pCO2(eq))

        The increase in the atmosphere depends on the height of the emissions in a given year and the net sink rate of the total increase in the atmosphere above equilibrium, not only of the emissions.
        dCO2/dt thus can be positive, negative or zero.

        If the current emissions would stabilize at 4.3 ppmv/year, the increase in the atmosphere would stabilize at 4.3 / 0.02 = 215 ppmv above equilibrium or just over 500 ppmv.

        There is nothing dumb in assuming that the mass balance must be obeyed at any moment in time…

    • @bartemis
      Your explanation in your link is just out of scope. No physical assumption whatsoever is needed to just observe that, if, during a period of time, a source net produced 9 while the result only increased by 4, then all other source+sink must have net reduced by 5 (because sinks ramped up or appeared, other source dwindled, or any combination). In any case, other sources/sink cannot have net produced, too.

      • paqyfelyc,

        Bart’s escape route is that the natural cycle dynamically increased over time: if the natural cycle increased a fourfold since 1960, then the residual of the sinks would go up a fourfold (that is observed), as the resistance increases with a higher circulation speed. Because of the much larger quantities circulating in nature, the small addition by a fourfold increase of human emissions in the same period doesn’t play much role.

        Problem for that theory is that there is not the slightest indication of an increased natural carbon cycle, to the contrary: recent estimates of the residence time of any CO2 (whatever the source) in the atmosphere gives an increase compared to older estimates, which is consistent with a rather stable carbon cycle in an increased mass of CO2 in the atmosphere.

  28. This may be the most ridiculous and unrealistic prediction of future CO2 levels, Evah! It makes the same colossal blunder almost all of the doomsday scenarios make : it ignores the imminent appearance of a energy revolution that will be brought about by molten salt nuclear reactors, , which will commercialize within 10 years,at most. These reactors will replace existing generators for purely economic reasons. There will be no need for subsidies for these nuclear reactors. Or any need to convince people that they will be the safe and physically incapable of causing harm. And can burn Thorium is need be. And if you are looking for more good news about electric cars, 120 models have been announced by the world’s automakers – due in showrooms over the next 3 years. And, if that isn’t enough, Toshiba just completed testing a new variation battery that can be recharged in 6 minutes (32kWhr battery) and can retain 90% of its capacity after 5,000 recharge cycles. That amounts to over 1 million miles. It also resists the effects of cold temperatures.

    • hm …. Any new energy will takes decades just to appear in the energy picture. Current powerplants will remanin for decades.
      Besides, if CO2 stop to rise or even flatten, we are doomed. Warmunists will take credit, pretend they succeed in stoping a disaster, and strenghen their power. We need CO2 to rise to drive warmunists and doomsayers back in the dark age they belong.
      And. Dont make so much fuss about batteries. These things are just tank, you still have to fill them up with something. Charging a 30kWh battery in 6 minutes require a 300kW power, just compare that to your house power…

  29. I’m going with a 6th possibility, that CO2 and population are each affected (“driven” is such a presumptive term) by a number of factors, many of which are unrelated to each other while some of which are.

  30. Roger, like the UN’s favorite climate model, the disaster scenario RPC 8.5, their population stats are similarly exaggerated. Growth rates of population peaked in 1990 (90million added /yr) and projected to drop to 40million a year by 2050. Population should peak at or below ~10million and if prosperity can be spread unhindered by stopping the interference of neomxist мisаитнгорisт economy wreckers, it could fall to below the 10million peak. Folks, we are 85% there! With greening of the planet, big harvests, a healthy prosperous population, we will be approaching Garden of Eden Earth. This itself will mark the end of аlагмisм, dуsторiaisм, and maybe, finally, global магхisм.

  31. Roger, you may also wish to take into account the following:

    “Here, we study the questions why we still live in an interglacial world and when we should expect the end of the Holocene under natural conditions (no anthropogenic influence) or under anthropogenic perturbations (also referred to as “Anthropocene”), questions which attracted considerable interest in recent years. It was argued that without earlier anthropogenic activity we would live already in glacial world (Ruddiman’s hypothesis). Tzedakis et al. (Nature Geoscience, 2012), using MIS 19 as the best analogy in terms of the orbital parameters for the Holocene, suggested that the new glacial inception would start within the next 1500 years, assuming natural CO2 level of 240 ppm. However, 240 ppm is much lower than preindustrial CO2 level and CO2 concentrations during several most recent interglacials (starting from MIS 11). Here, using the comprehensive Earth system model of intermediate complexity CLIMBER-2, carefully calibrated for the simulations of the past eight glacial cycles, we show that (i) although climate conditions during late Holocene were very close to the bifurcation transition to the glacial climate state (Calov and Ganopolski, Geophys. Res. Lett., 2005), it is very unlikely that under pre-industrial CO2 level (280 ppm) glacial inception would occur within the next several thousand years; (ii) it is likely that the current interglacial, even without anthropogenic CO2 emission, would be the longest interglacial during the past million years; (iii) current CO2 level makes new glacial inception virtually impossible within the next 50,000 years; (iv) in agreement with earlier result of Archer and Ganopolski (Geochem. Geophys. Geosyst., 2007) based on a conceptual model of glacial cycles, we found that consumption of a large portion of available fossil fuel could postpone the next glacial inception by hundreds of thousand years.”

    The last part of the final sentence is a real corker.

  32. too simple: you just cannot connect atm CO2 directly to anything (population or whatever), you have to connect flux, out and in. Population may (or not…) drive human CO2 outgasing, but you have to make assumption about the way extra CO2 is sucked up by other process. Which may be flat, linear, quadratic (for instance: more CO2 -> more photosynthesis x more plants -> square less CO2) or even exponential.

    Besides, i think we should be far more worried by the impact if AI and information control, than climate. Humanity will thrive whatever the climate turns to be, it may not survive an AI take over

  33. These calculations ignore the most fundamental wisdom. First of all, CO2 sinks consume about 1,8% of elevated atmospheric CO2 p.a.. Next fyi, one ppm in the atmosphere corresponds to 7.79Gt of CO2.
    So at 550ppm that would mean CO2 sinks will consume like (550-280)*7.79 * 0.018 = 38Gt of CO2 p.a. That would be a long term target to achieve in a distant future, if we continue to emit like we do at the moment.

    CO2 predictions in the “4th order Polynomaial Trend” is completely absurd for that reason. First the “high estimate” indicates an increase of 16ppm per year in 2050. That would require emissions of 16*7.79 = 124.6Gt p.a. But furthermore we would need to compensate for the effect natural CO2 sinks, which amounts to (660-280)*7.79*0.018 = 53.3Gt. So mankind would need to emit 177.9Gt p.a. in 2050.
    For the same reasons, even the “medium estimate” would require 74.4Gt p.a., which may not seem impossible, but rather unlikely.
    The “low estimate” however would be consistant with about 29Gt emissions in 2050, which may seem low by todays standards. As developing nations do and will not care about the emissions, that seems unlikely too.

    So realistically we will see something between the low and medium estimate, which of course will be completely irrelevant for climate anyhow.

  34. Maybe we should look at Henrys Law from 1803.
    The amount of gases in the atmosphere, including CO2, is a function of the air temperature.
    The warmer it gets, the more CO2 there is in the atmosphere.
    The only true statement we can make about the climate, is that is always changing.
    With ice-age as one extreme, we can only speculate about the other extreme.
    The atmosphere is warmer now than during The Little Ice Age.
    Consequently, there will be more CO2 in the atmosphere now than 200 years ago regardless of the number of people emitting CO2 one way or another.
    Since it is a lagging function, we will still see an increase even if the temperature curve is relatively flat now.

    • Kjell,

      The solubility of CO2 in seawater changes with about 16 ppmv/K. That means that the increase of CO2 since the LIA for 0.8 K temperature increase is about 13 ppmv at the new equilibrium. For the current average ocean surface temperature, that means a CO2 level of ~290 ppmv in the atmosphere. We are at 400+ ppmv. The extra 110 ppmv can’t be from the increased ocean surface temperature…

  35. Jim Ross, October 8, 2017 at 1:26 pm

    “Take the δ13C decline:
    That definitely excludes the oceans as source of the increase of CO2 in the atmosphere.”

    I disagree. The literature is not very helpful on this, and seems incapable of addressing the biological pump, but we know (or think we know) that phytoplankton discriminate against 13C in the same way (and proportion) that land-based plants do.

    That is true, but the net effect is an increase of 13C at the surface: when phytoplankton produces organics, it prefers 12CO2, thus 13CO2 is relative left in the ocean surface, where most biolife is present. Via the food chain, a lot of bio-CO2 returns in the waters (and air), but some drops out into the deep oceans.
    As that is low-13C, the ocean surface remains higher in δ13C than the deep oceans. The latter are around zero per mil δ13C, while the ocean surface is between 1-5 per mil δ13C, depending on the abundancy of biolife…
    Thus any oceanic CO2, either circulation or addition would increase the δ13C level of the current atmosphere (at -8 per mil), while we see a firm decrease.

    Of course, it is always more complicated than said here: there is a discrimination between 13CO2 and 12CO2 at the border between water and air and reverse: heavier isotopes tend to move slower into another medium. That makes that over the pre-industrial Holocene, the equilibrium δ13C level was about -6.4 +/- 0.2 per mil in the atmosphere. Human emissions dropped the δ13C level with 1.6 per mil to below -8 per mil in current times:

    Free access to the pre-print:

    As you can see, the same drop is visible in surface waters (coralline sponges) as in the atmosphere (ice cores, firn, direct measurements), because both are in close contact and exchange CO2 with a rapid mixing rate of less than a year.

    That drop is larger than during the glacial-interglacial transitions and reverse and not coupled with huge temperature/ice/land/biosphere changes as during the transitions: and

    • Thanks for showing this plot again. It’s funny how no-one mentions the scales, which obviously were chosen by the author to show the match between CO2 and δ13C.

      The left scale is linear in δ13C but, in order to get alignment with the CO2 data, the author has quite rightly used a right-hand scale that is linear in the reciprocal of CO2. Such a relationship reflects a constant δ13C value for the incremental CO2! Further, we can compute that value simply by comparing the two scales: taking 1/CO2 values of, say, 0.0035 and 0.0029 (right scale) and reading off the equivalent δ13C values (outer left scale) of -6.47 and -7.56 respectively gives a constant δ13C value (on average) for the incremental CO2 since 1750-1800 of -12.8 per mil. Close enough to -13 (as demonstrated by the measurements at the South Pole I showed above) I think you’ll agree. Of course, the match from 1950 onwards is simply showing the same thing as my plot, but it is the alignment prior to 1950 that adds to our knowledge about the growth of atmospheric CO2.

      So, this plot supports a view that all the growth in atmospheric CO2 since 1750 or thereabouts has had a δ13C content of close to -13 per mil. It is the apparent constancy of this value that interests me and, of course, the implications of this for any proposed model. However, I suspect that most people looking at the plot are not aware of the significance of the choice of scales.

  36. Jim Ross,

    In the upthread discussion you plotted the O2/N2 ratio vs. CO2. That shows a high correlation. That can be explained as follows.

    The emissions – increase ratio in the atmosphere also is almost linear:

    That is just by coincidence, as human emissions increased more or less linear per year, giving a slightly quadratic emissions total over time and so does the residual increase in the atmosphere. That gives a highly linear correlation between the two.

    As the constant increasing CO2 level is mainly caused by fossil fuel burning, that uses a constant increasing amount of oxygen, as long as the quantities and the mix don’t change too fast.
    In this case, the mix did slowly move from coal (1 O2 for 1 C) to oil (1.5 O2 for 1 C + 2 H) to natural gas (2 O2 for 1 C + 4 H). That means that the per molecule use of fossil fuels the oxygen may double over a longer period of time (and back again at gas).

    If the shift in fuel mix happens gradually, that will not change the linearity of the correlation, it only will influence the slope, which gets steeper as gradually more O2 is used by the increase in fossil fuel use + the increase from the change in fuel mix.

    The same is true for the comparison δ13C and 1/CO2: only the slope changes with a gradual change in fuel mix towards lower-13C fuels, not necessary the linearity.

    Thus one need to look at the total and mix of all the fuels used, calculate the total oxygen use and average drop in δ13C of that mix. Then add in the ~40 GtC (deep) ocean exchanges at -6.4 per mil (which is the pre-industrial average caused by the ocean-atmosphere exchanges)…

    Eventually one can add in the increasing uptake by the biosphere, and the shift in isotopes by the biosphere as Ralph Keeling did to fit the details…

    Will be a nice job for you…

    • Ferdinand,

      Hmmm, a straight line with (only) changes in slope. Interesting!

      I have no interest in developing my own models as I am not trying to prove an alternative hypothesis. I started looking at the data and the published models in an effort to convince myself that the very logical sounding hypothesis that all (or most) of the growth in atmospheric CO2 is from anthropogenic emissions. Given the level of support for such a view, I thought this would be an easy task, but the reality has been very different and I remain unconvinced that the hypothesis has been proved.

      Since you are convinced about this, based on a great deal of your own research that you share here on WUWT, could you tell me if the CDIAC “global carbon budget” (which I believe is also the IPCC view) is consistent with your analysis. Based on the latest release (, November 2016), it would seem to be their view that:

      1. All (100%) of atmospheric CO2 growth is from emissions. This is evident from the fact that they subtract the atmospheric growth from total emissions and then “assign” the rest to either the “ocean” sink or the “land” sink, in the same year.
      2. Roughly 27% of total emissions (give or take 3 or 4%) is absorbed by the oceans each year, regardless of the estimated size of total emissions that year and, even more strangely (to me at least), showing no correlation whatsoever with ENSO.
      3. The remainder (emissions minus atmospheric growth minus ocean sink) is absorbed by the land sink. Simple arithmetic calculation as shown in the published spreadsheet: no independent verification as far as I can see.
      4. In two years (1987 and 1998), the land sink is calculated as negative, i.e. there is a net release of CO2 – this is within the quoted error margin, however, so perhaps it is simply their view that in these two years the land sink did not remove any emissions at all.
      5. In other years, the land sink removes anything up to over 50% of emissions.
      6. In some years, then, the two sinks combined can remove 80% of anthropogenic emissions (La Niña or Pinatubo). In other years, as little as 21% is removed (El Niño).

      Of course, we know that annual variations in atmospheric CO2 growth rate correlate extremely well with temperature/ENSO, but CDIAC’s model puts all of this variation down to the land sink alone (with higher temperatures leading to less uptake). Do you agree with this aspect of the hypothesis?

      • Jim Ross,

        1. That simply is the mass balance. As long as human emissions are higher than the increase in the atmosphere, all increase (in total mass, not from the original human molecules) is from the emissions and nature acts as a sink.
        Bart has a mathematical possible alternative, with high turnover of huge natural fluxes, dwarfing human emissions. That is only possible if the natural fluxes increased a fourfold since 1960, as human emissions and the increase in the atmosphere did. There is no evidence for any increase in natural cycle, to the contrary…

        2. and 3. Ocean uptake is simple physics: just a matter of temperature and CO2 pressure over the equilibrium level for that temperature. That process is much more pressure sensitive than temperature sensitive.
        Take e.g. the uptake at the polar oceans (~40 GtC/year):
        The pCO2 difference between atmosphere and the polar waters is 400-150 = 250 µatm difference, pushing 40 GtC into the deep oceans.
        See Feely e.a. at:

        If the seawater temperature near the poles increases with 1 K, that gives a local increase of the equilibrium pCO2 of the waters from 150 to 166 µatm and the local pCO2 difference drops to 234 µatm and the output drops from 40 GtC to 37.4 GtC/year, a 6.5% drop. Together with the increase in output at the equator at warmer temperatures that gives an initial net input of CO2, but in a few years the resulting increase in the atmosphere pushes more CO2 in the sinks and less out of the sources. At 16 ppmv extra in the atmosphere, everything is back in (dis)equilibrium as before the temperature increase.

        Uptake by the biosphere can be calculated from the oxygen balance, which shows much more variability, the uptake by the biosphere is far more temperature sensitive than pressure sensitive.
        The oxygen balance can be found at:
        Especially Fig. 7, which gives the opposite view: net uptake/release by the biosphere and the residual is what the oceans do…

        That it is mainly the biosphere and not the oceans which are responsible for a fast reaction of CO2 on (ocean) temperatures like El Niño and Pinatubo can be seen in the opposite δ13C and CO2 changes. If the CO2 changes were mainly from the ocean surface, δ13C and CO2 changes would parallel each other:

        4. In the above graph, the huge influence of the 1998 El Niño on vegetation is visible as good as in the O2 balance of FIg. 7. Detailed investigations showed that the negative uptake is almost all in tropical forests, where changed rain patterns dried out large parts of the forests with more release (from debris) than uptake and more forest fires as result.

        5. A La Niña reverses the effect of an El Niño on tropical vegetation, which restores the loss in 1-2 years…

        6. The Pinatubo had an extra effect besides a drop in temperature: due to far more scattered sunlight from the stratospheric aerosols, photosynthesis was enhanced, as leaves which were normally in the shadow of other leaves during part of the day, now received enough sunlight all day long to remain active…

        Thus indeed, land based CO2 sinks are the main reactant on temperature changes and CDIAC did a good job…

      • Ferdinand,

        A simple “yes” would have sufficed! I am familiar with your arguments, but am also very aware that models: (i) provide no more than a single, non-unique, possible explanation of the observations; (ii) the results depend critically on the input assumptions; and, (iii) there is a real danger of getting into circular arguments. You refer to Bender et al (2005). It contains a number of key assumptions, fails to explain certain characteristics of the data and provides a conclusion regarding the relative size of the two sinks that differs from CDIAC by up to a factor of four!

        I am surprised that you are still using the misleading derivative plot to suggest that it demonstrates that vegetation (δ13C of circa -25 per mil) dominates the variability instead of showing the actual CO2 and δ13C values. These data demonstrate the fact that there are times when both CO2 and δ13C values are increasing in parallel, as you know. More specifically, what we do know is that the long term decrease in atmospheric δ13C reflects an average value for incremental CO2 of -13 per mil and that this value decreases during El Niño and increases during La Niña. This point cannot even be controversial, since the “thinning” model would fail otherwise (see Randerson et al, 2002, Figure 5, and consider the implications of varying the size of the land sink due to ENSO):

        But then this is still only one possible solution and it requires that all of the input parameters/assumptions that are the basis for Figure 5 must remain more or less constant over the longer term, or vary in a way that maintains the known long-term value of δ13C for the incremental atmospheric CO2 (the black arrow on Figure 5), which brings us back to Ralph Keeling’s problem and his proposal which would add yet another variable to the Figure 5 diagram.

  37. Since about 95% of carbon dioxide in the atmosphere is from natural causes it would seem that 95% of the increase in CO2 would be caused naturally. . The global warming that began around 1850 is most likely the major reason for the increased greening of the Earth. This greening would appear to be the primary reason for the global CO2 increase. The satelite CO2 measurements show the three most dense areas of CO2 to be the Brazilian rainforest, the jungles of Central Africa and the heavily vegetative area of Southeast Asia and Southeast China.

    • Your first sentence is obviously false. Most systems grow out adding something else, not out of linear increase of the already there. For instance, +98% of the population is made of people born more than 1 year ago, while more than 100% (no error!) of the increase is due to people born last year
      Your second is plausible but unproven (and impossible to prove)
      Your third is weird hypothesis (why would greening increase CO2, when green things eat CO2?).

    • Bill Everett,

      Based on the δ13C level in the atmosphere, human CO2 now is about 9%, natural is around 91%. Natural cycle is around 150 GtC/year bidrectional, human emissions are around 9 GtC/year one-way.
      That is the problem for your theory: even if natural emissions increase a tenfold, that doesn’t influence the increase in the atmosphere, as long as the sinks increase equally. Since 1959 in every year the sinks are larger than the natural sources, thus not the cause of any increase in the atmosphere…
      The satellite shows CO2 levels, not CO2 fluxes. CO2 levels over the equator are higher due to deep ocean upwelling, while the polar sinks take a lot of CO2 with them. That is a flux of ~40 GtC/year from equator to poles, again more sink than source…

  38. The author of this claim did not talk about how much of a difference switching to renewable energy sources would have on CO2 levels in the atmosphere. The author states that none of the measures taken by industrialized countries to reduce CO2 levels seem to have any noticeable effect up to 2015. However, he is not considering the use of future technological advancements such as the electric car, in society, which can reduce CO2 levels greatly. Also, he is not considering Earth’s natural processes as possibility for increasing CO2 levels. For example, according to the article published in the Journal Nature, it was found that the soil releasing CO2 into the atmosphere is the main problem, not humans (Fang, 2010). Also, he does not talk about the issue in terms of major CO2 emitting countries, rather as an entire world, but this is questionable as smaller countries and cities contribute minimally.

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