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 2^nd-order to 6^th-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 http://esa.un.org/unpd/wpp/Download/Standard/Population/, 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 5^th– and 6^th-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 2^nd-, 3^rd– and 4^th-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.

The results shown span a broad range, from 439 ppm to 659 ppm. However, this can be narrowed down somewhat. The 4^th-order polynomial trend line shown in figure 2 is considered somewhat suspect because, unlike the 2^nd– and 3^rd-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 4^th-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.

Summary

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.