*Carl Edward Rasmussen, University of Cambridge writes (Sept. 14, 2018) on growth in carbon dioxide levels:*

*"So, what does the data tell us? It shows that all is not well in the state of the atmosphere! In order to prevent further warming, the carbon dioxide levels must not grow any further. On the growth curve, this corresponds the curve having to settle down to 0 ppm/y. There is absolutely no hint in the data that this is happening. On the contrary, the rate of growth is itself growing, having now reached about 2.3 ppm/y the highest growth rate ever seen in modern times. This is not just a "business as usual" scenario, it is worse than that, we're actually moving backward, becoming more and more unsustainable with every year. This shows unequivocally that the efforts undertaken so-far to limit green house gases such as carbon dioxide are woefully inadequate."*##
**Atmospheric
Carbon Dioxide Growth Rate**

**Atmospheric Carbon Dioxide Growth Rate**

**by**

**Carl Edward Rasmussen**

http://mlg.eng.cam.ac.uk/carl/words/carbon.html

14 Septermber, 2018

Release of green house gases, such as carbon dioxide, or CO

_{2}, into the atmosphere is causing global warming. The underlying physical mechanism has been well understood at least since the 1970s. More recently, attempts have been made to limit the release of green house gases both nationally and globally, most prominently the Kyoto Protocol in force from 2005 and the Paris Agreement in force from 2016. In this note I assess the progress made so far in limiting atmospheric carbon dioxide concentration.

### The Keeling Curve

### Seasonal variation

### There is a fairly pronounced seasonal fluctuation, which is caused by plants taking up more carbon dioxide in the summer than in winter. Here, we're not primarily interested in the seasonal variation, but we will still have to understand what it looks like, in order to remove its effects from the data. The seasonal component itself looks like this, figure 2:

In figure 1, a de-seasonalised blue region has been superimposed on the data. The (small) width of the blue area indicates the 95% confidence for the underlying de-seasonalised value. Since we are only basing our inferences about carbon dioxide concentration on finitely many, slightly noisy measurements, we can't be absolutely sure exactly what the concentration is at a certain time. But we can be 95% confident that the actual value is within the blue band.

###
CO_{2} growth
rate

### What is the growth of carbon dioxide in the graph? The growth rate is the instantaneous slope of the de-seasonalised curve (also called the derivative) and is measured in parts per million per year [ppm/y]. However, the raw instantaneous growth rate isn't that useful to plot for two reasons: firstly, the instantaneous growth rate is not itself that interesting, because it doesn't reveal much about how the carbon dioxide concentration is evolving over finite intervals of time, and secondly, the instantaneous growth rate is both very variable and associated with a large amount of statistical uncertainty, as our data only contains monthly measurements. To overcome this issue, we either 1) first compute the instantaneous growth rate and then average the result locally in time, or 2) first average the concentration values locally in time, and then compute the growth rates. In fact these two views are mathematically equivalent, so you can use whichever interpretation you prefer. The resulting growth rates are shown in figure 3:

The National Oceanographic and Atmospheric Administration (NOAA) also provide a graph of carbon dioxide growth, which looks similar to the plots presented here. The difference is that the plots presented here emphasises the continuous nature of the process (rather than discrete yearly, or decade-long average growth events), and they quantify uncertainty.

So, what does the data tell us? It shows that all is not well in the state of the atmosphere! In order to prevent further warming, the carbon dioxide levels must not grow any further. On the growth curve, this corresponds the curve having to settle down to 0 ppm/y. There is absolutely no hint in the data that this is happening. On the contrary, the rate of growth is itself growing, having now reached about 2.3 ppm/y the highest growth rate ever seen in modern times. This is not just a "business as usual" scenario, it is worse than that, we're actually moving backward, becoming more and more unsustainable with every year. This shows unequivocally that the efforts undertaken so-far to limit green house gases such as carbon dioxide are woefully inadequate.

### Misleading interpretations of the data

### Unfortunately, the carbon dioxide data has been subject to some misleading interpretations, due to poor statistical reasoning. For example in the Nature Communications paper [Keenan et al, 2016] entitled "Recent pause in the growth rate of atmospheric CO

_{2}due to enhanced terrestrial carbon uptake", the authors identify "a pause in the growth rate of atmospheric CO

_{2}", lasting from 2002 to (at least) 2014. They also identify a "point of structural change" in the growth rate in 2002. In fact it is highly unlikely that any such pause or point of structural change actually exists. On the growth rate figure above, the decadal average growth rate was 1.93±0.01 ppm/y at the start of 2002 and 2.37±0.07 ppm/y at the end of 2014 (mean ± 2 std dev), so the growth rate has indeed grown. In fact, the growth rate of the growth rate (also called the acceleration) within the start of 2002 to end of 2014 interval is 0.0339±0.0055 ppm/y

^{2}, whose lower bound is close to the average acceleration in the 40 years prior to that (1962 to 2002) at 0.0295±0.0016 ppm/y

^{2}, showing that it is very likely that the growth rate has in fact grown faster in the 2002 to 2014 interval, than during the 40 years prior to that. Publishing such flippant ideas should be avoided, as they create confusion where there should be clarity. It would be prudent of the authors to retract their paper (or explain why it is a valuable contribution when it doesn't agree with observations).

### The Long Term

It is indisputable, that in the long term, the carbon dioxide growth must be brought down to zero, otherwise the earth will just keep getting warmer. However, it is unrealistic to assume that carbon dioxide growth can be halted instantaneously. It is more realistic to assume that the reduction in the growth will take place gradually. The level at which the concentration will stop growing depends on the schedule of the growth reduction. Let's assume that the global growth will be reduced at a fixed relative rate, at some percentage per year, indefinitely. Below is a figure showing what the equilibrium carbon dioxide concentration will be depending on the rate of growth reduction:The graph shows that the faster the growth rate is reduced, the lower the final concentration. To limit the final level to be twice the preindustrial level will require roughly an annual 1.5% reduction in the growth rate if we start now; if we first wait 25 years with taking action, close to 3.5% reduction per year will be required. A doubling of the carbon dioxide concentration is estimated to cause a warming of between 1.5°C-4.5°C, see IPCC 5th assessment report, and see also the concept of climate sensitivity. Reduction rates of less than about 0.3% will lead to very large concentrations. (But note that currently the growth rate is

*growing*by about 1.3% per year, not reducing at all.)

And even if it could somehow actually be stopped right now, there is a lag time of several decades before the warming itself might cease. Further degradation of the situation is already baked in. It’s like watching a slow-motion car wreck unfold. From inside the car.

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