numbers, not adjectives — D. J. C. MacKay

Global Temperature vs Atmospheric CO2 Concentration

by Carl Edward Rasmussen, 2023-07-01

According to the scientifically well understood mechanism of the greenhouse effect, we know that increasing the concentration of greenhouse gases, such as CO2, in the atmosphere causes warming. Good models of the magnitude of this effect are available, but an accurate quantification is challenging for a number of reasons. The primary difficulty is connected to the quantification of multiple feedback effects in the atmosphere; for example, increasing CO2 causes an increase in the temperature of the troposphere (the part of the atmosphere closest to the ground) which enables it to hold more water vapour, which is also a greenhouse gas, which further increases the temperature and so on. Note that although much of the warming here is mediated by water vapour, it is still caused by increases in CO2.

To assess the relationship empirically, I plot the average yearly global land ocean temperature anomaly in degrees Celcius (with a baseline of the preindustrial average 1850-1900) as a function of the Mauna Loa yearly average atmospheric concentration of CO2 in parts per million in a scatter plot:

Temperature vs carbon dioxide

Before discussing this scatter plot any further, I should be the first to highlight that correlation does not imply causation. This is a true statement. It means that, in the absence of any other information, the correlation observed in the above figure would be consistent with either "increasing CO2 causes warming", or "warming causes increased CO2" or "increased CO2 and warming are both caused by some other factor". However, in the case of climate change, we do have other information, namely an understanding of the causal mechanism of the greenhouse effect.

Here we are using the scatter plot to empirically test the strength of the relationship within the 64 years of CO2 measurements at Mauna Loa. The strength of this relationship is remarkable. The discrepancies between a straight line superimposed on the graph to the measurements have a standard deviation of less than 0.1°C, and there doesn't seem to be significant systematic deviation. On the other hand, there is no intrinsic reason to think that the relationship should necessarily be close to a straight line, indeed there are a number of reasons why not. For example, CO2 is just one of several greenhouse gases. Also, from a theoretical perspective we would expect the effect of CO2 to be less than proportional to the concentration. Other compounds such as aerosols have an effect on temperature. And we expect the effect of the greenhouse gas to take time to manifest itself. Finally, temperature is affected by other processes, such as El Niño and La Liña events. Nevertheless, empirically we find that these effects, over the 64 year time period considered, only manifest themselves weakly or more or less seem to average out, leaving a close to straight line relationship between CO2 concentration and temperature anomaly.

The size of the relationship is the slope of the curve which is very close to 0.01°C/ppm, or equivalently 0.1°C/10 ppm. Since the rate of increase of CO2 is currently about 2.4 ppm/year, this means that if the empirical relationship from the graph persists, the global temperature will likely rise about 0.024°C per year, or 2.4°C per century, or equivalently about 0.1°C every 4 years. With this growth rate the Paris agreement limit of 1.5°C warming will likely be breached by around year 2035.