Analysis of the Relationship Between Land Air Temperatures and Atmospheric Carbon Dioxide Concentrations

Guest essay by Clyde H. Spencer

Before getting into the details of the analysis, it must be stated that there are a number of issues with the available temperature data sets. Some critics have dismissed the historical ocean pH measurements because of the poor spatial sampling. However, the same criticism can be made about historical temperatures. There are still concerns about the influence of the Urban Heat Island effect on recent temperature readings. In addition, the temperature record is a moving target because there are on-going changes made to try to correct for the shortcomings of a system that wasn’t intended to be used to track long-term changes. Therefore, if you attempt to reproduce my results, you will probably find that the data have changed. The Berkeley Earth Surface Temperature (BEST) project was started because of distrust in the other existing data sets. I have chosen to use BEST data (08-Jan-2016) because it is readily available and some consider it to be superior to the government data sets. Any conclusions need to be taken with reservation.

Unfortunately, the most detailed atmospheric carbon dioxide (CO₂) concentration data that are available cover only about the last 56 years. The Mauna Loa CO₂ data are available from the Scripps Oceanographic website. A scatter-plot of BEST monthly temperatures versus logarithm base-2 (Log₂) PPM (parts per million) CO₂ concentration was prepared for the period of 1958 through 2015. (See Fig. 1, below) The point cloud for the monthly data is not particularly tight. Indeed, the least-squares fit regression-lines only show an R² value a little above 0.5 for both the average global high and low temperatures. The classic interpretation of the R² value is that it represents the amount of variance in the dependent variable (temperature) that can be explained by the independent variable (CO₂ concentration). That is, in this situation, only a little more than half of the rise in temperature can be related to the increase of CO₂ in the last half-century. Of that CO₂ increase, the combustion of fossil fuels probably only accounts for about 75%. (See Spencer, 2015).

Using raw PPM rather than the LOG₂ of the PPM CO₂ gives slightly higher correlation coefficient with the monthly high-temperatures. (0.533 v. 0.528). Whereas, the opposite is true for low temperatures (0.548 v. 0.550). Thus, it seems that the average low-temperatures behave slightly better with respect to the theory that CO₂ is impeding radiative cooling.

Using a 2^nd-order fit instead of a linear fit increases the correlations slightly. However, the trend-line curves upward with the high temperatures for the most recent data, but downwards for the low temperatures. The apparent opposite results, suggest that something is affecting the high and low temperatures differently. I have pointed out previously, (Spencer, 2015) that the difference between the high and low temperatures has been increasing in recent years and seems to be the result of the high temperatures increasing more rapidly than the low temperatures. That is the opposite of what one would expect if CO₂ were the main driver.

Fig. 1 Monthly average temperature versus Mauna Loa CO₂ concentration

Substituting the presumed concentration of CO₂ (277 PPM) for the pre-industrial era into the linear regression equations yields high and low temperatures estimates of 13.537 and 2.207 degrees C, respectively. That gives an average of 7.872°C, compared to an average temperature of 8.367 for 1771 from the BEST database. It is a surprisingly good agreement for a linear prediction based on temperatures that generally appear to increase in a saw-tooth pattern.

While the correlation of temperature with CO₂ looks compelling, what if it is because the CO₂ is coincidentally highly correlated with something else such as natural, in-phase long-term temperature trends or it is simply a proxy for the totality of anthropogenic influences? Remember that correlation does not mean causation!

However, using annual Law Dome CO₂ data from 1759 through 2015, the relationship is less well-behaved. (See Fig. 2, below) The correlation coefficient (0.5638) for average temperature versus CO₂ is, approximately, what is observed for the Mauna Loa monthly CO₂ data. Non-linear behavior is particularly striking for Log₂ CO₂ concentrations less than 8.35 (≈pre-1972). There also seems to be particularly serious problems with the estimate of CO₂ concentrations (284 PPM) or temperature around 1805 to 1840. Note that the slope of the regression line is similar to those in Figure 1

Fig. 2 Average annual BEST global land surface-temperature versus Law Dome ice-core CO₂

It is generally thought that pre-industrial CO₂ levels were relatively constant, only showing very slow increases. However, at low levels of CO₂, the temperatures were varying in a manner not expected from the theoretical model. Some of the low temperatures associated with the downward spike in temperatures with a CO₂ log₂ concentration of 8.15 may be the result of the eruption of Mt. Tambora (1815), but not all. The temperatures apparently started to decline a decade before the eruption, and remained low longer than the typical two or three years after a major eruption. The decline in temperatures resulting from the 1883 eruption of Krakatoa is barely discernible at a concentration of 8.18. There are also high temperatures paired with low CO₂ concentrations.

Assuming that the relationship between CO₂ concentrations and temperature is as shown in Figure 1, then the historical temperature data are not trustworthy. If the temperature data, which are 12-month averages, are correct, then there appears to be a serious problem with the assumed control of CO₂ over temperatures! Alternatively, the CO₂ concentration would have to have been varying considerably at this time to explain the different temperatures. This goes to the heart of my opening statement about the veracity of the historical temperature data and the ability to say anything about temperature increases for anything other than the modern record. Although it is not highly probable, in my judgment, one has to at least entertain the possibility that the modern rise in temperature along with CO₂ is a coincidence.

A plot of estimated atmospheric CO₂ concentration versus population for the period of 1958 to the present day shows that the rate of growth of CO₂ is greater than the population rate. A 2^nd-order least squares fit gives an R² value of 0.999. (See Figure 3 below.)

Fig. 3 Annual Mauna Loa CO₂ concentration versus world population

The correlation of historical, global CO₂-increases, with population increase, is so high that one must entertain the possibility that the CO₂ is a proxy for the totality of anthropogenic effects when used to predict temperatures.

One such effect is anthropogenic water vapor. Combustion produces water from all hydrocarbons, along with CO₂. Water used in steel rolling mills, and many other industrial applications, evaporates under conditions it would not have done so were it not for Man. Similarly, water used to cool nuclear reactors and other power plants is released into the atmosphere; it initially condenses into visible water droplets, and then evaporates, increasing the relative humidity. Reservoirs in arid regions provide water vapor both from the reservoir surface and the fields the impounded water irrigates; the water vapor would not have been present before the dams were built. Lastly, massive depletion of underground aquifers, largely for agricultural irrigation, has brought water vapor into contact with the atmosphere during the growing season in arid and semi-arid regions to change the balance of the relative humidity. The essential point here is that ‘Greenhouse Gas’ theory predicts that increasing CO₂ will warm the atmosphere slightly and cause additional evaporation of water, which amplifies the CO₂ warming. Man is providing additional areas from which water can evaporate.

Another anthropogenic effect is Urban Heat Island contamination of the temperature records as the cities have encroached on what were formerly rural areas. The BEST project claims to have disproved that hypothesis, but it is my opinion that they didn’t search far enough outside the city limits, nor in the right direction. Quattrochi et al. (Project Atlanta, 1999) have demonstrated that the heat and pollution from central Atlanta (GA) influences the weather for miles downwind from the city. Additionally, Watts (2015) has demonstrated a woeful lack of adherence to standards in the siting of many temperature-recording stations. I don’t think this is “settled science.”

A plot of BEST global average land-temperatures versus world population (Figure 4, below) produces what appears to be a near-linear trend with an R² value (0.782). However, fitting a 2^nd-order polynomial produces a trend line with an R² value of 0.811.

Fig. 4 Average annual global land-temperatures vs. world population

This suggests that all anthropogenic influences may account for as much as 81% of the variance in the land temperatures. I should note that if one plots 12-month smoothed BEST temperature data in Figure 1, instead of monthly temperatures, a linear correlation of similar magnitude is obtained. Therefore, the nominal R² value of about 0.5 is likely an upper bound on the CO₂ impact alone.

Atmospheric CO₂ is characterized as a “well-mixed gas.” However, the NASA OCO-2 satellite shows a range of about 4% throughout the world, integrated over a 1-month period (see Fig. 5, below). That is approximately 10% of the claimed total increase in CO₂ during the Industrial Era. Notably, there is no obvious evidence for the Northern Hemisphere industrial emissions. The preponderance of high values is over the southern oceans, which might be the result of out-gassing. The Amazon basin also shows elevated CO₂; it is unclear whether that is a result of human burning activities or normal decay of vegetation. One needs to ask why OCO-2 isn’t confirming the presumed Northern Hemisphere anthropogenic CO₂ when it is blamed for the historic temperature increases, and why there is a larger increase in high-latitude temperatures where CO₂ has the lowest concentrations!

Fig. 5 CO₂ concentrations from the OCO-2 satellite, July 2015 (NASA/GES DISC)

In summary, approximately 81% of the warming in the last century may have resulted from all anthropogenic influences, as suggested by figure 4. This includes water vapor, CO₂, methane, nitrous oxide, and land use changes to the albedo and thermal mass. CO₂ may account for as much as 52% to 56% of the contribution from anthropogenic drivers (See Figs. 1 & 2). Fossil fuel-CO₂ represents less than 75% of anthropogenic CO₂. If we were successful in completely phasing out fossil fuels over the next 100 years, we would have a reduction of 50% in average CO₂ emissions. If the Earth is warming at a nominal rate of 1°C per 100 years from all influences, then we can hope, at best, for a reduction in temperature increase of 20% (0.54×0.75×0.50) or 0.20°C. That is to say, if the world were to phase out fossil fuels in the next 100 years the warming would be 0.80 degrees instead of 1.00°C! Unfortunately, eliminating fossil fuel use will probably not be successful in significantly reducing future temperature increases, even if it can be accomplished.