My Carefully Selected Quotes,
by Ye Editor
"SUMMARY
The proper way of looking for causal relationships between time series data (e.g. between atmospheric CO2 and temperature) is discussed. While statistical analysis alone is unlikely to provide “proof” of causation, use of the ‘master equation’ is shown to avoid common pitfalls.
Correlation analysis of natural and anthropogenic forcings with year-on-year changes in Mauna Loa CO2 suggest a role for increasing global temperature at least partially explaining observed changes in CO2, but purely statistical analysis cannot tie down the magnitude.
One statistically-based model using anthropogenic and natural forcings suggests ~15% of the rise in CO2 being due to natural factors, with an excellent match between model and observations for the COVID-19 related downturn in global economic activity in 2020.
Introduction
The record of atmospheric CO2 concentration at Mauna Loa, Hawaii since 1959 is the longest continuous record we have of actual (not inferred) atmospheric CO2 concentrations. I’ve visited the laboratory where the measurements are taken and received a tour of the facility and explanation of their procedures.
The geographic location is quite good for getting a yearly estimate of global CO2 concentrations because it is largely removed from local anthropogenic sources, and at a high enough altitude that substantial mixing during air mass transport has occurred, smoothing out sudden changes due to, say, transport downwind of the large emissions sources in China.
The measurements are nearly continuous and procedures have been developed to exclude data which is considered to be influenced by local anthropogenic or volcanic processes.
Most researchers consider the steady rise in Mauna Loa CO2 since 1959 to be entirely due to anthropogenic greenhouse gas emissions, mostly from the burning of fossil fuels. I won’t go into the evidence for an anthropogenic origin here (e.g. the decrease in atmospheric oxygen, and changes in atmospheric carbon isotopes over time).
Instead, I will address evidence for some portion of the CO2 increase being natural in origin. I will be using empirical data analysis for this. The results will not be definitive; I’m mostly trying to show how difficult it is to determine cause-and-effect from the available statistical data analysis alone.
Inferring Causation from the “Master Equation”
Many processes in physics can be addressed with some form of the “master equation“, which is a simple differential equation with the time derivative of one (dependent) variable being related to some combination of other (independent) variables that are believed to cause changes in the dependent variable.
This equation form is widely used to describe the time rate of change of many physical processes, such as is done in weather forecast models and climate models.
In the case of the Mauna Loa CO2 data, Fig. 1 shows the difference between the raw data (Fig. 1a) and the more physically-relevant year-to-year changes in CO2 (Fig. 1b).
... there are clearly natural processes at work in addition to the anthropogenic source. Also note those natural fluctuations are much bigger than the ~6% reduction in emissions between 2019 and 2020 due to the COVID-19 economic slowdown, a point that was emphasized in a recent study that claimed satellite CO2 observations combined with a global model of CO2 transports was able to identify the small reduction in CO2 emissions.
... El Nino and La Nina (as well as other natural modes of climate variability) also impact yearly changes in CO2 concentrations.
... In addition to the master equation having a basis in physical processes, it avoids the problem of linear trends in two datasets being mistakenly attributed to a cause-and-effect relationship.
Any time series of data that has just a linear trend is perfectly correlated with every other time series having just a linear trend, and yet that perfect correlation tells us nothing about causation.
... Now, this data manipulation doesn’t guarantee we can infer causation, because with a limited set of data (63 years in the case of Mauna Loa CO2 data), you can expect to get some non-zero correlation even when no causal relationship exists. Using the ‘master equation’ just puts us a step closer to inferring causation.
/// You might wonder, if the IPCC is correct and all of the CO2 increase has been due to anthropogenic emissions, why doesn’t it have the highest correlation?
The answer could be as simple as noise in the data, especially considering the emissions estimates from China (the largest emitter) are quite uncertain.
The role of major volcanic eruptions in the Mauna Loa CO2 record is of considerable interest. When the atmospheric transmission of sunlight is reduced from a major volcanic eruption (El Chichon in 1983, and especially Pinatubo in 1991), the effect on atmospheric CO2 is to reduce the rate of rise.
This is believed to be the result of scattered, diffuse sky radiation penetrating deeper into vegetation canopies and causing enhanced photosynthesis and thus a reduction in atmospheric CO2.
... On average, the yearly increase in Mauna Loa CO2 equals 49.1% of total global emissions (in ppm/yr) plus a regression constant of 0.181 ppm/yr.
Conclusions
The Mauna Loa CO2 data need to be converted to year-to-year changes before being empirically compared to other variables to ferret out possible causal mechanisms.
This in effect uses the ‘master equation’ (a time differential equation) which is the basis of many physically-based treatments of physical systems.
It, in effect, removes the linear trend in the dependent variable from the correlation analysis, and trends by themselves have no utility in determining cause-versus-effect from purely statistical analyses.
When the CO2 data are analyzed in this way, the greatest correlations are found with global (or tropical) surface temperature changes and estimated yearly anthropogenic emissions.
Curiously, reversing the direction of causation between surface temperature and CO2 (yearly changes in Sea Surface Temperature being caused by increasing CO2) yields a very low correlation.
Using a regression model that has one anthropogenic source term and three natural forcing terms, a high level of agreement between model and observations is found, including during the COVID-19 year of 2020 when global CO2 emissions were reduced by about 6%."