More Trouble with the Curve

Suppose the earth’s atmosphere were a bathtub, and that human-generated (anthropogenic) carbon dioxide emissions were being dumped into the bathtub through a faucet. An exponential curve included in the last post on this blog shows the growing amount of carbon dioxide in the bathtub starting in 1750, when the industrial revolution began, and extending through the year 2007. The amount of CO2 in the bathtub grew very slowly for a while but then increased at faster and faster rates. The exponential curve showing the amount of carbon dioxide that has flowed into the bathtub since 1750 is steeper and steeper over time because more carbon dioxide flows through the faucet every year from burning more fossil fuels.

A related graph, below, represents how much carbon dioxide is coming out of the faucet every year from use of fossil fuels, rather than how much has entered the bathtub. The graph shows annual carbon dioxide emissions by year from 1870 to 2010. The shape of this curve is also exponential, like the growing amount that has flowed into the bathtub. The similarity in shape is a special characteristic of exponential curves: a graph of the rate of change of an exponential function is itself an exponential function.

Carbon emissions by year

      The figure above comes from p.4 of an International Energy Agency publication called “2012 CO2 Emissions Overview.”

This graph shows, for example, that between the years 1970 and 2010 annual human-caused carbon dioxide emissions from burning fossil fuel more than doubled, from about 15 gigatons per year to more than 30 gigatons per year. (A gigaton is one billion tons.)

The previous blog post reported that humanity “had not yet begun” to change the exponential growth of carbon dioxide (and thus carbon) in the atmosphere, but that might not be quite accurate. I learned that global emissions “stalled” in 2014, meaning that annual emissions did not grow between 2013 and 2014 but were the same each year. Ignoring the fact that the graph above represents only the years through 2010 (not 2014), stalling means that the graph is flat for the years 2013 and 2014, at a figure of about 32 gigatons per year.

This stalling phenomenon has happened several times over the past 40 years; see, for example, the noticeable dip in the curve above during a recession in the 1980s. Nonetheless, the exponential growth trend has proved to be far more powerful over the years than the few times when annual emissions stalled. Starting in 2015 or soon afterward, the exponential growth in CO2 emission each year might well increase again, as it has been doing for decades with only brief “blips” in the exponential growth pattern.

However, for sake of argument, suppose that CO2 annual emissions from burning fossil fuels truly peaked in 2014 and will never grow larger. Nonetheless, in order to avoid more than a 2° C increase in global temperature, scientists say that humanity would need to reduce annual emissions from fossil fuel use to zero by about 2050, i.e. rapidly reduce the flow from our anthropogenic CO2 “faucet” over the next few decades, and then turn the faucet off entirely by mid-century. The curve in the graph above would need to plummet downward and then reach zero annual emissions by 2050.

The last time annual anthropogenic CO2 emissions were anywhere near zero was hundreds of years ago, before the industrial revolution, as can be seen above. The exponential growth of annual emissions has been going on so long with such potentially catastrophic results that the World Bank warned in 2012, and continues to warn, that unless current patterns change quickly the earth will probably become 4° C warmer by the year 2100 (equivalent to more than a 7° Fahrenheit increase). Results would be devastating, they say. How many people have understood and accepted this information?


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