Mathematics, Mass Extinction, Climate Change, & The Threshold Of Catastrophe

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Daniel Rothman is a professor of geophysics at the MIT Department of Earth, Atmospheric and Planetary Sciences. He has recently completed a statistical analysis of the significant changes in the earth’s carbon cycle over the past 540 million years. During that time, there have been five mass extinctions. His research has identified what he calls “thresholds of catastrophe” in the carbon cycle. These are concentrations of carbon dioxide which, if exceeded, lead to an unstable environment, climate change, and mass extinctions.

Extinctions And Carbon Dioxide

MIT and mass extinctionsExtinctions do not take place overnight. We do not go to bed one evening and wake up to find that most plant and animal life on earth has disappeared overnight. An extinction can take place over thousands or even millions of years, depending in large measure upon how quickly a spike in carbon dioxide concentrations occurs. The more gradual the CO2 rise, the more gradual the changes occur.

Unless you are one of those people who think Charles Darwin and his theory of evolution is so much horse puckey (millions of Americans believe just that), evolution over a long enough period will allow life on earth to adapt to changes in climate and environment. But such changes take place over a very long time — often 100,000 years or more. The changes expected to take place globally before the end of this century will not allow people and other living things enough time to adapt through evolutionary changes. That’s the kind of climate change that leads to mass extinctions.

Two Components Of Carbon Dioxide Increase

The rapid pace of change today has no historic counterpart. Carbon dioxide levels going back more than 500 million years rose at a far slower pace, making it difficult to compare one to the other. That’s where Professor Rothman and his mathematical models come into play. Here is the abstract of his research as published by Science Advances.

The history of the Earth system is a story of change. Some changes are gradual and benign, but others, especially those associated with catastrophic mass extinction, are relatively abrupt and destructive. What sets one group apart from the other?

Here, I hypothesize that perturbations of Earth’s carbon cycle lead to mass extinction if they exceed either a critical rate at long time scales or a critical size at short time scales. By analyzing 31 carbon isotopic events during the past 542 million years, I identify the critical rate with a limit imposed by mass conservation.

Identification of the crossover time scale separating fast from slow events then yields the critical size. The modern critical size for the marine carbon cycle is roughly similar to the mass of carbon that human activities will likely have added to the oceans by the year 2100.

Climate Change And The Threshold Of Catastrophe

Rothman calculates that human activity will have added about 310 gigatons of carbon dioxide to the atmosphere and oceans by 2100. That’s the point at which the world will be on the “threshold of catastrophe” as it transitions into “unknown territory.” The changes that follow may take up to 10,000 years to play out, but that is still one tenth of the amount of time needed for evolutionary changes to keep pace. The result? Mass extinction Number Six.

“This is not saying that disaster occurs the next day,” Rothman says. “It’s saying that, if left unchecked, the carbon cycle would move into a realm which would be no longer stable, and would behave in a way that would be difficult to predict. In the geologic past, this type of behavior is associated with mass extinction.”

“How can you really compare these great events in the geologic past, which occur over such vast timescales, to what’s going on today, which is centuries at the longest?” Rothman says. “So I sat down one summer day and tried to think about how one might go about this systematically.” The result was a mathematical model that correlates the rate and magnitude of alterations in the carbon cycle to the timespan over which those changes occur.  He hypothesized that his formula should predict mass extinctions or other global catastrophes.

Then he applied his formula to historical data. After searching hundreds of geochemistry studies, he identified 31 times in the past 542 million years in which a significant change occurred in the earth’s carbon cycle. For each event, he noted the amount of CO2 change and the time during which the change occurred. “It became evident that there was a characteristic rate of change that the system basically didn’t like to go past,” Rothman says.

Catastrophic Events

His modeling identified a certain threshold of change that separated benign events from those that destabilized the environment and moved it toward catastrophic consequences. The end-Permian extinction — during which 95% of all species on earth disappeared — was the farthest over the line. “Then it became a question of figuring out what it meant,” Rothman says.

Rothman determined that a critical part of the earth’s carbon cycle involves the small amount of carbon dioxide that sinks to the bottom of the oceans, where it is sequestered in the bottom. But if the rate of carbon dioxide being added to the environment becomes too fast, that sequestration process is overwhelmed and cannot function to tamp down the effects of the extra carbon. That’s when the carbon cycle trips over into unstable territory.

IPCC Scenarios

The Intergovernmental Panel on Climate Change has postulated that there are four possible scenarios for future additions of carbon dioxide to the environment. The best-case scenario predicts that humans will add 300 gigatons of carbon to the oceans by 2100, a number that is right in line with the amount Rothman predicts will occur. The worst case scenario is 500 gigatons — an amount well past his threshold for catastrophe.

“There should be ways of pulling back [emissions of carbon dioxide],” Rothman says. “But this work points out reasons why we need to be careful, and it gives more reasons for studying the past to inform the present.” None of which will occur while the #FakePresident sits in the White House and his evil henchmen move forward with their plan to destroy the federal government. Perhaps China will pick up the slack. Of all the nations on earth, it seems to be the one least likely to consider catastrophic climate change little more than a hoax.

Source and graphic credit: MIT via  Science Daily

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Steve Hanley

Steve writes about the interface between technology and sustainability from his home in Florida or anywhere else The Force may lead him. He is proud to be "woke" and doesn't really give a damn why the glass broke. He believes passionately in what Socrates said 3000 years ago: "The secret to change is to focus all of your energy not on fighting the old but on building the new." You can follow him on Substack and LinkedIn but not on Fakebook or any social media platforms controlled by narcissistic yahoos.

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