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Section 4.2 Understanding the Issue

The earth's climate is constantly changing, with periods of warming and cooling alternating throughout history and prehistory. Scientists are able to measure the earth's climate by using temperature records for the last roughly 150 years, and using reconstruction from ice cores and seafloor cores before that. There are many factors that cause the earth's climate to change, including changes in the sun, changes in the tilt of the earth's axis, meteorites, volcanos, and changes in vegetation []. Some of these changes, like changes in the sun or the tilt of the earth's axis, happen slowly over millions of years and cause similarly slow changes in climate.
Rapid changes in climate tend to be caused by natural disasters, like volcanic eruptions. These changes tend to be small and localized, unless the natural disaster is cataclysmic - like the event, theorized to be caused by a meteor strike in the Yucatan peninsula, which caused the extinction of many dinosaurs between the Cretaceous and Paleogene periods. This event caused a global temperature drop of \(28^circ C\) []. Changes in climate due to cataclysmic events - even like the one which caused the last mass extinction before modern times - tend to be temporary. That severe cooling event only lasted for 3-4 years.
The world is currently experiencing such a cataclysmic rise in global temperatures. While the global temperature has been higher in the past - for example, during the Cretaceous period - there is no evidence that the world has experienced such a rapid warming period over the past million year []. Global temperatures have risen by \(1^\circ\)C since records started in 1880, with 2/3 of that warming coming since 1975 - indicating that warming is accelerating []. Projections indicate that the globe could warm by \(5^\circ\) in the 21st century alone [].
Unlike past changes to the climate, the current change is driven almost entirely by the actions of a single species - ours. As early as the 1820s, the French mathematician and physicist Joseph Fourier realized that the Earth's atmosphere must trap some of the sun's warmth - otherwise the Earth would be as cold as the moon []. In 1859, the Irish physicist John Tyndall proved in a laboratory setting that certain gases - including water vapor (\(H_2O\)), carbon dioxide (\(CO_2\)), and methane (\(CH_4\)) - were trapping heat in the Earth's atmosphere. In 1896, a Swedish physicist, Svante Arrhenius, who was studying carbon dioxide levels during the current time and during the last ice age, coined the term greenhouse effect [].

Definition 4.2.1. The Greenhouse Effect.

The greenhouse effect refers to the way that certain gases, primarily water vapor, carbon dioxide, methane, and ozone, trap heat inside the Earth's atmosphere. These four gases are commonly called greenhouse gases.
The greenhouse effect is not, in and of itself, a bad thing. In fact, without the greenhouse effect, the Earth would be a lifeless shell. The moon receives essentially the same solar energy as the Earth, but its surface temperatures swing between \(260^\circ\)F (\(127^\circ\)C) during the day to \(-280^\circ\)F (\(-173^\circ\)C) at night []. The greenhouse effect traps heat in the Earth's atmosphere, releasing it more slowly, and creates a temperature range where life can exist. The Earth's natural cycles and processes cause many slow, gradual changes to these greenhouse gases, resulting in slow, gradual fluctuations in the Earth's temperatures.
The current global warming is being driven by a very rapid increase in the amount of these greenhouse gases in the atmosphere. This increase can be explained primarily by human changes to the planet - the burning of fossil fuels, deforestation, and large-scale agriculture. As human beings produce more of these greenhouse gases, the global climate has warmed at a corresponding rate. The corresponding changes to the Earth's climate are called anthropogenic climate change.

Definition 4.2.2. Anthropogenic Climate Change.

Anthropogenic climate change is change to the Earth's climate resulting from human causes, as opposed to climate change caused by natural causes, like volcanic eruptions, natural fluctuations in greenhouse gases, or changes to solar energy.
There are actually several different types of human activity which can cause changes to climate, aside from greenhouse gas emissions. One example is human-caused changes to the Earth's albedo - the lightness or darkness of the Earth's surface. Lighter colored materials tend to reflect more sunlight, causing a cooling effect, while darker colored materials tend to absorb more sunlight. Human activity has caused some areas of the Earth's surface to become darker, like urban areas and areas which were once covered in snow and ice, and thus to absorb more heat. We have also caused other areas to become lighter, like forests that have been replaced by fields and areas which have become desert, creating a cooling effect (like the moon, deserts tend to be very hot during the day and very cold at night).
The amount of climate change caused by greenhouse gas emissions, though, vastly outweighs all other sources. The amount of greenhouse gases in the Earth's atmosphere has, in the last 100 years, risen to levels not seen in the last 400,000 years.
Graph showing atmospheric co2 over the last 400,000 years. Image description available.
Figure 4.2.3.
This unprecedented rapid change to greenhouse gas levels has caused a corresponding rapid increase in global temperatures. While the Earth's biosphere (a collective term for all life on the planet, including plants, animals, and all other organisms, and the environments that support that life) has survived changes of similar magnitude in the past, those changes have been much slower. The natural processes of evolution which allow life to adapt to climate changes tend to happen slowly, over many generations. So, while some species with very short life-cycles (like bacteria, or even insects) may be able to adapt to the changes through evolution, longer-lived species will only be able to survive by moving to another area. Scientists estimate that 95% of species will experience local extinction (meaning either extinction or departure from that area) after a \(2.86^\circ\)C risee in temperatures, and that 16-30% of species could go extinct by 2070 [].
While human beings are unlikely to go extinct - our intelligence has made us more adaptable than other species - climate change has already begun to affect our species. Research has shown that production of the 10 largest crops in the world has already dropped by 1% since 1974 below where it would be without the impact of climate change []. The United Nations High Commission on Refugees estimates that between 2008 and 2019, there were over 21.5 million displacements of people - when an individual was forced to flee their home - caused by weather-related events, more than twice as many as those caused by conflicts or violence []. The same data shows that climate disasters like droughts, cyclones, and floods can have destabilizing effects on countries, especially those already experiencing conflict, like Afghanistan, Yemen, and Mozambique.
Climate change - and the greenhouse gas emissions which are driving that change are a major concern for people around the world. The need to find solutions to this crisis becomes more urgent with every passing year. Mathematics can help us to understand the causes of the greenhouse effect and to determine the best strategies for slowing - and one day stopping - the pace of climate change.