From the feud between President Trump and Greta Thunberg to the more recent destructive wildfires in Australia, it seems the topic of climate change has, fittingly, never been more heated. And though some believe in climate change and others disregard it, an opinion is meaningless in the presence of fact. So, with that in mind, let us inspect the mathematical background behind climate change. 

At first glance, climate change might seem rather fake. After all, winter still feels pretty cold and summer still feels pretty hot (if you experience these seasons), so what’s the matter with all of these debates? How could the Earth possibly be getting warmer? Let’s consider a hypothetical scenario, one where the Earth is in fact becoming warmer. These warmer temperatures would destroy icebergs and habitats, causing an increase in ocean levels. This will then permanently affect the weather: precipitation, droughts, ocean ecosystems, everything. Again, a hypothetical scenario. 

Modern day supercomputers are doing the math and they are all pointing to global warming. Sorry, the above is not a hypothetical scenario — it’s real life. NASA has developed several model projections detailing average global temperatures, and this has been used in coordination with the Navier-Stokes equation, which measures the motion of fluids and gases within the ocean and atmosphere. However, the Navier-Stokes equation, one of the Clay Institute’s seven millennium problems, has remained unsolved for centuries — and with good reason. A coupled set of five differential equations with six variables, one could imagine the difficulties of finding the general solutions for such a problem. Analytical attempts to solve the equations have been fruitless, as it is simply not feasible.

As previously mentioned, modern day supercomputers are performing calculations, but these are just approximations. Compiled into a field of study known as Computational Fluid Dynamics (CFD), such efforts have produced a rough estimate of average global temperatures. NASA’s recent study has found that the Earth is on average 1.4 degrees (0.8 Celsius) warmer than it was in 1880. From a surface perspective, this is a trivial matter because 1.4 degrees higher or lower feels the same, right? Let’s look at it from another perspective: consider how much energy would be needed to raise the entire Earth’s temperature by 1.4 degrees. One doesn’t need to be a chemist to realize that this quantity would be enormous. The impact is even more devastating, and since every effect cannot be explored here, consider just one: acidification of the oceans. 

Carbon dioxide is perhaps the most “mainstream” greenhouse gas, with initiatives such as reducing one’s carbon footprint gaining traction in recent decades. Carbon dioxide isn’t that reactive by itself, but once it is absorbed by seaweed (for photosynthesis), the products undergo another series of chemical reactions. Consequently, hydrogen ions are produced and released in the ocean, which, by definition, increases acidity. This leads to numerous chain effects, most notably being the impediment of calcium carbonate formation. Calcium carbonate is made up of calcium and carbonate ions, the latter of which is a base. Since acids and bases tend to neutralize each other, the increase in acidity directly leads to a decrease in carbonate ions. The shells of oysters, clams, sea urchins, and even coral all rely on calcium carbonate, and the lack of carbonate means that their shells become increasingly weaker. These organisms are on the bottom of the food chain, so the impact on higher-level consumers are disastrous as well. 

Despite this, there is still much to deliberate on the topic of climate change. As mentioned above, the Navier-Stokes problem remains unsolved, and will likely remain unsolved for years to come. And though researchers and scientists argue about the rate at which the Earth is heating up, the point remains: climate change is real. There is no need to have a political debate over the existence of a phenomenon proven by fact. Yet even if climate change didn’t exist, our computers and mathematical processes were faulty, and the media was lying about the changes being seen on our planet, what’s wrong with trying to keep the Earth a little more stable?