The industrial scale burning of coal, then oil and natural gas, beginning in earnest in the late 1800s drove a multi-decade rise in atmospheric CO₂ that is the primary driver of modern global warming. Keeling-curve style measurements and long-term reconstructions show CO₂ rising steadily from pre-industrial levels to greater than 400 ppm today (Trends).

The post-WWII economic boom—sharp increases in energy use, industrial production, automobile ownership, fertilizer use, air travel, and urbanization—produced a rapid spike in greenhouse-gas emissions and other planetary changes that greatly amplified warming trends already underway. Steffen et al.’s “Great Acceleration” analyses (and companion dashboards) are a standard reference. And post-war, the glorification of automobile transportation has only gone up, as cars have become a standard of transportation in the modern era (Steffen). While electric automobiles have made their debut, their effects are not entirely certain, as gas-powered vehicles are still preferable to many.

And of course, wildfires over the past several years have contributed greatly. Areas in California such as the Palisades have been crucial pinpoints to the detrimental effects of industrialization gone wrong. Clearing forests for agriculture, pasture, and timber (especially in the tropics) released large quantities of CO₂ and reduced the planet’s ability to reabsorb emissions; land-use change is estimated to account for roughly a quarter of historic anthropogenic greenhouse-gas fluxes and remains a major source (Chapter). IPCC and FAO analyses document the extent and climate impact of forest loss. Specifically, emissions from deforestation have declined 25 percent over 14 years since 2001, while emissions from degradation have increased from 0.4 to 1 Gt CO₂ per year. They make up 22% of all human-caused emissions. The effects are detrimental.

Over the summer, a general framework for enhancing global warming predictions and effects was developed in the hopes of pointing to the roots of global warming issues. Stochastic processes were used to model predictions. Stochastic differential equations often are utilized in the context of monitoring or simulating heavy turbulence. The “turbulence” isn’t your usual noise or disruption, but rather the immense chaos underlying some events.

The climate itself is inherently stochastic, as it is influenced by countless random and interacting processes. For example, the weather is impacted by the decisions of large technology companies to dump waste or utilize fossil fuels in pursuit of producing products. At the same time, millions of people are throwing away cigarettes on the ground. And so, what happens to the weather is a collection of these events that are extremely “turbulent”. Based on recent developments in stochastic models, which are innovations of the Heston and GARCH models, it may be possible to incorporate SDEs into models of temperature or precipitation, or even sea levels. Take, for example, the model dTt = f(Tt, t)dt + σ(Tt, t)dWt where Tt is the temperature, f represents deterministic climate forcing (the general tendency for the climate to get warmer), and σ dWt the random fluctuations in weather patterns.

Ultimately, the data emphasizes the importance of supporting pro-climate changes. The temperatures are increasing, and our planet is heating up faster than we perceive. It is likely from this model, which demonstrates an 11.4% overall increase in temperatures over the industrial period, that the temperature should increase by 18 percent in the next 50 years given that events do not deviate too heavily from the production methods we currently utilize. But indeed, it is expected that companies and policies will continue to employ “restrictions” rather than “bans” on toxic production for capitalistic pursuits.

Additionally, due to events such as presidential elections and extreme policy shifts, as well as international economic events that occur frequently, it is probable that a discrete process be added to this simulation. Perhaps such an event follows a Poisson-like distribution, and this way we can analyze extreme climate changes in response to events that occur in that relative time frame.

Are stochastic differential equations the way forward, and can they tell us something about the planet? We believe so. The implications of this model are versatile, and it is likely that the temperatures will increase at higher rates than the previous industrial years despite increasing methods and awareness of global warming issues. But one thing is clear: small actions will not be sufficient in the long run. It is important to advocate policy-making that favors pro-climate change, and it is necessary for society to de-emphasize the need for rapid economic growth. Math is telling us to cool down.