Climate change leads to an overall temperature increase, but it also significantly amplifies extreme weather events. The article uses the Gaussian distribution as a model to illustrate how minor temperature shifts can result in a notable rise in the frequency of extreme conditions, such as hotter summers and milder winters. Historical data from Frankfurt highlights the stark increase in probabilities for unusually high temperatures, demonstrating the real-world implications of gradual climate warming.
Global warming is leading to milder average temperatures, but extreme weather events are changing even more dramatically.
Do you remember the old ten-mark notes? They featured Carl Friedrich Gauss (1777 to 1855), one of the greatest mathematicians in history. On the reverse side was the Gaussian bell curve he introduced. This curve is not just used for decorating banknotes; it has applications in various fields of science and technology, including climatology. It helps us understand why extreme weather events should occur more frequently, even with seemingly moderate warming.
Imagine a wooden board dotted with nails spaced evenly apart, resembling a Fakir cushion. Cover this setup with a transparent sheet and place it upright. Below, arrange several containers side by side, and from above, drop small balls through the labyrinth of nails.
These balls, when dropped on the so-called Galton board (https://en.wikipedia.org/wiki/Galton_board), will be randomly deflected left or right by the nails. When they reach the bottom, they land in one of the containers. Most balls tend to accumulate in the central containers, while some fall further out, and very rarely, a ball might be deflected consistently in one direction, landing in one of the outermost containers.
The distribution of balls in the containers is described by the normal distribution introduced by Gauss. This principle applies whenever deviations from a mean value — the average container — are purely random, with larger deviations becoming increasingly unlikely. Analyzing the average temperature in Germany over several years reveals a similar normal distribution, where cooler and warmer years appear to alternate randomly.
However, in the last few decades, we have been witnessing a systematic warming trend, analogous to shifting the drop point in our nail board experiment. This shift will result in a systematic change in the distribution of balls in the containers. An interesting question arises: how much does the number of balls in the outer containers change? In climate terms, this correlates with occurrences of particularly hot summers or mild winters.
The likelihood of these events corresponds to the area under the bell curve beyond a chosen temperature threshold. In the Galton board experiment, this represents the number of balls in the outer containers relative to the total. Due to the unique shape of the bell curve, even a slight shift in the drop point can significantly increase the number of balls on the outer sides. Similarly, the probability of experiencing heat waves or mild winters in this region rises markedly with a seemingly small increase in temperature.
For instance, in 1901, the probability of the average temperature in August in Frankfurt am Main exceeding 22 degrees Celsius was just 0.1 percent. Such a hot August was expected to occur only about once every thousand years. Today, that probability has skyrocketed to over 15 percent, meaning roughly one in six Augusts is now likely to be that warm.
In 1826, a mean annual temperature exceeding 11.5 degrees Celsius in Frankfurt was also predicted to happen only once in about a thousand years. Nowadays, higher temperatures are recorded on average every two years, and this year, likely the hottest on record globally, is expected to reach around 12.5 degrees Celsius.