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Researchers at the Centre de Recerca Matemàtica and the Universitat Autònoma de Barcelona (UAB) have mathematically described the frequency of various dangerous natural phenomena according to their size. By means of new statistical tools, they have shown how the frequencies of earthquakes, hurricanes, torrential rains and impacts of meteorites in the atmosphere can be described with the same mathematical law. However, other phenomena, such as forest fires and land sinks, would follow a different law.

Researchers from the CRM Álvaro Corral and Álvaro González have analyzed data on thousands of episodes of different intensities of these phenomena and have been able to describe them with the same mathematical technique the functions that relate the frequency of these phenomena with the value of their magnitude or size.

According to the study, most of these severe events follow the so-called power law, according to which events are becoming increasingly abundant as they are smaller, without a size 'normal'. According to the experts, if these situations and their magnitude are analyzed in depth, an approximate calculation can be made about how long they take place. The greater the devastation capacity of a phenomenon, the smaller the frequency with which they become. For example, few earthquakes are devastating, but those of lesser magnitude often appear.

"Thanks to this study, we can improve the risk estimates of catastrophic events in different parts of the world, according to the historical record of each region," says Álvaro Corral. The scientists consider remarkable the fact that phenomena of so diverse nature obey the distribution of law of power. For example, forest fires would be an exception to this rule, as they can also be described as "avalanches" of sudden release of energy that had accumulated in the form of biomass.

The authors say that this data contradicts prior research and that better physical models are needed to explain the magnitudes that these processes achieve. In any case, the information on the frequency and intensity of the phenomena is very important when calculating the associated risks.​

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Corral, Á. & González, À. (2019). Power law size distributions in Geoscience revisited. Earth and Space Science, 6, 673-697. https://doi.org/10.1029/2018ea000479​