# Natural Disasters Obey the Same Mathematical Patterns

The most accurate statistical analysis to date of a whole set of natural phenomena that can cause disasters has revealed that they obey the same mathematical patterns.

Álvaro Corral and Álvaro González, researchers at the Center for Mathematical Research (CRM) and the Department of Mathematics of the Autonomous University of Barcelona examined thousands of earthquakes, hurricanes, forest fires, meteorite impacts in the atmosphere, torrential rains and soil subsidence due to the karst phenomena, a slow process of chemical dissolution, which takes place on calcareous rock.

In conclusion, these researchers have managed to describe with the same mathematical technique the functions that relate to the frequency of different phenomena to the value of their magnitude or size.

Most of them follow the so-called power law, according to which events are increasingly abundant the smaller they are, without having a “normal” or typical size.

However, the frequency of other phenomena, such as forest fires in each region, follows another mathematical distribution, the so-called lognormal distribution, from the smallest to the most devastating, which burns hundreds of thousands of hectares.

The new study has made it possible to specify how these functions are adjusted in each case, and whether they are still valid or not for borderline cases (for example, events of extremely large magnitude), in order to describe with the same patterns events of very different magnitudes and different origin.

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The researchers explained that “thanks to this study, risk estimates of catastrophic events in different areas of the world can be improved, according to the historical record of each region.”

Scientists consider remarkable the fact that phenomena of such a diverse nature obey the distribution of power law.

For Corral, “there are interpretations that this happens whenever the phenomenon occurs following a behavior called ‘avalanche’, quickly releasing energy that has accumulated over time, but there is still much to investigate in this area.”

Forest fires, the researchers explain,  would be an exception to that rule, as they can also be described as “avalanches” of a sudden release of energy that had accumulated in the form of biomass.

“We do not know in detail why some ‘avalanche’ phenomena follow a lognormal distribution, and this actually contradicts previous studies. Better physical models will be necessary to explain the magnitude reached by these processes,” reflect the authors of the study published in Earth and Space Science.

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