In 1941 Hans Jenny made a seminal contribution to Soil Sciences by proposing a mathematical equation within the so-called soil-landscape model, which, although essentially descriptive, constitutes the central paradigm of this discipline. In a recent work carried out with the participation of the Universities of Oviedo, Autónoma de Madrid (UAM), Pontificia de Comillas, European Commission (JRC), CIEMAT and the company AgrowingData, machine learning techniques have been used to understand this expression, turning it into a true mathematical description of soils with important practical applications.

World Soil Day is celebrated every December 5, when FAO launches a campaign to raise awareness of the importance of soil and its relationship with water, in order to achieve sustainable and resilient agrifood systems. These two elements are the basis for food production, ecosystems and human well-being. Better management of these elements will improve the planet’s capacity to withstand the extreme weather events that lie ahead.

In addition, on July 5, 2023, the proposal for the first Soil Monitoring Law was presented to the European Parliament, which aims to define, identify and monitor the degree of soil contamination in Europe in order to meet the objective of having all soils in Europe "healthy" by 2050.

** Jenny’s equation**

At the 1959 Courant Conference the Nobel laureate Eugene Wigner popularized the concept of "the unreasonable efficiency of mathematics in the natural sciences" [2], one of the deepest beliefs in the roots of knowledge. This idea, especially true in Physics, has been rather neglected in other disciplines, such as Biology or Geology, which have accepted paradigms based on an extensive and recursive use of specially designed taxonomies. The situation is obviously changing nowadays, but it should be noted that as early as 1941 Jenny [1] made a seminal contribution to Soil Science, establishing a mathematical relationship (see figure) between soil types and the variables that influence their formation. Although the existing techniques at the time did not allow the translation of this idea into a defined mathematical function, its impact was such that it became, and remains to date, the central paradigm of this science.

Recently, a group of researchers from several institutions have given a twist to the question. In a paper, published in the journal *Scientific Reports* [1] of the* Nature* group, these authors propose an alternative solution: using self-organizing maps, which are one of the modern techniques of machine learning, to provide an environment that converts Jenny’s expression into a true mathematical expression.

**Self-Organizing Maps (SOM) in Machine Learning**

In a first step, the MAO algorithm is trained with a fraction of an extensive database. In our case, this fraction consisted of the values obtained in a field study in which 15 variables related to soil-forming factors were studied in 442 locations in the Principality of Asturias with different soil types. In a second step, the MAO algorithm finds the relevant associations that exist between the previous factors, which are translated into a predictive mathematical algorithm, somewhat more complicated than a simple equation, which is then validated with the rest of the values in the database. Thus, it would be possible to predict the type of soil that exists in a locality outside the scope of the original study, or even to make a complete edaphological map of the Principality and surrounding regions, a task that is already being carried out at present.

"The idea behind the method is to determine the relevance of each of the symbols that Jenny included in her famous expression. In this way, it can be simplified to the maximum and made to act automatically without the need for the judgment of an expert in the field, although paradoxically this has been essential in the preliminary analysis", the authors detail.

**A new perspective in Soil Science**

The study concludes that, for each soil type, only a few variables, typically 6 different ones in each case, and associated with the forming factors, are relevant. This reduces the complexity of the "Jenny predictor algorithm" because it eliminates much of the statistical noise between variables in the database, which is crucial in the case of multivariate analysis with similar or opposite magnitudes.

The study also provides the fingerprint of each observable soil type. This facilitates the quantitative extraction of this edaphological knowledge on the basis of baseline data.

In short, the finding offers a new perspective on soil science and Jenny’s paradigmatic expression, which entails important practical applications among which are some of great importance such as soil management, its use and improvement, or the preparation of edaphological maps.

**Bibliographic reference:**

[1] Prieto-Castillo F, Rodríguez-Rastrero M, Yunta F, Borondo F, and Borondo J. 2023 Disentangling Jenny’s equation by machine learning. Sci.Rep.13,20916. doi:10.1038/s41598’023 -44171-x

[2] Wigner E. (1960) The unreasonable effectiveness of mathematics in the natural sciences. Commun. Pure Appl.Math.13,1. doi:10.1002/cpa.3160130102

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