Mathematical models for the description of soil genesis

• Published in: Journal of plant nutrition and soil science Vol. 181; no. 6; pp. 847 - 854
• Main Author: Hornig, Winfried
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.12.2018
• Subjects: Animal populations; animals; climate; Complex systems; Computer simulation; equations; Iterative methods; Mathematical analysis; Mathematical models; micro morphology; Soil formation; soil geography; Soil properties; soil science history; topography
• ISSN: 1436-8730; 1522-2624
• DOI: 10.1002/jpln.201800048

To capture the development of soils and their properties mathematically or even predict the formation of soils for certain times and places is a tempting idea of science and has continued a subject of discussions for decades. Soil formation and soil properties depend on soil forming factors. In his Fundamental Equation, Jenny defines soil as a function of climate, organisms, topography, parent material and time. The equation should be used to determine the role of one single variable, when all other factors remain constant. However, the Fundamental Equation gives the impression that all processes are determined and soils as a whole can be calculated. But the factors influence the soil formation only indirectly via the effect on several soil forming processes. It seems to be impossible to understand every detail of soil development completely or to reduce such a complex system to only one considerable value. By this reason, several functions, based on different scientific theories, shall help to discover less or more isolated processes of soil formation. The so‐called Logistic Equation, created to calculate the development of animal populations, may help to describe soil formation as a whole. The combination of the Logistic Equation and the Fundamental Equation results in iterative series of equations with changing steps of soil genesis. They repeatedly take the place of parent material factor and so soil becomes a factor of its own development. Additionally, time can be eliminated as a factor to be considered, because it is taken into account by the series of equations. Important changes of the external factors of the Fundamental Equation result in a new equation series as a part of the whole equation system. Interactions and retroactive effects can be considered and the possibility of iterative computation may lead to a better simulation of the complex system soil. Thus, the presented approach can be a starting point for a modern mathematical model for calculating soil genesis in general.