Getting to the bottom of soil: Understanding the basis for nutrition using math

[Translate to Englisch:] Blindtext
© Florian Berger/

If you uncover a piece of soil in your garden with a spade, you will see a seemingly unspectacular crumbly structure when looking at the piece with your naked eye. "But the soil is subject to constant change – with immediate consequences for issues of food security or climate change", explains Prof. Dr. Nadja Ray. She holds the Chair of Geomatics and Geomathematics at the Catholic University of Eichstätt-Ingolstadt (KU). In several projects funded by the German Research Foundation (DFG) and in collaboration with researchers from soil science, biophysics, geochemistry, microbiology, and hydrogeology, the mathematician focuses on the smallest structures of the soil, which have been little investigated to date. Mathematics can help significantly in gaining fundamental insights beyond laboratory experiments to understand the functionality of soils.

The so-called microaggregates as basic building blocks of the soil form a network of tiny pores. They have a size of 250 micrometers or less and consist of minerals and organic matter, for example. But taken together, the small structures have a large effect, which in turn unfolds on a larger scale – both as storage for water and for carbon. In general, microaggregates are considered in research as a medium that can store carbon for several hundred years and thus continuously hold organic matter in soils. In addition, microbial communities form in the fine structure in the smallest space, which regulate different properties of the soil. However, a great deal of knowledge was still lacking for a precise understanding of the processes in microaggregates. The three-dimensional buildup and remodeling, as well as processes that contribute to the stabilization of the smallest soil structure, have only been intensively researched in the last ten years.

Modeling of a microaggregate that includes particulate organic matter (POM) with varying carbon content (OC) in addition to pores (pore) and solid matter (solid).
Modeling of a microaggregate that includes particulate organic matter (POM) with varying carbon content (OC) in addition to pores (pore) and solid matter (solid).

A classic way to gain insights into microaggregates is by examining soil samples – including through computed tomography. "For one thing, this is a time-consuming and costly procedure. In addition, it merely creates a snapshot of a very small section that has been taken from its natural environment. We're not only interested in the photo, but also in the video, you could say", explains Professor Ray. At this point, math comes in to broaden the perspective as part of the German Research Foundation’s project "MadSoil": Based on the findings obtained through experiments, Professor Ray and her colleague Dr. Alexander Prechtel from the University of Erlangen have created mathematical models together with doctoral students that can be used to dynamically visualize the processes in the soil in time and space. The goal here is not to merely replicate reality in detail, but to use computing power to model and understand the fundamental processes happening in the soil. "We do not simply want to describe and map, we want to understand: What happens when you change a particular influencing factor that would be difficult to eliminate in an experiment? Which parts in the system are important, which are less relevant", describes Ray. In this way, for example, the cycle of decay and reformation of a microaggregate can be modeled, which depends on many factors such as electrical charges or mineral composition. Carbon degradation products also affect the stability of the microaggregate. In addition, the substances are not evenly distributed in the microaggregate and this can also be taken into account in mathematical models.

 Prof. Dr. Nadja Ray
© Iannicelli Prof. Dr. Nadja Ray

What is appealing about the DFG research group's interdisciplinary approach is the ongoing exchange with other scientific disciplines and the struggle for mutual understanding of subject-specific research. This is also true for a DFG priority program involving Professor Ray, which focuses on maize as a widespread crop. In the process, different perspectives intertwine: While some researchers focus on the entire plant and its growth, for example, Ray concentrates on the mathematical modeling of processes that take place in the immediate vicinity of the roots. Ray explains: "The fine roots compress soil particles as they grow, so the plant itself is actually changing the soil. The resulting cavity can later be used by other roots when the plant has exceeded its lifetime." What role these biopores play and how the plant and soil interact is one of the questions investigated in the project. It also looks at the effect of so-called mucilage – a kind of gel that is excreted by the roots. Among other things, it serves as a buffer in dry periods and also acts as a glue in the soil structure. However, this substance is difficult to distinguish from water in computed tomography images. Mathematical modeling and computer simulations could therefore complement experimental findings. In addition to understanding the fine architecture of soil, Ray aims to lay foundations for insights into the transport of nutrients and water in soil: "In perspective, against the backdrop of climate change, it is also important to find out which factors influence crop growth and which are particularly robust to changing conditions." A deeper understanding of such processes requires interplay between scientific disciplines. She said that based on experiments and conceptual ideas from the geosciences, mathematical models could be created that could then be used to test hypotheses and inspire further practical experiments.

Professor Ray is part of the team of researchers at the new Mathematical Institute for Machine Learning and Data Science (MIDS). The City of Ingolstadt supports MIDS through two endowed chairs, one of which is held by Professor Ray. She is also a lecturer in the Bachelor's degree program in "Data Science". The institute aims to scientifically exploit the potential of digitalization, develop it further in a responsible way, and teach young people the basics of artificial intelligence and machine learning. The variety of topics ranges from mathematical modeling of climate and weather to soil science and signal processing to aspects of machine learning and digital business models.

More information on the MIDS can be found at