Topological Analysis of the Dynamics of Soil Pore Space Structure: The Betti Numbers as an Indicator of Physical Degradation

The relevance of this work is driven by the need for a rapid assessment of the physical state of agrogray heavy loamy soils (Phaeozems (Loamic, Aric, Densic), WRB-2022)) caused by excessive compaction. The particular goal is to quantitatively describe the dynamics of soil pore space in the course of the transition from an air-dry to a moist state and to identify the topological indicators of degradation. The same monolith samples are used in the experiment; they were consistently examined using the X-ray microcomputed tomography in the air-dry (hygroscopic moisture) and in the moist (close to field capacity) states to simulate the change in moisture content without destructuring. The pore space of four horizons (0–90 cm) is examined in a layerwise manner using X-ray microcomputed tomography (resolution, 31.7 µm; n =12), followed by the analysis using Minkowski functionals and Betti numbers. Betti numbers b0 and b1 are the topological invariants indicating the number of isolated pore components and independent pore channels in the samples, respectively, and translating the visual pore pattern into a quantitative metric of connectivity. The macropore (d > 75 µm) volume decreases by 15–30%, while b1 decreases by 38% in the arable layer and by 57% in the compacted subsoil layer. We introduce the pore structure mobility coefficient (PSMC = b0 wet/b0 dry), negatively correlated with bulk density (r = –0.88) and positively, with hydraulic conductivity (r = 0.94); The PSMC of <0.8 reliably marks a compacted plow pan in the studied site. Our results are applicable to agrophysical monitoring and a detailed monitoring of degradation. Thus, the topological indicators combined with common physical soil characteristics expand the diagnostic possibilities and enable the ranking of horizons according to the degree of their physical degradation.