Relative entropy as an index of soil structure

Soil structure controls key soil functions in both natural and agro-ecosystems. Thus, numerous attempts have been made to develop methods aiming at its characterization. Here we propose an index of soil structure that uses relative entropy to quantify differences in the porosity and pore(void)-size distribution (VSD) between a structured soil derived from soil water retention data and the same soil without structure (a so-called reference soil) estimated from its particle-size distribution (PSD). The difference between these VSDs, which is the result of soil structure, is quantified using the Kullback-Leibler Divergence (KL divergence). We applied the method to soil data from two Swedish field experiments that investigate the long-term effects of soil management (fallow vs. inorganic fertilizer vs. manure) and land use (afforested land vs. agricultural land dominated by grass/clover ley) on soil properties. The KL divergence was larger for the soil receiving regular addition of manure compared with the soils receiving no organic amendments. Furthermore, soils under afforested land showed significantly larger KL divergences compared to agricultural soils near the soil surface, but smaller KL divergences in deeper soil layers, which closely mirrored the distribution of organic matter in the soil profile. Indeed, a significant positive correlation (r = 0.374, p < 0.001) was found between soil organic carbon concentrations and KL divergences across all sites and treatments. Despite challenges related to modelling the VSD of the reference soil without structure, the proposed index proved useful for evaluating differences in soil structure in response to soil management and land-use change and reflected the expected effects of soil organic matter on soil structure. We conclude that relative entropy shows great potential to serve as an easy-to-use index of soil structure, as it only requires widely available data on soil physical and hydraulic properties. Highlights A new index of soil structure is proposed based on relative entropy A method is developed that separates the effects of soil texture and structure on the pore space The index identified soil structural differences in response to land use and soil organic carbon concentrations (SOC) The index shows the potential to serve as an easy-to-use metric of soil structure