Relative entropy as an index of soil structure

Abstract

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

Soil, Climate, Time and Site Factors as Drivers of Soil Structure Evolution in Agricultural Soils from a Temperate-Boreal Region

“…The KL divergence is a quantitative measure of how one probability distribution differs from a second one, which is considered to be the reference distribution. Applied as an index of soil structure, the KL divergence is determined from two VSDs, where one VSD is that of the structured soil and the other that of a hypothetical so-called reference soil (Klöffel et al, 2022). The latter is defined as the same soil 'without structure'.…”

“…However, since the poresize distribution is the result of both properties of the soil mineral phase (e.g., particle-size distribution, particle shape) and soil structure, a major challenge has been to separate the effects of soil texture and structure. While previous indices of soil structure based on the SWRC did not account the effects of soil texture (e.g., Dexter, 2004;Yoon and Giménez, 2012), this issue has been addressed in a recently proposed index of soil structure by Klöffel et al (2022). This index quantifies the difference between two pore/void-size distributions (VSD) using the concept of relative entropy, also known as the Kullback-Leibler (KL) divergence (Kullback & Leibler, 1951), where one VSD is for the structured soil and the second is derived from soil texture for a hypothetical soil without structure.…”

“…The KL divergence as an index of soil structure has so far only been tested on a small dataset (Klöffel et al, 2022). However, an important advantage of this index is that only data on particle-size distribution (PSD), total porosity and soil water retention are required.…”

“…The twin aims of this study were (i) to further test the utility of the KL divergence (Klöffel et al, 2022) as an integrated measure of soil structure on a larger dataset and (ii) to identify the main drivers of soil structure evolution and their relative importance in agricultural soils of a temperate-boreal region. To these ends, we made use of existing soil survey databases containing measurements of soil water retention and particle-size distribution for agricultural soils in Sweden and Norway and applied a random forest analysis to explore relationships between the KL divergence and a range of covariates characterizing soil, climate, time and site factors that are known or expected to affect soil structure.…”

Above- and below-ground links mediated by arboreal ants and host tree modify soil aggregation scaling, infiltration, and chemistry

“…Indeed, changes in scaling law exponents are generally considered indicators of more fundamental changes in underlying rules (i.e., ‘regime’ shifts) of a system, which for soils, can be shifts in relative aggregate formation versus fragmentation, such as those caused by more fungal agglomeration versus invertebrate burrowing, but also represents a generalized mechanism that can apply to cluster-forming systems more broadly such as networks. Beyond the physical limits of natural patterns (Halley et al 2004), shared scaling patterns across biology and ecology have been generally interpreted as indicators of habitat complexity (Loke and Chisholm 2022), biodiversity maintenance (Ostling et al 2004), entropy (Harte, Umemura, and Brush 2021; Klöffel et al 2022), and comparable solutions to optimizing information flow or conserving energy during system changes or adaptation (West, Brown, and Enquist 1997). As a result, analyses of soils that draw from complex systems theory, such as fractal dimensions of soil aggregate size scaling or power law distributions, or similar long-tailed families including log-normal and exponential arising from partially hierarchical soil aggregation (Tisdall and Oades 1982; Melo, Figueiredo, and Filho 2021), continue to offer integrated information about how soils function and respond to key soil biota, like aggregate fragmentation by invertebrates during niche or nest construction (Maaß, Hückelheim, and Rillig 2019) and formation by associated microbial activity (Maaß, Caruso, and Rillig 2015).…”