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.

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相对熵作为土壤结构的指标

土壤结构控制着自然和农业生态系统中的关键土壤功能。因此，已经进行了许多尝试来开发针对其表征的方法。在这里，我们提出了一种土壤结构指数，该指数使用相对熵来量化从土壤保水数据得出的结构化土壤与没有结构的相同土壤（所谓的参考土壤）从其粒度分布（PSD）估计。这些 VSD 之间的差异是土壤结构的结果，使用 Kullback-Leibler 散度（KL 散度）进行量化。我们将该方法应用于来自两个瑞典田间试验的土壤数据，这些试验调查了土壤管理（休耕与无机肥料与粪肥）和土地利用（绿化土地与肥沃土地）的长期影响。以草/三叶草为主的农业用地）对土壤特性的影响。与未施有机肥的土壤相比，定期施肥的土壤 KL 差异较大。此外，与土壤表面附近的农业土壤相比，绿化土地下的土壤显示出明显更大的 KL 散度，但在较深的土壤层中 KL 散度较小，这密切反映了土壤剖面中有机质的分布。事实上，显着的正相关（但在较深的土壤层中 KL 差异较小，这密切反映了土壤剖面中有机质的分布。事实上，显着的正相关（但在较深的土壤层中 KL 差异较小，这密切反映了土壤剖面中有机质的分布。事实上，显着的正相关（r  = 0.374, p  < 0.001）在所有地点和处理的土壤有机碳浓度和 KL 差异之间发现。尽管在模拟无结构参考土壤的 VSD 方面存在挑战，但所提出的指数被证明可用于评估土壤结构响应土壤管理和土地利用变化的差异，并反映土壤有机质对土壤结构的预期影响。我们得出结论，相对熵显示出作为易于使用的土壤结构指标的巨大潜力，因为它只需要广泛可用的土壤物理和水力特性数据。