Development and validation of a box and flux model to describe major, trace and Potentially Toxic Elements (PTEs) in Scottish soils

Luigi Gallini*, Andrew Hursthouse, Antonio Scopa*

*Corresponding author for this work

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The box and flux model is a mathematical tool used to describe and forecast the major and trace elements perturbations of the Earth biogeochemical cycles. This mathematical tool describes the biogeochemical cycles, using kinetics of first, second and even third order. The theory and history of the box and flux modeling are shortly revised and discussed within the framework of Jim
Lovelok’s Gaia theory. The objectives of the investigation were to evaluate the natural versus anthropic load of Potentially Toxic Elements (PTEs) of the Scottish soils, investigate the soil components adsorbing and retaining the PTEs in non-mobile species, evaluate the aging factor of the anthropic PTEs and develop a model which describes the leaching of PTEs in layered soils. In the Scottish land, the soil-to-rock enrichment factor inversely correlates with the boiling point of the PTEs. The same is observed in NW Italy and USA soils, suggesting the common source of the PTEs. The residence time in soils of the measured PTEs linearly correlates with the Soil Organic Matter (SOM). The element property which mostly explains the adsorption capacity for PTEs’ is the ionic potential (IP). The downward migration rates of the PTEs inversely correlate with SOM, and in
Scottish soil, they range from 0.5 to 2.0 cm·year−1. Organic Bentoniteis the most important soil phase adsorbing cation bivalent PTEs. The self-remediation time of the polluted soil examined ranged from 50 to 100 years. The aging factor, the adsorption of PTEs’ into non-mobile species, and occlusion into the soil mineral lattice was not effective. The box and flux model developed, tested and validatedhere does not describe the leaching of PTEs following the typical Gaussian shape distribution of the physical diffusion models. Indeed, the mathematical model proposed is sensitive to the inhomogeneity of the layered soils.
Original languageEnglish
Article number8930
Number of pages18
JournalInternational Journal of Environmental Research and Public Health
Issue number17
Publication statusPublished - 25 Aug 2021


  • soil property variability
  • soil contamination
  • pseudo-total elemental pool
  • box and flux mathematical model


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