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International Journal ofEnvironmental Researchand Public HealthArticleDevelopment and Validation of a Box and Flux Model toDescribe Major, Trace and Potentially Toxic Elements (PTEs) inScottish SoilsLuigi Gallini 1,2, *, Andrew Hursthouse 31234* Citation: Gallini, L.; Hursthouse, A.;Scopa, A. Development andValidation of a Box and Flux Model toDescribe Major, Trace and PotentiallyToxic Elements (PTEs) in ScottishSoils. Int. J. Environ. Res. Public Health2021, 18, 8930. https://doi.org/10.3390/ijerph18178930Academic Editors:Takeji Takamura-Enya,Kentaro Misaki and PaulB. TchounwouReceived: 14 June 2021and Antonio Scopa 4, *Liceo Scientifico “Carlo Cattaneo”, Dipartimento di Scienze, Via Sostegno, 41/10, 10146 Torino, ItalySezione di Chimica Agraria, Di.Va.P.R.A., Università di Torino, Largo Paolo Braccini, 2, 10095 Grugliasco, ItalySchool of Computing, Engineering & Physical Sciences, University of the West of Scotland,Paisley PA1 2BE, UK; [email protected] di Scienze Agrarie, Forestali, Alimentari ed Ambientali (SAFE), Università della Basilicata,Vialedell’Ateneo Lucano, 10, 85100 Potenza, ItalyCorrespondence: [email protected] (L.G.); [email protected] (A.S.); Tel.: 39-0971-205240 (A.S.)Abstract: The box and flux model is a mathematical tool used to describe and forecast the major andtrace elements perturbations of the Earth biogeochemical cycles. This mathematical tool describes thebiogeochemical cycles, using kinetics of first, second and even third order. The theory and history ofthe box and flux modeling are shortly revised and discussed within the framework of Jim Lovelok’sGaia theory. The objectives of the investigation were to evaluate the natural versus anthropic load ofPotentially Toxic Elements (PTEs) of the Scottish soils, investigate the soil components adsorbing andretaining the PTEs in non-mobile species, evaluate the aging factor of the anthropic PTEs and developa model which describes the leaching of PTEs in layered soils. In the Scottish land, the soil-to-rockenrichment factorinversely correlates with the boiling point of the PTEs. The same is observed inNW Italy and USA soils, suggesting the common source of the PTEs. The residence time in soils ofthe measured PTEs linearly correlates with the Soil Organic Matter (SOM). The element propertywhich mostly explains the adsorption capacity for PTEs’ is the ionic potential (IP). The downwardmigration rates of the PTEs inversely correlate with SOM, and in Scottish soil, they range from 0.5 to2.0 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 noteffective. The box and flux model developed, tested and validatedhere does not describe the leachingof 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.Accepted: 21 August 2021Published: 25 August 2021Keywords: soil property variability; soil contamination; pseudo-total elemental pool; box and fluxmathematical modelPublisher’s Note: MDPI stays neutralwith regard to jurisdictional claims inpublished maps and institutional affiliations.Copyright: 2021 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/1. IntroductionIn the geodynamic earth system, elements cycle between several compartments, mostrelevant of which are the atmosphere, hydrosphere, pedosphere, biosphere and lithosphere,but also across ecosystems in biogeochemical equilibria with these principal planetaryreservoirs. As demonstrated by Jim Lovelock’s Gaia theory, many of the important drivingforces of the earth’s dynamic biogeochemical system, as well as most of the relevant geochemical reaction kinetics, rule the flux of elements between the different earth reservoirs,modulated by the biological activity of living organism [1,2]. Most of the chemical equilibria controlling geodynamics are modulated by simple and multiple retroactive feedback,which ensures some buffering capacity to earth ecosystem and some degree of homeostasisto overall planet earth [3].4.0/).Int. J. Environ. Res. Public Health 2021, 18, 8930. mdpi.com/journal/ijerph

Int. J. Environ. Res. Public Health 2021, 18, 89302 of 17Any chemical element is characterized by specific concentration ranges within whichthe elements may affect organisms living in an ecosystem. The range of Potential ToxicElements (PTEs) include those with direct toxicity or where they exceed the range ofconcentration essential or needed for the ecosystem stability and development [4].Soil as part of the dynamic earth system is the most important planetary sink for manyof the PTEs released in the environment by human activity, and since the beginning ofthe industrial revolution in the 18th Century, there has been an exponential increase inmost of the earth environmental ecosystems which are in biogeochemical equilibria, and inparticular with soils and sediments.The intensive agricultural and industrial activity has led to PTE accumulation inagricultural soils threatening the environment, as well as the quality, quantity and securityof cultivated products [5]. Many anthropogenic PTEs flushed from contaminated soilinto the aquatic ecosystem—and consequently, negatively affecting its biodiversity andstability—eventually accumulate in the marine food chain and affect the security of fish,and the state of human health and fertility rates [6].The biogeochemical cycles of major chemical elements among earth compartmentscan be controlled by first-, second-, or even third-order kinetics, but generally the biogeochemical cycles of the PTEs in trace amounts can be described by simple first-order kinetics.The biogeochemical cycles of individual major and traces elements can be coupled togetherto achieve more detailed and complex models carefully describing the biogeochemicalequilibria [7]. It is reasonable to believe that, by coupling together the major elementbiogeochemical cycles with trace element cycles, we can achieve a more detailed EarthGeochemical Reference Model (GERM). This geochemical reference model could find wideapplication in the environmental impact assessment of contaminated land and ecosystems(see https://earthref.org/GERMRD/ (accessed on 21 April 2021)).To evaluate the anthropogenic contribution versus natural origin of the PTEs detectedin the environmental compartments, it is critical to estimate the chemical kinetics of the interactions of PTEs with minerals, rocks, solution, gasses and interaction of the bioavailablePTEs with the organism living in the relevant environmental compartment. Fate, mobility,distribution and bioavailability of PTEs depending on the chemical–physical properties ofsoils, rocks and sediments, which are in turn determined by chemical–physical kineticsreactions mostly controlled by living organisms (these include: complexation, hydrolysis,dissolution, solubility, oxidation, reduction, precipitation, adsorption, methylation andrelease into atmosphere or translocation, and leaching toward groundwater, uptake intobiota, uptake into terrestrial biomass and the related ecosystems) [8]. Most of the rates ofthe chemical–physical reaction kinetics reported in the literature are enhanced by enzymaticsystem of living organisms by several orders of magnitude greater than the basic inorganickinetic reaction rates. As a general rule, the PTEs persist in the earth ecosystem due tothe long time required to isolate them in poorly-mobile and non-bioavailable chemicalspecies [9,10].Box and flux models have been employed to describe the fate and behavior of anthropogenic PTEs fluxes in localized ecosystems. Historically, the box and flux model wasinitially developed to describe and forecast the leaching of radionuclide in soils [11,12].With regionalized and georeferenced box and flux models used to describe and forecastthe fate and the effects of anthropogenic fluxes of major and trace PTEs in ecosystemAsian oceanic waters [13,14]. The same approach was used to describe and forecast thefluxes of anthropogenic PTEs in the Canadian continental agricultural ecosystem [13,15–19],and employed to describe trace PTEs leaching from soils to groundwater in very localized cases [12,15,20]. Ultimately box and flux models were used to describe and forecastthe fluxes of PTEs contaminating pedosphere into the food chain and to evaluate theanthropogenic perturbation of biogeochemical cycles.Therefore, box and flux models are mathematical tools that are widely used to notonly model the earth biogeochemical equilibria, but also the response to perturbation ofthese equilibria. The box and flux model have been applied to describe the major elements

Int. J. Environ. Res. Public Health 2021, 18, x FOR PEER REVIEW3 of 18Therefore, box and flux models are mathematical tools that are widely used to not3 of 17only model the earth biogeochemical equilibria, but also the response to perturbationofthese equilibria. The box and flux model have been applied to describe the major elementsC, N, S and P biogeochemical cycles, but also to evaluate the short- and long-term effectscausedindustrialgrowth thatare kineticallybiogeochemicalcyclesofC, N, SbyandP biogeochemicalcycles,but also to perturbingevaluate thetheshortand tintheenvironmentalecosystem.caused by industrial growth that are kinetically perturbing the biogeochemical cycles ofIn thiselementsstudy, e soil–rockenrichment factorthe majortracePTEsenvironmentalecosystem.of PTEs,the anthropogenicand the propertiesof thethat affectthe mobilityIn thisstudy, we used PTElocalloadsoil systemsto determinethe csofthatPTEs,the anthropogenicPTEweloadand thethepropertiesof the soil thataffect adsorbedonsoilcolloids,ininsolubleamorthat pollution. Furthermore, we evaluate the chemical–physical processes and kinetics thatphousprecipitatesin non-bioavailablephases occludedin the soil,forming icPTEs adsorbedon soil colloids,in insolubleminerallattices.ultimate aim ofphasesthese occludedmeasuresinwasdevelopandvalidateminerala newprecipitatesand Thein non-bioavailablethe tosoil,formingcrystallineboxand flowmodel thatdescribesmobilityof toPTEsin soilsand,finally,a todeterminelattices.The ultimateaimof these themeasureswasdevelopandvalidatenewbox andtheso-calledflushingsoil PTEs.flowmodel “self-remediation”that describes the ormobilityofratesPTEsofinanthropogenicsoils and, finally,to determine theso-called “self-remediation” or flushing rates of anthropogenic soil PTEs.2. Materials and Methods2. MaterialsandMethods2.1.Descriptionof StudyArea2.1. Description of Study AreaThe soil selected to test and validate the model was developed on the top of a drumThe soilselectedmetersto test long,and validatemodel wasdevelopedon thetop of aUK.drumlin,lin, severalhundredlocatedthein K.Thequaternary geology map of the British Geological Survey Service (www.largeiquaternary geology map of the British Geological Survey Service rtal.html?id 1003899 (accessed on 21 April 2021)) indicateduk/iip/mapsportal.html?id 1003899 (accessed on 21 April 2021)) indicated the soil beingthe soil being studied was derived from a fluvial–glacial parent material that had beenstudied was derived from a fluvial–glacial parent material that had been deposited duringdeposited during the last glaciations. The alluvial soil was classified as Gleyic Fluvisolthe last glaciations. The alluvial soil was classified as Gleyic Fluvisol [21]. It has been[21]. It has been polluted by atmospheric emissions from an adjacent smelter operation,polluted by atmospheric emissions from an adjacent smelter operation, peaking in thepeaking in the 1950s until 1987 when it was decommissioned. Climatic conditions of the1950s until 1987 when it was decommissioned. Climatic conditions of the area, averagearea, average of the monthly data, was collected by the Scottish meteorological serviceof the monthly data, was collected by the Scottish meteorological service (www.metoffice.(www.metoffice.gov.uk (accessed on 11 June 2000, stored by Gallini L.)), from 1990 togov.uk (accessed on 11 June 2000, stored by Gallini L.)), from 1990 to 1995, and are shown1995, and are shown in Figure 1.in Figure 1.Int. J. Environ. Res. Public Health 2021, 18, unty,County,Glasgow,Glasgow, ScotlandScotland (UK).2.2.SoilSoilProfileProfile2.2.Ap horizon (0–25 cm). This was a typically eluvial ploughed horizon, with a sharpAp horizon (0–25 cm). This was a typically eluvial ploughed horizon, with a sharpboundary and a strong brown color due to the organic matter content. The porosity wasboundary and a strong brown color due to the organic matter content. The porosity washigh, and the plasticity moderate. The soil aggregates were irregular. Throughout thehigh, and the plasticity moderate. The soil aggregates were irregular. Throughout thehorizon, strong biological activity was observed: worms and abundant grassroots werehorizon, strong biological activity was observed: worms and abundant grassroots werefound. A relevant flux of PTEs f