Thermodynamic mathematical model of the Kastanozem complex and new principles of sustainable semiarid protective silviculture management

The Kastanozem complex in the dry steppe of southern Russia underlies an artificially-constructed forest strips. Deep ploughing to a depth of 45 cm was used to process the soil prior to planting. Between 20 and 40 cm depth, soil density was high, 1.57 t m⁻³. Soil hardness was also high, 440 psi. Soil aggregates greater than 5 cm in size were impermeable to tree roots. The content of such aggregates was high, comprising 35%. The number of tree roots with diameters greater than 0.5 cm that cross the soil profile was as low as 0.15 to 0.3 pcs cm⁻². The soil matric potential signifying water availability was low in the vegetation period −0.9 MPa to a depth of 1.0 m. According to modelling experiments, the main salt components in the soil solution drive the transfer of soil organic matter (SOM) and heavy metals (HM). The composition of the soil solution determined by the calcium carbonate equilibrium (CCE) and the association and complexation of ions. ION-3 software was used to calculate the ion equilibrium in the soil solution. Macro-ions Cа²⁺, Mg²⁺, SO₄²⁻, and CO₃²⁻ partly bonded as ion pairs. Oversaturation of the soil solution with CaCO₃ was calculated according to the analytical content of macro-ion, which was high up to 1000 units, and its value decreased in response to ionic strength, activity, association, complexation, and thermodynamic equilibrium of macro-ions in the soil solution. Oversaturation calculated for Salic Solonetz and Gleyic Solonetz soil solutions was small considering the SOM content. Calculations indicate the profile and lateral loss of C from the soil to the vadose zone. The content of Pb in the soil solution was calculated sirca 75%–80%. The calculated coefficient of Pb²⁺ association was as high as 52.0. The probability of Pb passivation by SOM in the Kastanozem complex was significant. The probability of uncontrolled transfer and accumulation of HM in the soil and vadose zone was high. Biogeosystem Technique (BGT*) transcendental methodology, an innovative methodology created for stable geomorphological system formation to achieve sustainable agriculture and silviculture, was applied. The BGT* elements were: intra-soil milling of the 30–60 cm soil layer for geophysical conditioning; intra-soil continuously-discrete pulse watering for plants and trees to improve the hydrologic regime. The BGT* methodology reduced HM mobility, controlled biodegradation, enriched nutrient biogeochemical cycling, increased C content, increased soil productivity, and reversible carbon sequester in biological form.