Simulation of the Heavy Metal Transport in Unsaturated Soils: Use of Scale Factors to Quantify Variable Sorption Isotherms

Heavy metals are toxic soil pollutants that are retarded in soils by sorption at the solid phase. At a small scale (of a soil sample), the sorption process can be observed and quantified using sorption isotherms. However, most environmental problems have to be treated and solved at large scales (e.g., a field scale). At the field scale, heavy metal sorption isotherms are commonly highly variable in space. This spatial variability makes a representative quantification of the sorption process (e.g., for the soil protection or for the management of soil functions) and its consideration in reactive transport modelling (e.g., for groundwater protection) difficult. Many transport simulation studies therefore treat soils as homogeneous to avoid the need for complex datasets and calculations. In this study we used a recently developed method of scale sorption factors to quantify the spatial variability of heavy metal sorption in soils at the field scale. This method reduces the variability of sorption isotherms into a single average relation while preserving their variation through the scale factors. We investigated the spatial variability of heavy metal sorption isotherms for an agricultural field on a Luvisol developed over a loess material near Hannover, Germany. Fifty samples were taken from A and B horizons along a 250-m transect. Sorption isotherms for heavy metals and soil properties, such as pH, CEC, and texture, were measured and scale factors were calculated. The heavy metal transport was simulated with the HYDRUS model using a unique reference sorption isotherm (derived using the scale procedure or mixed soil samples). Spatial variability of sorption at every sampling point was further represented using a scale factor, which was either directly calculated (using a scaling procedure) or indirectly estimated (using regression models with another heavy metal or from soil properties). For comparison, variability of sorption was also simulated using the original, measured Freundlich parameters. The results show that scale factors are well suited for predicting spatially variable retardation and transport of heavy metals in soil, although a certain reduction of variability is to be expected. In the case of extreme situations, transport simulations with scale factors are not well suited to describe the depth distribution of heavy metal concentrations, especially when using indirectly calculated scale factors.