Contaminants released at or near the earth surface may travel through the soil unsaturated zone to arrive at and pollute underlying groundwater resources (Zuang et al., 2021). Understanding chemical transport through soil is of paramount importance to predict the fate of contaminants in the environment, including contamination of shallow aquifers. Significant effort has been invested on the development of simulation models of solute transport through soil. However, even if some important questions remain unanswered, our understanding of preferential flow processes in the soil and vadose zone continues to improve steadily leading to more reliable predictive modeling tools (Jarvis et al., 2016). Sometimes, the porous system involved in the transport of solutes is homogeneous, because the macroporosity is reduced by excessive tillage and traffic of heavy machinery despite having a clay content greater than 9%, as highlighted by Koestel et al.. (2012). Under these conditions, solute transport occurs in conditions of physical equilibrium, as reported by Portocarrero et al., (2019) for soils under sugarcane production. On the other hand, it may happen that the macroporosity of the soil has a greater participation, or even dominates, the transport of solutes in conditions of non-physical equilibrium. One of the most common models of solute transport through soil is the mobile-immobile (MIM) equation which includes the preferential flow of solutes in heterogeneous media (Coats and Smith, 1964);
Where D is the dispersion coefficient, V is the pore water velocity, Cm is the resident concentration in the mobile liquid phase, Cim is the concentration in the immobile liquid phase and θm and θim are the volume fraction of mobile and immobile water, respectively. The Convection-Dispersion model is recovered when the immobile fraction of the soil solution is equal to zero. The MIM model is generally more powerful and versatile, and could better explain the flow of water and solutes in porous, structured media under laboratory-controlled conditions (Brusseau and Rao, 1990; Goncalves et al., 2001; Griffioen et al., 1998; Haggerty et al., 2004, Chen et al., 2022).
In general, D and the pore water velocity (V) are derived from experimental data of breakthrough curves of solute determined in the effluent from cores or columns of finite length (Bedmar et al., 2008; Okada et al., 2014) or by sampling the soil solution at several depths into a soil profile (Wang, et al., 2006). The parameters V and D vary in space, both horizontally and with depth (Biggar and Nielsen, 1976; Jury, 1982). Dispersivity λ is a related parameter defined as λ = D/V that describes the variation in the local velocities of the dominant water flow around the average value (Comegna et al., 2001) and is generally considered a characteristic of structured soils. The transport parameter λ describes the dispersion of a pulse of solute applied to the soil surface and has a large influence on predicting average annual concentration of a chemical (Boesten, 2004). Vanderborght and Vereecken (2007) using a database of dispersivities from 57 scientific papers, reported that dispersivity values increase with the length of the soil column over which dispersivity is measured, suggesting that field experiments are more appropriate than laboratory experiments for determining dispersivity. At the field scale, follow-up tracer studies will support modeling of seasonal and annual hydrological dynamics on water flow and solute transport, as a good hydrographic fit does not necessarily denote a fair representation of actual internal flow and transportation pathways on the ground. (Varvaris et al., 2019).
The complex heterogeneity of soil has favored the development of transport theories that are based on conceptual models, such as the transfer function approach (Jury, 1982). A transfer model can predict the flux density in a system with boundaries defined as a function of the inflow, without the need to describe the complex processes that take place in the soil. Jury (1982) suggested a log-normal probability transfer function to configure the convective log-normal (CLT) model. The CLT model appears to be a robust tool to mimic the transport at several depths (Severino et al., 2010). Although mathematically convenient, the physical relevance of this assumption is sometimes questionable (Gao et al., 2009). The pdf requires the soil to be conceptualized as a set of water circulation tubes without lateral mix of the transported solute and also requires the uniform application of the solute over the whole soil surface (Jury, 1982).
Several reviews have been produced on the various strategies used to simulate solute transport in soils, ranging from deterministic to stochastic (Feyen et al., 1998; Jury and Fluhler, 1992; Nielsen et al., 1986; Vanclooster et al., 2005; and Jarvis et al., 2008). It is increasingly clear that current models are not exhaustive when describing the phenomenon in its totality and are difficult to apply at a regional level due to soil heterogeneity and the large number of chemical, physical and biological parameters that must be taken into account (Jury and Fluhler, 1992). Scale dependence of model paramaters, particularly dispersivity has also been invoked as a possible cause of model uncertainty (Vanderborght and Vereecken, 2007). In a review, Yang et al., (2021) analyzed the great variety in the mathematical representation of physical transport processes at different temporal and spatial scales, which generate great challenges in multiscale modeling and numerical simulation of flow and transport. of solutes in porous media. These authors recognize the progress of the models, however, they consider that the scale coupling between the pore and Darcy scales in porous media has not been well resolved yet.
The parameterization of these models is an important component of the simulation effort, being identified as the main challenge by some authors (Varvaris et al., 2021). The literature contains a large body of experimental work, performed mainly under laboratory conditions (Vanderborght and Vereecken, 2007; Koestel et al., 2012). Field experiments involving measurement of chemical transport are rare, particularly those involving multiple replicates in space allowing for a representation of the horizontal heterogeneity of the soil system (e.g., Biggar and Nielsen, 1976). Similarly, measurements of the phenomenon of solute transport at various depths provide information on the soil as an integrator of the transport process and it allows testing the scaling properties of transport parameters. Flux density (q) has an effect on the transport of solutes under field conditions (Costa and Prunty, 2006; Abasi et al., 2003).
The objectives of this work were to obtain parameters V and D in the field as a function of flux density and depth and to test the effect of three previous N treatments in these solute transport parameters. Bromide concentration data of soil water samples from three depths and five water flows were used to adjust 180 breakthrough curves for estimating solute transport parameters in soil: V, D and dispersivity (λ). According to the literature review by Vanderborght and Vereecken (2007), there are only 60 field dispersivity values in the range of depths and flux densities covered in this work.