A Lagrangian model framework for the simulation of fluid flow and solute transport in soils
Authors: Sternagel Alexander , Loritz Ralf , Zehe Erwin 
Published: February 2023

We develop an integrated model framework for the simulation of a multitude of soil hydrological processes, such as (reactive) solute transport together with (preferential) water flow and diffusive mixing on the pore scale. This framework is called the Lagrangian Soil Water and Solute Transport (LAST) Model. It bases on a new theoretical concept and should serve as alternative to the common theories of the Darcy-Richards equation and the advection-dispersion-equation (ADE), which have limitations under more natural conditions.In the LAST-Model framework, soil water is represented by discrete water particles of constant mass. The model applies a Lagrangian perspective on the trajectories of particles through a partially saturated soil domain. Particle displacements along the trajectories are calculated by a non-linear, space domain random walk that combines physics and stochastic. We gradually extend the scope of the LAST-Model framework by additional routines.We implement routines for solute transport and preferential flow. Water particles are assigned by a solute mass and in this way, solutes are distributed together with the displacement of water particles. For preferential flow, a structural macropore domain is implemented as a second flow domain. Particles can infiltrate and travel purely by gravity in the macropore domain, independent from capillary-flow conditions in the soil matrix. As a result, they can bypass the bulk water fractions in the soil matrix before re-infiltrating the matrix and accumulating in greater depths.We modify the solute transport routine to allow for the simulation of the transport of reactive substances. Specific routines for sorption and degradation processes are implemented. Sorption is represented by an explicit solute mass transfer between water particles and the solid phase by means of non-linear Freundlich isotherms, and driven by a concentration gradient. Adsorbed solutes are then assumed to be microbially degraded following first-order decay kinetics.We introduce the diffusive pore mixing (DIPMI) approach as additional routine for the simulation of pore-size-dependent diffusive mixing of water and solutes over the pore space. This approach should produce more reliable descriptions of frequently observed (imperfect) mixing behaviours, in contrast to the common assumption of averaging concentrations over all pore sizes in a single time step.Each model extension is tested by simulations of field and laboratory experiments as well as sensitivity analyses. Simulation results are compared against observed data and results of a benchmark model that uses the Darcy-Richards theory and the ADE. The most important findings of the studies can be summarized as:The structural macropore domain is key for a successful representation of preferential water flow and (reactive) solute transport. In heterogeneous soils, LAST simulations match better the observed redistribution and depth-accumulation of solutes compared to simulations with the Darcy-Richards + ADE model.
Imperfect, diffusive mixing on the pore scale has a significant influence on macroscopic leaching behaviours and chemical/isotopic compositions of soil water fractions.
The particle-based approach of the LAST-Model framework is a promising tool for further soil- and ecohydrological application fields.