F. San José Martínez

Modelling solute transport in soil columns using advective-dispersive equations with fractional spatial derivatives

Solute transport in soils is commonly simulated with the advective-dispersive equation, or ADE. It has been reported that this model cannot take into account several important features of solute movement through soil. Recently, a new model has been suggested that results in a solute transport equation with fractional spatial derivatives, or FADE. We have assembled a database on published solute transport experiments in soil columns to test the new model. The FADE appears to be a useful generalization of the ADE. The order of the fractional differentiation reflects differences in physical conditions of the solute transport in soil.

Volume, Surface, Connectivity and Size Distribution of Soil Pore Space in CT Images: Comparison of Samples at Different Depths from Nearby Natural and Tillage Areas

The study of soil structure, i.e., the pores, is of vital importance in different fields of science and technology. Total pore volume (porosity), pore surface, pore connectivity and pore size distribution are some (probably the most important) of the geometric measurements of pore space. The technology of X-ray computed tomography allows us to obtain 3D images of the inside of a soil sample enabling study of the pores without disturbing the samples. In this work we performed a set of geometrical measures, some of them from mathematical morphology, to assess and quantify any possible difference that tillage may have caused on the soil. We compared samples from tilled soil with samples from a soil with natural vegetation taken in a very close area. Our results show that the main differences between these two groups of samples are total surface area and pore connectivity per unit pore volume.

Solute Transport Simulated With the Fractional Advective-Dispersive Equation

Solute transport in soils and sediments is commonly simulated with the parabolic advective-dispersive equation, or ADE. Although the solute dispersivity in this equation is regarded as a constant, it has been found to increase with the distance from the solute source. This can be explained assuming the movement of solute particles belongs to the family of Levy motions. A one-dimensional solute transport equation was derived for Levy motions using fractional derivatives to describe the dispersion. This fractional advective-dispersive equation, or FADE, has two parameters — the fractional dispersion coefficient and the order of fractional differentiation α, 0<α≤2. Scale effects are reflected by the value of α, and the fractional dispersion coefficient is independent of scale. The ADE is a special case of the FADE. Our objectives were (a) to test applicability of the FADE to field data on solute transport in soils, and (b) to develop a numerical method to solve FADE that would assure the solute mass conservation. Analytical solutions of the FADE and the ADE were successfully fitted to the data from field experiments on chloride transport in sandy loam and bromide transport in clay loam soils. A numerical method to solve the boundary problem for FADE was proposed and tested, that uses the mass-conserving flux boundary condition. The FADE is a promising model to address the scale-dependence in solute dispersion in soils and sediments.Copyright

Morphological Functions with Parallel Sets for the Pore Space of X-ray CT Images of Soil Columns

During the last few decades, new imaging techniques like X-ray computed tomography have made available rich and detailed information of the spatial arrangement of soil constituents, usually referred to as soil structure. Mathematical morphology provides a plethora of mathematical techniques to analyze and parameterize the geometry of soil structure. They provide a guide to design the process from image analysis to the generation of synthetic models of soil structure in order to investigate key features of flow and transport phenomena in soil. In this work, we explore the ability of morphological functions built over Minkowski functionals with parallel sets of the pore space to characterize and quantify pore space geometry of columns of intact soil. These morphological functions seem to discriminate the effects on soil pore space geometry of contrasting management practices in a Mediterranean vineyard, and they provide the first step toward identifying the statistical significance of the observed differences.