The distribution of anoxic volume in a fractal model of soil

Abstract

A simple description of soil respiration is combined with a three-dimensional random fractal lattice as a model of soil structure. The lattice consists of gas-filled pores and soil matrix that is a combination of the solid phase and water. A respiration process is assumed to take place in the soil matrix. Oxygen transport occurs by diffusion in the gas-filled pores and, at a much slower rate, in the soil matrix. The stationary state of this process is characterized by the fraction of the matrix that has zero oxyen concentration, i.e., the anoxic fraction. The anoxic fraction of a three-dimensional lattice appears to be largely determined by the presence and distribution of pores that are not connected to the surface of the lattice. Local gradients in connected gas-filled pores play an insignificant role due to the enormous difference in diffusion coefficient between the gas-filled pores and the saturated soil matrix. Analytical and numerical results for the fractal model are compared with calculations for a dual-porosity model comprising spherical aggegates with a lognormal radius distribution. A one-dimensional fractal lattice and the dual-porosity model yield qualitatively similar predictions, suggesting an anoxic fraction that decreases exponentially with the square root of the local oxygen concentration. However, the anoxic fraction of a three-dimensional fractal lattice decreases much faster than exponentially, implying that large clumps of soil matrix are comparatively rare. We propose that this is due to aggregation of soil particles in more than a single dimension, which has important consequences for anaerobic processes in soil. The fractal model accounts for the geometrical implications of three dimensions. A lognormal radius distribution is essentially a one-dimensional structure model.