The distribution of anoxic volume in a fractal model of soil

A simple description of soil respiration is combined with a three-dimension al random fractal lattice as a model of soil structure. The lattice consist s of gas-filled pores and soil matrix that is a combination of the solid ph ase and water. A respiration process is assumed to take place in the soil m atrix. 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 proce ss is characterized by the fraction of the matrix that has zero oxygen conc entration, i.e., the anoxic fraction. The anoxic fraction of a three-dimens ional lattice appears to be largely determined by the presence and distribu tion of pores that are not connected to the surface of the lattice. Local g radients in connected gas-filled pores play an insignificant role due to th e enormous difference in diffusion coefficient between the gas-filled pores and the saturated soil matrix. Analytical and numerical results for the fr actal model are compared with calculations for a dual-porosity model compri sing spherical aggregates with a lognormal radius distribution. A one-dimen sional fractal lattice and the dual-porosity model yield qualitatively simi lar predictions, suggesting an anoxic fraction that decreases exponentially with the square root of the local oxygen concentration. However, the anoxi c fraction of a three-dimensional fractal lattice decreases much faster tha n exponentially, implying that large clumps of soil matrix are comparativel y rare. We propose that this is due to aggregation of soil particles in mor e than a single dimension, which has important consequences for anaerobic p rocesses in soil. The fractal model accounts for the geometrical implicatio ns of three dimensions. A lognormal radius distribution is essentially a on e-dimensional structure model. (C) 1999 Elsevier Science B.V. All rights re served.