MODELING THE GEOMETRY OF WORM BURROW SYSTEMS IN RELATION WITH OXYGEN DIFFUSION

An approximate method is described that enables the application of diffusion models to a system of worm burrows. The geometry of the real burrow system is replaced by a model system consisting of soil cylinders with different radii, each with a worm burrow along its axis. A process model, describing for instance oxygen diffusion and soil respiration, is then applied to the cylinders of the model system. Each cylinder radius represents a characteristic length scale that occurs in the system and a weight factor expresses the relative abundance of each scale. The weights are obtained from the statistical distribution of the distance from a point in the soil to the nearest burrow axis. Hence, application of the method requires distance measurements in three dimensions. In case of randomly located burrows, the distance distribution can also be obtained from measurements in a cross section of the system. As an example, cross sections of a sulphide-containing, homogeneous clay soil are studied. The black clay has become partly oxic due to the presence of worm burrows from which oxygen has entered the soil. The oxidized soil has a light color. Digitized photographs of cross sections are analyzed with the help of an oxidation model for randomly positioned burrows. Assuming a constant distance over which oxygen has entered the soil, predictions are made about the pattern of oxidized soil visible at a cross-sectional surface. These model results are compared with the observations. The assumption of a fixed penetration distance does not explain the observed patterns. Differences in burrow age form the most likely explanation.