Conventional and fractal geometry in soil science

Publisher Summary The geometric properties of soil elementary particles, aggregates, peds, pores, exposed soil surfaces, contours, etc., are of utmost importance for understanding and managing soils. Lengths, areas, volumes, mutual positions in space, counts per range of sizes, etc., are values to operate for anyone who studies or uses soils. Both direct and indirect measurements of geometric quantities are in use in soil studies. Indirect, or proxy, geometrical measurements are common. Non-geometrical values are converted into a geometrical value using a physical model thought to be approximately valid in soils. For example, to obtain particle size distribution, time of the transport of particles of a particular size is estimated from the Stokes model of viscous flow, and then the time is converted to diameters. To obtain pore size distribution, pore radii are computed using capillary models, and pressures are converted to radii. To estimate surface area, the model of ideal monolayer is used so that masses of adsorbed molecules are converted to area values. This list can be expanded easily. Ideal geometrical objects, such as spheres, circles, and segments, are widely used as models in indirect and direct measurements in soil science. Soil particles are assumed to be spheres when the Stokes model is applied. Pores are presumed to be cylinders to compute radii of pores from capillary pressure values. Molecules are thought to be spheres in calculations of the surface area from the monomolecular coverage. Soil aggregates are viewed as spheres when their diameters are measured by the sieve analysis. Using ideal geometrical models is an approximation that introduces uncontrollable errors in the measurements.