Simulation and testing of self-similar structures for soil particle-size distributions using iterated function systems

Abstract

Particle-size distribution (PSD) is a fundamental soil physical property. The PSD is commonly reported in terms of the mass percentages of sand, silt and clay present. A method of generating the entire PSD from this limited description would be extremely useful for modeling purposes. We simulated soil PSDs using an iterated function system (IFS) following Martín and Taguas [Martín, M.A., Taguas, F.J., 1998. Fractal modeling, characterization and simulation of particle-size distribution in soil. Proc. R. Soc. Lond. A 454, 1457–1468]. By means of similarities and probabilities, an IFS determines how a fractal (self-similar) distribution reproduces its structure at different length scales. The IFS allows one to simulate intermediate distributional values for soil textural data. A total of 171 soils from SCS [Soil Conservation Service, 1975. Soil taxonomy: a basic system of soil classification for making and interpreting soil surveys. Agricultural Handbook no. 436. USDA-SCS, USA, pp. 486–742] were used to test the ability of different IFSs to reconstruct complete PSDs. For each soil, textural data consisting of the masses in eight different size fractions were used, and different PSDs were predicted using different combinations of three similarities. The five remaining data points were then compared with the simulated ones in terms of mean error. Those similarities that gave the, lowest mean error were identified as the best ones for each soil. Fifty-three soils had an error less than 10%, and 120 had an error less than 20%. The similarities corresponding to the sand, silt and clay fractions, i.e., IFS {0.002, 0.05}, did not, in general, produce good results. However, for soils classified as sand, silt loam, silt, clay loam, silty clay loam and silty clay, the same similarities always produced the lowest mean error, indicating the existence of a self-similar structure. This structure was not the same for all classes, although loams and clays were both best simulated by the IFS {0.002, 0.02}. It is concluded that IFSs are a powerful tool for identifying self-similarity in soil PSDs, and for reconstructing PSDs using data from a limited number of textural classes.