Multifractal analysis of soil spatial variability

Multifractal formalism mas utilized to study variability of different soil properties, including soil-test P and K, organic matter content, pH, Ca and Rig contents, and ration exchange rapacity. Data from 1752 samples collect ed from a 259-ha agricultural field in central Illinois were used in the st udy. Based on the theory of multifractals a set of generalized fractal dime nsions, D(q), and an f(alpha) spectrum were computed for each of the studie d soil properties. The D(q) curves were fitted with a three-parameter mathe matical function, which produced excellent fitting results with the coeffic ient of determination between measured and fitted values higher than 0.98 f or all the studied data sets. We analyzed precision produced by the inverse distance interpolation procedure with different power to distance values a nd found the optimal power value to be related to one of the studied multif ractal parameters. For the studied data, the multifractal parameter was the only data property that could be used as au a priori indicator of an optim al power value. The research demonstrated, first, that multifractal paramet ers reflected many of the major aspects of soil data variability and provid ed a unique quantitative characterization of the data spatial distributions and, second, that multifractal parameters might be useful for choosing an appropriate interpolation procedure for mapping soil data.