Multifractal Analysis of Soil Spatial Variability

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Abstract
Multifractal formalism was utilized to study variability of different soil properties, including soil‐test P and K, organic matter content, pH, Ca and Mg contents, and cation exchange capacity. Data from 1752 samples collected from a 259‐ha agricultural field in central Illinois were used in the study. Based on the theory of multifractals a set of generalized fractal dimensions, D(q), and an f(α) spectrum were computed for each of the studied soil properties. The D(q) curves were fitted with a three‐parameter mathematical function, which produced excellent fitting results with the coefficient of determination between measured and fitted values higher than 0.98 for all the studied data sets. We analyzed precision produced by the inverse distance interpolation procedure with different power to distance values and found the optimal power value to be related to one of the studied multifractal parameters. For the studied data, the multifractal parameter was the only data property that could be used as an a priori indicator of an optimal power value. The research demonstrated, first, that multifractal parameters reflected many of the major aspects of soil data variability and provided 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.