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Multifractal Analysis of Soil Spatial Variability

^a Dep. of Natural Resources and Environmental Sciences, 1102 S. Goodwin Ave., Univ. of Illinois, Urbana, IL 61801 USA

View larger version (62K): [in a new window]   Fig. 1 Sample locations and five grids used in the multifractal calculations, with grid sizes ranging from (a) 50 m to (e) 800 m. For each grid, we show the grid size, , the total number of the cells in the grid, n, and the equation for calculating soil property value in the grid cell, µi, based on the soil property values in the initial cells, µini

View larger version (29K): [in a new window]   Fig. 2 Partition function q() plotted vs. cell size in a log–log scale at selected q-values for (a) P, (b) Mg, (c) pH, and (d) cation exchange capacity (CEC). The slope of the log q()/log line defines the mass exponent (q) (Eq. [3])

View larger version (19K): [in a new window]   Fig. 3 Experimental D(q) data and fitting curves of Eq. [11] for (a) P, Ca, Mg, and organic matter (OM) and for (b) K, pH, and cation exchange capacity (CEC)

View larger version (73K): [in a new window]   Fig. 4 Geostatistical and multifractal characteristics of the two scenarios for cation exchange capacity (CEC) data distribution. Maps of CEC data for (a) first and (b) second scenarios were obtained using inverse distance weighting and are shown, along with (c) corresponding sample variograms, and (d) multifractal spectra

View larger version (62K): [in a new window]   Fig. 5 Multifractal f() spectra along with soil property distribution maps and histograms for (a) P; (b) K; (c) organic matter, OM; (d) pH; (e) Ca; (f) Mg; and (g) cation exchange capacity, CEC. Maps were obtained by interpolating the experimental data using the inverse distance weighted interpolation procedure. Histogram classes correspond to map classes and were obtained by dividing the data range into 12 equal-sized intervals

View larger version (12K): [in a new window]   Fig. 6 The optimal values of the power to distance (p) parameter of the inverse distance interpolation procedure plotted vs. the difference between the minimum and maximum values of the multifractal parameter f(), [f(max) - f(min)]