Stochastic Simulations of Spatial Variability Based on Multifractal Characteristics

Using multifractal characteristics in the stochastic simulation of environmental and agronomic variables has the potential for producing simulations that better represent features of interest, including distribution properties of the high and low values, than simulations based on geostatistical characteristics. The objective of this study was to compare the performance of stochastic simulations that reproduce certain multifractal characteristics with simulations that reproduce variogram model parameters. Data on corn ( Zea mays L.) and wheat ( Triticum aestivum L.) yields collected at 1100 and 880 sampling locations, respectively, were used in the simulations. Wheat data represented an example of a variable exhibiting a multifractal scaling and corn an example of a variable exhibiting a monofractal scaling. The conditional simulations were conducted using a simulated annealing procedure. Two simulation scenarios were compared. The first scenario consisted of using the order of the structure function q = 2, which is equivalent to simulating a data set with a certain variogram, that is, a monofractal simulation. The second scenario used the histogram and the structure function with exponent values for q ranging from 1 to 5, a multifractal simulation. Based on 50 simulations, the performances of the two scenarios in representing the highest and lowest values were compared. There was no significant difference in performance of monofractal and multifractal simulations for the variable exhibiting monofractal scaling (corn). For the variable with multifractal scaling (wheat), however, multifractal simulations performed better in predicting low values. For soil or agronomic variables exhibiting multifractal scaling, stochastic simulations based on multifractal characteristics could be preferable to those based on variogram parameters.

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