Stochastic Simulations of Spatial Variability Based on Multifractal Characteristics

Abstract

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.

Pedometrics Research in the Vadose Zone—Review and Perspectives

“…Other methods to deal with this variation of relationship with scales include multifractal scaling, which is fully discussed in Tarquis et al (2008) and Kravchenko (2008). The empirical mode decomposition (EMD) is a relatively new technique that has been designed to analyze nonlinear and nonstationary data.…”

Application of Multifractal and Joint Multifractal Analysis in Examining Soil Spatial Variation: A Review

“…This may be due to inclusion of multi-scale characteristics in calculating secondary terrain indices such as the wetness index. The spatial variability of crop yield also found to exhibit multifractal in nature [47,[113][114][115]. A stochastic simulation study showed that the spatial variability in the production of wheat crop was multifractal, while the production of corn was monofractal [115].…”

“…The variability in crop yield with respect to the nitrate nitrogen level in soil was also studied using joint multifractal analysis [114]. Various authors also developed models to better predict the crop yield based on the multifractal nature of the crop yield and terrain indices [115].…”

Assessing soil particle-size distribution on experimental plots with similar texture under different management systems using multifractal parameters

“…Geostatistical analysis has been also used to identify differences between treatments (López and Arrúe, 1995). Multifractals can be used not only to describe the irregular distribution of a measure but also to characterize measures defined on a geometrical support (Eghball et al, 1999;Kravchenko et al, 1999;Kravchenko, 2008;Cheng, 2008). Advantages of multifractal analysis over traditional statistics and geostatistics have been tested (Kravchenko et al, 1999;Cheng, 2008).…”