Page Banner

United States Department of Agriculture

Agricultural Research Service

Title: Fractal Analysis of Spatial and Temporal Variability

Authors
item Eghball, Bahman
item Hergert, Gary - UNIV OF NE
item Lesoing, G - UNIV OF NE

Submitted to: Fractals In Soil Science
Publication Type: Book / Chapter
Publication Acceptance Date: November 1, 2000
Publication Date: December 20, 2000
Citation: EGHBALL, B., HERGERT, G., LESOING, G.W. FRACTAL ANALYSIS OF SPATIAL AND TEMPORAL VARIABILITY. FRACTALS IN SOIL SCIENCE P. 259-272. 2000.

Interpretive Summary: Characterizing spatial and temporal variability is important in variable rate or long-term studies. This study was conducted to compare spatial variability of soil nitrate in a variable rate nitrogen (N) application study and temporal variability of soybean yield in a long-term organic vs. inorganic treatment study. In the variable rate study, conventional uniform N application was compared with variable rate and variable rate minus 15% N. In the long-term experiment, soybean yields under organic (manure application), fertilizer, and fertilizer plus herbicide systems were studied from 1975 to 1991. Using geostatistics, two parameters of fractal dimension, which is an indication of variability pattern and log k, which indicates extent of variability were determined. There was no significant effect of the N treatments on the fractal dimension values in the variable rate study. The extent of spatial variability for residual soil nitrate became significantly less after imposing N application regimes. The variable rate N application had lower log k values than uniform application indicating reduced soil variability with variable rate N application. In the long-term study, all three management systems had similar fractal dimension and log k values for soybean yield indicating similar temporal yield variability for the three systems. The three management systems used did not change temporal effects on soybean yield. Average temperature in August significantly influenced soybean grain yield in the 15 years of the study. Fractal and covariance analyses can be effectively used to compare treatments or management systems for temporal or spatial variability.

Technical Abstract: This study was conducted to compare spatial variability of soil nitrate in a VRAT nitrogen (N) application study and temporal variability of soybean (Glycine max L.) yield in a long-term organic vs. inorganic study. In the VRAT study, conventional uniform N application was compared with variable rate and variable rate minus 15% N. In the long-term experiment, soybean yields under organic (manure application), fertilizer, and fertilizer plus herbicide systems were studied from 1975 to 1991. Semivariograms were estimated for soil parameters in the VRAT and soybean yield in the long-term study. The slope of the regression line of log semivariogram vs. log lag (h, distance or year) was used to estimate the fractal dimension (D), which is an indication of variability pattern. The intercepts (log k) of the log-log lines, which indicate extent of variability, were also compared between treatments. There was no significant effect of the N treatments on the D values in the VRAT study. The extent of spatial variability for residual soil nitrate became significantly less after imposing N application regimes. The variable rate N application had lower log k values than uniform application indicating reduced soil variability with VRAT N application. In the long-term study, all three management systems had similar D and log k values for soybean yield indicating similar temporal yield variability for the three systems. Average temperature in August significantly influenced soybean grain yield in the 15 years of the study. Fractal and covariance analyses can be effectively used to compare treatments or management systems for temporal or spatial variability.

Last Modified: 11/25/2014
Footer Content Back to Top of Page