Fractal analysis of spatial and temporal variability

Bahman Eghball, Gary W. Hergert, Gary W. Lesoing, Richard B. Ferguson

Research output: Contribution to journalArticlepeer-review


Characterizing spatial and temporal variability is important in variable rate (VRAT) or long-term studies. 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 nitrate in the VRAT and for 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 nitrate 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. The three management systems used did not change temporal effects on soybean yield. Rainfall during July and August accounted for 65% of variability in soybean grain yield. Fractal and covariance analyses can be effectively used to compare treatments or management systems for spatial or temporal variability.

Original languageEnglish (US)
Pages (from-to)349-362
Number of pages14
Issue number3-4
StatePublished - Mar 1999
Externally publishedYes


  • Covariance analysis
  • Fractal dimension
  • Grid sampling
  • Long-term study
  • Manure application
  • Precision agriculture
  • Semivariogram
  • Site-specific management
  • Variable rate N application

ASJC Scopus subject areas

  • Soil Science


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