Quantifying spatial variability of selected soil trace elements and their scaling relationships using multifractal techniques.

Multifractal techniques were utilized to quantify the spatial variability of selected soil trace elements and their scaling relationships in a 10.24-ha agricultural field in northeast China. 1024 soil samples were collected from the field and available Fe, Mn, Cu and Zn were measured in each sample. Descriptive results showed that Mn deficiencies were widespread throughout the field while Fe and Zn deficiencies tended to occur in patches. By estimating single multifractal spectra, we found that available Fe, Cu and Zn in the study soils exhibited high spatial variability and the existence of anomalies ([α(q)max-α(q)min]≥0.54), whereas available Mn had a relatively uniform distribution ([α(q)max-α(q)min]≈0.10). The joint multifractal spectra revealed that the strong positive relationships (r≥0.86, P<0.001) among available Fe, Cu and Zn were all valid across a wider range of scales and over the full range of data values, whereas available Mn was weakly related to available Fe and Zn (r≥0.18, P