Multiscale sources of spatial variation in soil. II. A non‐Brownian fractal model and its application in soil survey

Abstract

SummaryStochastic fractals (for example, the fractional Brownian noises) model the often observed power law relation between the variance of a soil property and the length of transect sampled, but fail to account for abrupt changes of the mean (i.e. soil boundaries), for second‐order stationarity and for the non self‐similarity of variations at different scales that are observed in real data. This paper proposes a non‐Brownian, nested model to account for situations where differences of soil have been caused by superimposed, independently acting soil‐forming processes having different weights and acting at separate, discrete scales. The model is explained and theoretical examples of the semivariograms and confidence limits that arise from it are given. The model is applied to three sets of experimental data and is found to give a remarkably good fit where lateral mixing of soil has been negligible and soil boundaries are sharp. The implications for efficient mapping in situations where the soil results from a number of superimposed, independent causes are discussed.