Fractal and the statistical analysis of spatial distributions of Fe–Mn concretions in soddy-podsolic soils

Abstract

Fe–Mn concretions are stable indicators of water regimes in loamy and clay podsolic and soddy-podsolic soils. Their spatial distribution is, in a large part, an inheritance of several processes in a heterogeneous soil medium. The objective of this study was to examine whether fractal models are appropriate to describe the spatial distributions of concretions. Data were collected at three locations in the Moscow region. At the first location, there were eight plots at depths from 13 to 34 cm and the distributions of concretions larger that 0.5 mm were mapped by staining the individual concretions. At the remaining two locations, soil cores of different sizes were taken from two depths. Concretions were extracted from these cores and sieved to separate them by size. A method of thorough sampling of the area was employed that used estimates of fractal dimension for the every possible position a fixed geometrical form by using the box counting technique. These estimates were studied statistically and by comparison with simulated data. We found concretion distribution on the fixed depth to have at least three components. The first of them represents the background, i.e., it corresponds to the random and independent distributions of concretions. The second component has fractal nature. The third component represents dense nests and it is probably connected with favorable conditions for microorganisms forming concretions. Estimated dimensions greater than 2.5 belong to the nest component and less than 1.6—to the fractal one. The interval (1.6; 2.5) of them can be accounted for only by the random distribution.