Submitted to: Vadose Zone Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/14/2007
Publication Date: 8/6/2008
Citation: Tarquis, A., Bird, N.R., Whitmore, A.P., Cartagena, M.C., Pachepsky, Y.A. 2008. Multiscale analysis of soil transect data. Vadose Zone Journal. 7:563-569. Interpretive Summary: Spatial variability is an intrinsic property of soils and sediments. The significance of this variability has led scientists and practitioners to the realization of the need to quantify it. Statistics of soil or sediment properties have become essential components of data collection in vadose zone research. The accumulation of such statistics has eventually led to understanding that they change with scale of sampling or description. Recently fractal geometry has become an important source of scaling laws in soil hydrology. Fractal geometry became very popular during last twenty years because of its promise to relate features of natural objects observed at different scales. As fractal geometry was applied to understand changes in soil and sediment properties with scale, it became clear that true fractals do not exist in soils and sediments to the same extent as regular geometrical shapes. The most substantial deviation from the fractal model was that the frequencies of rare phenomena were predicted incorrectly. A compact representation of the information about changes in variability with scale is needed no matter whether particular scale-dependence models are or are not applicable. The objective of this work has been to develop new model-free parameters to document scale dependent changes in spatial variability and to test methods to find these parameters with data on soil properties along a transect. We present two such parameters - the relative entropy and the intra-scale correlation coefficient - and compare their behaviour in cases when soil properties follow and do not follow fractal scaling. The new parameters track the scale dependence as it unfolds and thus provide more insight into the effect of scale on the variability of soil properties.
Technical Abstract: A deeper understanding of spatial variability of soil properties and the relationship between them is needed to scale up measured soil properties and to model soil processes. The object of this study was to characterize the spatial scaling properties of a set of soil physical properties measured on a common 1024-m transect across arable fields at Silsoe in Bedfordshire, east-central England. Properties studied were volumetric water content, porosity, pH and N2O flux. The multifractal analysis (MFA) was applied to each data set showing that only N2O flux had a self-affine structure. In order to describe the scaling behaviour in the other cases we defined and applied the relative entropy (E). Finally, a new intra-scale correlation function (R) was derived and applied to study the spatial intra-scaling behaviour of the correlations between two measures. The results are discussed in the context of multiscaling modelling.