Wavelet analysis of soil variation at nanometre- to micrometre-scales: an example of organic carbon content in a micro-aggregate

This paper demonstrates the potential of wavelet analysis to investigate fine-scale spatial variation in soil without statistical assumptions that are generally implausible. We analysed the optical densities of different forms of carbon which were measured at intervals of 50 nm along a 16-mu m transect on a soil micro-aggregate using near-edge X-ray fine-structure spectroscopy (NEXAFS). We found different patterns of scale-dependent variation between the carbon forms, which could be represented by pair-wise wavelet correlations at the different scales, and by principal components analysis of all the correlations at each scale. These results represent only one small soil micro-aggregate and are not presented as general findings about soil carbon, but they do indicate that fine-scale variation of soil carbon can be complex in ways that the wavelet analysis can accommodate but alternative spatial statistics such as variograms cannot. Among the patterns of variation that the analysis could identify were scale-dependent correlations of the different forms of carbon. In some cases, positive correlations were found at coarser scales and negative at the finest scales, suggesting a multi-scale pattern in which contrasting forms of carbon are deposited in common clumps but at finer scales either one or the other form dominates. Aromatic and carboxylic carbon varied jointly in this way. Other forms of carbon, such as carboxylic and aliphatic carbon, were strongly correlated at the finest scales but not the coarser scales. We found evidence for changes in the variance and correlation of forms of carbon along the transect, indicating that the spatial distribution of carbon at these fine scales may be very complex in ways that are inconsistent with the assumptions of geostatistics. This quantitative analysis of the spatial patterns of different soil components at micro-scales offers a basis for formulating and testing specific hypotheses on replicated samples.