Spatial analysis of categorical soil variables with the wavelet transform

This paper describes a wavelet transform for the analysis of categorical (multistate) soil variables, i.e. ones (such as profile classes) that have two or more discrete states. The states are transformed to a continuous variable by a mapping which is optimized by scale and location to highlight local variation. The method is illustrated with data from a transect across a gilgai landscape in Australia. A categorical variable on relief, with three states, was recorded from the sample sites, from which soil cores had also been collected and analysed. The wavelet analysis showed a transient feature of the variation at scales up to 32 m. There was an interval where the characteristic alternation of depressions with the level plain was interrupted. The variation at scale 64 m appeared to be non-stationary. The relief was more variable on one side of a change point than it was on the other. This complex variation of relief was matched by that of the electrical conductivity of the soil, most strongly at the 64-m scale. The periodicity of conductivity, and the strength of its correlation with relief, were also different either side of the change point identified in the analysis of relief alone. Conductivity also showed similar transient features to relief. Evidently the wavelet transform can be used to elucidate the variation of categorical soil variables. The information from such an analysis is likely to be useful for planning surveys of the soil to measure continuous variables by sampling and laboratory analysis.