Characterizing scale- and location-specific variation in non-linear soil systems using the wavelet transform


Correspondence: A. Biswas. E-mail:


The combined action of physical, chemical and biological soil processes, which occur at different intensities and scales, causes complex spatial variation in soil that is difficult to characterize. The presence of non-stationarity and non-linearity increases this complexity. Wavelet transforms have been used to analyse non-stationary soil spatial variation. In this study we used the wavelet transform to characterize the spatial variation of non-linear soil systems. In the wavelet transform, a mathematical function (mother wavelet) is used to examine the frequency behaviour of a spatial series by translating or dilating the function. The effective resolution in identifying the frequency is dependent on the translation-dilation parameter, which is further dependent on the central frequency of the mother wavelet. The central frequency of the commonly used mother wavelet (Morlet) has been modified in this study to capture up to 95% of the uncertainty in identifying frequency components present in spatial series. Increased central frequency resulted in more oscillations within a localized window and thus provided enhanced frequency resolution, which helped to identify the instantaneous (≡ localized) frequency (IF). Identification of the IF can reduce the local unpredictability and enable characterization of non-linear systems. We have demonstrated the method with a case study using soil water storage and clay content data. The wavelet spectra and the wavelet IF spectra provided improved spatial resolution in identifying the dominant frequency (scale) of variation in the spatial series. Information on dominant scales can be used for scale-specific prediction of soil properties and multiscale soil mapping and modelling.