Multiresolution analysis of data on electrical conductivity of soil using wavelets

The variation of soil properties at the field scale can be complex. Particular challenges for the analysis of data on soil variables arise when components of variation operate at a range of scales, show intermittent effects, and are not spatially stationary in the variance, fluctuating more in some regions than in others. Wavelet analysis addresses these problems. Any data set of finite variance (appropriately sampled) may be analysed with the dilations and translations of a basic wavelet function. Wavelet functions oscillate locally and damp rapidly to zero either side of their centre, so that they only respond to variation within a local neighbourhood. To provide a complete analysis of a data set the wavelet must be translated across the data, generating a set of local coefficients. The basic wavelet can also be dilated to analyse the data at a specified spatial scale. A single wavelet coefficient therefore describes the variation of a variable in some locality at a particular spatial scale. Data were collected at a variable, 32.4 ha salt affected site in the Tulare Lake Bed region of California using electrical conductivity sensors (mobile fixed-array, electrical resistivity equipment). We show how wavelets can be used to analyse the variation within these data, how the analysis partitions the variance of the data by scale and location, and how it can be used to extract components from the data which appear to be more useful for predicting soil properties than are the raw data.