Wavelet Transforms Applied to Irregularly Sampled Soil Data

Wavelet transforms have been used widely to analyse environmental data. These data typically comprise a series of measurements taken at regular intervals in time or space. The analysis offers a decomposition of the data that distinguishes components at different spatial scales but also, unlike Fourier analysis, can resolve local intermittent features. Most wavelet methods require the data to be sampled at regular intervals and little attention has been paid to developing methods for data that are not. In this paper, we derive a discrete Haar wavelet transform for irregularly sampled data and show how the resulting wavelet coefficients can be used to estimate contributions of variance. We discuss the interpretation of these statistics using data on apparent soil electrical conductivity of soil measured across a landscape as an example.