Wavelet analysis of the variability of nitrous oxide emissions from soil at decameter to kilometer scales

We analyzed data on nitrous oxide emissions and on soil properties that were collected on a 7.5-km transect across an agricultural landscape in eastern England using the discrete wavelet packet transform. We identified a wavelet packet "best basis" for the emission data. Wavelet packet basis functions are used to decompose the data into a set of coefficients that represent the variation in the data at different spatial frequencies and locations. The "best basis" for a set of data is adapted to the variability in the data by ensuring that the spatial resolution of local features is good at those spatial frequencies where variation is particularly intermittent. The best basis was shown to be adapted to represent such intermittent variation, most markedly at wavelengths of 100 m or less. Variation at these wavelengths was shown to be correlated particularly with chemical properties of the soil, such as nitrate content. Variation at larger wavelengths showed less evidence of intermittency and was found to be correlated with soil chemical and physical constraints on emission rates. In addition to frequency-dependent intermittent variation, it was found that the variance of emission rates at some wavelengths changed at particular locations along the transect. One factor causing this appeared to be contrasts in parent material. The complex variation in emission rates identified by these analyses has implications for how emission rates are estimated.