Scale- and location-dependent correlation of nitrous oxide emissions with soil properties: an analysis using wavelets

This paper shows how the wavelet transform can be used to analyse the complex spatial covariation of the rate of nitrous oxide (N2O) emissions from the soil with soil properties that are expected to control the evolution of N2O. We use data on N2O emission rates from soil cores collected at 4-m intervals on a 1024-m transect across arable land at Silsoe in England. Various soil properties, particularly those expected to influence N2O production in the soil, were also determined on these cores. We used the adapted maximal overlap discrete wavelet transform (AMODWT) coefficients for the N2O emissions and soil variables to compute their wavelet covariances and correlations. These showed that, over the transect as a whole, some soil properties were significantly correlated with N2O emissions at fine spatial scales (soil carbon content), others at intermediate scales (soil water content) and others at coarse spatial scales (soil pH). Ammonium did not appear to be correlated with N2O emissions at any scale, suggesting that nitrification was not a significant source of N2O from these soils in the conditions that pertained at sampling. We used a procedure to detect changes in the wavelet correlations at several spatial scales. This showed that certain soil properties were correlated with N2O emissions only under certain conditions of topography or parent material. This is not unexpected given that N2O is generated by biological processes in the soil, so the rate of emission may be subject to one limiting factor in one environment and a different factor elsewhere. Such changes in the relationship between variables from one part of the landscape to another is not consistent with the geostatistical assumption that our data are realizations of coregionalized random variables.