Detecting nonlinearity in the spatial series of nitrous oxide emission by delay vector variance

Soil spatial variability may exhibit nonlinearity and this has been assumed in studies without proper quantification. Owing to the complexity of underlying biogeochemical processes, greenhouse gas emission, in particular, nitrous oxide (N2O) flux from soil, is highly variable over space and time. The goal of this work was to examine the nonlinearity associated with the spatial series of N2O flux from soil using the delay vector variance (DVV) method. DVV uses the predictability of a spatial series in a phase-space to identify linearity/nonlinearity within a data series using a surrogate data methodology to derive a test statistic. A two-piece closed vented chamber was used to measure N2O fluxes along a transect of 128 points located within the hummocky landscape of central Saskatchewan, Canada. There was nonlinearity associated with the spatial series of early spring and spring measurements. The uneven distribution of snowmelt water facilitated the favourable situations for denitrifying bacterial activity creating hotspots for denitrification processes. The flux measured during the fall season exhibited a nonlinear pattern, whereas the flux measured during the time of plant growth exhibited a linear pattern over space. Strong evapotranspiration demand during the growing season in the semi-arid climate of the study area controlled the hydrological processes and thus, the spatial N2O flux measurements giving rise to a linear spatial pattern. The DVV detected nonlinearity in a spatial series will improve the understanding of the complexity of underlying soil processes.