Boundary line analysis of the effect of water-filled pore space on nitrous oxide emission from cores of arable soil

The boundary line has been proposed as a model of the effects of a variable on a biological response, when this variable might limit the response in only some of a set of observations. It is proposed that the upper boundary (in some circumstances the lower boundary) represents the response function of interest. Boundary-line analysis is a method for estimating this response function from data. The approach has been used to model the emission of N2O from soil in response to various soil properties. However, the methods that have been used to identify the boundary are based on somewhat ad hoc partitions of the data. A statistical model that we have presented previously has not been applied to this problem in soil science, and we do so here to represent how the water-filled pore space (WFPS) of the soil affects the rate of N2O emission. We derive a boundary-line response that can be shown to be a better model for the data than an unbounded alternative by statistical criteria. Furthermore, the fitted boundary-response model is consistent with past empirical observations and modelling studies with respect to both the WFPS at which the potential emission rate is largest and the measurement error for the emission rates themselves. We show how the fitted model might be used to interpret data on soil volumetric water content with respect to seasonal changes in potential emissions, and to compare potential emissions between soil series that have contrasting physical properties.