Nitrous oxide (N2O) is a potent greenhouse gas and a precursor to compounds which deplete stratospheric ozone. Agricultural soils are the principal anthropogenic N2O source, which includes urine patches of cattle fed by grazing pasture. While such N2O emissions can be measured, involved time and space scales are usually only minutes and metres, respectively. Nevertheless, climate change stakeholders need large-scale national emissions over time to construct annual N2O emissions inventories for international treaty compliance requirements. We have developed a mathematical model to bridge the gap between measurement and stakeholder requirements for N2O emissions from grazing cattle urine patches.

Our methodology begins with the emissions from a patch. Convolution integrals are then used to spatially and temporally scale the emissions from discrete grazing events to paddock, farm and region levels across the year. The model developed shows how the emissions are smoothed out with scaling and the implications from the scaling.