A stochastic model of urinary nitrogen and water flow in grassland soil in New Zealand

A mathematical model of urinary nitrogen and water flow in soil has been developed that incorporated stochastic rainfall and stochastic temperature events. This model was used to characterise the variability in urine patch nitrogen leaching at Taupo, New Zealand. This stochastic model was also used to more accurately determine the effect of urinary patch overlap on cow urinary nitrogen flow and leaching in soil. Nitrogen leaching from single urine deposits on pasture in the winter ranged from 0 to 75% of applied nitrogen as a result of stochastic rainfall events. Rainfall effects explained 98% of the variance in nitrogen leaching due to stochastic rainfall and temperature effects combined. The model predicted that on average 38, 61, and 71% of the nitrogen in single, double and triple urine patches is leached in the winter. Nitrogen leaching rates were significantly greater in the winter than the summer months. The distribution in the amount of nitrogen leached from single urine patches was close to normal in the winter but approximately exponentially distributed in the summer. The variability in total nitrogen leached from a field also decreased as the stocking rate increased. A quantitative modelling framework is crucial for understanding nitrogen transport in pastoral systems and for effectively setting and enforcing restrictions imposed by regulatory bodies on nitrogen losses from pastoral farming and this study represents a component of this framework.