Optimizing organic fertilizer applications under steady-state conditions

Because organic N fertilizers must be mineralized before they become plant-available, application designs should consider time and temperature effects on N release as well as crop N requirements. This study presents deterministic (DOpt) and stochastic (SOpt) linear optimization models to determine sustainable land application schedules. The easily solved models minimize the amount of N that is applied while assuring than crop N demands are met as they develop. Temperature effects on N mineralization were included by using the Arrhenius equation to create a temperature-adjusted time series. Uncertainties associated with mineralization rates and the temperature-adjustment (Q10) factor are considered by SOpt. Examples are presented for a summer maize (Zea mays L.) and winter triticale (Triticum aestivum L. x Secale cereale L.) rotation operated by a hypothetical dairy operation in Stanislaus County, California. Monte Carlo simulations were used to test the models. A closed-form solution for estimating the time until steady state is presented and steady-state conditions were reached within 7 yr after applications were initiated. Because of temperature effects, DOpt solutions were 12% greater during the winter and 29% lower during the summer than a reference approach that applied liquid manure at 130% of the crop N demand. Stochastic linear optimization values were 1.7% greater than DOpt values in the summer and 6.2% greater in the winter. Surplus N estimates from Monte Carlo simulations averaged 104 kg ha(-1) for DOpt and 126 ka ha(-1) for SOpt, but SOpt was much less likely to result in crop N deficits. Linear optimization is a viable tool for scheduling organic N applications.