Field scale fertilizer recommendations: The spatial scaling problem

Soil fertility may vary considerably within a field. The effects of variable soil fertility on the relationships among average crop yield response, average soil test, and fertilizer applied evenly to a field have not been examined. This paper develops stochastic equations to describe the average yield gain on a field basis from the application of a single constant rate of fertilizer, in fields with variable soil fertility. The equations are solved numerically for the specific case of nitrogen fertilizer on corn (Zea mays L.) in Ontario, Canada. The results suggest that since the relationships among yield response, soil test, and applied fertilizer are non-linear, a single soil test calibration cannot exist for fields with different spatial variability. Soil test calibrations obtained from sites with low variability (for example small plots) will not hold for sites with higher variability (for example farm fields). Calibrations obtained from sites with low variability will under-predict the optimum economic fertilizer rate for sites with low variability will under-predict the optimum economic fertilizer rate for sites with high variability. The results do not invalidate soil test calibration relationships per se. The challenge is to combine these calibrations with additional knowledge about the spatial distribution and field-scale variability of soil test values in order to maximize economic benefit. Key words: Spatial variability, soil test, fertilizer recommendation, yield, corn, field scale