Field-scale N fertilizer recommendations: The spatial covariance problem

Abstract

Theory is needed to estimate field-scale crop response and calibration relationships (soil test versus recommended fertilizer rate) from local scale measurements, in fields with spatially variable soil properties. The objective of this study is to present a theoretical stochastic framework for examining the influence of the spatial variability of soil properties, and covariance between soil properties, on field-scale crop response to fertilizer. An analytical solution of the general stochastic scaling equation is given for the specific case of wheat grain yield response to applied N fertilizer with variable soil-N test and available water in Saskatchewan, Canada. The analytical solution indicates spatial variance of soil properties within fields influences field average yield response to applied fertilizer. The field-scale maximum economic rate of fertilizer N (MERN), depends not only on the average soil properties, but also on (1) the amount of variability of soil properties in the field, and (2) the correlation between the spatial patterns of soil properties (e.g., soil test and available water). For the specific soil examined, positive spatial correlation between soil-N test and available water significantly increases MERN, for the same average soil test and available water. Negative correlation decreases MERN.