Optimal grid size for site‐specific nutrient application

Abstract

This article develops a theoretical framework to determine the economically optimal grid size when sampling to guide precision application of inputs. Our theoretical model shows that a finer grid is optimal with increases in output price. A coarser grid is optimal with increased sampling costs and increased spatial correlation. With an exponential variogram, for example, the optimal grid size increases as the range increases. An applied example of lime application for winter wheat is used to demonstrate the framework. Spatial variograms for pH and Buffer pH were estimated using data from nine farmer fields. At the average spatial variability from these fields and using typical Oklahoma wheat yields of 40 bu/ac, grid sampling was economical when prices were above $5.43/bu. The optimal grid sizes were slightly larger than the 2.5‐acre sizes that are typically used by producers. The empirical example verified the theory in that it found that optimal grid size decreased with higher output prices and crop yields and increased with greater spatial correlation. For example, optimal grid size approximately doubled as the range of the exponential correlation function doubled.