Assessing sampling designs for determining fertilizer practice from yield data

Many farmers sample their soil to measure the concentrations of plant nutrients, so as to decide how much fertilizer to apply. Now that fertilizer can be applied at variable rates farmers want to know whether maps of nutrient concentration made from grid samples or of field subdivisions (zones within their fields) are merited: do such maps lead to greater profit than would a single measurement on a bulked sample for each field when all costs are taken into account? We have examined the merits of grid-based and zone-based sampling strategies over single field-based averages using continuous spatial data on wheat yields at harvest in six fields in southern England and simulated concentrations of phosphorus (P) in the soil. We have taken into account current prices of wheat, P fertilizer and sampling and laboratory analysis. Variograms of yield provide guides for sampling. We show that where variograms have large variances and long effective ranges grid-sampling and mapping are feasible and have large probabilities of being cost-effective. Where effective ranges are short, sampling must be dense to reveal the spatial variation and be expensive, and variable-rate application of fertilizer is likely to be impracticable and almost certainly not cost-effective. We found zone-based sampling was less likely to be cost effective in a similar situation when the management zones were poorly correlated to P concentrations.