How many sampling points are needed to estimate the mean nitrate-N content of agricultural fields? A geostatistical simulation approach with uncertain variograms

Knowledge of how many sampling points are needed to estimate the mean content of soil nutrients in agricultural fields, given a precision requirement on the estimated mean, is limited. This paper describes a versatile geostatistical simulation approach for predicting the variance of the mean nitrate-N (NO3-N) content within an agricultural field estimated by random sampling. In fall of 2016 sixteen agricultural fields were sampled on a square grid to model the spatial variation of NO3-N. On twelve out of sixteen fields NO3-N showed a lognormal distribution rather than a normal distribution. Variograms for (log-transformed) NO3-N are estimated using a Bayesian approach, resulting in 100 vectors with possible variogram parameters per field, obtained by MCMC sampling from the posterior distribution. Each of these variograms is used to simulate 100 maps of NO3-N, resulting in 100 × 100 maps of NO3-N per field. Each map is used to compute the variance of the estimated mean with stratified simple random sampling of 5,10,…,50 points, with one point per compact geographical stratum. For each sample size (number of sampling points) the mean, median and P90 of the uncertainty distribution are computed. Based on the medians, the sample size required for a maximum expanded measurement uncertainty of 50% varies from <5 to >50. This large variation in required sample size shows the large variation among the sixteen fields in variance of NO3-N within a field.