A new criterion based on estimator variance for model sampling in precision agriculture

International audienceModel sampling has proven to be an interesting approach to optimize the sampling of an agronomic variable of interest at the field level. The use of a model improves the quality of the estimates by making it possible to integrate the information provided by one or more auxiliary data. It has been shown that such an approach gives better estimations compared to more traditional approaches. Through a statistical work describing the properties of model sampling variance, this paper details how the different factors either related to sample characteristics or to the correlation between the auxiliary data and the variable of interest, affect estimation error. The resulting equations show that the use of samples with a mean close to the field mean and with a substantial dispersion reduces the estimation variance. On the basis of these statistical considerations, a variance criterion is defined to compare sample properties. The lower the value of the criterion of a sample, the lower the variance of the estimate and the expected errors. These theoretical insights were applied to real commercial vine fields in order to validate the demonstration. Nine vine fields were considered with the objective to provide the best yield estimation. High resolution vegetative index derived from airborne multispectral image was used to drive the sampling and the estimation. The theoretical considerations were verified on the nine fields; as the observed estimation errors correspond quite well to the values predicted by the equations. The selection of a large number of random samples from these fields confirms that samples associated with higher values of the chosen criterion result, on average, in larger yield estimation errors. Samples with the highest criterion values are associated with mean estimation errors up to two times larger than those of average samples. Random sampling is also compared to two target sampling approaches (Clustering based on quantiles or on k-means algorithm) commonly considered in the literature, whose characteristics improve the value of the proposed criterion. It is shown that these sampling strategies produce samples associated with criterion values up to 100 times smaller than random sampling. The use of these easy-to-implement methods thus guarantees to reduce the variance of the estimation and the estimation errors