Assessing ranked set sampling and ancillary data to improve fruit load estimates in peach orchards

Abstract

Fruit load estimation at plot level before harvest is a key issue in fruit growing. To face this challenge, two sampling methods to estimate fruit load in a peach tree orchard were compared: simple random sampling (SRS) and ranked set sampling (RSS). The study was carried out in a peach orchard (Prunus persica cv. ‘Platycarpa’) covering a total area of 2.24 ha. Having previously sampled the plot systematically to cover the entire area (104 individual trees or sampling points), both sampling methods (SRS and RSS) were tested by taking samples from this population with varying sample sizes from N = 4 to N = 12. Since RSS requires ancillary information to obtain the samples (ranking mechanism), several proximal and remote sensors already used or recently introduced in agriculture were assessed as data sources. A total of 14 variables provided by 5 different sensors and platforms were considered as potential ancillary variables. Among them, RGB images captured by an unmanned aerial vehicle (UAV), and used to estimate the canopy projected area of individual trees, proved to be the best of the options. This was shown by the high correlation (R = 0.85) between this area and the fruit load, providing RSS with the UAV-based canopy projected area the lowest Coefficient of Error (CE) for a given tree sample size. Then, comparing relative efficiency between random sampling (SRS) and RSS, the latter enables more precise fruit load estimates for any of the considered sample sizes. Interest and opportunity of RSS can be raised from two points of view. In terms of confidence, RSS managed to reduce the variance of fruit load estimates by about half compared to SRS. Sampling errors above the 10% threshold were always produced significantly fewer times using RSS, regardless of the sample size. In terms of operation within the plot, sample size could be reduced by 50%, from N = 10 for SRS to N = 5 for RSS, and this being expected sampling errors less than 10% in practically 70% of the samplings performed in both cases. In summary, fruit growers can take advantage of the combined use of appropriate data (RGB images from UAV) and RSS to optimize sample sizes and operational sampling costs in fruit growing.