Spatial–Temporal Variability of Soybean Yield Using Separable Covariance Structure

(1) Understanding and characterizing the spatial and temporal variability of agricultural data is a key aspect of precision agriculture, particularly in soil management.
Modeling the spatiotemporal dependency structure through geostatistical methods is essen tial for accurately estimating the parameters that define this structure and for performing Kriging-based interpolation. This study aimed to analyze the spatiotemporal variability of the soybean yield over ten crop years (2012–2013 to 2021–2022) in an agricultural area located in Cascavel, Paraná, Brazil. (2) Spatial analyses were conducted using two ap proaches: the Gaussian linear spatial model with independent multiple repetitions and the spatiotemporal model with a separable covariance structure. (3) The results showed that the maps generated using the Gaussian linear spatial model with multiple independent repetitions exhibited similar patterns to the individual soybean yield maps for each crop year. However, when comparing the kriged soybean yield maps based on independent multiple repetitions with those derived from the spatiotemporal model with a separable covariance structure, the accuracy indices indicated that the maps were dissimilar. (4) This suggests that incorporating the spatiotemporal structure provides additional informa tion, making it a more comprehensive approach for analyzing soybean yield variability.
The best model was chosen through cross-validation and a trace. Thus, incorporating a spatiotemporal model with a separable covariance structure increases the accuracy and in terpretability of soybean yield analyses, making it a more effective tool for decision-making in precision agriculture.