Spatial–Temporal Variability of Soybean Yield Using Separable Covariance Structure

Tamara Cantú Maltauro (), Miguel Angel Uribe-Opazo, Luciana Pagliosa Carvalho Guedes, Manuel Galea and Orietta Nicolis
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Tamara Cantú Maltauro: Postgraduate Program in Agricultural Engineering (PGEAGRI), Technological and Exact Sciences Center, Western Paraná State University (UNIOESTE), Cascavel 85819-110, Brazil
Miguel Angel Uribe-Opazo: Postgraduate Program in Agricultural Engineering (PGEAGRI), Technological and Exact Sciences Center, Western Paraná State University (UNIOESTE), Cascavel 85819-110, Brazil
Luciana Pagliosa Carvalho Guedes: Postgraduate Program in Agricultural Engineering (PGEAGRI), Technological and Exact Sciences Center, Western Paraná State University (UNIOESTE), Cascavel 85819-110, Brazil
Manuel Galea: Department of Statistics, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile
Orietta Nicolis: Engineering Faculty, Andres Bello University, Valparaíso 2520000, Chile

Agriculture, 2025, vol. 15, issue 11, 1-21

Abstract: (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 essential 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 approaches: 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 information, 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 interpretability of soybean yield analyses, making it a more effective tool for decision-making in precision agriculture.

Keywords: accuracy indexes; precision agriculture; spatiotemporal geostatistics; thematic maps (search for similar items in EconPapers)
JEL-codes: Q1 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 (search for similar items in EconPapers)
Date: 2025
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