Analysis of Spatial Dependence Using the Wave Covariance Structure in Soybean Productivity Associated With Soil Attributes

Objective: The aim of this study is to investigate the interaction between soybean yield and the physical and chemical attributes of the soil, with the goal of developing techniques used in precision agriculture to increase productivity, reduce costs, and minimize environmental impacts. Theoretical Framework: This work is based on the principles of geostatistics, particularly the Wave spatial dependence structure, which is used to model the semivariance function when it exhibits the "hole effect." Method: The research involves a study of soybean yield conducted in a commercial area of 172.04 hectares during the 2022/2023 growing season. Calcium (Ca), copper (Cu), acidity (pH), potassium (K), phosphorus (P), and soil penetration resistance (SPR) levels were used as covariates to explain soybean yield (Prod) through a Gaussian linear spatial model (GLSM). The Thin Plate Spline (TPS) interpolation method was applied to interpolate the physical and chemical soil attributes, considered as fixed covariates, while soybean yield was interpolated using External Drift Kriging (EDK) based on the GLSM. Additionally, techniques for local influence diagnostics were developed and applied to identify observations impacting the results, utilizing the Wave geostatistical model. Results and Discussion: The results revealed that the generated soybean yield map provides important information for defining management zones, optimizing input use, and promoting greater profitability. Furthermore, the removal of locally influential observations alters parameter estimation, the significance of parameters associated with the covariates in the GLSM, and the construction of the interpolated soybean yield map. In the discussion, the results were contextualized in light of the theoretical framework, emphasizing the relevance of the Wave structure and the integration of interpolation techniques in the study of spatial variability. Research Implications: The practical and theoretical implications of this research include improvements in agricultural management by providing support for the delineation of management zones that balance productivity and sustainability. Theoretically, the study contributes to advancing the use of geostatistical models, such as the Wave model, in the analysis of spatial data in precision agriculture. Originality/Value: This study contributes to the literature by exploring the application of the Wave model in an agricultural context, combined with the use of interpolation techniques and local influence diagnostics. Its originality lies in the methodological combination of spatial interpolators and the development of local influence techniques.