Correlação espacial bivariada para o redimensionamento do tamanho amostral efetivo

Abstract

Determining the spatial variability of soil and plant attributes is critical for farmland management. This practice requires that an appropriate sample planning be carried out in order to collect as few georeferenced samples as possible, with a view to maintaining sampling quality and saving financial and operational resources. Furthermore, geostatistical studies involving the spatial distribution of stochastic processes, in which observations are georeferenced, may show spatial structures that are not totally independent between the attributes. In these cases, it is recommended to calculate the association between the variables by resorting to a bivariate spatial correlation metric, in addition to utilizing a bivariate geostatistical model. Therefore, in the first scientific paper of this research, the bivariate spatial correlation was analyzed considering variables with different structures of spatial dependence and, for this, the bivariate Lee index was calculated. The results showed that the radius of spatial dependence common to both variables was the parameter that most influenced the Lee index value, whereas the higher the value of this parameter, the greater the bivariate spatial correlation. Subsequently, in the second paper, based on the assumption of the existence of spatial correlation between pairs of variables, the study aimed to redimension the sample size by calculating the bivariate effective sample size (ESSbi), utilizing the bivariate Gaussian common component model (BGCCM). This is because most of the proposals in the literature for the ESSbi adopt alternatives in their methodologies that aim to avoid the usage of a spatial correlation structure between the variables or consider the bivariate coregionalization model (BCRM). The difference is that in the BGCCM structure, in addition to having a common Gaussian random field shared by the pair of variables, there is also a Gaussian random field associated with each variable individually. Whilst in BCRM, the individual spatial correlation structure of one of the variables is necessarily disregarded from the model. In order to verify the theoretical feasibility of the ESSbi proposal, all properties that affect the univariate methodology were verified for the bivariate one, performing simulation studies or algebraically. The ESSbi was also applied to a real data set of organic matter (OM) and sum of bases (SB), collected in an agricultural area with soybean plantation, in which it was found that 60% of the sample observations of the OM-SB pair contained spatially duplicated information. Moreover, the sample redimensioning obtained for the real data set proved to be feasible in terms of the quality obtained in the spatial prediction.