Reduction of Sample Size in the Soil Physical-Chemical Attributes Using the Multivariate Effective Sample Size

Abstract

Financial investment with collection and laboratory analysis of soil samples is an important factor to be considered when mapping agricultural areas with soybean planting. One of the alternatives is to use the spatial autocorrelation between the sample points to reduce the number of elements sampled, thus restricting the collection of redundant information. This work aimed to reduce the sample size of this agricultural area, composed of 102 sample points, and use it to analyze the spatial dependence of soil macro- and micro- nutrients, as well as the soil penetration resistance. The agricultural area used in this study has 167.35 ha, cultivated with soybean, which the soil is Red Dystroferric Latosol, and the sampling design has used in this agricultural area is the lattice plus close pairs. The reduction of the sample size was made by the multivariate effective sample size (ESSmulti) methodology. The studies with the simulation data and the soil attributes showed an inverse relationship between the practical range and the estimated value of the univariate effective sample size. With the calculation of ESSmulti, the sample configuration was reduced to 53 points. The Overall Accuracy and Tau concordance index showed differences between the thematic maps elaborated with the original and reduced sampling designs. However, the analysis of the variance inflation factor and the standard error of the spatial dependence parameters showed efficient results with the resized sample size.

Effective Sample Size with the Bivariate Gaussian Common Component Model

“…The studies using real soil chemical and physical attributes data developed by Griffith [2,3], Canton et al [10], and Vallejos and Acosta [4], in which the univariate ESS was calculated, obtained sample reductions that varied from 30% to 61%. In the studies by Canton et al [11] and Vallejos and Acosta [6], in which multivariate ESS values were estimated, the sample reductions varied between 21% and 60%. However, although the maximum reduction obtained in these studies corroborated that of this paper (60%), the correlation structure between two variables was constructed using a matrix of spatial weights or crossed semivariogram.…”

“…The maximum ESS value was considered in this study to obtain a single sample reduction. Canton et al [11] made a sample reduction using the multivariate ESS; however, the method only considered a weighted ESS version, to avoid using a spatial correlation between the variables. Vallejos and Acosta [6] proposed a multivariate method to estimate ESS, dividing the attributes into groups of two and using the bivariate coregionalization model (BCRM).…”

Spatialization of Granulometric and Chemical Characteristics in Irrigated Hydromorphic Soil

“…For the chemical attributes, spatial dependence was also observed, indicating that the study area was not homogeneous. Normally, for each crop the soil receives fertilizers (that can vary in types, dosages, times and forms of application), and this can be an additional cause of spatial variability in chemical attributes (Canton et al, 2021). The research data were mostly adjustable to the Gaussian model (47% of attributes), followed by exponential (29%) and spherical (23%) models, considering the two layers (0.0-0.2 m).…”