ABSTRACT Precision agriculture can improve the decision-making process in agricultural production, as it gathers, processes and analyzes spatial data, allowing, for example, specific fertilizer application in each location. One of the proposals to deal with spatial heterogeneity of the soil or the distribution of chemical properties is to define application zones (homogeneous subareas). These zones allow reducing both spatial variability of the yield of the crop under study and of the environmental impacts. Considering the soil data, application zones can also represent strata or indicators to direct future soil sampling, thus seeking sample size reduction, for example. This study aimed to obtain an optimized sampling redesign using application zones generated from the assessment of five clustering methods (Fuzzy C-means, Fanny, K-means, McQuitty and Ward). Soil samples were collected in an agricultural area located in the city of Cascavel-Paraná-Brazil, and analyzed in the laboratory to determine the soil chemical properties, referring to four soybean harvest years (2013-2014, 2014-2015, 2015-2016 and 2016-2017). The application zones were obtained through a dissimilarity matrix that aggregates information about the Euclidean distance between the sample elements and the spatial dependence structure of the properties. Subsequently, an optimized sampling redesign, with reduction of the initial sample points, was obtained in these application zones. For the harvest years under study, the K-means and Ward clustering methods efficiently defined the application zones, dividing the study area into two or three application zones. Among the reduced sample configurations obtained by the optimization process, when comparing the initial sample configuration, the one optimized by 25 % (selecting 75 % of the initial configuration points, which corresponds to 76 sample points) was the most effective in terms of the accuracy indices (overall accuracy, Kappa, Tau). This fact indicates greater similarity between the thematic maps of these sample configurations. In this way, the reduced sample configurations could be used to generate the application zones and reduce the costs regarding the laboratory analyses involved in the study. decisionmaking decision making production gathers data allowing example location homogeneous subareas. subareas . subareas) impacts Fuzzy Cmeans, Cmeans C means, means C-means Fanny Kmeans, Kmeans K Ward. Ward) CascavelParanáBrazil, CascavelParanáBrazil Cascavel Paraná Brazil, Brazil Cascavel-Paraná-Brazil 20132014, 20132014 2013 2014, 2014 (2013-2014 20142015, 20142015 2015, 2015 2014-2015 20152016 2016 2015-201 20162017. 20162017 2017 2016-2017) Subsequently points 2 selecting 7 overall Kappa Tau. Tau Tau) way 2013201 201 (2013-201 2014201 2014-201 2015201 2015-20 2016201 2016-2017 201320 20 (2013-20 201420 2014-20 201520 2015-2 201620 2016-201 20132 (2013-2 20142 2014-2 20152 2015- 20162 2016-20 (2013- 2014- 2016-2 (2013 2016- (201 (20 (2 (

ABSTRACT: In geostatistical modeling of soil chemical properties, one or more influential observations in a dataset may impair the construction of interpolation maps and their accuracy. An alternative to avoid the problem would be to use most robust models, based on distributions that have heavier tails. Therefore, this study proposes a spatial linear model based on the slash distribution (SSLM) in order to characterize the spatial variability of soybean yields as a function of soil chemical properties. The likelihood ratio statistic (LR) was applied to verify the significance of parameters associated with the model. We evaluated the sensitivity of the maximum likelihood estimators by means of local influence analysis for both the soybean response and the linear predictor. In the proposed model, we analyzed data gathered from a commercial grain production area (127.18 ha) located in the western part of the state of Paraná (Brazil). The results showed that the slash distribution allowed us to adjust the high kurtosis of the data set distribution and the LR test confirmed that the soil chemical properties of phosphorus, potassium, pH, and organic matter were significant for the SSLM. Diagnostic analysis indicated that the atypical value of the sample set was not influential in the parameter estimation process. Construction of the interpolation map based on the proposed model is not affected when considering the atypical and/or influential observations. Thus, SSLM becomes a robust alternative in the study of soybean yield variability as a function of soil chemical properties, making it possible to investigate the productive potential of the areas.

The study on spatial variability of soil properties performed through geostatistical techniques allow us to identify the spatial distribution of phenomena by means of a spatial model that considers degree of dependence among observed data, depending on distance and also the direction that separate them, if there is geometric anisotropy, in other words, a directional trend in spatial continuity. However, the main difficulty in decision making regarding the use of anisotropic spatial model focuses on its relevance to the parameters that express the geometric anisotropy in a spatial model exercise in relation to the estimation space. This study aims at identifying the degree of influence of geometric anisotropy on the accuracy of spatial estimation using simulated data sets with different sample sizes and soil chemical properties such as: Fe, potential acidity (H + Al), organic matter and Mn. Comparing the isotropic and anisotropic models, especially for smaller sample sizes (100 and 169) showed an increased sum of squares of differences between predictions anisotropy factor (Fα) equals 2. Furthermore, from Fα equals 2.5, over 50% of the simulations showed values of overall accuracy (OA) of less than 0.80 and values for the concordance index Kappa (K) and Tau (T) from 0.67 to 0.80, indicating differences between thematic maps. Similar conclusions were obtained for chemical properties of the soil, from Fα equals 2, showing that there are relevant differences regarding the inclusion or not of geometric anisotropy.

No estudo do mapeamento da fertilidade do solo, pelas técnicas de geoestatística, algumas características estruturais da variabilidade espacial devem ser consideradas, tais como continuidade espacial e ausência de anisotropia. Neste contexto, o presente trabalho apresenta uma análise da anisotropia no estudo da variabilidade espacial das variáveis químicas do solo: ferro (Fe), acidez potencial (H + Al), matéria orgânica (MO) e Mn, de um conjunto de dados de 128 parcelas sem manejo químico localizado, espacialmente referenciados, estudados entre 1998 e 2002, em um Latossolo Vermelho distroférrico, em Cascavel-PR. A identificação da anisotropia foi realizada por meio da construção de semivariogramas direcionais com modelos ajustados, e a correção da anisotropia realizou-se por meio de transformações lineares e de modelos combinados. Em seguida, utilizou-se um modelo ajustado ao semivariograma omnidirecional para construção de mapas temáticos de variabilidade das variáveis estudadas. Observou-se a existência de anisotropia geométrica para a variável H + Al. Já as variáveis MO, Mn e Fe mostraram a presença de anisotropia combinada, sendo corrigida inicialmente a anisotropia geométrica e, posteriormente, a anisotropia zonal. Por meio do estudo da anisotropia, foi possível eliminar as direções privilegiadas, melhorando assim o ajuste dos semivariogramas e produzindo mapas temáticos das variáveis químicas estudadas com maior acurácia.

Studies on soil fertility mapping based on geostatistics should consider some spatial variability characteristics such as spatial continuity and absence of anisotropy. The present study reports an anisotropic analysis of the spatial variability of the following soil chemical variables: iron (Fe), potential acidity (H + Al), organic matter (OM) and manganese (Mn) of a data set of 128 plots without local chemical management, spatially referenced, studied between 1998 and 2002 in a dystrophic Red Latosol (Oxisol), in Cascavel, Paraná, Brazil. Anisotropy was identified through the construction of directional semivariograms with adjusted models and corrected through linear transformations and by combined models. Thereafter a model was used adjusted to the omnidirectional semivariogram for the construction of thematic variability maps of the studied variables. The existence of geometric anisotropy was observed for the variable H + Al. The variables MO, Mn and Fe evidenced the presence of combined anisotropy. The geometric anisotropy was first corrected and then the zonal anisotropy was adjusted. Based on anisotropy it was possible to eliminate the biased directions, enhancing the semivariogram fitting and precision of the thematic maps of chemical variables.