Delineation of Homogeneous Zones Based on Geostatistical Models Robust to Outliers

Abstract

Measures of the apparent electrical conductivity (ECa) of soil are used in many studies as indicators of spatial variability in physicochemical characteristics of production fields. Based on these measures, management zones (MZs) are delineated to improve agricultural management. However, these measures include outliers. The presence or incorrect identification and exclusion of outliers affect the variogram function and result in unreliable parameter estimates. Thus, the aim of this study was to model ECa data with outliers using methods based on robust approximation theory and model-based geostatistics to delineate MZs. Robust estimators developed by Cressie-Hawkins, Genton and MAD Dowd were tested. The Cressie-Hawkins semivariance estimator was selected, followed by the semivariogram cubic fit using Akaike information criterion (AIC). The robust kriging with an external drift plug-in was applied to fitted estimates, and the fuzzy k-means classifier was applied to the resulting ECa kriging map. Models with multiple MZs were evaluated using fuzzy k-means, and a map with two MZs was selected based on the fuzzy performance index (FPI), modified partition entropy (MPE) and Fukuyama-Sugeno and Xie-Beni indices. The defined MZs were validated based on differences between the ECa means using mixed linear models. The independent errors model was chosen for validation based on its AIC value. Thus, the results demonstrate that it is possible to delineate an MZ map without outlier exclusion, evidencing the efficacy of this methodology. DELINEAMENTO DE ZONAS HOMOGÊNEAS PORGEOESTATÍSTICA BASEADA EM MODELOS ROBUSTA À OUTLIERS RESUMO -Diversas pesquisas utilizam medidas de condutividade elétrica aparente do solo (CEa) como indicador da variabilidade espacial de atributos físico-químicos existentes no campo de produção. Com base nestas medidas, zonas de manejo (ZM) são delineadas para aperfeiçoamento da gestão agrícola. Entretanto, estas amostras têm apresentado presença de outliers. Todavia, a presença ou incorreta detecção e exclusão de outliers altera o formato do variograma, exibindo estimativas não fidedignas para os seus parâmetros. Dessa forma, objetivou-se nesta pesquisa, tratar dados amostrais da CEa por meio de métodos robustos à presença de outliers, fundamentados na teoria de aproximações robusta e na geoestatística baseada em modelos, para o delineamento de ZM. Assim, estimadores robustos de Cressie Hawkins, Genton"s e MAD Dowd foram avaliados. Nesta avaliação, selecionou-se o estimador de semivariância de Cressie Hawkins. E na sequência, optou-se pelo ajuste cúbico do semivariograma via Critério de Informação de Akaike (AIC). As estimativas obtidas com este ajuste foram aplicadas na plug-in robusto de krigagem. E coerentemente o mapa de krigagem da CEa obtido foi utilizado no classificador fuzzy k-means. Com uso do fuzzy k-means, diferentes ZM foram avaliadas, selecionando-se o mapa com duas ZM por meio dos índices FPI, MPE, Fukuyama-Sugeno e xie beni. As ZM estabelecidas foram validadas quanto as suas diferenças ...

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