Detrending non stationary data for geostatistical applications

Abstract

The use of geostatistics requires at least that the intrinsic hypothesis be satisfied. The presence of a trend in the data invalidates this hypothesis. One of the ways of solving this problem is by subtracting a function fitted to the original data and working with the residuals. This technique also represents a change to a smaller scale of the variability and surface roughness. This paper describes the detrending technique of subtracting a trend surface fitted by the least squares method and discusses the results using topographical data as examples. The objective is to show how the detrending technique works for different scales and degrees of trend and how to interpret the results. It is shown that the simplest the surfaces fitted that does the work of removing the trend the best are the results obtained. The use of jack knifing is proved useful to validate the resulting semivariograms. For most of the applications and depending upon the scale, a linear or a parabolic surface works reasonably well. The back transformation of the data afterwards is very easily done by adding back the subtracted trend surface.Key words: Semivariograms, stationarity, topography, scale of variation. RESUMO REMOÇÃO DE TENDÊNCIA DE DADOS NÃO ESTACIONáRIOS PARA APLICAÇÕES DE GEOESTATÍSTICAO uso de geoestatistica exige que pelo menos a hipótese intrínseca seja satisfeita. A presença de tendência invalida esta hipótese. Uma das maneiras mais práticas de resolver esta questão é subtrair dos dados originais uma função ajustada por mínimos quadrados, trabalhando com a função residual resultante. Esta técnica representa uma mudança de escala da variabilidade e da rugosidade da superfície para uma escala menor. Este trabalho descreve a técnica da remoção da tendência pela subtração de uma superfície ajustada por mínimos quadrados e discute os resultados usando dados topográficos como exemplos. O objetivo é mostrar como usar esta técnica para remover tendências de superfícies de diferentes escalas e com diferentes graus de superfície e como interpretar os resultados. Foi mostrado que quanto mais simples for a superfície ajustada que resolve o problema de tendência, melhores são os resultados obtidos. O uso da validação cruzada provou ser útil para validar os semivariogramas resultantes. Para a maioria das aplicações e dependendo da escala, uma superfície linear ou parabólica funciona muito bem. A transformação de retorno nos dados é bastante fácil e é feita somando de volta a superfície subtraída.Palavras-chave: erro reduzido, estacionaridade, topografia, variação de escala.

Using codispersion analysis to characterize spatial patterns in species co‐occurrences

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Terrain data conflation using an improved pattern-based multiple-point geostatistical approach

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Using codispersion analysis to quantify and understand spatial patterns in species–environment relationships

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“…As a result, most spatial processes are assumed to have only second-order stationarity: only the mean, variance and covariance need to be stationary (Vieira et al, 2010). However, even second-order stationarity is unlikely in many ecological cases, and we assume only the 'intrinsic hypothesis' -that the mean and the semivariance of the distribution are dependent on interpoint distances, not specific locations (Vieira et al, 2010).…”

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