Guide for the spatial analysis of compositional data
DOI:
https://doi.org/10.21701/bolgeomin.122.4.005Keywords:
Aitchison geometry, composition, covariance function, simplexAbstract
Dealing with spatially-dependent compositional databases (including proportions, data in percentages, concentrations etc) should pay heed to the mathematical properties of these kinds of data: a valid composition must have positive components whose sum is at most a constant (1, 100% etc.). Generally speaking this is easily done by working on a set of log-ratios of components rather than using the raw data. To study the spatial variability of these databases it is best to estimate and model the lr-variograms, i.e. the set of variograms of all possible pairwise log-ratios of components in the composition. Such lr-variograms contain all the information necessary to deal with intrinsic stationary compositions and may be modelled with standard geostatistical tools such as the linear model of coregionalization. Moreover, the properties of the model can be studied and relationships inferred between components and possible processes linked to a given spatial scale. Finally, component-by-component interpolation and mapping is straightforward with existing kriging and simulation techniques: these tools and concepts should be applied to any set of invertible component log-ratios, i.e. log-ratio transformations, in such a way that the original composition can be recovered from the transformed data and vice versa.
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Universitat de Girona
Grant numbers BR01/03
