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A linear mixed model, with non-stationary mean and covariance, for soil potassium based on gamma radiometry

By K.A. Haskard, B.G. Rawlins and R.M. Lark


In this paper we present a linear mixed model for\ud the potassium content of soil across a large region of eastern\ud England in which the mean is modelled as a linear function of\ud the passive gamma-ray emissions of the earth surface in the\ud energy interval commonly associated with potassium decay.\ud Non-stationary models are proposed for the random effect,\ud which is the variation not captured by this regression. Specifically,\ud we assume that the local spectrum of the standardized\ud random effect can be obtained by tempering a common (stationary)\ud spectrum, that is to say raising its values to a power,\ud the tempering parameter, which is itself modelled as a linear\ud function of the radiometric data. This allows the “smoothness”\ud of the random effect to vary locally. In addition the local\ud spatially correlated variance and “nugget” variance (apparently\ud uncorrelated given the resolution of the sampling)\ud can also be modelled as a function of the radiometric data.\ud Using the radiometric signal as a covariate gave some improvement\ud in the precision of predictions of soil potassium\ud at validation sites. In addition, there was evidence that nonstationary\ud models for the random effect fitted the data better\ud than stationary models, and this difference was statistically\ud significant. Non-stationary models also appeared to describe\ud the error variance of predictions at the validation sites better.\ud Further work is needed on selection among alternative nonstationary\ud models, since simple procedures used here, based\ud on comparing log-likelihood ratios of nested models and the\ud Akaike information criterion for non-nested models, did not\ud identify the model which gave the best account of the prediction\ud error variances at validation sites

Topics: Ecology and Environment
Publisher: European Geosciences Union
Year: 2010
DOI identifier: 10.5194/bg-7-2081-2010
OAI identifier: oai:nora.nerc.ac.uk:12561

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