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

Haskard, K.A.; Rawlins, B.G.; Lark, R.M.. 2010 A linear mixed model, with non-stationary mean and covariance, for soil potassium based on gamma radiometry. Biogeosciences, 7. 2081-2089.

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

Item Type: Publication - Article
Digital Object Identifier (DOI):
Programmes: BGS Programmes 2010 > Land Use, Planning and Development
ISSN: 1726-4170
Additional Information. Not used in RCUK Gateway to Research.: Biogeosciences (BG) is an international scientific journal dedicated to the publication and discussion of research articles, short communications and review papers on all aspects of the interactions between the biological, chemical and physical processes in terrestrial or extraterrestrial life with the geosphere, hydrosphere and atmosphere
NORA Subject Terms: Ecology and Environment
Date made live: 06 Dec 2010 15:12 +0 (UTC)

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