Expert elicitation for the variogram

Expert elicitation for the variogram
Phuong N. Truong1, Gerard B. M. Heuvelink1 and John Paul Gosling2

1. Department of Environmental Sciences, Wageningen University, P.O. Box 47, 6700 AA, Wageningen, The Netherlands (phuong.truong@wur.nl, gerard.heuvelink@wur.nl)
2. Department of Statistics, University of Leeds, Leeds, LS2 9JT, UK (j.p.gosling@leeds.ac.uk)

Abstract: The variogram is the keystone of Kriging. Much research has been devoted to modelling the variogram from structural analysis of observations. However, there are many instances when the variogram is needed and there are no observations to base on. This can be due to budget constraints, physical or temporal obstacles, or a demand for a priori variogram in Bayesian geostatistics and spatial sampling design. Using expert knowledge that is elicited with a formal statistical expert elicitation procedure is suggested. In this study, we designed a protocol for a wellstructured elicitation procedure to elicit the variogram from expert knowledge. The protocol has two main stages: elicitation of the marginal probability distribution and elicitation of the variogram. We built a web-based tool to facilitate the procedure. A case study was carried out to quantify spatial accuracy of a legacy map of the volumetric soil water content at field capacity. Expert elicitation returns a variogram that has a Matérn model shape with nugget = 0.45, partial sill = 54.57, range = 25410 meters and kappa = 0.40. The results show that the online elicitation tool satisfactorily captured expert opinion although, currently, it is only a prototype that needs to be further developed.

Keywords: Spatial variability, Variogram, Expert knowledge, Soil property map, Uncertainty quantification.

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