Geostatistics provides an efficient mechanism, i.e. Kriging, for characterising spatial data and their accuracy. The variogram is the keystone of Kriging. Much research have been devoted to modelling the variogram from a structural analysis of available observations. However, there are many instances when the variogram of a spatial variable is needed and there are no observations to base them 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, to name a few. Experts can be very knowledgeable about the spatial variability of some variable. The experts are therefore an important source of information when observations are lacking. Formal expert elicitation has gradually become a mature research field and proved to be able to extract reliable information from experts to form a sound scientific database. For this reason, we attempted to derive reliable information from the experts to model the variogram of a spatial variable using formal expert elicitation techniques.

In particular, we have designed a protocol for a well-structured elicitation procedure to use for an intrinsic stationary spatial random field. There are two main stages in the elicitation procedure: elicitation of the marginal probability distribution and elicitation of the semivariance. The elicitation of the marginal probability distribution was based on the bisectional elicitation method where the three quartiles (the median, the lower and upper quartiles) were elicited from the experts through formal questioning. Elicitation of the semivariance focused on the difference of the variable?s values at two locations at a given lag apart in the case where the marginal probability distribution was normal, or the ratio of the variable?s values at two locations apart in the case of a log-normal marginal probability distribution. The elicited values from the second stage were used to calculate semivariances at lags and a variogram model was fitted to these judgements. We next developed a transparent, web-based tool to facilitate the expert elicitation procedure. The tool has three main components: (1) a web interface for elicitation and feedback, (2) statistical calculation and mathematical aggregation to merge the opinions of multiple experts and (3) database management. The experts and problem owners can interact with the tool online.

In order to evaluate our protocol, we carried out a case study where the experts used the tool to quantify the spatial accuracy of the mapped volumetric soil water content at field capacity for the East Anglian chalk area of the UK. We invited soil experts from UK and the Netherlands, who are familiar with the study site and soil property, to take part in the exercise. The results from the case study show that the online elicitation tool satisfactorily captures expert opinion although, currently, it is only a prototype that needs to be further developed.