Modelling the electrical conductivity of soil in the Yangtze delta in three dimensions

• Variation in salinity in soil in the Yangtze delta was analysed geostatistically.
• Strong lateral and vertical trends and covariances of the residuals were estimated by REML.
• The anisotropy could be represented by a non-affine transformation.
• Space–time covariance functions led to satisfactory fitting.
• Kriged predictions were mapped as three-dimensional charts.

Numerous processes, past and present, have given rise to lateral and vertical variation in the soil and to its individual properties such as its salinity and electrical conductivity. The resulting patterns of variation are complex and appear to comprise both random and deterministic components. The latter dominates vertically as trends in most soil profiles, and in the situation we describe it is prominent in the horizontal plane, too. Describing this variation requires flexible choice of covariance function. The processes of model estimation and prediction by kriging in three dimensions are similar to those in two dimensions. The extra complexity of the three-dimensional variation requires practitioners to appreciate fully the assumptions that their choices of model imply and to establish ways of testing the validity of these assumptions. We have examined several covariance functions more commonly used to describe simultaneously variation in space and time and adapted them to model three-dimensional variation in soil. We have applied these covariance functions to model the variation in salinity in reclaimed land in the Yangtze delta of China where the apparent electrical conductivity (ECa) has been measured at numerous points down to 1.1 m. The models take into account random and deterministic components in both the horizontal and vertical dimensions. The most suitable mixed model was then used to krige the ECa on a fine grid from which three-dimensional diagrams of the salinity are displayed.