Assessing interpolation error for space-time monitoring data

\ In Europe, since 1990, a survey on environmental monitoring has been taking place every 5 years, using moss samples to study the distribution of heavy metal concentration and assess contamination sources, resulting on the identification of statistical association of several heavy metal concentrations in mosses. With this work, we propose an extension of an existing spatio-temporal model, introduced in Host et al. (JASA 90(431):853-861, 1995), allowing for prediction at unsampled locations of pollution data in the presence of covariates related to each country specificities, when separately modelling the spatial mean field, the spatial variance field and the space-time residual field. Moreover, this model allows to estimate an interpolation error, as an accuracy measure, derived dependently on the case study. For a validation purpose, a simulation study is conducted, showing that the use of the proposed model leads to more accurate prediction values. Results obtained by the proposed methodology for the most recent available survey, are compared with results obtained with no temporal information, namely when Ordinary Kriging, according to the definition in Cressie (Statistics for spatial data, Wiley, New York, 1993), is used to derive illustrative prediction maps based only on the most recent data. An exercise of cross-validation is performed relative to each of the scenarios considered and the average interpolation errors are presented. While assessing interpolation errors, we conclude that the monitoring specificities of each country and the information of preceding surveys allow for more accurate prediction results.