Assessing interpolation error for space-time monitoring data

Abstract

In Europe, since 1990, a survey on environmental monitoring has been taking place every five years, using moss samples to study the distribu- tion of heavy metal concentration and assess contamination sources, resulting on the identification of statistical association of several heavy metal concen- trations in mosses. With this work, we propose an extension of an existing spatio-temporal model, introduced in Høst et al. (1995), allowing for prediction at unsampled locations of pollution data in the presence of covariates related to each country speci- ficities, when separately modelling the spatial mean field, the spatial variance field and the space-time residual field. Moreover, this model allows to esti- mate 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 infor- mation, namely when Ordinary Kriging, according to the definition in Cressie (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.