Multivariate Spatial Prediction in the Presence of Non-Linear Trend and Covariance Non-Stationarity

When two or more spatial processes are punctually observed over a region, a multivariate predictor can account for spatial cross-covariance among the variables and thus potentially yield more reliable predictions and lower estimated prediction standard errors. If the spatial processes exhibit first- and/or second-order non-stationarity, however, standard cokriging-based predictors may not be adequate. A new cokriging-based multivariate predictor is presented capable of modelling non-linear trend, non-stationary spatial covariance, and the case where the covariable also enters as a covariate. This method is used to predict 1991 sulphate deposition over the conterminous US with the aid of the more spatially dense National Weather Service precipitation data. It is found that there are only small differences between sulphate predictions and estimated prediction standard errors and those computed under enforced zero cross-covariance. Failing to include the covariate effect of precipitation, however, results in non-negligible differences in such predictions and prediction standard error estimates.