Spatio-temporal prediction inside a free-air CO2 enrichment system

The Japanese RiceFACE (Free-Air CO2 Enrichment) project was a three-year investigation into the effect of elevated CO2 on rice. Four rings were built to emit elevated levels of CO2. The aim of the FACE system is to provide a level Of CO2 enrichment 200 ppm above ambient throughout the plot, without changing any other aspect of the microclimate within the plot. However, there can be substantial spatial variation in the CO2 level from the center to the edges of the plots. One of our main objectives was to predict the seasonal mean levels Of CO2 for multiple subregions within the plots. However, the dataset was very large and followed a nonnormal distribution. Furthermore, the mean and variance were nonstationary. To overcome these difficulties daily means were used rather than individual measurements, the mean was modeled with multiple covariates that varied over both time and space, and the variance was modeled as an increasing function of the square of the distance from the center of the plot. A separable space-time covariance structure was used, and estimation was performed using nonlinear methods, REML, and EGLS. Finally, cross-validation was used to assess the validity of the model.