Geostatistical prediction of nitrous oxide emissions from soil using data, process models and expert opinion

Geostatistical techniques can be used to predict spatially correlated variables at unsampled locations. We can incorporate information from soil process models in the geostatistical methodology via regression kriging (RK), which we consider in a Bayesian statistical framework (BRK). The resulting predictions are better than those obtained from the process model alone or by ordinary kriging. We consider approaches to predict the nitrous oxide emissions from soil along a transect in Bedfordshire in the UK. In this case study, there exists uncertainty about the most appropriate model to represent the denitrification process. We account for this uncertainty by model averaging (MA); the MA predictions are a weighted average of the BRK predictions based on the individual models. We consider several approaches to calculate weights for MA. We use Bayesian model averaging (BMA) to investigate whether the local data from the neighbourhood of a prediction location can provide useful information for calculating the model weights. We use the opinions of an expert on the relevant soil processes to define probabilities for the candidate models, and investigate how this information benefits the MA and BMA predictions. If we would prefer not to base analysis on the opinions of a single expert, we could use a linear opinion pool to merge the opinions of multiple experts, which we demonstrate through a simple example. We show the conditions under which MA and BMA improve predictions in this case study, and suggest reasons for these improvements. We use the BMA model weights, which are calculated from local data, to provide information about the ability of the models to represent the spatial variability of the data along the transect.