Statistical sampling approaches for soil monitoring

This paper describes three statistical sampling approaches for regional soil monitoring, a design-based, a model-based and a hybrid approach. In the model-based approach a space-time model is exploited to predict global statistical parameters of interest such as the space-time mean. In the hybrid approach this model is a time-series model of the spatial means. In the design-based approach no model is used: estimates are model-free. Full design-based inference requires that both sampling locations and times are selected by probability sampling, whereas the hybrid approach requires probability sampling of locations only. In a case study on soil eutrophication and acidification, a rotational panel design was implemented with probability sampling of locations and non-probability sampling of times. The hybrid and model-based predictions of the space-time means and trend of the mean for pH and ammonium at three depths in the soil profile were very similar. For pH the standard errors of the space-time means were about equal, but for ammonium the full model-based predictor was more precise than the hybrid predictor. For soil monitoring I advocate the selection of sampling locations by probability sampling so that the statistical inference approach is flexible. Selecting locations by a self-weighting probability sampling design ensures that the model-based predictor is not affected by selection bias.