Spatial monitoring of a non-stationary soil property: phosphorus in a Florida water conservation area

Ecological restoration plans in the Florida Everglades require detailed information about the status and change of the nutrient content of the soil. The soil total phosphorus (TP) content is of particular importance as the system is naturally P limited and the TP enrichment has led to changes in the wetland vegetation communities. One way to provide the relevant information is by geostatistical prediction from sampled data. However, conventional geostatistical models assume that properties being monitored are realizations of second-order stationary random functions. The assumption of second-order stationarity is not appropriate for soil TP in Water Conservation Area 1 (WCA-1) of the Florida Everglades because the mean and variance of soil TP are larger at sites adjacent to the canals which bound WCA-1 and deliver P to the system than at sites in the interior of the region. We develop a novel linear mixed-model framework for spatial monitoring of a property for which this assumption is not valid. Specifically we use this non-stationary model to map the status and change of TP within WCA-1 from surveys carried out in 1991 and 2003. We fit the parameters of the model by residual maximum likelihood (REML) and compare the effectiveness of this non-stationary model with the conventional stationary model. Conventional second-order stationary models fail to represent accurately the large uncertainty in predictions of TP adjacent to the canals. The non-stationary model predicts an invading front of P entering the interior of the region which is not evident in the predictions from the stationary model. Tests on the log-likelihood and the standardized squared prediction error of the fitted models provide further evidence in favour of the non-stationary model. The sampling intensity required to ensure a certain precision of TP predictions varies across WCA-1 with the variance of TP. Therefore we apply a spatial simulated annealing optimization algorithm to design future monitoring surveys based upon our non-stationary model which ensure that the status and change are efficiently and effectively predicted across the region.