Effects of spatial pattern persistence on the performance of sampling designs for regional trend monitoring analyzed by simulation of space-time fields

The effect of the persistence of spatial patterns on the performance of space-time sampling designs is explored by a simulation study. The performance is evaluated on the basis of the covariance matrix of the two parameters (intercept and slope) of a linear model for the change over time of the spatial means or totals. The evaluated sampling approach is hybrid, i.e. design-based estimation of spatial means from spatial probability samples is combined with time-series modelling of the spatial means. A simulation algorithm is presented for approximating the covariance matrix of the time-series model parameters from a full space-time model. Designs were evaluated on the basis of the determinant of this matrix and the variance of the estimated trend parameter. As a space-time model a sum-metric space-time variogram is used, the parameters of which are chosen such that the persistence of spatial patterns varies from nearly absent to very strong. Based on the extensive simulations, recommendations on the type of space-time design can most easily be made for situations with either very strong or no persistence of spatial patterns. With strong persistence the supplemented panel (SuP) design is recommendable. With no persistence the independent-synchronous (IS) and serially alternating (SA) designs are the best choice. These designs performed well with regard to both quality criteria. With moderate persistence of spatial patterns the choice of design type is more complicated. The IS and static-synchronous (SS) design performed best on one quality criterion, but worst on the other. Therefore, with moderate pattern persistence, the compromise designs, either SuP or SA, can be a good choice, unless one of the two quality criteria has priority. An R script is provided for ex ante evaluation of space-time designs in real-world applications.