CUSUM environmental monitoring in time and space

We consider the situation where there are n sampling sites in an area, with an environmental variable measured at some or all of the sites at m sample times. We assume that there is interest in knowing whether the environmental variable displays systematic changes over time at the sites. A cumulative sum type of analysis with associated randomization tests has been proposed before for this situation, when there is negligible correlation between the observations in different times at one site, and no correlation between the results at different sites. A modification that allows for serial correlation at the individual sites but with no correlation between sites has also been proposed before. In the present paper we discuss how the method can be modified further to allow for spatial correlation between the sites, by applying it only to a reduced set of sites that are far enough apart to give effectively independent results. Simulation results indicate that this strategy is effective providing that the level of spatial correlation is not too high.