SpaceTime Dynamic Design of Environmental Monitoring Networks

Methods for constructing optimal spatial sampling designs for environmental monitoring networks, widely applied in a large number of disciplines, generally produce static designs that are optimal under models with no explicit temporal structure. However, environmental processes tend to exhibit both spatial and temporal variability; hence, static networks may not capture the essential spatiotemporal variability of the process. Static designs, often necessary due to geopolitical and economic considerations, could be supplemented with mobile monitoring devices. The design problem is to decide where mobile monitors should be located at time t + 1 based on observations through time t. We propose a simple, general, dynamical space-time model that allows estimation of prediction error covariance at time t + 1, given information up to time t. We then seek the optimal spatial locations at time t + 1 that satisfy some design criterion. Several experiments show the importance of spatial and temporal structure in the selection of optimal designs. Data from the Chicago area ozone monitoring network are used to demonstrate potential dynamical designs under realistic space-time dependence assumptions.