Estimating and modeling spatio-temporal correlation structures for river monitoring networks

The European environmental legislation forces local authorities to improve the river water quality. In order to assess the presence of trends or the effect of certain actions on the river water quality, a statistical methodology is needed which can deal with data originating from river monitoring networks. Since both temporal and spatial components affect the output of such a monitoring network, their dependence structure has to be modeled. Current spatio-temporal models used for the analysis of data arising from environmental studies are not appropriate because they do not deal properly with the particular spatial dependence structure underlying river monitoring networks. In this article, a state-space model is developed in which the state variable is defined by a directed acyclic graph (DAG) derived from the river network topology. In reality the dependence structure based on the DAG may be obscured by environmental factors. This is taken into account by embedding the state variable in an observation model. Finally, the state-space model is extended with a linear model for the mean. An efficient ECM-like algorithm is proposed for parameter estimation, using the Kalman filter and smoother in both E- and CM-steps. In a case-study the method is applied to assess the effect of the activation of a waste water treatment plant on the dissolved oxygen concentration, in time as well as in space.