When introducing new wastewater treatment plants (WWTP), investors and policy makers often want to know if there indeed is a beneficial effect of the installation of a WWTP on the river water quality. Such an effect can be established in time as well as in space. Since both temporal and spatial components affect the output of a monitoring network, their dependence structure has to be modelled. River water quality data typically come from a river monitoring network for which the spatial dependence structure is unidirectional. Thus the traditional spatio-temporal models are not appropriate, as they cannot take advantage of this directional information. In this paper, a state-space model is presented in which the spatial dependence of the state variable is represented by a directed acyclic graph, and the temporal dependence by a first-order autoregressive process. The state-space model is extended with a linear model for the mean to estimate the effect of the activation of a WWTP on the dissolved oxygen concentration downstream.
Spatio-temporal statistical models for river monitoring networks
L. Clement, O. Thas, P.A. Vanrolleghem, J.P. Ottoy; Spatio-temporal statistical models for river monitoring networks. Water Sci Technol 1 January 2006; 53 (1): 9–15. doi: https://doi.org/10.2166/wst.2006.002
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