Bayesian spatio-temporal models for stream networks.

Spatio-temporal models are widely used in many research areas including ecology. The recent proliferation of the use of in-situ sensors in streams and rivers supports space-time water quality modelling and monitoring in near real-time. In this paper, we introduce a new family of dynamic spatio-temporal models, in which spatial dependence is established based on stream distance and temporal autocorrelation is incorporated using vector autoregression approaches. We propose several variations of these novel models using a Bayesian framework. Our results show that our proposed models perform well using spatio-temporal data collected from real stream networks, particularly in terms of out-of-sample RMSPE. This is illustrated considering a case study of water temperature data in the northwestern United States.