A novel Bayesian maximum entropy-based approach for optimal design of water quality monitoring networks in rivers

Comprehensive river water quality monitoring and assessment helps to identify emerging water quality problems as well as developing sustainable water management strategies to maintain and protect healthy rivers and ecosystems. However, the cost of these efforts is a major concern due to large monitoring networks in rivers and watersheds. This paper presents a Bayesian Maximum Entropy (BME)-based framework to optimize the locations of Water Quality Monitoring Stations (WQMS) in rivers to obtain the highest value of information with the lowest number of monitoring stations. In this study, BME is employed as a flexible, accurate, and effective approach in geostatistics to optimize the spatiotemporal coverage of potential WQMS. In addition, an information-entropy model is proposed, using Value of Information (VOI) and Transinformation Entropy (TE), in a multi-objective optimization model to relax the computational burden and allow the entire decision space to be explored. The proposed model provides a set of Pareto-optimal solutions (WQMS locations) with tradeoffs between VOI (highest information) and TE (lowest overlap). This framework was applied to the Rappahannock River in eastern Virginia, United States. The results of this study revealed that only 5 monitoring stations, optimally placed along the river, could capture 76% of the information that 45 monitoring stations provided. This significantly reduces the costs of deploying and maintaining monitoring stations. Our approach will provide improved estimates of water quality in a cost-effective manner and can be transferrable to other regions to develop an accurate spatiotemporal estimation of potential WQMS.