Observability-Based Sensor Placement Improves Contaminant Tracing in River Networks

This study presents a new methodology for identifying near-optimal sensor locations for contaminant source tracing in river networks. We define an optimal sensor placement as one that enables the best overall reconstruction of contaminant concentrations from observed data. To establish a physical basis for the problem, we first derive a linear time-invariant (LTI) model for riverine contaminant transport using the one-dimensional advection-reaction-diffusion equation. We then formulate an optimization problem to find the sensor placement that maximizes the observability of the modeled system and identify two heuristics for efficiently achieving this goal. By evaluating each sensor placement strategy on its ability to reconstruct initial contaminant loads from observed outputs, we find that the best sensor placement is obtained by maximizing the rank of the LTI system's Observability Gramian. This sensor placement strategy enables the best overall reconstruction of both magnitudes and distributions of nonpoint-source contaminants. Our methodology will enable researchers to build sensor networks that better interpolate pollutant loads in ungauged locations, improve contaminant source identification, and inform more effective pollution control strategies. © 2021. The Authors.