Observability-Based Sensor Placement Improves Contaminant Source Identification in River Networks

As high-frequency sensing of surface water quality becomes increasingly feasible over larger spatial scales, new methods for sensor site selection are desperately needed. In this study, we present a new methodology for identifying near-optimal sensor locations for contaminant source identification in river networks. We define an optimal sensor placement as one that enables the best overall reconstruction of contaminant concentrations from sparse sensor data. Using an advection-reaction-diffusion model of contaminant transport, we derive an optimization routine to find the sensor placement that maximizes the observability of the modeled system---thereby enabling the best estimation of internal states (contaminant loads) from observed outputs (sensor measurements). Evaluating various observability-based sensor placement heuristics, we find that the best sensor placement is obtained by maximizing the rank of the system's Observability Gramian. This sensor placement strategy enables the best overall reconstruction of both magnitudes and distributions of nonpoint-source contaminants when only limited sensor data are available. 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.