Premium
Observability‐Based Sensor Placement Improves Contaminant Tracing in River Networks
Author(s) -
Bartos Matthew,
Kerkez Branko
Publication year - 2021
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2020wr029551
Subject(s) - observability , tracing , computer science , heuristics , controllability , wireless sensor network , mathematical optimization , nonpoint source pollution , environmental science , pollution , mathematics , computer network , ecology , biology , operating system
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.