Reconstruction of Sparse Stream Flow and Concentration Time-Series Through Compressed Sensing

Monitoring water quality at high frequency is challenging and costly. Compressed sensing (CS) offers an approach to reconstruct high-frequency water quality data from limited measurements, given that water quality signals are commonly “sparse” in the frequency domain. In this study, we investigated the sparsity of stream flow and concentration time-series and tested reconstruction with CS. All stream signals were sparse using 15-min discrete time-series transformed to the Fourier domain. Stream temperature, conductance, dissolved oxygen, and nitrate plus nitrite (NO_x-N) concentration were sparser than discharge, turbidity, and total phosphorus (TP) concentration. CS effectively reconstructed these signals with only 5%–10% of measurements needed. Stream NO_x-N and TP loads were well estimated with errors of −6.6% ± 3.8% and −9.0% ± 2.9% with effective sampling frequencies of 10 and 0.4 days, respectively. For broader applications in environmental geosciences and engineering domains, CS can be integrated with dimensionality reduction and optimization techniques for more efficient sampling schemes.