A comprehensive study on spectral analysis and anomaly detection of river water quality dynamics with high time resolution measurements

Systemic analysis of hydrology and water quality fluctuations using a data-intensive approach is an emerging research area and is significant for understanding hydrological processes. However, there is very limited understanding of the high-frequency characteristics of water quality fluctuations in the frequency domain. This study proposes a generic systemic framework to comprehensively analyse river water quality dynamics using a combination of Fourier and wavelet spectral analyses with high temporal resolution measurements. This framework identifies long-term, short-term, periodic, aperiodic, normal baseline and abnormal fluctuations, with particularly focus on detecting transient anomaly events due to their importance for watershed management. This study was conducted on the Potomac River, USA, where seven parameters, water temperature (Temp), pH, dissolved oxygen (DO), conductance (Cond), turbidity (Turb), nitrate plus nitrite (NOx-N) and discharge (Disc), were monitored every 15 min for two years at five sites/sub-catchments. Fast Fourier transform (FFT) revealed that Temp, pH and DO exhibited typical low-frequency periodic fluctuations, such as seasonal and bi-annual fluctuations, as well as interesting high-frequency periodic fluctuations, such as 12-hour and 8-hour fluctuations, which were identified as periodic anomalies. Cond, Turb and NOx-N presented universal temporal scaling phenomena, i.e., 1/f fluctuation, at all sites, as shown by the power spectral density. The scaling exponent β ranged between 1 and 3 and presented the order of β > β > β The continuous wavelet transform (CWT) associated with contour-based scalograms successfully identified the time, location, duration and magnitude of transient anomaly events and classified two anomaly patterns: abrupt changes and large swings. The two patterns exhibited clearly different spectral energy distributions, i.e., pseudo-frequencies, on the CWT scales. A preliminary causality analysis found that the frequency of occurrence of turbidity anomaly events (FOA) was proportional to the product of the developed land area percentage and FOA, and FOA was proportional to the product of forest land area percentage and FOA. Wavelet coherence analysis showed different hysteresis characteristics of different water quality parameters. In particular, Turb and NOx-N presented significantly different coherent fluctuation behaviours between high-frequency and low-frequency regions. Some findings of this study are still difficult to explain at this stage. High-frequency monitoring combined with spectral analysis provides new insights into the details of water quality dynamics, which can help to develop a new index and framework for the reliability, resilience, and management of watershed water quality vulnerability. These results can also be used to design new algorithms for online anomaly detection.