Spectral Estimation of UV-Vis Absorbance Time Series for Water Quality Monitoring

Context: Signals recorded as multivariate time series by UV-Vis absorbance captors installed in urban sewer systems, can be non-stationary, yielding complications in the analysis of water quality monitoring. This work proposes to perform spectral estimation using the Box-Cox transformation and differentiation in order to obtain stationary multivariate time series in a wide sense. Additionally, Principal Component Analysis (PCA) is applied to reduce their dimensionality. Method: Three different UV-Vis absorbance time series for different Colombian locations were studied: (i) El- Salitre Wastewater Treatment Plant (WWTP) in Bogota; (ii) Gibraltar Pumping Station (GPS) in Bogota; and (iii) San-Fernando WWTP in ItagtiI. Each UV-Vis absorbance time series had equal sample number (5705). The estimation of the spectral power density is obtained using the average of modified periodograms with rectangular window and an overlap of 50 %, with the 20 most important harmonics from the Discrete Fourier Transform (DFT) and Inverse Fast Fourier Transform (IFFT). Results: Absorbance time series dimensionality reduction using PCA, resulted in 6, 8 and 7 principal components for each study site respectively, altogether explaining more than 97 % of their variability. Values of differences below 30 % for the UV range were obtained for the three study sites, while for the visible range the maximum differences obtained were: (i) 35 % for El-Salitre WWTP; (ii) 61 % for GPS; and (iii) 75 % for San-Fernando WWTP. Conclusions: The Box-Cox transformation and the differentiation process applied to the UV-Vis absorbance time series for the study sites (El-Salitre, GPS and San-Fernando), allowed to reduce variance and to eliminate tendency of the time series. A pre-processing of UV-Vis absorbance time series is recommended to detect and remove outliers and then apply the proposed process for spectral estimation.