The influence of the correlation-covariance structure of measurement errors over uncertainties propagation in online monitoring: application to environmental indicators in SUDS

This paper presents a methodology to assess the influence of the correlation-covariance structure of measurement errors in online monitoring over the propagation of uncertainties, applied to wet-weather environmental indicators in sustainable urban drainage systems (SUDSs). The effect of auto-correlated and heteroskedastic errors in measured time-series over the estimated probability density function (PDF) of different environmental indicators is analyzed for a wide variety of possible error structures in the data. For this purpose, multiple correlation-covariance structures are randomly generated from exploring the parametric space of a linear exponent autoregressive (LEAR) model, employing a Bayesian-based Markov Chain Monte Carlo sampling technique. Significant differences tests are proposed to identify the most correlated parameters of the correlation-covariance error model with statistics of the environmental indicator PDFs. The method is applied to total suspended solids (TSS) and chemical oxygen demand (COD) time-series recorded during 13 rainfall events at the inlet and outlet of a SUDS train (stormwater settling tank-horizontal constructed wetland). In this case, results showed that the total error in the estimation of the analyzed environmental indicators is mostly explained by standard uncertainties (flattening of the PDFs) rather than bias contributions (displacement of the PDFs). The correlation-covariance model parameters related to the temporal delimitation of hydrographs/pollutographs and the intensity of the autocorrelation showed to have the strongest influence in the propagation of measurement errors (flattening/displacement of the PDFs).

Automated summary

This paper presents a methodology to assess the influence of the correlation-covariance structure of measurement errors in online monitoring over the propagation of uncertainties. The study analyzed the effect of auto-correlated and heteroskedastic errors on the estimated probability density function of different environmental indicators. Results showed that the temporal delimitation of hydrographs/pollutographs and the intensity of the autocorrelation have the strongest influence in the propagation of measurement errors.