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 (SUDS). The effect of autocorrelated and heteroscedastic 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 indicators PDFs. The methodology 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). For 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).