Multivariate autoregressive modelling and conditional simulation for temporal uncertainty analysis of an urban water system in Luxembourg
Authors: Torres-Matallana Jairo Arturo , Leopold Ulrich , Heuvelink Gerard B. M. 
Published: January 2021

Abstract. Uncertainty is often ignored in urban water systems modelling. Commercial software used in engineering practice often ignores the uncertainties of input variables and their propagation because of a lack of user-friendly implementations. This can have serious consequences, such as the wrong dimensioning of urban drainage systems (UDSs) and the inaccurate estimation of pollution released to the environment. This paper introduces an uncertainty analysis in urban drainage modelling, built on existing methods and applied to a case study in the Haute-Sûre catchment in Luxembourg. The case study makes use of the EmiStatR model which simulates the volume and substance flows in UDS using simplified representations of the drainage system and processes. A Monte Carlo uncertainty propagation analysis showed that uncertainties in chemical oxygen demand (COD) and ammonium (NH4) loads and concentrations can be large and have a high temporal variability. Furthermore, a stochastic sensitivity analysis that assesses the uncertainty contributions of input variables to the model output response showed that precipitation has the largest contribution to output uncertainty related with water quantity variables, such as volume in the chamber, overflow volume, and flow. Regarding the water quality variables, the input variable related to COD in wastewater has an important contribution to the uncertainty for the COD load (66 %) and COD concentration (62 %). Similarly, the input variable related to NH4 in wastewater plays an important role in the contribution of total uncertainty for the NH4 load (34 %) and NH4 concentration (35 %). The Monte Carlo (MC) simulation procedure used to propagate input uncertainty showed that, among the water quantity output variables, the overflow flow is the most uncertain output variable, with a coefficient of variation (cv) of 1.59. Among water quality variables, the annual average spill COD concentration and the average spill NH4 concentration were the most uncertain model outputs (coefficients of variation of 0.99 and 0.82, respectively). Also, low standard errors for the coefficient of variation were obtained for all seven outputs. These were never greater than 0.05, which indicates that the selected MC replication size (1500 simulations) was sufficient. We also evaluated how the uncertainty propagation can more comprehensively explain the impact of water quality indicators for the receiving river. While the mean model water quality outputs for COD and NH4 concentrations were slightly above the threshold, the 0.95 quantile was 2.7 times above the mean value for COD concentration and 2.4 times above the mean value for NH4. This implies that there is a considerable probability that these concentrations in the spilled combined sewer overflow (CSO) are substantially larger than the threshold. However, COD and NH4 concentration levels of the river water will likely stay below the water quality threshold, due to rapid dilution after CSO spill enters the river.