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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  10 Jul 2020

10 Jul 2020

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A revised version of this preprint is currently under review for the journal HESS.

Multivariate autoregressive modelling and conditional simulation for temporal uncertainty propagation in urban water systems

Jairo Arturo Torres-Matallana1,2, Ulrich Leopold2, and Gerard B. M. Heuvelink1 Jairo Arturo Torres-Matallana et al.
  • 1Soil Geography and Landscape Group, Wageningen University
  • 2Research Group for Sustainable Urban and Built Environment, Department for Environmental Research and Innovation, Luxembourg Institute of Science and Technology

Abstract. Uncertainty is often ignored in urban water systems modelling. Commercial software used in engineering practice often ignores 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 (UDS) and the inaccurate estimation of pollution released to the environment. This paper introduces an uncertainty analysis framework in urban drainage modelling and applies it to a case study in the Haute-Sûre catchment in Luxembourg. The framework 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. Further, 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 the wastewater has an important contribution to the uncertainty for COD load (66 %) and COD concentration (62 %). Similarly, the input variable related to NH4 in the wastewater plays an important role in the contribution of total uncertainty for NH4 load (34 %) and NH4 concentration (35 %). The Monte Carlo 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 oncentration 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 (1,500 simulations) was sufficient. We also evaluated how uncertainty propagation can explain more comprehensively 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 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.

Jairo Arturo Torres-Matallana et al.

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Jairo Arturo Torres-Matallana et al.

Model code and software

R code and data to reproduce figures 03 to 06 Jairo Arturo Torres-Matallana

Jairo Arturo Torres-Matallana et al.


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Publications Copernicus
Short summary
This study aimed to select and characterise the main sources of input uncertainty in urban sewer systems, while accounting for temporal correlations of uncertain model inputs, by propagating input uncertainty through the model. We discuss the water quality impact of the model outputs to the environment, specifically in combined sewer systems, in relation to the uncertainty analysis, which constitutes valuable information for the environmental authorities and decision-makers.
This study aimed to select and characterise the main sources of input uncertainty in urban sewer...