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

Abstract

<jats:p>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. </jats:p>

Reply to Anonymous Referee #2

“…L215-255: Remove the description as the model is already described in Torres-Matallana et al (2017) Reply: We agree that we provided too much detail. We have moved the text from line 223 onward to the Supporting Information.…”

Multivariate autoregressive modelling and conditional simulation for temporal uncertainty analysis of an urban water system in Luxembourg

“…2.3 that, in the case study, precipitation data are recorded at stations Esch-sur-Sûre and Dahl. Torres-Matallana et al (2017) present a model to simulate precipitation inside a target catchment given a known precipitation time series in a nearby location outside the catchment, while accounting for the uncertainty that is introduced due to spatial variation in precipitation. The method used for input precipitation uncertainty characterisation is essentially the same as the application of a Kalman filter/smoother (Kalman, 1960;Webster and Heuvelink, 2006).…”

A Data-Driven Surrogate Modelling Approach for Acceleration of Short-Term Simulations of a Dynamic Urban Drainage Simulator

“…Therefore, it was required to apply a different approach for characterizing uncertainty in this regard. We applied the multivariate autoregressive modelling and conditional simulation approach for rainfall time series uncertainty characterization as developed in reference [35]. This method, is suitable to simulate rainfall time series R(t) in a target catchment given known rainfall time series in two nearby locations in the catchment RM1(t) and RM2(t), while accounting for the uncertainty that is introduced due to spatial variation in rainfall, and the uncertainty in the measurement itself given the ratio between two nearby measurements.…”

“…This simulation should be conditional to LPo, where Po is an observed time series at a nearby location of RM1. Details about this conditional simulation are provided in reference [35]. We used the R-package mAr [37] to calibrate the parameters of Equation (4) given two observed time series RM1(t) and RM2(t) to compute Lδ(t) for those non-zero values in the two time series.…”

“…Parameters of the synthetic rainfall generator calibrated. Vector µ, matrix A, and variance-covariance matrix C for definition of σ R2 , σ δ 2 and ρ Rδ (Adapted from[35]). The presented values are case study specific.…”