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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-Sure 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 u

This repository contains the R code and data to reproduce figures from the "Multivariate autoregressive modelling and conditional simulation for temporal uncertainty analysis of an urban water system in Luxembourg" paper.

Urban drainage modelling typically requires development of highly detailed simulators due to the nature of various underlying surface and drainage processes, which makes them computationally too expensive. Application of such simulators is still challenging in activities such as real-time control (RTC), uncertainty quantification analysis or model calibration in which numerous simulations are required. The focus of this paper is to present a rather simple hybrid surrogate modelling (or emulation) strategy to simplify and accelerate a detailed urban drainage simulator (UDS). The proposed surrogate modelling strategy includes: a) identification of the variables to be emulated; b) development of a simplified conceptual model in which every component contributing to the variables identified in step (a) is replaced by a function; c) definition of these functions, either based on knowledge about the mechanisms of the simulator, or based on the data produced by the simulator; and finally, d) validation of the results produced by the surrogate model in comparison with the original detailed simulator. Herein, a detailed InfoWorks ICM simulator was selected for surrogate modelling. The case study area was a small urban drainage network in Luxembourg. An emulator was developed to map the rainfall time series, as input, to a storage tank volume and combined sewer overflow (CSO) in the case study network. The results showed that the introduced strategy provides a reliable method to simplify the simulator and reduce its run time significantly. For the specific case study, the emulator was approximately 1300 times faster than the original detailed simulator. For quantification of the emulation error, an ensemble of 500 rainfall scenarios with 1 month duration was generated by application of a multivariate autoregressive model for conditional simulation of rainfall time series. The results produced by the emulator were compared to the ones produced by the simulator. Finally, as an, Sanitary Engineering

In this study, applicability of a data-driven Gaussian Process Emulator (GPE) technique to develop a dynamic surrogate model for a computationally expensive urban drainage simulator is investigated. Considering rainfall time series as the main driving force is a challenge in this regard due to the high dimensionality problem. However, this problem can be less relevant when the focus is only on short-term simulations. The novelty of this research is the consideration of short-term rainfall time series as training parameters for the GPE. Rainfall intensity at each time step is counted as a separate parameter. A method to generate synthetic rainfall events for GPE training purposes is introduced as well. Here, an emulator is developed to predict the upcoming daily time series of the total wastewater volume in a storage tank and the corresponding Combined Sewer Overflow (CSO) volume. Nash-Sutcliffe Efficiency (NSE) and Volumetric Efficiency (VE) are calculated as emulation error indicators. For the case study herein, the emulator is able to speed up the simulations up to 380 times with a low accuracy cost for prediction of the total storage tank volume (medians of NSE = 0.96 and VE = 0.87). CSO events occurrence is detected in 82% of the cases, although with some considerable accuracy cost (medians of NSE = 0.76 and VE = 0.5). Applicability of the emulator for consecutive short-term simulations, based on real observed rainfall time series is also validated with a high accuracy (NSE = 0.97, VE = 0.89)., Sanitary Engineering

Many complex urban drainage quality models are computationally expensive. Complexity and computing times may become prohibitive when these models are used in a Monte Carlo (MC) uncertainty analysis of long time series, in particular for practitioners. Computationally scalable and fast "surrogate" models may reduce the overall computation time for practical applications in which often large data sets would be needed otherwise. We developed a simplified semi-distributed urban water quality model, EmiStatR, which brings uncertainty and sensitivity analyses of urban drainage water quality models within reach of practitioners. Its lower demand in input data and its scalability allow for simulating water volume and pollution loads in combined sewer overflows in several catchments fast and efficiently. The scalable code implemented in EmiStatR reduced the computation time significantly (by a factor of around 24 when using 32 cores). EmiStatR can be applied efficiently to test hypotheses by using MC uncertainty studies or long-term simulations.

Integrated environmental modelling requires coupling sub-models at different spatial and temporal scales, thus accounting for change of support procedures (aggregation and disaggregation). We introduce the R-package spatio-temporal Uncertainty Propagation across multiple scales, stUPscales, which constitutes a contribution to state-of-the-art open source tools that support uncertainty propagation analysis in temporal and spatio-temporal domains. We illustrate the tool with an uncertainty propagation example in environmental modelling, specifically in the urban water domain. The functionalities of the class setup and the methods and functions MC.setup, MC.sim, MC.analysis and Agg.t are explained, which are used for setting up, running and analysing Monte Carlo uncertainty propagation simulations, and for spatio-temporal aggregation. We also show how the package can be used to model and predict variables that vary in space and time by using a spatio-temporal variogram model and space-time ordinary kriging. stUPscales takes uncertainty characterisation and propagation a step further by including temporal and spatio-temporal auto- and cross-correlation, resulting in more realistic (spatio-)temporal series of environmental variables. Due to its modularity, the package allows the implementation of additional methods and functions for spatio-temporal disaggregation of model inputs and outputs, when linking models across multiple space-time scales.

In this study, applicability of a data-driven Gaussian Process Emulator (GPE) technique to develop a dynamic surrogate model for a computationally expensive urban drainage simulator is investigated. Considering rainfall time series as the main driving force is a challenge in this regard due to the high dimensionality problem. However, this problem can be less relevant when the focus is only on short-term simulations. The novelty of this research is the consideration of short-term rainfall time series as training parameters for the GPE. Rainfall intensity at each time step is counted as a separate parameter. A method to generate synthetic rainfall events for GPE training purposes is introduced as well. Here, an emulator is developed to predict the upcoming daily time series of the total wastewater volume in a storage tank and the corresponding Combined Sewer Overflow (CSO) volume. Nash-Sutcliffe Efficiency (NSE) and Volumetric Efficiency (VE) are calculated as emulation error indicators. For the case study herein, the emulator is able to speed up the simulations up to 380 times with a low accuracy cost for prediction of the total storage tank volume (medians of NSE = 0.96 and VE = 0.87). CSO events occurrence is detected in 82% of the cases, although with some considerable accuracy cost (medians of NSE = 0.76 and VE = 0.5). Applicability of the emulator for consecutive short-term simulations, based on real observed rainfall time series is also validated with a high accuracy (NSE = 0.97, VE = 0.89).

Due to the rapidly increasing percentage of the population living in urban centres, there is a need to focus on the energy demand of these cities and the use of renewable energies instead of fossil fuels. In this paper, we develop a spatial model to determine the potential per parcel for using shallow geothermal energy, for space heating and hot water. The method is based on the space heating and hot water energy demand of each building and the specific heat extraction potential of the subsurface per parcel. With this information, along with the available space per parcel for boreholes, the percentage of the energy demand that could be supplied by geothermal energy is calculated. The potential reduction in CO2 emissions should all possible geothermal energy be utilised, is also calculated. The method is applied to Ludwigsburg, Germany. It was found that CO2 emissions could potentially be reduced by 29.7% if all space heating and hot water requirements were provided by geothermal energy, which would contribute to the sustainability of a city. The method is simple in execution and could be applied to other cities as the data used should be readily available. Another advantage is the implementation into the web based Smart City Energy platform which allows interactive exploration of solutions across the city.