Informal uncertainty analysis (GLUE) of continuous flow simulation in a hybrid sewer system with infiltration inflow – consistency of containment ratios in calibration and validation?

Abstract

Abstract. Monitoring of flows in sewer systems is increasingly applied to calibrate urban drainage models used for long-term simulation. However, most often models are calibrated without considering the uncertainties. The generalized likelihood uncertainty estimation (GLUE) methodology is here applied to assess parameter and flow simulation uncertainty using a simplified lumped sewer model that accounts for three separate flow contributions: wastewater, fast runoff from paved areas, and slow infiltrating water from permeable areas. Recently GLUE methodology has been critisised for generating prediction limits without statistical coherence and consistency and for the subjectivity in the choice of a threshold value to distinguish "behavioural" from "nonbehavioural" parameter sets. In this paper we examine how well the GLUE methodology performs when the behavioural parameter sets deduced from a calibration period are applied to generate prediction bounds in validation periods. By retaining an increasing number of parameter sets we aim at obtaining consistency between the GLUE generated 90 % prediction limits and the actual containment ratio (CR) in calibration. Due to the large uncertainties related to spatiotemporal rain variability during heavy convective rain events, flow measurement errors, possible model deficiencies as well as epistemic uncertainties, it was not possible to obtain an overall CR of more than 80 %. However, the GLUE generated prediction limits still proved rather consistent, since the overall CRs obtained in calibration corresponded well with the overall CRs obtained in validation periods for all proportions of retained parameter sets evaluated. When focusing on wet and dry weather periods separately, some inconsistencies were however found between calibration and validation and we address here some of the reasons why we should not expect the coverage of the prediction limits to be identical in calibration and validation periods in real-world applications. The large uncertainties result in wide posterior parameter limits, that cannot be used for interpretation of, for example, the relative size of paved area vs. the size of infiltrating area. We should therefore try to learn from the significant discrepancies between model and observations from this study, possibly by using some form of non-stationary error correction procedure, but it seems crucial to obtain more representative rain inputs and more accurate flow observations to reduce parameter and model simulation uncertainty.

Reconstruction of multi‐decadal groundwater level time‐series using a lumped conceptual model

“…This was first applied in a hydrological model application by Beven and Binley (1992) but has been applied to a wide variety of hydrological and environmental modelling applications since then (e.g. Freer et al, 1996;Piñol et al, 2005;Viola et al, 2009;Shen et al, 2012;Breinholt et al, 2013). In the GLUE approach the uncertainty in predictions is estimated using a set of behavioural models, which are weighted according to a likelihood measure describing how well they performed during calibration.…”

“…This index describes the proportion of observed values that are enclosed by chosen lower and upper GLUE likelihood-weighted prediction limits. Examples of its use in hydrological modelling studies include those of Xiong and O'Connor (2008), Li et al (2010b), Franz and Hogue (2011) and Breinholt et al (2013). We calculated the CR for each site using the 5 and 95% GLUE prediction limits, and for various NSE likelihood threshold values of 0.4 and above.…”

Quantification of parametric uncertainty of ANN models with GLUE method for different streamflow dynamics

“…However, when using threshold values of 0.6 and 0.65, sufficient parameter sets (C40) were obtained (Gong et al 2011). Furthermore, a decrease in the number of behavioural parameter sets was found as the threshold values increased, similarly to Gong et al (2011) and Breinholt et al (2013).…”

“…The GLUE method acknowledges multiple parameter sets rather than one optimal solution that gives acceptable simulations of the considered system. Many hydrological studies have employed the GLUE method to quantify uncertainty and evaluate models (see Breinholt et al 2013;Tian et al 2014;Uniyal et al 2015), however, there are few applications of the GLUE method to ANN models. Rogiers et al (2012) employed the GLUE method to quantify the uncertainty associated with the hydraulic conductivity predictions obtained from an ANN model that uses the entire grain-size distribution.…”

Using multi-event hydrologic and hydraulic signatures from water level sensors to diagnose locations of uncertainty in integrated urban drainage models used in living digital twins

“…Such a classification of model performance at the whole-system level would assist iterative model improvements, allow assessing the uncertainties in the model, and help understand for which processes and management objectives a given model can provide trustworthy estimates. There has been a wide focus in the urban draining community on ameliorating model errors through parameter calibration techniques targeting the hydrological (rainfall-runoff) part of integrated urban drainage models (e.g., Deletic et al 2012;Breinholt et al 2013;Tscheikner-Gratl et al 2016;Vonach et al 2019). However, there has been relatively little focus on technical and structural errors that cause large problems in practice, such as faulty asset data, missing physical processes, and others.…”