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

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 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 the GLUE methodology has been critised for generating prediction limits without statistical coherence and consistency and for the subjectivity in the choice of a threshold value to distinguish "behavioral" from "non-behavioral" 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 spatio-temporal rain variability during heavy convective rain events, flow measurement errors, as well as model limitations, 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 propagate to the parameters and result in wide posterior parameter limits, that cannot be used for interpretation of e.g. the relative size of paved area vs. the size of infiltrating area. From this study 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 () but has been applied to a wide variety of hydrological and environmental modelling applications since then (e.g. Freer et al ., ; Piñol et al ., ; Viola et al ., ; Shen et al ., ; Breinholt et al ., ). 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.…”

Addressing subjective decision-making inherent in GLUE-based multi-criteria rainfall–runoff model calibration

“…Although Hornberger's Generalized Sensitivity Analysis (Hornberger and Spear, 1981) approach is central to GLUE, the methodology is most commonly used in the hydrological literature as a tool for parameter estimation and uncertainty propagation and analysis (e.g., Abebe et al, 2010;Breinholt et al, 2013;Liu et al, 2012;Mannina, 2011;Setegn et al, 2010;Tolson and Shoemaker, 2008;van Griensven and Meixner, 2007;Zhang et al, 2012). GLUE's implementation requires some subjective decisions such as the use of informal likelihood measures and the threshold for filtering behavioural solutions.…”

Evaluation of Maximum a Posteriori Estimation as Data Assimilation Method for Forecasting Infiltration-Inflow Affected Urban Runoff with Radar Rainfall Input

“…In the examined case, the large variations in A and T trans between individual rain events suggest that incorporating slow and fast runoff as two separate regimes could improve results. This has previously been shown to be the case for simulation models and stochastic grey-box models for the same case study area [16,37]. A somewhat more complex model structure would of course increase the predictive performance but not eliminate the necessity of updating the model entirely.…”

“…It has a total area of 1300 ha and an area-velocity flow meter is located downstream of the catchment as seen in Figure 5. The area is part of a larger complex catchment area connected to the wastewater treatment plant in Avedøre, and is already well known from several research studies [36][37][38][39][40]. The drainage system is known to have problems with infiltrating water, which causes the hydraulic response of the system to be very different from wet to dry periods of the year, a phenomenon that is very difficult to model deterministically (see the explanations in Section 2.4).…”

“…Breinholt et al [37] examined parameter variations in a similar, yet slightly more complex, linear reservoir model used for simulation of flow in the same case study area. They found that it is very difficult to estimate prior distributions related to wet weather parameters (which in this study are A and T trans ).…”