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

Abstract

Digital twins of urban drainage systems require simulation models that can adequately replicate the physical system. All models have their limitations, and it is important to investigate when and where simulation results are acceptable and to communicate the level of performance transparently to end-users. This paper first defines a classification of four possible ‘locations of uncertainty’ in integrated urban drainage models. It then develops a structured framework for identifying and diagnosing various types of errors. This framework compares model outputs with in-sewer water level observations based on hydrologic and hydraulic signatures. The approach is applied on a real case study in Odense, Denmark, with examples from three different system sites: a typical manhole, a small flushing chamber, and an internal overflow structure. This allows diagnosing different model errors ranging from issues in the underlying asset database and missing hydrologic processes to limitations in the model software implementation. Structured use of signatures is promising for continuous, iterative improvements of integrated urban drainage models. It also provides a transparent way to communicate the level of model adequacy to end-users.

All models are wrong, but are they useful? Assessing reliability across multiple sites to build trust in urban drainage modelling

“…Since the three objectives are related to rain induced events and not dry weather conditions, a time-varying event definition was applied for the time series with a focus on water levels that are above the water level variations on a normal dry weather day influenced by infiltration-inflow (Pedersen et al, 2022). These events were found for the observed and modelled time 160 series, separately and jointly; the joint events were applied in this study.…”

“…Signatures are metrics that extract specific characteristics of a time series event, as illustrated for water levels in Figure 3. Peak level, duration and Area Under Curve (AUC) were previously described in Pedersen et al (2022). Where the two first are standard parameters used in common practice, the third (AUC) calculates a 'surrogate volume' for an event from a reference 165 level (similar to the area under a flow hydrograph, but with a different unit).…”

“…Known system anomalies 200 were identified based on manual inspection of the outlier events. • Events, where the rain input uncertainty is particularly high, quantified by the coefficient of variation (CV) of the rain depth of the rain gauges within a 5 km surrounding (Pedersen et al, 2022), were given a weight from zero to one. The weight w was calculated as w = 1-CV.…”

“…10 years (2010-2021) with a time step of 5 sec in the pipe-flow module. Water level time series from 23 sites in the study area are included in the analyses; these have durations between 2 and 11 years and include between 127 and 2,246 rain induced events with the 320 event definition described in Pedersen et al (2022). Observations and model output are in this paper presented in water level time series with a temporal resolution of 1 min.…”

“…Signatures have been applied in general hydrology for many years, and many different signatures (primarily based on flow as the measured variable) have been developed (McMillan, 2020a, b). Applying signatures from multiple events based on time series of measured water level have recently proven to be a promising tool for diagnosing errors in urban drainage models (Pedersen et al, 2022). By combining signatures with other variables characterising the direct (in-sewer) or indirect environment ("surrounding states"), tendencies can potentially be 80 detected.…”