Improving uncertainty estimation in urban hydrological modeling by statistically describing bias

摘要

Hydrodynamic models are useful tools for urban water management.Unfortunately, it is still challenging to obtain accurate results andplausible uncertainty estimates when using these models. In particular, withthe currently applied statistical techniques, flow predictions are usuallyoverconfident and biased. In this study, we present a flexible and relativelyefficient methodology (i) to obtain more reliable hydrological simulations interms of coverage of validation data by the uncertainty bands and (ii) toseparate prediction uncertainty into its components. Our approachacknowledges that urban drainage predictions are biased. This is mostly dueto input errors and structural deficits of the model. We address this issueby describing model bias in a Bayesian framework. The bias becomes anautoregressive term additional to white measurement noise, the only errortype accounted for in traditional uncertainty analysis. Toallow for bigger discrepancies during wet weather, we make the variance ofbias dependent on the input (rainfall) or/and output (runoff) of the system.Specifically, we present a structured approach to select, among fivevariants, the optimal bias description for a given urban or natural casestudy. We tested the methodology in a small monitored stormwater systemdescribed with a parsimonious model. Our results clearly show that flowsimulations are much more reliable when bias is accounted for than when it isneglected. Furthermore, our probabilistic predictions can discriminatebetween three uncertainty contributions: parametric uncertainty, bias, andmeasurement errors. In our case study, the best performing bias descriptionis the output-dependent bias using a log-sinh transformation of data andmodel results. The limitations of the framework presented are some ambiguitydue to the subjective choice of priors for bias parameters and its inabilityto address the causes of model discrepancies. Further research should focuson quantifying and reducing the causes of bias by improving the modelstructure and propagating input uncertainty.