Combining Hydraulic Knowledge and a Rainfall-Stage Model for Indirectly Estimating Rating Curves in Urban Streams: A Feasibility Assessment

Streamflow estimates are necessary for devising effective flood management strategies in urban areas. However, rating curves (RC), which formally summarize stage-discharge relationships, are rarely available, mainly because of difficulties in measuring flow velocities in such environments. As a result, in the absence of gaugings, researchers and practitioners frequently resort to simplified hydraulic approaches for computing flood discharges, which renders validation and uncertainty assessment in flood-related studies unfeasible. In this paper, we explore a Bayesian framework that combines empirical information on stages and expert prior hydraulic knowledge for indirectly estimating rating curves from rainfall-runoff (RR) simulations. We investigate advantages and drawbacks of the proposed rainfall-stage model in a Brazilian urban catchment, in which 25 gaugings, which were not utilized in inference, are available for model scrutiny. Our results demonstrate that, although deriving a synthetic RC was feasible, uncertainty in stage predictions was too large. However, the explicit treatment of RC and RR errors allowed estimating true discharges, which is useful for flood routing along the river reach. Overall, the synthetic RC provided physical realism to the stage-discharge relationship. Yet, the rainfall-stage model was strongly affected by the lack of gaugings, which suggests actual monitoring should be highly beneficial for decision making.