Time-varying Uncertainty Bands for Streamflow Time Series Using Probabilistic Dynamic Rating Curves

In model calibration or model selection, information from streamflow records plays an important role, since objective functions for calibration often depend on some measure of discrepancy between streamflow simulations and observations. Several advances have been made to better characterize model predictive uncertainty, while little work has been done to better characterize the dynamic nature of the uncertainty in observed streamflow. Current practice consists of deriving streamflow from stage measurements through rating curves. The authors hypothesize that a more natural and dynamic rating curve can be developed through a weighing scheme that assimilates recent observations and other exogenous information into the rating curve model, effectively making it an extension of the hydrological model. Coupling all available information, and extracting useful signals, can provide an understanding of the temporal changes of the parameters in the model that represent the hydraulic controls of the stream channel. The rating curve model is therefore physically grounded and more reliable when extrapolating low and high discharge values. Inclusion of new information, like electrical conductivity, has already been shown to reduce the uncertainty in stationary rating curves, but no development has been done on non-stationary curves. New observations will be assimilated into the model for real-time calibration of the parameters while establishing the complex time-dependent relationship that is ignored by traditional rating curves. This new rating curve model allows for a more explicit and accurate representation of time-varying uncertainty in observed streamflow time series. Accurately quantifying this key source of uncertainty in catchment hydrology is an important building block towards better model evaluation.