A method for extending stage-discharge relationships using a hydrodynamic model and quantifying the associated uncertainty

Streamflow discharge is a fundamental dataset required to effectively manage water and land resources. However, developing robust stage - discharge relationships called rating curves, from which streamflow discharge is derived, is time consuming and costly, particularly in remote areas and especially at high stage levels. As a result stage - discharge relationships are often heavily extrapolated. Hydrodynamic (HD) models are physically based models used to simulate the flow of water along river channels and over adjacent floodplains. In this paper we demonstrate a method by which a HD model can be used to generate a 'synthetic' stage - discharge relationship at high stages. The method uses a both-side Box-Cox transformation to calibrate the synthetic rating curve such that the regression residuals are as close to the normal distribution as possible. By doing this both-side transformation, the statistical uncertainty in the synthetically derived stage - discharge relationship can be calculated. This enables people trying to make decisions to determine whether the uncertainty in the synthetically generated rating curve at high stage levels is acceptable for their decision. The proposed method is demonstrated in two streamflow gauging stations in north Queensland, Australia.