Bayesian inference of synthetic daily rating curves by coupling Chebyshev Polynomials and the GR4J model

Abstract

In fluvial dynamics studies, there are instances where it becomes necessary to estimate the daily discharge of a river in locations where only one instantaneous level record is available per day. In such cases, there may be no rating curve, or one that is unreliable, making it difficult to make accurate discharge estimates. A daily rating curve would be an estimate of the daily discharge of a river, from a single instantaneous stage level. This work proposes to estimate synthetic (non-gauged) daily rating curves from nearby gauged locations using a rainfall-runoff model. A rainfall-runoff model (GR4J) is coupled with an instantaneous/stage–daily/discharge relationship based on third order Chebyshev polynomials. The parameters in the joint daily rating curve and rainfall-runoff model are optimized and uncertainty is quantified with Bayesian inference and the Delayed Rejection Adaptive Metropolis algorithm assuming model residuals to be normally distributed N(0,σ). A case study with four gauging sites in New South Wales, Australia, and periods with no changes in the stage-discharge relationship were selected. The method is implemented four times across the gauging sites, where three sites are assumed gauged and one site is assumed to have only instantaneous water level records. The results of this methodology can help provide a more comprehensive understanding of the hydrological functioning of systems, where only one instantaneous stage level per day is available. This is particularly useful in situations where historical observations or satellite altimetry data in rivers is used to estimate daily flows.