Bayesian inference of synthetic daily rating curves by coupling Chebyshev polynomials and the GR4J model
- 1Programa Nacional de Investigación en Producción y Sustentabilidad Ambiental, Instituto Nacional de Investigación Agropecuaria, Colonia, Uruguay(rafaelnavas23@gmail.com)
- 2ARC IITC for Data Analytics for Resources and Environments & School of Life and Environmental Sciences, The University of Sydney, Sydney, NSW 2006, Australia
- 3Departamento del Agua, Centro Universitario Regional Litoral Norte, Universidad de la República, Salto, Uruguay
Building Rating Curves is complex since it depends on the availability of direct instantaneous stage-velocity/area measurements (gaugings) and variable hydraulic conditions. This work proposes a methodology to estimate synthetic (non-gauged) daily rating curves. A regional rainfall-runoff model (GR4J) is coupled with an instantaneous/stage - daily/discharge relationship based on third-order Chebyshev polynomials. Bayesian inference with Delayed Rejection Adaptive Metropolis algorithm is used to optimize the parameters and to quantify the uncertainty in the joint daily rating curve and the regional rainfall-runoff model. The likelihood function based on the model residuals is assumed to be gaussian, homoscedastic, and independent. As a study area, a region with 4 gauging sites located in New South Wales, Australia was chosen, and periods with no changes in the stage-discharge relationship were selected. Then, the method is implemented 4 times across the gauging sites, where 3 sites are supposed to be gauged and 1 site is supposed to be partially gauged (with only instantaneous water level). The proposed approach can increase the spatial representation of hydrological data when used in combination with satellite river altimetry. Another extension would be to identify the error if fewer gaugings are available. Future works could address how to incorporate heteroscedastic, autocorrelation, and zero-inflation of model residuals; as well as how to account for the variation in the range of model residuals across the gauging sites.
- u: gauged site
- v: partially gauged site
- q: streamflow (mm/day)
- h: water level (m)
- h^: Transformed h
- Ø: climatological forcing (mm/day, P & PET)
- ε: model residuals
- x1...x4: GR4J parameters
- x5...x7:Chebyshev parameters
- σ: variance of residuals
Gauging sites (Figure 1) are located in Lachlan River at Reids Flat (3742 km2), Lachlan River at Narrawa (2256 km2), Abercrombie River at Abercrombie (2636 km2), and Abercrombie River at Hadley (1635 km2).
The best fit of the prediction is obtained in the central limb of the rating curves (Figure 2).
As a result, the misfit residuals show a pattern of under and over estimations for high/low
flows (Figure 3).
How to cite: Navas, R., Vervoort, W., and Gamazo, P.: Bayesian inference of synthetic daily rating curves by coupling Chebyshev polynomials and the GR4J model, IAHS-AISH Scientific Assembly 2022, Montpellier, France, 29 May–3 Jun 2022, IAHS2022-2, https://doi.org/10.5194/iahs2022-2, 2022.
