Bayesian Discharge Rating Curves Based on the Generalized Power Law

Birgir Hrafnkelsson (), Rafael Daníel Vias (), Sölvi Rögnvaldsson (), Axel Örn Jansson () and Sigurdur M. Gardarsson ()
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Birgir Hrafnkelsson: University of Iceland
Rafael Daníel Vias: The Science Institute
Sölvi Rögnvaldsson: The Science Institute
Axel Örn Jansson: The Science Institute
Sigurdur M. Gardarsson: University of Iceland

A chapter in Statistical Modeling Using Bayesian Latent Gaussian Models, 2023, pp 109-127 from Springer

Abstract: Abstract Most methods for directly measuring discharge of a water stream are time-consuming and expensive, while water elevation is easier to measure. Therefore, the relationship between discharge and water elevation is usually utilized to infer discharge through a discharge rating curve. The power-law rating curve is extensively used in hydrology but often provides an inadequate fit to data. We present a recently developed extension of the power-law rating curve, referred to as the generalized power-law rating curve. It is constructed by linking the physics of open-channel flow to the power-law formulation. The power-law exponent is modeled with a stochastic process that is a function of water elevation, allowing for a more flexible rating curve. To reliably infer generalized power-law rating curves, we propose a robust Bayesian hierarchical model. Its error variance varies with water elevation, thus handling uncertainty more accurately. The model is implemented in an R package, bdrc, available on the Comprehensive R Archive Network. The usage of the package is demonstrated with an application to data from the Swedish Meteorological and Hydrological Institute.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-39791-2_3

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DOI: 10.1007/978-3-031-39791-2_3

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