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Bayesian Discharge Rating Curves Based on the Generalized Power Law

In: Statistical Modeling Using Bayesian Latent Gaussian Models

Author

Listed:
  • 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)

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.

Suggested Citation

  • Birgir Hrafnkelsson & Rafael Daníel Vias & Sölvi Rögnvaldsson & Axel Örn Jansson & Sigurdur M. Gardarsson, 2023. "Bayesian Discharge Rating Curves Based on the Generalized Power Law," Springer Books, in: Birgir Hrafnkelsson (ed.), Statistical Modeling Using Bayesian Latent Gaussian Models, pages 109-127, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-39791-2_3
    DOI: 10.1007/978-3-031-39791-2_3
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