Evaluating the applicability of the generalized power-law rating curve model

Hydrologic research and operations make extensive use of streamflow time series. In most applications, these time series are estimated from rating curves, which relate flow to some easy-to-measure surrogate, typically stage. The conventional stage-discharge rating takes the form of a segmented power law, with one segment for each hydrologic control at the stream gauge. However, these ratings are difficult to estimate with numerical methods, such that most are still developed manually. A few automated algorithms have emerged, but their use is sporadic, and their relative merits have not been rigorously assessed. One recently developed approach, the generalized power-law, avoids the segmenting problem by representing the power-law exponent as a Gaussian process. On one hand, this representation is more flexible and easier to fit, but that flexibility might also allow unrealistic solutions. This study evaluates the operational viability of the generalized power-law rating curve model under a range of conditions, using observations from 180 streams in Iceland, Sweden, and the United States. Overall, the model proved flexible and computationally robust, generating convincing rating curves across a range of geographic settings and was comparable to curves generated by a segmented rating model. Lastly, we propose a model-selection algorithm based on information theory to help identify the best rating curve model for a particular stream gauge. • The generalized power-law model (GPLM) extends the classical power-law model. • Fits rating curves using only paired observations of discharge and stage. • Combines data-driven methods with causal structure for accurate rating curves. • Out-of-sample predictive accuracy comparable with segmented power-law models. • First study to assess GPLM across a large sample of measurement sites.