Bayesian discharge rating curves based on B-spline smoothing functions

Abstract

Discharge in rivers is commonly estimated by the use of a rating curve constructed from pairs of measured water elevations and discharges at a specific location. The Bayesian approach has been successfully applied to estimate discharge rating curves that are based on the standard power-law. In this paper the standard power-law model is extended by adding a B-spline function. The extended model is compared to the standard power-law model by applying the models to discharge data sets from sixty one different rivers. In addition four rivers are analyzed in detail to demonstrate the benefit of the extended model. The models are compared using two measures, the Deviance Information Criterion (DIC) and Bayes factor. The former provides robust comparison of fit adjusting for the different complexity of the models and the latter measures the evidence of one model against the other. The extended model captures deviations in the data from the standard power-law but reduces to the standard power-law when that model is adequate. The extended model provides substantially better fit than the standard power-law model for about 30% of the rivers and performs better for 60% of the rivers when extrapolating large discharge values.