Bayesian Generalized Rating Curves

Abstract

A rating curve is a curve or a model that describes the relationship between water elevation, or stage, and discharge in an observation site in a river. The rating curve is fit from paired observations of stage and discharge. The rating curve then predicts discharge given observations of stage and this methodology is applied as stage is substantially easier to directly observe than discharge. In this thesis a statistical rating curve model is proposed working within the framework of Bayesian hierarchical models. The model is a novel extension of the "power law" relationship commonly assumed in hydraulic practice and a reference model based only on that relationship is also fitted. The models are fitted to 78 datasets from observation sites in Icelandic rivers and four datasets are analyzed in detail. Model criterions DIC and posterior probability show that for about 30\% of the datasets there is strong evidence in favor of the new model while for many datasets there is no substantial evidence against either model.