Objective segmentation in compound rating curves

Compound rating curves are often encountered in hydrology. The purpose of today's standard hydrometric practice is primarily to find the segmentation limits through subjective analysis. It is difficult to control the quality of rating curves whose design is based on personal judgment. This paper presents a method for objective segmentation in two-segmental situations based on the Heaviside function and a non-linear regression where the intersection between segments is a constraint. Variable projection methods are applied in order to simplify the modelling process. Besides finding the most likely phase-shift, the model also estimates all rating curve parameters while factoring in additional approximated uncertainty. The Likelihood Ratio test, the Akaike Information Criterion and the Bayesian Information Criterion are applied in order to select the appropriate model. The proposed model is applied on real measurement data from a Norwegian gauging station. The practical case study and complementary studies using other datasets from Norway and Canada reveal that implementing the proposed model leads to numerical challenges and inferential difficulties regarding the point of cut-off/intersection. These are caused by non-regularity and multimodality in the log-likelihood function.