Streamflow is one of the most important variables in hydrology but is difficult to measure continuously. As a result, nearly all streamflow time series are estimated from rating curves
that define a mathematical relationship between streamflow and some easy-to-measure surrogate like water-surface elevation (stage). Most ratings are still fit manually, which is time-consuming and subjective. To improve that process, the U.S. Geological Survey (USGS), among others, is evaluating algorithms to automate that fitting. Several automated methods already exist,
and each parameterizes the rating curve slightly differently. Because of the nonconvex nature of the problem, those differences can greatly affect performance.
After some trial and error, we settled on reparameterizing the classic segmented power law somewhat like a Bayesian physics-informed neural network. Being physics-informed and Bayesian, the algorithm requires minimal data and also estimates uncertainty.
Its implementation is open source and easily modified so that others can contribute to improving the quality of USGS streamflow data.