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.

A document by Timothy Hodson. Click on the document to view its contents.

As science becomes increasingly cross-disciplinary and scientific models become increasingly cross-coupled, standardized practices of model evaluation are more important than ever. For normally distributed data, mean-squared error (MSE) is ideal as an objective and general-purpose measure of model performance, but MSE gives little insight into what aspects of model performance are ‘good’ or ‘bad’. This apparent weakness has led to a myriad of specialized error metrics, which are often aggregated to form a composite score. Such scores are inherently subjective, however, and while their components are interpretable, the composite itself is not. We contend that a better approach to model benchmarking and interpretation is to decompose the MSE into more interpretable components. To demonstrate the versatility of this approach, we outline some fundamental types of decomposition and apply them to predictions at 1,021 streamgages across the conterminous United States from three streamflow models. Through this demonstration, we show that each component in a decomposition represents a distinct concept and that simple decompositions can be combined to represent more complex concepts forming an expressive language through which to interrogate models and data.