The hydrologic pendulum: How information-theory can complement machine learning and physically-based approaches for discharge prediction

Predicting river and stream discharge over a continental extent is a major imperative for national agencies and for integrating land-surface models with global climate models. One salient challenge is that, presently, predictive models typically fall at either of two extremes of a "pendulum," each of which has characteristics not ideal for prediction. At one extreme are physically grounded models that often involve many uncertain calibration parameters. These models do well in their representation of small-scale phenomena but perform more poorly at the scale of the catchment, particularly when integrating over heterogeneous flow paths and multiple storage timescales. At the other extreme are purely data-driven models that represent discharge statistically but are not transferable to other locations and may not be suitable in a nonstationary climate. We use the example of discharge prediction in Dry Creek, ID, USA to demonstrate how emerging data-driven techniques aid in development of iterative forecasts that converge upon the modeling pendulum's middle ground. We use an information-theoretic approach to identify and rank the principal predictor variables and their critical time scales of aggregation and of response. These variables and associated time scales highlight the dominant physical processes and the role of storage in river discharge, which can aid in the conceptualization of physical models. Importantly, this method also provides a simple framework to inform data-driven approaches, greatly improving their predictive and interpretive skill, while reducing computational cost and addressing the challenge of equifinality by eliminating a full parameter space search. We test this method on the Dry Creek dataset of climatic and watershed storage (e.g., soil moisture, snow water equivalent) variables, and demonstrate that the resulting small subset of selected, aggregated, and lagged variables can accurately predict discharge characteristics with machine-learning methods of varying degrees of complexity. Furthermore, we show that identifying critical timescales of a few commonly available climatic variables can shed light on the behavior of storage variables, and that these variables are sufficient to provide a good characterization of discharge at the site.