Parsimonious streamflow forecasting system based on a dynamical systems approach

Abstract

Operational hydrologic forecasting often relies on the use of physically-based computer models at the catchment scale. However, our understanding of streamflow generation is still evolving and incomplete, and oftentimes linearization assumptions must be made to make physically-based hydrologic and hydraulic models tractable. In addition to uncertainty in the physical runoff-generation mechanisms, many physically-based approaches do not formally assimilate observed streamflow data. Streamflow is their output, deterministically simulated from observed inputs (such as precipitation, temperature, etc.). Divergences between observed and simulated streamflow may be due to input uncertainty, calibration issues, or problems with the inherent physical process representation. Thus, data-driven approaches that are responsive to observed streamflow by including assimilation as an essential feature are promising in operational hydrology. In this study, we use a novel forcings-weighted k-Nearest Neighbor (kNN) nonlinear timeseries forecasting method developed in the context of the modeling of nonlinear dynamical systems. The rainfall-runoff transform is assumed to be a low-dimensional system of (unknown) nonlinear differential equations; the deterministic state space is reconstructed based on the streamflow timeseries; and a forecast is generated based on how “similar” the current hydrograph is to historical events encoded within the reconstructed state space, weighted by the similarity of forcings. We tested the model in a long-term test period with no real data assimilation, and in forecast mode with daily data assimilation. When used for forecasting, we also illustrate two different uncertainty quantification approaches: forecast postprocessing and internal-to-the-model ensemble generation. The method is conceptually and computationally simple, but offers promising results. We tested the model in three different scenarios. First, investigating a long-term test period with no real data assimilation in a rainfall-dominated research catchment at the Coweeta Hydrologic Lab in North Carolina, USA. The simulation exhibited an NSE of 0.73. Next, we included a conceptual snowmelt model to drive the long term simulation and studied boreal-temperate transition zone catchments in northern Minnesota, USA. The study area included a small (<0.1 mi2) reference research catchment at the Marcell Experimental Forest, and a large river basin (>19 k mi2) with incomplete forcings information. The kNN method yielded NSEs from 0.28 to 0.50. And finally, we conducted a pseudo-operational forecasting test for a large river basin in northern Minnesota, USA with a focus on performance forecasting a flood-of-record on the Rainy River. The test involved reforecasting, data assimilation, and implementation of ensemble and postprocessing bias correction uncertainty-quantification schemes. The technique demonstrated good performance capturing a flood-of-record on a large catchment (−5.7 to −3.3 % crest error with 1-day of lead time). For the entire test period in forecast mode, the 1-day lead time NSE was 0.99, going down to 0.79 for the 7-day lead time, showing its general utility as an operational forecasting tool.