Insights on Streamflow Predictability Across Scales Using Horizontal Visibility Graph Based Networks

Streamflow is a dynamical process that integrates water movement in space and time within basin boundaries. The authors characterize the dynamics associated with streamflow time-series data from 64 U.S. Geological Survey (USGS) unregulated stream-gauge stations in the state of Iowa. They employ a novel approach called visibility graph (VG) that uses the concept of mapping time series into complex networks to investigate the time evolutionary behavior of dynamical systems. The authors focus on a simple variant of the VG algorithm called horizontal visibility graph (HVG). The tracking of dynamics, and consequently the predictability of streamflow processes is carried out by extracting two key pieces of information called characteristic exponent, λ, of degree distribution and global clustering coefficient, GC, pertaining to the HVG-derived network. The authors use these two measures to identify whether streamflow has its origin in random or chaotic processes. They show that the characterization of streamflow dynamics is sensitive to data attributes. Through a systematic and comprehensive analysis, the authors illustrate that streamflow dynamics characterization is sensitive to the normalization and the time scale of streamflow time series. At a daily scale, streamflow at all stations used in the analysis reveals randomness with strong spatial scale (basin size) dependence. This has implications for predictability of streamflow and floods. The authors demonstrate that dynamics transition through potentially chaotic to randomly correlated processes as the averaging time scale increases. Finally, the temporal trends of λ and GC are statistically significant at about 40% of the total number of stations analyzed. Attributing these trends to factors such as changing climate or land use requires further research.